Finite Group Databasebeta

← #30611387

Subgroups — #30611387

Order 15616.

898 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462716C211yesmaximal, characteristic, complemented
2#21462339C211yesmaximal, characteristic, complemented
3#21461263C211yesmaximal, characteristic, complemented
4#21461260C211yesmaximal, characteristic, complemented
5#21461243C211yesmaximal, characteristic, complemented
6#21461238C211yesmaximal, characteristic
7#21461232C211yesmaximal, characteristic, complemented
8#21461231C211yesmaximal, characteristic, complemented
9#21461223C211yesmaximal, characteristic, complemented
10#21461220C211yesmaximal, characteristic, complemented
11#21461213C211yesmaximal, characteristic, complemented
12#21461209C211yesmaximal, characteristic
13#21461192C211yesmaximal, characteristic, complemented
14#21461191C211yesmaximal, characteristic, complemented
15#21459674C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840813—21no—
19#16840812—21no—
20#16840785C2211yescharacteristic
21#16840785C2211yescharacteristic
22#16840784C2211yescharacteristic
23#16840784C2211yescharacteristic
24#16840781C2211yescharacteristic
25#16840780C2211yescharacteristic
26(C2×#6923)⋊Q8—21no—
27#16840711—21no—
28#16840711—21no—
29#16840707C2211yescharacteristic
30#16840707C2211yescharacteristic
31#16840706C2211yescharacteristic
32C4⋊C4×#6923—21no—
33C4×C4⋊#6923C2211yescharacteristic
34#16840698C2211yescharacteristic
35#16840698C2211yescharacteristic
36#16840616C2211yescharacteristic
37#16840616C2211yescharacteristic
38#16840616C2211yescharacteristic
39#16840616C2211yescharacteristic
40#16840616C2211yescharacteristic
41#16840616C2211yescharacteristic
42#16840616C2211yescharacteristic
43#16840616C2211yescharacteristic
44#16840614C2211yescharacteristic
45#16840614C2211yescharacteristic
46#16840614C2211yescharacteristic
47#16840614C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840494C411yescharacteristic, complemented
53#16840494C411yescharacteristic, complemented
54#16840488C411yescharacteristic, complemented
55#16840488C411yescharacteristic, complemented
56#16840486C411yescharacteristic, complemented
57#16840479—21no—
58#16840479—21no—
59#16840472C411yescharacteristic, complemented
60#16840469C411yescharacteristic, complemented
61#16840454—21no—
62#16840451—21no—
63#16840353—21no—
64#16840353—21no—
65#16840335—21no—
66#16840317C2211yescharacteristic
67#16840309C2211yescharacteristic
68#16840299C2211yescharacteristic
69#16840299C2211yescharacteristic
70#16840291C2211yescharacteristic
71#16840291C2211yescharacteristic
72#16840242—21no—
73C4×Q8×D61C2211yescharacteristic
74C61×#556C411yescharacteristic, complemented
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4×#6923—21no—
78C2×C4×#6923—21no—
79C2×C4×#6923—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83C4⋊#92420—21no—
84C4⋊#92420—21no—
85C4⋊#92420—21no—
86#14519834C2311yescharacteristic
87#14519834C2311yescharacteristic
88#14519834C2311yescharacteristic
89#14519834C2311yescharacteristic
90#14519832—21no—
91#14519832—21no—
92#14519832—21no—
93#14519832—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96(C2×#6923)⋊C4—21no—
97(C2×#6923)⋊C4—21no—
98(C2×#6923)⋊C4—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×#11758222—21no—
108C2×Q8×D61D411yescharacteristic
109#14519777C2×C411yescharacteristic
110#14519776—21no—
111#14519776—21no—
