Finite Group Databasebeta

← #30611630

Subgroups — #30611630

Order 15616.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462659C211yesmaximal, characteristic, complemented
2#21462505C211yesmaximal, characteristic, complemented
3#21461309C211yesmaximal, characteristic, complemented
4#21461306C211yesmaximal, characteristic, complemented
5#21461305C211yesmaximal, characteristic, complemented
6#21461300C211yesmaximal, characteristic, complemented
7#21461297C211yesmaximal, characteristic, complemented
8#21461296C211yesmaximal, characteristic, complemented
9#21461290C211yesmaximal, characteristic, complemented
10#21461287C211yesmaximal, characteristic, complemented
11#21461280C211yesmaximal, characteristic, complemented
12#21461280C211yesmaximal, characteristic, complemented
13#21461272C211yesmaximal, characteristic, complemented
14C2×#16840618C211yesmaximal, characteristic, complemented
15#21459781C211yesmaximal, characteristic
16#16840814—21no—
17#16840794—21no—
18#16840793—21no—
19#16840789—21no—
20#16840787—21no—
21#16840786—21no—
22#16840785C2211yescharacteristic, complemented
23#16840785C2211yescharacteristic, complemented
24#16840784C2211yescharacteristic, complemented
25#16840783C2211yescharacteristic, complemented
26#16840783C2211yescharacteristic, complemented
27#16840782C2211yescharacteristic, complemented
28#16840782C2211yescharacteristic, complemented
29#16840768—21no—
30#16840735—21no—
31C4×#11758217C2211yescharacteristic, complemented
32C4×#11758217C2211yescharacteristic, complemented
33#16840721C2211yescharacteristic, complemented
34C2×#14519832C2211yescharacteristic, complemented
35C2×#14519832C2211yescharacteristic, complemented
36#16840619C2211yescharacteristic, complemented
37#16840619C2211yescharacteristic, complemented
38#16840619C2211yescharacteristic, complemented
39#16840619C2211yescharacteristic, complemented
40#16840618C2211yescharacteristic
41#16840618C2211yescharacteristic
42#16840618C2211yescharacteristic
43#16840618C2211yescharacteristic
44#16840618C2211yescharacteristic, complemented
45#16840618C2211yescharacteristic, complemented
46#16840618C2211yescharacteristic, complemented
47#16840618C2211yescharacteristic, complemented
48#16840618C2211yescharacteristic, complemented
49#16840618C2211yescharacteristic, complemented
50#16840618C2211yescharacteristic, complemented
51#16840618C2211yescharacteristic, complemented
52#16840497C411yescharacteristic
53#16840486C411yescharacteristic
54#16840478—21no—
55#16840439—21no—
56#16840439—21no—
57#16840423C411yescharacteristic
58#16840423C411yescharacteristic
59#16840407—21no—
60#16840403C411yescharacteristic
61#16840403C411yescharacteristic
62D4×D244C411yescharacteristic
63#16840386—21no—
64#16840352—21no—
65#16840352—21no—
66#16840313C2211yescharacteristic
67#16840299C2211yescharacteristic
68#16840298C2211yescharacteristic
69#16840298C2211yescharacteristic
70C2×#14519766C2211yescharacteristic
71C2×#14519766C2211yescharacteristic
72#16840234—21no—
73C4×#11758224C2211yescharacteristic
74D4×Q8×C61C411yescharacteristic
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—
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90C22⋊#92420—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93C22⋊#92420—21no—
94#14519832—21no—
95#14519832—21no—
96#14519832—21no—
97#14519832C2311yescharacteristic
98#14519832C2311yescharacteristic
99#14519832C2311yescharacteristic
100#14519832C2311yescharacteristic
101#14519832C2311yescharacteristic
102#14519832C2311yescharacteristic
103#14519832C2311yescharacteristic
104#14519832C2311yescharacteristic
105C4×#92420—21no—
106C4×#92420—21no—
107C2×#11758226C2×C411yescharacteristic
