Finite Group Databasebeta

← #30611938

Subgroups — #30611938

Order 15616.

964 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462739C211yesmaximal, characteristic, complemented
2#21462466C211yesmaximal, characteristic, complemented
3#21461359C211yesmaximal, characteristic, complemented
4#21461358C211yesmaximal, characteristic, complemented
5#21461351C211yesmaximal, characteristic, complemented
6#21461350C211yesmaximal, characteristic, complemented
7#21461341C211yesmaximal, characteristic, complemented
8#21461340C211yesmaximal, characteristic, complemented
9#21461334C211yesmaximal, characteristic, complemented
10#21461331C211yesmaximal, characteristic, complemented
11#21461331C211yesmaximal, characteristic, complemented
12#21461330C211yesmaximal, characteristic, complemented
13#21461317C211yesmaximal, characteristic, complemented
14C2×#16840621C211yesmaximal, characteristic, complemented
15#21459721C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840814—21no—
18#16840795—21no—
19#16840793—21no—
20#16840791—21no—
21#16840785C2211yescharacteristic
22#16840782C2211yescharacteristic
23#16840779C2211yescharacteristic
24#16840769—21no—
25#16840768—21no—
26#16840768—21no—
27#16840767C2211yescharacteristic
28#16840767C2211yescharacteristic
29#16840765C2211yescharacteristic
30#16840765C2211yescharacteristic
31#16840765C2211yescharacteristic
32C2×#14519844C2211yescharacteristic
33C2×#14519844C2211yescharacteristic
34C2×#14519844C2211yescharacteristic
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#16840620C2211yescharacteristic
49#16840620C2211yescharacteristic
50#16840620C2211yescharacteristic
51#16840620C2211yescharacteristic
52#16840479—21no—
53#16840476C411yescharacteristic
54#16840475C411yescharacteristic
55#16840471C411yescharacteristic
56#16840468C411yescharacteristic
57#16840464C411yescharacteristic
58#16840460C411yescharacteristic
59#16840458C411yescharacteristic
60#16840421—21no—
61#16840418—21no—
62#16840410—21no—
63#16840380—21no—
64#16840378—21no—
65#16840339—21no—
66#16840318C2211yescharacteristic
67#16840315C2211yescharacteristic
68#16840309C2211yescharacteristic
69#16840307C2211yescharacteristic
70#16840307C2211yescharacteristic
71C2×#14519776C2211yescharacteristic
72#16840241—21no—
73C4×#11758224C2211yescharacteristic
74C61×#553C411yescharacteristic
75#14519864—44no—
76C2×#11758213—21no—
77C2×#11758213—21no—
78C2×#11758217—21no—
79C2×#11758217—21no—
80C2×#11758217—21no—
81C2×D61⋊C8—21no—
82C22×#92420—21no—
83C22×#92420—21no—
84C22×#92420—21no—
85#14519844—21no—
86#14519844—21no—
87#14519844—21no—
88#14519844—21no—
89#14519844—21no—
90#14519844C2311yescharacteristic
91#14519844C2311yescharacteristic
92#14519844C2311yescharacteristic
93#14519844C2311yescharacteristic
94#14519844C2311yescharacteristic
95#14519844C2311yescharacteristic
96#14519844C2311yescharacteristic
97#14519844C2311yescharacteristic
98C4⋊#92420—21no—
99C4⋊#92420—21no—
100C4⋊#92420—21no—
101C4⋊#92420—21no—
102#14519834—21no—
103C22⋊#92420—21no—
104C22⋊#92420—21no—
105#14519832—21no—
106#14519832—21no—
107C4×#92420—21no—
108C2×#11758222—21no—
109C2×#11758224—21no—
110C2×#11758224—21no—
111C2×#11758224D411yescharacteristic
112C22×Dic122—21no—
113#14519776—21no—
114#14519776—21no—
115#14519776C2×C411yescharacteristic
116#14519776C2×C411yescharacteristic
117#14519776C2311yescharacteristic
118#14519776C2311yescharacteristic
119#14519776C2311yescharacteristic
120#14519773C2311yescharacteristic
121#14519772—21no—
122#14519772—21no—
123#14519770—21no—
124#14519769C2×C411yescharacteristic