112#14519776C2×C411yescharacteristic
113#14519773C2×C411yescharacteristic
114#14519772—21no—
115#14519772—21no—
116#14519772—21no—
117#14519772—21no—
118#14519770—21no—
119#14519770—21no—
120#14519769—21no—
121#14519769—21no—
122#14519769C2×C411yescharacteristic
123#14519769C2×C411yescharacteristic
124#14519768—21no—
125#14519768—21no—
126#14519768—21no—
127#14519768C2×C411yescharacteristic
128#14519768C2×C411yescharacteristic
129#14519766C2×C411yescharacteristic
130#14519766C2×C411yescharacteristic
131#14519763—21no—
132#14519763—21no—
133#14519763—21no—
134#14519762—21no—
135#14519762—21no—
136#14519761—21no—
137#14519761—21no—
138#14519759—21no—
139#14519759—21no—
140#14519759—21no—
141#14519759—21no—
142#14519757—21no—
143#14519757—21no—
144#14519756—21no—
145#14519755—21no—
146#14519755—21no—
147#14519754—21no—
148#14519754—21no—
149#14519753—21no—
150#14519753C2311yescharacteristic
151#14519753C2311yescharacteristic
152#14519752C2311yescharacteristic
153#14519750—21no—
154#14519748C2311yescharacteristic
155Q8×Dic61C2×C411yescharacteristic
156Q8×Dic61C2×C411yescharacteristic
157Q8×Dic61C2×C411yescharacteristic
158Q8×Dic61C2×C411yescharacteristic
159Q8×Dic61D411yescharacteristic
160C4×Dic122—21no—
161C4×Dic122—21no—
162C4×Dic122C2×C411yescharacteristic
163C4×Dic122C2×C411yescharacteristic
164C4×Dic122C2×C411yescharacteristic
165#14519742—21no—
166#14519742D411yescharacteristic
167#14519742D411yescharacteristic
168#14519742D411yescharacteristic
169C4×D244—21no—
170C4×D244—21no—
171C4×D244C2×C411yescharacteristic
172C4×D244C2×C411yescharacteristic
173C4×D244C2×C411yescharacteristic
174D4×Dic61C2×C411yescharacteristic
175D4×Dic61C2×C411yescharacteristic
176C4×C22⋊D61—21no—
177#14519737—21no—
178#14519737—21no—
179#14519737—21no—
180#14519737—21no—
181#14519735—21no—
182#14519735—21no—
183#14519734—21no—
184#14519734—21no—
185#14519733—21no—
186#14519733—21no—
187C2×C4⋊Dic61—21no—
188C4⋊C4×D61—21no—
189C4⋊C4×D61D411yescharacteristic
190C4⋊C4×D61D411yescharacteristic
191C4⋊C4×D61D411yescharacteristic
192C42×D61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61C2×C411yescharacteristic
196#126×C61—21no—
197#126×C61—21no—
198#124×C61C2×C411yescharacteristic
199#124×C61C2×C411yescharacteristic
200C22⋊Q8×C61—21no—
201C4×Q8×C61C2×C411yescharacteristic
202C4×Q8×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205#117×C61—21no—
206C22×#6923—21no—
207C22×#6923—21no—
208C22×#6923—21no—
209C22×#6923—21no—
210C2×Q8×C61C22⋊C411yescharacteristic
211C2×Q8×C61C22×C411yescharacteristic
212C2×Q8×C61C22×C411yescharacteristic
213C2×D4×C61C22×C411yescharacteristic
214C22×C4×C61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220Q8×D61—41no—
221Q8×D61—41no—
222#11758222—42no—
223#11758222—42no—
224C2×D244—21no—
225C2×D244C22×C411yescharacteristic
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2411yescharacteristic
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122C22⋊C411yescharacteristic
239C2×Dic122C22⋊C411yescharacteristic
240C2×Dic122C22⋊C411yescharacteristic
241C2×#92420—21no—
242C2×#92420—21no—
243C2×#92420—21no—
244C2×#92420—21no—
245C4⋊#6923—42no—
246C4⋊#6923—42no—
247C4×#6923—42no—
248C4×#6923—42no—
249C4×#6923—42no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61C22⋊C411yescharacteristic
255C4⋊C4×C61C22⋊C411yescharacteristic
256C4⋊C4×C61C22⋊C411yescharacteristic
