Finite Group Databasebeta

← #32880366

Subgroups — #32880366

Order 18176.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602391C211yesmaximal, characteristic, complemented
2#22601356C211yesmaximal, characteristic, complemented
3#22601239C211yesmaximal, characteristic, complemented
4#22600989C211yesmaximal, characteristic, complemented
5#22600971C211yesmaximal, characteristic, complemented
6#22600929C211yesmaximal, characteristic, complemented
7#22600825C212yesmaximal, complemented
8#22600262C211yesmaximal, characteristic, complemented
9#22600184C212yesmaximal, complemented
10#22600164C212yesmaximal, complemented
11#22600153C211yesmaximal, characteristic, complemented
12#22599936C211yesmaximal, characteristic, complemented
13#22599816C212yesmaximal, complemented
14#22599025C212yesmaximal, complemented
15#22598895C211yesmaximal, characteristic, complemented
16#22598533C212yesmaximal, complemented
17#22598524C212yesmaximal, complemented
18#22598439C211yesmaximal, characteristic, complemented
19#22598427C211yesmaximal, characteristic, complemented
20#22597316C211yesmaximal, characteristic, complemented
21#22597172C212yesmaximal, complemented
22C2×C4×#11765850C211yesmaximal, characteristic, complemented
23C71×#3519C211yesmaximal, characteristic, complemented
24C2×#14556154C2212yes—
25C22×#11765850C2211yescharacteristic
26#17986722C2211yescharacteristic, complemented
27#17986706C2212yescomplemented
28#17986687—21no—
29#17986672—22no—
30Q8×D284C2211yescharacteristic, complemented
31#17986657—21no—
32#17986654C2211yescharacteristic, complemented
33#17986653C2211yescharacteristic, complemented
34#17986645C2212yescomplemented
35#17986620C2212yescomplemented
36#17986590—22no—
37#17986556C2211yescharacteristic, complemented
38#17986509—21no—
39C22⋊Q8×D71—21no—
40#17986479C2212yescomplemented
41C2×C4×D284C2211yescharacteristic, complemented
42#17986409C2212yescomplemented
43#17986395C2211yescharacteristic, complemented
44#17986386C2212yescomplemented
45#17986371C2211yescharacteristic, complemented
46#17986356C2212yescomplemented
47#17986351C2211yescharacteristic, complemented
48#17986345C2212yescomplemented
49#17986345C2211yescharacteristic, complemented
50#17986340C2212yescomplemented
51#17986334C2212yescomplemented
52#17986323C2212yescomplemented
53#17986315C2212yescomplemented
54#17986315C2212yescomplemented
55#17986310C2212yescomplemented
56#17986303C2212yescomplemented
57#17986296C2212yescomplemented
58#17986289C2212yescomplemented
59#17986286C2211yescharacteristic, complemented
60#17986286C2211yescharacteristic, complemented
61#17986279C2211yescharacteristic, complemented
62#17986279C2212yescomplemented
63#17986279C2211yescharacteristic, complemented
64#17986250C2212yescomplemented
65#17986243C2212yescomplemented
66#17986233C2212yescomplemented
67#17986226C2212yescomplemented
68#17986226C2212yescomplemented
69#17986226C2212yescomplemented
70#17986214C2212yes—
71#17986214C2212yescomplemented
72#17986204C2211yescharacteristic, complemented
73#17986204C2211yescharacteristic, complemented
74#17986196C2212yescomplemented
75#17986191C2211yescharacteristic, complemented
76#17986191C2212yescomplemented
77#17986191C2211yescharacteristic, complemented
78#17986150C2212yes—
79#17986150C2212yescomplemented
80#17986142C2212yescomplemented
81#17986142C2212yescomplemented
82#17986133C2212yes—
83#17986132C2212yescomplemented
84#17986130C2211yescharacteristic, complemented
85Q8×C71⋊C8C2211yescharacteristic, complemented
86#17986109C2212yes—
87#17986109C2212yescomplemented
88#17986109C2212yescomplemented
89#17986099C2212yescomplemented
90#17986099C2212yescomplemented
91#17986099C2212yescomplemented
92C4×#11765853C2212yescomplemented
93C4×#11765853C2212yescomplemented
94C4×#11765853C2212yescomplemented