108C2×#11758226C2×C411yescharacteristic
109C2×#11758224D411yescharacteristic
110C22×D244C2×C411yescharacteristic
111C22×D244C2×C411yescharacteristic
112C2×D4×D61—21no—
113#14519774C2×C411yescharacteristic
114#14519772—21no—
115#14519772—21no—
116#14519772—21no—
117#14519772—21no—
118#14519772—21no—
119#14519768C2311yescharacteristic
120#14519766—21no—
121#14519766—21no—
122#14519766—21no—
123#14519766—21no—
124#14519766—21no—
125#14519766—21no—
126#14519766C2×C411yescharacteristic
127#14519766C2×C411yescharacteristic
128#14519766C2×C411yescharacteristic
129#14519766C2×C411yescharacteristic
130#14519766C2311yescharacteristic
131#14519766C2311yescharacteristic
132#14519766C2311yescharacteristic
133#14519765—21no—
134#14519762—21no—
135#14519762—21no—
136#14519762—21no—
137#14519762—21no—
138#14519762—21no—
139#14519761—21no—
140#14519761—21no—
141#14519757—21no—
142#14519753—21no—
143#14519753—21no—
144#14519753C2×C411yescharacteristic
145#14519752—21no—
146#14519752—21no—
147#14519752—21no—
148#14519752—21no—
149#14519752—21no—
150#14519752C2×C411yescharacteristic
151#14519751—21no—
152#14519751—21no—
153#14519751C2×C411yescharacteristic
154#14519751C2×C411yescharacteristic
155#14519747—21no—
156#14519747—21no—
157#14519747—21no—
158#14519747—21no—
159Q8×Dic61C2×C411yescharacteristic
160Q8×Dic61C2×C411yescharacteristic
161C4×Dic122C2×C411yescharacteristic
162#14519742D411yescharacteristic
163C4×D244—21no—
164C4×D244—21no—
165C4×D244C2×C411yescharacteristic
166D4×Dic61D411yescharacteristic
167#14519739—21no—
168#14519739—21no—
169#14519739C2×C411yescharacteristic
170#14519739C2×C411yescharacteristic
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61C2×C411yescharacteristic
174C4×C22⋊D61C2×C411yescharacteristic
175#14519737—21no—
176#14519737—21no—
177#14519737D411yescharacteristic
178#14519737D411yescharacteristic
179#14519735—21no—
180#14519735—21no—
181#14519735—21no—
182#14519735D411yescharacteristic
183#14519734—21no—
184#14519733D411yescharacteristic
185#14519733D411yescharacteristic
186C2×#11758198—21no—
187C2×#11758198—21no—
188C2×#11758198—21no—
189C2×#11758198—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C22×Q8×C61C2×C411yescharacteristic
196C22×Q8×C61C2×C411yescharacteristic
197C4⋊Q8×C61—21no—
198C4⋊Q8×C61C2×C411yescharacteristic
199C22⋊Q8×C61—21no—
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61C2×C411yescharacteristic
202C22⋊Q8×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204C4×D4×C61—21no—
205C4×D4×C61C2×C411yescharacteristic
206C23×D61—21no—
207C23×D61—21no—
208C2×Q8×C61—21no—
209C2×Q8×C61—21no—
210C2×Q8×C61—81no—
211C2×Q8×C61—81no—
212C2×Q8×C61C22×C411yescharacteristic
213C2×Q8×C61C22×C411yescharacteristic
214C2×Q8×C61C22×C411yescharacteristic
215C2×D4×C61C22⋊C411yescharacteristic
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61C22⋊C411yescharacteristic
223C2×C22⋊D61C22⋊C411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228#11758226—81no—
229#11758226—81no—
230#11758224—42no—
231D4×D61—44no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—81no—
240C2×D244—81no—
241C2×D244C22×C411yescharacteristic
242C2×D244C22×C411yescharacteristic
243C2×D244C22×C411yescharacteristic
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61C22×C411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×Dic122C22⋊C411yescharacteristic
253#11758217—42no—
254#11758217—42no—
255C2×#92420—21no—
256C2×#92420—21no—
257C2×#92420—21no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—21no—
261C2×#92420—21no—
262C2×#92420—21no—
263C2×#92420—42no—
264C2×#92420—42no—
265D61⋊C8—42no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61C22⋊C411yescharacteristic
