Finite Group Databasebeta

← #30610855

Subgroups — #30610855

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462747C211yesmaximal, characteristic, complemented
2#21462502C211yesmaximal, characteristic, complemented
3#21461178C211yesmaximal, characteristic, complemented
4#21461175C211yesmaximal, characteristic, complemented
5#21461172C211yesmaximal, characteristic, complemented
6#21461158C211yesmaximal, characteristic, complemented
7#21461150C211yesmaximal, characteristic, complemented
8#21461145C211yesmaximal, characteristic, complemented
9#21461136C211yesmaximal, characteristic, complemented
10#21461131C211yesmaximal, characteristic, complemented
11#21461124C211yesmaximal, characteristic, complemented
12#21461119C211yesmaximal, characteristic, complemented
13#21461114C211yesmaximal, characteristic, complemented
14C2×D4⋊#92420C211yesmaximal, characteristic, complemented
15#21459424C211yesmaximal, characteristic
16#16840812—21no—
17#16840791—21no—
18#16840791—21no—
19D4×#92420—21no—
20#16840787—21no—
21#16840786—21no—
22#16840783C2211yescharacteristic, complemented
23#16840783C2211yescharacteristic, complemented
24#16840781C2211yescharacteristic, complemented
25#16840781C2211yescharacteristic, complemented
26#16840780C2211yescharacteristic, complemented
27#16840779C2211yescharacteristic, complemented
28#16840778C2211yescharacteristic, complemented
29#16840768—21no—
30#16840766C2211yescharacteristic, complemented
31C2×C4⋊#92420C2211yescharacteristic, complemented
32C2×C4⋊#92420C2211yescharacteristic, complemented
33#16840735—21no—
34C4×#11758217C2211yescharacteristic, complemented
35C2×C4×#92420C2211yescharacteristic, complemented
36Q8⋊#92420C2211yescharacteristic, complemented
37Q8⋊#92420C2211yescharacteristic, complemented
38Q8⋊#92420C2211yescharacteristic, complemented
39Q8⋊#92420C2211yescharacteristic, complemented
40#16840610C2211yescharacteristic, complemented
41#16840610C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic, complemented
43#16840610C2211yescharacteristic, complemented
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48D4⋊#92420C2211yescharacteristic, complemented
49D4⋊#92420C2211yescharacteristic, complemented
50D4⋊#92420C2211yescharacteristic, complemented
51D4⋊#92420C2211yescharacteristic, complemented
52#16840494C411yescharacteristic
53#16840471C411yescharacteristic
54#16840470C411yescharacteristic
55#16840459C411yescharacteristic
56#16840458C411yescharacteristic
57#16840455—21no—
58#16840438—21no—
59#16840435—21no—
60#16840400C411yescharacteristic
61#16840399—21no—
62D4×C22⋊D61C411yescharacteristic
63#16840307C2211yescharacteristic
64#16840298C2211yescharacteristic
65#16840291C2211yescharacteristic
66#16840289—21no—
67#16840272—21no—
68#16840268—21no—
69#41×Dic61C2211yescharacteristic
70C4×#11758224C2211yescharacteristic
71C2×D4×Dic61C2211yescharacteristic
72C2×#14519737—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#546C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758217—21no—
77C22×#92420—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80#14519844—21no—
81#14519844—21no—
82C4⋊#92420—21no—
83C4⋊#92420—21no—
84C4⋊#92420—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87C4⋊#92420C2311yescharacteristic
