Finite Group Databasebeta

← #32883420

Subgroups — #32883420

Order 18176.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602012C211yesmaximal, characteristic, complemented
2#22600550C211yesmaximal, characteristic, complemented
3#22600535C211yesmaximal, characteristic, complemented
4#22600505C211yesmaximal, characteristic, complemented
5#22600430C211yesmaximal, characteristic, complemented
6#22600385C211yesmaximal, characteristic, complemented
7#22600310C211yesmaximal, characteristic, complemented
8#22600236C211yesmaximal, characteristic, complemented
9#22600221C211yesmaximal, characteristic, complemented
10#22600070C211yesmaximal, characteristic, complemented
11#22600058C211yesmaximal, characteristic, complemented
12#22600006C211yesmaximal, characteristic, complemented
13#22599982C211yesmaximal, characteristic, complemented
14#22599921C211yesmaximal, characteristic, complemented
15#22599891C211yesmaximal, characteristic, complemented
16#22599881C211yesmaximal, characteristic, complemented
17#22599866C211yesmaximal, characteristic, complemented
18#22599417C211yesmaximal, characteristic, complemented
19#22599395C211yesmaximal, characteristic, complemented
20#22599246C211yesmaximal, characteristic, complemented
21#22599237C211yesmaximal, characteristic, complemented
22#22599166C211yesmaximal, characteristic, complemented
23#22599117C211yesmaximal, characteristic, complemented
24#22598548C211yesmaximal, characteristic, complemented
25#22598533C211yesmaximal, characteristic, complemented
26#22597652C211yesmaximal, characteristic, complemented
27#22597652C211yesmaximal, characteristic, complemented
28#22597580C211yesmaximal, characteristic, complemented
29#22597556C211yesmaximal, characteristic, complemented
30#22597388C211yesmaximal, characteristic, complemented
31C71×#3539C211yesmaximal, characteristic, complemented
32C2×#14556175C2211yescharacteristic
33C22×#11765865C2211yescharacteristic
34C2×#14556158C2211yescharacteristic
35C2×#14556158C2211yescharacteristic, complemented
36C2×#14556158C2211yescharacteristic, complemented
37C2×#14556153C2211yescharacteristic
38C2×#14556148C2211yescharacteristic
39C2×#14556148C2211yescharacteristic
40C2×#14556148C2211yescharacteristic, complemented
41C2×#14556148C2211yescharacteristic, complemented
42D4×Dic142C2211yescharacteristic
43D4×Dic142C2211yescharacteristic
44#17986658C2211yescharacteristic
45#17986658C2211yescharacteristic
46#17986654C2211yescharacteristic
47#17986654C2211yescharacteristic
48#17986647—21no—
49#17986647—21no—
50#17986645C2211yescharacteristic
51#17986645C2211yescharacteristic
52#17986636—21no—
53#17986636—21no—
54#17986578—21no—
55#17986577C2211yescharacteristic
56#17986575C2211yescharacteristic
57#17986572—21no—
58#17986509—21no—
59C2×#14556107C2211yescharacteristic
60C22⋊Q8×D71—21no—
61#17986479C2211yescharacteristic
62#17986391C2211yescharacteristic, complemented
63#17986386C2211yescharacteristic, complemented
64#17986378C2211yescharacteristic, complemented
65#17986371C2211yescharacteristic, complemented
66#17986369C2211yescharacteristic, complemented
67#17986369C2211yescharacteristic, complemented
68#17986356C2211yescharacteristic, complemented
69#17986356C2211yescharacteristic, complemented
70#17986340C2211yescharacteristic
71#17986340C2211yescharacteristic
72#17986340C2211yescharacteristic, complemented
73#17986340C2211yescharacteristic, complemented
74#17986334C2211yescharacteristic, complemented
75#17986332C2211yescharacteristic, complemented
76#17986329C2211yescharacteristic, complemented
77#17986327C2211yescharacteristic, 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
87#17986255C2211yescharacteristic
88#17986255C2211yescharacteristic, complemented
89#17986250C2211yescharacteristic, complemented
90#17986247C2211yescharacteristic, complemented
91#17986243C2211yescharacteristic
92#17986243C2211yescharacteristic
93#17986243C2211yescharacteristic, complemented
94#17986238C2211yescharacteristic, complemented
95#17986238C2211yescharacteristic, complemented
96#17986238C2211yescharacteristic, complemented
97#17986233C2211yescharacteristic, complemented
98#17986230C2211yescharacteristic, complemented
99#17986226C2211yescharacteristic, complemented
100#17986226C2211yescharacteristic, complemented
101#17986226C2211yescharacteristic, complemented
102#17986221C2211yescharacteristic, complemented
103#17986221C2211yescharacteristic, complemented
104#17986214C2211yescharacteristic, complemented
105#17986214C2211yescharacteristic, complemented
106#17986209C2211yescharacteristic, complemented
107#17986209C2211yescharacteristic, complemented
108#17986206C2211yescharacteristic, complemented
109#17986204C2211yescharacteristic, complemented
110#17986204C2211yescharacteristic, complemented
111#17986201C2211yescharacteristic, complemented
112#17986196C2211yescharacteristic, complemented
113#17986191C2211yescharacteristic, complemented
114#17986161C2211yescharacteristic
115#17986161C2211yescharacteristic
116#17986161C2211yescharacteristic, complemented
117#17986161C2211yescharacteristic, complemented
118#17986161C2211yescharacteristic, complemented
119#17986161C2211yescharacteristic, complemented
120#17986159C2211yescharacteristic
121#17986159C2211yescharacteristic
122#17986159C2211yescharacteristic
123#17986159C2211yescharacteristic
124#17986159C2211yescharacteristic
