Finite Group Databasebeta

← #30611308

Subgroups — #30611308

Order 15616.

930 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462511C211yesmaximal, characteristic, complemented
2#21462329C211yesmaximal, characteristic, complemented
3#21461257C211yesmaximal, characteristic, complemented
4#21461252C211yesmaximal, characteristic, complemented
5#21461251C211yesmaximal, characteristic, complemented
6#21461235C211yesmaximal, characteristic
7#21461231C211yesmaximal, characteristic, complemented
8#21461230C211yesmaximal, characteristic, complemented
9#21461217C211yesmaximal, characteristic, complemented
10#21461212C211yesmaximal, characteristic, complemented
11#21461211C211yesmaximal, characteristic, complemented
12#21461195C211yesmaximal, characteristic
13#21461191C211yesmaximal, characteristic, complemented
14#21461190C211yesmaximal, characteristic, complemented
15#21459569C211yesmaximal, characteristic
16#16840787—21no—
17#16840787—21no—
18#16840785C2211yescharacteristic
19#16840784C2211yescharacteristic
20#16840781C2211yescharacteristic
21#16840780C2211yescharacteristic
22#16840768—21no—
23#16840734C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25#16840726—21no—
26#16840713—21no—
27#16840712—21no—
28#16840712—21no—
29#16840706C2211yescharacteristic
30#16840706C2211yescharacteristic
31#16840704C2211yescharacteristic
32C4⋊C4×#6923—21no—
33C4×C22⋊#6923C2211yescharacteristic
34#16840698C2211yescharacteristic
35#16840698C2211yescharacteristic
36#16840616C2211yescharacteristic
37#16840616C2211yescharacteristic
38#16840616C2211yescharacteristic
39#16840616C2211yescharacteristic
40#16840615C2211yescharacteristic
41#16840615C2211yescharacteristic
42#16840615C2211yescharacteristic
43#16840615C2211yescharacteristic
44#16840615C2211yescharacteristic
45#16840615C2211yescharacteristic
46#16840615C2211yescharacteristic
47#16840615C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840481—21no—
53#16840466—21no—
54#16840449—21no—
55#16840448—21no—
56#16840448—21no—
57#16840446—21no—
58#16840442—21no—
59#16840440—21no—
60#16840389C411yescharacteristic, complemented
61#16840379C411yescharacteristic, complemented
62#16840374C411yescharacteristic, complemented
63#16840372C411yescharacteristic, complemented
64#16840332C411yescharacteristic, complemented
65#16840317C2211yescharacteristic
66#16840316C2211yescharacteristic
67#16840294C2211yescharacteristic
68#16840291C2211yescharacteristic
69#16840272C2211yescharacteristic
70C22⋊Q8×D61C2211yescharacteristic
71#16840241C411yescharacteristic, complemented
72#16840238C411yescharacteristic, complemented
73#117×D61C2211yescharacteristic
74C61×#542C411yescharacteristic, complemented
75C2×#11758217—21no—
76C22×#92420—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923—21no—
80C2×C22⋊#6923—21no—
81C2×C22⋊#6923—21no—
82C2×C4×#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923—21no—
85#14519844—21no—
86#14519844—21no—
87C4⋊#92420—21no—
88C4⋊#92420—21no—
89#14519834—21no—
90#14519834—21no—
91#14519834C2311yescharacteristic
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94#14519834C2311yescharacteristic
95#14519832—21no—
96#14519832—21no—
97C4×#92420—21no—
98C4×#92420—21no—
99(C2×#6923)⋊C4—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4C2311yescharacteristic
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107C2×#11758224C2×C411yescharacteristic
108C2×Q8×D61C2×C411yescharacteristic
109C22×C4×D61C2311yescharacteristic
110#14519777C2×C411yescharacteristic
111#14519776C2×C411yescharacteristic
112#14519775—21no—