95C4×#11765850C2211yescharacteristic
96C4×#11765850C2211yescharacteristic
97C4×#11765850C2211yescharacteristic
98C4×#11765850C2211yescharacteristic
99C4×#11765850C2212yescomplemented
100C4×#11765850C2211yescharacteristic, complemented
101C4×#11765850C2211yescharacteristic, complemented
102C4×#11765850C2211yescharacteristic, complemented
103C4×#11765850C2211yescharacteristic, complemented
104#17986077C2211yescharacteristic, complemented
105#17986071C2212yescomplemented
106D4×C71⋊C8C2211yescharacteristic, complemented
107D4×C71⋊C8C2212yescomplemented
108#17986060C2212yescomplemented
109#17986056C2211yescharacteristic, complemented
110#17986042C2212yescomplemented
111C2×#14556061C2211yescharacteristic, complemented
112#17985993C2212yescomplemented
113C2×#14556049C2211yescharacteristic
114C2×#14556049C2212yescomplemented
115C2×#14556048C2211yescharacteristic, complemented
116#17985955C2212yescomplemented
117C2×C4×C71⋊C8C2211yescharacteristic, complemented
118#555×C71C2211yescharacteristic, complemented
119#554×C71C2211yescharacteristic, complemented
120#553×C71—21no—
121#553×C71C2212yes—
122#550×C71C2211yescharacteristic, complemented
123#546×C71—21no—
124#546×C71—22no—
125D42×C71C2212yes—
126D42×C71C2211yescharacteristic, complemented
127#540×C71C2212yescomplemented
128#538×C71—22no—
129#532×C71C2211yescharacteristic
130#529×C71C2211yescharacteristic
131#525×C71—21no—
132C2×#121×C71—21no—
133#518×C71C2212yescomplemented
134C2×C4×D4×C71C2211yescharacteristic
135C2×#11765865C2312yes—
136C2×#11765864—21no—
137C2×Q8×D71—21no—
138C22×D284C2311yescharacteristic
139C22×C4×D71—21no—
140#14556154—28no—
141C2×#11765853C2312yes—
142C2×#11765853C2312yes—
143C2×#11765853C2312yes—
144C2×#11765853C2312yes—
145C2×#11765850—24no—
146C2×#11765850C2311yescharacteristic
147C2×#11765850C2311yescharacteristic
148C2×#11765850C2311yescharacteristic
149C2×#11765850C2312yes—
150C2×#11765850C2312yes—
151C2×#11765850C2311yescharacteristic
152C2×#11765849C2312yes—
153C22×C71⋊C8C2311yescharacteristic
154C22×C71⋊C8C2311yescharacteristic
155C22×C71⋊C8C2312yes—
156#14556128C2311yescharacteristic
157#14556128C2312yes—
158#14556128C2311yescharacteristic
159#14556123—22no—
160#14556123—22no—
161#14556120—21no—
162#14556119—22no—
163#14556116C2312yes—
164#14556114—22no—
165#14556113—22no—
166#14556112—22no—
167#14556110—22no—
168#14556110—22no—
169#14556108—22no—
170#14556108—21no—
171#14556108—21no—
172#14556107—21no—
173#14556107C2312yes—
174#14556107C2312yes—
175#14556106—22no—
176#14556105—22no—
177#14556105—22no—
178#14556104—21no—
179#14556102C2312yes—
180#14556101—22no—
181#14556099—21no—
182#14556096—22no—
183C4×Dic142—21no—
184C4×Dic142C2312yes—
185C4×Dic142C2312yes—
186C4×D284—21no—
187C4×D284—21no—
188C4×D284C2311yescharacteristic
189C4×D284C2311yescharacteristic
190C4×D284C2311yescharacteristic
191C4×D284C2311yescharacteristic
192C4×D284C2312yes—
193D4×Dic71—22no—
194(C22⋊D71)⋊C4—22no—
195(C22⋊D71)⋊C4—22no—
196#14556087—21no—
197#14556086—22no—
198#14556086—21no—
199C2×C4⋊Dic71C2312yes—
200C2×C4⋊Dic71C2311yescharacteristic
201C4⋊C4×D71—22no—
202C4⋊C4×D71—21no—
203C2×(C2×D71)⋊C4—21no—
204C22⋊C4×D71—22no—
205#14556061C2311yescharacteristic
206#14556061C2312yes—
207#14556061C2312yes—
208#14556061C2311yescharacteristic
209#14556061C2311yescharacteristic
210#14556061C2311yescharacteristic
211#14556059C2312yes—
212#14556059C2312yes—
213#14556059C2312yes—
214#14556059C2312yes—
215C4⋊(C71⋊C8)C2311yescharacteristic
216C4⋊(C71⋊C8)C2311yescharacteristic
217C4⋊(C71⋊C8)C2312yes—
218C4⋊(C71⋊C8)C2312yes—
219#14556051C2312yes—
220#14556051C2312yes—
221#14556051C2312yes—
222#14556051C2312yes—
223#14556049C2312yes—
224#14556049C2312yes—
225#14556049C2311yescharacteristic
226#14556049C2312yes—
227#14556049C2312yes—
