Finite Group Databasebeta

← #30610870

Subgroups — #30610870

Order 15616.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462744C211yesmaximal, characteristic, complemented
2#21462502C211yesmaximal, characteristic, complemented
3#21461183C211yesmaximal, characteristic, complemented
4#21461181C211yesmaximal, characteristic, complemented
5#21461167C211yesmaximal, characteristic, complemented
6#21461156C211yesmaximal, characteristic, complemented
7#21461153C211yesmaximal, characteristic, complemented
8#21461152C211yesmaximal, characteristic, complemented
9#21461141C211yesmaximal, characteristic, complemented
10#21461129C211yesmaximal, characteristic, complemented
11#21461127C211yesmaximal, characteristic, complemented
12#21461117C211yesmaximal, characteristic, complemented
13#21461116C211yesmaximal, characteristic, complemented
14#21461112C211yesmaximal, characteristic, complemented
15#21459438C211yesmaximal, characteristic
16#16840814—21no—
17#16840794—21no—
18#16840793—21no—
19#16840789—21no—
20#16840787—21no—
21#16840786—21no—
22#16840784C2211yescharacteristic
23#16840783C2211yescharacteristic
24#16840781C2211yescharacteristic
25#16840780C2211yescharacteristic
26#16840779C2211yescharacteristic
27#16840778C2211yescharacteristic
28#16840778C2211yescharacteristic
29#16840768—21no—
30#16840765C2211yescharacteristic
31D61⋊(C4⋊C8)C2211yescharacteristic
32C2×C4⋊#92420C2211yescharacteristic
33#16840735—21no—
34C4×#11758217C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840612C2211yescharacteristic
37#16840612C2211yescharacteristic
38#16840612C2211yescharacteristic
39#16840612C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840612C2211yescharacteristic
43#16840612C2211yescharacteristic
44Q8⋊#92420C2211yescharacteristic
45Q8⋊#92420C2211yescharacteristic
46Q8⋊#92420C2211yescharacteristic
47Q8⋊#92420C2211yescharacteristic
48#16840610C2211yescharacteristic
49#16840610C2211yescharacteristic
50#16840610C2211yescharacteristic
51#16840610C2211yescharacteristic
52#16840490C411yescharacteristic
53#16840480C411yescharacteristic
54#16840480C411yescharacteristic
55#16840453—21no—
56#16840448—21no—
57#16840448—21no—
58#16840427C411yescharacteristic
59#16840420—21no—
60#16840417C411yescharacteristic
61#16840414C411yescharacteristic
62#16840414C411yescharacteristic
63#16840317C2211yescharacteristic
64#16840314C2211yescharacteristic
65#16840314C2211yescharacteristic
66#16840295—21no—
67#16840295—21no—
68#16840291—21no—
69C4×#11758226C2211yescharacteristic
70#16840230C2211yescharacteristic
71#16840230C2211yescharacteristic
72C4×#11758224C2211yescharacteristic
73C4×Q8×D61—21no—
74C61×#556C411yescharacteristic
75C2×#11758217—21no—
76C2×#11758217—21no—
77C2×D61⋊C8—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84C4⋊#92420—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87C4⋊#92420C2311yescharacteristic
88C4⋊#92420C2311yescharacteristic
89C4⋊#92420C2311yescharacteristic
90C4⋊#92420C2311yescharacteristic
91#14519834—21no—
92#14519834—21no—
93#14519834—21no—
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96C22⋊#92420—21no—
97C22⋊#92420—21no—
98#14519832—21no—
99#14519832—21no—
100#14519832—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420C2311yescharacteristic
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C2×#11758226C2×C411yescharacteristic
108C2×#11758222C2×C411yescharacteristic
109C2×#11758222C2×C411yescharacteristic
110C2×#11758224D411yescharacteristic
111C2×Q8×D61—21no—
112#14519777C2×C411yescharacteristic