113#14519775C2×C411yescharacteristic
114#14519770—21no—
115#14519770—21no—
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519770—21no—
120#14519770—21no—
121#14519769C2×C411yescharacteristic
122#14519768—21no—
123#14519768—21no—
124#14519768C2×C411yescharacteristic
125#14519767—21no—
126#14519767—21no—
127#14519767—21no—
128#14519767—21no—
129#14519767—21no—
130#14519764—21no—
131#14519764C2×C411yescharacteristic
132#14519759—21no—
133#14519759—21no—
134#14519759—21no—
135#14519759—21no—
136#14519759—21no—
137#14519758—21no—
138#14519757C2311yescharacteristic
139#14519757C2311yescharacteristic
140#14519756C2×C411yescharacteristic
141#14519756C2×C411yescharacteristic
142#14519755—21no—
143#14519755—21no—
144#14519755—21no—
145#14519754—21no—
146#14519754—21no—
147#14519754—21no—
148#14519754—21no—
149#14519753—21no—
150#14519753—21no—
151#14519753C2311yescharacteristic
152#14519748C2311yescharacteristic
153#14519745—21no—
154Q8×Dic61—21no—
155Q8×Dic61C2×C411yescharacteristic
156C4×Dic122—21no—
157C4×Dic122—21no—
158C4×Dic122C2×C411yescharacteristic
159C4×Dic122C2×C411yescharacteristic
160#14519742—21no—
161#14519742C2×C411yescharacteristic
162#14519742C2×C411yescharacteristic
163D4×Dic61—21no—
164D4×Dic61C2×C411yescharacteristic
165C4×C22⋊D61—21no—
166C4×C22⋊D61—21no—
167#14519737—21no—
168#14519737—21no—
169#14519737—21no—
170#14519736—21no—
171#14519736C2×C411yescharacteristic
172#14519735—21no—
173#14519735—21no—
174#14519735C2×C411yescharacteristic
175#14519735D411yescharacteristic
176#14519735D411yescharacteristic
177#14519734—21no—
178#14519734—21no—
179#14519734C2×C411yescharacteristic
180#14519734C2×C411yescharacteristic
181#14519733—21no—
182#14519733—21no—
183#14519733D411yescharacteristic
184#14519733D411yescharacteristic
185C2×#11758196—21no—
186C4⋊C4×D61—21no—
187C4⋊C4×D61C2×C411yescharacteristic
188C4⋊C4×D61D411yescharacteristic
189C4⋊C4×D61D411yescharacteristic
190C22⋊C4×D61—21no—
191C22⋊C4×D61D411yescharacteristic
192C22⋊C4×D61D411yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic
196#126×C61—21no—
197#124×C61—21no—
198#124×C61C2×C411yescharacteristic
199#123×C61—21no—
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61C2×C411yescharacteristic
202#121×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic
206C23×D61C2×D411yescharacteristic
207C22×#6923—21no—
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C2×Q8×C61—21no—
212C2×Q8×C61C22×C411yescharacteristic
213C2×D4×C61—21no—
214C2×D4×C61C22×C411yescharacteristic
215C22×C4×C61—21no—
216C22×C4×C61C22×C411yescharacteristic
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61C2×D411yescharacteristic
222Q8×D61—42no—
223#11758224—42no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—42no—
227C2×C4×D61C22×C411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2411yescharacteristic
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122C22×C411yescharacteristic
238C2×Dic122C22×C411yescharacteristic
239C22⋊#6923—42no—
240C22⋊#6923—81no—
241#11758217—42no—
242C2×#92420—21no—
243C2×#92420—21no—
244C2×#92420—21no—
245C2×#92420—21no—
246C2×#92420—42no—
247C4⋊#6923—42no—
248C4⋊#6923—81no—
249C4⋊#6923—81no—
250C4×#6923—42no—
251C4×#6923—42no—
252C4×#6923—42no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61C22⋊C411yescharacteristic
257C4⋊C4×C61C22⋊C411yescharacteristic
258C4⋊C4×C61C22×C411yescharacteristic
259C4⋊C4×C61C22×C411yescharacteristic
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61C22⋊C411yescharacteristic
266C22⋊C4×C61C22⋊C411yescharacteristic
