Finite Group Databasebeta

← #30611679

Subgroups — #30611679

Order 15616.

896 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462662C211yesmaximal, characteristic, complemented
2#21462658C211yesmaximal, characteristic, complemented
3#21461308C211yesmaximal, characteristic, complemented
4#21461304C211yesmaximal, characteristic, complemented
5#21461303C211yesmaximal, characteristic, complemented
6#21461295C211yesmaximal, characteristic, complemented
7#21461294C211yesmaximal, characteristic, complemented
8#21461285C211yesmaximal, characteristic, complemented
9#21461284C211yesmaximal, characteristic, complemented
10#21461282C211yesmaximal, characteristic, complemented
11#21461282C211yesmaximal, characteristic, complemented
12#21461274C211yesmaximal, characteristic, complemented
13#21461270C211yesmaximal, characteristic, complemented
14#21461269C211yesmaximal, characteristic, complemented
15#21459738C211yesmaximal, characteristic
16#16840814—21no—
17#16840811—21no—
18#16840796—21no—
19#16840795—21no—
20#16840795—21no—
21#16840792—21no—
22#16840791—21no—
23#16840789—21no—
24#16840785C2211yescharacteristic
25#16840785C2211yescharacteristic
26#16840785C2211yescharacteristic
27#16840784C2211yescharacteristic
28#16840783C2211yescharacteristic
29#16840782C2211yescharacteristic
30C4×#11758213C2211yescharacteristic
31C4×#11758213C2211yescharacteristic
32C4×#11758213C2211yescharacteristic
33C4×#11758217C2211yescharacteristic
34#16840721C2211yescharacteristic
35C2×#14519832C2211yescharacteristic
36#16840619C2211yescharacteristic
37#16840619C2211yescharacteristic
38#16840619C2211yescharacteristic
39#16840619C2211yescharacteristic
40#16840619C2211yescharacteristic
41#16840619C2211yescharacteristic
42#16840619C2211yescharacteristic
43#16840619C2211yescharacteristic
44#16840617C2211yescharacteristic
45#16840617C2211yescharacteristic
46#16840617C2211yescharacteristic
47#16840617C2211yescharacteristic
48#16840617C2211yescharacteristic
49#16840617C2211yescharacteristic
50#16840617C2211yescharacteristic
51#16840617C2211yescharacteristic
52#16840459—21no—
53#16840459—21no—
54#16840457—21no—
55#16840457—21no—
56#16840455—21no—
57#16840455—21no—
58#16840449—21no—
59#16840449—21no—
60#16840375C411yescharacteristic
61#16840374C411yescharacteristic
62#16840366C411yescharacteristic
63#16840341C411yescharacteristic
64#16840341C411yescharacteristic
65#16840310C2211yescharacteristic
66#16840294C2211yescharacteristic
67#16840294C2211yescharacteristic
68#16840293C2211yescharacteristic
69#16840293C2211yescharacteristic
70#125×D61C2211yescharacteristic
71#16840241C411yescharacteristic
72#16840241C411yescharacteristic
73#16840230C2211yescharacteristic
74C61×#540C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758213—21no—
77C2×#11758213—21no—
78C2×#11758217—21no—
79C2×D61⋊C8—21no—
80C22×#92420—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84#14519844—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834—21no—
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93#14519832—21no—
94#14519832—21no—
95#14519832C2311yescharacteristic
96#14519832C2311yescharacteristic
97#14519832C2311yescharacteristic
98#14519832C2311yescharacteristic
99#14519832C2311yescharacteristic
100#14519832C2311yescharacteristic
101#14519832C2311yescharacteristic
102#14519832C2311yescharacteristic
103C4×#92420—21no—
104C4×#92420—21no—