125#17986159C2211yescharacteristic
126#17986159C2211yescharacteristic, complemented
127#17986159C2211yescharacteristic, complemented
128#17986154C2211yescharacteristic
129#17986154C2211yescharacteristic, complemented
130#17986154C2211yescharacteristic, complemented
131#17986154C2211yescharacteristic, complemented
132#17986154C2211yescharacteristic, complemented
133#17986149C2211yescharacteristic
134#17986144C2211yescharacteristic, complemented
135#17986144C2211yescharacteristic, complemented
136#17986142C2211yescharacteristic
137#17986142C2211yescharacteristic
138#17986142C2211yescharacteristic
139#17986142C2211yescharacteristic
140#17986142C2211yescharacteristic
141#17986142C2211yescharacteristic
142#17986142C2211yescharacteristic, complemented
143#17986142C2211yescharacteristic, complemented
144#17986137C2211yescharacteristic
145#17986137C2211yescharacteristic, complemented
146#17986137C2211yescharacteristic, complemented
147#17986137C2211yescharacteristic, complemented
148#17986137C2211yescharacteristic, complemented
149#17986132C2211yescharacteristic
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
159#17986077C2211yescharacteristic
160#17986071C2211yescharacteristic
161#17986071C2211yescharacteristic
162#17986071C2211yescharacteristic, complemented
163#17986071C2211yescharacteristic, complemented
164D4×C71⋊C8C2211yescharacteristic, complemented
165D4×C71⋊C8C2211yescharacteristic, complemented
166#17986060C2211yescharacteristic, complemented
167#17986060C2211yescharacteristic, complemented
168#17986007C2211yescharacteristic
169#17986003C2211yescharacteristic
170#17985998C2211yescharacteristic, complemented
171#17985998C2211yescharacteristic, complemented
172#17985993C2211yescharacteristic
173#17985993C2211yescharacteristic
174C2×#14556051C2211yescharacteristic, complemented
175C2×#14556051C2211yescharacteristic, complemented
176#17985966C2211yescharacteristic, complemented
177#17985966C2211yescharacteristic, complemented
178#17985963C2211yescharacteristic
179C2×C22⋊(C71⋊C8)C2211yescharacteristic
180#560×C71—21no—
181#560×C71—21no—
182#553×C71—21no—
183#553×C71—21no—
184#553×C71C2211yescharacteristic
185#553×C71C2211yescharacteristic, complemented
186#552×C71C2211yescharacteristic
187#552×C71C2211yescharacteristic, complemented
188#550×C71C2211yescharacteristic
189#550×C71C2211yescharacteristic, complemented
190#547×C71C2211yescharacteristic
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
202#525×C71C2211yescharacteristic
203#14556175—42no—
204#14556175—42no—
205C2×#11765865—21no—
206C2×#11765865—21no—
207C2×#11765865—42no—
208C2×#11765865—42no—
209C2×#11765865C2311yescharacteristic
210C2×#11765865C2311yescharacteristic
211C2×#11765865C2311yescharacteristic
212C2×#11765865C2311yescharacteristic
213C2×#11765865C2311yescharacteristic
214C2×#11765865C2311yescharacteristic
215C2×#11765864—21no—
216C2×#11765864—21no—
217C2×#11765864—21no—
218C22×Dic142C2311yescharacteristic
219C22×Dic142C2311yescharacteristic
220C22×Dic142C2311yescharacteristic
221C22×Dic142C2311yescharacteristic
222C2×Q8×D71—21no—
223C22×D284C2311yescharacteristic
224C22×C22⋊D71—21no—
225C22×C4×D71—21no—
226#14556158—42no—
227#14556158—42no—
228#14556158—42no—
229#14556153—42no—
230#14556148—42no—
231#14556148—42no—
232#14556148—42no—
233#14556148—42no—
234C2×#11765855C2311yescharacteristic
235C2×#11765855C2311yescharacteristic
236C2×#11765855C2311yescharacteristic
237C2×#11765855C2311yescharacteristic
238C2×#11765855C2311yescharacteristic
239C2×#11765855C2311yescharacteristic
240C2×#11765855C2311yescharacteristic
241C2×#11765855C2311yescharacteristic
242C2×#11765853C2311yescharacteristic
243C2×#11765853C2311yescharacteristic
244C2×#11765853C2311yescharacteristic
245C2×#11765853C2311yescharacteristic
246C2×#11765853C2311yescharacteristic
247C2×#11765853C2311yescharacteristic
248C2×#11765853C2311yescharacteristic
249C2×#11765853C2311yescharacteristic
250C2×#11765852C2311yescharacteristic
251C2×#11765852C2311yescharacteristic
252C2×#11765852C2311yescharacteristic
253C2×#11765852C2311yescharacteristic
254C2×#11765850C2311yescharacteristic
255C2×#11765850C2311yescharacteristic
256C2×#11765850C2311yescharacteristic
257C2×#11765850C2311yescharacteristic
258C2×#11765849C2311yescharacteristic
259C2×#11765849C2311yescharacteristic
260C2×#11765849C2311yescharacteristic
261C2×#11765849C2311yescharacteristic
262C22×C71⋊C8C2311yescharacteristic
263C22×C71⋊C8C2311yescharacteristic
264C22×C71⋊C8C2311yescharacteristic
265C22×C71⋊C8C2311yescharacteristic
266#14556128C2311yescharacteristic
267#14556128C2311yescharacteristic
268#14556127—21no—
269#14556127—21no—
270#14556116C2311yescharacteristic
271#14556116C2311yescharacteristic
272#14556114—21no—
273#14556114—21no—
274#14556113—21no—
275#14556113—21no—
276#14556112—21no—
277#14556112—21no—
278#14556110—21no—
279#14556110—21no—
280#14556110—21no—
281#14556110—21no—
282#14556108—21no—
283#14556108—21no—
284#14556107—21no—
285#14556107—21no—
286#14556107C2311yescharacteristic
287#14556107C2311yescharacteristic
288#14556107C2311yescharacteristic
289#14556107C2311yescharacteristic
290#14556107C2311yescharacteristic
291#14556107C2311yescharacteristic
292#14556106—21no—
293#14556106—21no—
294#14556105—21no—
295#14556105—21no—
296#14556105—21no—
297#14556105—21no—
298#14556104—21no—
