Finite Group Databasebeta

← #30611331

Subgroups — #30611331

Order 15616.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462511C211yesmaximal, characteristic, complemented
2#21462326C211yesmaximal, characteristic, complemented
3#21461262C211yesmaximal, characteristic, complemented
4#21461251C211yesmaximal, characteristic, complemented
5#21461247C211yesmaximal, characteristic
6#21461242C211yesmaximal, characteristic, complemented
7#21461233C211yesmaximal, characteristic, complemented
8#21461227C211yesmaximal, characteristic, complemented
9#21461222C211yesmaximal, characteristic, complemented
10#21461211C211yesmaximal, characteristic, complemented
11#21461207C211yesmaximal, characteristic
12#21461202C211yesmaximal, characteristic, complemented
13#21461193C211yesmaximal, characteristic, complemented
14C2×#16840615C211yesmaximal, characteristic, complemented
15#21459574C211yesmaximal, 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#16840711—21no—
27#16840711—21no—
28#16840709—21no—
29#16840707C2211yescharacteristic
30#16840706C2211yescharacteristic
31#16840705C2211yescharacteristic
32C4×C4⋊#6923C2211yescharacteristic
33C22⋊C4×#6923—21no—
34#16840698C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36#16840615C2211yescharacteristic
37#16840615C2211yescharacteristic
38#16840615C2211yescharacteristic
39#16840615C2211yescharacteristic
40#16840615C2211yescharacteristic
41#16840615C2211yescharacteristic
42#16840615C2211yescharacteristic
43#16840615C2211yescharacteristic
44#16840615C2211yescharacteristic
45#16840615C2211yescharacteristic
46#16840615C2211yescharacteristic
47#16840615C2211yescharacteristic
48#16840614C2211yescharacteristic
49#16840614C2211yescharacteristic
50#16840614C2211yescharacteristic
51#16840614C2211yescharacteristic
52#16840486—21no—
53#16840473—21no—
54#16840454—21no—
55#16840454—21no—
56#16840450—21no—
57#16840450—21no—
58#16840439—21no—
59#16840439—21no—
60#16840386C411yescharacteristic, complemented
61#16840386C411yescharacteristic, complemented
62#16840375C411yescharacteristic, complemented
63#16840375C411yescharacteristic, complemented
64#16840338C411yescharacteristic, complemented
65#16840317C2211yescharacteristic
66#16840317C2211yescharacteristic
67#16840297C2211yescharacteristic
68#16840297C2211yescharacteristic
69#16840274C2211yescharacteristic
70C2×#14519757C2211yescharacteristic
71#16840243C411yescharacteristic, complemented
72#16840239C411yescharacteristic, complemented
73#117×D61C2211yescharacteristic
74C61×#544C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758217—21no—
77C22×#92420—21no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923—21no—
80C2×C22⋊#6923—21no—
81C2×C4×#6923—21no—
82C2×C4×#6923—21no—
83#14519844—21no—
84#14519844—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834C2311yescharacteristic
90#14519834C2311yescharacteristic
91#14519834C2311yescharacteristic
92#14519834C2311yescharacteristic
93#14519832—21no—
94#14519832—21no—
95C4×#92420—21no—
96C4×#92420—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×#11758222C2×C411yescharacteristic
108C22×Dic122C2×C411yescharacteristic
109C22×C4×D61C2311yescharacteristic
110#14519777C2×C411yescharacteristic, complemented
111#14519777C2×C411yescharacteristic, complemented
112#14519772—21no—
113#14519772—21no—
114#14519772—21no—
115#14519772—21no—
116#14519772—21no—
117#14519772—21no—
118#14519772—21no—
119#14519772—21no—
120#14519768—21no—
121#14519768—21no—
122#14519768—21no—
123#14519768—21no—