105C4×#92420—21no—
106C4×#92420—21no—
107C2×#11758222C2×C411yescharacteristic
108C2×#11758224C2×C411yescharacteristic
109C2×#11758224C2×C411yescharacteristic
110#14519777C2×C411yescharacteristic
111#14519772—21no—
112#14519772—21no—
113#14519770—21no—
114#14519770—21no—
115#14519770—21no—
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519769C2×C411yescharacteristic
120#14519768—21no—
121#14519768—21no—
122#14519768C2311yescharacteristic
123#14519768C2311yescharacteristic
124#14519767—21no—
125#14519767—21no—
126#14519767—21no—
127#14519767—21no—
128#14519764C2311yescharacteristic
129#14519764C2311yescharacteristic
130#14519759—21no—
131#14519759—21no—
132#14519758—21no—
133#14519758—21no—
134#14519758—21no—
135#14519758—21no—
136#14519757C2×C411yescharacteristic
137#14519757C2×C411yescharacteristic
138#14519756C2×C411yescharacteristic
139#14519756C2×C411yescharacteristic
140#14519754—21no—
141#14519754—21no—
142#14519750—21no—
143#14519750—21no—
144#14519749—21no—
145#14519749—21no—
146#14519749—21no—
147#14519749—21no—
148#14519748—21no—
149#14519748—21no—
150#14519748—21no—
151#14519748—21no—
152#14519748C2×C411yescharacteristic
153#14519748C2×C411yescharacteristic
154C4×Dic122C2×C411yescharacteristic
155C4×Dic122C2×C411yescharacteristic
156#14519742C2×C411yescharacteristic
157#14519742C2×C411yescharacteristic
158#14519742D411yescharacteristic
159#14519742D411yescharacteristic
160D4×Dic61—21no—
161D4×Dic61—21no—
162D4×Dic61—21no—
163D4×Dic61—21no—
164D4×Dic61C2×C411yescharacteristic
165D4×Dic61C2×C411yescharacteristic
166#14519739D411yescharacteristic
167#14519739D411yescharacteristic
168C4×C22⋊D61—21no—
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61—21no—
172#14519737—21no—
173#14519737—21no—
174#14519737D411yescharacteristic
175#14519737D411yescharacteristic
176#14519737D411yescharacteristic
177#14519737D411yescharacteristic
178#14519736—21no—
179#14519736—21no—
180#14519734C2×C411yescharacteristic
181#14519734C2×C411yescharacteristic
182#14519733—21no—
183#14519733—21no—
184#14519733—21no—
185#14519733—21no—
186C2×#11758196—21no—
187C2×#11758196—21no—
188C4⋊C4×D61—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61C2×C411yescharacteristic
191C4⋊C4×D61C2×C411yescharacteristic
192C2×C4×Dic61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195#127×C61C2×C411yescharacteristic
196#125×C61C2×C411yescharacteristic
197#123×C61—21no—
198#123×C61—21no—
199#121×C61—21no—
200#121×C61—21no—
201#121×C61C2×C411yescharacteristic
202#121×C61C2×C411yescharacteristic
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61C22×C411yescharacteristic
211C2×D4×C61C22×C411yescharacteristic
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C22×C411yescharacteristic
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61C22⋊C411yescharacteristic
220C2×C22⋊D61C22⋊C411yescharacteristic
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227#11758224—42no—
228#11758224—42no—
229#11758222—42no—
230C2×D244C22⋊C411yescharacteristic
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61C22×C411yescharacteristic
234C2×C4×D61C22×C411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61C2×D411yescharacteristic
239C2×Dic122C22⋊C411yescharacteristic
240C2×Dic122C22×C411yescharacteristic
241C2×Dic122C22×C411yescharacteristic
242#11758217—42no—
243C2×#92420—21no—
244C2×#92420—21no—
245C2×#92420—21no—
246C2×#92420—21no—