299#14556102C2311yescharacteristic
300#14556102C2311yescharacteristic
301#14556101—21no—
302#14556101—21no—
303#14556100—21no—
304#14556100—21no—
305#14556100—21no—
306#14556100—21no—
307#14556099—21no—
308#14556099—21no—
309#14556099—21no—
310#14556096—21no—
311#14556096—21no—
312C4×Dic142C2311yescharacteristic
313C4×Dic142C2311yescharacteristic
314C4×D284C2311yescharacteristic
315C4×D284C2311yescharacteristic
316D4×Dic71—21no—
317D4×Dic71—21no—
318(C22⋊D71)⋊C4—21no—
319(C22⋊D71)⋊C4—21no—
320(C22⋊D71)⋊C4—21no—
321(C22⋊D71)⋊C4—21no—
322#14556086—21no—
323C2×C4⋊Dic71C2311yescharacteristic
324C2×Dic71⋊C4—21no—
325C4⋊C4×D71—21no—
326C4⋊C4×D71—21no—
327C4⋊C4×D71—21no—
328C2×C22⋊Dic71—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#14556051C2311yescharacteristic
356#14556051C2311yescharacteristic
357#14556051C2311yescharacteristic
358#14556051C2311yescharacteristic
359#14556051C2311yescharacteristic
360#14556051C2311yescharacteristic
361#14556051C2311yescharacteristic
362#14556051C2311yescharacteristic
363#14556049C2311yescharacteristic
364#14556049C2311yescharacteristic
365#14556049C2311yescharacteristic
366#14556049C2311yescharacteristic
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—
491#11765865—22no—
492#11765865—22no—
493#11765865—22no—
494#11765865—22no—
495#11765865—22no—
496#11765865—22no—
497#11765865—41no—
498#11765865—41no—
499#11765865—41no—
500#11765865—41no—
501#11765865—41no—
502#11765865—41no—
503#11765865—44no—
504#11765865—44no—
505#11765864—44no—
506#11765864—44no—
507#11765864—44no—
508C2×Dic142—22no—
509C2×Dic142—22no—
510C2×Dic142—22no—
511C2×Dic142—21no—
512C2×Dic142—21no—
513C2×Dic142—21no—
514C2×Dic142—21no—
515C2×Dic142—41no—
516C2×Dic142—41no—
517C2×Dic142—41no—
518C2×Dic142—41no—
519C2×Dic142—41no—
520C2×Dic142C2411yescharacteristic
521C2×Dic142C2411yescharacteristic
522C2×Dic142C2411yescharacteristic
523C2×Dic142C2411yescharacteristic
524Q8×D71—44no—
525C2×D284—22no—
526C2×D284—21no—
527C2×D284—41no—
528C2×D284C2411yescharacteristic
529C2×D284C2411yescharacteristic
530C2×C22⋊D71—21no—
531C2×C22⋊D71—21no—
532C2×C22⋊D71—21no—
533C2×C22⋊D71—21no—
534C2×C22⋊D71—21no—
535C2×C22⋊D71—21no—
536C2×C22⋊D71—21no—
537C2×C22⋊D71—21no—
538C2×C22⋊D71—44no—
539C22×Dic71—21no—
540C22×Dic71—21no—
541C22×Dic71—21no—
542C22×Dic71—21no—
543C22×Dic71—21no—
544C2×C4×D71—21no—
545C2×C4×D71—21no—
546C2×C4×D71—21no—
547C2×C4×D71—21no—
548C2×C4×D71—21no—
549C2×C4×D71—21no—
550C2×C4×D71—21no—
551C2×C4×D71—21no—
552C2×C4×D71—44no—
553#11765855—22no—
554#11765855—22no—
555#11765855—41no—
556#11765855—41no—
557#11765855—41no—
558#11765855—41no—
559#11765855—41no—
560#11765855—41no—
561#11765853—22no—
562#11765853—22no—
563#11765853—41no—
564#11765853—41no—
565#11765853—41no—
566#11765853—41no—
567#11765853—41no—
568#11765853—41no—
569#11765852—22no—
570#11765852—22no—
571#11765852—41no—
572#11765852—41no—
573#11765850—22no—
574#11765850—22no—
575#11765850—41no—
576#11765850—41no—
577#11765849—41no—
578#11765849—41no—
579#11765849—41no—
580#11765849—41no—
581C2×C71⋊C8—41no—
582C2×C71⋊C8—41no—
583C2×C71⋊C8—41no—
584C2×C71⋊C8—41no—
585C2×C71⋊C8C2411yescharacteristic
586C2×C71⋊C8C2411yescharacteristic
587C2×C71⋊C8C2411yescharacteristic
588C2×C71⋊C8C2411yescharacteristic
589C2×C71⋊C8C2411yescharacteristic
590C2×C71⋊C8C2411yescharacteristic
591C2×C71⋊C8C2411yescharacteristic
592C2×C71⋊C8C2411yescharacteristic
593C4⋊Dic71—21no—
594C4⋊Dic71—21no—
595C4⋊Dic71—21no—
596C4⋊Dic71—21no—
597C4⋊Dic71—21no—
598C4⋊Dic71C2411yescharacteristic
599C4⋊Dic71C2411yescharacteristic
600Dic71⋊C4—21no—
601Dic71⋊C4—21no—
602Dic71⋊C4—21no—
603Dic71⋊C4—21no—
604Dic71⋊C4—21no—
605Dic71⋊C4—21no—
606Dic71⋊C4—21no—
607Dic71⋊C4—21no—
608C22⋊Dic71—21no—
609C22⋊Dic71—21no—
610C22⋊Dic71—21no—
611C22⋊Dic71—21no—
612C22⋊Dic71—21no—
613C22⋊Dic71—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—
622C4×Dic71—21no—
623C4×Dic71—21no—
624C24×C71C2×D411yescharacteristic
625#41×C71—41no—
626#41×C71—41no—
627#41×C71—41no—
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—
635C2×Q8×C71C2×D411yescharacteristic
636C2×Q8×C71C2411yescharacteristic
637C2×Q8×C71C2411yescharacteristic
638C2×D4×C71—21no—
639C2×D4×C71—21no—
640C2×D4×C71—21no—
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×C71C2×D411yescharacteristic
651C2×D4×C71C2×D411yescharacteristic
652C2×D4×C71C2×D411yescharacteristic
653C2×D4×C71C2×D411yescharacteristic
654C2×D4×C71C2×D411yescharacteristic
655C2×D4×C71C2×D411yescharacteristic
656C2×D4×C71C2×D411yescharacteristic
657C2×D4×C71C2411yescharacteristic
658C2×D4×C71C2411yescharacteristic
659C22×C4×C71—21no—
660C22×C4×C71—21no—
661C22×C4×C71—21no—
662C22×C4×C71—21no—
663C22×C4×C71—21no—
664C22×C4×C71—21no—
665C22×C4×C71—21no—
666C22×C4×C71—21no—
667C22×C4×C71—41no—
668C22×C4×C71—41no—
669C22×C4×C71C2×D411yescharacteristic
670C22×C4×C71C2×D411yescharacteristic
671C22×C4×C71C2×D411yescharacteristic
672C22×C4×C71C2411yescharacteristic
673C22×C4×C71C2411yescharacteristic
674C22×C4×C71C2411yescharacteristic
675C22×C4×C71C2411yescharacteristic
676C22×C4×C71C2411yescharacteristic
677C4⋊C4×C71—21no—
678C4⋊C4×C71—21no—
679C4⋊C4×C71—21no—
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×C71C2×D411yescharacteristic
694C4⋊C4×C71C2×D411yescharacteristic
695C4⋊C4×C71C2×D411yescharacteristic
696C4⋊C4×C71C2×D411yescharacteristic
697C4⋊C4×C71C2×D411yescharacteristic
