Finite Group Databasebeta

← #30610757

Subgroups — #30610757

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462738C211yesmaximal, characteristic, complemented
2#21462628C211yesmaximal, characteristic, complemented
3#21461178C211yesmaximal, characteristic, complemented
4#21461174C211yesmaximal, characteristic, complemented
5#21461170C211yesmaximal, characteristic, complemented
6#21461164C211yesmaximal, characteristic, complemented
7#21461158C211yesmaximal, characteristic, complemented
8#21461156C211yesmaximal, characteristic, complemented
9#21461152C211yesmaximal, characteristic, complemented
10#21461144C211yesmaximal, characteristic, complemented
11#21461138C211yesmaximal, characteristic, complemented
12#21461134C211yesmaximal, characteristic, complemented
13#21461130C211yesmaximal, characteristic, complemented
14#21461124C211yesmaximal, characteristic, complemented
15#21459232C211yesmaximal, characteristic
16#16840813—21no—
17#16840813—21no—
18#16840797—21no—
19#16840797—21no—
20#16840793—21no—
21#16840793—21no—
22#16840793—21no—
23#16840793—21no—
24#16840783C2211yescharacteristic
25#16840783C2211yescharacteristic, complemented
26#16840779C2211yescharacteristic
27#16840779C2211yescharacteristic, complemented
28#16840778C2211yescharacteristic, complemented
29#16840778C2211yescharacteristic, complemented
30#16840765C2211yescharacteristic
31#16840765C2211yescharacteristic, complemented
32C2×C4⋊#92420C2211yescharacteristic, complemented
33C4×#11758217C2211yescharacteristic
34C4×#11758217C2211yescharacteristic, complemented
35C2×C4×#92420C2211yescharacteristic, complemented
36#16840612C2211yescharacteristic, complemented
37#16840612C2211yescharacteristic, complemented
38#16840612C2211yescharacteristic, complemented
39#16840612C2211yescharacteristic, complemented
40#16840610C2211yescharacteristic, complemented
41#16840610C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic, complemented
43#16840610C2211yescharacteristic, complemented
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48D4⋊#92420C2211yescharacteristic
49D4⋊#92420C2211yescharacteristic
50D4⋊#92420C2211yescharacteristic
51D4⋊#92420C2211yescharacteristic
52#16840390C411yescharacteristic
53#16840381—21no—
54#16840379C411yescharacteristic
55#16840379C411yescharacteristic
56#16840366—21no—
57#16840365C411yescharacteristic
58#16840365C411yescharacteristic
59#16840347—21no—
60#16840347—21no—
61#16840340C411yescharacteristic
62#16840329C411yescharacteristic
63#16840310—21no—
64#16840307C2211yescharacteristic
65#16840307C2211yescharacteristic
66#16840293C2211yescharacteristic
67#16840293C2211yescharacteristic
68#16840291—21no—
69#16840268—21no—
70#16840268—21no—
71#41×Dic61C2211yescharacteristic
72#16840230C2211yescharacteristic
73C2×D4×Dic61C2211yescharacteristic
74C61×#535C411yescharacteristic
75C2×#11758217—21no—
76C2×#11758217—21no—
77C2×#11758217—21no—
78C2×#11758217—21no—
79C22×#92420—21no—
80C22×#92420—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844—21no—
84#14519844—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87C4⋊#92420C2311yescharacteristic
88C4⋊#92420C2311yescharacteristic
89C4⋊#92420C2311yescharacteristic
90C4⋊#92420C2311yescharacteristic
91C22⋊#92420—21no—
92C22⋊#92420—21no—
93C22⋊#92420—21no—
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96C22⋊#92420—21no—
97#14519832—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×#11758222C2×C411yescharacteristic
108C2×#11758224—21no—
109C2×#11758224—21no—