257C4⋊C4×C61C22×C411yescharacteristic
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C42×C61—21no—
264C42×C61—21no—
265C42×C61C22×C411yescharacteristic
266C42×C61C22×C411yescharacteristic
267C42×C61C22×C411yescharacteristic
268C22⋊Dic61—21no—
269C22⋊Dic61—21no—
270C22⋊Dic61—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61C22⋊C411yescharacteristic
289C4⋊Dic61C22⋊C411yescharacteristic
290C4⋊Dic61C22⋊C411yescharacteristic
291C4⋊Dic61C22×C411yescharacteristic
292C4⋊Dic61C22×C411yescharacteristic
293C4⋊Dic61C22×C411yescharacteristic
294#11758196—21no—
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#11758196C22⋊C411yescharacteristic
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61C22×C411yescharacteristic
314C4×Dic61C22×C411yescharacteristic
315C4×Dic61C22×C411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C23×C61—21no—
323C22×D61—21no—
324C22×D61C22×D411yescharacteristic
325C2×#6923—22no—
326C2×#6923—41no—
327C2×#6923—41no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333C2×#6923—41no—
334C2×#6923—41no—
335C2×#6923—41no—
336C2×#6923—41no—
337Q8×C61—41no—
338Q8×C61—41no—
339Q8×C61—41no—
340D4×C61—41no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—42no—
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C23×C411yescharacteristic
352C22⋊D61—42no—
353C22⋊D61—41no—
354C22⋊D61—41no—
355C22⋊D61—81no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—81no—
360C2×Dic61—81no—
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61C2×C22⋊C411yescharacteristic
363C2×Dic61C2×C22⋊C411yescharacteristic
364C2×Dic61C2×C22⋊C411yescharacteristic
365C2×Dic61C2×C22⋊C411yescharacteristic
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C22×D411yescharacteristic
368D244—41no—
369D244—41no—
370D244—41no—
371C4×D61—21no—
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—21no—
375C4×D61—21no—
376C4×D61—21no—
377C4×D61—41no—
378C4×D61—41no—
379C4×D61—41no—
380C4×D61—41no—
381C4×D61—42no—
382C4×D61—81no—
383C4×D61—81no—
384Dic122—41no—
385Dic122—41no—
386Dic122—41no—
387Dic122—42no—
388Dic122—81no—
389#92420—41no—
390#92420—41no—
391#92420—41no—
392#92420—41no—
393#17624—611nomaximal, Sylow
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61C22×C22⋊C411yescharacteristic
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61#57511yescharacteristic
404C2×D61#57511yescharacteristic
405#6923—42no—
406#6923—81no—
407#6923—81no—
408#6923—81no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61—41no—
419Dic61—21no—
420Dic61—21no—
421Dic61—21no—
422Dic61—21no—
423Dic61—21no—
424Dic61—21no—
425Dic61—21no—
426Dic61—41no—
427Dic61—41no—
428Dic61—41no—
429#3507—611no—
430#2983—611no—
431#2356—611no—
432#1521—611no—
433#1521—611no—
434#1515—611no—
435#1514—611no—
436#1512—611no—
437#1512—611no—
438#1509—611no—
439#1509—611no—
440#1506—611no—
441#1505—611no—
442#1500—611no—
443#1500—611no—
444C2×C61—81no—
445C2×C61#288411yescharacteristic
446C2×C61#289611yescharacteristic
447C2×C61#290111yescharacteristic
448D61—21no—
449D61—21no—
450D61—81no—
451#559—611no—
452#559—611no—
453#557—611no—
454#557—611no—
455#556—611no—
456#556—1221no—
457#556—1221no—
458#556#692311yescharacteristic, complemented
459#554—611no—
460#554—611no—
461#552—1221no—
462#552—1221no—
463#539—1221no—
464#539—1221no—
465#536—1221no—
466#533—611no—
467#532—611no—
468#529—611no—
469#529—611no—
470#529—611no—
471#529—611no—
