Finite Group Databasebeta

← #30611968

Subgroups — #30611968

Order 15616.

904 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462748C211yesmaximal, characteristic
2#21462748C211yesmaximal, characteristic
3#21461359C211yesmaximal, characteristic, complemented
4#21461349C211yesmaximal, characteristic, complemented
5#21461348C211yesmaximal, characteristic, complemented
6#21461341C211yesmaximal, characteristic, complemented
7#21461341C211yesmaximal, characteristic, complemented
8#21461340C211yesmaximal, characteristic, complemented
9#21461340C211yesmaximal, characteristic, complemented
10#21461335C211yesmaximal, characteristic, complemented
11#21461329C211yesmaximal, characteristic, complemented
12#21461325C211yesmaximal, characteristic, complemented
13D61⋊#332C211yesmaximal, characteristic, complemented
14C2×#16840621C211yesmaximal, characteristic, complemented
15#21459634C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840792—21no—
19#16840792—21no—
20#16840791—21no—
21#16840791—21no—
22#16840789—21no—
23#16840789—21no—
24#16840785C2211yescharacteristic
25#16840785C2211yescharacteristic
26#16840782C2211yescharacteristic
27#16840782C2211yescharacteristic
28#16840780C2211yescharacteristic
29#16840780C2211yescharacteristic
30#16840767C2211yescharacteristic
31#16840767C2211yescharacteristic
32C2×#14519844C2211yescharacteristic
33C2×#14519844C2211yescharacteristic
34D61⋊(C4⋊C8)C2211yescharacteristic
35D61⋊(C4⋊C8)C2211yescharacteristic
36#16840621C2211yescharacteristic
37#16840621C2211yescharacteristic
38#16840621C2211yescharacteristic
39#16840621C2211yescharacteristic
40#16840621C2211yescharacteristic
41#16840621C2211yescharacteristic
42#16840621C2211yescharacteristic
43#16840621C2211yescharacteristic
44#16840621C2211yescharacteristic
45#16840621C2211yescharacteristic
46#16840621C2211yescharacteristic
47#16840621C2211yescharacteristic
48#16840621C2211yescharacteristic
49#16840621C2211yescharacteristic
50#16840621C2211yescharacteristic
51#16840621C2211yescharacteristic
52#16840492—21no—
53#16840489—21no—
54#16840468—21no—
55#16840466—21no—
56#16840466—21no—
57#16840427—21no—
58#16840425—21no—
59#16840425—21no—
60#16840392C411yescharacteristic
61#16840392C411yescharacteristic
62#16840390C411yescharacteristic
63#16840389C411yescharacteristic
64#16840389C411yescharacteristic
65#16840318C2211yescharacteristic
66#16840318C2211yescharacteristic
67#16840315C2211yescharacteristic
68C2×#14519776C2211yescharacteristic
69C4⋊Q8×D61C2211yescharacteristic
70C4⋊Q8×D61C2211yescharacteristic
71#16840243C411yescharacteristic
72#16840242C411yescharacteristic
73#16840230C2211yescharacteristic
74C61×#544C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758213—21no—
77C2×D61⋊C8—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80C22×#92420—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84#14519844—21no—
85#14519844C2311yescharacteristic
86#14519844C2311yescharacteristic
87#14519844C2311yescharacteristic
88#14519844C2311yescharacteristic
89#14519844C2311yescharacteristic
90#14519844C2311yescharacteristic
91#14519844C2311yescharacteristic
92#14519844C2311yescharacteristic
93C4⋊#92420—21no—
94C4⋊#92420—21no—
95#14519834—21no—
96#14519834—21no—
97#14519834—21no—
98#14519834—21no—
99C22⋊#92420—21no—
100C22⋊#92420—21no—
101#14519832—21no—
102#14519832—21no—
103#14519832—21no—
104#14519832—21no—
105C4×#92420—21no—
106C4×#92420—21no—
107C2×#11758222C2×C411yescharacteristic