110C23×Dic61—21no—
111#14519777—21no—
112#14519776C2×C411yescharacteristic
113#14519776C2×C411yescharacteristic
114#14519773C2×C411yescharacteristic
115#14519773C2×C411yescharacteristic
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519770—21no—
120#14519769—21no—
121#14519768C2×C411yescharacteristic
122#14519768C2×C411yescharacteristic
123#14519764—21no—
124#14519764—21no—
125#14519764C2×C411yescharacteristic
126#14519764C2×C411yescharacteristic
127#14519763—21no—
128#14519763—21no—
129#14519761—21no—
130#14519761—21no—
131#14519759—21no—
132#14519759—21no—
133#14519758—21no—
134#14519758—21no—
135#14519758—21no—
136#14519758—21no—
137#14519756C2×C411yescharacteristic
138#14519756C2×C411yescharacteristic
139#14519754—21no—
140#14519754—21no—
141#14519754—21no—
142#14519754—21no—
143#14519753—21no—
144#14519751C2×C411yescharacteristic
145#14519751C2×C411yescharacteristic
146#14519749—21no—
147#14519749—21no—
148#14519749—21no—
149#14519749—21no—
150#14519749—21no—
151#14519749—21no—
152#14519748—21no—
153#14519748—21no—
154#14519748—21no—
155#14519748—21no—
156#14519748—21no—
157#14519746—21no—
158#14519746—21no—
159Q8×Dic61D411yescharacteristic
160Q8×Dic61D411yescharacteristic
161#14519742C2×C411yescharacteristic
162#14519742C2311yescharacteristic
163D4×Dic61—21no—
164D4×Dic61—21no—
165D4×Dic61—21no—
166D4×Dic61—21no—
167D4×Dic61C2×C411yescharacteristic
168D4×Dic61C2×C411yescharacteristic
169D4×Dic61D411yescharacteristic
170D4×Dic61D411yescharacteristic
171D4×Dic61D411yescharacteristic
172D4×Dic61D411yescharacteristic
173D4×Dic61D411yescharacteristic
174D4×Dic61D411yescharacteristic
175D4×Dic61C2311yescharacteristic
176D4×Dic61C2311yescharacteristic
177#14519739C2×C411yescharacteristic
178#14519739C2311yescharacteristic
179#14519737—21no—
180#14519737—21no—
181#14519737—21no—
182#14519737—21no—
183#14519736C2×C411yescharacteristic
184#14519736C2×C411yescharacteristic
185#14519736C2×C411yescharacteristic
186#14519734—21no—
187#14519733—21no—
188#14519733—21no—
189C2×C4⋊Dic61C2×C411yescharacteristic
190C2×C22⋊Dic61—21no—
191C2×C4×Dic61C2311yescharacteristic
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C42×D61—21no—
195C2×#41×C61C2×C411yescharacteristic
196C22×D4×C61C2×C411yescharacteristic
197#127×C61—21no—
198#124×C61—21no—
199#121×C61C2×C411yescharacteristic
200#121×C61C2×C411yescharacteristic
201#121×C61C2×C411yescharacteristic
202#121×C61C2×C411yescharacteristic
203#120×C61—21no—
204#120×C61—21no—
205#117×C61C2×C411yescharacteristic
206C24×C61—21no—
207#41×C61—42no—
208C2×Q8×C61C22⋊C411yescharacteristic
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—42no—
215C2×D4×C61C22⋊C411yescharacteristic
216C2×D4×C61C22⋊C411yescharacteristic
217C2×D4×C61C22⋊C411yescharacteristic
218C2×D4×C61C22×C411yescharacteristic
219C2×D4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
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—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—81no—
236C22×Dic61—81no—
237C22×Dic61C2×D411yescharacteristic
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243#11758224—81no—
244#11758224—81no—
245#11758224—81no—
246#11758224—81no—
247#11758222—42no—
248C2×D244C22×C411yescharacteristic
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×Dic122—21no—
253C2×Dic122—21no—
254C2×Dic122C22×C411yescharacteristic
255#11758217—42no—
256#11758217—42no—
257#11758217—81no—
258#11758217—81no—
259C2×#92420—21no—
260C2×#92420—21no—
