Finite Group Databasebeta

← #32883482

Subgroups — #32883482

Order 18176.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602001C211yesmaximal, characteristic, complemented
2#22600602C211yesmaximal, characteristic, complemented
3#22600587C211yesmaximal, characteristic, complemented
4#22600475C211yesmaximal, characteristic, complemented
5#22600460C211yesmaximal, characteristic, complemented
6#22600355C211yesmaximal, characteristic, complemented
7#22600340C211yesmaximal, characteristic, complemented
8#22600184C211yesmaximal, characteristic, complemented
9#22600169C211yesmaximal, characteristic, complemented
10#22600096C211yesmaximal, characteristic, complemented
11#22600066C211yesmaximal, characteristic, complemented
12#22599960C211yesmaximal, characteristic, complemented
13#22599940C211yesmaximal, characteristic, complemented
14#22599921C211yesmaximal, characteristic, complemented
15#22599891C211yesmaximal, characteristic, complemented
16#22599881C211yesmaximal, characteristic, complemented
17#22599866C211yesmaximal, characteristic, complemented
18#22599406C211yesmaximal, characteristic, complemented
19#22599384C211yesmaximal, characteristic, complemented
20#22599246C211yesmaximal, characteristic, complemented
21#22599237C211yesmaximal, characteristic, complemented
22#22599150C211yesmaximal, characteristic, complemented
23#22599101C211yesmaximal, characteristic, complemented
24#22598548C211yesmaximal, characteristic, complemented
25#22598533C211yesmaximal, characteristic, complemented
26#22597641C211yesmaximal, characteristic, complemented
27#22597641C211yesmaximal, characteristic, complemented
28#22597580C211yesmaximal, characteristic, complemented
29#22597556C211yesmaximal, characteristic, complemented
30#22597388C211yesmaximal, characteristic, complemented
31C71×#3539C211yesmaximal, characteristic, complemented
32C2×#14556174C2211yescharacteristic
33C22×#11765865C2211yescharacteristic
34C2×#14556158C2211yescharacteristic, complemented
35C2×#14556153C2211yescharacteristic, complemented
36C2×#14556153C2211yescharacteristic, complemented
37C2×#14556153C2211yescharacteristic, complemented
38C2×#14556148C2211yescharacteristic, complemented
39C2×#14556148C2211yescharacteristic, complemented
40C2×#14556148C2211yescharacteristic, complemented
41C2×#14556148C2211yescharacteristic, complemented
42#17986670C2211yescharacteristic
43#17986670C2211yescharacteristic
44#17986658C2211yescharacteristic
45#17986658C2211yescharacteristic
46#17986645C2211yescharacteristic
47#17986645C2211yescharacteristic
48#17986641—21no—
49#17986641—21no—
50D4×D284C2211yescharacteristic
51D4×D284C2211yescharacteristic
52#17986631—21no—
53#17986631—21no—
54#17986579—21no—
55#17986577C2211yescharacteristic
56#17986568C2211yescharacteristic
57#17986565—21no—
58#17986512—21no—
59C2×#14556102C2211yescharacteristic
60#121×D71—21no—
61#17986479C2211yescharacteristic
62#17986391C2211yescharacteristic, complemented
63#17986386C2211yescharacteristic, complemented
64#17986375C2211yescharacteristic, complemented
65#17986373C2211yescharacteristic, complemented
66#17986365C2211yescharacteristic, complemented
67#17986365C2211yescharacteristic, complemented
68#17986356C2211yescharacteristic, complemented
69#17986356C2211yescharacteristic, complemented
70#17986334C2211yescharacteristic, complemented
71#17986332C2211yescharacteristic, complemented
72#17986329C2211yescharacteristic, complemented
73#17986327C2211yescharacteristic, complemented
74#17986323C2211yescharacteristic, complemented
75#17986323C2211yescharacteristic, complemented
76#17986323C2211yescharacteristic, complemented
77#17986323C2211yescharacteristic, complemented
78#17986317C2211yescharacteristic, complemented
79#17986315C2211yescharacteristic, complemented
80#17986312C2211yescharacteristic, complemented
81#17986310C2211yescharacteristic, complemented
82#17986303C2211yescharacteristic, complemented
83#17986303C2211yescharacteristic, complemented
84#17986296C2211yescharacteristic, complemented
85#17986296C2211yescharacteristic, complemented
86#17986255C2211yescharacteristic, complemented
87#17986250C2211yescharacteristic, complemented
88#17986250C2211yescharacteristic, complemented
89#17986250C2211yescharacteristic, complemented
90#17986247C2211yescharacteristic, complemented
91#17986247C2211yescharacteristic, complemented
92#17986247C2211yescharacteristic, complemented
93#17986243C2211yescharacteristic, complemented
94#17986238C2211yescharacteristic, complemented
95#17986233C2211yescharacteristic, complemented
96#17986233C2211yescharacteristic, complemented
97#17986233C2211yescharacteristic, complemented
98#17986230C2211yescharacteristic, complemented
99#17986230C2211yescharacteristic, complemented
100#17986230C2211yescharacteristic, complemented
101#17986226C2211yescharacteristic, complemented
102#17986221C2211yescharacteristic, complemented
103#17986221C2211yescharacteristic, complemented
104#17986214C2211yescharacteristic, complemented
105#17986214C2211yescharacteristic, complemented
106#17986206C2211yescharacteristic, complemented
107#17986201C2211yescharacteristic, complemented
108#17986199C2211yescharacteristic, complemented
109#17986199C2211yescharacteristic, complemented
110#17986196C2211yescharacteristic, complemented
111#17986194C2211yescharacteristic, complemented
112#17986194C2211yescharacteristic, complemented
113#17986191C2211yescharacteristic, complemented
114#17986161C2211yescharacteristic, complemented
115#17986161C2211yescharacteristic, complemented
116#17986159C2211yescharacteristic
117#17986159C2211yescharacteristic
118#17986159C2211yescharacteristic, complemented
119#17986159C2211yescharacteristic, complemented
120#17986159C2211yescharacteristic, complemented
121#17986159C2211yescharacteristic, complemented
122#17986159C2211yescharacteristic, complemented
123#17986159C2211yescharacteristic, complemented
124#17986154C2211yescharacteristic, complemented
125#17986149C2211yescharacteristic, complemented
126#17986149C2211yescharacteristic, complemented
127#17986149C2211yescharacteristic, complemented
128#17986149C2211yescharacteristic, complemented
129#17986149C2211yescharacteristic, complemented
130#17986144C2211yescharacteristic, complemented
131#17986144C2211yescharacteristic, complemented
132#17986144C2211yescharacteristic, complemented
133#17986144C2211yescharacteristic, complemented
134#17986144C2211yescharacteristic, complemented
135#17986144C2211yescharacteristic, complemented