272C4⋊C4×C61C22×C411yescharacteristic
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61C22⋊C411yescharacteristic
276C22⋊C4×C61C22⋊C411yescharacteristic
277C42×C61—21no—
278C42×C61C22×C411yescharacteristic
279C22⋊Dic61C22⋊C411yescharacteristic
280C22⋊Dic61C22⋊C411yescharacteristic
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61C22⋊C411yescharacteristic
308C4⋊Dic61C22×C411yescharacteristic
309#11758196—21no—
310#11758196—21no—
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313#11758196C22⋊C411yescharacteristic
314#11758196C22⋊C411yescharacteristic
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×D61—21no—
330C22×D61—21no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—81no—
334C22×D61—81no—
335C22×D61—81no—
336C22×D61—81no—
337C22×D61C2×C22⋊C411yescharacteristic
338Q8×C61—41no—
339Q8×C61—41no—
340Q8×C61—41no—
341Q8×C61—81no—
342Q8×C61—81no—
343D4×C61—22no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—81no—
351C2×C4×C61—81no—
352C2×C4×C61C2×C22⋊C411yescharacteristic
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C23×C411yescharacteristic
357C22⋊D61—22no—
358C22⋊D61—41no—
359C22⋊D61—42no—
360C22⋊D61—42no—
361C2×Dic61—22no—
362C2×Dic61—21no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C2×C22⋊C411yescharacteristic
371C2×Dic61C22×D411yescharacteristic
372C2×Dic61C22×D411yescharacteristic
373D244—41no—
374D244—41no—
375D244—41no—
376D244—42no—
377D244—81no—
378D244—81no—
379D244—81no—
380D244—81no—
381D244—81no—
382D244—81no—
383C4×D61—41no—
384C4×D61—41no—
385C4×D61—41no—
386C4×D61—42no—
387C4×D61—81no—
388C4×D61—81no—
389C4×D61—81no—
390C4×D61—81no—
391Dic122—41no—
392#92420—22no—
393#92420—41no—
394#92420—41no—
395#92420—41no—
396#92420—41no—
397#92420—41no—
398#92420—41no—
399#92420—41no—
400#17679—611nomaximal, Sylow
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—21no—
406C22×C61#42112yes—
407C22×C61C22×C22⋊C411yescharacteristic
408C2×D61—21no—
409C2×D61—21no—
410C2×D61—21no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61—41no—
414C2×D61—41no—
415C2×D61—41no—
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—162no—
421C2×D61—162no—
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—41no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61—41no—
431Dic61—21no—
432Dic61—21no—
433Dic61—21no—
434Dic61—21no—
435Dic61—21no—
436Dic61—21no—
437Dic61—21no—
438Dic61—41no—
439#3514—611no—
440#2970—611no—
441#2923—611no—
442#1536—611no—
443#1535—611no—
444#1535—611no—
445#1533—611no—
446#1532—611no—
447#1532—611no—
448#1530—611no—
449#1529—611no—
450#1527—611no—
451#1527—611no—
452#1524—611no—
453C2×#329—611no—
454C2×C61—22no—
455C2×C61—41no—
456C2×C61#288811yescharacteristic
457C2×C61C2×#42111yescharacteristic
458C2×C61#290111yescharacteristic
459D61—41no—
460D61—81no—
461D61—81no—
462D61—81no—
463#559—611no—
464#556—611no—
465#555—1221no—
466#551—1221no—
467#551—1221no—
468D4×Q8#692311yescharacteristic
469#548—611no—
470#548—611no—
471#546—611no—
472#546—611no—
473#546—1221no—
474D42—611no—
475#542—1221no—
476#538—1221no—
477#538—1221no—
478#532—611no—
479#529—611no—
480#529—611no—
481#529—611no—
482C2×#124—611no—
483C2×#124—611no—
484#518—1221no—
485C4×#41—611no—
486#446—1221no—
487#435—1221no—
488#435—1221no—
489C8×D4—1221no—
490#433—1221no—
491#433—1221no—
492#432—611no—
493#432—611no—
494#432—611no—
495#432—611no—
496#432—611no—
497#432—611no—
498#432—611no—
499#424—1221no—
500#408—1221no—
501C4×M16—611no—
502C4×M16—611no—
503C2×#97—611no—
504C2×#97—611no—
505C2×#97—611no—
506#330—611no—
507#330—611no—
508#330—611no—
509#330—611no—
510#329—611no—
511#329—611no—
512#329—611no—
513#329—611no—