108C22×Dic122—21no—
109C2×Q8×D61—21no—
110C2×Q8×D61—21no—
111#14519777C2×C411yescharacteristic
112#14519777C2×C411yescharacteristic
113#14519776—21no—
114#14519776—21no—
115#14519776—21no—
116#14519776—21no—
117#14519776—21no—
118#14519776—21no—
119#14519776—21no—
120#14519776C2×C411yescharacteristic
121#14519776C2×C411yescharacteristic
122#14519776C2311yescharacteristic
123#14519776C2311yescharacteristic
124#14519776C2311yescharacteristic
125#14519776C2311yescharacteristic
126#14519775—21no—
127#14519775—21no—
128#14519775—21no—
129#14519775—21no—
130#14519769C2×C411yescharacteristic
131#14519769C2×C411yescharacteristic
132#14519768—21no—
133#14519768C2×C411yescharacteristic
134#14519768C2×C411yescharacteristic
135#14519767—21no—
136#14519767—21no—
137#14519767—21no—
138#14519767—21no—
139#14519757—21no—
140#14519757—21no—
141#14519755—21no—
142#14519755—21no—
143#14519755—21no—
144#14519755—21no—
145#14519755—21no—
146#14519755—21no—
147#14519755—21no—
148#14519755—21no—
149#14519754—21no—
150#14519754—21no—
151#14519754—21no—
152#14519754—21no—
153#14519753—21no—
154#14519753—21no—
155C4×Dic122—21no—
156C4×Dic122—21no—
157C4×Dic122—21no—
158#14519742—21no—
159#14519742—21no—
160#14519742—21no—
161#14519742—21no—
162#14519742—21no—
163#14519742D411yescharacteristic
164#14519742D411yescharacteristic
165C4×D244—21no—
166#14519739—21no—
167#14519739D411yescharacteristic
168#14519739D411yescharacteristic
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171#14519737—21no—
172#14519737—21no—
173#14519737D411yescharacteristic
174#14519737D411yescharacteristic
175#14519737D411yescharacteristic
176#14519737D411yescharacteristic
177#14519736C2×C411yescharacteristic
178#14519735C2×C411yescharacteristic
179#14519735C2×C411yescharacteristic
180#14519735C2×C411yescharacteristic
181#14519735C2×C411yescharacteristic
182#14519734C2×C411yescharacteristic
183#14519734C2×C411yescharacteristic
184C2×C4⋊Dic61C2×C411yescharacteristic
185C2×#11758196—21no—
186C4⋊C4×D61—21no—
187C4⋊C4×D61—21no—
188C4⋊C4×D61C2×C411yescharacteristic
189C4⋊C4×D61C2×C411yescharacteristic
190C4⋊C4×D61C2×C411yescharacteristic
191C4⋊C4×D61C2×C411yescharacteristic
192C2×C4×Dic61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61—21no—
196C4⋊Q8×C61C2×C411yescharacteristic
197C4⋊Q8×C61C2×C411yescharacteristic
198#125×C61—21no—
199#125×C61C2×C411yescharacteristic
200#125×C61C2×C411yescharacteristic
201C22⋊Q8×C61—21no—
202C22⋊Q8×C61—21no—
203#117×C61C2×C411yescharacteristic
204#117×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61C22×C411yescharacteristic
210C2×C22⋊D61C22⋊C411yescharacteristic
211C2×C22⋊D61C22⋊C411yescharacteristic
212C22×Dic61—21no—
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215Q8×D61—81no—
216Q8×D61—81no—
217Q8×D61—81no—
218Q8×D61—81no—
219#11758222—24no—
220C2×D244C22⋊C411yescharacteristic
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61C22×C411yescharacteristic
226C2×C4×D61C22×C411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—81no—
240C2×Dic122—81no—
241C2×Dic122C22⋊C411yescharacteristic
242C2×#92420—21no—
243C2×#92420—21no—
244C2×#92420—21no—
245C2×#92420—21no—
246C2×#92420—21no—
247C2×#92420—21no—
248C2×#92420—21no—
249C2×#92420—21no—
250C2×#92420—81no—
251C2×#92420—81no—
252#11758213—81no—
253#11758213—81no—
254D61⋊C8—81no—
255D61⋊C8—81no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61C22⋊C411yescharacteristic
264C4⋊C4×C61C22⋊C411yescharacteristic