228#14556049C2311yescharacteristic
229#14556049C2311yescharacteristic
230#14556049C2311yescharacteristic
231#14556049C2312yes—
232#14556049C2312yes—
233#14556048C2311yescharacteristic
234#14556048C2312yes—
235#14556048C2311yescharacteristic
236#14556048C2311yescharacteristic
237#14556048C2311yescharacteristic
238#14556048C2312yes—
239C22⋊(C71⋊C8)C2312yes—
240C22⋊(C71⋊C8)C2312yes—
241C22⋊(C71⋊C8)C2312yes—
242#14556039C2312yes—
243#14556039C2312yes—
244C4×C71⋊C8C2311yescharacteristic
245C4×C71⋊C8C2311yescharacteristic
246C4×C71⋊C8C2312yes—
247C4×C71⋊C8C2311yescharacteristic
248C4×C71⋊C8C2311yescharacteristic
249C2×#41×C71—21no—
250C2×#41×C71—21no—
251C22×D4×C71—22no—
252C22×D4×C71—21no—
253C22×D4×C71C2312yes—
254C22×D4×C71C2311yescharacteristic
255C23×C4×C71—21no—
256C4⋊Q8×C71C2311yescharacteristic
257#127×C71C2311yescharacteristic
258#127×C71C2312yes—
259#126×C71—22no—
260#126×C71D412yes—
261#125×C71D411yescharacteristic
262#125×C71C2312yes—
263#124×C71—22no—
264#124×C71—21no—
265#124×C71D411yescharacteristic
266#123×C71—22no—
267#123×C71—22no—
268#123×C71—22no—
269#123×C71D412yes—
270C22⋊Q8×C71—21no—
271C22⋊Q8×C71—22no—
272C22⋊Q8×C71D411yescharacteristic
273#121×C71—22no—
274#121×C71—21no—
275#121×C71—21no—
276#121×C71—21no—
277#121×C71—21no—
278#121×C71—22no—
279#121×C71—22no—
280#121×C71—22no—
281#121×C71—22no—
282#121×C71D411yescharacteristic
283#121×C71C2312yes—
284#121×C71C2312yes—
285#121×C71C2312yes—
286#120×C71—22no—
287#120×C71—22no—
288#120×C71—22no—
289C4×Q8×C71C2311yescharacteristic
290C4×D4×C71—22no—
291C4×D4×C71—22no—
292C4×D4×C71—22no—
293C4×D4×C71—21no—
294C4×D4×C71—21no—
295C4×D4×C71—21no—
296C4×D4×C71C2311yescharacteristic
297C4×D4×C71C2311yescharacteristic
298C4×D4×C71C2311yescharacteristic
299C4×D4×C71C2311yescharacteristic
300C4×D4×C71C2312yes—
301C4×D4×C71C2312yes—
302C4×D4×C71C2312yes—
303C4×D4×C71C2312yes—
304C4×D4×C71C2311yescharacteristic
305#117×C71—21no—
306#117×C71C2312yes—
307#117×C71C2312yes—
308C2×C4⋊C4×C71—21no—
309C2×C4⋊C4×C71C2311yescharacteristic
310C2×C22⋊C4×C71—21no—
311C2×C22⋊C4×C71—22no—
312C2×C22⋊C4×C71—22no—
313C2×C42×C71C2311yescharacteristic
314C23×D71—21no—
315#11765865—24no—
316#11765865—42no—
317#11765864—82no—
318C2×Dic142—21no—
319C2×Dic142—22no—
320C2×Dic142C2412yes—
321Q8×D71—82no—
322C2×D284—22no—
323C2×D284—21no—
324C2×D284—41no—
325C2×D284C2411yescharacteristic
326C2×D284C2411yescharacteristic
327C2×C22⋊D71—22no—
328C2×C22⋊D71—22no—
329C22×Dic71—21no—
330C22×Dic71—22no—
331C2×C4×D71—21no—
332C2×C4×D71—21no—
333C2×C4×D71—22no—
334C2×C4×D71—21no—
335C2×C4×D71—21no—
336C2×C4×D71—22no—
337C2×C4×D71—82no—
338#11765853—24no—
339#11765853—24no—
340#11765853—42no—
341#11765853—42no—
342#11765850—22no—
343#11765850—22no—
344#11765850—24no—
345#11765850—22no—
346#11765850—42no—
347#11765850#4114yescomplemented
348#11765849—24no—
349C2×C71⋊C8—22no—
350C2×C71⋊C8—42no—
351C2×C71⋊C8—41no—
352C2×C71⋊C8C2411yescharacteristic
353C2×C71⋊C8C2411yescharacteristic
354C2×C71⋊C8C2411yescharacteristic
355C2×C71⋊C8C2412yes—
356C2×C71⋊C8C2412yes—
357C2×C71⋊C8C2411yescharacteristic
358C4⋊Dic71—22no—
359C4⋊Dic71—21no—
360C4⋊Dic71—21no—
361C4⋊Dic71—21no—
362C4⋊Dic71—21no—
363C4⋊Dic71—22no—
364C4⋊Dic71C2411yescharacteristic
365C4⋊Dic71C2411yescharacteristic
366C4⋊Dic71C2412yes—
367Dic71⋊C4—22no—
368Dic71⋊C4—22no—
369Dic71⋊C4—22no—
370Dic71⋊C4—22no—
371C22⋊Dic71—22no—
372C22⋊Dic71—22no—
373(C2×D71)⋊C4—22no—
374(C2×D71)⋊C4—22no—
375(C2×D71)⋊C4—21no—
376(C2×D71)⋊C4—21no—
377(C2×D71)⋊C4—21no—
378(C2×D71)⋊C4—21no—
379(C2×D71)⋊C4—22no—
380(C2×D71)⋊C4—22no—
381C4×Dic71—22no—
382C4×Dic71—22no—
383C24×C71—21no—
384C24×C71—22no—
385#41×C71—82no—
386#41×C71—82no—
387C2×Q8×C71—21no—
388C2×Q8×C71C2×D411yescharacteristic
389C2×D4×C71—22no—
390C2×D4×C71—24no—
391C2×D4×C71—22no—