125#14519768C2×C411yescharacteristic
126#14519768C2×C411yescharacteristic
127#14519765—21no—
128#14519764—21no—
129#14519763—21no—
130#14519763—21no—
131#14519763—21no—
132#14519763—21no—
133#14519763—21no—
134#14519762—21no—
135#14519761—21no—
136#14519759—21no—
137#14519757—21no—
138#14519756—21no—
139#14519755—21no—
140#14519755—21no—
141#14519755—21no—
142#14519755—21no—
143#14519754—21no—
144#14519754—21no—
145#14519754—21no—
146#14519754—21no—
147#14519752C2×C411yescharacteristic
148#14519751—21no—
149#14519751C2×C411yescharacteristic
150#14519751C2×C411yescharacteristic
151#14519750—21no—
152#14519750—21no—
153#14519749—21no—
154#14519749—21no—
155#14519749—21no—
156#14519749—21no—
157#14519749—21no—
158#14519748C2×C411yescharacteristic
159C4×Dic122—21no—
160C4×Dic122—21no—
161C4×Dic122C2×C411yescharacteristic
162#14519742—21no—
163#14519742—21no—
164#14519742D411yescharacteristic
165C4×D244C2×C411yescharacteristic
166D4×Dic61—21no—
167D4×Dic61C2×C411yescharacteristic
168D4×Dic61C2×C411yescharacteristic
169D4×Dic61D411yescharacteristic
170#14519739C2×C411yescharacteristic
171#14519739C2×C411yescharacteristic
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61C2×C411yescharacteristic
175C4×C22⋊D61C2×C411yescharacteristic
176#14519737—21no—
177#14519737—21no—
178#14519737—21no—
179#14519737D411yescharacteristic
180#14519737D411yescharacteristic
181#14519736C2×C411yescharacteristic
182#14519735C2×C411yescharacteristic
183#14519735C2×C411yescharacteristic
184#14519735D411yescharacteristic
185#14519734—21no—
186#14519733—21no—
187#14519733D411yescharacteristic
188#14519733D411yescharacteristic
189C2×C4⋊Dic61C2×C411yescharacteristic
190C2×#11758196—21no—
191C2×#11758196—21no—
192C4⋊C4×D61—21no—
193C2×C4×Dic61C2311yescharacteristic
194C2×C4×Dic61C2311yescharacteristic
195C42×D61C2311yescharacteristic
196#126×C61—21no—
197#125×C61C2×C411yescharacteristic
198#123×C61—21no—
199#121×C61—21no—
200#121×C61C2×C411yescharacteristic
201#121×C61C2×C411yescharacteristic
202C4×D4×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic
206C2×C4⋊C4×C61C2×C411yescharacteristic
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61C22⋊C411yescharacteristic
210C2×D4×C61C22×C411yescharacteristic
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61C22⋊C411yescharacteristic
221C2×C22⋊D61C22⋊C411yescharacteristic
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229#11758224—22no—
230#11758224—22no—
231#11758224—42no—
232#11758224—42no—
233#11758224—81no—
234#11758224—81no—
235#11758222—81no—
236#11758222—81no—
237C2×D244—21no—
238C2×D244C22×C411yescharacteristic
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61C22×C411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×Dic122—21no—
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—81no—
251C2×Dic122—81no—
252C2×Dic122C22⋊C411yescharacteristic
253#11758217—42no—
254#11758217—42no—
255#11758217—81no—
256C2×#92420—21no—
257C2×#92420—21no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—21no—
261C2×#92420—21no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—42no—
265C2×#92420—42no—
266C2×#92420—81no—
267#11758213—42no—
268#11758213—81no—
269D61⋊C8—42no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61C22⋊C411yescharacteristic
274C4⋊C4×C61C22×C411yescharacteristic
275C4⋊C4×C61C22×C411yescharacteristic
276C4⋊C4×C61C22×C411yescharacteristic
277C22⋊C4×C61—21no—
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61C22⋊C411yescharacteristic
282C22⋊C4×C61C22⋊C411yescharacteristic
283C42×C61—21no—
284C42×C61C22×C411yescharacteristic