698C4⋊C4×C71C2×D411yescharacteristic
699C4⋊C4×C71C2411yescharacteristic
700C4⋊C4×C71C2411yescharacteristic
701C4⋊C4×C71C2411yescharacteristic
702C4⋊C4×C71C2411yescharacteristic
703C22⋊C4×C71—21no—
704C22⋊C4×C71—21no—
705C22⋊C4×C71—21no—
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×C71C2×D411yescharacteristic
720C22⋊C4×C71C2×D411yescharacteristic
721C22⋊C4×C71C2×D411yescharacteristic
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
729C42×C71—21no—
730C42×C71—21no—
731C42×C71—21no—
732C42×C71—21no—
733C42×C71C2411yescharacteristic
734C42×C71C2411yescharacteristic
735C23×C71—21no—
736C23×C71—21no—
737C23×C71—41no—
738C23×C71—41no—
739C23×C71—41no—
740C23×C71C22×D411yescharacteristic
741C23×C71C22×D411yescharacteristic
742C23×C71C22×D411yescharacteristic
743C23×C71C22×D411yescharacteristic
744C23×C71C22×D411yescharacteristic
745C22×D71—21no—
746C22×D71—21no—
747C22×D71—42no—
748C22×D71—42no—
749C22×D71—81no—
750Q8×C71—21no—
751Q8×C71—21no—
752Q8×C71—21no—
753Q8×C71—21no—
754Q8×C71—41no—
755D4×C71—21no—
756D4×C71—21no—
757D4×C71—21no—
758D4×C71—21no—
759D4×C71—41no—
760D4×C71—41no—
761D4×C71—41no—
762D4×C71—41no—
763D4×C71—41no—
764D4×C71—41no—
765D4×C71—41no—
766D4×C71—81no—
767D4×C71—81no—
768D4×C71—81no—
769D4×C71—81no—
770D4×C71—81no—
771D4×C71—81no—
772D4×C71—81no—
773D4×C71—81no—
774D4×C71—81no—
775D4×C71—81no—
776D4×C71—81no—
777D4×C71—81no—
778C2×C4×C71—21no—
779C2×C4×C71—21no—
780C2×C4×C71—21no—
781C2×C4×C71—21no—
782C2×C4×C71—21no—
783C2×C4×C71—21no—
784C2×C4×C71—21no—
785C2×C4×C71—21no—
786C2×C4×C71—21no—
787C2×C4×C71—21no—
788C2×C4×C71—21no—
789C2×C4×C71—21no—
790C2×C4×C71—21no—
791C2×C4×C71—21no—
792C2×C4×C71—21no—
793C2×C4×C71—21no—
794C2×C4×C71—41no—
795C2×C4×C71—41no—
796C2×C4×C71—41no—
797C2×C4×C71—81no—
798C2×C4×C71—81no—
799C2×C4×C71—81no—
800C2×C4×C71—81no—
801C2×C4×C71—81no—
802C2×C4×C71—81no—
803C2×C4×C71—81no—
804C2×C4×C71—81no—
805C2×C4×C71C22×D411yescharacteristic
806C2×C4×C71C22×D411yescharacteristic
807C2×C4×C71C22×D411yescharacteristic
808C2×C4×C71C22×D411yescharacteristic
809C2×C4×C71C22×D411yescharacteristic
810C2×C4×C71C22×D411yescharacteristic
811C2×C4×C71C22×D411yescharacteristic
812C2×C4×C71C22×D411yescharacteristic
813C2×C4×C71C22×D411yescharacteristic
814C2×C4×C71C2511yescharacteristic
815C22⋊D71—24no—
816C22⋊D71—42no—
817C22⋊D71—42no—
818C22⋊D71—42no—
819C22⋊D71—42no—
820C22⋊D71—42no—
821C22⋊D71—81no—
822C22⋊D71—81no—
823C2×Dic71—21no—
824C2×Dic71—21no—
825C2×Dic71—21no—
826C2×Dic71—21no—
827C2×Dic71—21no—
828C2×Dic71—21no—
829C2×Dic71—42no—
830C2×Dic71—42no—
831C2×Dic71—42no—
832C2×Dic71—42no—
833C2×Dic71—81no—
834D284—21no—
835D284—21no—
836D284—21no—
837D284—42no—
838D284H(5,𝔽2)12yes—
839C4×D71—24no—
840C4×D71—42no—
841C4×D71—42no—
842C4×D71—42no—
843C4×D71—42no—
844C4×D71—42no—
845C4×D71—81no—
846C4×D71—81no—
847Dic142—21no—
848Dic142—21no—
849Dic142—21no—
850Dic142—21no—
851Dic142—21no—
852Dic142—21no—
853Dic142—21no—
854Dic142—42no—
855Dic142—42no—
856Dic142—42no—
857Dic142—42no—
858Dic142H(5,𝔽2)12yes—
859C71⋊C8—21no—
860C71⋊C8—21no—
861C71⋊C8—21no—
862C71⋊C8—21no—
863C71⋊C8—21no—
864C71⋊C8—21no—
865C71⋊C8—21no—
866C71⋊C8—21no—
867C22×C71—21no—
868C22×C71—21no—
869C22×C71—21no—
870C22×C71—21no—
871C22×C71—21no—
872C22×C71—21no—
873C22×C71—21no—
874C22×C71—21no—
875C22×C71—21no—
876C22×C71—21no—
877C22×C71—21no—
878C22×C71—21no—
879C22×C71—21no—
880C22×C71—21no—
881C22×C71—21no—
882C22×C71—41no—
883C22×C71—41no—
884C22×C71—41no—
885C22×C71—41no—
886C22×C71—41no—
887C22×C71—41no—
888C22×C71—82no—
889C22×C71C23×D411yescharacteristic
890C2×D71—22no—
891C2×D71—41no—
892C2×D71—41no—
893C2×D71—41no—
894C2×D71—41no—
895C2×D71—41no—
896C2×D71—84no—
897C4×C71—21no—
898C4×C71—21no—
899C4×C71—21no—
900C4×C71—21no—
901C4×C71—21no—
902C4×C71—21no—
903C4×C71—21no—
904C4×C71—21no—
905C4×C71—21no—
906C4×C71—41no—
907C4×C71—41no—
908C4×C71—41no—
909C4×C71—41no—
910C4×C71—41no—
911C4×C71—41no—
912C4×C71C2×H(5,𝔽2)11yescharacteristic
913C4×C71C2×H(5,𝔽2)11yescharacteristic
914Dic71—22no—
915Dic71—41no—
916Dic71—41no—
917Dic71—41no—
918Dic71—41no—
919Dic71—41no—
920#61626—711nomaximal, Sylow
921C2×C71—41no—
922C2×C71—41no—
923C2×C71—41no—
924C2×C71—41no—
925C2×C71—41no—
926C2×C71—81no—
927C2×C71—81no—
928C2×C71#348411yescharacteristic
929C2×C71#358411yescharacteristic
930C2×C71#358611yescharacteristic
931D71—42no—
932D71—81no—
933#3539D7111yescharacteristic, complemented
934#3489—711no—
935#3323—711no—
936#3322—711no—
937#3320—711no—
938#3315—711no—
939#3312—711no—
940#3307—711no—
941#3301—711no—
942#3300—711no—
943#3284—711no—
944#3283—711no—
945#3278—711no—
946#3276—711no—
947#3271—711no—
948#3269—711no—
949#3268—711no—
950#3267—711no—
951#3223—711no—
952#3221—711no—
953#3204—711no—
954#3203—711no—
955#3196—711no—
956#3190—711no—
957#3120—711no—
958#3119—711no—
959#3013—711no—
960#3013—711no—
961#3005—711no—
962#3002—711no—
963#2976—711no—
964C71#6162611yescharacteristic, complemented, Sylow
965C2×2−1+4—711no—
966C22×#41—711no—
967C2×#137—711no—
968C2×#137—711no—
969C2×#137—711no—
970C2×AGL(1,ℤ/8)—711no—
971C2×#135—711no—
972C2×#135—711no—
973C2×#135—711no—
974C2×#135—711no—
975#560—21no—
976#560—21no—
977#553—21no—
978#553—21no—
979#553C2×D7111yescharacteristic
980#553C2×D7111yescharacteristic, complemented
981#552C2×D7111yescharacteristic
