Finite Group Databasebeta

← #30611971

Subgroups — #30611971

Order 15616.

926 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462748C211yesmaximal, characteristic, complemented
2#21462746C211yesmaximal, characteristic, complemented
3#21461355C211yesmaximal, characteristic, complemented
4#21461350C211yesmaximal, characteristic, complemented
5#21461349C211yesmaximal, characteristic, complemented
6#21461344C211yesmaximal, characteristic, complemented
7#21461343C211yesmaximal, characteristic, complemented
8#21461339C211yesmaximal, characteristic, complemented
9#21461339C211yesmaximal, characteristic, complemented
10#21461336C211yesmaximal, characteristic, complemented
11#21461331C211yesmaximal, characteristic, complemented
12#21461321C211yesmaximal, characteristic, complemented
13#21461316C211yesmaximal, characteristic, complemented
14D61⋊#332C211yesmaximal, characteristic, complemented
15#21459724C211yesmaximal, characteristic
16#16840814—21no—
17#16840812—21no—
18#16840794—21no—
19#16840794—21no—
20#16840792—21no—
21#16840791—21no—
22#16840790—21no—
23#16840789—21no—
24#16840785C2211yescharacteristic
25#16840785C2211yescharacteristic
26#16840785C2211yescharacteristic
27#16840782C2211yescharacteristic
28#16840780C2211yescharacteristic
29#16840779C2211yescharacteristic
30#16840767C2211yescharacteristic
31#16840765C2211yescharacteristic
32C2×#14519844C2211yescharacteristic
33D61⋊(C4⋊C8)C2211yescharacteristic
34D61⋊(C4⋊C8)C2211yescharacteristic
35D61⋊(C4⋊C8)C2211yescharacteristic
36#16840622C2211yescharacteristic
37#16840622C2211yescharacteristic
38#16840622C2211yescharacteristic
39#16840622C2211yescharacteristic
40#16840621C2211yescharacteristic
41#16840621C2211yescharacteristic
42#16840621C2211yescharacteristic
43#16840621C2211yescharacteristic
44#16840621C2211yescharacteristic
45#16840621C2211yescharacteristic
46#16840621C2211yescharacteristic
47#16840621C2211yescharacteristic
48#16840620C2211yescharacteristic
49#16840620C2211yescharacteristic
50#16840620C2211yescharacteristic
51#16840620C2211yescharacteristic
52#16840479—21no—
53#16840474—21no—
54#16840466—21no—
55#16840463—21no—
56#16840457—21no—
57#16840422—21no—
58#16840420—21no—
59#16840410—21no—
60#16840386C411yescharacteristic
61#16840383C411yescharacteristic
62#16840381C411yescharacteristic
63#16840342C411yescharacteristic
64#16840341C411yescharacteristic
65#16840316C2211yescharacteristic
66#16840314C2211yescharacteristic
67#16840311C2211yescharacteristic
68#16840309C2211yescharacteristic
69#16840307C2211yescharacteristic
70C4⋊Q8×D61C2211yescharacteristic
71#16840244C411yescharacteristic
72#16840241C411yescharacteristic
73#16840230C2211yescharacteristic
74C61×#542C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×D61⋊C8—21no—
78C2×D61⋊C8—21no—
79C2×D61⋊C8—21no—
80C22×#92420—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844C2311yescharacteristic
84#14519844C2311yescharacteristic
85#14519844C2311yescharacteristic
86#14519844C2311yescharacteristic
87#14519844C2311yescharacteristic
88#14519844C2311yescharacteristic
89#14519844C2311yescharacteristic
90#14519844C2311yescharacteristic
91C4⋊#92420—21no—
92C4⋊#92420—21no—
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×#11758226C2×C411yescharacteristic
108C2×#11758222—21no—
109C2×#11758222C2×C411yescharacteristic
110C2×#11758224—21no—
111C2×#11758224C2×C411yescharacteristic
112C2×Q8×D61—21no—
113#14519777C2×C411yescharacteristic
114#14519776—21no—
115#14519776C2311yescharacteristic