113#14519776C2×C411yescharacteristic
114#14519776C2×C411yescharacteristic
115#14519775C2×C411yescharacteristic
116#14519775C2×C411yescharacteristic
117#14519771—21no—
118#14519771—21no—
119#14519770—21no—
120#14519770—21no—
121#14519769—21no—
122#14519768—21no—
123#14519767—21no—
124#14519767—21no—
125#14519767—21no—
126#14519767—21no—
127#14519763—21no—
128#14519763—21no—
129#14519762—21no—
130#14519762—21no—
131#14519759—21no—
132#14519759—21no—
133#14519759—21no—
134#14519759—21no—
135#14519757C2×C411yescharacteristic
136#14519757C2×C411yescharacteristic
137#14519756C2×C411yescharacteristic
138#14519756C2×C411yescharacteristic
139#14519755—21no—
140#14519755—21no—
141#14519754—21no—
142#14519754—21no—
143#14519753—21no—
144#14519753—21no—
145#14519750—21no—
146#14519750—21no—
147#14519748—21no—
148Q8×Dic61—21no—
149Q8×Dic61C2311yescharacteristic
150C4×Dic122—21no—
151C4×Dic122—21no—
152C4×Dic122—21no—
153C4×Dic122C2×C411yescharacteristic
154#14519742—21no—
155#14519742—21no—
156#14519742C2×C411yescharacteristic
157#14519742C2×C411yescharacteristic
158#14519742D411yescharacteristic
159#14519742C2311yescharacteristic
160#14519742C2311yescharacteristic
161C4×D244—21no—
162C4×D244C2×C411yescharacteristic
163D4×Dic61D411yescharacteristic
164#14519739—21no—
165#14519739C2×C411yescharacteristic
166#14519739C2×C411yescharacteristic
167#14519739C2311yescharacteristic
168C4×C22⋊D61C2×C411yescharacteristic
169C4×C22⋊D61C2×C411yescharacteristic
170#14519737—21no—
171#14519737—21no—
172#14519737—21no—
173#14519737—21no—
174#14519737D411yescharacteristic
175#14519737D411yescharacteristic
176#14519735—21no—
177#14519735—21no—
178#14519735C2×C411yescharacteristic
179#14519735D411yescharacteristic
180#14519734—21no—
181#14519734—21no—
182#14519733—21no—
183#14519733—21no—
184#14519733D411yescharacteristic
185#14519733D411yescharacteristic
186C4⋊C4×D61—21no—
187C4⋊C4×D61—21no—
188C4⋊C4×D61—21no—
189C2×C4×Dic61C2311yescharacteristic
190C2×C4×Dic61C2311yescharacteristic
191C42×D61—21no—
192C42×D61—21no—
193C42×D61—21no—
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic
196#126×C61—21no—
197#126×C61—21no—
198#124×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200C22⋊Q8×C61C2×C411yescharacteristic
201C4×Q8×C61—21no—
202C4×Q8×C61C2×C411yescharacteristic
203C4×D4×C61C2×C411yescharacteristic
204#117×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61C22×C411yescharacteristic
208C2×D4×C61C22⋊C411yescharacteristic
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C22×C411yescharacteristic
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C2×C22⋊D61C22⋊C411yescharacteristic
214C2×C22⋊D61C22⋊C411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219#11758226—22no—
220#11758226—41no—
221Q8×D61—44no—
222#11758224—42no—
223#11758222—22no—
224#11758222—22no—
225#11758222—41no—
226#11758222—41no—
227C2×D244—21no—
228C2×D244C22×C411yescharacteristic
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61C22×C411yescharacteristic
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122C22⋊C411yescharacteristic
242C2×Dic122C22×C411yescharacteristic
243C2×Dic122C22×C411yescharacteristic
244#11758217—42no—
245#11758217—81no—
246C2×#92420—21no—
247C2×#92420—21no—
248C2×#92420—21no—
249C2×#92420—21no—
250C2×#92420—21no—
251C2×#92420—21no—
252C2×#92420—21no—
253C2×#92420—21no—
254C2×#92420—42no—
255C2×#92420—81no—
256D61⋊C8—81no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61C22⋊C411yescharacteristic
262C4⋊C4×C61C22×C411yescharacteristic