514#329—611no—
515#329—611no—
516#329—611no—
517#329—611no—
518#329—611no—
519#329—611no—
520#329—611no—
521#329—611no—
522C61#1767911yescharacteristic, complemented, Sylow
523C2×#41—611no—
524C2×#41—611no—
525C2×#41—611no—
526C22×Q8C2×#692311yescharacteristic
527C22×Q8C2×#692311yescharacteristic
528C22×D4—611no—
529C22×D4—611no—
530C22×D4—1221no—
531C2×M16—1221no—
532C2×M16—1221no—
533C22×C8—1221no—
534C22×C8—1221no—
535C22×C8—1221no—
536C4⋊Q8—21no—
537C4⋊Q8C2×#692311yescharacteristic
538#127—611no—
539#126—1221no—
540#126—1221no—
541#126—1221no—
542#126—1221no—
543#126—1221no—
544#125—611no—
545#124—611no—
546#124—611no—
547#124—611no—
548#124—611no—
549#124—611no—
550#124—611no—
551#124—611no—
552#124—1221no—
553#124—1221no—
554#124—1221no—
555#124—1221no—
556#124—1221no—
557#124—1221no—
558#124—1221no—
559#123—1221no—
560#123—1221no—
561#123—1221no—
562#123—1221no—
563#123—1221no—
564#123—1221no—
565#123—1221no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—611no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8C2×#692311yescharacteristic
573C22⋊Q8C2×#692311yescharacteristic
574#121—611no—
575#121—611no—
576#121—611no—
577#121—1221no—
578#121—1221no—
579#121—1221no—
580#121—1221no—
581#121—1221no—
582#121—1221no—
583#121—1221no—
584#120—1221no—
585#120—1221no—
586#120—1221no—
587#120—1221no—
588C4×Q8—611no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—611no—
592C4×Q8C2×#692311yescharacteristic
593C4×D4—21no—
594C4×D4—611no—
595C4×D4—611no—
596C4×D4—611no—
597C4×D4—611no—
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—611no—
602C4×D4—1221no—
603C4×D4—1221no—
604C4×D4—1221no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4C2×#692311yescharacteristic
611#117—611no—
612#117—611no—
613#117—611no—
614#117—1221no—
615#117—1221no—
616#117—1221no—
617#117—1221no—
618C2×C22⋊C4—1221no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42—611no—
627C4⋊C8—1221no—
628C4⋊C8—1221no—
629C4⋊C8—1221no—
630C4⋊C8—1221no—
631C4⋊C8—1221no—
632C4⋊C8—1221no—
633C4⋊C8—1221no—
634C22⋊C8—1221no—
635C22⋊C8—1221no—
636C22⋊C8—1221no—
637C22⋊C8—1221no—
638C22⋊C8—1221no—
639C22⋊C8—1221no—
640C22⋊C8—1221no—
641#97—611no—
642#97—611no—
643#97—611no—
644#97—611no—
645#97—611no—
646#97—611no—
647#97—611no—
648#97—611no—
649#97—1221no—
650#97—1221no—
651#97—1221no—
652C4×C8—1221no—
653C4×C8—1221no—
654C24—1221no—
655C24—1221no—
656#41—4881no—
657#41—4881no—
658#41—2442no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—81no—
662C2×Q8—81no—
663C2×Q8—611no—
664C2×Q8C22×#692311yescharacteristic
665C2×Q8C22×#692311yescharacteristic
666C2×Q8C22×#692311yescharacteristic
667C2×D4—611no—
668C2×D4—611no—
669C2×D4—611no—
670C2×D4—611no—
671C2×D4—611no—
672C2×D4—1221no—
673C2×D4—1221no—
674C2×D4—1221no—
675C2×D4—1221no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—4881no—
682C2×D4—4881no—
683C2×D4—2444no—
684C2×D4C22⋊#692311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4C22×#692311yescharacteristic
700C22×C4C22×#692311yescharacteristic
701M16—2442no—
702M16—2442no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—2442no—
712C2×C8—2442no—
713C2×C8—2442no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—611no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—611no—
723C4⋊C4—611no—
724C4⋊C4—611no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4C22⋊#692311yescharacteristic
731C4⋊C4C22×#692311yescharacteristic
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—611no—
735C22⋊C4—611no—
736C22⋊C4—611no—
737C22⋊C4—611no—
738C22⋊C4—1221no—
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—1221no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—1221no—