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61C22⋊C411yescharacteristic
290C22⋊Dic61C22⋊C411yescharacteristic
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#11758198C22⋊C411yescharacteristic
300#11758198C22⋊C411yescharacteristic
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61C22⋊C411yescharacteristic
305C4⋊Dic61C22×C411yescharacteristic
306C4⋊Dic61C22×C411yescharacteristic
307C4⋊Dic61C22×C411yescharacteristic
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196C22⋊C411yescharacteristic
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320#11758196C22⋊C411yescharacteristic
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61C22×C411yescharacteristic
325C4×Dic61C22×C411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2×D411yescharacteristic
332C4×Dic61C2411yescharacteristic
333C23×C61—21no—
334C23×C61C2×C22⋊C411yescharacteristic
335C23×C61C2×C22⋊C411yescharacteristic
336C22×D61—21no—
337C22×D61C2×C22⋊C411yescharacteristic
338D4×C61—22no—
339D4×C61—41no—
340D4×C61—42no—
341D4×C61—81no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—81no—
348C2×C4×C61—81no—
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C2×C22⋊C411yescharacteristic
353C2×C4×C61C23×C411yescharacteristic
354C22⋊D61—22no—
355C22⋊D61—22no—
356C22⋊D61—42no—
357C22⋊D61—41no—
358C22⋊D61—41no—
359C22⋊D61—41no—
360C22⋊D61—41no—
361C22⋊D61—81no—
362C22⋊D61—81no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61—42no—
373C2×Dic61—81no—
374C2×Dic61—81no—
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61AGL(1,ℤ/8)12yes—
381C2×Dic61#13712yes—
382C2×Dic61C22×D411yescharacteristic
383C2×Dic61C22×D411yescharacteristic
384D244—41no—
385D244—81no—
386C4×D61—21no—
387C4×D61—21no—
388C4×D61—21no—
389C4×D61—21no—
390C4×D61—41no—
391C4×D61—42no—
392C4×D61—81no—
393C4×D61—81no—
394Dic122—22no—
395Dic122—41no—
396Dic122—41no—
397Dic122—41no—
398Dic122—41no—
399Dic122—41no—
400Dic122—41no—
401Dic122—81no—
402Dic122—81no—
403#92420—41no—
404#92420—41no—
405#92420—41no—
406#92420—41no—
407#92420—41no—
408#92420—41no—
409#92420—41no—
410#92420—41no—
411#17765—611nomaximal, Sylow
412C22×C61—21no—
413C22×C61—21no—
414C22×C61—21no—
415C22×C61—21no—
416C22×C61—21no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61#41712yes—
421C22×C61C22×C22⋊C411yescharacteristic
422C2×D61—21no—
423C2×D61—21no—
424C2×D61—21no—
425C2×D61—41no—
426C2×D61—41no—
427C2×D61—41no—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61—41no—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
439Dic61—21no—
440Dic61—41no—
441Dic61—41no—
442Dic61—41no—
443Dic61#41712yes—
444Dic61C2×AGL(1,ℤ/8)11yescharacteristic
445Dic61C2×#13711yescharacteristic
446Dic61#57611yescharacteristic
447Dic61#57711yescharacteristic
448#3511—611no—
449#2989—611no—
450#2906—611no—
451#1561—611no—
452#1561—611no—
453#1557—611no—
454#1557—611no—
455#1552—611no—
456#1552—611no—
457#1549—611no—
458#1547—611no—
459#1547—611no—
460#1547—611no—
461#1540—611no—
462C2×#332—611no—
463C2×C61—22no—
464C2×C61—41no—
465C2×C61—81no—
466C2×C61#288911yescharacteristic
467C2×C61C2×#41711yescharacteristic
468C2×C61#289711yescharacteristic
469D61—41no—
470D61—81no—
471C2×#131—1221no—
472#556—1221no—
473#555—611no—
474#555—611no—
475#554—611no—
476#554—611no—
477#553—611no—
478#553—611no—
479#553—611no—
480#553#692311yescharacteristic
481#548—1221no—
482#548—1221no—
483#547—1221no—
484#542—1221no—
485#542—1221no—
486#537—1221no—
487#533—611no—
488#533—611no—
489#532—611no—
490#532—611no—
491#532—611no—
492C2×C4⋊Q8—611no—
493#520—1221no—
494C4×#41—611no—
495#446—1221no—