88C4⋊#92420C2311yescharacteristic
89C4⋊#92420C2311yescharacteristic
90C4⋊#92420C2311yescharacteristic
91#14519834—21no—
92#14519834—21no—
93#14519834—21no—
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96C22⋊#92420—21no—
97C22⋊#92420—21no—
98#14519832—21no—
99#14519832—21no—
100#14519832—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420C2311yescharacteristic
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C2×#11758224—21no—
108C2×#11758224D411yescharacteristic
109C22×C22⋊D61—21no—
110C2×D4×D61C2×C411yescharacteristic
111C23×Dic61—21no—
112C22×C4×D61—21no—
113#14519776C2×C411yescharacteristic
114#14519773C2×C411yescharacteristic
115#14519772—21no—
116#14519772—21no—
117#14519770—21no—
118#14519770—21no—
119#14519769C2×C411yescharacteristic
120#14519768C2×C411yescharacteristic
121#14519767—21no—
122#14519766C2×C411yescharacteristic
123#14519763—21no—
124#14519763—21no—
125#14519761—21no—
126#14519761—21no—
127#14519760—21no—
128#14519759—21no—
129#14519759—21no—
130#14519759—21no—
131#14519758—21no—
132#14519757—21no—
133#14519756—21no—
134#14519754—21no—
135#14519754—21no—
136#14519754—21no—
137#14519753C2×C411yescharacteristic
138#14519751C2×C411yescharacteristic
139#14519751C2×C411yescharacteristic
140#14519749—21no—
141#14519749—21no—
142#14519749—21no—
143#14519749—21no—
144#14519748—21no—
145#14519748C2×C411yescharacteristic
146#14519746—21no—
147#14519745—21no—
148#14519745—21no—
149Q8×Dic61C2×C411yescharacteristic
150Q8×Dic61C2311yescharacteristic
151C4×Dic122C2×C411yescharacteristic
152#14519742D411yescharacteristic
153C4×D244C2×C411yescharacteristic
154D4×Dic61—21no—
155D4×Dic61—21no—
156D4×Dic61—21no—
157D4×Dic61—21no—
158D4×Dic61C2×C411yescharacteristic
159D4×Dic61C2×C411yescharacteristic
160D4×Dic61C2×C411yescharacteristic
161D4×Dic61D411yescharacteristic
162D4×Dic61C2311yescharacteristic
163D4×Dic61C2311yescharacteristic
164#14519739C2311yescharacteristic
165C4×C22⋊D61—21no—
166C4×C22⋊D61C2×C411yescharacteristic
167C4×C22⋊D61C2×C411yescharacteristic
168#14519737—21no—
169#14519737—21no—
170#14519737—21no—
171#14519737—21no—
172#14519737—21no—
173#14519737—21no—
174#14519737—21no—
175#14519737—21no—
176#14519737D411yescharacteristic
177#14519737D411yescharacteristic
178#14519736—21no—
179#14519736C2×C411yescharacteristic
180#14519735—21no—
181#14519735D411yescharacteristic
182#14519733—21no—
183#14519733D411yescharacteristic
184#14519733D411yescharacteristic
185C2×C4⋊Dic61C2×C411yescharacteristic
186C2×#11758196—21no—
187C4⋊C4×D61C2×C411yescharacteristic
188C2×C22⋊Dic61—21no—
189C2×#11758198—21no—
190C22⋊C4×D61—21no—
191C2×C4×Dic61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C22×D4×C61C2×C411yescharacteristic
197#124×C61C2×C411yescharacteristic
198#123×C61—21no—
199C22⋊Q8×C61C2×C411yescharacteristic
200#121×C61—21no—
201#121×C61C2×C411yescharacteristic
202#120×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205C2×C22⋊C4×C61—21no—
206C24×C61—21no—
207C23×D61—21no—
208#41×C61—22no—
209#41×C61—41no—
210C2×Q8×C61C22×C411yescharacteristic
211C2×D4×C61—22no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—41no—
216C2×D4×C61C22⋊C411yescharacteristic
217C2×D4×C61C22×C411yescharacteristic