124#14519768—21no—
125#14519768—21no—
126#14519766—21no—
127#14519766—21no—
128#14519765C2×C411yescharacteristic, complemented
129#14519765C2×C411yescharacteristic, complemented
130#14519762—21no—
131#14519762—21no—
132#14519762—21no—
133#14519762—21no—
134#14519761—21no—
135#14519761—21no—
136#14519761—21no—
137#14519757—21no—
138#14519757—21no—
139#14519757—21no—
140#14519757—21no—
141#14519757C2×C411yescharacteristic
142#14519757C2×C411yescharacteristic
143#14519757C2×C411yescharacteristic
144#14519757C2311yescharacteristic
145#14519757C2311yescharacteristic
146#14519757C2311yescharacteristic
147#14519753—21no—
148#14519753—21no—
149#14519753—21no—
150#14519753—21no—
151#14519752C2×C411yescharacteristic
152#14519752C2311yescharacteristic
153#14519747—21no—
154Q8×Dic61—21no—
155Q8×Dic61—21no—
156C4×Dic122—21no—
157C4×Dic122—21no—
158#14519742C2×C411yescharacteristic, complemented
159#14519742C2×C411yescharacteristic, complemented
160#14519742C2×C411yescharacteristic, complemented
161#14519742C2×C411yescharacteristic, complemented
162#14519742C2×C411yescharacteristic, complemented
163#14519742C2×C411yescharacteristic, complemented
164C4×D244—21no—
165C4×D244—21no—
166#14519739—21no—
167#14519739—21no—
168#14519739C2×C411yescharacteristic, complemented
169#14519739C2×C411yescharacteristic, complemented
170C4×C22⋊D61—21no—
171C4×C22⋊D61—21no—
172#14519736C2×C411yescharacteristic
173#14519735—21no—
174#14519735—21no—
175#14519735—21no—
176#14519735—21no—
177#14519735—21no—
178#14519735D411yescharacteristic
179#14519735D411yescharacteristic
180#14519734C2×C411yescharacteristic
181#14519734C2×C411yescharacteristic
182#14519733—21no—
183#14519733—21no—
184#14519733D411yescharacteristic
185#14519733D411yescharacteristic
186C2×C4⋊Dic61—21no—
187C4⋊C4×D61—21no—
188C4⋊C4×D61D411yescharacteristic
189C4⋊C4×D61D411yescharacteristic
190C2×#11758198—21no—
191C22⋊C4×D61D411yescharacteristic
192C22⋊C4×D61D411yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61—21no—
196C4⋊Q8×C61C2×C411yescharacteristic, complemented
197C4⋊Q8×C61C2×C411yescharacteristic, complemented
198#125×C61—21no—
199#125×C61C2×C411yescharacteristic, complemented
200#125×C61C2×C411yescharacteristic, complemented
201C22⋊Q8×C61—21no—
202C22⋊Q8×C61—21no—
203#117×C61C2×C411yescharacteristic
204#117×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C23×D61C2×D411yescharacteristic
207C22×#6923—21no—
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—42no—
212C22×#6923—42no—
213C22×#6923—81no—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61C22×C411yescharacteristic
218C2×C22⋊D61—21no—
219C22×Dic61—21no—
220C22×Dic61C2×D411yescharacteristic
221#11758222—42no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244C22×C411yescharacteristic
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—42no—
229C2×C4×D61C22×C411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2411yescharacteristic
237C2×Dic122—21no—
238C2×Dic122—42no—
239C2×Dic122C22×C411yescharacteristic
240C2×Dic122C22×C411yescharacteristic
241C2×Dic122C22×C411yescharacteristic
242C22⋊#6923—42no—
243#11758217—42no—
244C2×#92420—21no—
245C2×#92420—21no—
246C2×#92420—21no—
247C2×#92420—21no—
248C2×#92420—42no—
249C4⋊#6923—42no—
250C4⋊#6923—81no—
251C4×#6923—42no—
252C4×#6923—81no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61C22⋊C411yescharacteristic
261C4⋊C4×C61C22⋊C411yescharacteristic
262C4⋊C4×C61C22×C411yescharacteristic
263C4⋊C4×C61C22×C411yescharacteristic
264C4⋊C4×C61C22×C411yescharacteristic