116#14519776C2311yescharacteristic
117#14519775—21no—
118#14519775C2311yescharacteristic
119#14519773C2311yescharacteristic
120#14519772—21no—
121#14519772—21no—
122#14519770—21no—
123#14519767—21no—
124#14519767—21no—
125#14519766—21no—
126#14519765C2×C411yescharacteristic
127#14519763—21no—
128#14519763—21no—
129#14519763—21no—
130#14519763—21no—
131#14519762—21no—
132#14519761—21no—
133#14519759—21no—
134#14519757C2×C411yescharacteristic
135#14519756C2×C411yescharacteristic
136#14519755—21no—
137#14519755—21no—
138#14519755—21no—
139#14519754—21no—
140#14519754—21no—
141#14519754—21no—
142#14519753—21no—
143#14519753C2×C411yescharacteristic
144#14519752—21no—
145#14519752C2×C411yescharacteristic
146#14519751C2×C411yescharacteristic
147#14519750—21no—
148#14519750—21no—
149#14519750—21no—
150#14519750—21no—
151#14519750—21no—
152#14519750—21no—
153#14519749—21no—
154#14519749—21no—
155#14519748—21no—
156#14519748C2×C411yescharacteristic
157Q8×Dic61C2×C411yescharacteristic
158C4×Dic122—21no—
159C4×Dic122C2×C411yescharacteristic
160#14519742—21no—
161#14519742C2×C411yescharacteristic
162#14519742D411yescharacteristic
163#14519742D411yescharacteristic
164C4×D244—21no—
165C4×D244C2×C411yescharacteristic
166D4×Dic61C2×C411yescharacteristic
167#14519739—21no—
168#14519739C2×C411yescharacteristic
169#14519739D411yescharacteristic
170#14519739D411yescharacteristic
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173#14519737—21no—
174#14519737—21no—
175#14519737—21no—
176#14519737—21no—
177#14519737D411yescharacteristic
178#14519737D411yescharacteristic
179#14519737D411yescharacteristic
180#14519737D411yescharacteristic
181#14519734—21no—
182#14519734—21no—
183#14519734C2×C411yescharacteristic
184#14519734C2×C411yescharacteristic
185#14519733—21no—
186#14519733—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
195C4⋊Q8×C61C2×C411yescharacteristic
196#126×C61—21no—
197#124×C61—21no—
198#124×C61C2×C411yescharacteristic
199#123×C61—21no—
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61C2×C411yescharacteristic
202#121×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61C22×C411yescharacteristic
208C2×D4×C61—21no—
209C2×D4×C61C22×C411yescharacteristic
210C22×C4×C61—21no—
211C22×C4×C61C22×C411yescharacteristic
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61C22⋊C411yescharacteristic
218C2×C22⋊D61C22⋊C411yescharacteristic
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223#11758226—42no—
224Q8×D61—81no—
225Q8×D61—81no—
226#11758224—42no—
227#11758224—81no—
228#11758224—81no—
229#11758222—42no—
230#11758222—81no—
231#11758222—81no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244C22⋊C411yescharacteristic
235C2×D244C22×C411yescharacteristic
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61C22×C411yescharacteristic
242C2×C4×D61C22×C411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122C22⋊C411yescharacteristic
251C2×Dic122C22×C411yescharacteristic
252#11758217—81no—
253C2×#92420—21no—
254C2×#92420—21no—
255C2×#92420—21no—
256C2×#92420—21no—
257C2×#92420—21no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—21no—
261C2×#92420—81no—
262#11758213—81no—
263D61⋊C8—81no—
264D61⋊C8—81no—
265D61⋊C8—81no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61C22⋊C411yescharacteristic
270C4⋊C4×C61C22⋊C411yescharacteristic
271C4⋊C4×C61C22×C411yescharacteristic
272C4⋊C4×C61C22×C411yescharacteristic
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊C4×C61C22⋊C411yescharacteristic