136#17986142C2211yescharacteristic
137#17986142C2211yescharacteristic
138#17986142C2211yescharacteristic, complemented
139#17986142C2211yescharacteristic, complemented
140#17986142C2211yescharacteristic, complemented
141#17986142C2211yescharacteristic, complemented
142#17986142C2211yescharacteristic, complemented
143#17986142C2211yescharacteristic, complemented
144#17986137C2211yescharacteristic, complemented
145#17986132C2211yescharacteristic, complemented
146#17986132C2211yescharacteristic, complemented
147#17986132C2211yescharacteristic, complemented
148#17986132C2211yescharacteristic, complemented
149#17986132C2211yescharacteristic, complemented
150#17986109C2211yescharacteristic, complemented
151#17986104C2211yescharacteristic, complemented
152#17986099C2211yescharacteristic, complemented
153#17986097C2211yescharacteristic, complemented
154C4×#11765855C2211yescharacteristic, complemented
155C4×#11765852C2211yescharacteristic, complemented
156C4×#11765853C2211yescharacteristic, complemented
157C4×#11765850C2211yescharacteristic, complemented
158#17986077C2211yescharacteristic, complemented
159#17986077C2211yescharacteristic, complemented
160#17986071C2211yescharacteristic, complemented
161#17986071C2211yescharacteristic, complemented
162#17986071C2211yescharacteristic, complemented
163#17986071C2211yescharacteristic, complemented
164D4×C71⋊C8C2211yescharacteristic, complemented
165D4×C71⋊C8C2211yescharacteristic, complemented
166#17986060C2211yescharacteristic, complemented
167#17986060C2211yescharacteristic, complemented
168#17986007C2211yescharacteristic, complemented
169#17986003C2211yescharacteristic, complemented
170#17985998C2211yescharacteristic, complemented
171#17985998C2211yescharacteristic, complemented
172#17985993C2211yescharacteristic, complemented
173#17985993C2211yescharacteristic, complemented
174C2×#14556048C2211yescharacteristic, complemented
175C2×#14556048C2211yescharacteristic, complemented
176#17985966C2211yescharacteristic, complemented
177#17985966C2211yescharacteristic, complemented
178#17985963C2211yescharacteristic, complemented
179C2×C22⋊(C71⋊C8)C2211yescharacteristic, complemented
180#560×C71—21no—
181#560×C71—21no—
182#553×C71—21no—
183#553×C71—21no—
184#553×C71C2211yescharacteristic, complemented
185#553×C71C2211yescharacteristic, complemented
186#552×C71C2211yescharacteristic, complemented
187#552×C71C2211yescharacteristic, complemented
188#550×C71C2211yescharacteristic, complemented
189#550×C71C2211yescharacteristic, complemented
190#547×C71C2211yescharacteristic, complemented
191#547×C71C2211yescharacteristic, complemented
192#541×C71C2211yescharacteristic, complemented
193#540×C71—21no—
194#540×C71—21no—
195#540×C71C2211yescharacteristic, complemented
196#539×C71—21no—
197#539×C71—21no—
198#537×C71C2211yescharacteristic, complemented
199#537×C71C2211yescharacteristic, complemented
200#525×C71C2211yescharacteristic
201#525×C71C2211yescharacteristic, complemented
202#525×C71C2211yescharacteristic, complemented
203#14556174—42no—
204#14556174—42no—
205C2×#11765866—21no—
206C2×#11765865—21no—
207C2×#11765865—21no—
208C2×#11765865—42no—
209C2×#11765865—42no—
210C2×#11765865C2311yescharacteristic
211C2×#11765865C2311yescharacteristic
212C2×#11765865C2311yescharacteristic
213C2×#11765865C2311yescharacteristic
214C2×#11765865C2311yescharacteristic
215C2×#11765865C2311yescharacteristic
216C22×Dic142C2311yescharacteristic
217C22×D284C2311yescharacteristic
218C22×D284C2311yescharacteristic
219C22×D284C2311yescharacteristic
220C22×D284C2311yescharacteristic
221C22×C22⋊D71—21no—
222C22×C22⋊D71—21no—
223C2×D4×D71—21no—
224C2×D4×D71—21no—
225C2×D4×D71—21no—
226C2×D4×D71—21no—
227C2×D4×D71—21no—
228C22×C4×D71—21no—
229#14556158—42no—
230#14556153—42no—
231#14556153—42no—
232#14556153—42no—
233#14556148—42no—
234#14556148—42no—
235#14556148—42no—
236#14556148—42no—
237C2×#11765855C2311yescharacteristic
238C2×#11765855C2311yescharacteristic
239C2×#11765855C2311yescharacteristic
240C2×#11765855C2311yescharacteristic
241C2×#11765853C2311yescharacteristic
242C2×#11765853C2311yescharacteristic
243C2×#11765853C2311yescharacteristic
244C2×#11765853C2311yescharacteristic
245C2×#11765852C2311yescharacteristic
246C2×#11765852C2311yescharacteristic
247C2×#11765852C2311yescharacteristic
248C2×#11765852C2311yescharacteristic
249C2×#11765852C2311yescharacteristic
250C2×#11765852C2311yescharacteristic
251C2×#11765852C2311yescharacteristic
252C2×#11765852C2311yescharacteristic
253C2×#11765850C2311yescharacteristic
254C2×#11765850C2311yescharacteristic
255C2×#11765850C2311yescharacteristic
256C2×#11765850C2311yescharacteristic
257C2×#11765850C2311yescharacteristic
258C2×#11765850C2311yescharacteristic
259C2×#11765850C2311yescharacteristic
260C2×#11765850C2311yescharacteristic
261C2×#11765849C2311yescharacteristic
262C2×#11765849C2311yescharacteristic
263C2×#11765849C2311yescharacteristic
264C2×#11765849C2311yescharacteristic
265C22×C71⋊C8C2311yescharacteristic
266C22×C71⋊C8C2311yescharacteristic
267C22×C71⋊C8C2311yescharacteristic
268C22×C71⋊C8C2311yescharacteristic
269#14556125C2311yescharacteristic
270#14556125C2311yescharacteristic
271#14556124—21no—
272#14556124—21no—
273#14556116C2311yescharacteristic
274#14556116C2311yescharacteristic
275#14556114—21no—
276#14556114—21no—
277#14556113—21no—
278#14556113—21no—
279#14556107C2311yescharacteristic
280#14556107C2311yescharacteristic
281#14556106—21no—
282#14556106—21no—
283#14556104—21no—
284#14556103—21no—
285#14556103—21no—
286#14556103—21no—
287#14556103—21no—
288#14556102—21no—
289#14556102—21no—
290#14556102C2311yescharacteristic
291#14556102C2311yescharacteristic
292#14556102C2311yescharacteristic
293#14556102C2311yescharacteristic
294#14556102C2311yescharacteristic
295#14556102C2311yescharacteristic
296#14556101—21no—
297#14556101—21no—
298#14556101—21no—
299#14556101—21no—
300#14556101—21no—
301#14556101—21no—
302#14556100—21no—
303#14556100—21no—
304#14556100—21no—
305#14556100—21no—
306#14556099—21no—
307#14556098—21no—
308#14556098—21no—
309#14556098—21no—
310#14556098—21no—
311#14556098—21no—
312#14556098—21no—
313#14556096—21no—
314#14556096—21no—
315C4×Dic142C2311yescharacteristic
316C4×Dic142C2311yescharacteristic
317C4×D284C2311yescharacteristic
318C4×D284C2311yescharacteristic
319#14556090—21no—
320#14556090—21no—
321(C22⋊D71)⋊C4—21no—
322(C22⋊D71)⋊C4—21no—
323(C22⋊D71)⋊C4—21no—
324(C22⋊D71)⋊C4—21no—
325#14556086—21no—