265C4⋊C4×C61C22×C411yescharacteristic
266C22⋊C4×C61—21no—
267C22⋊C4×C61C22⋊C411yescharacteristic
268C22⋊C4×C61C22⋊C411yescharacteristic
269C42×C61—21no—
270C42×C61C22×C411yescharacteristic
271C42×C61C22×C411yescharacteristic
272C22⋊Dic61C22⋊C411yescharacteristic
273C22⋊Dic61C22⋊C411yescharacteristic
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198C22⋊C411yescharacteristic
289#11758198C22⋊C411yescharacteristic
290#11758198C22⋊C411yescharacteristic
291#11758198C22⋊C411yescharacteristic
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61—21no—
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61C22⋊C411yescharacteristic
303C4⋊Dic61C22⋊C411yescharacteristic
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×C61C2×C22⋊C411yescharacteristic
327C22×D61—22no—
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—21no—
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—
346C2×#6923—84no—
347Q8×C61—81no—
348Q8×C61—81no—
349C2×C4×C61—22no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
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—
362C2×Dic61—22no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—42no—
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C2×C22⋊C411yescharacteristic
371C2×Dic61C2×C22⋊C411yescharacteristic
372C2×Dic61C22×D411yescharacteristic
373D244—41no—
374D244—41no—
375D244—41no—
376D244—81no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—21no—
380C4×D61—21no—
381C4×D61—41no—
382C4×D61—41no—
383C4×D61—41no—
384C4×D61—41no—
385C4×D61—41no—
386C4×D61—41no—
387C4×D61—42no—
388C4×D61—81no—
389C4×D61—81no—
390Dic122—42no—
391Dic122—41no—
392Dic122—41no—
393Dic122—41no—
394#92420—41no—
395#92420—41no—
396#92420—41no—
397#92420—41no—
398#17609—611nomaximal, Sylow
399C22×C61—21no—
400C22×C61—21no—
401C22×C61#41012yes—
402C22×C61C22×C22⋊C411yescharacteristic
403C2×D61—21no—
404C2×D61—21no—
405C2×D61—21no—
406C2×D61—21no—
407C2×D61—21no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61#57711yescharacteristic
414C2×D61#57811yescharacteristic
415#6923—42no—
416#6923—81no—
417#6923—81no—
418#6923—81no—
419C4×C61—21no—
420C4×C61—21no—
421C4×C61—21no—
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—41no—
426C4×C61—41no—
427C4×C61—41no—
428C4×C61—41no—
429Dic61—21no—
430Dic61—21no—
431Dic61—21no—
432Dic61—21no—
433Dic61—21no—
434Dic61—21no—
435Dic61—41no—
436Dic61—41no—
437Dic61—41no—
438#3495—611no—
439#2924—611no—
440#2343—611no—
441#1521—611no—
442#1518—611no—
443#1516—611no—
444#1515—611no—
445#1512—611no—
446#1511—611no—
447#1509—611no—
448#1506—611no—
449#1504—611no—
450#1503—611no—
451#1500—611no—
452C2×#328—611no—
453C2×C61—22no—
454C2×C61C2×#41011yescharacteristic
455C2×C61#289811yescharacteristic
456C2×C61#290111yescharacteristic
457D61—21no—
458D61—21no—
459D61—41no—
460D61—81no—
461#556—1221no—
462#554—1221no—
463#552—1221no—
464#552—1221no—
465#552—1221no—
466#552—1221no—
467#551—1221no—
468#551—1221no—
469#544#692311yescharacteristic, complemented
470#542—611no—
471#542—611no—
472#541—611no—
473#541—611no—
474#536—611no—
475#533—611no—
476#533—611no—
477#529—611no—
478#529—611no—
479#525—611no—
480C2×C22⋊Q8—611no—
481#520—611no—
482#519—611no—
483C2×#117—611no—
484#433—1221no—
485#433—1221no—
486#432—611no—
487#432—611no—
488#431—611no—
489#431—611no—
490#424—1221no—
491#407—611no—
492C2×C22⋊C8—611no—
493#405—1221no—
494#387—1221no—
495#387—1221no—
496#385—1221no—
497#383—611no—
498#382—611no—
499#381—611no—
500C4×C4⋊C4—611no—
501C4×C22⋊C4—1221no—