392C2×D4×C71—22no—
393C2×D4×C71—22no—
394C2×D4×C71—22no—
395C2×D4×C71—21no—
396C2×D4×C71—21no—
397C2×D4×C71—22no—
398C2×D4×C71—21no—
399C2×D4×C71—22no—
400C2×D4×C71—41no—
401C2×D4×C71—42no—
402C2×D4×C71—82no—
403C2×D4×C71—84no—
404C2×D4×C71C2×D411yescharacteristic
405C2×D4×C71C2×D412yes—
406C2×D4×C71C2411yescharacteristic
407C2×D4×C71C2412yes—
408C2×D4×C71C2411yescharacteristic
409C22×C4×C71—21no—
410C22×C4×C71—21no—
411C22×C4×C71—21no—
412C22×C4×C71—21no—
413C22×C4×C71—22no—
414C22×C4×C71—22no—
415C22×C4×C71—22no—
416C22×C4×C71—21no—
417C22×C4×C71—82no—
418C22×C4×C71C2×D411yescharacteristic
419C22×C4×C71C2×D411yescharacteristic
420C22×C4×C71C2411yescharacteristic
421C22×C4×C71C2412yes—
422C4⋊C4×C71—21no—
423C4⋊C4×C71—22no—
424C4⋊C4×C71—21no—
425C4⋊C4×C71—22no—
426C4⋊C4×C71C2×D411yescharacteristic
427C4⋊C4×C71C2×D411yescharacteristic
428C4⋊C4×C71C2×D412yes—
429C4⋊C4×C71C2×D412yes—
430C4⋊C4×C71C2×D412yes—
431C4⋊C4×C71C2×D412yes—
432C4⋊C4×C71C2411yescharacteristic
433C4⋊C4×C71C2411yescharacteristic
434C4⋊C4×C71C2412yes—
435C22⋊C4×C71—22no—
436C22⋊C4×C71—21no—
437C22⋊C4×C71—22no—
438C22⋊C4×C71—21no—
439C22⋊C4×C71—22no—
440C22⋊C4×C71—21no—
441C22⋊C4×C71—22no—
442C22⋊C4×C71—21no—
443C22⋊C4×C71—22no—
444C22⋊C4×C71—22no—
445C22⋊C4×C71—22no—
446C22⋊C4×C71C2×D412yes—
447C22⋊C4×C71C2×D412yes—
448C22⋊C4×C71C2×D412yes—
449C22⋊C4×C71C2×D412yes—
450C22⋊C4×C71C2×D412yes—
451C42×C71—22no—
452C42×C71C2×D411yescharacteristic
453C42×C71C2×D411yescharacteristic
454C42×C71C2411yescharacteristic
455C42×C71C2411yescharacteristic
456C42×C71C2412yes—
457C23×C71—21no—
458C23×C71—21no—
459C23×C71—22no—
460C23×C71—42no—
461C23×C71—44no—
462C23×C71—42no—
463C23×C71—81no—
464C23×C71—82no—
465C23×C71—82no—
466C23×C71C22×D412yes—
467C23×C71C22×D411yescharacteristic
468C22×D71—21no—
469C22×D71—21no—
470C22×D71—42no—
471C22×D71—42no—
472C22×D71—81no—
473Q8×C71—22no—
474Q8×C71—81no—
475D4×C71—24no—
476D4×C71—22no—
477D4×C71—21no—
478D4×C71—22no—
479D4×C71—21no—
480D4×C71—22no—
481D4×C71—21no—
482D4×C71—44no—
483D4×C71—42no—
484D4×C71—44no—
485D4×C71—42no—
486D4×C71—82no—
487D4×C71—82no—
488D4×C71—81no—
489D4×C71—82no—
490D4×C71—82no—
491D4×C71C2×#4112yes—
492C2×C4×C71—22no—
493C2×C4×C71—22no—
494C2×C4×C71—21no—
495C2×C4×C71—22no—
496C2×C4×C71—21no—
497C2×C4×C71—22no—
498C2×C4×C71—21no—
499C2×C4×C71—22no—
500C2×C4×C71—21no—
501C2×C4×C71—42no—
502C2×C4×C71—42no—
503C2×C4×C71—81no—
504C2×C4×C71—81no—
505C2×C4×C71—82no—
506C2×C4×C71—82no—
507C2×C4×C71—82no—
508C2×C4×C71—81no—
509C2×C4×C71C22×D412yes—
510C2×C4×C71C22×D411yescharacteristic
511C2×C4×C71C22×D411yescharacteristic
512C2×C4×C71C22×D411yescharacteristic
513C2×C4×C71C22×D411yescharacteristic
514C2×C4×C71C22×D412yes—
515C2×C4×C71C22×D412yes—
516C2×C4×C71C22×D411yescharacteristic
517C2×C4×C71C2511yescharacteristic
518C22⋊D71—44no—
519C22⋊D71—82no—
520C2×Dic71—22no—
521C2×Dic71—21no—
522C2×Dic71—22no—
523C2×Dic71—21no—
524C2×Dic71—81no—
525C2×Dic71—82no—
526D284—21no—
527D284—21no—
528D284—21no—
529D284—42no—
530D284C2×#4112yes—
531C4×D71—44no—
532C4×D71—42no—
533C4×D71—42no—
534C4×D71—81no—
535C4×D71—81no—
536C4×D71—82no—
537Dic142—22no—
538Dic142—22no—
539Dic142—42no—
540Dic142—82no—
541C71⋊C8—21no—
542C71⋊C8—22no—
543C71⋊C8—21no—
544C71⋊C8—22no—
545C71⋊C8—21no—
546C71⋊C8C2×#4112yes—
547C22×C71—21no—
548C22×C71—21no—
549C22×C71—22no—
550C22×C71—22no—
551C22×C71—22no—
552C22×C71—22no—
553C22×C71—41no—
554C22×C71—41no—
555C22×C71—41no—
556C22×C71—42no—
557C22×C71—41no—
558C22×C71—42no—
559C22×C71—42no—
560C22×C71—41no—
561C22×C71—84no—
562C22×C71—164no—
563C22×C71#57712yes—
564C22×C71C23×D411yescharacteristic
565C2×D71—22no—
566C2×D71—41no—
567C2×D71—41no—
568C2×D71—41no—
569C2×D71—41no—
570C2×D71—41no—
571C2×D71—84no—
572C4×C71—22no—
573C4×C71—21no—
574C4×C71—22no—