261C2×#92420—21no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—21no—
265C2×#92420—21no—
266C2×#92420—21no—
267C2×#92420—42no—
268C2×#92420—81no—
269C4⋊C4×C61C22×C411yescharacteristic
270C4⋊C4×C61C22×C411yescharacteristic
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C42×C61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61C22⋊C411yescharacteristic
288C22⋊Dic61C22⋊C411yescharacteristic
289C22⋊Dic61C22⋊C411yescharacteristic
290C22⋊Dic61C22⋊C411yescharacteristic
291C22⋊Dic61C22⋊C411yescharacteristic
292C22⋊Dic61C22⋊C411yescharacteristic
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297C4⋊Dic61—21no—
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61C22⋊C411yescharacteristic
301C4⋊Dic61C22⋊C411yescharacteristic
302C4⋊Dic61C22⋊C411yescharacteristic
303C4⋊Dic61C22⋊C411yescharacteristic
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—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61C22×C411yescharacteristic
319C4×Dic61C22×C411yescharacteristic
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×C61—21no—
330C23×C61—42no—
331C23×C61—81no—
332C23×C61—81no—
333C23×C61C2×C22⋊C411yescharacteristic
334C23×C61C2×C22⋊C411yescharacteristic
335C23×C61C2×C22⋊C411yescharacteristic
336C22×D61—21no—
337Q8×C61—41no—
338D4×C61—22no—
339D4×C61—22no—
340D4×C61—41no—
341D4×C61—41no—
342D4×C61—41no—
343D4×C61—42no—
344D4×C61—81no—
345D4×C61—81no—
346D4×C61—81no—
347D4×C61—81no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C23×C411yescharacteristic
357C22⋊D61—42no—
358C22⋊D61—81no—
359C22⋊D61—81no—
360C22⋊D61—81no—
361C22⋊D61—81no—
362C22⋊D61—81no—
363C22⋊D61—81no—
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—21no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—81no—
381C2×Dic61—81no—
382C2×Dic61—81no—
383C2×Dic61C2×C22⋊C411yescharacteristic
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C2×C22⋊C411yescharacteristic
386C2×Dic61C2×C22⋊C411yescharacteristic
387C2×Dic61C2×C22⋊C411yescharacteristic
388C2×Dic61C2×C22⋊C411yescharacteristic
389C2×Dic61C22×D411yescharacteristic
390C2×Dic61C22×D411yescharacteristic
391D244—22no—
392C4×D61—42no—
393C4×D61—41no—
394C4×D61—41no—
395C4×D61—81no—
396Dic122—22no—
397Dic122—81no—
398Dic122—81no—
399#92420—22no—
400#92420—41no—
401#92420—41no—
402#92420—41no—
403#92420—41no—
404#92420—41no—
405#92420—41no—
406#92420—41no—
407#17505—611nomaximal, Sylow
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—21no—
411C22×C61—21no—
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—41no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61—84no—
424C22×C61C22×C22⋊C411yescharacteristic
425C2×D61—41no—
426C2×D61—41no—
427C2×D61—41no—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—41no—
432C4×C61—41no—
433C4×C61#56812yes—
434Dic61—21no—
435Dic61—21no—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
439Dic61—21no—
440Dic61—21no—
441Dic61—41no—
442Dic61—41no—
443Dic61—41no—
444Dic61#57611yescharacteristic
445Dic61#57711yescharacteristic
446#3460—611no—
447#2989—611no—
448#2965—611no—
449#1496—611no—
450#1495—611no—
451#1494—611no—
452#1492—611no—
453#1490—611no—
454#1489—611no—
455#1488—611no—
456#1486—611no—
457#1484—611no—
458#1483—611no—
459#1482—611no—
460#1480—611no—
461C2×C61—41no—
462C2×C61—41no—
463C2×C61—41no—
464C2×C61—81no—
465C2×C61—81no—
466C2×C61#287911yescharacteristic
467C2×C61#289711yescharacteristic
468C2×C61#290111yescharacteristic
469D61—81no—
470#544—611no—
471#542—611no—
472#542—611no—
473#542—1221no—
474#540—611no—
475#540—611no—
