Finite Group Databasebeta

← #30610759

Subgroups — #30610759

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#21462741C211yesmaximal, characteristic, complemented
2#21462630C211yesmaximal, characteristic, complemented
3#21461179C211yesmaximal, characteristic, complemented
4#21461175C211yesmaximal, characteristic, complemented
5#21461171C211yesmaximal, characteristic, complemented
6#21461165C211yesmaximal, characteristic, complemented
7#21461158C211yesmaximal, characteristic, complemented
8#21461154C211yesmaximal, characteristic, complemented
9#21461150C211yesmaximal, characteristic, complemented
10#21461144C211yesmaximal, characteristic, complemented
11#21461139C211yesmaximal, characteristic, complemented
12#21461135C211yesmaximal, characteristic, complemented
13#21461131C211yesmaximal, characteristic, complemented
14#21461125C211yesmaximal, characteristic, complemented
15#21459232C211yesmaximal, characteristic
16#16840814—21no—
17#16840814—21no—
18#16840795—21no—
19#16840795—21no—
20#16840794—21no—
21#16840794—21no—
22#16840792—21no—
23#16840792—21no—
24#16840784C2211yescharacteristic, complemented
25#16840783C2211yescharacteristic
26#16840781C2211yescharacteristic, complemented
27#16840781C2211yescharacteristic, complemented
28#16840780C2211yescharacteristic, complemented
29#16840779C2211yescharacteristic
30#16840766C2211yescharacteristic, complemented
31#16840765C2211yescharacteristic
32D61⋊(C4⋊C8)C2211yescharacteristic, complemented
33C4×#11758213C2211yescharacteristic, complemented
34C4×#11758217C2211yescharacteristic
35C4×D61⋊C8C2211yescharacteristic, complemented
36Q8⋊#92420C2211yescharacteristic, complemented
37Q8⋊#92420C2211yescharacteristic, complemented
38Q8⋊#92420C2211yescharacteristic, complemented
39Q8⋊#92420C2211yescharacteristic, complemented
40D4⋊#92420C2211yescharacteristic
41D4⋊#92420C2211yescharacteristic
42D4⋊#92420C2211yescharacteristic
43D4⋊#92420C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48D4⋊#92420C2211yescharacteristic, complemented
49D4⋊#92420C2211yescharacteristic, complemented
50D4⋊#92420C2211yescharacteristic, complemented
51D4⋊#92420C2211yescharacteristic, complemented
52#16840390C411yescharacteristic
53#16840381C411yescharacteristic
54#16840381C411yescharacteristic
55#16840379—21no—
56#16840366C411yescharacteristic
57#16840366C411yescharacteristic
58#16840365—21no—
59#16840347—21no—
60#16840347—21no—
61#16840340C411yescharacteristic
62#16840329C411yescharacteristic
63#16840310C2211yescharacteristic
64#16840310C2211yescharacteristic
65#16840307—21no—
66#16840293—21no—
67#16840291C2211yescharacteristic
68#16840291C2211yescharacteristic
69#16840268—21no—
70#16840268—21no—
71#41×Dic61C2211yescharacteristic
72#16840230C2211yescharacteristic
73C2×D4×Dic61C2211yescharacteristic
74C61×#535C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×#11758217—21no—
79C2×D61⋊C8—21no—
80C2×D61⋊C8—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
91#14519834—21no—
92#14519834—21no—
93#14519834—21no—
94#14519834—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#14519777C2×C411yescharacteristic
112#14519777C2×C411yescharacteristic
113#14519776—21no—
114#14519773—21no—
115#14519770—21no—
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519769C2×C411yescharacteristic
120#14519769C2×C411yescharacteristic
121#14519768—21no—
122#14519764—21no—
123#14519764—21no—
124#14519764—21no—
125#14519763—21no—
126#14519763—21no—
127#14519761—21no—
128#14519761—21no—
129#14519759—21no—
130#14519759—21no—
131#14519758—21no—
132#14519758—21no—
133#14519758—21no—
134#14519758—21no—
135#14519756—21no—
136#14519754—21no—
137#14519754—21no—
138#14519754—21no—
139#14519754—21no—
140#14519753C2×C411yescharacteristic
141#14519753C2×C411yescharacteristic
142#14519751—21no—
143#14519749—21no—
144#14519749—21no—
145#14519749—21no—
146#14519749—21no—
147#14519749—21no—
148#14519749—21no—
149#14519748—21no—
150#14519748—21no—
151#14519748C2×C411yescharacteristic
152#14519748C2×C411yescharacteristic
153#14519748C2×C411yescharacteristic
154#14519748C2×C411yescharacteristic
155#14519748C2×C411yescharacteristic
156#14519748C2×C411yescharacteristic
157#14519746—21no—
158#14519746—21no—
159Q8×Dic61C2×C411yescharacteristic
160Q8×Dic61C2311yescharacteristic
161#14519742D411yescharacteristic
162#14519742D411yescharacteristic
163D4×Dic61—21no—
164D4×Dic61—21no—
165D4×Dic61—21no—
166D4×Dic61—21no—