279C22⋊C4×C61C22⋊C411yescharacteristic
280C42×C61—21no—
281C42×C61C22×C411yescharacteristic
282C42×C61C22×C411yescharacteristic
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—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#11758198C22⋊C411yescharacteristic
295#11758198C22⋊C411yescharacteristic
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—21no—
301C4⋊Dic61C22×C411yescharacteristic
302C4⋊Dic61C22×C411yescharacteristic
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196C22⋊C411yescharacteristic
314#11758196C22⋊C411yescharacteristic
315#11758196C22⋊C411yescharacteristic
316#11758196C22⋊C411yescharacteristic
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61C22×C411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2411yescharacteristic
328C23×C61—21no—
329C23×C61C2×C22⋊C411yescharacteristic
330C22×D61—21no—
331C22×D61C2×C22⋊C411yescharacteristic
332C22×D61C2×C22⋊C411yescharacteristic
333Q8×C61—41no—
334Q8×C61—81no—
335D4×C61—41no—
336D4×C61—81no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—41no—
341C2×C4×C61—81no—
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C2×C22⋊C411yescharacteristic
344C2×C4×C61C2×C22⋊C411yescharacteristic
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C23×C411yescharacteristic
348C22⋊D61—22no—
349C22⋊D61—41no—
350C22⋊D61—42no—
351C22⋊D61—41no—
352C22⋊D61—41no—
353C22⋊D61—41no—
354C22⋊D61—41no—
355C22⋊D61—81no—
356C22⋊D61—81no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—42no—
365C2×Dic61—81no—
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C22×D411yescharacteristic
371C2×Dic61C22×D411yescharacteristic
372D244—22no—
373D244—41no—
374D244—42no—
375D244—81no—
376C4×D61—22no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—21no—
380C4×D61—21no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—21no—
385C4×D61—41no—
386C4×D61—42no—
387C4×D61—81no—
388C4×D61—81no—
389C4×D61—81no—
390C4×D61—81no—
391Dic122—41no—
392Dic122—41no—
393Dic122—41no—
394Dic122—41no—
395Dic122—41no—
396Dic122—41no—
397Dic122—81no—
398#92420—41no—
399#92420—41no—
400#92420—41no—
401#92420—41no—
402#92420—41no—
403#92420—41no—
404#92420—41no—
405#92420—41no—
406#17775—611nomaximal, Sylow
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61C22×C22⋊C411yescharacteristic
414C2×D61—21no—
415C2×D61—21no—
416C2×D61—21no—
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61#41312yes—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—21no—
429C4×C61—41no—
430C4×C61—41no—
431C4×C61—41no—
432Dic61—21no—
433Dic61—21no—
434Dic61—21no—
435Dic61—21no—
436Dic61—41no—
437Dic61—41no—
438Dic61—41no—
439Dic61#57611yescharacteristic
440Dic61#57711yescharacteristic
441Dic61#57711yescharacteristic
442Dic61#57811yescharacteristic
443#3511—611no—
444#2990—611no—
445#2990—611no—
446#1559—611no—
447#1557—611no—
448#1556—611no—
449#1554—611no—
450#1553—611no—
451#1551—611no—
452#1551—611no—
453#1550—611no—
454#1547—611no—
455#1542—611no—
456#1540—611no—
457C2×#332—611no—
458C2×C61—41no—
459C2×C61—81no—
460C2×C61C2×#41311yescharacteristic
461C2×C61#289711yescharacteristic
462C2×C61#289811yescharacteristic
463D61—22no—
464D61—41no—
465D61—81no—
466#556—1221no—
467#555—1221no—
468#554—1221no—
469#553—1221no—
470#553—1221no—
471#548—1221no—
472#548—1221no—
473#547—1221no—
474#542—611no—
475#542—611no—
476#542—611no—
477#542#692311yescharacteristic
478#537—611no—
479#537—611no—
480#533—611no—
481#533—611no—
482#532—611no—
483#532—611no—
484#532—611no—
485C2×C4⋊Q8—611no—