496#436—1221no—
497#435—1221no—
498#435—1221no—
499#432—611no—
500#432—611no—
501#431—611no—
502#424—1221no—
503#424—1221no—
504#424—1221no—
505#423—611no—
506#423—611no—
507#423—611no—
508#423—611no—
509#423—611no—
510C2×C4⋊C8—611no—
511C2×C4⋊C8—611no—
512C2×C4⋊C8—611no—
513C2×C4⋊C8—611no—
514#332—611no—
515#332—611no—
516#332—611no—
517#332—611no—
518#332—611no—
519#332—611no—
520#332—611no—
521#332—611no—
522#332—611no—
523#332—611no—
524#332—611no—
525#332—611no—
526#331—611no—
527#331—611no—
528#331—611no—
529#331—611no—
530C61#1776511yescharacteristic, complemented, Sylow
531C2×#41—611no—
532C2×#41—1221no—
533C2×#41—1221no—
534C2×#41—1221no—
535C22×Q8—1221no—
536#131—2444no—
537C2×M16—1221no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1221no—
541C2×M16—1221no—
542C22×C8—1221no—
543C22×C8—1221no—
544C22×C8—1221no—
545C22×C8—1221no—
546C4⋊Q8—611no—
547C4⋊Q8—611no—
548C4⋊Q8—611no—
549C4⋊Q8—611no—
550C4⋊Q8—611no—
551C4⋊Q8—1221no—
552C4⋊Q8—1221no—
553#127—611no—
554#126—21no—
555#126—1221no—
556#126—1221no—
557#126—1221no—
558#125—611no—
559#125—611no—
560#125—611no—
561#125C2×#692311yescharacteristic
562#124—1221no—
563#124—1221no—
564#124—1221no—
565#124—1221no—
566#124—1221no—
567#124—1221no—
568#124—1221no—
569#123—21no—
570#123—1221no—
571#123—1221no—
572#123—1221no—
573C22⋊Q8—1221no—
574C22⋊Q8—1221no—
575C22⋊Q8—1221no—
576C22⋊Q8—1221no—
577C22⋊Q8—1221no—
578C22⋊Q8—1221no—
579C22⋊Q8—1221no—
580C22⋊Q8—1221no—
581C22⋊Q8—1221no—
582C22⋊Q8—1221no—
583#121—21no—
584#121—611no—
585#121—611no—
586#121—611no—
587#121—611no—
588#121—1221no—
589#121—1221no—
590#121—1221no—
591#121—1221no—
592#121—1221no—
593#121—1221no—
594#121—1221no—
595#121—1221no—
596#121C2×#692311yescharacteristic
597#121C2×#692311yescharacteristic
598C4×Q8—611no—
599C4×Q8—611no—
600C4×Q8—1221no—
601C4×Q8—1221no—
602C4×Q8—1221no—
603C4×Q8—1221no—
604C4×D4—21no—
605C4×D4—611no—
606C4×D4—611no—
607C4×D4—611no—
608C4×D4—611no—
609C4×D4—611no—
610C4×D4—611no—
611C4×D4—611no—
612C4×D4—611no—
613C4×D4—611no—
614C4×D4—611no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4C2×#692311yescharacteristic
622C4×D4C2×#692311yescharacteristic
623#117—611no—
624#117—611no—
625#117—611no—
626#117—611no—
627#117—611no—
628#117—611no—
629#117—1221no—
630#117—1221no—
631#117C2×#692311yescharacteristic
632C2×C4⋊C4—611no—
633C2×C4⋊C4—1221no—
634C2×C4⋊C4—1221no—
635C2×C4⋊C4—1221no—
636C2×C4⋊C4C2×#692311yescharacteristic
637C2×C42—611no—
638C2×C42—611no—
639C2×C42—611no—
640C4⋊C8—611no—
641C4⋊C8—611no—
642C4⋊C8—611no—
643C4⋊C8—611no—
644C4⋊C8—611no—
645C4⋊C8—611no—
646C4⋊C8—611no—
647C4⋊C8—611no—
648C4⋊C8—1221no—
649C4⋊C8—1221no—
650C4⋊C8—1221no—
651C4⋊C8—1221no—
652C4⋊C8—1221no—
653C4⋊C8—1221no—
654C4⋊C8—1221no—
655C4⋊C8—1221no—
656C4⋊C8—1221no—
657C22⋊C8—1221no—
658C22⋊C8—1221no—
659C22⋊C8—1221no—
660#97—1221no—
661#97—1221no—
662C4×C8—1221no—
663#41—1222no—
664#41—1222no—
665#41—4881no—
666#41—4881no—
667#41—4881no—
668#41—4881no—
669#41—2442no—
670#41—2442no—
671C2×Q8—611no—
672C2×Q8—1221no—
673C2×Q8—1221no—
674C2×Q8—1221no—
675C2×Q8—1221no—
676C2×Q8—1221no—
677C2×Q8—4881no—
678C2×Q8—4881no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—611no—
682C2×D4—611no—
683C2×D4—611no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4C22⋊#692311yescharacteristic
691C2×D4C22×#692311yescharacteristic
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4C22×#692311yescharacteristic
708C22×C4C22×#692311yescharacteristic
709M16—4881no—
710M16—4881no—
711M16—2442no—
712M16—2442no—
713M16—2442no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—4881no—