575C4×C71—21no—
576C4×C71—21no—
577C4×C71—21no—
578C4×C71—22no—
579C4×C71—41no—
580C4×C71—41no—
581C4×C71—42no—
582C4×C71#57612yes—
583C4×C71C22×#4111yescharacteristic
584C4×C71#58511yescharacteristic
585Dic71—42no—
586Dic71—42no—
587Dic71—41no—
588Dic71—41no—
589#61496—711nomaximal, Sylow
590C2×C71—22no—
591C2×C71—42no—
592C2×C71—42no—
593C2×C71—81no—
594C2×C71—82no—
595C2×C71D4×#4111yescharacteristic
596C2×C71C2×#57611yescharacteristic
597C2×C71C2×#57711yescharacteristic
598D71—42no—
599D71—81no—
600#3520—711no—
601#3519D7111yescharacteristic, complemented
602#3397—711no—
603#3384—711no—
604#3360—711no—
605#3358—711no—
606#3354—711no—
607#3346—712no—
608#3303—711no—
609#3297—712no—
610#3295—712no—
611#3294—711no—
612#3272—711no—
613#3264—712no—
614#3179—712no—
615#3167—711no—
616#3119—712no—
617#3118—712no—
618#3110—711no—
619#3109—711no—
620#2966—711no—
621#2946—712no—
622C2×C4×D8—711no—
623C71#6149611yescharacteristic, complemented, Sylow
624C2×AGL(1,ℤ/8)—712no—
625C22×D8—711no—
626#556—711no—
627#555C2×D7111yescharacteristic, complemented
628#554—712no—
629#554C2×D7111yescharacteristic, complemented
630#553—21no—
631#553C2×D7112yes—
632#552—1421no—
633#551—1422no—
634#550C2×D7111yescharacteristic, complemented
635D4×Q8—711no—
636#548—1421no—
637#547—711no—
638#547—711no—
639#546—21no—
640#546—22no—
641#546—712no—
642D42C2×D7112yes—
643D42C2×D7111yescharacteristic, complemented
644#542—712no—
645#540C2×D7112yescomplemented
646#539—1422no—
647#538—22no—
648#533—711no—
649#532C2×D7111yescharacteristic
650#529C2×D7111yescharacteristic
651#525—21no—
652#525—1421no—
653C2×C22⋊Q8—1421no—
654C2×#121—21no—
655#520—712no—
656#518C2×D7112yescomplemented
657C2×C4×D4—711no—
658C2×C4×D4C2×D7111yescharacteristic
659#501—712no—
660#498—711no—
661#496—712no—
662#492—711no—
663#488—712no—
664#487—711no—
665#486—711no—
666#486—712no—
667#485—712no—
668#484—712no—
669#482—712no—
670#481—712no—
671#481—712no—
672#480—712no—
673#479—712no—
674#478—712no—
675#476—711no—
676#476—711no—
677#476—712no—
678#474—712no—
679#474—711no—
680#474—711no—
681#469—712no—
682#468—712no—
683#466—712no—
684#465—712no—
685#465—712no—
686#465—712no—
687#463—712no—
688#463—712no—
689#461—711no—
690#461—711no—
691#460—712no—
692#459—711no—
693#459—712no—
694#459—711no—
695#450—712no—
696#450—712no—
697#449—712no—
698#449—712no—
699#447—712no—
700#447—712no—
701#446—711no—
702C8×Q8—711no—
703#442—712no—
704#442—712no—
705#442—712no—
706#440—712no—
707#440—712no—
708#440—712no—
709C4×SD16—712no—
710C4×SD16—712no—
711C4×SD16—712no—
712C4×D8—711no—
713C4×D8—711no—
714C4×D8—712no—
715C4×D8—711no—
716C4×D8—711no—
717C4×D8—711no—
718C4×D8—711no—
719C4×D8—711no—
720C4×D8—711no—
721#436—711no—
722#435—712no—
723C8×D4—711no—
724C8×D4—712no—
725#433—712no—
726#432—711no—
727#428—712no—
728C2×#107—711no—
729#416—712no—
730C2×#102—711no—
731C2×#102—712no—
732C2×#102—711no—
733#405—712no—
734C2×C4×C8—711no—
735C2×#41—21no—
736C2×#41—21no—
737C2×#41—712no—
738C2×#41—1421no—
739C22×Q8—1421no—
740C22×D4—22no—
741C22×D4—21no—
742C22×D4—711no—
743C22×D4C22×D7111yescharacteristic
744C22×D4C22×D7112yes—
745C23×C4—21no—
746C23×C4—1421no—
747AGL(1,ℤ/8)—1428no—
748C2×SD16—712no—
749C2×SD16—712no—
750C2×SD16—712no—
751C2×SD16—712no—
752C2×D8—712no—
753C2×D8—711no—
754C2×D8—711no—
755C2×D8—711no—
756C2×D8—711no—
757C2×D8—712no—
758C2×D8—1424no—
759C2×M16—712no—
760C22×C8—711no—
761C22×C8—712no—
762C22×C8—711no—
763C4⋊Q8—711no—
764C4⋊Q8—712no—
765C4⋊Q8—711no—
766C4⋊Q8C22×D7111yescharacteristic
767#127C22×D7111yescharacteristic
768#127C22×D7112yes—
769#126—22no—
770#126—1422no—
771#126—1422no—
772#126C22⋊D7112yes—
773#125—1422no—
774#125—1421no—
775#125C22⋊D7111yescharacteristic
776#125C22×D7112yes—
777#124—22no—
778#124—21no—
779#124—712no—
780#124—1422no—