326C2×C4⋊Dic71C2311yescharacteristic
327C4⋊C4×D71—21no—
328C2×(C2×D71)⋊C4—21no—
329C22⋊C4×D71—21no—
330C22⋊C4×D71—21no—
331#14556061C2311yescharacteristic
332#14556061C2311yescharacteristic
333#14556061C2311yescharacteristic
334#14556061C2311yescharacteristic
335#14556059C2311yescharacteristic
336#14556059C2311yescharacteristic
337#14556059C2311yescharacteristic
338#14556059C2311yescharacteristic
339C4⋊(C71⋊C8)C2311yescharacteristic
340C4⋊(C71⋊C8)C2311yescharacteristic
341C4⋊(C71⋊C8)C2311yescharacteristic
342C4⋊(C71⋊C8)C2311yescharacteristic
343#14556052C2311yescharacteristic
344#14556052C2311yescharacteristic
345#14556052C2311yescharacteristic
346#14556052C2311yescharacteristic
347#14556051C2311yescharacteristic
348#14556051C2311yescharacteristic
349#14556051C2311yescharacteristic
350#14556051C2311yescharacteristic
351#14556051C2311yescharacteristic
352#14556051C2311yescharacteristic
353#14556051C2311yescharacteristic
354#14556051C2311yescharacteristic
355#14556049C2311yescharacteristic
356#14556049C2311yescharacteristic
357#14556049C2311yescharacteristic
358#14556049C2311yescharacteristic
359#14556048C2311yescharacteristic
360#14556048C2311yescharacteristic
361#14556048C2311yescharacteristic
362#14556048C2311yescharacteristic
363#14556048C2311yescharacteristic
364#14556048C2311yescharacteristic
365#14556048C2311yescharacteristic
366#14556048C2311yescharacteristic
367#14556048C2311yescharacteristic
368#14556048C2311yescharacteristic
369#14556048C2311yescharacteristic
370#14556048C2311yescharacteristic
371#14556048C2311yescharacteristic
372#14556048C2311yescharacteristic
373#14556048C2311yescharacteristic
374#14556048C2311yescharacteristic
375C22⋊(C71⋊C8)C2311yescharacteristic
376C22⋊(C71⋊C8)C2311yescharacteristic
377C22⋊(C71⋊C8)C2311yescharacteristic
378C22⋊(C71⋊C8)C2311yescharacteristic
379C22⋊(C71⋊C8)C2311yescharacteristic
380C22⋊(C71⋊C8)C2311yescharacteristic
381C22⋊(C71⋊C8)C2311yescharacteristic
382C22⋊(C71⋊C8)C2311yescharacteristic
383C22⋊(C71⋊C8)C2311yescharacteristic
384C22⋊(C71⋊C8)C2311yescharacteristic
385C22⋊(C71⋊C8)C2311yescharacteristic
386C22⋊(C71⋊C8)C2311yescharacteristic
387#14556039C2311yescharacteristic
388#14556039C2311yescharacteristic
389C4×C71⋊C8C2311yescharacteristic
390C4×C71⋊C8C2311yescharacteristic
391C2×#41×C71C2311yescharacteristic
392C2×#41×C71C2311yescharacteristic
393C2×#41×C71C2311yescharacteristic
394C2×#41×C71C2311yescharacteristic
395C2×#41×C71C2311yescharacteristic
396C23×C4×C71C2311yescharacteristic
397C4⋊Q8×C71C2311yescharacteristic
398#127×C71—21no—
399#127×C71—21no—
400#127×C71C2311yescharacteristic
401#126×C71—21no—
402#126×C71—21no—
403#126×C71—21no—
404#126×C71—21no—
405#126×C71—21no—
406#126×C71—21no—
407#125×C71—21no—
408#125×C71—21no—
409#125×C71—21no—
410#125×C71—21no—
411#125×C71C2311yescharacteristic
412#125×C71C2311yescharacteristic
413#123×C71—21no—
414#123×C71—21no—
415#123×C71—21no—
416#123×C71—21no—
417#123×C71—21no—
418#123×C71—21no—
419#123×C71—21no—
420#123×C71—21no—
421#123×C71—21no—
422#123×C71—21no—
423#123×C71—21no—
424#123×C71—21no—
425#123×C71D411yescharacteristic
426#123×C71D411yescharacteristic
427C22⋊Q8×C71—21no—
428C22⋊Q8×C71—21no—
429C22⋊Q8×C71D411yescharacteristic
430C22⋊Q8×C71D411yescharacteristic
431C22⋊Q8×C71C2311yescharacteristic
432C22⋊Q8×C71C2311yescharacteristic
433C22⋊Q8×C71C2311yescharacteristic
434C22⋊Q8×C71C2311yescharacteristic
435C22⋊Q8×C71C2311yescharacteristic
436C22⋊Q8×C71C2311yescharacteristic
437#121×C71—21no—
438#121×C71—21no—
439#121×C71—21no—
440#121×C71—21no—
441#121×C71—21no—
442#121×C71—21no—
443#121×C71—21no—
444#121×C71—21no—
445#121×C71—21no—
446#121×C71—21no—
447#121×C71—21no—
448#121×C71—21no—
449#121×C71—21no—
450#121×C71—21no—
451#121×C71—21no—
452#121×C71—21no—
453#121×C71D411yescharacteristic
454#121×C71D411yescharacteristic
455#121×C71C2311yescharacteristic
456#121×C71C2311yescharacteristic
457#121×C71C2311yescharacteristic
458#121×C71C2311yescharacteristic
459#121×C71C2311yescharacteristic
460#121×C71C2311yescharacteristic
461#120×C71—21no—
462#120×C71—21no—
463#120×C71D411yescharacteristic
464#120×C71D411yescharacteristic
465C4×Q8×C71C2311yescharacteristic
466C4×Q8×C71C2311yescharacteristic
467C4×D4×C71—21no—
468C4×D4×C71—21no—
469C4×D4×C71—21no—
470C4×D4×C71—21no—
471C4×D4×C71—21no—
472C4×D4×C71—21no—
473C4×D4×C71—21no—
474C4×D4×C71—21no—
475C4×D4×C71C2311yescharacteristic
476C4×D4×C71C2311yescharacteristic
477C4×D4×C71C2311yescharacteristic
478C4×D4×C71C2311yescharacteristic
479C4×D4×C71C2311yescharacteristic
480C4×D4×C71C2311yescharacteristic
481#117×C71—21no—
482#117×C71—21no—
483#117×C71C2311yescharacteristic
484#117×C71C2311yescharacteristic
485#117×C71C2311yescharacteristic
486C2×C4⋊C4×C71—21no—
487C2×C4⋊C4×C71—21no—
488C2×C4⋊C4×C71C2311yescharacteristic
489C2×C4⋊C4×C71C2311yescharacteristic
490C23×D71—21no—
491C23×D71—21no—
492C23×D71—21no—
493C23×D71—21no—
494#11765866—44no—
495#11765865—22no—
496#11765865—22no—
497#11765865—22no—
498#11765865—22no—
499#11765865—22no—
500#11765865—22no—
501#11765865—41no—
502#11765865—41no—
503#11765865—41no—
504#11765865—41no—
505#11765865—41no—
506#11765865—41no—
507#11765865—44no—
508#11765865—44no—
509C2×Dic142—22no—
510C2×Dic142—21no—
511C2×Dic142—41no—
512C2×Dic142C2411yescharacteristic
513C2×Dic142C2411yescharacteristic
514C2×D284—22no—
515C2×D284—22no—
516C2×D284—22no—
517C2×D284—21no—
518C2×D284—21no—
519C2×D284—21no—
520C2×D284—21no—
521C2×D284—21no—
522C2×D284—21no—
523C2×D284—21no—
524C2×D284—21no—
525C2×D284—41no—
526C2×D284—41no—
527C2×D284—41no—
528C2×D284—41no—
529C2×D284—41no—
530C2×D284C2411yescharacteristic
531C2×D284C2411yescharacteristic
532C2×D284C2411yescharacteristic
533C2×D284C2411yescharacteristic
534C2×C22⋊D71—21no—
535C2×C22⋊D71—21no—
536C2×C22⋊D71—21no—
537C2×C22⋊D71—21no—
538C2×C22⋊D71—21no—
539C2×C22⋊D71—21no—
540C2×C22⋊D71—21no—
541C2×C22⋊D71—21no—
542C2×C22⋊D71—21no—
543C2×C22⋊D71—21no—
544C2×C22⋊D71—21no—
545C2×C22⋊D71—21no—
546C2×C22⋊D71—44no—
547C2×C22⋊D71—82no—
548D4×D71—44no—
549D4×D71—44no—
550D4×D71—44no—
551D4×D71—82no—
552D4×D71—82no—
553C22×Dic71—21no—
554C22×Dic71—21no—
555C2×C4×D71—21no—
556C2×C4×D71—21no—
557C2×C4×D71—21no—
558C2×C4×D71—21no—
559C2×C4×D71—21no—
560C2×C4×D71—21no—
561C2×C4×D71—21no—
562C2×C4×D71—21no—
563C2×C4×D71—44no—
564#11765855—22no—
565#11765855—22no—
566#11765855—41no—
567#11765855—41no—
568#11765853—22no—
569#11765853—22no—
570#11765853—41no—
571#11765853—41no—
572#11765852—22no—
573#11765852—22no—
574#11765852—41no—