486#520—611no—
487#520—611no—
488C4×#41—611no—
489#446—1221no—
490#446—1221no—
491#435—1221no—
492#435—1221no—
493#435—1221no—
494#435—1221no—
495C8×D4—1221no—
496C8×D4—1221no—
497#432—611no—
498#432—611no—
499#432—611no—
500#432—611no—
501#431—611no—
502#431—611no—
503#423—611no—
504#423—611no—
505C2×C4⋊C8—611no—
506C2×C4⋊C8—611no—
507C2×C4⋊C8—611no—
508C2×C4⋊C8—611no—
509#333—611no—
510#333—611no—
511#333—611no—
512#333—611no—
513#332—611no—
514#332—611no—
515#332—611no—
516#332—611no—
517#332—611no—
518#332—611no—
519#332—611no—
520#332—611no—
521#331—611no—
522#331—611no—
523#331—611no—
524#331—611no—
525C61#1777511yescharacteristic, complemented, Sylow
526C2×#41—611no—
527C2×#41—611no—
528C2×#41—611no—
529C2×#41—1221no—
530C2×#41—1221no—
531C22×Q8—1221no—
532C2×M16—1221no—
533C2×M16—1221no—
534C22×C8—1221no—
535C22×C8—1221no—
536C22×C8—1221no—
537C22×C8—1221no—
538C4⋊Q8—611no—
539C4⋊Q8—611no—
540C4⋊Q8—611no—
541C4⋊Q8—611no—
542C4⋊Q8—1221no—
543C4⋊Q8—1221no—
544C4⋊Q8C2×#692311yescharacteristic
545#127—611no—
546#126—21no—
547#126—1221no—
548#126—1221no—
549#126—1221no—
550#125—1221no—
551#125—1221no—
552#124—21no—
553#124—611no—
554#124—1221no—
555#124—1221no—
556#124—1221no—
557#124—1221no—
558#124—1221no—
559#124C2×#692311yescharacteristic
560#123—21no—
561#123—1221no—
562#123—1221no—
563#123—1221no—
564C22⋊Q8—21no—
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⋊Q8C2×#692311yescharacteristic
576#121—611no—
577#121—611no—
578#121—611no—
579#121—1221no—
580#121—1221no—
581#121—1221no—
582#121—1221no—
583#121—1221no—
584#121—1221no—
585#121—1221no—
586#121—1221no—
587#121—1221no—
588#121—1221no—
589#121C2×#692311yescharacteristic
590C4×Q8—611no—
591C4×Q8—611no—
592C4×Q8—611no—
593C4×Q8—611no—
594C4×Q8—611no—
595C4×Q8—1221no—
596C4×Q8—1221no—
597C4×Q8C2×#692311yescharacteristic
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—611no—
602C4×D4—611no—
603C4×D4—611no—
604C4×D4—611no—
605C4×D4—611no—
606C4×D4—611no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4—1221no—
615C4×D4C2×#692311yescharacteristic
616#117—611no—
617#117—611no—
618#117—1221no—
619#117—1221no—
620#117—1221no—
621#117—1221no—
622#117C2×#692311yescharacteristic
623C2×C4⋊C4—611no—
624C2×C4⋊C4—611no—
625C2×C4⋊C4—1221no—
626C2×C4⋊C4—1221no—
627C2×C4⋊C4—1221no—
628C2×C42—611no—
629C2×C42—611no—
630C2×C42—611no—
631C4⋊C8—611no—
632C4⋊C8—611no—
633C4⋊C8—611no—
634C4⋊C8—611no—
635C4⋊C8—611no—
636C4⋊C8—611no—
637C4⋊C8—611no—
638C4⋊C8—611no—
639C4⋊C8—1221no—
640C4⋊C8—1221no—
641C4⋊C8—1221no—
642C4⋊C8—1221no—
643C4⋊C8—1221no—
644C4⋊C8—1221no—
645C22⋊C8—1221no—
646C22⋊C8—1221no—
647C22⋊C8—1221no—
648C22⋊C8—1221no—
649C22⋊C8—1221no—
650C22⋊C8—1221no—
651#97—1221no—
652#97—1221no—
653#97—1221no—
654#97—1221no—
655C4×C8—1221no—
656C4×C8—1221no—
657#41—4881no—
658#41—4881no—
659#41—4881no—
660#41—4881no—
661#41—2442no—
662#41—2442no—
663#41—2442no—
664C2×Q8—21no—
665C2×Q8—611no—
666C2×Q8—611no—
667C2×Q8—1221no—
668C2×Q8—1221no—
669C2×Q8—1221no—
670C2×Q8—4881no—
671C2×Q8—4881no—
672C2×Q8C22×#692311yescharacteristic
673C2×D4—21no—
674C2×D4—611no—
675C2×D4—611no—
676C2×D4—611no—
677C2×D4—611no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4C22×#692311yescharacteristic
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—611no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4C22×#692311yescharacteristic
703M16—4881no—
704M16—4881no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—4881no—
714C2×C8—4881no—
715C2×C8—4881no—