218C2×D4×C61C22×C411yescharacteristic
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C22×C411yescharacteristic
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—44no—
230C2×C22⋊D61C22⋊C411yescharacteristic
231C2×C22⋊D61C22⋊C411yescharacteristic
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—81no—
239C22×Dic61—81no—
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244#11758224—42no—
245#11758224—81no—
246#11758224—81no—
247D4×D61—22no—
248D4×D61—41no—
249C2×D244C22×C411yescharacteristic
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—81no—
254C2×C4×D61—81no—
255C2×C4×D61C22×C411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×Dic122—21no—
259C2×Dic122C22⋊C411yescharacteristic
260#11758217—42no—
261C2×#92420—21no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—21no—
265C2×#92420—21no—
266C2×#92420—21no—
267C2×#92420—21no—
268C2×#92420—21no—
269C2×#92420—42no—
270C2×#92420—81no—
271C2×#92420—81no—
272#11758213—81no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61C22⋊C411yescharacteristic
275C4⋊C4×C61C22×C411yescharacteristic
276C22⋊C4×C61—21no—
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×C61C22×C411yescharacteristic
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61C22⋊C411yescharacteristic
292C22⋊Dic61C22⋊C411yescharacteristic
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61C22⋊C411yescharacteristic
307C4⋊Dic61C22×C411yescharacteristic
308C4⋊Dic61C22×C411yescharacteristic
309C4⋊Dic61C22×C411yescharacteristic
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196C22⋊C411yescharacteristic
317#11758196C22⋊C411yescharacteristic
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61C22×C411yescharacteristic
324C4×Dic61C22×C411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2411yescharacteristic
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—42no—
335C23×C61—42no—
336C23×C61—81no—
337C23×C61C2×C22⋊C411yescharacteristic
338C23×C61C2×C22⋊C411yescharacteristic
339C22×D61—21no—
340C22×D61—42no—
341C22×D61—42no—
342C22×D61—81no—
343C22×D61C2×C22⋊C411yescharacteristic
344Q8×C61—21no—
345Q8×C61—21no—
346D4×C61—22no—
347D4×C61—21no—
348D4×C61—21no—
349D4×C61—21no—
350D4×C61—42no—
351D4×C61—42no—
352D4×C61—81no—
353D4×C61#13112yes—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—42no—
361C2×C4×C61—81no—
362C2×C4×C61C2×C22⋊C411yescharacteristic
363C2×C4×C61C2×C22⋊C411yescharacteristic
364C2×C4×C61C2×C22⋊C411yescharacteristic
365C2×C4×C61C2×C22⋊C411yescharacteristic
366C2×C4×C61C23×C411yescharacteristic
367C22⋊D61—22no—
368C22⋊D61—41no—
369C22⋊D61—42no—
370C22⋊D61—42no—
371C22⋊D61—42no—
372C22⋊D61—42no—
373C22⋊D61—81no—
374C22⋊D61—81no—
375C2×Dic61—22no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—41no—
384C2×Dic61—42no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—81no—
390C2×Dic61—81no—
391C2×Dic61—81no—
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C2×C22⋊C411yescharacteristic
394C2×Dic61C2×C22⋊C411yescharacteristic
395C2×Dic61C2×C22⋊C411yescharacteristic
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C22×D411yescharacteristic
398C2×Dic61C22×D411yescharacteristic
399D244—21no—
400D244—21no—
401C4×D61—21no—
402C4×D61—21no—
403C4×D61—21no—