575#11765852—41no—
576#11765852—41no—
577#11765852—41no—
578#11765852—41no—
579#11765852—41no—
580#11765850—22no—
581#11765850—22no—
582#11765850—41no—
583#11765850—41no—
584#11765850—41no—
585#11765850—41no—
586#11765850—41no—
587#11765850—41no—
588#11765849—41no—
589#11765849—41no—
590#11765849—41no—
591#11765849—41no—
592C2×C71⋊C8—41no—
593C2×C71⋊C8—41no—
594C2×C71⋊C8—41no—
595C2×C71⋊C8—41no—
596C2×C71⋊C8C2411yescharacteristic
597C2×C71⋊C8C2411yescharacteristic
598C2×C71⋊C8C2411yescharacteristic
599C2×C71⋊C8C2411yescharacteristic
600C2×C71⋊C8C2411yescharacteristic
601C2×C71⋊C8C2411yescharacteristic
602C2×C71⋊C8C2411yescharacteristic
603C2×C71⋊C8C2411yescharacteristic
604C4⋊Dic71—21no—
605C4⋊Dic71C2411yescharacteristic
606C4⋊Dic71C2411yescharacteristic
607Dic71⋊C4—21no—
608Dic71⋊C4—21no—
609Dic71⋊C4—21no—
610Dic71⋊C4—21no—
611C22⋊Dic71—21no—
612C22⋊Dic71—21no—
613(C2×D71)⋊C4—21no—
614(C2×D71)⋊C4—21no—
615(C2×D71)⋊C4—21no—
616(C2×D71)⋊C4—21no—
617(C2×D71)⋊C4—21no—
618(C2×D71)⋊C4—21no—
619(C2×D71)⋊C4—21no—
620(C2×D71)⋊C4—21no—
621(C2×D71)⋊C4—21no—
622(C2×D71)⋊C4—21no—
623(C2×D71)⋊C4—21no—
624(C2×D71)⋊C4—21no—
625C4×Dic71—21no—
626C4×Dic71—21no—
627C24×C71C2×D411yescharacteristic
628#41×C71—41no—
629#41×C71—41no—
630#41×C71—41no—
631#41×C71—41no—
632#41×C71—41no—
633#41×C71—41no—
634#41×C71—41no—
635#41×C71—41no—
636#41×C71—41no—
637#41×C71—41no—
638C2×Q8×C71C2×D411yescharacteristic
639C2×Q8×C71C2411yescharacteristic
640C2×Q8×C71C2411yescharacteristic
641C2×D4×C71—21no—
642C2×D4×C71—21no—
643C2×D4×C71—21no—
644C2×D4×C71—21no—
645C2×D4×C71—21no—
646C2×D4×C71—21no—
647C2×D4×C71—21no—
648C2×D4×C71—21no—
649C2×D4×C71—21no—
650C2×D4×C71—21no—
651C2×D4×C71—21no—
652C2×D4×C71—21no—
653C2×D4×C71C2×D411yescharacteristic
654C2×D4×C71C2×D411yescharacteristic
655C2×D4×C71C2×D411yescharacteristic
656C2×D4×C71C2×D411yescharacteristic
657C2×D4×C71C2×D411yescharacteristic
658C2×D4×C71C2×D411yescharacteristic
659C2×D4×C71C2×D411yescharacteristic
660C2×D4×C71C2411yescharacteristic
661C2×D4×C71C2411yescharacteristic
662C22×C4×C71—21no—
663C22×C4×C71—21no—
664C22×C4×C71—21no—
665C22×C4×C71—21no—
666C22×C4×C71—21no—
667C22×C4×C71—21no—
668C22×C4×C71—21no—
669C22×C4×C71—21no—
670C22×C4×C71—41no—
671C22×C4×C71—41no—
672C22×C4×C71C2×D411yescharacteristic
673C22×C4×C71C2×D411yescharacteristic
674C22×C4×C71C2×D411yescharacteristic
675C22×C4×C71C2411yescharacteristic
676C22×C4×C71C2411yescharacteristic
677C22×C4×C71C2411yescharacteristic
678C22×C4×C71C2411yescharacteristic
679C22×C4×C71C2411yescharacteristic
680C4⋊C4×C71—21no—
681C4⋊C4×C71—21no—
682C4⋊C4×C71—21no—
683C4⋊C4×C71—21no—
684C4⋊C4×C71—21no—
685C4⋊C4×C71—21no—
686C4⋊C4×C71—21no—
687C4⋊C4×C71—21no—
688C4⋊C4×C71—21no—
689C4⋊C4×C71—21no—
690C4⋊C4×C71—21no—
691C4⋊C4×C71—21no—
692C4⋊C4×C71—21no—
693C4⋊C4×C71—21no—
694C4⋊C4×C71—21no—
695C4⋊C4×C71—21no—
696C4⋊C4×C71C2×D411yescharacteristic
697C4⋊C4×C71C2×D411yescharacteristic
698C4⋊C4×C71C2×D411yescharacteristic
699C4⋊C4×C71C2×D411yescharacteristic
700C4⋊C4×C71C2×D411yescharacteristic
701C4⋊C4×C71C2×D411yescharacteristic
702C4⋊C4×C71C2411yescharacteristic
703C4⋊C4×C71C2411yescharacteristic
704C4⋊C4×C71C2411yescharacteristic
705C4⋊C4×C71C2411yescharacteristic
706C22⋊C4×C71—21no—
707C22⋊C4×C71—21no—
708C22⋊C4×C71—21no—
709C22⋊C4×C71—21no—
710C22⋊C4×C71—21no—
711C22⋊C4×C71—21no—
712C22⋊C4×C71—21no—
713C22⋊C4×C71—21no—
714C22⋊C4×C71—21no—
715C22⋊C4×C71—21no—
716C22⋊C4×C71—21no—
717C22⋊C4×C71—21no—
718C22⋊C4×C71—21no—
719C22⋊C4×C71—21no—
720C22⋊C4×C71—21no—
721C22⋊C4×C71—21no—
722C22⋊C4×C71C2×D411yescharacteristic
723C22⋊C4×C71C2×D411yescharacteristic
724C22⋊C4×C71C2×D411yescharacteristic
725C22⋊C4×C71C2×D411yescharacteristic
726C22⋊C4×C71C2×D411yescharacteristic
727C22⋊C4×C71C2×D411yescharacteristic
728C22⋊C4×C71C2×D411yescharacteristic
729C22⋊C4×C71C2×D411yescharacteristic
730C22⋊C4×C71C2×D411yescharacteristic
731C22⋊C4×C71C2×D411yescharacteristic
732C42×C71—21no—
733C42×C71—21no—
734C42×C71—21no—
735C42×C71—21no—
736C42×C71C2411yescharacteristic
737C42×C71C2411yescharacteristic
738C23×C71—21no—
739C23×C71—21no—
740C23×C71—41no—
741C23×C71—41no—
742C23×C71—41no—
743C23×C71C22×D411yescharacteristic
744C23×C71C22×D411yescharacteristic
745C23×C71C22×D411yescharacteristic
746C23×C71C22×D411yescharacteristic
747C23×C71C22×D411yescharacteristic
748C22×D71—21no—
749C22×D71—21no—
750C22×D71—21no—
751C22×D71—21no—
752C22×D71—42no—
753C22×D71—42no—
754C22×D71—42no—
755C22×D71—42no—
756C22×D71—42no—
757C22×D71—81no—
758C22×D71—81no—
759C22×D71—81no—
760C22×D71—81no—
761C22×D71—81no—
762C22×D71—81no—
763C22×D71—81no—
764Q8×C71—21no—
765Q8×C71—21no—
766Q8×C71—21no—
767Q8×C71—21no—
768Q8×C71—41no—
769D4×C71—21no—
770D4×C71—21no—
771D4×C71—21no—
772D4×C71—21no—
773D4×C71—41no—
774D4×C71—41no—
775D4×C71—41no—
776D4×C71—41no—
777D4×C71—41no—
778D4×C71—41no—
779D4×C71—41no—
780D4×C71—81no—
781D4×C71—81no—
782D4×C71—81no—
783D4×C71—81no—
784D4×C71—81no—
785D4×C71—81no—
786D4×C71—81no—
787D4×C71—81no—
788D4×C71—81no—
789D4×C71—81no—
790D4×C71—81no—
791D4×C71—81no—
792C2×C4×C71—21no—
793C2×C4×C71—21no—
794C2×C4×C71—21no—
795C2×C4×C71—21no—
796C2×C4×C71—21no—
797C2×C4×C71—21no—
798C2×C4×C71—21no—
799C2×C4×C71—21no—
800C2×C4×C71—21no—
801C2×C4×C71—21no—
802C2×C4×C71—21no—
803C2×C4×C71—21no—
804C2×C4×C71—21no—
805C2×C4×C71—21no—
806C2×C4×C71—21no—
807C2×C4×C71—21no—
808C2×C4×C71—41no—
809C2×C4×C71—41no—
810C2×C4×C71—41no—
811C2×C4×C71—81no—
812C2×C4×C71—81no—
813C2×C4×C71—81no—
814C2×C4×C71—81no—
815C2×C4×C71—81no—
816C2×C4×C71—81no—
817C2×C4×C71—81no—
818C2×C4×C71—81no—
819C2×C4×C71C22×D411yescharacteristic
820C2×C4×C71C22×D411yescharacteristic
821C2×C4×C71C22×D411yescharacteristic
822C2×C4×C71C22×D411yescharacteristic
823C2×C4×C71C22×D411yescharacteristic
824C2×C4×C71C22×D411yescharacteristic
825C2×C4×C71C22×D411yescharacteristic
826C2×C4×C71C22×D411yescharacteristic
827C2×C4×C71C22×D411yescharacteristic
828C2×C4×C71C2511yescharacteristic
829C22⋊D71—24no—
830C22⋊D71—42no—
831C22⋊D71—42no—
832C22⋊D71—42no—
833C22⋊D71—42no—
834C22⋊D71—42no—
835C22⋊D71—42no—
836C22⋊D71—42no—
837C22⋊D71—81no—
838C22⋊D71—81no—
839C22⋊D71—81no—
840C22⋊D71—81no—
841C2×Dic71—21no—
842C2×Dic71—21no—
843C2×Dic71—21no—
844C2×Dic71—21no—
845C2×Dic71—42no—
846C2×Dic71—81no—
847D284—21no—
848D284—21no—
849D284—21no—
850D284—21no—
851D284—21no—
852D284—21no—
853D284—21no—
854D284—42no—
855D284—42no—
856D284—42no—
857D284—42no—
858D284—81no—
859D284—81no—
860D284—81no—
861D284—81no—