502#376—611no—
503C2×#95—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#328—611no—
516#327—611no—
517#327—611no—
518#327—611no—
519#327—611no—
520C61#1760911yescharacteristic, complemented, Sylow
521C2×#41—611no—
522C22×Q8—611no—
523C23×C4—611no—
524C23×C4—1221no—
525C2×M16—1221no—
526C22×C8—1221no—
527C4⋊Q8—21no—
528C4⋊Q8—611no—
529C4⋊Q8—611no—
530C4⋊Q8C2×#692311yescharacteristic, complemented
531C4⋊Q8C2×#692311yescharacteristic, complemented
532#126—1221no—
533#126—1221no—
534#126—1221no—
535#126—1221no—
536#126—1221no—
537#126—1221no—
538#126—1221no—
539#126—1221no—
540#125—21no—
541#125—1221no—
542#125—1221no—
543#125—1221no—
544#125—1221no—
545#125—1221no—
546#125—1221no—
547#125C2×#692311yescharacteristic, complemented
548#125C2×#692311yescharacteristic, complemented
549#124—611no—
550#124—611no—
551#124—1221no—
552#124—1221no—
553#123—1221no—
554#123—1221no—
555#123—1221no—
556#123—1221no—
557#123—1221no—
558#123—1221no—
559#123—1221no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—611no—
563C22⋊Q8—611no—
564C22⋊Q8—611no—
565C22⋊Q8—611no—
566C22⋊Q8—611no—
567C22⋊Q8—611no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8—1221no—
574C22⋊Q8—1221no—
575C22⋊Q8—1221no—
576#121—611no—
577#121—611no—
578#120—1221no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—611no—
583C4×Q8—611no—
584C4×Q8—611no—
585C4×Q8—1221no—
586C4×Q8—1221no—
587C4×Q8—1221no—
588C4×Q8—1221no—
589C4×D4—611no—
590C4×D4—611no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597#117—611no—
598#117—611no—
599#117—611no—
600#117—611no—
601#117—611no—
602#117—611no—
603#117—611no—
604#117—1221no—
605#117—1221no—
606#117—1221no—
607#117—1221no—
608#117—1221no—
609#117—1221no—
610#117—1221no—
611#117C2×#692311yescharacteristic
612#117C2×#692311yescharacteristic
613C2×C4⋊C4—611no—
614C2×C4⋊C4—611no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—1221no—
619C2×C4⋊C4C2×#692311yescharacteristic
620C2×C22⋊C4—611no—
621C2×C22⋊C4—611no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42—1221no—
627C2×C42—1221no—
628C4⋊C8—1221no—
629C4⋊C8—1221no—
630C4⋊C8—1221no—
631C4⋊C8—1221no—
632C22⋊C8—611no—
633C22⋊C8—611no—
634C22⋊C8—611no—
635C22⋊C8—611no—
636C22⋊C8—1221no—
637C22⋊C8—1221no—
638#97—1221no—
639#97—1221no—
640C4×C8—1221no—
641C4×C8—1221no—
642#95—611no—
643#95—611no—
644#95—611no—
645#95—611no—
646#95—1221no—
647#95—1221no—
648#95—1221no—
649#95—1221no—
650#95—1221no—
651#95—1221no—
652C24—611no—
653#41—2442no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—611no—
657C2×Q8—611no—
658C2×Q8—611no—
659C2×Q8—1221no—
660C2×Q8—2442no—
661C2×D4—611no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4—1221no—
665C22×C4—21no—
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—611no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—4881no—
684C22×C4—2442no—
685C22×C4—2442no—
686C22×C4—2442no—
687C22×C4C22×#692311yescharacteristic
688M16—2442no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—2442no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
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—4881no—
724C4⋊C4—2442no—
725C4⋊C4C22⋊#692311yescharacteristic
726C4⋊C4C22⋊#692311yescharacteristic
727C4⋊C4C22×#692311yescharacteristic
728C4⋊C4C22×#692311yescharacteristic
729C4⋊C4C22×#692311yescharacteristic
730C4⋊C4C22×#692311yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—611no—
733C22⋊C4—611no—
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—2442no—
753C22⋊C4C22⋊#692311yescharacteristic