723C2×C8—2442no—
724C2×C8—2442no—
725C2×C8—2442no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—611no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—611no—
734C4⋊C4—611no—
735C4⋊C4—611no—
736C4⋊C4—611no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4C22⋊#692311yescharacteristic
750C4⋊C4C22×#692311yescharacteristic
751C4⋊C4C22×#692311yescharacteristic
752C4⋊C4C22×#692311yescharacteristic
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—611no—
758C22⋊C4—611no—
759C22⋊C4—611no—
760C22⋊C4—611no—
761C22⋊C4—1221no—
762C22⋊C4—1221no—
763C22⋊C4—1221no—
764C22⋊C4—1221no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4—1221no—
773C22⋊C4C22⋊#692311yescharacteristic
774C22⋊C4C22⋊#692311yescharacteristic
775C42—21no—
776C42—611no—
777C42—611no—
778C42—611no—
779C42—611no—
780C42—611no—
781C42—611no—
782C42—611no—
783C42—611no—
784C42—611no—
785C42—1221no—
786C42—1221no—
787C42—1221no—
788C42C22×#692311yescharacteristic
789C23—21no—
790C23—611no—
791C23—1221no—
792C23C2×C22⋊#692311yescharacteristic
793C23C2×C22⋊#692311yescharacteristic
794Q8—1222no—
795Q8—4881no—
796Q8—4881no—
797Q8—2441no—
798Q8—2441no—
799Q8—2441no—
800Q8—2441no—
801Q8—2441no—
802Q8—2441no—
803D4—22no—
804D4—41no—
805D4—42no—
806D4—81no—
807D4—1222no—
808D4—1222no—
809D4—4881no—
810D4—4881no—
811D4—4881no—
812D4—2441no—
813D4—2441no—
814D4—2441no—
815D4—2441no—
816D4—2441no—
817D4—2442no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—612no—
826C2×C4—612no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—611no—
830C2×C4—611no—
831C2×C4—611no—
832C2×C4—611no—
833C2×C4—611no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1221no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—4881no—
848C2×C4—4881no—
849C2×C4—4881no—
850C2×C4—4881no—
851C2×C4—2441no—
852C2×C4—2442no—
853C2×C4—2442no—
854C2×C4C2×C22⋊#692311yescharacteristic
855C2×C4C2×C22⋊#692311yescharacteristic
856C2×C4C2×C22⋊#692311yescharacteristic
857C2×C4C2×C22⋊#692311yescharacteristic
858C2×C4C23×#692311yescharacteristic
859C8—2441no—
860C8—2441no—
861C8—2441no—
862C8—2441no—
863C8—2441no—
864C8—2441no—
865C8—2441no—
866C8—2441no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—1221no—
876C22—1221no—
877C22—1221no—
878C22—2441no—
879C22—2441no—
880C22—2441no—
881C22#1684075312yes—
882C22C22×C22⋊#692311yescharacteristic
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—611no—
892C4—611no—
893C4—612no—
894C4—611no—
895C4—611no—
896C4—1221no—
897C4—1221no—
898C4—1221no—
899C4—1221no—
900C4—2441no—
901C4—2441no—
902C4—2441no—
903C2—22no—
904C2—41no—
905C2—81no—
906C2—4881no—
907C2—2441no—
908C2#2146243111yescharacteristic
909C2C2×#1684075311yescharacteristic
910C2#2146244011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#553C4
socleC22×C61C22×C22⋊C4
prime radical#21459721C2
cosocleC4×Dic61C24
hypercenter#553#6923
hypocenterC61#17765
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #21462739C2semidirect
2. #21462466C2semidirect
3. #21461359C2semidirect
4. #21461358C2semidirect
5. #21461351C2semidirect
6. #21461350C2semidirect
7. #21461341C2semidirect
8. #21461340C2semidirect
9. #21461334C2semidirect
10. #21461331C2semidirect
11. #21461331C2semidirect
12. #21461330C2semidirect
13. #21461317C2semidirect
14. C2×#16840621C2semidirect
530. C61#17765semidirect

Maximal subgroups

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

subgroupindex
#214627392
#214624662
#214613592
#214613582
#214613512
#214613502
#214613412
#214613402
#214613342
#214613312
#214613302
#214613172
C2×#168406212
#214597212
#1776561