862D284H(5,𝔽2)12yes—
863C4×D71—24no—
864C4×D71—42no—
865C4×D71—42no—
866C4×D71—42no—
867C4×D71—42no—
868C4×D71—42no—
869C4×D71—81no—
870C4×D71—81no—
871Dic142—21no—
872Dic142—21no—
873Dic142—21no—
874Dic142—42no—
875Dic142H(5,𝔽2)12yes—
876C71⋊C8—21no—
877C71⋊C8—21no—
878C71⋊C8—21no—
879C71⋊C8—21no—
880C71⋊C8—21no—
881C71⋊C8—21no—
882C71⋊C8—21no—
883C71⋊C8—21no—
884C22×C71—21no—
885C22×C71—21no—
886C22×C71—21no—
887C22×C71—21no—
888C22×C71—21no—
889C22×C71—21no—
890C22×C71—21no—
891C22×C71—21no—
892C22×C71—21no—
893C22×C71—21no—
894C22×C71—21no—
895C22×C71—21no—
896C22×C71—21no—
897C22×C71—21no—
898C22×C71—21no—
899C22×C71—41no—
900C22×C71—41no—
901C22×C71—41no—
902C22×C71—41no—
903C22×C71—41no—
904C22×C71—41no—
905C22×C71—82no—
906C22×C71C23×D411yescharacteristic
907C2×D71—22no—
908C2×D71—41no—
909C2×D71—41no—
910C2×D71—41no—
911C2×D71—41no—
912C2×D71—41no—
913C2×D71—41no—
914C2×D71—41no—
915C2×D71—41no—
916C2×D71—41no—
917C2×D71—41no—
918C2×D71—41no—
919C2×D71—84no—
920C2×D71—162no—
921C2×D71—162no—
922C2×D71—162no—
923C4×C71—21no—
924C4×C71—21no—
925C4×C71—21no—
926C4×C71—21no—
927C4×C71—21no—
928C4×C71—21no—
929C4×C71—21no—
930C4×C71—21no—
931C4×C71—21no—
932C4×C71—41no—
933C4×C71—41no—
934C4×C71—41no—
935C4×C71—41no—
936C4×C71—41no—
937C4×C71—41no—
938C4×C71C2×H(5,𝔽2)11yescharacteristic
939C4×C71C2×H(5,𝔽2)11yescharacteristic
940Dic71—22no—
941Dic71—41no—
942Dic71—41no—
943Dic71—41no—
944#61628—711nomaximal, Sylow
945C2×C71—41no—
946C2×C71—41no—
947C2×C71—41no—
948C2×C71—41no—
949C2×C71—41no—
950C2×C71—81no—
951C2×C71—81no—
952C2×C71#348411yescharacteristic
953C2×C71#358411yescharacteristic
954C2×C71#358511yescharacteristic
955D71—42no—
956D71—81no—
957D71—81no—
958D71—81no—
959#3539D7111yescharacteristic, complemented
960#3488—711no—
961#3327—711no—
962#3326—711no—
963#3318—711no—
964#3317—711no—
965#3310—711no—
966#3309—711no—
967#3297—711no—
968#3296—711no—
969#3287—711no—
970#3284—711no—
971#3274—711no—
972#3272—711no—
973#3271—711no—
974#3269—711no—
975#3268—711no—
976#3267—711no—
977#3222—711no—
978#3220—711no—
979#3204—711no—
980#3203—711no—
981#3194—711no—
982#3188—711no—
983#3120—711no—
984#3119—711no—
985#3012—711no—
986#3012—711no—
987#3005—711no—
988#3002—711no—
989#2976—711no—
990C71#6162811yescharacteristic, complemented, Sylow
991C2×H(5,𝔽2)—711no—
992C22×#41—711no—
993C2×#137—711no—
994C2×AGL(1,ℤ/8)—711no—
995C2×AGL(1,ℤ/8)—711no—
996C2×AGL(1,ℤ/8)—711no—
997C2×#135—711no—
998C2×#135—711no—
999C2×#135—711no—
1000C2×#135—711no—
1001#560—21no—
1002#560—21no—
1003#553—21no—
1004#553—21no—
1005#553C2×D7111yescharacteristic, complemented
1006#553C2×D7111yescharacteristic, complemented
1007#552C2×D7111yescharacteristic, complemented
1008#552C2×D7111yescharacteristic, complemented
1009#550—711no—
1010#550—711no—
1011#550C2×D7111yescharacteristic, complemented
1012#550C2×D7111yescharacteristic, complemented
1013#548—711no—
1014#548—711no—
1015#547C2×D7111yescharacteristic, complemented
1016#547C2×D7111yescharacteristic, complemented
1017#546—711no—
1018#546—711no—
1019#546—1421no—
1020#546—1421no—
1021D42—711no—
1022D42—711no—
1023D42—1421no—
1024D42—1421no—
1025#541C2×D7111yescharacteristic, complemented
1026#540—21no—
1027#540—21no—
1028#540C2×D7111yescharacteristic, complemented
1029#539—21no—
1030#539—21no—
1031#537—711no—
1032#537—1421no—
1033#537C2×D7111yescharacteristic, complemented
1034#537C2×D7111yescharacteristic, complemented
1035#535—711no—
1036#535—1421no—
1037#525—1421no—
1038#525C2×D7111yescharacteristic
1039#525C2×D7111yescharacteristic, complemented
1040#525C2×D7111yescharacteristic, complemented
1041C2×#121—711no—
1042C2×#121—1421no—
1043#520—711no—
1044#497—711no—
1045#496—711no—
1046#493—711no—
1047#492—711no—
1048#490—711no—
1049#490—711no—
1050#488—711no—
1051#488—711no—
1052#484—711no—
1053#484—711no—
1054#483—711no—
1055#483—711no—
1056#482—711no—
1057#482—711no—
1058#482—711no—
1059#482—711no—
1060#481—711no—
1061#481—711no—
1062#480—711no—
1063#480—711no—
1064#479—711no—
1065#479—711no—
1066#478—711no—
1067#478—711no—
1068#470—711no—
1069#469—711no—
1070#469—711no—
1071#469—711no—
1072#468—711no—
1073#468—711no—
1074#468—711no—
1075#468—711no—
1076#467—711no—
1077#466—711no—
1078#466—711no—
1079#466—711no—
1080#465—711no—
1081#465—711no—
1082#465—711no—
1083#465—711no—
1084#464—711no—
1085#464—711no—
1086#463—711no—
1087#463—711no—
1088#462—711no—
1089#461—711no—
1090#460—711no—
1091#460—711no—
1092#460—711no—
1093#459—711no—
1094#459—711no—
1095#459—711no—
1096#452—711no—
1097#452—711no—
1098#452—711no—
1099#452—711no—
1100#452—711no—
1101#452—711no—
1102#452—711no—
1103#452—711no—
1104#452—711no—
1105#452—711no—
1106#451—711no—
1107#450—711no—
1108#450—711no—
1109#450—711no—
1110#450—711no—
1111#450—711no—
1112#449—711no—
1113#449—711no—
1114#449—711no—
1115#449—711no—
1116#449—711no—
1117#449—711no—
1118#449—711no—
1119#449—711no—
1120#449—711no—
1121#449—711no—
1122#449—711no—
1123#449—711no—
1124#449—711no—
1125#449—711no—
1126#448—711no—
1127#447—711no—
1128#447—711no—
1129#447—711no—
1130#447—711no—
1131#447—711no—
1132#442—711no—
1133#441—711no—
1134#440—711no—
1135#440—711no—
1136C4×Q16—711no—
1137C4×SD16—711no—
1138C4×SD16—711no—
1139C4×D8—711no—
1140#436—711no—
1141#436—711no—
1142#435—711no—
1143#435—711no—
1144#435—711no—
1145#435—711no—
1146C8×D4—711no—
1147C8×D4—711no—
1148#433—711no—
1149#433—711no—
1150#419—711no—
1151#418—711no—
1152#417—711no—
1153#417—711no—
1154#416—711no—
1155#416—711no—
1156C2×#102—711no—
1157C2×#102—711no—
1158#408—711no—
1159#408—711no—
1160#407—711no—
1161C2×C22⋊C8—711no—
1162H(5,𝔽2)—2842no—
1163H(5,𝔽2)—2842no—
1164C2×#41—2842no—
1165C2×#41—2842no—
1166C2×#41—711no—
1167C2×#41—711no—
1168C2×#41—711no—
1169C2×#41—711no—
1170C2×#41—711no—
1171C2×#41—711no—
1172C2×#41—1421no—
1173C2×#41—1421no—
1174C2×#41—1421no—
1175C2×#41C22×D7111yescharacteristic
1176C2×#41C22×D7111yescharacteristic
1177C2×#41C22×D7111yescharacteristic
1178C2×#41C22×D7111yescharacteristic
1179C2×#41C22×D7111yescharacteristic
1180C22×Q8—711no—
1181C22×D4—711no—
1182C22×D4—711no—
1183C22×D4—711no—
1184C22×D4—711no—
1185C22×D4—1421no—
1186C22×D4—1421no—
1187C22×D4—1421no—
1188C22×D4—1421no—
1189C22×D4—1421no—
1190C22×D4—1421no—
1191C22×D4—1421no—
1192C23×C4—1421no—
1193C23×C4C22×D7111yescharacteristic
1194#137—2842no—
1195AGL(1,ℤ/8)—2842no—
1196AGL(1,ℤ/8)—2842no—
1197AGL(1,ℤ/8)—2842no—
1198#135—2842no—
1199#135—2842no—
1200#135—2842no—
1201#135—2842no—
1202C2×Q16—711no—
1203C2×Q16—711no—