265C4⋊C4×C61C22×C411yescharacteristic
266C4⋊C4×C61C22×C411yescharacteristic
267C4⋊C4×C61C22×C411yescharacteristic
268C4⋊C4×C61C22×C411yescharacteristic
269C22⋊C4×C61—21no—
270C22⋊C4×C61C22⋊C411yescharacteristic
271C22⋊C4×C61C22⋊C411yescharacteristic
272C42×C61—21no—
273C42×C61C22×C411yescharacteristic
274C42×C61C22×C411yescharacteristic
275C22⋊Dic61—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198C22⋊C411yescharacteristic
281#11758198C22⋊C411yescharacteristic
282#11758198C22⋊C411yescharacteristic
283#11758198C22⋊C411yescharacteristic
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61C22×C411yescharacteristic
290C4⋊Dic61C22×C411yescharacteristic
291C4⋊Dic61C22×C411yescharacteristic
292C4⋊Dic61C22×C411yescharacteristic
293#11758196—21no—
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#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196C22⋊C411yescharacteristic
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
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
327C22×D61C2×C22⋊C411yescharacteristic
328C22×D61C2×C22⋊C411yescharacteristic
329Q8×C61—81no—
330Q8×C61—81no—
331C2×C4×C61—22no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—81no—
337C2×C4×C61C2×C22⋊C411yescharacteristic
338C2×C4×C61C2×C22⋊C411yescharacteristic
339C2×C4×C61C2×C22⋊C411yescharacteristic
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C2×C22⋊C411yescharacteristic
342C2×C4×C61C23×C411yescharacteristic
343C22⋊D61—22no—
344C22⋊D61#10114yes—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—81no—
354C2×Dic61C2×C22⋊C411yescharacteristic
355C2×Dic61C2×C22⋊C411yescharacteristic
356C2×Dic61C2×C22⋊C411yescharacteristic
357C2×Dic61C2×C22⋊C411yescharacteristic
358C2×Dic61C22×D411yescharacteristic
359C2×Dic61C22×D411yescharacteristic
360D244—22no—
361C4×D61—22no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—21no—
365C4×D61—21no—
366C4×D61—21no—
367C4×D61—21no—
368C4×D61—21no—
369C4×D61—21no—
370C4×D61—22no—
371C4×D61—81no—
372C4×D61—81no—
373C4×D61—81no—
374C4×D61—81no—
375Dic122—22no—
376Dic122—41no—
377Dic122—41no—
378Dic122—41no—
379Dic122—41no—
380Dic122—41no—
381Dic122—41no—
382Dic122—41no—
383Dic122—41no—
384Dic122—81no—
385Dic122—81no—
386Dic122—81no—
387Dic122—81no—
388#92420—41no—
389#92420—41no—
390#92420—41no—
391#92420—41no—
392#92420—41no—
393#92420—41no—
394#92420—41no—
395#92420—41no—
396#17774—611nomaximal, Sylow
397C22×C61—21no—
398C22×C61—21no—
399C22×C61C2×#10112yes—
400C22×C61C22×C22⋊C411yescharacteristic
401C2×D61—21no—
402C2×D61—21no—
403C2×D61—21no—
404C2×D61—21no—
405C2×D61—21no—
406C2×D61C2×#10112yes—
407C4×C61—21no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61—41no—
416C4×C61—41no—
417Dic61—21no—
418Dic61—21no—
419Dic61—21no—
420Dic61—41no—
421Dic61—41no—
422Dic61—41no—
423Dic61—41no—
424Dic61C2×#10112yes—
425Dic61#57611yescharacteristic
426Dic61#57711yescharacteristic
427Dic61#57711yescharacteristic
428Dic61#57811yescharacteristic
429#3503—611no—
430#2990—611no—
431#2990—611no—
432#1561—611no—
433#1556—611no—
434#1556—611no—
435#1552—611no—
436#1552—611no—
437#1552—611no—
438#1552—611no—
439#1549—611no—
440#1546—611no—
441#1544—611no—
442C2×#332—611no—
443C2×#332—611no—
444C2×C61—22no—
445C2×C61C22×#10111yescharacteristic
446C2×C61#289711yescharacteristic
447C2×C61#289811yescharacteristic
448D61—22no—
449D61—41no—
450Q82—1221no—
451#557—1221no—
452#554—1221no—
453#554—1221no—
454#554—1221no—
455D4×Q8—1221no—
456D4×Q8—1221no—