716C2×C8—4881no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—611no—
723C4⋊C4—611no—
724C4⋊C4—611no—
725C4⋊C4—611no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4C22⋊#692311yescharacteristic
740C4⋊C4C22⋊#692311yescharacteristic
741C4⋊C4C22×#692311yescharacteristic
742C4⋊C4C22×#692311yescharacteristic
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—611no—
749C22⋊C4—611no—
750C22⋊C4—611no—
751C22⋊C4—611no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—1221no—
757C22⋊C4—1221no—
758C22⋊C4—1221no—
759C22⋊C4—1221no—
760C22⋊C4—1221no—
761C22⋊C4—1221no—
762C22⋊C4—1221no—
763C22⋊C4C22⋊#692311yescharacteristic
764C22⋊C4C22⋊#692311yescharacteristic
765C42—21no—
766C42—611no—
767C42—611no—
768C42—611no—
769C42—611no—
770C42—611no—
771C42—611no—
772C42—611no—
773C42—611no—
774C42—1221no—
775C42—1221no—
776C42—1221no—
777C42C22×#692311yescharacteristic
778C42C22×#692311yescharacteristic
779C23—21no—
780C23—611no—
781C23—611no—
782C23—1221no—
783C23C2×C22⋊#692311yescharacteristic
784Q8—41no—
785Q8—81no—
786Q8—4881no—
787Q8—2441no—
788Q8—2441no—
789Q8—2441no—
790Q8—2441no—
791Q8—2441no—
792Q8—2441no—
793D4—41no—
794D4—81no—
795D4—1222no—
796D4—1222no—
797D4—4881no—
798D4—4881no—
799D4—4881no—
800D4—2441no—
801D4—2442no—
802D4—2441no—
803D4—2441no—
804D4—2441no—
805D4—2441no—
806D4—2441no—
807D4—2442no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—81no—
813C2×C4—611no—
814C2×C4—611no—
815C2×C4—611no—
816C2×C4—611no—
817C2×C4—611no—
818C2×C4—611no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1222no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—4881no—
836C2×C4—4881no—
837C2×C4—4881no—
838C2×C4—4881no—
839C2×C4—4881no—
840C2×C4—2441no—
841C2×C4—2442no—
842C2×C4—2442no—
843C2×C4C2×C22⋊#692311yescharacteristic
844C2×C4C2×C22⋊#692311yescharacteristic
845C2×C4C2×C22⋊#692311yescharacteristic
846C2×C4C2×C22⋊#692311yescharacteristic
847C2×C4C2×C22⋊#692311yescharacteristic
848C2×C4C23×#692311yescharacteristic
849C8—2441no—
850C8—2441no—
851C8—2441no—
852C8—2441no—
853C8—2441no—
854C8—2441no—
855C8—2441no—
856C8—2441no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—612no—
864C22—1221no—
865C22—1221no—
866C22—1221no—
867C22—1221no—
868C22—1221no—
869C22—2441no—
870C22—2441no—
871C22—2441no—
872C22C22×C22⋊#692311yescharacteristic
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—611no—
883C4—611no—
884C4—611no—
885C4—611no—
886C4—1221no—
887C4—1221no—
888C4—1221no—
889C4—1221no—
890C4—2441no—
891C4—2441no—
892C4—2441no—
893C2—41no—
894C2—81no—
895C2—1222no—
896C2—4881no—
897C2—2441no—
898C2D61⋊#41311yescharacteristic
899C2#2146244011yescharacteristic
900C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#542C4
socleC22×C61C22×C22⋊C4
prime radical#21459724C2
cosocleC4×Dic61C24
hypercenter#542#6923
hypocenterC61#17775
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #21462748C2semidirect
2. #21462746C2semidirect
3. #21461355C2semidirect
4. #21461350C2semidirect
5. #21461349C2semidirect
6. #21461344C2semidirect
7. #21461343C2semidirect
8. #21461339C2semidirect
9. #21461339C2semidirect
10. #21461336C2semidirect
11. #21461331C2semidirect
12. #21461321C2semidirect
13. #21461316C2semidirect
14. D61⋊#332C2semidirect
525. C61#17775semidirect

Maximal subgroups

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

subgroupindex
#214627482
#214627462
#214613552
#214613502
#214613492
#214613442
#214613432
#214613392
#214613362
#214613312
#214613212
#214613162
D61⋊#3322
#214597242
#1777561