754C22⋊C4C22⋊#692311yescharacteristic
755C42—21no—
756C42—611no—
757C42—611no—
758C42—611no—
759C42—611no—
760C42—611no—
761C42—611no—
762C42—1221no—
763C42—1221no—
764C42—1221no—
765C42—1221no—
766C42—1221no—
767C42—1221no—
768C42—4881no—
769C42—2442no—
770C42C22×#692311yescharacteristic
771C42C22×#692311yescharacteristic
772C23—611no—
773C23—611no—
774C23—1221no—
775C23—1221no—
776C23—1222no—
777C23—1221no—
778C23—2441no—
779C23C2×C22⋊#692311yescharacteristic
780Q8—81no—
781Q8—81no—
782Q8—2441no—
783Q8—2441no—
784Q8—2441no—
785Q8—2442no—
786D4—4881no—
787D4—2441no—
788D4—2441no—
789D4—2441no—
790D4—2442no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—81no—
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—1221no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—4881no—
813C2×C4—4881no—
814C2×C4—4884no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2442no—
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×C4—2441no—
833C2×C4—2442no—
834C2×C4C2×C22⋊#692311yescharacteristic
835C2×C4C2×C22⋊#692311yescharacteristic
836C2×C4C2×C22⋊#692311yescharacteristic
837C2×C4C2×C22⋊#692311yescharacteristic
838C2×C4C2×C22⋊#692311yescharacteristic
839C2×C4C23×#692311yescharacteristic
840C8—2441no—
841C8—2441no—
842C8—2441no—
843C8—2441no—
844C22—21no—
845C22—21no—
846C22—611no—
847C22—611no—
848C22—1221no—
849C22—1221no—
850C22—1221no—
851C22—1221no—
852C22—1221no—
853C22—2442no—
854C22—2442no—
855C22—2441no—
856C22—2441no—
857C22—2441no—
858C22#1684074312yes—
859C22C22×C22⋊#692311yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—41no—
870C4—1221no—
871C4—1221no—
872C4—1221no—
873C4—1221no—
874C4—1221no—
875C4—1221no—
876C4—4881no—
877C4—4881no—
878C4—4881no—
879C4—2442no—
880C4—2441no—
881C4—2441no—
882C4—2441no—
883C2—22no—
884C2—1221no—
885C2—1221no—
886C2—4881no—
887C2—2441no—
888C2C2×#1684074311yescharacteristic
889C2#2146244111yescharacteristic
890C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#544C4
socleC22×C61C22×C22⋊C4
prime radical#16840274C22
cosocleC2×C4×D61C24
hypercenter#544#6923
hypocenterC61#17609
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
1. #21462511C2semidirect
2. #21462326C2semidirect
3. #21461262C2semidirect
4. #21461251C2semidirect
6. #21461242C2semidirect
7. #21461233C2semidirect
8. #21461227C2semidirect
9. #21461222C2semidirect
10. #21461211C2semidirect
12. #21461202C2semidirect
13. #21461193C2semidirect
14. C2×#16840615C2semidirect
60. #16840386C4semidirect
61. #16840386C4semidirect
62. #16840375C4semidirect
63. #16840375C4semidirect
64. #16840338C4semidirect
71. #16840243C4semidirect
72. #16840239C4semidirect
74. C61×#544C4semidirect
110. #14519777C2×C4semidirect
111. #14519777C2×C4semidirect
128. #14519765C2×C4semidirect
129. #14519765C2×C4semidirect
158. #14519742C2×C4semidirect
159. #14519742C2×C4semidirect
160. #14519742C2×C4semidirect
161. #14519742C2×C4semidirect
162. #14519742C2×C4semidirect
163. #14519742C2×C4semidirect
168. #14519739C2×C4semidirect
169. #14519739C2×C4semidirect
196. C4⋊Q8×C61C2×C4semidirect
197. C4⋊Q8×C61C2×C4semidirect
199. #125×C61C2×C4semidirect
200. #125×C61C2×C4semidirect
469. #544#6923semidirect
520. C61#17609semidirect
530. C4⋊Q8C2×#6923semidirect
531. C4⋊Q8C2×#6923semidirect
547. #125C2×#6923semidirect
548. #125C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625112
#214623262
#214612622
#214612512
#214612472
#214612422
#214612332
#214612272
#214612222
#214612112
#214612072
#214612022
#214611932
C2×#168406152
#214595742
#1760961