781#124C22⋊D7111yescharacteristic
782#123—22no—
783#123—22no—
784#123—22no—
785#123—1422no—
786#123—1422no—
787#123—1422no—
788#123—1422no—
789#123C22⋊D7112yes—
790C22⋊Q8—21no—
791C22⋊Q8—22no—
792C22⋊Q8—712no—
793C22⋊Q8—712no—
794C22⋊Q8—1421no—
795C22⋊Q8—1421no—
796C22⋊Q8—1422no—
797C22⋊Q8—1421no—
798C22⋊Q8—1421no—
799C22⋊Q8—1422no—
800C22⋊Q8—1422no—
801C22⋊Q8—1422no—
802C22⋊Q8C22⋊D7111yescharacteristic
803#121—22no—
804#121—21no—
805#121—21no—
806#121—21no—
807#121—21no—
808#121—22no—
809#121—22no—
810#121—22no—
811#121—22no—
812#121—712no—
813#121—1421no—
814#121—1422no—
815#121C22⋊D7111yescharacteristic
816#121C22×D7112yes—
817#121C22×D7112yes—
818#121C22×D7112yes—
819#120—22no—
820#120—22no—
821#120—22no—
822#120—1422no—
823C4×Q8—712no—
824C4×Q8—712no—
825C4×Q8—1421no—
826C4×Q8C22×D7111yescharacteristic
827C4×D4—22no—
828C4×D4—22no—
829C4×D4—22no—
830C4×D4—21no—
831C4×D4—21no—
832C4×D4—21no—
833C4×D4—711no—
834C4×D4—711no—
835C4×D4—711no—
836C4×D4—711no—
837C4×D4—712no—
838C4×D4—1422no—
839C4×D4—1422no—
840C4×D4—1422no—
841C4×D4—1421no—
842C4×D4—1421no—
843C4×D4C22×D7111yescharacteristic
844C4×D4C22×D7111yescharacteristic
845C4×D4C22×D7111yescharacteristic
846C4×D4C22×D7111yescharacteristic
847C4×D4C22×D7112yes—
848C4×D4C22×D7112yes—
849C4×D4C22×D7112yes—
850C4×D4C22×D7112yes—
851C4×D4C22×D7111yescharacteristic
852#117—21no—
853#117—1421no—
854#117—1422no—
855#117—1421no—
856#117C22×D7112yes—
857#117C22×D7112yes—
858C2×C4⋊C4—21no—
859C2×C4⋊C4—711no—
860C2×C4⋊C4—712no—
861C2×C4⋊C4—1422no—
862C2×C4⋊C4—1421no—
863C2×C4⋊C4C22×D7111yescharacteristic
864C2×C22⋊C4—21no—
865C2×C22⋊C4—22no—
866C2×C22⋊C4—22no—
867C2×C22⋊C4—1421no—
868C2×C22⋊C4—1422no—
869C2×C42C22×D7111yescharacteristic
870#107—711no—
871#107—711no—
872#107—711no—
873#107—711no—
874#107—712no—
875#107—712no—
876#106—712no—
877#106—712no—
878#106—712no—
879#106—712no—
880C4⋊C8—711no—
881C4⋊C8—711no—
882C4⋊C8—712no—
883C4⋊C8—712no—
884#103—712no—
885#103—712no—
886#103—712no—
887#103—712no—
888#102—711no—
889#102—711no—
890#102—711no—
891#102—711no—
892#102—712no—
893#102—712no—
894#102—712no—
895#102—712no—
896#102—712no—
897#102—712no—
898#102—711no—
899#102—711no—
900#102—711no—
901#102—711no—
902#102—712no—
903#102—712no—
904C22⋊C8—712no—
905C22⋊C8—712no—
906C22⋊C8—712no—
907#97—712no—
908#97—712no—
909C4×C8—711no—
910C4×C8—711no—
911C4×C8—711no—
912C4×C8—711no—
913C4×C8—712no—
914C24—21no—
915C24—22no—
916C24—1421no—
917#41—82no—
918#41—82no—
919#41—2842no—
920#41—5682no—
921#41—1424no—
922C2×Q8—21no—
923C2×Q8—5682no—
924C2×Q8—712no—
925C2×Q8—1421no—
926C2×Q8—1422no—
927C2×Q8C2×C22⋊D7111yescharacteristic
928C2×D4—22no—
929C2×D4—24no—
930C2×D4—22no—
931C2×D4—22no—
932C2×D4—22no—
933C2×D4—22no—
934C2×D4—21no—
935C2×D4—21no—
936C2×D4—22no—
937C2×D4—21no—
938C2×D4—22no—
939C2×D4—41no—
940C2×D4—42no—
941C2×D4—82no—
942C2×D4—84no—
943C2×D4—2841no—
944C2×D4—711no—
945C2×D4—711no—
946C2×D4—1422no—
947C2×D4—1422no—
948C2×D4—1422no—
949C2×D4—1421no—
950C2×D4C2×C22⋊D7112yes—
951C2×D4C2×C22⋊D7111yescharacteristic
952C2×D4C23×D7111yescharacteristic
953C2×D4C23×D7112yes—
954C2×D4C23×D7111yescharacteristic
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—22no—
960C22×C4—22no—
961C22×C4—22no—
962C22×C4—21no—
963C22×C4—82no—
964C22×C4—5682no—
965C22×C4—1422no—
966C22×C4—1421no—
967C22×C4—1421no—
968C22×C4—1421no—
969C22×C4—1422no—
970C22×C4—1422no—
971C22×C4—1421no—
972C22×C4—1421no—
973C22×C4C2×C22⋊D7111yescharacteristic
974C22×C4C2×C22⋊D7111yescharacteristic
975C22×C4C23×D7111yescharacteristic
976C22×C4C23×D7112yes—
977SD16—2842no—
978SD16—2842no—
979SD16—1424no—
980SD16—1424no—
981D8—2842no—
982D8—714no—
983D8—1422no—
984D8—1422no—
985D8—1424no—
986D8—1422no—
987M16—1424no—
988C2×C8—2842no—
989C2×C8—2841no—
990C2×C8—711no—