1204C2×Q16—711no—
1205C2×Q16—711no—
1206C2×SD16—711no—
1207C2×SD16—711no—
1208C2×SD16—711no—
1209C2×SD16—711no—
1210C2×SD16—711no—
1211C2×SD16—711no—
1212C2×SD16—711no—
1213C2×SD16—711no—
1214C2×SD16—711no—
1215C2×SD16—711no—
1216C2×SD16—711no—
1217C2×SD16—711no—
1218C2×D8—711no—
1219C2×D8—711no—
1220C2×D8—711no—
1221C2×D8—711no—
1222C2×D8—711no—
1223C2×D8—711no—
1224C2×D8—711no—
1225C2×D8—711no—
1226C2×M16—711no—
1227C2×M16—711no—
1228C2×M16—711no—
1229C2×M16—711no—
1230C22×C8—711no—
1231C22×C8—711no—
1232C22×C8—711no—
1233C22×C8—711no—
1234C4⋊Q8C22×D7111yescharacteristic
1235#127—21no—
1236#127—21no—
1237#127—711no—
1238#127—711no—
1239#127—1421no—
1240#127—1421no—
1241#127C22×D7111yescharacteristic
1242#126—21no—
1243#126—21no—
1244#126—21no—
1245#126—21no—
1246#126—21no—
1247#126—21no—
1248#125—21no—
1249#125—21no—
1250#125—21no—
1251#125—21no—
1252#125C22×D7111yescharacteristic
1253#125C22×D7111yescharacteristic
1254#124—711no—
1255#124—711no—
1256#124—1421no—
1257#124—1421no—
1258#123—21no—
1259#123—21no—
1260#123—21no—
1261#123—21no—
1262#123—21no—
1263#123—21no—
1264#123—21no—
1265#123—21no—
1266#123—21no—
1267#123—21no—
1268#123—21no—
1269#123—21no—
1270#123—1421no—
1271#123—1421no—
1272#123C22⋊D7111yescharacteristic
1273#123C22⋊D7111yescharacteristic
1274C22⋊Q8—21no—
1275C22⋊Q8—21no—
1276C22⋊Q8—711no—
1277C22⋊Q8—711no—
1278C22⋊Q8—1421no—
1279C22⋊Q8—1421no—
1280C22⋊Q8—1421no—
1281C22⋊Q8C22⋊D7111yescharacteristic
1282C22⋊Q8C22⋊D7111yescharacteristic
1283C22⋊Q8C22×D7111yescharacteristic
1284C22⋊Q8C22×D7111yescharacteristic
1285C22⋊Q8C22×D7111yescharacteristic
1286C22⋊Q8C22×D7111yescharacteristic
1287C22⋊Q8C22×D7111yescharacteristic
1288C22⋊Q8C22×D7111yescharacteristic
1289#121—21no—
1290#121—21no—
1291#121—21no—
1292#121—21no—
1293#121—21no—
1294#121—21no—
1295#121—21no—
1296#121—21no—
1297#121—21no—
1298#121—21no—
1299#121—21no—
1300#121—21no—
1301#121—21no—
1302#121—21no—
1303#121—21no—
1304#121—21no—
1305#121—711no—
1306#121—711no—
1307#121—711no—
1308#121—711no—
1309#121—711no—
1310#121—711no—
1311#121—1421no—
1312#121—1421no—
1313#121—1421no—
1314#121—1421no—
1315#121—1421no—
1316#121—1421no—
1317#121—1421no—
1318#121—1421no—
1319#121—1421no—
1320#121—1421no—
1321#121—1421no—
1322#121—1421no—
1323#121—1421no—
1324#121—1421no—
1325#121—1421no—
1326#121—1421no—
1327#121—1421no—
1328#121C22⋊D7111yescharacteristic
1329#121C22⋊D7111yescharacteristic
1330#121C22×D7111yescharacteristic
1331#121C22×D7111yescharacteristic
1332#121C22×D7111yescharacteristic
1333#121C22×D7111yescharacteristic
1334#121C22×D7111yescharacteristic
1335#121C22×D7111yescharacteristic
1336#120—21no—
1337#120—21no—
1338#120—1421no—
1339#120—1421no—
1340#120—1421no—
1341#120—1421no—
1342#120—1421no—
1343#120—1421no—
1344#120—1421no—
1345#120—1421no—
1346#120C22⋊D7111yescharacteristic
1347#120C22⋊D7111yescharacteristic
1348C4×Q8—711no—
1349C4×Q8—711no—
1350C4×Q8C22×D7111yescharacteristic
1351C4×Q8C22×D7111yescharacteristic
1352C4×D4—21no—
1353C4×D4—21no—
1354C4×D4—21no—
1355C4×D4—21no—
1356C4×D4—21no—
1357C4×D4—21no—
1358C4×D4—21no—
1359C4×D4—21no—
1360C4×D4—711no—
1361C4×D4—711no—
1362C4×D4—1421no—
1363C4×D4—1421no—
1364C4×D4—1421no—
1365C4×D4—1421no—
1366C4×D4—1421no—
1367C4×D4—1421no—
1368C4×D4C22×D7111yescharacteristic
1369C4×D4C22×D7111yescharacteristic
1370C4×D4C22×D7111yescharacteristic
1371C4×D4C22×D7111yescharacteristic
1372C4×D4C22×D7111yescharacteristic
1373C4×D4C22×D7111yescharacteristic
1374#117—21no—
1375#117—21no—
1376#117—1421no—
1377#117C22×D7111yescharacteristic
1378#117C22×D7111yescharacteristic
1379#117C22×D7111yescharacteristic
1380C2×C4⋊C4—21no—
1381C2×C4⋊C4—21no—
1382C2×C4⋊C4—711no—
1383C2×C4⋊C4—1421no—
1384C2×C4⋊C4C22×D7111yescharacteristic
1385C2×C4⋊C4C22×D7111yescharacteristic
1386C2×C22⋊C4—1421no—
1387C2×C22⋊C4—1421no—
1388C2×C22⋊C4—1421no—
1389#107—711no—
1390#107—711no—
1391#107—711no—
1392#107—711no—
1393#106—711no—
1394#106—711no—
1395#106—711no—
1396#106—711no—
1397C4⋊C8—711no—
1398C4⋊C8—711no—
1399C4⋊C8—711no—
1400C4⋊C8—711no—
1401#103—711no—
1402#103—711no—
1403#103—711no—
1404#103—711no—
1405#103—711no—
1406#103—711no—
1407#103—711no—
1408#103—711no—
1409#103—711no—
1410#103—711no—
1411#103—711no—
1412#103—711no—
1413#102—711no—
1414#102—711no—
1415#102—711no—
1416#102—711no—
1417#102—711no—
1418#102—711no—
1419#102—711no—
1420#102—711no—
1421#102—711no—
1422#102—711no—
1423#102—711no—
1424#102—711no—
1425#102—711no—
1426#102—711no—
1427#102—711no—
1428#102—711no—
1429#102—711no—
1430#102—711no—
1431#102—711no—
1432#102—711no—
1433C22⋊C8—711no—
1434C22⋊C8—711no—
1435C22⋊C8—711no—
1436C22⋊C8—711no—
1437C22⋊C8—711no—
1438C22⋊C8—711no—
1439C22⋊C8—711no—
1440C22⋊C8—711no—
1441C22⋊C8—711no—
1442C22⋊C8—711no—
1443C22⋊C8—711no—
1444C22⋊C8—711no—
1445#97—711no—
1446#97—711no—
1447C4×C8—711no—
1448C4×C8—711no—
1449C24—1421no—
1450C24—1421no—
1451C24—1421no—
1452C24—1421no—
1453C24C2×C22⋊D7111yescharacteristic
1454#41—41no—
1455#41—41no—
1456#41—41no—
1457#41—41no—
1458#41—41no—
1459#41—41no—
1460#41—41no—
1461#41—41no—
1462#41—41no—
1463#41—41no—
1464#41—2841no—
1465#41—2841no—
1466#41—2841no—
1467#41—2841no—
1468#41—2841no—
1469#41—2841no—
1470#41—2844no—
1471#41—2844no—
1472#41—2844no—
1473#41—1422no—
1474#41—1422no—
1475#41—1422no—
1476#41—1422no—
1477#41—1422no—
1478#41—1422no—
1479C2×Q8—2841no—
1480C2×Q8—711no—
1481C2×Q8—711no—
1482C2×Q8—1422no—
1483C2×Q8—1421no—
1484C2×Q8C2×C22⋊D7111yescharacteristic
1485C2×Q8C23×D7111yescharacteristic
1486C2×Q8C23×D7111yescharacteristic
1487C2×D4—21no—
1488C2×D4—21no—
1489C2×D4—21no—
1490C2×D4—21no—
1491C2×D4—21no—
1492C2×D4—21no—
1493C2×D4—21no—
1494C2×D4—21no—
1495C2×D4—21no—
1496C2×D4—21no—
1497C2×D4—21no—
1498C2×D4—21no—
1499C2×D4—2841no—
1500C2×D4—2841no—
1501C2×D4—2841no—
1502C2×D4—2841no—
1503C2×D4—2841no—
1504C2×D4—2844no—
1505C2×D4—2844no—
1506C2×D4—2844no—
1507C2×D4—2844no—
1508C2×D4—5682no—
1509C2×D4—5682no—
1510C2×D4—5682no—
1511C2×D4—711no—
1512C2×D4—711no—
1513C2×D4—711no—
1514C2×D4—711no—
1515C2×D4—1422no—
1516C2×D4—1422no—
1517C2×D4—1422no—
1518C2×D4—1421no—
1519C2×D4—1421no—
1520C2×D4—1421no—
1521C2×D4—1421no—
1522C2×D4—1421no—
1523C2×D4—1421no—
1524C2×D4—1421no—
1525C2×D4—1421no—
1526C2×D4—1421no—
1527C2×D4—1421no—
1528C2×D4—1421no—
1529C2×D4—1421no—
1530C2×D4—1421no—
1531C2×D4—1421no—
1532C2×D4—1421no—
1533C2×D4—1421no—
1534C2×D4—1421no—
1535C2×D4—1421no—
1536C2×D4—1421no—
1537C2×D4—1421no—
1538C2×D4C2×C22⋊D7111yescharacteristic