982#552C2×D7111yescharacteristic, complemented
983#550C2×D7111yescharacteristic
984#550C2×D7111yescharacteristic, complemented
985D4×Q8—711no—
986D4×Q8—711no—
987#548—711no—
988#548—711no—
989#547—711no—
990#547—711no—
991#547—1421no—
992#547—1421no—
993#547C2×D7111yescharacteristic
994#547C2×D7111yescharacteristic, complemented
995#546—711no—
996#546—711no—
997#546—1421no—
998#546—1421no—
999#541C2×D7111yescharacteristic, complemented
1000#540—21no—
1001#540—21no—
1002#540C2×D7111yescharacteristic, complemented
1003#539—21no—
1004#539—21no—
1005#537—711no—
1006#537—1421no—
1007#537C2×D7111yescharacteristic, complemented
1008#537C2×D7111yescharacteristic, complemented
1009#536—711no—
1010#536—1421no—
1011#525—1421no—
1012#525C2×D7111yescharacteristic
1013#525C2×D7111yescharacteristic
1014#525C2×D7111yescharacteristic
1015C2×C22⋊Q8—711no—
1016C2×C22⋊Q8—1421no—
1017#520—711no—
1018#497—711no—
1019#496—711no—
1020#494—711no—
1021#492—711no—
1022#491—711no—
1023#491—711no—
1024#488—711no—
1025#488—711no—
1026#485—711no—
1027#485—711no—
1028#485—711no—
1029#485—711no—
1030#484—711no—
1031#484—711no—
1032#483—711no—
1033#483—711no—
1034#481—711no—
1035#481—711no—
1036#480—711no—
1037#480—711no—
1038#479—711no—
1039#479—711no—
1040#478—711no—
1041#478—711no—
1042#470—711no—
1043#470—711no—
1044#470—711no—
1045#469—711no—
1046#468—711no—
1047#468—711no—
1048#468—711no—
1049#468—711no—
1050#467—711no—
1051#467—711no—
1052#467—711no—
1053#466—711no—
1054#465—711no—
1055#465—711no—
1056#465—711no—
1057#465—711no—
1058#464—711no—
1059#464—711no—
1060#463—711no—
1061#463—711no—
1062#462—711no—
1063#462—711no—
1064#462—711no—
1065#461—711no—
1066#461—711no—
1067#461—711no—
1068#460—711no—
1069#459—711no—
1070#452—711no—
1071#452—711no—
1072#452—711no—
1073#452—711no—
1074#452—711no—
1075#452—711no—
1076#452—711no—
1077#452—711no—
1078#452—711no—
1079#452—711no—
1080#452—711no—
1081#452—711no—
1082#452—711no—
1083#452—711no—
1084#451—711no—
1085#451—711no—
1086#451—711no—
1087#451—711no—
1088#451—711no—
1089#450—711no—
1090#449—711no—
1091#449—711no—
1092#449—711no—
1093#449—711no—
1094#449—711no—
1095#449—711no—
1096#449—711no—
1097#449—711no—
1098#449—711no—
1099#449—711no—
1100#448—711no—
1101#448—711no—
1102#448—711no—
1103#448—711no—
1104#448—711no—
1105#447—711no—
1106#442—711no—
1107#441—711no—
1108#440—711no—
1109#440—711no—
1110C4×Q16—711no—
1111C4×SD16—711no—
1112C4×SD16—711no—
1113C4×D8—711no—
1114#436—711no—
1115#436—711no—
1116#435—711no—
1117#435—711no—
1118#435—711no—
1119#435—711no—
1120C8×D4—711no—
1121C8×D4—711no—
1122#433—711no—
1123#433—711no—
1124#419—711no—
1125#418—711no—
1126#417—711no—
1127#417—711no—
1128#416—711no—
1129#416—711no—
1130C2×#103—711no—
1131C2×#103—711no—
1132#408—711no—
1133#408—711no—
1134#407—711no—
1135C2×C22⋊C8—711no—
11362−1+4—2842no—
11372−1+4—2842no—
1138C2×#41—2842no—
1139C2×#41—2842no—
1140C2×#41—711no—
1141C2×#41—711no—
1142C2×#41—711no—
1143C2×#41—711no—
1144C2×#41—711no—
1145C2×#41—711no—
1146C2×#41—1421no—
1147C2×#41—1421no—
1148C2×#41—1421no—
1149C2×#41—1421no—
1150C2×#41—1421no—
1151C2×#41C22×D7111yescharacteristic
1152C2×#41C22×D7111yescharacteristic
1153C2×#41C22×D7111yescharacteristic
1154C2×#41C22×D7111yescharacteristic
1155C2×#41C22×D7111yescharacteristic
1156C22×Q8—711no—
1157C22×Q8—711no—
1158C22×Q8—711no—
1159C22×Q8—711no—
1160C22×Q8—1421no—
1161C22×D4—711no—
1162C22×D4—1421no—
1163C23×C4—1421no—
1164C23×C4C22×D7111yescharacteristic
1165#137—2842no—
1166#137—2842no—
1167#137—2842no—
1168AGL(1,ℤ/8)—2842no—
1169#135—2842no—
1170#135—2842no—
1171#135—2842no—
1172#135—2842no—
1173C2×Q16—711no—
1174C2×Q16—711no—
1175C2×Q16—711no—
1176C2×Q16—711no—
1177C2×Q16—711no—
1178C2×Q16—711no—
1179C2×Q16—711no—
1180C2×Q16—711no—
1181C2×SD16—711no—
1182C2×SD16—711no—
1183C2×SD16—711no—
1184C2×SD16—711no—
1185C2×SD16—711no—
1186C2×SD16—711no—
1187C2×SD16—711no—
1188C2×SD16—711no—
1189C2×SD16—711no—
1190C2×SD16—711no—
1191C2×SD16—711no—
1192C2×SD16—711no—
1193C2×D8—711no—
1194C2×D8—711no—
1195C2×D8—711no—
1196C2×D8—711no—
1197C2×M16—711no—
1198C2×M16—711no—
1199C2×M16—711no—
1200C2×M16—711no—
1201C22×C8—711no—
1202C22×C8—711no—
1203C22×C8—711no—
1204C22×C8—711no—
1205C4⋊Q8—711no—
1206C4⋊Q8—711no—
1207C4⋊Q8—1421no—
1208C4⋊Q8—1421no—
1209C4⋊Q8C22×D7111yescharacteristic
1210#127—21no—
1211#127—21no—
1212#127C22×D7111yescharacteristic
1213#126—21no—
1214#126—21no—
1215#126—21no—
1216#126—21no—
1217#126—21no—
1218#126—21no—
1219#125—21no—
1220#125—21no—
1221#125—21no—
1222#125—21no—
1223#125C22×D7111yescharacteristic
1224#125C22×D7111yescharacteristic
1225#124—711no—
1226#124—711no—
1227#124—1421no—
1228#124—1421no—
1229#123—21no—
1230#123—21no—
1231#123—21no—
1232#123—21no—
1233#123—21no—
1234#123—21no—
1235#123—21no—
1236#123—21no—
1237#123—21no—
1238#123—21no—
1239#123—21no—
1240#123—21no—
1241#123—1421no—
1242#123—1421no—
1243#123—1421no—
1244#123—1421no—
1245#123—1421no—
1246#123—1421no—
1247#123—1421no—
1248#123—1421no—
1249#123C22⋊D7111yescharacteristic
1250#123C22⋊D7111yescharacteristic
1251C22⋊Q8—21no—
1252C22⋊Q8—21no—
1253C22⋊Q8—711no—
1254C22⋊Q8—711no—
1255C22⋊Q8—711no—
1256C22⋊Q8—711no—
1257C22⋊Q8—711no—
1258C22⋊Q8—711no—
1259C22⋊Q8—1421no—
1260C22⋊Q8—1421no—
1261C22⋊Q8—1421no—
1262C22⋊Q8—1421no—
1263C22⋊Q8—1421no—
1264C22⋊Q8—1421no—
1265C22⋊Q8—1421no—
1266C22⋊Q8—1421no—
1267C22⋊Q8—1421no—