247C2×#92420—21no—
248C2×#92420—21no—
249C2×#92420—21no—
250C2×#92420—21no—
251C2×#92420—42no—
252#11758213—42no—
253#11758213—42no—
254#11758213—42no—
255D61⋊C8—42no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61C22⋊C411yescharacteristic
259C4⋊C4×C61C22⋊C411yescharacteristic
260C4⋊C4×C61C22×C411yescharacteristic
261C4⋊C4×C61C22×C411yescharacteristic
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61C22⋊C411yescharacteristic
267C22⋊C4×C61C22⋊C411yescharacteristic
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⋊Dic61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—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
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#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61C22×C411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2411yescharacteristic
322C23×C61—21no—
323C23×C61—21no—
324C23×C61C2×C22⋊C411yescharacteristic
325C22×D61C2×C22⋊C411yescharacteristic
326C22×D61C2×C22⋊C411yescharacteristic
327D4×C61—41no—
328D4×C61—41no—
329D4×C61—81no—
330D4×C61—81no—
331D4×C61—81no—
332D4×C61—81no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—41no—
336C2×C4×C61—81no—
337C2×C4×C61—81no—
338C2×C4×C61C2×C22⋊C411yescharacteristic
339C2×C4×C61C2×C22⋊C411yescharacteristic
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C2×C22⋊C411yescharacteristic
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C23×C411yescharacteristic
344C22⋊D61—22no—
345C22⋊D61—41no—
346C22⋊D61—42no—
347C22⋊D61—42no—
348C22⋊D61—81no—
349C22⋊D61—81no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—42no—
357C2×Dic61—42no—
358C2×Dic61—81no—
359C2×Dic61—81no—
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61C2×C22⋊C411yescharacteristic
363C2×Dic61C2×C22⋊C411yescharacteristic
364C2×Dic61C22×D411yescharacteristic
365C2×Dic61C22×D411yescharacteristic
366D244—41no—
367C4×D61—22no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—41no—
371C4×D61—41no—
372C4×D61—41no—
373C4×D61—81no—
374C4×D61—81no—
375Dic122—22no—
376Dic122—41no—
377Dic122—41no—
378#92420—22no—
379#92420—22no—
380#92420—41no—
381#92420—41no—
382#92420—41no—
383#92420—41no—
384#92420—41no—
385#92420—41no—
386#17687—611nomaximal, Sylow
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61C22×C22⋊C411yescharacteristic
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—21no—
403C4×C61—21no—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—21no—
407C4×C61—21no—
408C4×C61—21no—
409C4×C61—41no—
410C4×C61—41no—
411Dic61—21no—
412Dic61—21no—
413Dic61—21no—
414Dic61—21no—
415Dic61—21no—
416Dic61—41no—
417Dic61—41no—
418Dic61—41no—
419Dic61—41no—
420Dic61#41312yes—
421#3512—611no—
422#2971—611no—
423#2970—611no—
424#1536—611no—
425#1535—611no—
426#1535—611no—
427#1532—611no—
428#1532—611no—
429#1529—611no—
430#1529—611no—
431#1528—611no—
432#1528—611no—
433#1525—611no—
434#1524—611no—
435#1524—611no—
436C2×C61—41no—
437C2×C61—81no—
438C2×C61—81no—
439C2×C61C2×#41311yescharacteristic
440C2×C61#290111yescharacteristic
441C2×C61#290111yescharacteristic
442D61—41no—
443D61—41no—
444#553—1221no—
445#553—1221no—
446#553—1221no—
447#553—1221no—
448#553—1221no—
449#553—1221no—
450#552—1221no—
451#552—1221no—
452#541—611no—
453#541—611no—
454#540—611no—
455#540#692311yescharacteristic
456#537—611no—
457#537—611no—
458#532—611no—
459#529—611no—
460#529—611no—
461#529—611no—