1539C2×D4C2×C22⋊D7111yescharacteristic
1540C2×D4C2×C22⋊D7111yescharacteristic
1541C2×D4C2×C22⋊D7111yescharacteristic
1542C2×D4C2×C22⋊D7111yescharacteristic
1543C2×D4C2×C22⋊D7111yescharacteristic
1544C2×D4C2×C22⋊D7111yescharacteristic
1545C2×D4C23×D7111yescharacteristic
1546C2×D4C23×D7111yescharacteristic
1547C22×C4—21no—
1548C22×C4—21no—
1549C22×C4—21no—
1550C22×C4—21no—
1551C22×C4—21no—
1552C22×C4—21no—
1553C22×C4—21no—
1554C22×C4—21no—
1555C22×C4—41no—
1556C22×C4—41no—
1557C22×C4—2844no—
1558C22×C4—1421no—
1559C22×C4—1421no—
1560C22×C4—1421no—
1561C22×C4—1421no—
1562C22×C4—1421no—
1563C22×C4—1421no—
1564C22×C4—1421no—
1565C22×C4—1421no—
1566C22×C4—1421no—
1567C22×C4—1421no—
1568C22×C4C2×C22⋊D7111yescharacteristic
1569C22×C4C2×C22⋊D7111yescharacteristic
1570C22×C4C2×C22⋊D7111yescharacteristic
1571C22×C4C23×D7111yescharacteristic
1572C22×C4C23×D7111yescharacteristic
1573C22×C4C23×D7111yescharacteristic
1574C22×C4C23×D7111yescharacteristic
1575C22×C4C23×D7111yescharacteristic
1576Q16—2841no—
1577Q16—2841no—
1578Q16—1422no—
1579Q16—1422no—
1580SD16—2841no—
1581SD16—2841no—
1582SD16—2841no—
1583SD16—2841no—
1584SD16—2841no—
1585SD16—2841no—
1586SD16—2841no—
1587SD16—2841no—
1588SD16—1422no—
1589SD16—1422no—
1590SD16—1422no—
1591SD16—1422no—
1592D8—2841no—
1593D8—2841no—
1594D8—2841no—
1595D8—2841no—
1596D8—2841no—
1597D8—2841no—
1598D8—1422no—
1599D8—1422no—
1600M16—2841no—
1601M16—2841no—
1602M16—2841no—
1603M16—2841no—
1604C2×C8—2841no—
1605C2×C8—2841no—
1606C2×C8—2841no—
1607C2×C8—2841no—
1608C2×C8—711no—
1609C2×C8—711no—
1610C2×C8—711no—
1611C2×C8—711no—
1612C2×C8—711no—
1613C2×C8—711no—
1614C2×C8—711no—
1615C2×C8—711no—
1616C4⋊C4—21no—
1617C4⋊C4—21no—
1618C4⋊C4—21no—
1619C4⋊C4—21no—
1620C4⋊C4—21no—
1621C4⋊C4—21no—
1622C4⋊C4—21no—
1623C4⋊C4—21no—
1624C4⋊C4—21no—
1625C4⋊C4—21no—
1626C4⋊C4—21no—
1627C4⋊C4—21no—
1628C4⋊C4—21no—
1629C4⋊C4—21no—
1630C4⋊C4—21no—
1631C4⋊C4—21no—
1632C4⋊C4—711no—
1633C4⋊C4—711no—
1634C4⋊C4—1421no—
1635C4⋊C4—1421no—
1636C4⋊C4—1421no—
1637C4⋊C4—1421no—
1638C4⋊C4—1421no—
1639C4⋊C4C2×C22⋊D7111yescharacteristic
1640C4⋊C4C2×C22⋊D7111yescharacteristic
1641C4⋊C4C2×C22⋊D7111yescharacteristic
1642C4⋊C4C2×C22⋊D7111yescharacteristic
1643C4⋊C4C2×C22⋊D7111yescharacteristic
1644C4⋊C4C2×C22⋊D7111yescharacteristic
1645C4⋊C4C23×D7111yescharacteristic
1646C4⋊C4C23×D7111yescharacteristic
1647C4⋊C4C23×D7111yescharacteristic
1648C4⋊C4C23×D7111yescharacteristic
1649C22⋊C4—21no—
1650C22⋊C4—21no—
1651C22⋊C4—21no—
1652C22⋊C4—21no—
1653C22⋊C4—21no—
1654C22⋊C4—21no—
1655C22⋊C4—21no—
1656C22⋊C4—21no—
1657C22⋊C4—21no—
1658C22⋊C4—21no—
1659C22⋊C4—21no—
1660C22⋊C4—21no—
1661C22⋊C4—21no—
1662C22⋊C4—21no—
1663C22⋊C4—21no—
1664C22⋊C4—21no—
1665C22⋊C4—1421no—
1666C22⋊C4—1421no—
1667C22⋊C4—1421no—
1668C22⋊C4—1421no—
1669C22⋊C4—1421no—
1670C22⋊C4—1421no—
1671C22⋊C4—1421no—
1672C22⋊C4—1421no—
1673C22⋊C4—1421no—
1674C22⋊C4—1421no—
1675C22⋊C4—1421no—
1676C22⋊C4—1421no—
1677C22⋊C4—1421no—
1678C22⋊C4—1421no—
1679C22⋊C4C2×C22⋊D7111yescharacteristic
1680C22⋊C4C2×C22⋊D7111yescharacteristic
1681C22⋊C4C2×C22⋊D7111yescharacteristic
1682C22⋊C4C2×C22⋊D7111yescharacteristic
1683C22⋊C4C2×C22⋊D7111yescharacteristic
1684C22⋊C4C2×C22⋊D7111yescharacteristic
1685C22⋊C4C2×C22⋊D7111yescharacteristic
1686C22⋊C4C2×C22⋊D7111yescharacteristic
1687C22⋊C4C2×C22⋊D7111yescharacteristic
1688C22⋊C4C2×C22⋊D7111yescharacteristic
1689C42—21no—
1690C42—21no—
1691C42—21no—
1692C42—21no—
1693C42—1421no—
1694C42—1421no—
1695C42C23×D7111yescharacteristic
1696C42C23×D7111yescharacteristic
1697C23—21no—
1698C23—21no—
1699C23—41no—
1700C23—41no—
1701C23—41no—
1702C23—2842no—
1703C23—2842no—
1704C23—2842no—
1705C23—2842no—
1706C23—2842no—
1707C23—5681no—
1708C23—5681no—
1709C23—5681no—
1710C23—5681no—
1711C23—5681no—
1712C23—5681no—
1713C23—5681no—
1714C23—1421no—
1715C23—1421no—
1716C23—1421no—
1717C23—1421no—
1718C23C22×C22⋊D7111yescharacteristic
1719C23C22×C22⋊D7111yescharacteristic
1720C23C22×C22⋊D7111yescharacteristic
1721C23C22×C22⋊D7111yescharacteristic
1722C23C22×C22⋊D7111yescharacteristic
1723Q8—21no—
1724Q8—21no—
1725Q8—21no—
1726Q8—21no—
1727Q8—41no—
1728Q8—2842no—
1729Q8—712no—
1730Q8—1421no—
1731Q8—1421no—
1732Q8—1421no—
1733D4—21no—
1734D4—21no—
1735D4—21no—
1736D4—21no—
1737D4—41no—
1738D4—41no—
1739D4—41no—
1740D4—41no—
1741D4—41no—
1742D4—41no—
1743D4—41no—
1744D4—81no—
1745D4—81no—
1746D4—81no—
1747D4—81no—
1748D4—81no—
1749D4—81no—
1750D4—81no—
1751D4—81no—
1752D4—81no—
1753D4—81no—
1754D4—81no—
1755D4—81no—
1756D4—2842no—
1757D4—2842no—
1758D4—2842no—
1759D4—2842no—
1760D4—2842no—
1761D4—2842no—
1762D4—2842no—
1763D4—2842no—
1764D4—2842no—
1765D4—2842no—
1766D4—2842no—
1767D4—5681no—
1768D4—5681no—
1769D4—5681no—
1770D4—5681no—
1771D4—5681no—
1772D4—5681no—
1773D4—5681no—
1774D4—5681no—
1775D4—712no—
1776D4—1424no—
1777D4—1421no—
1778D4—1421no—
1779D4—1421no—
1780D4—1421no—
1781D4—1421no—
1782D4—1421no—
1783D4—1421no—
1784C2×C4—21no—
1785C2×C4—21no—
1786C2×C4—21no—
1787C2×C4—21no—
1788C2×C4—21no—
1789C2×C4—21no—
1790C2×C4—21no—
1791C2×C4—21no—
1792C2×C4—21no—
1793C2×C4—21no—
1794C2×C4—21no—
1795C2×C4—21no—
1796C2×C4—21no—
1797C2×C4—21no—
1798C2×C4—21no—
1799C2×C4—21no—
1800C2×C4—41no—
1801C2×C4—41no—
1802C2×C4—41no—
1803C2×C4—81no—
1804C2×C4—81no—
1805C2×C4—81no—
1806C2×C4—81no—
1807C2×C4—81no—
1808C2×C4—81no—
1809C2×C4—81no—
1810C2×C4—81no—
1811C2×C4—2842no—
1812C2×C4—2842no—
1813C2×C4—2842no—
1814C2×C4—2842no—
1815C2×C4—2842no—
1816C2×C4—2842no—
1817C2×C4—5681no—
1818C2×C4—5681no—
1819C2×C4—5681no—
1820C2×C4—1424no—
1821C2×C4—1421no—
1822C2×C4—1421no—
1823C2×C4—1421no—
1824C2×C4—1421no—
1825C2×C4C22×C22⋊D7111yescharacteristic
1826C2×C4C22×C22⋊D7111yescharacteristic
1827C2×C4C22×C22⋊D7111yescharacteristic
1828C2×C4C22×C22⋊D7111yescharacteristic
1829C2×C4C22×C22⋊D7111yescharacteristic
1830C2×C4C22×C22⋊D7111yescharacteristic
1831C2×C4C22×C22⋊D7111yescharacteristic
1832C2×C4C22×C22⋊D7111yescharacteristic
1833C2×C4C22×C22⋊D7111yescharacteristic
1834C2×C4C24×D7111yescharacteristic
1835C8—1421no—
1836C8—1421no—
1837C8—1421no—
1838C8—1421no—
1839C8—1421no—
1840C8—1421no—
1841C8—1421no—
1842C8—1421no—
1843C22—21no—
1844C22—21no—
1845C22—21no—
1846C22—21no—
1847C22—21no—
1848C22—21no—
1849C22—21no—
1850C22—21no—
1851C22—21no—
1852C22—21no—
1853C22—21no—
1854C22—21no—
1855C22—21no—
1856C22—21no—
1857C22—21no—
1858C22—41no—
1859C22—41no—
1860C22—41no—
1861C22—41no—
1862C22—41no—
1863C22—41no—
1864C22—82no—
1865C22—2841no—
1866C22—2841no—
1867C22—2841no—
1868C22—2841no—