167D4×Dic61—21no—
168D4×Dic61—21no—
169D4×Dic61C2×C411yescharacteristic
170D4×Dic61C2×C411yescharacteristic
171D4×Dic61C2×C411yescharacteristic
172D4×Dic61C2311yescharacteristic
173D4×Dic61C2311yescharacteristic
174D4×Dic61C2311yescharacteristic
175#14519739D411yescharacteristic
176#14519739D411yescharacteristic
177#14519737—21no—
178#14519737—21no—
179#14519737D411yescharacteristic
180#14519737D411yescharacteristic
181#14519737D411yescharacteristic
182#14519737D411yescharacteristic
183#14519736—21no—
184#14519736C2×C411yescharacteristic
185#14519734C2×C411yescharacteristic
186#14519734C2×C411yescharacteristic
187#14519733—21no—
188#14519733—21no—
189C2×C4⋊Dic61C2×C411yescharacteristic
190C2×C22⋊Dic61—21no—
191C2×C4×Dic61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C22×D4×C61C2×C411yescharacteristic
197#127×C61C2×C411yescharacteristic
198#127×C61C2×C411yescharacteristic
199#124×C61C2×C411yescharacteristic
200#124×C61C2×C411yescharacteristic
201#121×C61—21no—
202#121×C61—21no—
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—21no—
215C2×D4×C61—42no—
216C2×D4×C61C22×C411yescharacteristic
217C2×D4×C61C22×C411yescharacteristic
218C2×D4×C61C22×C411yescharacteristic
219C22×C4×C61—21no—
220C22×C4×C61C22×C411yescharacteristic
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61C22⋊C411yescharacteristic
228C2×C22⋊D61C22⋊C411yescharacteristic
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—81no—
237C22×Dic61—81no—
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240#11758224—81no—
241#11758224—81no—
242#11758224—81no—
243#11758224—81no—
244#11758222—42no—
245C2×D244C22⋊C411yescharacteristic
246C2×C4×D61C22×C411yescharacteristic
247C2×C4×D61C22×C411yescharacteristic
248C2×C4×D61C2×D411yescharacteristic
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×Dic122—21no—
253C2×Dic122—21no—
254C2×Dic122C22⋊C411yescharacteristic
255#11758217—42no—
256#11758217—81no—
257C2×#92420—21no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—21no—
261C2×#92420—21no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—21no—
265#11758213—42no—
266#11758213—81no—
267D61⋊C8—42no—
268D61⋊C8—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×C61C22⋊C411yescharacteristic
276C22⋊C4×C61C22⋊C411yescharacteristic
277C42×C61C22×C411yescharacteristic
278C42×C61C22×C411yescharacteristic
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⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—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⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61C22×C411yescharacteristic
304C4⋊Dic61C22×C411yescharacteristic
305C4⋊Dic61C22×C411yescharacteristic
306C4⋊Dic61C22×C411yescharacteristic
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×C61—21no—
330C23×C61—21no—
331C23×C61—42no—
332C23×C61—81no—
333C23×C61—81no—
334C23×C61C2×C22⋊C411yescharacteristic
335C22×D61C2×C22⋊C411yescharacteristic
336C22×D61C2×C22⋊C411yescharacteristic
337Q8×C61—22no—
338D4×C61—22no—
339D4×C61—22no—
340D4×C61—22no—
341D4×C61—42no—
342D4×C61—42no—
343D4×C61—81no—
344D4×C61—81no—
345D4×C61—81no—
346D4×C61—81no—
347C2×C4×C61—22no—
348C2×C4×C61—21no—
349C2×C4×C61—42no—
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C2×C22⋊C411yescharacteristic
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C23×C411yescharacteristic
356C22⋊D61—41no—
357C22⋊D61—41no—
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—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61—81no—
378C2×Dic61—81no—
379C2×Dic61—81no—
380C2×Dic61—81no—
381C2×Dic61C2×C22⋊C411yescharacteristic
382C2×Dic61C2×C22⋊C411yescharacteristic
383C2×Dic61C2×C22⋊C411yescharacteristic
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C22×D411yescharacteristic
386C2×Dic61C22×D411yescharacteristic
387D244—41no—
388C4×D61—22no—
389C4×D61—22no—
390C4×D61—21no—
391C4×D61—21no—
392C4×D61—21no—
393C4×D61—21no—
394C4×D61—41no—
395C4×D61—41no—
396Dic122—41no—
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—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61—84no—
421C22×C61C22×C22⋊C411yescharacteristic
422C2×D61—21no—
423C2×D61—21no—
424C2×D61—21no—
425C2×D61—21no—
426C2×D61—21no—
427C2×D61—21no—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—41no—
434C4×C61#56812yes—
435Dic61—21no—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
439Dic61—21no—
440Dic61—41no—
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—81no—