263C4⋊C4×C61C22×C411yescharacteristic
264C4⋊C4×C61C22×C411yescharacteristic
265C22⋊C4×C61—21no—
266C22⋊C4×C61—21no—
267C22⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61C22⋊C411yescharacteristic
270C22⋊C4×C61C22⋊C411yescharacteristic
271C42×C61—21no—
272C42×C61—21no—
273C42×C61—21no—
274C42×C61C22×C411yescharacteristic
275C22⋊Dic61—21no—
276C22⋊Dic61—21no—
277C22⋊Dic61C22⋊C411yescharacteristic
278C22⋊Dic61C22⋊C411yescharacteristic
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198C22⋊C411yescharacteristic
287#11758198C22⋊C411yescharacteristic
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61C22⋊C411yescharacteristic
294C4⋊Dic61C22×C411yescharacteristic
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310#11758196C22⋊C411yescharacteristic
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61C22×C411yescharacteristic
318C4×Dic61C22×C411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2411yescharacteristic
326C23×C61C2×C22⋊C411yescharacteristic
327C23×C61C2×C22⋊C411yescharacteristic
328C22×D61—21no—
329C22×D61C2×C22⋊C411yescharacteristic
330Q8×C61—21no—
331Q8×C61—21no—
332Q8×C61—42no—
333D4×C61—41no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C2×C22⋊C411yescharacteristic
344C2×C4×C61C2×C22⋊C411yescharacteristic
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C23×C411yescharacteristic
347C22⋊D61—22no—
348C22⋊D61—41no—
349C22⋊D61—42no—
350C22⋊D61—42no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—22no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—41no—
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61C2×C22⋊C411yescharacteristic
363C2×Dic61C2×C22⋊C411yescharacteristic
364C2×Dic61C2×C22⋊C411yescharacteristic
365C2×Dic61C22×D411yescharacteristic
366C2×Dic61C22×D411yescharacteristic
367D244—21no—
368D244—42no—
369D244#13112yes—
370C4×D61—21no—
371C4×D61—21no—
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—41no—
375C4×D61—42no—
376C4×D61—42no—
377C4×D61—42no—
378C4×D61—42no—
379C4×D61—42no—
380C4×D61—41no—
381C4×D61—41no—
382C4×D61—42no—
383Dic122—22no—
384Dic122—21no—
385Dic122—21no—
386Dic122—21no—
387Dic122—21no—
388Dic122—42no—
389Dic122—42no—
390#92420—41no—
391#92420—41no—
392#92420—41no—
393#92420—41no—
394#92420—41no—
395#92420—41no—
396#92420—41no—
397#92420—41no—
398#17523—611nomaximal, Sylow
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61C22×C22⋊C411yescharacteristic
406C2×D61—21no—
407C2×D61—22no—
408C2×D61—21no—
409C2×D61—21no—
410C2×D61—41no—
411C2×D61—41no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61—41no—
419C4×C61—41no—
420C4×C61C2×#13111yescharacteristic
421C4×C61#56811yescharacteristic
422Dic61—21no—
423Dic61—21no—
424Dic61—21no—
425Dic61—21no—
426Dic61—21no—
427Dic61—41no—
428Dic61—41no—
429Dic61—41no—
430Dic61#42112yes—
431Dic61#57711yescharacteristic
432Dic61#57811yescharacteristic
433#3482—611no—
434#2990—611no—
435#2922—611no—
436#1497—611no—
437#1497—611no—
438#1493—611no—
439#1489—611no—
440#1488—611no—
441#1488—611no—
442#1485—611no—
443#1481—611no—
444#1481—611no—
445#1477—611no—
446#1477—611no—
447#1476—611no—
448C2×C61—41no—
449C2×C61—41no—
450C2×C61#288011yescharacteristic
451C2×C61#289811yescharacteristic
452C2×C61C2×#42111yescharacteristic
453D61—41no—
454D61—42no—
455#557—611no—
456#556—611no—
457#556—611no—
458#556#692311yescharacteristic
459#552—1221no—
460#552—1221no—
461#552—1221no—
462D4×Q8—611no—
463#548—1221no—
464#547—611no—
465#547—611no—
466#547—611no—
467#533—611no—
468#533—611no—
469#533—611no—
470#529—1221no—
471#529—1221no—