472#520—1221no—
473C2×C4×Q8—611no—
474#446—1221no—
475#446—1221no—
476#446—1221no—
477#446—1221no—
478#432—611no—
479#432—611no—
480#432—611no—
481#432—611no—
482#431—611no—
483#431—611no—
484#391—1221no—
485#387—1221no—
486#387—1221no—
487#383—611no—
488#383—611no—
489#382—611no—
490C4×C4⋊C4—611no—
491C4×C4⋊C4—1221no—
492#376—611no—
493#376—611no—
494#328—611no—
495#328—611no—
496#328—611no—
497#328—611no—
498#328—611no—
499#328—611no—
500#328—611no—
501#328—611no—
502#327—611no—
503#327—611no—
504#327—611no—
505#327—611no—
506#327—611no—
507#327—611no—
508#327—611no—
509#327—611no—
510C61#1762411yescharacteristic, complemented, Sylow
511C2×#41—1221no—
512C22×Q8—611no—
513C4⋊Q8—611no—
514C4⋊Q8—611no—
515C4⋊Q8—1221no—
516C4⋊Q8—1221no—
517C4⋊Q8C2×#692311yescharacteristic
518#127—611no—
519#126—21no—
520#126—21no—
521#126—1221no—
522#126—1221no—
523#126—1221no—
524#126—1221no—
525#126—1221no—
526#126—1221no—
527#125—611no—
528#125—611no—
529#125—611no—
530#125—611no—
531#125—1221no—
532#125—1221no—
533#125—1221no—
534#125—1221no—
535#125—1221no—
536#124—611no—
537#124—611no—
538#124—1221no—
539#124—1221no—
540#124—1221no—
541#124C2×#692311yescharacteristic
542#124C2×#692311yescharacteristic
543#123—1221no—
544#123—1221no—
545#123—1221no—
546#123—1221no—
547#123—1221no—
548#123—1221no—
549#123—1221no—
550#123—1221no—
551C22⋊Q8—21no—
552C22⋊Q8—611no—
553C22⋊Q8—611no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561C22⋊Q8—1221no—
562#121—611no—
563#121—611no—
564#121—1221no—
565C4×Q8—611no—
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—611no—
575C4×Q8—611no—
576C4×Q8—1221no—
577C4×Q8—1221no—
578C4×Q8—1221no—
579C4×Q8C2×#692311yescharacteristic
580C4×Q8C2×#692311yescharacteristic
581C4×Q8C2×#692311yescharacteristic
582C4×D4—611no—
583C4×D4—611no—
584C4×D4—611no—
585C4×D4—611no—
586C4×D4—611no—
587C4×D4—1221no—
588C4×D4—1221no—
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4C2×#692311yescharacteristic
595#117—21no—
596#117—1221no—
597#117—1221no—
598#117—1221no—
599#117—1221no—
600#117—1221no—
601#117—1221no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4—1221no—
607C2×C4⋊C4—1221no—
608C2×C4⋊C4—1221no—
609C2×C42—611no—
610C2×C42—611no—
611C2×C42—611no—
612C2×C42—1221no—
613C2×C42—1221no—
614C2×C42—1221no—
615C4⋊C8—1221no—
616C4⋊C8—1221no—
617C4⋊C8—1221no—
618C4⋊C8—1221no—
619C4⋊C8—1221no—
620C4⋊C8—1221no—
621C22⋊C8—611no—
622C22⋊C8—611no—
623C22⋊C8—611no—
624C22⋊C8—611no—
625#97—1221no—
626#97—1221no—
627#97—1221no—
628#97—1221no—
629C4×C8—1221no—
630C4×C8—1221no—
631#95—611no—
632#95—611no—
633#95—611no—
634#95—611no—
635#95—1221no—
636#95—1221no—
637#95—1221no—
638#95—1221no—
639#95—1221no—
640#95—1221no—
641#95—1221no—
642#41—2442no—
643#41—2442no—
644C2×Q8—611no—
645C2×Q8—611no—
646C2×Q8—611no—
647C2×Q8—1221no—
648C2×Q8—1221no—
649C2×Q8—2441no—
650C2×Q8—2441no—
651C2×Q8C22⋊#692311yescharacteristic
652C2×Q8C22×#692311yescharacteristic
653C2×Q8C22×#692311yescharacteristic
654C2×D4—611no—
655C2×D4—1221no—
656C2×D4—1221no—
657C2×D4—1221no—
658C2×D4—1221no—
659C2×D4C22×#692311yescharacteristic
660C22×C4—21no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—611no—
686C4⋊C4—611no—
687C4⋊C4—611no—
688C4⋊C4—611no—
689C4⋊C4—611no—
690C4⋊C4—611no—
691C4⋊C4—611no—
692C4⋊C4—611no—
693C4⋊C4—611no—
694C4⋊C4—611no—
695C4⋊C4—611no—
696C4⋊C4—611no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