267C42×C61—21no—
268C42×C61C22×C411yescharacteristic
269C42×C61C22×C411yescharacteristic
270C22⋊Dic61—21no—
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276C22⋊Dic61C22⋊C411yescharacteristic
277C22⋊Dic61C22⋊C411yescharacteristic
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198C22⋊C411yescharacteristic
283#11758198C22⋊C411yescharacteristic
284#11758198C22⋊C411yescharacteristic
285#11758198C22⋊C411yescharacteristic
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61C22⋊C411yescharacteristic
293C4⋊Dic61C22⋊C411yescharacteristic
294C4⋊Dic61C22×C411yescharacteristic
295C4⋊Dic61C22×C411yescharacteristic
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#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313#11758196C22⋊C411yescharacteristic
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61C22×C411yescharacteristic
321C4×Dic61C22×C411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326C23×C61—21no—
327C23×C61C2×C22⋊C411yescharacteristic
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61C2×C22⋊C411yescharacteristic
333C22×D61C22×D411yescharacteristic
334C2×#6923—22no—
335C2×#6923—41no—
336C2×#6923—41no—
337C2×#6923—41no—
338C2×#6923—41no—
339C2×#6923—41no—
340C2×#6923—41no—
341C2×#6923—41no—
342C2×#6923—41no—
343C2×#6923—41no—
344C2×#6923—41no—
345C2×#6923—41no—
346Q8×C61—41no—
347Q8×C61—81no—
348D4×C61—41no—
349D4×C61—81no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—41no—
354C2×C4×C61—81no—
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C2×C22⋊C411yescharacteristic
357C2×C4×C61C2×C22⋊C411yescharacteristic
358C2×C4×C61C2×C22⋊C411yescharacteristic
359C2×C4×C61C2×C22⋊C411yescharacteristic
360C2×C4×C61C23×C411yescharacteristic
361C22⋊D61—42no—
362C22⋊D61—41no—
363C22⋊D61—41no—
364C2×Dic61—22no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—42no—
370C2×Dic61—81no—
371C2×Dic61C2×C22⋊C411yescharacteristic
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C22×D411yescharacteristic
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—21no—
380C4×D61—21no—
381C4×D61—22no—
382C4×D61—22no—
383C4×D61—41no—
384C4×D61—41no—
385C4×D61—41no—
386C4×D61—41no—
387C4×D61—42no—
388C4×D61—81no—
389Dic122—42no—
390Dic122—41no—
391Dic122—41no—
392Dic122—81no—
393#92420—41no—
394#92420—41no—
395#92420—41no—
396#92420—41no—
397#17605—611nomaximal, Sylow
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61C22×C22⋊C411yescharacteristic
405C2×D61—21no—
406C2×D61—21no—
407C2×D61—21no—
408C2×D61—21no—
409C2×D61—21no—
410C2×D61—81no—
411C2×D61—81no—
412C2×D61#57711yescharacteristic
413C2×D61#57811yescharacteristic
414#6923—42no—
415#6923—81no—
416#6923—81no—
417#6923—81no—
418C4×C61—21no—
419C4×C61—21no—
420C4×C61—21no—
421C4×C61—21no—
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—41no—
425C4×C61—41no—
426C4×C61—41no—
427Dic61—21no—
428Dic61—21no—
429Dic61—21no—
430Dic61—21no—
431Dic61—21no—
432Dic61—41no—
433Dic61—41no—
434Dic61—41no—
435Dic61—41no—
436Dic61#41012yes—
437#3495—611no—
438#2924—611no—
439#2346—611no—
440#1520—611no—
441#1518—611no—
442#1518—611no—
443#1513—611no—
444#1512—611no—
445#1512—611no—
446#1508—611no—
447#1506—611no—
448#1506—611no—
449#1501—611no—
450#1500—611no—
451#1500—611no—
452C2×C61—41no—
453C2×C61—81no—
454C2×C61C2×#41011yescharacteristic
455C2×C61#289811yescharacteristic
456C2×C61#290111yescharacteristic
457D61—21no—
458D61—21no—
459D61—41no—
460#556—1221no—
461#554—1221no—
462#552—1221no—
463#552—1221no—
464#552—1221no—
465#552—1221no—
466#551—1221no—
467#551—1221no—
468#544—611no—
469#542—611no—