404C4×D61—21no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—81no—
409C4×D61—81no—
410Dic122—41no—
411Dic122—81no—
412#92420—41no—
413#92420—41no—
414#92420—41no—
415#92420—41no—
416#92420—41no—
417#92420—41no—
418#92420—41no—
419#92420—41no—
420#17521—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—22no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—84no—
433C22×C61#42112yes—
434C22×C61C22×C22⋊C411yescharacteristic
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—41no—
439C2×D61—41no—
440C2×D61—41no—
441C2×D61—84no—
442C4×C61—21no—
443C4×C61—21no—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—41no—
447C4×C61—41no—
448C4×C61C2×#13111yescharacteristic
449C4×C61#56811yescharacteristic
450Dic61—21no—
451Dic61—21no—
452Dic61—21no—
453Dic61—21no—
454Dic61—21no—
455Dic61—21no—
456Dic61—41no—
457Dic61—41no—
458Dic61—41no—
459Dic61#57611yescharacteristic
460Dic61#57711yescharacteristic
461#3481—611no—
462#2990—611no—
463#2922—611no—
464#1496—611no—
465#1495—611no—
466#1494—611no—
467#1490—611no—
468#1488—611no—
469#1486—611no—
470#1483—611no—
471#1482—611no—
472#1480—611no—
473#1478—611no—
474#1477—611no—
475C2×D4⋊C8—611no—
476C2×C61—22no—
477C2×C61—42no—
478C2×C61—41no—
479C2×C61—81no—
480C2×C61#288011yescharacteristic
481C2×C61#289711yescharacteristic
482C2×C61C2×#42111yescharacteristic
483D61—41no—
484D61—81no—
485#559—611no—
486#554—611no—
487#554—611no—
488#553—611no—
489#553—611no—
490#553—1221no—
491#551—1221no—
492#551—1221no—
493#546—611no—
494#546—1221no—
495#546#692311yescharacteristic
496D42—611no—
497#532—611no—
498#529—611no—
499#529—611no—
500#529—1221no—
501#525—1221no—
502#525—1221no—
503C4×#41—611no—
504C4×#41—611no—
505C2×C4×D4—611no—
506C2×C4×D4—611no—
507C2×C4×D4—1221no—
508#446—1221no—
509#435—1221no—
510#435—1221no—
511C8×D4—1221no—
512#433—1221no—
513#433—1221no—
514#432—611no—
515#432—611no—
516#431—611no—
517#431—611no—
518#431—611no—
519#431—611no—
520#431—611no—
521#424—1221no—
522#423—611no—
523C2×C4⋊C8—611no—
524C2×C4⋊C8—611no—
525#408—1221no—
526C4×M16—611no—
527C2×C4×C8—611no—
528Q8⋊C8—611no—
529Q8⋊C8—611no—
530Q8⋊C8—611no—
531Q8⋊C8—611no—
532D4⋊C8—611no—
533D4⋊C8—611no—
534D4⋊C8—611no—
535D4⋊C8—611no—
536D4⋊C8—611no—
537D4⋊C8—611no—
538D4⋊C8—611no—
539D4⋊C8—611no—
540D4⋊C8—611no—
541D4⋊C8—611no—
542D4⋊C8—611no—
543D4⋊C8—611no—
544C61#1752111yescharacteristic, complemented, Sylow
545C2×#41—611no—
546C2×#41—1221no—
547C2×#41C2×#692311yescharacteristic
548C22×D4—611no—
549C22×D4—1221no—
550C22×D4C2×#692311yescharacteristic
551C23×C4—1221no—
552C23×C4—1221no—
553C2×M16—1221no—
554C2×M16—1221no—
555C22×C8—1221no—
556C22×C8—1221no—
557C22×C8—1221no—
558C4⋊Q8—611no—
559#127—611no—
560#126—1221no—
561#126—1221no—
562#126—1221no—
563#126—1221no—
564#125—611no—
565#125—611no—
566#125—1221no—
567#124—611no—
568#124—1221no—
569#124—1221no—
570#124C2×#692311yescharacteristic
571#123—21no—
572#123—1221no—
573#123—1221no—
574#123—1221no—
575#123—1221no—
576#123—1221no—
577#123—1221no—
578#123—1221no—
579C22⋊Q8—611no—
580C22⋊Q8—1221no—
581C22⋊Q8—1221no—
582C22⋊Q8—1221no—
583C22⋊Q8—1221no—
584C22⋊Q8—1221no—
585C22⋊Q8C2×#692311yescharacteristic
586#121—21no—
587#121—611no—
588#121—611no—
589#121—611no—
590#121—1221no—
591#121—1221no—
592#121—1221no—