1268C22⋊Q8—1421no—
1269C22⋊Q8—1421no—
1270C22⋊Q8C22⋊D7111yescharacteristic
1271C22⋊Q8C22⋊D7111yescharacteristic
1272C22⋊Q8C22×D7111yescharacteristic
1273C22⋊Q8C22×D7111yescharacteristic
1274C22⋊Q8C22×D7111yescharacteristic
1275C22⋊Q8C22×D7111yescharacteristic
1276C22⋊Q8C22×D7111yescharacteristic
1277C22⋊Q8C22×D7111yescharacteristic
1278#121—21no—
1279#121—21no—
1280#121—21no—
1281#121—21no—
1282#121—21no—
1283#121—21no—
1284#121—21no—
1285#121—21no—
1286#121—21no—
1287#121—21no—
1288#121—21no—
1289#121—21no—
1290#121—21no—
1291#121—21no—
1292#121—21no—
1293#121—21no—
1294#121—711no—
1295#121—711no—
1296#121—1421no—
1297#121—1421no—
1298#121—1421no—
1299#121—1421no—
1300#121—1421no—
1301#121—1421no—
1302#121—1421no—
1303#121—1421no—
1304#121—1421no—
1305#121C22⋊D7111yescharacteristic
1306#121C22⋊D7111yescharacteristic
1307#121C22×D7111yescharacteristic
1308#121C22×D7111yescharacteristic
1309#121C22×D7111yescharacteristic
1310#121C22×D7111yescharacteristic
1311#121C22×D7111yescharacteristic
1312#121C22×D7111yescharacteristic
1313#120—21no—
1314#120—21no—
1315#120—1421no—
1316#120—1421no—
1317#120C22⋊D7111yescharacteristic
1318#120C22⋊D7111yescharacteristic
1319C4×Q8—711no—
1320C4×Q8—711no—
1321C4×Q8C22×D7111yescharacteristic
1322C4×Q8C22×D7111yescharacteristic
1323C4×D4—21no—
1324C4×D4—21no—
1325C4×D4—21no—
1326C4×D4—21no—
1327C4×D4—21no—
1328C4×D4—21no—
1329C4×D4—21no—
1330C4×D4—21no—
1331C4×D4—711no—
1332C4×D4—711no—
1333C4×D4—1421no—
1334C4×D4—1421no—
1335C4×D4—1421no—
1336C4×D4—1421no—
1337C4×D4—1421no—
1338C4×D4—1421no—
1339C4×D4C22×D7111yescharacteristic
1340C4×D4C22×D7111yescharacteristic
1341C4×D4C22×D7111yescharacteristic
1342C4×D4C22×D7111yescharacteristic
1343C4×D4C22×D7111yescharacteristic
1344C4×D4C22×D7111yescharacteristic
1345#117—21no—
1346#117—21no—
1347#117—1421no—
1348#117C22×D7111yescharacteristic
1349#117C22×D7111yescharacteristic
1350#117C22×D7111yescharacteristic
1351C2×C4⋊C4—21no—
1352C2×C4⋊C4—21no—
1353C2×C4⋊C4—711no—
1354C2×C4⋊C4—1421no—
1355C2×C4⋊C4—1421no—
1356C2×C4⋊C4—1421no—
1357C2×C4⋊C4—1421no—
1358C2×C4⋊C4C22×D7111yescharacteristic
1359C2×C4⋊C4C22×D7111yescharacteristic
1360C2×C22⋊C4—1421no—
1361C2×C22⋊C4—1421no—
1362C2×C22⋊C4—1421no—
1363#107—711no—
1364#107—711no—
1365#107—711no—
1366#107—711no—
1367#106—711no—
1368#106—711no—
1369#106—711no—
1370#106—711no—
1371C4⋊C8—711no—
1372C4⋊C8—711no—
1373C4⋊C8—711no—
1374C4⋊C8—711no—
1375#103—711no—
1376#103—711no—
1377#103—711no—
1378#103—711no—
1379#103—711no—
1380#103—711no—
1381#103—711no—
1382#103—711no—
1383#103—711no—
1384#103—711no—
1385#103—711no—
1386#103—711no—
1387#103—711no—
1388#103—711no—
1389#103—711no—
1390#103—711no—
1391#103—711no—
1392#103—711no—
1393#103—711no—
1394#103—711no—
1395#102—711no—
1396#102—711no—
1397#102—711no—
1398#102—711no—
1399#102—711no—
1400#102—711no—
1401#102—711no—
1402#102—711no—
1403#102—711no—
1404#102—711no—
1405#102—711no—
1406#102—711no—
1407C22⋊C8—711no—
1408C22⋊C8—711no—
1409C22⋊C8—711no—
1410C22⋊C8—711no—
1411C22⋊C8—711no—
1412C22⋊C8—711no—
1413C22⋊C8—711no—
1414C22⋊C8—711no—
1415C22⋊C8—711no—
1416C22⋊C8—711no—
1417C22⋊C8—711no—
1418C22⋊C8—711no—
1419#97—711no—
1420#97—711no—
1421C4×C8—711no—
1422C4×C8—711no—
1423C24—1421no—
1424C24C2×C22⋊D7111yescharacteristic
1425#41—41no—
1426#41—41no—
1427#41—41no—
1428#41—41no—
1429#41—41no—
1430#41—41no—
1431#41—41no—
1432#41—41no—
1433#41—41no—
1434#41—41no—
1435#41—2841no—
1436#41—2841no—
1437#41—2841no—
1438#41—2841no—
1439#41—2841no—
1440#41—2841no—
1441#41—2844no—
1442#41—2844no—
1443#41—2844no—
1444#41—2844no—
1445#41—2844no—
1446#41—1422no—
1447#41—1422no—
1448#41—1422no—
1449#41—1422no—
1450#41—1422no—
1451#41—1422no—
1452C2×Q8—2841no—
1453C2×Q8—2841no—
1454C2×Q8—2841no—
1455C2×Q8—2841no—
1456C2×Q8—2841no—
1457C2×Q8—2844no—
1458C2×Q8—711no—
1459C2×Q8—711no—
1460C2×Q8—711no—
1461C2×Q8—711no—
1462C2×Q8—1422no—
1463C2×Q8—1422no—
1464C2×Q8—1422no—
1465C2×Q8—1421no—
1466C2×Q8—1421no—
1467C2×Q8—1421no—
1468C2×Q8—1421no—
1469C2×Q8C2×C22⋊D7111yescharacteristic
1470C2×Q8C23×D7111yescharacteristic
1471C2×Q8C23×D7111yescharacteristic
1472C2×D4—21no—
1473C2×D4—21no—
1474C2×D4—21no—
1475C2×D4—21no—
1476C2×D4—21no—
1477C2×D4—21no—
1478C2×D4—21no—
1479C2×D4—21no—
1480C2×D4—21no—
1481C2×D4—21no—
1482C2×D4—21no—
1483C2×D4—21no—
1484C2×D4—2841no—
1485C2×D4—2844no—
1486C2×D4—711no—
1487C2×D4—711no—
1488C2×D4—1422no—
1489C2×D4—1421no—
1490C2×D4—1421no—
1491C2×D4—1421no—
1492C2×D4—1421no—
1493C2×D4—1421no—
1494C2×D4—1421no—
1495C2×D4—1421no—
1496C2×D4—1421no—
1497C2×D4—1421no—
1498C2×D4C2×C22⋊D7111yescharacteristic
1499C2×D4C2×C22⋊D7111yescharacteristic
1500C2×D4C2×C22⋊D7111yescharacteristic
1501C2×D4C2×C22⋊D7111yescharacteristic
1502C2×D4C2×C22⋊D7111yescharacteristic
1503C2×D4C2×C22⋊D7111yescharacteristic
1504C2×D4C2×C22⋊D7111yescharacteristic
1505C2×D4C23×D7111yescharacteristic
1506C2×D4C23×D7111yescharacteristic
1507C22×C4—21no—
1508C22×C4—21no—
1509C22×C4—21no—
1510C22×C4—21no—
1511C22×C4—21no—
1512C22×C4—21no—
1513C22×C4—21no—
1514C22×C4—21no—
1515C22×C4—41no—
1516C22×C4—41no—
1517C22×C4—2844no—
1518C22×C4—1421no—
1519C22×C4—1421no—
1520C22×C4—1421no—
1521C22×C4—1421no—
1522C22×C4—1421no—
1523C22×C4—1421no—
1524C22×C4—1421no—
1525C22×C4—1421no—
1526C22×C4—1421no—
1527C22×C4—1421no—
1528C22×C4—1421no—
1529C22×C4—1421no—
1530C22×C4—1421no—
1531C22×C4C2×C22⋊D7111yescharacteristic