457D4×Q8—1221no—
458#544—611no—
459#544—611no—
460#544—611no—
461#544—611no—
462#544—611no—
463#544#692311yescharacteristic
464#533—611no—
465#533—611no—
466#533—611no—
467C2×C4⋊Q8—611no—
468C2×C4⋊Q8—611no—
469C2×C4⋊Q8—611no—
470#520—611no—
471#520—611no—
472C4×#41—611no—
473#446—1221no—
474#446—1221no—
475#435—1221no—
476#435—1221no—
477#435—1221no—
478#435—1221no—
479C8×D4—1221no—
480C8×D4—1221no—
481#432—611no—
482#432—611no—
483#432—611no—
484#432—611no—
485#431—611no—
486#431—611no—
487#423—611no—
488#423—611no—
489C2×C4⋊C8—611no—
490C2×C4⋊C8—611no—
491C2×C4⋊C8—611no—
492C2×C4⋊C8—611no—
493#332—611no—
494#332—611no—
495#332—611no—
496#332—611no—
497#332—611no—
498#332—611no—
499#332—611no—
500#332—611no—
501#332—611no—
502#332—611no—
503#332—611no—
504#332—611no—
505#332—611no—
506#332—611no—
507#332—611no—
508#332—611no—
509C61#1777411yescharacteristic, complemented, Sylow
510C2×#41—611no—
511C22×Q8—1221no—
512C22×Q8—1221no—
513C22×Q8—1221no—
514C2×M16—1221no—
515C2×M16—1221no—
516C22×C8—1221no—
517C22×C8—1221no—
518C22×C8—1221no—
519C22×C8—1221no—
520C4⋊Q8—21no—
521C4⋊Q8—611no—
522C4⋊Q8—611no—
523C4⋊Q8—611no—
524C4⋊Q8—611no—
525C4⋊Q8—611no—
526C4⋊Q8—611no—
527C4⋊Q8—611no—
528C4⋊Q8—611no—
529C4⋊Q8—1221no—
530C4⋊Q8—1221no—
531C4⋊Q8—1221no—
532C4⋊Q8—1221no—
533C4⋊Q8—1221no—
534C4⋊Q8—1221no—
535C4⋊Q8—1221no—
536C4⋊Q8—1221no—
537C4⋊Q8—1221no—
538C4⋊Q8—1221no—
539C4⋊Q8—1221no—
540C4⋊Q8C2×#692311yescharacteristic
541C4⋊Q8C2×#692311yescharacteristic
542#125—21no—
543#125—611no—
544#125—611no—
545#125—611no—
546#125—611no—
547#125—1221no—
548#125—1221no—
549#125—1221no—
550#125—1221no—
551#125—1221no—
552#125C2×#692311yescharacteristic
553#125C2×#692311yescharacteristic
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561C22⋊Q8—1221no—
562C22⋊Q8—1221no—
563C22⋊Q8—1221no—
564C22⋊Q8—1221no—
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×Q8—1221no—
578C4×Q8—1221no—
579C4×Q8—1221no—
580C4×Q8—1221no—
581C4×Q8—1221no—
582C4×D4—611no—
583C4×D4—611no—
584C4×D4—611no—
585C4×D4—611no—
586C4×D4—611no—
587C4×D4—611no—
588C4×D4—1221no—
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594#117—611no—
595#117—611no—
596#117—611no—
597#117—611no—
598#117—611no—
599#117—611no—
600#117—611no—
601#117C2×#692311yescharacteristic
602#117C2×#692311yescharacteristic
603C2×C4⋊C4—611no—
604C2×C4⋊C4—611no—
605C2×C4⋊C4—611no—
606C2×C4⋊C4—611no—
607C2×C4⋊C4—611no—
608C2×C4⋊C4—1221no—
609C2×C4⋊C4—1221no—
610C2×C4⋊C4—1221no—
611C2×C4⋊C4C2×#692311yescharacteristic
612C2×C42—611no—
613C2×C42—611no—
614C2×C42—611no—
615C4⋊C8—611no—
616C4⋊C8—611no—
617C4⋊C8—611no—
618C4⋊C8—611no—
619C4⋊C8—611no—
620C4⋊C8—611no—
621C4⋊C8—611no—
622C4⋊C8—611no—
623C4⋊C8—1221no—
624C4⋊C8—1221no—
625C4⋊C8—1221no—
626C4⋊C8—1221no—
627C4⋊C8—1221no—
628C4⋊C8—1221no—
629C22⋊C8—1221no—
630C22⋊C8—1221no—
631C22⋊C8—1221no—
632C22⋊C8—1221no—
633C22⋊C8—1221no—
634C22⋊C8—1221no—
635#97—1221no—
636#97—1221no—
637#97—1221no—
638#97—1221no—
639C4×C8—1221no—
640C4×C8—1221no—
641#41—1224no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—611no—
645C2×Q8—1221no—
646C2×Q8—1221no—
647C2×Q8—1221no—
648C2×Q8—1221no—
649C2×Q8—1221no—
650C2×Q8—1221no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8—4881no—
654C2×Q8—4881no—
655C2×Q8—4881no—
656C2×Q8—4881no—
657C2×Q8—4881no—
658C2×Q8—4881no—
659C2×D4—611no—
660C2×D4—611no—
661C2×D4—611no—
662C22×C4—21no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4C22×#692311yescharacteristic