472#529—1221no—
473C4×#41—611no—
474C4×#41—611no—
475C4×#41—611no—
476C4×#41—611no—
477C2×C4×Q8—1221no—
478#446—1221no—
479#435—1221no—
480#435—1221no—
481C8×D4—1221no—
482#433—1221no—
483#433—1221no—
484#432—611no—
485#432—611no—
486#431—611no—
487#431—611no—
488#431—611no—
489#431—611no—
490#431—611no—
491#424—1221no—
492#423—611no—
493C2×C4⋊C8—611no—
494C2×C4⋊C8—611no—
495#408—1221no—
496C4×M16—611no—
497C2×C4×C8—611no—
498Q8⋊C8—611no—
499Q8⋊C8—611no—
500Q8⋊C8—611no—
501Q8⋊C8—611no—
502Q8⋊C8—611no—
503Q8⋊C8—611no—
504Q8⋊C8—611no—
505Q8⋊C8—611no—
506Q8⋊C8—611no—
507Q8⋊C8—611no—
508Q8⋊C8—611no—
509Q8⋊C8—611no—
510D4⋊C8—611no—
511D4⋊C8—611no—
512D4⋊C8—611no—
513D4⋊C8—611no—
514C61#1752311yescharacteristic, complemented, Sylow
515C2×#41—611no—
516C2×#41—611no—
517C2×#41—611no—
518C2×#41—611no—
519C22×Q8—1221no—
520C2×M16—1221no—
521C2×M16—1221no—
522C22×C8—1221no—
523C22×C8—1221no—
524C22×C8—1221no—
525C4⋊Q8—611no—
526C4⋊Q8—611no—
527C4⋊Q8—611no—
528C4⋊Q8—611no—
529C4⋊Q8—611no—
530C4⋊Q8C2×#692311yescharacteristic
531#126—21no—
532#126—21no—
533#126—1221no—
534#126—1221no—
535#126—1221no—
536#126—1221no—
537#125—1221no—
538#125—1221no—
539#125—1221no—
540#125—1221no—
541#125—1221no—
542#125—1221no—
543#124—21no—
544#124—1221no—
545#124—1221no—
546#123—1221no—
547#123—1221no—
548#123—1221no—
549#123—1221no—
550#123—1221no—
551#123—1221no—
552C22⋊Q8—611no—
553C22⋊Q8—611no—
554C22⋊Q8—611no—
555C22⋊Q8—611no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561C22⋊Q8—1221no—
562C22⋊Q8C2×#692311yescharacteristic
563C22⋊Q8C2×#692311yescharacteristic
564#121—1221no—
565#121—1221no—
566#121—1221no—
567C4×Q8—21no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—611no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×Q8—1221no—
578C4×Q8—1221no—
579C4×Q8—1221no—
580C4×Q8—1221no—
581C4×Q8C2×#692311yescharacteristic
582C4×D4—611no—
583C4×D4—611no—
584C4×D4—611no—
585C4×D4—611no—
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—611no—
589C4×D4—611no—
590C4×D4—611no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4C2×#692311yescharacteristic
598#117—611no—
599#117—611no—
600#117—611no—
601#117—611no—
602#117—1221no—
603#117—1221no—
604#117—1221no—
605#117—1221no—
606#117—1221no—
607#117—1221no—
608#117C2×#692311yescharacteristic
609#117C2×#692311yescharacteristic
610C2×C4⋊C4—1221no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4—1221no—
613C2×C42—611no—
614C2×C42—611no—
615C2×C42—611no—
616C2×C42—1221no—
617C2×C42—1221no—
618C2×C42—1221no—
619C4⋊C8—611no—
620C4⋊C8—611no—
621C4⋊C8—611no—
622C4⋊C8—611no—
623C4⋊C8—1221no—
624C4⋊C8—1221no—
625C4⋊C8—1221no—
626C4⋊C8—1221no—
627C4⋊C8—1221no—
628C4⋊C8—1221no—
629C4⋊C8—1221no—
630C22⋊C8—1221no—
631C22⋊C8—1221no—
632C22⋊C8—1221no—
633C22⋊C8—1221no—
634C22⋊C8—1221no—
635C22⋊C8—1221no—
636C22⋊C8—1221no—
637#97—1221no—
638#97—1221no—
639#97—1221no—
640C4×C8—611no—
641C4×C8—611no—
642C4×C8—611no—
643C4×C8—611no—
644C4×C8—1221no—
645C4×C8—1221no—
646#41—1222no—
647#41—1222no—
648#41—1222no—
649#41—2441no—
650#41—2441no—
651#41—2442no—
652#41—2441no—
653C2×Q8—21no—
654C2×Q8—611no—
655C2×Q8—611no—
656C2×Q8—611no—
657C2×Q8—1221no—
658C2×Q8—1221no—
659C2×Q8—2444no—
660C2×Q8C22×#692311yescharacteristic
661C2×D4—611no—
662C2×D4—611no—
663C2×D4—611no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4C22⋊#692311yescharacteristic
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4C22×#692311yescharacteristic
683C22×C4C22×#692311yescharacteristic
684M16—4881no—
685M16—2442no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—4881no—