991C2×C8—711no—
992C2×C8—711no—
993C2×C8—711no—
994C2×C8—712no—
995C2×C8—712no—
996C2×C8—1422no—
997C4⋊C4—21no—
998C4⋊C4—22no—
999C4⋊C4—21no—
1000C4⋊C4—22no—
1001C4⋊C4—711no—
1002C4⋊C4—711no—
1003C4⋊C4—712no—
1004C4⋊C4—1422no—
1005C4⋊C4—1422no—
1006C4⋊C4—1422no—
1007C4⋊C4—1422no—
1008C4⋊C4—1422no—
1009C4⋊C4—1421no—
1010C4⋊C4—1421no—
1011C4⋊C4—1421no—
1012C4⋊C4—1421no—
1013C4⋊C4—1422no—
1014C4⋊C4C2×C22⋊D7111yescharacteristic
1015C4⋊C4C2×C22⋊D7111yescharacteristic
1016C4⋊C4C2×C22⋊D7112yes—
1017C4⋊C4C2×C22⋊D7112yes—
1018C4⋊C4C2×C22⋊D7112yes—
1019C4⋊C4C2×C22⋊D7112yes—
1020C4⋊C4C23×D7112yes—
1021C4⋊C4C23×D7111yescharacteristic
1022C4⋊C4C23×D7111yescharacteristic
1023C22⋊C4—22no—
1024C22⋊C4—21no—
1025C22⋊C4—22no—
1026C22⋊C4—21no—
1027C22⋊C4—22no—
1028C22⋊C4—21no—
1029C22⋊C4—22no—
1030C22⋊C4—21no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—1422no—
1035C22⋊C4—1422no—
1036C22⋊C4—1421no—
1037C22⋊C4—1421no—
1038C22⋊C4—1421no—
1039C22⋊C4—1421no—
1040C22⋊C4—1422no—
1041C22⋊C4—1422no—
1042C22⋊C4—1422no—
1043C22⋊C4—1422no—
1044C22⋊C4C2×C22⋊D7112yes—
1045C22⋊C4C2×C22⋊D7112yes—
1046C22⋊C4C2×C22⋊D7112yes—
1047C22⋊C4C2×C22⋊D7112yes—
1048C22⋊C4C2×C22⋊D7112yes—
1049C42—22no—
1050C42—1422no—
1051C42—1422no—
1052C42C2×C22⋊D7111yescharacteristic
1053C42C2×C22⋊D7111yescharacteristic
1054C42C23×D7111yescharacteristic
1055C42C23×D7111yescharacteristic
1056C42C23×D7112yes—
1057C23—21no—
1058C23—21no—
1059C23—22no—
1060C23—42no—
1061C23—44no—
1062C23—42no—
1063C23—81no—
1064C23—82no—
1065C23—82no—
1066C23—2842no—
1067C23—2842no—
1068C23—5681no—
1069C23—1421no—
1070C23—1421no—
1071C23C22×C22⋊D7112yes—
1072C23C22×C22⋊D7111yescharacteristic
1073Q8—22no—
1074Q8—81no—
1075Q8—2842no—
1076Q8—5682no—
1077Q8—1422no—
1078Q8—1422no—
1079D4—24no—
1080D4—21no—
1081D4—22no—
1082D4—21no—
1083D4—22no—
1084D4—21no—
1085D4—22no—
1086D4—44no—
1087D4—42no—
1088D4—44no—
1089D4—42no—
1090D4—82no—
1091D4—82no—
1092D4—81no—
1093D4—82no—
1094D4—82no—
1095D4—2842no—
1096D4—2844no—
1097D4—5682no—
1098D4—712no—
1099D4—1421no—
1100D4—1421no—
1101D4—1421no—
1102D4#41×D7112yes—
1103C2×C4—22no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—21no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—21no—
1110C2×C4—22no—
1111C2×C4—21no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—81no—
1115C2×C4—81no—
1116C2×C4—82no—
1117C2×C4—82no—
1118C2×C4—82no—
1119C2×C4—81no—
1120C2×C4—2844no—
1121C2×C4—2842no—
1122C2×C4—2842no—
1123C2×C4—5681no—
1124C2×C4—5681no—
1125C2×C4—5682no—
1126C2×C4—5681no—
1127C2×C4—5682no—
1128C2×C4—1422no—
1129C2×C4—1421no—
1130C2×C4—1422no—
1131C2×C4—1421no—
1132C2×C4C22×C22⋊D7112yes—
1133C2×C4C22×C22⋊D7111yescharacteristic
1134C2×C4C22×C22⋊D7112yes—
1135C2×C4C22×C22⋊D7111yescharacteristic
1136C2×C4C22×C22⋊D7111yescharacteristic
1137C2×C4C22×C22⋊D7111yescharacteristic
1138C2×C4C22×C22⋊D7112yes—
1139C2×C4C22×C22⋊D7111yescharacteristic
1140C2×C4C24×D7111yescharacteristic
1141C8—712no—
1142C8—1421no—
1143C8—1422no—
1144C8—1421no—
1145C8—1422no—
1146C8—1421no—
1147C22—21no—
1148C22—21no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—42no—
1157C22—42no—
1158C22—41no—
1159C22—41no—
1160C22—42no—
1161C22—84no—
1162C22—164no—
1163C22—2841no—
1164C22—2841no—
1165C22—2841no—
1166C22—2841no—
1167C22—2841no—
1168C22—5684no—
1169C22—1422no—
1170C22#1798681012yes—
1171C22C23×C22⋊D7111yescharacteristic
1172C4—21no—
1173C4—22no—
1174C4—21no—
1175C4—21no—
1176C4—22no—
1177C4—22no—
1178C4—21no—
1179C4—41no—
1180C4—41no—
1181C4—42no—
1182C4—2841no—
1183C4—2841no—
1184C4—2842no—
1185C4—2842no—
1186C4#1798680212yes—
1187C4C2×#41×D7111yescharacteristic
1188C4#1798683511yescharacteristic
1189C2—22no—
1190C2—42no—
1191C2—42no—
1192C2—81no—
1193C2—82no—
1194C2—2842no—
1195C2—5681no—
1196C2#41×C22⋊D7111yescharacteristic