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—2442no—
714C4⋊C4—2442no—
715C4⋊C4C22⋊#692311yescharacteristic
716C4⋊C4C22⋊#692311yescharacteristic
717C4⋊C4C22⋊#692311yescharacteristic
718C4⋊C4C22×#692311yescharacteristic
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C42—21no—
738C42—21no—
739C42—611no—
740C42—611no—
741C42—611no—
742C42—611no—
743C42—611no—
744C42—611no—
745C42—611no—
746C42—611no—
747C42—611no—
748C42—1221no—
749C42—1221no—
750C42—1221no—
751C42—1221no—
752C42—2442no—
753C42—2442no—
754C42—2442no—
755C42C22×#692311yescharacteristic
756C42C22×#692311yescharacteristic
757C42C22×#692311yescharacteristic
758C23—21no—
759C23—611no—
760C23—1221no—
761Q8—41no—
762Q8—41no—
763Q8—41no—
764Q8—4881no—
765Q8—2441no—
766Q8—2441no—
767Q8—2441no—
768Q8—2442no—
769D4—41no—
770D4—4881no—
771D4—2441no—
772D4—2441no—
773D4—2441no—
774D4—2442no—
775D4—2441no—
776D4—2441no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—42no—
781C2×C4—611no—
782C2×C4—611no—
783C2×C4—611no—
784C2×C4—611no—
785C2×C4—611no—
786C2×C4—611no—
787C2×C4—611no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1222no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—4881no—
799C2×C4—4881no—
800C2×C4—4881no—
801C2×C4—4881no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2442no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4C2×C22⋊#692311yescharacteristic
819C2×C4C2×C22⋊#692311yescharacteristic
820C2×C4C2×C22⋊#692311yescharacteristic
821C2×C4C2×C22⋊#692311yescharacteristic
822C2×C4C2×C22⋊#692311yescharacteristic
823C2×C4C2×C22⋊#692311yescharacteristic
824C2×C4C23×#692311yescharacteristic
825C8—2441no—
826C8—2441no—
827C8—2441no—
828C8—2441no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—611no—
833C22—611no—
834C22—1221no—
835C22—1221no—
836C22—2441no—
837C22—2441no—
838C22—2441no—
839C22C22×C22⋊#692311yescharacteristic
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—21no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—1221no—
851C4—1221no—
852C4—1221no—
853C4—1221no—
854C4—1221no—
855C4—1221no—
856C4—1221no—
857C4—4881no—
858C4—4881no—
859C4—4881no—
860C4—2442no—
861C4—2441no—
862C4—2441no—
863C4—2441no—
864C2—81no—
865C2—1221no—
866C2—1221no—
867C2—4881no—
868C2#2146242111yescharacteristic
869C2#2146243911yescharacteristic
870C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#556C4
socleC22×C61C22×C22⋊C4
prime radical#16840309C22
cosocleC2×C4×D61C24
hypercenter#556#6923
hypocenterC61#17624
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #21462716C2semidirect
2. #21462339C2semidirect
3. #21461263C2semidirect
4. #21461260C2semidirect
5. #21461243C2semidirect
7. #21461232C2semidirect
8. #21461231C2semidirect
9. #21461223C2semidirect
10. #21461220C2semidirect
11. #21461213C2semidirect
13. #21461192C2semidirect
14. #21461191C2semidirect
52. #16840494C4semidirect
53. #16840494C4semidirect
54. #16840488C4semidirect
55. #16840488C4semidirect
56. #16840486C4semidirect
59. #16840472C4semidirect
60. #16840469C4semidirect
74. C61×#556C4semidirect
458. #556#6923semidirect
510. C61#17624semidirect

Maximal subgroups

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

subgroupindex
#214627162
#214623392
#214612632
#214612602
#214612432
#214612382
#214612322
#214612312
#214612232
#214612202
#214612132
#214612092
#214611922
#214611912
#214596742
#1762461