470#542#692311yescharacteristic, complemented
471#541—611no—
472#541—611no—
473#536—611no—
474#533—611no—
475#533—611no—
476#529—611no—
477#529—611no—
478#525—611no—
479C2×C22⋊Q8—611no—
480#520—611no—
481#519—611no—
482C2×#117—611no—
483#433—1221no—
484#433—1221no—
485#432—611no—
486#432—611no—
487#431—611no—
488#431—611no—
489#424—1221no—
490#407—611no—
491C2×C22⋊C8—611no—
492#405—1221no—
493#389—1221no—
494#388—1221no—
495#388—1221no—
496#382—611no—
497#382—611no—
498#380—611no—
499C4×C4⋊C4—1221no—
500C4×C22⋊C4—611no—
501#376—611no—
502#376—611no—
503#328—611no—
504#328—611no—
505#328—611no—
506#328—611no—
507#328—611no—
508#328—611no—
509#328—611no—
510#328—611no—
511#328—611no—
512#328—611no—
513#328—611no—
514#328—611no—
515#327—611no—
516#327—611no—
517#327—611no—
518#327—611no—
519C61#1760511yescharacteristic, complemented, Sylow
520C2×#41—611no—
521C22×Q8—611no—
522C23×C4—611no—
523C2×M16—1221no—
524C22×C8—1221no—
525C4⋊Q8—611no—
526C4⋊Q8—611no—
527C4⋊Q8—611no—
528C4⋊Q8—1221no—
529C4⋊Q8C2×#692311yescharacteristic
530#126—21no—
531#126—1221no—
532#126—1221no—
533#126—1221no—
534#126—1221no—
535#126—1221no—
536#126—1221no—
537#126—1221no—
538#125—611no—
539#125—611no—
540#125—1221no—
541#125—1221no—
542#125—1221no—
543#125—1221no—
544#125—1221no—
545#125—1221no—
546#125—1221no—
547#124—21no—
548#124—611no—
549#124—1221no—
550#124C2×#692311yescharacteristic
551#123—21no—
552#123—1221no—
553#123—1221no—
554#123—1221no—
555#123—1221no—
556#123—1221no—
557#123—1221no—
558C22⋊Q8—21no—
559C22⋊Q8—611no—
560C22⋊Q8—611no—
561C22⋊Q8—611no—
562C22⋊Q8—611no—
563C22⋊Q8—611no—
564C22⋊Q8—1221no—
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8C2×#692311yescharacteristic
574#121—611no—
575#121C2×#692311yescharacteristic
576#120—1221no—
577C4×Q8—611no—
578C4×Q8—611no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—1221no—
583C4×Q8—1221no—
584C4×Q8—1221no—
585C4×Q8—1221no—
586C4×Q8C2×#692311yescharacteristic
587C4×D4—611no—
588C4×D4—1221no—
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4C2×#692311yescharacteristic
595#117—611no—
596#117—611no—
597#117—611no—
598#117—611no—
599#117—611no—
600#117—611no—
601#117—611no—
602#117—611no—
603#117—1221no—
604#117—1221no—
605#117—1221no—
606#117—1221no—
607#117—1221no—
608#117—1221no—
609#117—1221no—
610#117C2×#692311yescharacteristic
611C2×C4⋊C4—611no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—611no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—1221no—
619C2×C22⋊C4—611no—
620C2×C22⋊C4—611no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42—1221no—
627C2×C42—1221no—
628C2×C42—1221no—
629C4⋊C8—1221no—
630C4⋊C8—1221no—
631C4⋊C8—1221no—
632C4⋊C8—1221no—
633C22⋊C8—611no—
634C22⋊C8—611no—
635C22⋊C8—611no—
636C22⋊C8—611no—
637C22⋊C8—1221no—
638C22⋊C8—1221no—
639#97—1221no—
640#97—1221no—
641C4×C8—1221no—
642C4×C8—1221no—
643#95—611no—
644#95—611no—
645#95—611no—
646#95—611no—
647#95—1221no—
648#95—1221no—
649#95—1221no—
650#95—1221no—
651C24—611no—
652#41—2442no—
653C2×Q8—21no—
654C2×Q8—611no—
655C2×Q8—611no—
656C2×Q8—1221no—
657C2×Q8—1221no—
658C2×Q8—2442no—
659C2×Q8C22×#692311yescharacteristic
660C2×D4—21no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4C22×#692311yescharacteristic
664C22×C4—21no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—2442no—
683C22×C4C22×#692311yescharacteristic
684M16—2442no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—2442no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—611no—
694C4⋊C4—611no—
695C4⋊C4—611no—
696C4⋊C4—611no—
697C4⋊C4—611no—