593#121—1221no—
594#121—1221no—
595#121C2×#692311yescharacteristic
596#120—21no—
597#120—1221no—
598#120—1221no—
599#120—1221no—
600C4×Q8—611no—
601C4×Q8—611no—
602C4×Q8—611no—
603C4×Q8—611no—
604C4×D4—611no—
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—611no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4—1221no—
626C4×D4—1221no—
627C4×D4—1221no—
628C4×D4—1221no—
629C4×D4C2×#692311yescharacteristic
630C4×D4C2×#692311yescharacteristic
631#117—611no—
632#117—611no—
633#117—611no—
634#117—611no—
635#117—1221no—
636#117—1221no—
637#117—1221no—
638C2×C4⋊C4—611no—
639C2×C4⋊C4—611no—
640C2×C4⋊C4—1221no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—1221no—
643C2×C22⋊C4—1221no—
644C2×C22⋊C4—1221no—
645C2×C42—611no—
646C2×C42—611no—
647C2×C42—611no—
648C2×C42—1221no—
649C4⋊C8—611no—
650C4⋊C8—611no—
651C4⋊C8—611no—
652C4⋊C8—611no—
653C4⋊C8—1221no—
654C4⋊C8—1221no—
655C4⋊C8—1221no—
656C4⋊C8—1221no—
657C4⋊C8—1221no—
658C4⋊C8—1221no—
659C4⋊C8—1221no—
660C22⋊C8—1221no—
661C22⋊C8—1221no—
662C22⋊C8—1221no—
663C22⋊C8—1221no—
664C22⋊C8—1221no—
665C22⋊C8—1221no—
666C22⋊C8—1221no—
667#97—1221no—
668#97—1221no—
669#97—1221no—
670C4×C8—611no—
671C4×C8—611no—
672C4×C8—611no—
673C4×C8—611no—
674C4×C8—1221no—
675C4×C8—1221no—
676C24—21no—
677C24—1221no—
678#41—22no—
679#41—41no—
680#41—4881no—
681#41—4881no—
682#41—2442no—
683C2×Q8—611no—
684C2×Q8—1221no—
685C2×Q8C22×#692311yescharacteristic
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—611no—
692C2×D4—611no—
693C2×D4—611no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1222no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—2441no—
702C2×D4—2444no—
703C2×D4C22⋊#692311yescharacteristic
704C2×D4C22×#692311yescharacteristic
705C2×D4C22×#692311yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—4881no—
725C22×C4—4881no—
726C22×C4—4881no—
727C22×C4—4881no—
728C22×C4C22×#692311yescharacteristic
729C22×C4C22×#692311yescharacteristic
730M16—4881no—
731M16—2442no—
732C2×C8—1221no—
733C2×C8—1221no—
734C2×C8—1221no—
735C2×C8—1221no—
736C2×C8—1221no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—4881no—
741C2×C8—4881no—
742C2×C8—2442no—
743C4⋊C4—21no—
744C4⋊C4—611no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4C22⋊#692311yescharacteristic
763C4⋊C4C22×#692311yescharacteristic
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—611no—
770C22⋊C4—611no—
771C22⋊C4—611no—
772C22⋊C4—611no—
773C22⋊C4—1221no—
774C22⋊C4—1221no—
775C22⋊C4—1221no—
776C22⋊C4—1221no—
777C22⋊C4—1221no—
778C22⋊C4—1221no—
779C22⋊C4—1221no—
780C22⋊C4—1221no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4C22⋊#692311yescharacteristic
788C22⋊C4C22⋊#692311yescharacteristic
789C42—611no—
790C42—611no—
791C42—611no—
792C42—611no—
793C42—611no—
794C42—611no—
795C42—611no—
796C42—611no—
797C42—611no—
798C42—1221no—
799C42—1221no—
800C42—1221no—
801C42C22×#692311yescharacteristic
802C23—21no—
803C23—21no—
804C23—42no—
805C23—42no—
806C23—81no—
807C23—611no—
808C23—1221no—
809C23—4881no—
810C23—2442no—
811C23—2442no—
812C23C2×C22⋊#692311yescharacteristic
813C23C2×C22⋊#692311yescharacteristic
814Q8—21no—
815Q8—21no—
816Q8—4881no—
817Q8—2441no—
818D4—22no—
819D4—21no—
820D4—21no—
821D4—21no—
822D4—42no—
823D4—42no—