462#529—611no—
463C2×#125—611no—
464#520—611no—
465#520—611no—
466C4×#41—611no—
467#446—1221no—
468C8×Q8—1221no—
469#436—1221no—
470#436—1221no—
471#436—1221no—
472#435—1221no—
473#435—1221no—
474C8×D4—1221no—
475#432—611no—
476#432—611no—
477#432—611no—
478#432—611no—
479#432—611no—
480#432—611no—
481C4×M16—611no—
482C4×M16—611no—
483C4×M16—611no—
484C4×M16—611no—
485C2×#97—611no—
486C2×#97—611no—
487#330—611no—
488#330—611no—
489#330—611no—
490#330—611no—
491#330—611no—
492#330—611no—
493#330—611no—
494#330—611no—
495#329—611no—
496#329—611no—
497#329—611no—
498#329—611no—
499#329—611no—
500#329—611no—
501#329—611no—
502#329—611no—
503C61#1768711yescharacteristic, complemented, Sylow
504C2×#41—611no—
505C2×#41—611no—
506C2×#41—611no—
507C2×M16—1221no—
508C2×M16—1221no—
509C2×M16—1221no—
510C2×M16—1221no—
511C22×C8—1221no—
512C22×C8—1221no—
513C4⋊Q8—611no—
514#127C2×#692311yescharacteristic
515#126—1221no—
516#126—1221no—
517#126—1221no—
518#126—1221no—
519#126—1221no—
520#126—1221no—
521#126—1221no—
522#126—1221no—
523#125—611no—
524#125—611no—
525#125—611no—
526#125—1221no—
527#125—1221no—
528#125—1221no—
529#125—1221no—
530#125—1221no—
531#125—1221no—
532#125C2×#692311yescharacteristic
533#124—611no—
534#124—611no—
535#123—21no—
536#123—21no—
537#123—1221no—
538#123—1221no—
539#123—1221no—
540#123—1221no—
541#123—1221no—
542#123—1221no—
543C22⋊Q8—611no—
544C22⋊Q8—611no—
545C22⋊Q8—611no—
546C22⋊Q8—611no—
547C22⋊Q8—1221no—
548C22⋊Q8—1221no—
549#121—21no—
550#121—21no—
551#121—611no—
552#121—611no—
553#121—1221no—
554#121—1221no—
555#121—1221no—
556#121—1221no—
557#121—1221no—
558#121—1221no—
559#121—1221no—
560#121—1221no—
561#121—1221no—
562#121—1221no—
563#121C2×#692311yescharacteristic
564#121C2×#692311yescharacteristic
565C4×Q8—611no—
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×D4—611no—
572C4×D4—611no—
573C4×D4—611no—
574C4×D4—611no—
575C4×D4—611no—
576C4×D4—611no—
577C4×D4—611no—
578C4×D4—611no—
579C4×D4—1221no—
580C4×D4—1221no—
581C4×D4—1221no—
582C4×D4—1221no—
583C4×D4—1221no—
584C4×D4—1221no—
585C4×D4—1221no—
586C4×D4—1221no—
587C4×D4—1221no—
588C4×D4—1221no—
589C4×D4C2×#692311yescharacteristic
590C4×D4C2×#692311yescharacteristic
591#117—611no—
592#117—611no—
593#117—1221no—
594#117—1221no—
595#117—1221no—
596#117—1221no—
597#117—1221no—
598#117—1221no—
599#117C2×#692311yescharacteristic
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1221no—
606C2×C42—611no—
607C2×C42—611no—
608C2×C42—611no—
609C4⋊C8—1221no—
610C4⋊C8—1221no—
611C4⋊C8—1221no—
612C4⋊C8—1221no—
613C4⋊C8—1221no—
614C4⋊C8—1221no—
615C22⋊C8—1221no—
616C22⋊C8—1221no—
617C22⋊C8—1221no—
618C22⋊C8—1221no—
619C22⋊C8—1221no—
620C22⋊C8—1221no—
621#97—611no—
622#97—611no—
623#97—611no—
624#97—611no—
625#97—611no—
626#97—611no—
627#97—611no—
628#97—611no—
629#97—1221no—
630#97—1221no—
631C4×C8—1221no—
632C4×C8—1221no—
633C4×C8—1221no—
634C4×C8—1221no—
635#41—2442no—
636#41—2442no—
637#41—2442no—
638C2×Q8—611no—
639C2×Q8—611no—
640C2×Q8—611no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—611no—
646C2×D4—611no—
647C2×D4—611no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4C22×#692311yescharacteristic
653C2×D4C22×#692311yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4C22×#692311yescharacteristic
671M16—2442no—
672M16—2442no—
673M16—2442no—
674M16—2442no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—2442no—