476#540—1221no—
477#538—1221no—
478#538—1221no—
479#537—611no—
480#535—611no—
481#535#692311yescharacteristic
482#532—611no—
483#532—611no—
484#532—1221no—
485#529—611no—
486#529—611no—
487#529—1221no—
488#525—1221no—
489#525—1221no—
490C4×#41—611no—
491C4×#41—611no—
492C2×C4×D4—611no—
493#446—1221no—
494#446—1221no—
495#436—1221no—
496#436—1221no—
497#435—1221no—
498#435—1221no—
499#435—1221no—
500#435—1221no—
501#432—611no—
502#432—611no—
503#431—611no—
504#431—611no—
505#431—611no—
506#431—611no—
507#423—611no—
508#423—611no—
509C2×C4⋊C8—611no—
510C4×M16—611no—
511C4×M16—611no—
512C2×C4×C8—611no—
513Q8⋊C8—611no—
514Q8⋊C8—611no—
515Q8⋊C8—611no—
516Q8⋊C8—611no—
517D4⋊C8—611no—
518D4⋊C8—611no—
519D4⋊C8—611no—
520D4⋊C8—611no—
521D4⋊C8—611no—
522D4⋊C8—611no—
523D4⋊C8—611no—
524D4⋊C8—611no—
525D4⋊C8—611no—
526D4⋊C8—611no—
527D4⋊C8—611no—
528D4⋊C8—611no—
529C61#1750511yescharacteristic, complemented, Sylow
530C2×#41—611no—
531C2×#41—1221no—
532C2×#41—1221no—
533C2×#41C2×#692311yescharacteristic
534C22×D4C2×#692311yescharacteristic
535C23×C4—1221no—
536C2×M16—1221no—
537C2×M16—1221no—
538C2×M16—1221no—
539C2×M16—1221no—
540C22×C8—1221no—
541C22×C8—1221no—
542C4⋊Q8—611no—
543C4⋊Q8—611no—
544C4⋊Q8—1221no—
545#127—21no—
546#127—611no—
547#127—611no—
548#126—1221no—
549#126—1221no—
550#126—1221no—
551#126—1221no—
552#125—611no—
553#125—611no—
554#125—1221no—
555#124—21no—
556#124—611no—
557#124—611no—
558#124—1221no—
559#124—1221no—
560#124—1221no—
561#124—1221no—
562#123—1221no—
563#123—1221no—
564#123—1221no—
565#123—1221no—
566#123—1221no—
567#123—1221no—
568#123—1221no—
569#123—1221no—
570C22⋊Q8—611no—
571C22⋊Q8—611no—
572C22⋊Q8—1221no—
573C22⋊Q8—1221no—
574C22⋊Q8—1221no—
575C22⋊Q8—1221no—
576C22⋊Q8—1221no—
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#121—1221no—
590#121C2×#692311yescharacteristic
591#121C2×#692311yescharacteristic
592#121C2×#692311yescharacteristic
593#121C2×#692311yescharacteristic
594#120—21no—
595#120—21no—
596#120—1221no—
597#120—1221no—
598C4×Q8—611no—
599C4×Q8—611no—
600C4×Q8—611no—
601C4×Q8—611no—
602C4×D4—611no—
603C4×D4—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—1221no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4—1221no—
622#117—611no—
623#117—611no—
624#117—611no—
625#117—1221no—
626#117—1221no—
627#117—1221no—
628#117C2×#692311yescharacteristic
629C2×C4⋊C4—611no—
630C2×C22⋊C4—1221no—
631C2×C42—611no—
632C2×C42—611no—
633C2×C42—611no—
634C2×C42—1221no—
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—611no—
656C4×C8—611no—
657C4×C8—611no—
658C4×C8—611no—
659C4×C8—1221no—
660C4×C8—1221no—
661C24—21no—
662#41—42no—
663#41—4881no—
664#41—4881no—
665#41—4881no—
666#41—4881no—
667#41—2442no—
668C2×Q8—611no—
669C2×Q8—1221no—
670C2×Q8—1221no—
671C2×Q8C22⋊#692311yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—42no—
678C2×D4—611no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4C22⋊#692311yescharacteristic
687C2×D4C22⋊#692311yescharacteristic
688C2×D4C22⋊#692311yescharacteristic
689C2×D4C22×#692311yescharacteristic
690C2×D4C22×#692311yescharacteristic
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—4881no—
706C22×C4—4881no—
707C22×C4C22×#692311yescharacteristic
708C22×C4C22×#692311yescharacteristic
709C22×C4C22×#692311yescharacteristic
710M16—4881no—
711M16—4881no—
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—
724C4⋊C4—611no—
725C4⋊C4—611no—
726C4⋊C4—611no—
727C4⋊C4—611no—
728C4⋊C4—611no—