1532C22×C4C2×C22⋊D7111yescharacteristic
1533C22×C4C2×C22⋊D7111yescharacteristic
1534C22×C4C23×D7111yescharacteristic
1535C22×C4C23×D7111yescharacteristic
1536C22×C4C23×D7111yescharacteristic
1537C22×C4C23×D7111yescharacteristic
1538C22×C4C23×D7111yescharacteristic
1539Q16—2841no—
1540Q16—2841no—
1541Q16—2841no—
1542Q16—2841no—
1543Q16—2841no—
1544Q16—2841no—
1545Q16—1422no—
1546Q16—1422no—
1547SD16—2841no—
1548SD16—2841no—
1549SD16—2841no—
1550SD16—2841no—
1551SD16—2841no—
1552SD16—2841no—
1553SD16—2841no—
1554SD16—2841no—
1555SD16—1422no—
1556SD16—1422no—
1557SD16—1422no—
1558SD16—1422no—
1559D8—2841no—
1560D8—2841no—
1561D8—1422no—
1562D8—1422no—
1563M16—2841no—
1564M16—2841no—
1565M16—2841no—
1566M16—2841no—
1567C2×C8—2841no—
1568C2×C8—2841no—
1569C2×C8—2841no—
1570C2×C8—2841no—
1571C2×C8—711no—
1572C2×C8—711no—
1573C2×C8—711no—
1574C2×C8—711no—
1575C2×C8—711no—
1576C2×C8—711no—
1577C2×C8—711no—
1578C2×C8—711no—
1579C4⋊C4—21no—
1580C4⋊C4—21no—
1581C4⋊C4—21no—
1582C4⋊C4—21no—
1583C4⋊C4—21no—
1584C4⋊C4—21no—
1585C4⋊C4—21no—
1586C4⋊C4—21no—
1587C4⋊C4—21no—
1588C4⋊C4—21no—
1589C4⋊C4—21no—
1590C4⋊C4—21no—
1591C4⋊C4—21no—
1592C4⋊C4—21no—
1593C4⋊C4—21no—
1594C4⋊C4—21no—
1595C4⋊C4—711no—
1596C4⋊C4—711no—
1597C4⋊C4—1421no—
1598C4⋊C4—1421no—
1599C4⋊C4—1421no—
1600C4⋊C4—1421no—
1601C4⋊C4—1421no—
1602C4⋊C4—1421no—
1603C4⋊C4—1421no—
1604C4⋊C4—1421no—
1605C4⋊C4—1421no—
1606C4⋊C4—1421no—
1607C4⋊C4—1421no—
1608C4⋊C4—1421no—
1609C4⋊C4—1421no—
1610C4⋊C4C2×C22⋊D7111yescharacteristic
1611C4⋊C4C2×C22⋊D7111yescharacteristic
1612C4⋊C4C2×C22⋊D7111yescharacteristic
1613C4⋊C4C2×C22⋊D7111yescharacteristic
1614C4⋊C4C2×C22⋊D7111yescharacteristic
1615C4⋊C4C2×C22⋊D7111yescharacteristic
1616C4⋊C4C23×D7111yescharacteristic
1617C4⋊C4C23×D7111yescharacteristic
1618C4⋊C4C23×D7111yescharacteristic
1619C4⋊C4C23×D7111yescharacteristic
1620C22⋊C4—21no—
1621C22⋊C4—21no—
1622C22⋊C4—21no—
1623C22⋊C4—21no—
1624C22⋊C4—21no—
1625C22⋊C4—21no—
1626C22⋊C4—21no—
1627C22⋊C4—21no—
1628C22⋊C4—21no—
1629C22⋊C4—21no—
1630C22⋊C4—21no—
1631C22⋊C4—21no—
1632C22⋊C4—21no—
1633C22⋊C4—21no—
1634C22⋊C4—21no—
1635C22⋊C4—21no—
1636C22⋊C4—1421no—
1637C22⋊C4—1421no—
1638C22⋊C4—1421no—
1639C22⋊C4—1421no—
1640C22⋊C4—1421no—
1641C22⋊C4—1421no—
1642C22⋊C4—1421no—
1643C22⋊C4—1421no—
1644C22⋊C4—1421no—
1645C22⋊C4—1421no—
1646C22⋊C4—1421no—
1647C22⋊C4—1421no—
1648C22⋊C4—1421no—
1649C22⋊C4—1421no—
1650C22⋊C4C2×C22⋊D7111yescharacteristic
1651C22⋊C4C2×C22⋊D7111yescharacteristic
1652C22⋊C4C2×C22⋊D7111yescharacteristic
1653C22⋊C4C2×C22⋊D7111yescharacteristic
1654C22⋊C4C2×C22⋊D7111yescharacteristic
1655C22⋊C4C2×C22⋊D7111yescharacteristic
1656C22⋊C4C2×C22⋊D7111yescharacteristic
1657C22⋊C4C2×C22⋊D7111yescharacteristic
1658C22⋊C4C2×C22⋊D7111yescharacteristic
1659C22⋊C4C2×C22⋊D7111yescharacteristic
1660C42—21no—
1661C42—21no—
1662C42—21no—
1663C42—21no—
1664C42—1421no—
1665C42—1421no—
1666C42C23×D7111yescharacteristic
1667C42C23×D7111yescharacteristic
1668C23—21no—
1669C23—21no—
1670C23—41no—
1671C23—41no—
1672C23—41no—
1673C23—2842no—
1674C23—2842no—
1675C23—5681no—
1676C23—1421no—
1677C23—1421no—
1678C23C22×C22⋊D7111yescharacteristic
1679C23C22×C22⋊D7111yescharacteristic
1680C23C22×C22⋊D7111yescharacteristic
1681C23C22×C22⋊D7111yescharacteristic
1682C23C22×C22⋊D7111yescharacteristic
1683Q8—21no—
1684Q8—21no—
1685Q8—21no—
1686Q8—21no—
1687Q8—41no—
1688Q8—2842no—
1689Q8—2842no—
1690Q8—2842no—
1691Q8—2842no—
1692Q8—712no—
1693Q8—1421no—
1694Q8—1421no—
1695Q8—1421no—
1696Q8—1421no—
1697Q8—1421no—
1698Q8—1421no—
1699Q8—1421no—
1700D4—21no—
1701D4—21no—
1702D4—21no—
1703D4—21no—
1704D4—41no—
1705D4—41no—
1706D4—41no—
1707D4—41no—
1708D4—41no—
1709D4—41no—
1710D4—41no—
1711D4—81no—
1712D4—81no—
1713D4—81no—
1714D4—81no—
1715D4—81no—
1716D4—81no—
1717D4—81no—
1718D4—81no—
1719D4—81no—
1720D4—81no—
1721D4—81no—
1722D4—81no—
1723D4—2842no—
1724D4—2842no—
1725D4—2842no—
1726D4—2842no—
1727D4—2842no—
1728D4—2842no—
1729D4—5681no—
1730D4—5681no—
1731D4—712no—
1732D4—1424no—
1733D4—1421no—
1734D4—1421no—
1735D4—1421no—
1736C2×C4—21no—
1737C2×C4—21no—
1738C2×C4—21no—
1739C2×C4—21no—
1740C2×C4—21no—
1741C2×C4—21no—
1742C2×C4—21no—
1743C2×C4—21no—
1744C2×C4—21no—
1745C2×C4—21no—
1746C2×C4—21no—
1747C2×C4—21no—
1748C2×C4—21no—
1749C2×C4—21no—
1750C2×C4—21no—
1751C2×C4—21no—
1752C2×C4—41no—
1753C2×C4—41no—
1754C2×C4—41no—
1755C2×C4—81no—
1756C2×C4—81no—
1757C2×C4—81no—
1758C2×C4—81no—
1759C2×C4—81no—
1760C2×C4—81no—
1761C2×C4—81no—
1762C2×C4—81no—
1763C2×C4—2842no—
1764C2×C4—2842no—
1765C2×C4—2842no—
1766C2×C4—2842no—
1767C2×C4—2842no—
1768C2×C4—2842no—
1769C2×C4—2842no—
1770C2×C4—2842no—
1771C2×C4—2842no—
1772C2×C4—5681no—
1773C2×C4—5681no—
1774C2×C4—5681no—
1775C2×C4—1424no—
1776C2×C4—1421no—
1777C2×C4—1421no—
1778C2×C4—1421no—
1779C2×C4—1421no—
1780C2×C4—1421no—
1781C2×C4—1421no—
1782C2×C4C22×C22⋊D7111yescharacteristic
1783C2×C4C22×C22⋊D7111yescharacteristic
1784C2×C4C22×C22⋊D7111yescharacteristic
1785C2×C4C22×C22⋊D7111yescharacteristic
1786C2×C4C22×C22⋊D7111yescharacteristic
1787C2×C4C22×C22⋊D7111yescharacteristic
1788C2×C4C22×C22⋊D7111yescharacteristic
1789C2×C4C22×C22⋊D7111yescharacteristic
1790C2×C4C22×C22⋊D7111yescharacteristic
1791C2×C4C24×D7111yescharacteristic
1792C8—1421no—
1793C8—1421no—
1794C8—1421no—
1795C8—1421no—
1796C8—1421no—
1797C8—1421no—
1798C8—1421no—
1799C8—1421no—