1197C2C2×#1798680211yescharacteristic
1198C2C2×#1798681011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC71×#3519C2
socleC22×C71C23×D4
hypercenter#3519D71
hypocenterC71#61496
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ #529 ◁ #3519

Complements

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

NH ≅ G/Ntype
1. #22602391C2semidirect
2. #22601356C2semidirect
3. #22601239C2semidirect
4. #22600989C2semidirect
5. #22600971C2semidirect
6. #22600929C2semidirect
7. #22600825C2semidirect
8. #22600262C2semidirect
9. #22600184C2semidirect
10. #22600164C2semidirect
11. #22600153C2semidirect
12. #22599936C2semidirect
13. #22599816C2semidirect
14. #22599025C2semidirect
15. #22598895C2semidirect
16. #22598533C2semidirect
17. #22598524C2semidirect
18. #22598439C2semidirect
19. #22598427C2semidirect
20. #22597316C2semidirect
21. #22597172C2semidirect
22. C2×C4×#11765850C2semidirect
23. C71×#3519C2semidirect
26. #17986722C22semidirect
27. #17986706C22semidirect
30. Q8×D284C22semidirect
32. #17986654C22semidirect
33. #17986653C22semidirect
34. #17986645C22semidirect
35. #17986620C22semidirect
37. #17986556C22semidirect
40. #17986479C22semidirect
41. C2×C4×D284C22semidirect
42. #17986409C22semidirect
43. #17986395C22semidirect
44. #17986386C22semidirect
45. #17986371C22semidirect
46. #17986356C22semidirect
47. #17986351C22semidirect
48. #17986345C22semidirect
49. #17986345C22semidirect
50. #17986340C22semidirect
51. #17986334C22semidirect
52. #17986323C22semidirect
53. #17986315C22semidirect
54. #17986315C22semidirect
55. #17986310C22semidirect
56. #17986303C22semidirect
57. #17986296C22semidirect
58. #17986289C22semidirect
59. #17986286C22semidirect
60. #17986286C22semidirect
61. #17986279C22semidirect
62. #17986279C22semidirect
63. #17986279C22semidirect
64. #17986250C22semidirect
65. #17986243C22semidirect
66. #17986233C22semidirect
67. #17986226C22semidirect
68. #17986226C22semidirect
69. #17986226C22semidirect
71. #17986214C22semidirect
72. #17986204C22semidirect
73. #17986204C22semidirect
74. #17986196C22semidirect
75. #17986191C22semidirect
76. #17986191C22semidirect
77. #17986191C22semidirect
79. #17986150C22semidirect
80. #17986142C22semidirect
81. #17986142C22semidirect
83. #17986132C22semidirect
84. #17986130C22semidirect
85. Q8×C71⋊C8C22semidirect
87. #17986109C22semidirect
88. #17986109C22semidirect
89. #17986099C22semidirect
90. #17986099C22semidirect
91. #17986099C22semidirect
92. C4×#11765853C22semidirect
93. C4×#11765853C22semidirect
94. C4×#11765853C22semidirect
99. C4×#11765850C22semidirect
100. C4×#11765850C22semidirect
101. C4×#11765850C22semidirect
102. C4×#11765850C22semidirect
103. C4×#11765850C22semidirect
104. #17986077C22semidirect
105. #17986071C22semidirect
106. D4×C71⋊C8C22semidirect
107. D4×C71⋊C8C22semidirect
108. #17986060C22semidirect
109. #17986056C22semidirect
110. #17986042C22semidirect
111. C2×#14556061C22semidirect
112. #17985993C22semidirect
114. C2×#14556049C22semidirect
115. C2×#14556048C22semidirect
116. #17985955C22semidirect
117. C2×C4×C71⋊C8C22semidirect
118. #555×C71C22semidirect
119. #554×C71C22semidirect
122. #550×C71C22semidirect
126. D42×C71C22semidirect
127. #540×C71C22semidirect
133. #518×C71C22semidirect
347. #11765850#41semidirect
601. #3519D71semidirect
623. C71#61496semidirect
627. #555C2×D71semidirect
629. #554C2×D71semidirect
634. #550C2×D71semidirect
643. D42C2×D71semidirect
645. #540C2×D71semidirect
656. #518C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226023912
#226013562
#226012392
#226009892
#226009712
#226009292
#226008252
#226002622
#226001842
#226001642
#226001532
#225999362
#225998162
#225990252
#225988952
#225985332
#225985242
#225984392
#225984272
#225973162
#225971722
C2×C4×#117658502
C71×#35192
#6149671