677M16—4881no—
678M16—4881no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—1221no—
684C2×C8—1221no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—4881no—
688C2×C8—4881no—
689C2×C8—4881no—
690C2×C8—4881no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—611no—
699C4⋊C4—611no—
700C4⋊C4—611no—
701C4⋊C4—611no—
702C4⋊C4—611no—
703C4⋊C4—611no—
704C4⋊C4—611no—
705C4⋊C4—611no—
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—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4C22⋊#692311yescharacteristic
728C4⋊C4C22⋊#692311yescharacteristic
729C4⋊C4C22×#692311yescharacteristic
730C4⋊C4C22×#692311yescharacteristic
731C4⋊C4C22×#692311yescharacteristic
732C4⋊C4C22×#692311yescharacteristic
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⋊C4C22⋊#692311yescharacteristic
744C22⋊C4C22⋊#692311yescharacteristic
745C42—21no—
746C42—611no—
747C42—611no—
748C42—611no—
749C42—611no—
750C42—611no—
751C42—611no—
752C42—611no—
753C42—611no—
754C42—1221no—
755C42—1221no—
756C42—1221no—
757C42—1221no—
758C42—1221no—
759C42C22×#692311yescharacteristic
760C42C22×#692311yescharacteristic
761C23—611no—
762C23—611no—
763C23C2×C22⋊#692311yescharacteristic
764Q8—81no—
765Q8—81no—
766Q8—1222no—
767Q8—4881no—
768Q8—4881no—
769Q8—4881no—
770Q8—4881no—
771Q8—2441no—
772Q8—2441no—
773Q8—2441no—
774Q8—2441no—
775Q8—2441no—
776Q8—2441no—
777Q8—2441no—
778Q8—2441no—
779D4—614no—
780D4—1222no—
781D4—1222no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—81no—
788C2×C4—611no—
789C2×C4—611no—
790C2×C4—611no—
791C2×C4—611no—
792C2×C4—611no—
793C2×C4—611no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—4881no—
813C2×C4—4881no—
814C2×C4—4881no—
815C2×C4—4881no—
816C2×C4—4881no—
817C2×C4C2×C22⋊#692311yescharacteristic
818C2×C4C2×C22⋊#692311yescharacteristic
819C2×C4C2×C22⋊#692311yescharacteristic
820C2×C4C2×C22⋊#692311yescharacteristic
821C2×C4C2×C22⋊#692311yescharacteristic
822C2×C4C23×#692311yescharacteristic
823C8—2441no—
824C8—2441no—
825C8—2441no—
826C8—2441no—
827C8—2441no—
828C8—2441no—
829C8—2441no—
830C8—2441no—
831C22—21no—
832C22—21no—
833C22—612no—
834C22—1221no—
835C22—1221no—
836C22—1221no—
837C22—1221no—
838C22—1221no—
839C22D61⋊#10112yes—
840C22C22×C22⋊#692311yescharacteristic
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—21no—
846C4—21no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—612no—
852C4—611no—
853C4—611no—
854C4—611no—
855C4—611no—
856C4—1221no—
857C4—1221no—
858C4—1221no—
859C4—2441no—
860C4—2441no—
861C4—2441no—
862C4—2441no—
863C2—22no—
864C2—1222no—
865C2—2441no—
866C2C2×D61⋊#10111yescharacteristic
867C2#2146244011yescharacteristic
868C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#544C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758222C2×C4
cosocleC4×Dic61C24
hypercenter#544#6923
hypocenterC61#17774
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
3. #21461359C2semidirect
4. #21461349C2semidirect
5. #21461348C2semidirect
6. #21461341C2semidirect
7. #21461341C2semidirect
8. #21461340C2semidirect
9. #21461340C2semidirect
10. #21461335C2semidirect
11. #21461329C2semidirect
12. #21461325C2semidirect
13. D61⋊#332C2semidirect
14. C2×#16840621C2semidirect
509. C61#17774semidirect

Maximal subgroups

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

subgroupindex
#214627482
#214613592
#214613492
#214613482
#214613412
#214613402
#214613352
#214613292
#214613252
D61⋊#3322
C2×#168406212
#214596342
#1777461