824D4—81no—
825D4—1222no—
826D4—1221no—
827D4—1221no—
828D4—4881no—
829D4—4881no—
830D4—2441no—
831D4—2442no—
832D4—2442no—
833D4—2442no—
834D4—2442no—
835D4#1451986412yes—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—42no—
843C2×C4—81no—
844C2×C4—611no—
845C2×C4—611no—
846C2×C4—611no—
847C2×C4—611no—
848C2×C4—611no—
849C2×C4—611no—
850C2×C4—611no—
851C2×C4—1221no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1222no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—4881no—
864C2×C4—4881no—
865C2×C4—4881no—
866C2×C4—4881no—
867C2×C4—4881no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2442no—
877C2×C4C2×C22⋊#692311yescharacteristic
878C2×C4C2×C22⋊#692311yescharacteristic
879C2×C4C2×C22⋊#692311yescharacteristic
880C2×C4C2×C22⋊#692311yescharacteristic
881C2×C4C23×#692311yescharacteristic
882C8—2441no—
883C8—2441no—
884C8—2441no—
885C8—2441no—
886C8—2441no—
887C8—2441no—
888C8—2441no—
889C8—2441no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—22no—
894C22—21no—
895C22—21no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—84no—
902C22—1221no—
903C22—1221no—
904C22—1221no—
905C22—4884no—
906C22—2441no—
907C22—2441no—
908C22—2441no—
909C22#1684075912yes—
910C22C22×C22⋊#692311yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—41no—
916C4—41no—
917C4—611no—
918C4—611no—
919C4—1221no—
920C4—1221no—
921C4—1221no—
922C4—1221no—
923C4—1221no—
924C4—1221no—
925C4—2441no—
926C4—2441no—
927C4—2441no—
928C4C2×#1451986411yescharacteristic
929C4#1684084011yescharacteristic
930C2—22no—
931C2—41no—
932C2—42no—
933C2—81no—
934C2—4881no—
935C2—2441no—
936C2#2146240711yescharacteristic
937C2#2146244011yescharacteristic
938C2C2×#1684075911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#546C4
socleC22×C61C22×C22⋊C4
prime radical#21459424C2
cosocleC4×Dic61C24
hypercenter#546#6923
hypocenterC61#17521
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #21462747C2semidirect
2. #21462502C2semidirect
3. #21461178C2semidirect
4. #21461175C2semidirect
5. #21461172C2semidirect
6. #21461158C2semidirect
7. #21461150C2semidirect
8. #21461145C2semidirect
9. #21461136C2semidirect
10. #21461131C2semidirect
11. #21461124C2semidirect
12. #21461119C2semidirect
13. #21461114C2semidirect
14. C2×D4⋊#92420C2semidirect
22. #16840783C22semidirect
23. #16840783C22semidirect
24. #16840781C22semidirect
25. #16840781C22semidirect
26. #16840780C22semidirect
27. #16840779C22semidirect
28. #16840778C22semidirect
30. #16840766C22semidirect
31. C2×C4⋊#92420C22semidirect
32. C2×C4⋊#92420C22semidirect
34. C4×#11758217C22semidirect
35. C2×C4×#92420C22semidirect
36. Q8⋊#92420C22semidirect
37. Q8⋊#92420C22semidirect
38. Q8⋊#92420C22semidirect
39. Q8⋊#92420C22semidirect
40. #16840610C22semidirect
41. #16840610C22semidirect
42. #16840610C22semidirect
43. #16840610C22semidirect
48. D4⋊#92420C22semidirect
49. D4⋊#92420C22semidirect
50. D4⋊#92420C22semidirect
51. D4⋊#92420C22semidirect
544. C61#17521semidirect

Maximal subgroups

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

subgroupindex
#214627472
#214625022
#214611782
#214611752
#214611722
#214611582
#214611502
#214611452
#214611362
#214611312
#214611242
#214611192
#214611142
C2×D4⋊#924202
#214594242
#1752161