1800C22—21no—
1801C22—21no—
1802C22—21no—
1803C22—21no—
1804C22—21no—
1805C22—21no—
1806C22—21no—
1807C22—21no—
1808C22—21no—
1809C22—21no—
1810C22—21no—
1811C22—21no—
1812C22—21no—
1813C22—21no—
1814C22—21no—
1815C22—41no—
1816C22—41no—
1817C22—41no—
1818C22—41no—
1819C22—41no—
1820C22—41no—
1821C22—82no—
1822C22—2841no—
1823C22—2841no—
1824C22—2841no—
1825C22—2841no—
1826C22—2841no—
1827C22—5684no—
1828C22—1422no—
1829C22C23×C22⋊D7111yescharacteristic
1830C4—21no—
1831C4—21no—
1832C4—21no—
1833C4—21no—
1834C4—21no—
1835C4—21no—
1836C4—21no—
1837C4—21no—
1838C4—21no—
1839C4—41no—
1840C4—41no—
1841C4—41no—
1842C4—41no—
1843C4—41no—
1844C4—41no—
1845C4—2841no—
1846C4—2841no—
1847C4—2841no—
1848C4—2841no—
1849C4—2841no—
1850C4—1422no—
1851C4H(5,𝔽2)×D7111yescharacteristic
1852C4H(5,𝔽2)×D7111yescharacteristic
1853C2—41no—
1854C2—41no—
1855C2—41no—
1856C2—41no—
1857C2—41no—
1858C2—81no—
1859C2—81no—
1860C2—2842no—
1861C2—5681no—
1862C2#2260197111yescharacteristic
1863C2#2260311111yescharacteristic
1864C2#2260312611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC71×#3539C2
socleC22×C71C23×D4
hypercenter#3539D71
hypocenterC71#61626
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. #22602012C2semidirect
2. #22600550C2semidirect
3. #22600535C2semidirect
4. #22600505C2semidirect
5. #22600430C2semidirect
6. #22600385C2semidirect
7. #22600310C2semidirect
8. #22600236C2semidirect
9. #22600221C2semidirect
10. #22600070C2semidirect
11. #22600058C2semidirect
12. #22600006C2semidirect
13. #22599982C2semidirect
14. #22599921C2semidirect
15. #22599891C2semidirect
16. #22599881C2semidirect
17. #22599866C2semidirect
18. #22599417C2semidirect
19. #22599395C2semidirect
20. #22599246C2semidirect
21. #22599237C2semidirect
22. #22599166C2semidirect
23. #22599117C2semidirect
24. #22598548C2semidirect
25. #22598533C2semidirect
26. #22597652C2semidirect
27. #22597652C2semidirect
28. #22597580C2semidirect
29. #22597556C2semidirect
30. #22597388C2semidirect
31. C71×#3539C2semidirect
35. C2×#14556158C22semidirect
36. C2×#14556158C22semidirect
40. C2×#14556148C22semidirect
41. C2×#14556148C22semidirect
62. #17986391C22semidirect
63. #17986386C22semidirect
64. #17986378C22semidirect
65. #17986371C22semidirect
66. #17986369C22semidirect
67. #17986369C22semidirect
68. #17986356C22semidirect
69. #17986356C22semidirect
72. #17986340C22semidirect
73. #17986340C22semidirect
74. #17986334C22semidirect
75. #17986332C22semidirect
76. #17986329C22semidirect
77. #17986327C22semidirect
78. #17986317C22semidirect
79. #17986315C22semidirect
80. #17986312C22semidirect
81. #17986310C22semidirect
82. #17986303C22semidirect
83. #17986303C22semidirect
84. #17986296C22semidirect
85. #17986296C22semidirect
88. #17986255C22semidirect
89. #17986250C22semidirect
90. #17986247C22semidirect
93. #17986243C22semidirect
94. #17986238C22semidirect
95. #17986238C22semidirect
96. #17986238C22semidirect
97. #17986233C22semidirect
98. #17986230C22semidirect
99. #17986226C22semidirect
100. #17986226C22semidirect
101. #17986226C22semidirect
102. #17986221C22semidirect
103. #17986221C22semidirect
104. #17986214C22semidirect
105. #17986214C22semidirect
106. #17986209C22semidirect
107. #17986209C22semidirect
108. #17986206C22semidirect
109. #17986204C22semidirect
110. #17986204C22semidirect
111. #17986201C22semidirect
112. #17986196C22semidirect
113. #17986191C22semidirect
116. #17986161C22semidirect
117. #17986161C22semidirect
118. #17986161C22semidirect
119. #17986161C22semidirect
126. #17986159C22semidirect
127. #17986159C22semidirect
129. #17986154C22semidirect
130. #17986154C22semidirect
131. #17986154C22semidirect
132. #17986154C22semidirect
134. #17986144C22semidirect
135. #17986144C22semidirect
142. #17986142C22semidirect
143. #17986142C22semidirect
145. #17986137C22semidirect
146. #17986137C22semidirect
147. #17986137C22semidirect
148. #17986137C22semidirect
150. #17986109C22semidirect
151. #17986104C22semidirect
152. #17986099C22semidirect
153. #17986097C22semidirect
154. C4×#11765855C22semidirect
155. C4×#11765852C22semidirect
156. C4×#11765853C22semidirect
157. C4×#11765850C22semidirect
162. #17986071C22semidirect
163. #17986071C22semidirect
164. D4×C71⋊C8C22semidirect
165. D4×C71⋊C8C22semidirect
166. #17986060C22semidirect
167. #17986060C22semidirect
170. #17985998C22semidirect
171. #17985998C22semidirect
174. C2×#14556051C22semidirect
175. C2×#14556051C22semidirect
176. #17985966C22semidirect
177. #17985966C22semidirect
185. #553×C71C22semidirect
187. #552×C71C22semidirect
189. #550×C71C22semidirect
191. #547×C71C22semidirect
192. #541×C71C22semidirect
195. #540×C71C22semidirect
198. #537×C71C22semidirect
199. #537×C71C22semidirect
933. #3539D71semidirect
964. C71#61626semidirect
980. #553C2×D71semidirect
982. #552C2×D71semidirect
984. #550C2×D71semidirect
994. #547C2×D71semidirect
999. #541C2×D71semidirect
1002. #540C2×D71semidirect
1007. #537C2×D71semidirect
1008. #537C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226020122
#226005502
#226005352
#226005052
#226004302
#226003852
#226003102
#226002362
#226002212
#226000702
#226000582
#226000062
#225999822
#225999212
#225998912
#225998812
#225998662
#225994172
#225993952
#225992462
#225992372
#225991662
#225991172
#225985482
#225985332
#225976522
#225975802
#225975562
#225973882
C71×#35392
#6162671