695C2×C8—4881no—
696C2×C8—2442no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—611no—
702C4⋊C4—611no—
703C4⋊C4—611no—
704C4⋊C4—611no—
705C4⋊C4—611no—
706C4⋊C4—611no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4C22⋊#692311yescharacteristic
725C4⋊C4C22×#692311yescharacteristic
726C4⋊C4C22×#692311yescharacteristic
727C4⋊C4C22×#692311yescharacteristic
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—611no—
733C22⋊C4—611no—
734C22⋊C4—611no—
735C22⋊C4—611no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C22⋊C4—1221no—
742C22⋊C4—1221no—
743C22⋊C4—1221no—
744C22⋊C4—1221no—
745C22⋊C4C22⋊#692311yescharacteristic
746C22⋊C4C22⋊#692311yescharacteristic
747C42—21no—
748C42—21no—
749C42—21no—
750C42—611no—
751C42—611no—
752C42—611no—
753C42—611no—
754C42—611no—
755C42—611no—
756C42—611no—
757C42—611no—
758C42—611no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C42—1221no—
763C42—1221no—
764C42—1221no—
765C42C22×#692311yescharacteristic
766C23—611no—
767C23—1221no—
768C23C2×C22⋊#692311yescharacteristic
769C23C2×C22⋊#692311yescharacteristic
770Q8—21no—
771Q8—21no—
772Q8—42no—
773Q8—1222no—
774Q8—1221no—
775Q8—1221no—
776Q8—1221no—
777Q8—1221no—
778Q8—2442no—
779Q8—2442no—
780D4—41no—
781D4—612no—
782D4—1222no—
783D4—1221no—
784D4—2442no—
785D4—2441no—
786D4—2442no—
787D4—2442no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—611no—
797C2×C4—611no—
798C2×C4—611no—
799C2×C4—611no—
800C2×C4—611no—
801C2×C4—611no—
802C2×C4—611no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1222no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—2441no—
816C2×C4—2442no—
817C2×C4—2442no—
818C2×C4—2442no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2442no—
822C2×C4—2442no—
823C2×C4—2442no—
824C2×C4—2441no—
825C2×C4C2×C22⋊#692311yescharacteristic
826C2×C4C2×C22⋊#692311yescharacteristic
827C2×C4C2×C22⋊#692311yescharacteristic
828C2×C4C2×C22⋊#692311yescharacteristic
829C2×C4C23×#692311yescharacteristic
830C8—2441no—
831C8—2441no—
832C8—2441no—
833C8—2441no—
834C8—2441no—
835C8—2441no—
836C8—2441no—
837C8—2441no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—1221no—
845C22—1222no—
846C22—1221no—
847C22—1221no—
848C22—2441no—
849C22—2441no—
850C22C22×C22⋊#692311yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—611no—
860C4—611no—
861C4—612no—
862C4—1221no—
863C4—1221no—
864C4—1221no—
865C4—1221no—
866C4—1221no—
867C4—2441no—
868C4—2441no—
869C4—2441no—
870C4D61⋊#13111yescharacteristic
871C4#1684084111yescharacteristic
872C2—41no—
873C2—41no—
874C2—2441no—
875C2—2442no—
876C2#2146240911yescharacteristic
877C2#2146244111yescharacteristic
878C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#556C4
socleC22×C61C22×C22⋊C4
prime radical#21459438C2
cosocleC4×Dic61C24
hypercenter#556#6923
hypocenterC61#17523
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #21462744C2semidirect
2. #21462502C2semidirect
3. #21461183C2semidirect
4. #21461181C2semidirect
5. #21461167C2semidirect
6. #21461156C2semidirect
7. #21461153C2semidirect
8. #21461152C2semidirect
9. #21461141C2semidirect
10. #21461129C2semidirect
11. #21461127C2semidirect
12. #21461117C2semidirect
13. #21461116C2semidirect
14. #21461112C2semidirect
514. C61#17523semidirect

Maximal subgroups

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

subgroupindex
#214627442
#214625022
#214611832
#214611812
#214611672
#214611562
#214611532
#214611522
#214611412
#214611292
#214611272
#214611172
#214611162
#214611122
#214594382
#1752361