684C2×C8—2442no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—611no—
688C4⋊C4—611no—
689C4⋊C4—611no—
690C4⋊C4—611no—
691C4⋊C4—611no—
692C4⋊C4—611no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
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⋊C4C22⋊#692311yescharacteristic
712C4⋊C4C22⋊#692311yescharacteristic
713C4⋊C4C22×#692311yescharacteristic
714C4⋊C4C22×#692311yescharacteristic
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—611no—
720C22⋊C4—611no—
721C22⋊C4—611no—
722C22⋊C4—611no—
723C22⋊C4—1221no—
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⋊C4C22⋊#692311yescharacteristic
736C22⋊C4C22⋊#692311yescharacteristic
737C42—611no—
738C42—611no—
739C42—611no—
740C42—611no—
741C42—611no—
742C42—611no—
743C42—611no—
744C42—611no—
745C42—1221no—
746C42—1221no—
747C42—1221no—
748C42—1221no—
749C42C22×#692311yescharacteristic
750C42C22×#692311yescharacteristic
751C23—21no—
752C23—21no—
753C23—611no—
754C23—611no—
755C23C2×C22⋊#692311yescharacteristic
756Q8—1222no—
757Q8—2441no—
758Q8—2441no—
759D4—41no—
760D4—41no—
761D4—81no—
762D4—81no—
763D4—81no—
764D4—81no—
765D4—1222no—
766D4—4881no—
767D4—4881no—
768D4—2441no—
769D4—2441no—
770D4—2442no—
771D4—2442no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—41no—
775C2×C4—81no—
776C2×C4—81no—
777C2×C4—611no—
778C2×C4—611no—
779C2×C4—611no—
780C2×C4—611no—
781C2×C4—611no—
782C2×C4—611no—
783C2×C4—1222no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—4881no—
789C2×C4—4881no—
790C2×C4—4881no—
791C2×C4—4881no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2442no—
798C2×C4—2442no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4C2×C22⋊#692311yescharacteristic
802C2×C4C2×C22⋊#692311yescharacteristic
803C2×C4C2×C22⋊#692311yescharacteristic
804C2×C4C2×C22⋊#692311yescharacteristic
805C2×C4C2×C22⋊#692311yescharacteristic
806C2×C4C23×#692311yescharacteristic
807C8—1222no—
808C8—1222no—
809C8—2441no—
810C8—2441no—
811C8—2441no—
812C8—2441no—
813C8—2441no—
814C8—2441no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—1221no—
825C22—1221no—
826C22—1221no—
827C22—1221no—
828C22—1221no—
829C22—1221no—
830C22C22×C22⋊#692311yescharacteristic
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—41no—
838C4—41no—
839C4—612no—
840C4—1221no—
841C4—1221no—
842C4—1221no—
843C4—1221no—
844C4—1221no—
845C4—2441no—
846C4—2441no—
847C4—2441no—
848C4—2441no—
849C2—41no—
850C2—81no—
851C2—81no—
852C2—2441no—
853C2—2441no—
854C2D61⋊#41311yescharacteristic
855C2#2146244911yescharacteristic
856C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#540C4
socleC22×C61C22×C22⋊C4
prime radical#21459738C2
cosocleC4×Dic61C24
hypercenter#540#6923
hypocenterC61#17687
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #21462662C2semidirect
2. #21462658C2semidirect
3. #21461308C2semidirect
4. #21461304C2semidirect
5. #21461303C2semidirect
6. #21461295C2semidirect
7. #21461294C2semidirect
8. #21461285C2semidirect
9. #21461284C2semidirect
10. #21461282C2semidirect
11. #21461282C2semidirect
12. #21461274C2semidirect
13. #21461270C2semidirect
14. #21461269C2semidirect
503. C61#17687semidirect

Maximal subgroups

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

subgroupindex
#214626622
#214626582
#214613082
#214613042
#214613032
#214612952
#214612942
#214612852
#214612842
#214612822
#214612742
#214612702
#214612692
#214597382
#1768761