729C4⋊C4—611no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4C22×#692311yescharacteristic
744C4⋊C4C22×#692311yescharacteristic
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—611no—
751C22⋊C4—611no—
752C22⋊C4—611no—
753C22⋊C4—611no—
754C22⋊C4—611no—
755C22⋊C4—611no—
756C22⋊C4—1221no—
757C22⋊C4—1221no—
758C22⋊C4—1221no—
759C22⋊C4—1221no—
760C22⋊C4—1221no—
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—
770C42—21no—
771C42—611no—
772C42—611no—
773C42—611no—
774C42—611no—
775C42—611no—
776C42—611no—
777C42—611no—
778C42—611no—
779C42—611no—
780C42—611no—
781C42—1221no—
782C42—1221no—
783C23—21no—
784C23—21no—
785C23—42no—
786C23—81no—
787C23—81no—
788C23—1221no—
789C23C2×C22⋊#692311yescharacteristic
790C23C2×C22⋊#692311yescharacteristic
791C23C2×C22⋊#692311yescharacteristic
792Q8—41no—
793Q8—1222no—
794Q8—4881no—
795Q8—4881no—
796D4—22no—
797D4—22no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—42no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—1222no—
807D4—4881no—
808D4—4881no—
809D4—4881no—
810D4—4881no—
811D4—4881no—
812D4—4881no—
813D4—2442no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—611no—
820C2×C4—611no—
821C2×C4—611no—
822C2×C4—611no—
823C2×C4—611no—
824C2×C4—611no—
825C2×C4—611no—
826C2×C4—611no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—4881no—
837C2×C4—4881no—
838C2×C4—4881no—
839C2×C4—4881no—
840C2×C4—2442no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4C2×C22⋊#692311yescharacteristic
851C2×C4C2×C22⋊#692311yescharacteristic
852C2×C4C2×C22⋊#692311yescharacteristic
853C2×C4C23×#692311yescharacteristic
854C8—1222no—
855C8—2441no—
856C8—2441no—
857C8—2441no—
858C8—2441no—
859C8—2441no—
860C8—2441no—
861C8—2441no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—84no—
878C22—2441no—
879C22—2441no—
880C22—2441no—
881C22C22×C22⋊#692311yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—611no—
888C4—611no—
889C4—1221no—
890C4—1221no—
891C4—1221no—
892C4—1221no—
893C4—1221no—
894C4—1221no—
895C4—1221no—
896C4—2441no—
897C4—2441no—
898C4—2441no—
899C4#1684084012yes—
900C2—41no—
901C2—41no—
902C2—41no—
903C2—81no—
904C2—81no—
905C2—4881no—
906C2#2146240311yescharacteristic
907C2#2146244011yescharacteristic
908C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#535C4
socleC22×C61C22×C22⋊C4
prime radical#21459232C2
cosocleC4×Dic61C24
hypercenter#535#6923
hypocenterC61#17505
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #21462738C2semidirect
2. #21462628C2semidirect
3. #21461178C2semidirect
4. #21461174C2semidirect
5. #21461170C2semidirect
6. #21461164C2semidirect
7. #21461158C2semidirect
8. #21461156C2semidirect
9. #21461152C2semidirect
10. #21461144C2semidirect
11. #21461138C2semidirect
12. #21461134C2semidirect
13. #21461130C2semidirect
14. #21461124C2semidirect
25. #16840783C22semidirect
27. #16840779C22semidirect
28. #16840778C22semidirect
29. #16840778C22semidirect
31. #16840765C22semidirect
32. C2×C4⋊#92420C22semidirect
34. C4×#11758217C22semidirect
35. C2×C4×#92420C22semidirect
36. #16840612C22semidirect
37. #16840612C22semidirect
38. #16840612C22semidirect
39. #16840612C22semidirect
40. #16840610C22semidirect
41. #16840610C22semidirect
42. #16840610C22semidirect
43. #16840610C22semidirect
529. C61#17505semidirect

Maximal subgroups

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

subgroupindex
#214627382
#214626282
#214611782
#214611742
#214611702
#214611642
#214611582
#214611562
#214611522
#214611442
#214611382
#214611342
#214611302
#214611242
#214592322
#1750561