463C2×C61—81no—
464C2×C61—81no—
465C2×C61#287911yescharacteristic
466C2×C61#289711yescharacteristic
467C2×C61#290111yescharacteristic
468D61—41no—
469D61—41no—
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—1221no—
546#127C2×#692311yescharacteristic
547#127C2×#692311yescharacteristic
548#126—1221no—
549#126—1221no—
550#126—1221no—
551#126—1221no—
552#125—611no—
553#125—611no—
554#125—1221no—
555#124—1221no—
556#124—1221no—
557#124—1221no—
558#124—1221no—
559#124—1221no—
560#124C2×#692311yescharacteristic
561#124C2×#692311yescharacteristic
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—21no—
578#121—21no—
579#121—611no—
580#121—611no—
581#121—611no—
582#121—611no—
583#121—611no—
584#121—611no—
585#121—1221no—
586#121—1221no—
587#121—1221no—
588#121—1221no—
589#121—1221no—
590#121—1221no—
591#121—1221no—
592#121—1221no—
593#121—1221no—
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—21no—
678C2×D4—42no—
679C2×D4—611no—
680C2×D4—611no—
681C2×D4—611no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4C22×#692311yescharacteristic
689C2×D4C22×#692311yescharacteristic
690C2×D4C22×#692311yescharacteristic
691C22×C4—21no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—4881no—
708C22×C4—4881no—
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—611no—
750C22⋊C4—611no—
751C22⋊C4—611no—
752C22⋊C4—611no—
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⋊C4—1221no—
764C22⋊C4—1221no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4C22⋊#692311yescharacteristic
769C22⋊C4C22⋊#692311yescharacteristic
770C42—611no—
771C42—611no—
772C42—611no—
773C42—611no—
774C42—611no—
775C42—611no—
776C42—611no—
777C42—611no—
778C42—1221no—
779C42—1221no—
780C42—1221no—
781C42C22×#692311yescharacteristic
782C42C22×#692311yescharacteristic
783C23—21no—
784C23—21no—
785C23—21no—
786C23—42no—
787C23—81no—
788C23—81no—
789C23—611no—
790C23—611no—
791C23C2×C22⋊#692311yescharacteristic
792Q8—22no—
793Q8—4881no—
794Q8—4881no—
795Q8—2441no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—42no—
800D4—42no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—4881no—
806D4—4881no—
807D4—4881no—
808D4—4881no—
809D4—4881no—
810D4—4881no—
811D4—2441no—
812D4—2441no—
813D4—2441no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—42no—
817C2×C4—611no—
818C2×C4—611no—
819C2×C4—611no—
820C2×C4—611no—
821C2×C4—611no—
822C2×C4—611no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1222no—
830C2×C4—1222no—
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—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4C2×C22⋊#692311yescharacteristic
849C2×C4C2×C22⋊#692311yescharacteristic
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—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—84no—
875C22—1221no—
876C22—1221no—
877C22—1221no—
878C22—1221no—
879C22—1221no—
880C22—1221no—
881C22C22×C22⋊#692311yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—41no—
888C4—611no—
889C4—611no—
890C4—1221no—
891C4—1221no—
892C4—1221no—
893C4—1221no—
894C4—1221no—
895C4—2441no—
896C4—2441no—
897C4—2441no—
898C4—2441no—
899C4#1684084012yes—
900C2—41no—
901C2—81no—
902C2—81no—
903C2—81no—
904C2—2441no—
905C2—2441no—
906C2#2146240511yescharacteristic
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 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #21462741C2semidirect
2. #21462630C2semidirect
3. #21461179C2semidirect
4. #21461175C2semidirect
5. #21461171C2semidirect
6. #21461165C2semidirect
7. #21461158C2semidirect
8. #21461154C2semidirect
9. #21461150C2semidirect
10. #21461144C2semidirect
11. #21461139C2semidirect
12. #21461135C2semidirect
13. #21461131C2semidirect
14. #21461125C2semidirect
24. #16840784C22semidirect
26. #16840781C22semidirect
27. #16840781C22semidirect
28. #16840780C22semidirect
30. #16840766C22semidirect
32. D61⋊(C4⋊C8)C22semidirect
33. C4×#11758213C22semidirect
35. C4×D61⋊C8C22semidirect
36. Q8⋊#92420C22semidirect
37. Q8⋊#92420C22semidirect
38. Q8⋊#92420C22semidirect
39. Q8⋊#92420C22semidirect
48. D4⋊#92420C22semidirect
49. D4⋊#92420C22semidirect
50. D4⋊#92420C22semidirect
51. D4⋊#92420C22semidirect
529. C61#17505semidirect

Maximal subgroups

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

subgroupindex
#214627412
#214626302
#214611792
#214611752
#214611712
#214611652
#214611582
#214611542
#214611502
#214611442
#214611392
#214611352
#214611312
#214611252
#214592322
#1750561