698C4⋊C4—611no—
699C4⋊C4—611no—
700C4⋊C4—611no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
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—4881no—
722C4⋊C4—4881no—
723C4⋊C4—2442no—
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—21no—
733C22⋊C4—611no—
734C22⋊C4—611no—
735C22⋊C4—611no—
736C22⋊C4—611no—
737C22⋊C4—611no—
738C22⋊C4—611no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C22⋊C4—1221no—
742C22⋊C4—1221no—
743C22⋊C4—1221no—
744C22⋊C4—1221no—
745C22⋊C4—1221no—
746C22⋊C4—1221no—
747C22⋊C4—1221no—
748C22⋊C4—1221no—
749C22⋊C4—4881no—
750C22⋊C4—2442no—
751C22⋊C4C22⋊#692311yescharacteristic
752C22⋊C4C22⋊#692311yescharacteristic
753C42—21no—
754C42—611no—
755C42—611no—
756C42—611no—
757C42—611no—
758C42—611no—
759C42—611no—
760C42—1221no—
761C42—1221no—
762C42—1221no—
763C42—1221no—
764C42—1221no—
765C42—1221no—
766C42—2442no—
767C42—2442no—
768C42—2442no—
769C42C22×#692311yescharacteristic
770C42C22×#692311yescharacteristic
771C23—21no—
772C23—611no—
773C23—611no—
774C23—1221no—
775C23—1221no—
776C23—2441no—
777C23—2441no—
778C23C2×C22⋊#692311yescharacteristic
779Q8—41no—
780Q8—81no—
781Q8—4881no—
782Q8—2441no—
783Q8—2441no—
784Q8—2442no—
785D4—41no—
786D4—81no—
787D4—2441no—
788D4—2441no—
789D4—2442no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—41no—
794C2×C4—81no—
795C2×C4—611no—
796C2×C4—611no—
797C2×C4—611no—
798C2×C4—611no—
799C2×C4—611no—
800C2×C4—611no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—4881no—
814C2×C4—4881no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2442no—
820C2×C4—2442no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4C2×C22⋊#692311yescharacteristic
833C2×C4C2×C22⋊#692311yescharacteristic
834C2×C4C2×C22⋊#692311yescharacteristic
835C2×C4C2×C22⋊#692311yescharacteristic
836C2×C4C2×C22⋊#692311yescharacteristic
837C2×C4C23×#692311yescharacteristic
838C8—2441no—
839C8—2441no—
840C8—2441no—
841C8—2441no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—611no—
849C22—611no—
850C22—1221no—
851C22—1221no—
852C22—1221no—
853C22—1221no—
854C22—1221no—
855C22—4881no—
856C22—4881no—
857C22C22×C22⋊#692311yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—612no—
868C4—1221no—
869C4—1221no—
870C4—1221no—
871C4—1221no—
872C4—1221no—
873C4—4881no—
874C4—4881no—
875C4—4881no—
876C4—2442no—
877C4—2441no—
878C4—2441no—
879C4—2441no—
880C4—2441no—
881C2—41no—
882C2—81no—
883C2—1221no—
884C2—1221no—
885C2—2441no—
886C2D61⋊#41011yescharacteristic
887C2#2146244111yescharacteristic
888C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#542C4
socleC22×C61C22×C22⋊C4
prime radical#16840272C22
cosocleC2×C4×D61C24
hypercenter#542#6923
hypocenterC61#17605
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #21462511C2semidirect
2. #21462329C2semidirect
3. #21461257C2semidirect
4. #21461252C2semidirect
5. #21461251C2semidirect
7. #21461231C2semidirect
8. #21461230C2semidirect
9. #21461217C2semidirect
10. #21461212C2semidirect
11. #21461211C2semidirect
13. #21461191C2semidirect
14. #21461190C2semidirect
60. #16840389C4semidirect
61. #16840379C4semidirect
62. #16840374C4semidirect
63. #16840372C4semidirect
64. #16840332C4semidirect
71. #16840241C4semidirect
72. #16840238C4semidirect
74. C61×#542C4semidirect
470. #542#6923semidirect
519. C61#17605semidirect

Maximal subgroups

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

subgroupindex
#214625112
#214623292
#214612572
#214612522
#214612512
#214612352
#214612312
#214612302
#214612172
#214612122
#214612112
#214611952
#214611912
#214611902
#214595692
#1760561