757C22⋊C4—1221no—
758C22⋊C4—1221no—
759C22⋊C4C22⋊#692311yescharacteristic
760C22⋊C4C22⋊#692311yescharacteristic
761C42—21no—
762C42—611no—
763C42—611no—
764C42—611no—
765C42—611no—
766C42—611no—
767C42—611no—
768C42—611no—
769C42—611no—
770C42—611no—
771C42—1221no—
772C42—1221no—
773C42C22×#692311yescharacteristic
774C23—611no—
775C23—1221no—
776C23—1221no—
777C23—1221no—
778C23—4881no—
779C23—4881no—
780C23—4881no—
781C23—4881no—
782C23—2442no—
783C23—2442no—
784C23C2×C22⋊#692311yescharacteristic
785C23C2×C22⋊#692311yescharacteristic
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—81no—
790Q8—81no—
791Q8—2441no—
792D4—22no—
793D4—1222no—
794D4—4881no—
795D4—4881no—
796D4—4881no—
797D4—4881no—
798D4—4881no—
799D4—4881no—
800D4—2441no—
801D4—2441no—
802D4—2441no—
803D4—2442no—
804D4—2441no—
805D4—2442no—
806D4—2442no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—81no—
814C2×C4—81no—
815C2×C4—611no—
816C2×C4—611no—
817C2×C4—611no—
818C2×C4—611no—
819C2×C4—611no—
820C2×C4—611no—
821C2×C4—611no—
822C2×C4—1222no—
823C2×C4—1221no—
824C2×C4—4881no—
825C2×C4—4881no—
826C2×C4—4881no—
827C2×C4—4881no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2442no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4C2×C22⋊#692311yescharacteristic
836C2×C4C2×C22⋊#692311yescharacteristic
837C2×C4C2×C22⋊#692311yescharacteristic
838C2×C4C2×C22⋊#692311yescharacteristic
839C2×C4C23×#692311yescharacteristic
840C8—1222no—
841C8—2441no—
842C8—2441no—
843C8—2441no—
844C8—2441no—
845C8—2441no—
846C8—2441no—
847C8—2441no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—1221no—
854C22—1221no—
855C22—1221no—
856C22—9762no—
857C22—9762no—
858C22—2441no—
859C22—2441no—
860C22—2441no—
861C22—2441no—
862C22—2441no—
863C22—2441no—
864C22—2441no—
865C22—2441no—
866C22—2441no—
867C22#1684076112yes—
868C22C22×C22⋊#692311yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—1221no—
879C4—1221no—
880C4—1221no—
881C4—1221no—
882C4—1221no—
883C4—1221no—
884C4—1221no—
885C4—2441no—
886C2—22no—
887C2—41no—
888C2—4881no—
889C2—4881no—
890C2—4881no—
891C2—2441no—
892C2#2146242911yescharacteristic
893C2C2×#1684076111yescharacteristic
894C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radical#21459781C2
cosocleC4×Dic61C24
hypercenterD4×Q8#6923
hypocenterC61#17679
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. #21462659C2semidirect
2. #21462505C2semidirect
3. #21461309C2semidirect
4. #21461306C2semidirect
5. #21461305C2semidirect
6. #21461300C2semidirect
7. #21461297C2semidirect
8. #21461296C2semidirect
9. #21461290C2semidirect
10. #21461287C2semidirect
11. #21461280C2semidirect
12. #21461280C2semidirect
13. #21461272C2semidirect
14. C2×#16840618C2semidirect
22. #16840785C22semidirect
23. #16840785C22semidirect
24. #16840784C22semidirect
25. #16840783C22semidirect
26. #16840783C22semidirect
27. #16840782C22semidirect
28. #16840782C22semidirect
31. C4×#11758217C22semidirect
32. C4×#11758217C22semidirect
33. #16840721C22semidirect
34. C2×#14519832C22semidirect
35. C2×#14519832C22semidirect
36. #16840619C22semidirect
37. #16840619C22semidirect
38. #16840619C22semidirect
39. #16840619C22semidirect
44. #16840618C22semidirect
45. #16840618C22semidirect
46. #16840618C22semidirect
47. #16840618C22semidirect
48. #16840618C22semidirect
49. #16840618C22semidirect
50. #16840618C22semidirect
51. #16840618C22semidirect
522. C61#17679semidirect

Maximal subgroups

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

subgroupindex
#214626592
#214625052
#214613092
#214613062
#214613052
#214613002
#214612972
#214612962
#214612902
#214612872
#214612802
#214612722
C2×#168406182
#214597812
#1767961