1869C22—2841no—
1870C22—2841no—
1871C22—2841no—
1872C22—2841no—
1873C22—2841no—
1874C22—2841no—
1875C22—2841no—
1876C22—5684no—
1877C22—11362no—
1878C22—11362no—
1879C22—11362no—
1880C22—1422no—
1881C22C23×C22⋊D7111yescharacteristic
1882C4—21no—
1883C4—21no—
1884C4—21no—
1885C4—21no—
1886C4—21no—
1887C4—21no—
1888C4—21no—
1889C4—21no—
1890C4—21no—
1891C4—41no—
1892C4—41no—
1893C4—41no—
1894C4—41no—
1895C4—41no—
1896C4—41no—
1897C4—2841no—
1898C4—2841no—
1899C4—2841no—
1900C4—1422no—
1901C4H(5,𝔽2)×D7111yescharacteristic
1902C4H(5,𝔽2)×D7111yescharacteristic
1903C2—41no—
1904C2—41no—
1905C2—41no—
1906C2—41no—
1907C2—41no—
1908C2—81no—
1909C2—81no—
1910C2—2842no—
1911C2—5681no—
1912C2—5681no—
1913C2—5681no—
1914C2#2260197111yescharacteristic
1915C2#2260311111yescharacteristic
1916C2#2260311911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC71×#3539C2
socleC22×C71C23×D4
hypercenter#3539D71
hypocenterC71#61628
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ #525 ◁ #3539

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22602001C2semidirect
2. #22600602C2semidirect
3. #22600587C2semidirect
4. #22600475C2semidirect
5. #22600460C2semidirect
6. #22600355C2semidirect
7. #22600340C2semidirect
8. #22600184C2semidirect
9. #22600169C2semidirect
10. #22600096C2semidirect
11. #22600066C2semidirect
12. #22599960C2semidirect
13. #22599940C2semidirect
14. #22599921C2semidirect
15. #22599891C2semidirect
16. #22599881C2semidirect
17. #22599866C2semidirect
18. #22599406C2semidirect
19. #22599384C2semidirect
20. #22599246C2semidirect
21. #22599237C2semidirect
22. #22599150C2semidirect
23. #22599101C2semidirect
24. #22598548C2semidirect
25. #22598533C2semidirect
26. #22597641C2semidirect
27. #22597641C2semidirect
28. #22597580C2semidirect
29. #22597556C2semidirect
30. #22597388C2semidirect
31. C71×#3539C2semidirect
34. C2×#14556158C22semidirect
35. C2×#14556153C22semidirect
36. C2×#14556153C22semidirect
37. C2×#14556153C22semidirect
38. C2×#14556148C22semidirect
39. C2×#14556148C22semidirect
40. C2×#14556148C22semidirect
41. C2×#14556148C22semidirect
62. #17986391C22semidirect
63. #17986386C22semidirect
64. #17986375C22semidirect
65. #17986373C22semidirect
66. #17986365C22semidirect
67. #17986365C22semidirect
68. #17986356C22semidirect
69. #17986356C22semidirect
70. #17986334C22semidirect
71. #17986332C22semidirect
72. #17986329C22semidirect
73. #17986327C22semidirect
74. #17986323C22semidirect
75. #17986323C22semidirect
76. #17986323C22semidirect
77. #17986323C22semidirect
78. #17986317C22semidirect
79. #17986315C22semidirect
80. #17986312C22semidirect
81. #17986310C22semidirect
82. #17986303C22semidirect
83. #17986303C22semidirect
84. #17986296C22semidirect
85. #17986296C22semidirect
86. #17986255C22semidirect
87. #17986250C22semidirect
88. #17986250C22semidirect
89. #17986250C22semidirect
90. #17986247C22semidirect
91. #17986247C22semidirect
92. #17986247C22semidirect
93. #17986243C22semidirect
94. #17986238C22semidirect
95. #17986233C22semidirect
96. #17986233C22semidirect
97. #17986233C22semidirect
98. #17986230C22semidirect
99. #17986230C22semidirect
100. #17986230C22semidirect
101. #17986226C22semidirect
102. #17986221C22semidirect
103. #17986221C22semidirect
104. #17986214C22semidirect
105. #17986214C22semidirect
106. #17986206C22semidirect
107. #17986201C22semidirect
108. #17986199C22semidirect
109. #17986199C22semidirect
110. #17986196C22semidirect
111. #17986194C22semidirect
112. #17986194C22semidirect
113. #17986191C22semidirect
114. #17986161C22semidirect
115. #17986161C22semidirect
118. #17986159C22semidirect
119. #17986159C22semidirect
120. #17986159C22semidirect
121. #17986159C22semidirect
122. #17986159C22semidirect
123. #17986159C22semidirect
124. #17986154C22semidirect
125. #17986149C22semidirect
126. #17986149C22semidirect
127. #17986149C22semidirect
128. #17986149C22semidirect
129. #17986149C22semidirect
130. #17986144C22semidirect
131. #17986144C22semidirect
132. #17986144C22semidirect
133. #17986144C22semidirect
134. #17986144C22semidirect
135. #17986144C22semidirect
138. #17986142C22semidirect
139. #17986142C22semidirect
140. #17986142C22semidirect
141. #17986142C22semidirect
142. #17986142C22semidirect
143. #17986142C22semidirect
144. #17986137C22semidirect
145. #17986132C22semidirect
146. #17986132C22semidirect
147. #17986132C22semidirect
148. #17986132C22semidirect
149. #17986132C22semidirect
150. #17986109C22semidirect
151. #17986104C22semidirect
152. #17986099C22semidirect
153. #17986097C22semidirect
154. C4×#11765855C22semidirect
155. C4×#11765852C22semidirect
156. C4×#11765853C22semidirect
157. C4×#11765850C22semidirect
158. #17986077C22semidirect
159. #17986077C22semidirect
160. #17986071C22semidirect
161. #17986071C22semidirect
162. #17986071C22semidirect
163. #17986071C22semidirect
164. D4×C71⋊C8C22semidirect
165. D4×C71⋊C8C22semidirect
166. #17986060C22semidirect
167. #17986060C22semidirect
168. #17986007C22semidirect
169. #17986003C22semidirect
170. #17985998C22semidirect
171. #17985998C22semidirect
172. #17985993C22semidirect
173. #17985993C22semidirect
174. C2×#14556048C22semidirect
175. C2×#14556048C22semidirect
176. #17985966C22semidirect
177. #17985966C22semidirect
178. #17985963C22semidirect
179. C2×C22⋊(C71⋊C8)C22semidirect
184. #553×C71C22semidirect
185. #553×C71C22semidirect
186. #552×C71C22semidirect
187. #552×C71C22semidirect
188. #550×C71C22semidirect
189. #550×C71C22semidirect
190. #547×C71C22semidirect
191. #547×C71C22semidirect
192. #541×C71C22semidirect
195. #540×C71C22semidirect
198. #537×C71C22semidirect
199. #537×C71C22semidirect
201. #525×C71C22semidirect
202. #525×C71C22semidirect
959. #3539D71semidirect
990. C71#61628semidirect
1005. #553C2×D71semidirect
1006. #553C2×D71semidirect
1007. #552C2×D71semidirect
1008. #552C2×D71semidirect
1011. #550C2×D71semidirect
1012. #550C2×D71semidirect
1015. #547C2×D71semidirect
1016. #547C2×D71semidirect
1025. #541C2×D71semidirect
1028. #540C2×D71semidirect
1033. #537C2×D71semidirect
1034. #537C2×D71semidirect
1039. #525C2×D71semidirect
1040. #525C2×D71semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226020012
#226006022
#226005872
#226004752
#226004602
#226003552
#226003402
#226001842
#226001692
#226000962
#226000662
#225999602
#225999402
#225999212
#225998912
#225998812
#225998662
#225994062
#225993842
#225992462
#225992372
#225991502
#225991012
#225985482
#225985332
#225976412
#225975802
#225975562
#225973882
C71×#35392
#6162871