Finite Group Databasebeta

← #30610769

Subgroups — #30610769

Order 15616.

890 conjugacy classes of subgroups.

The subgroup lattice has 852 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#21461181C211yesmaximal, characteristic, complemented
4#21461174C211yesmaximal, characteristic, complemented
5#21461170C211yesmaximal, characteristic, complemented
6#21461167C211yesmaximal, characteristic, complemented
7#21461163C211yesmaximal, characteristic, complemented
8#21461154C211yesmaximal, characteristic, complemented
9#21461150C211yesmaximal, characteristic, complemented
10#21461149C211yesmaximal, characteristic, complemented
11#21461141C211yesmaximal, characteristic, complemented
12#21461134C211yesmaximal, characteristic, complemented
13#21461130C211yesmaximal, characteristic, complemented
14#21461127C211yesmaximal, characteristic, complemented
15#21459247C211yesmaximal, 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
26#16840779C2211yescharacteristic
27#16840779C2211yescharacteristic
28#16840778C2211yescharacteristic
29#16840778C2211yescharacteristic
30#16840765C2211yescharacteristic
31#16840765C2211yescharacteristic
32C2×C4⋊#92420C2211yescharacteristic
33C4×#11758217C2211yescharacteristic
34C4×#11758217C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840612C2211yescharacteristic
37#16840612C2211yescharacteristic
38#16840612C2211yescharacteristic
39#16840612C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840612C2211yescharacteristic
43#16840612C2211yescharacteristic
44Q8⋊#92420C2211yescharacteristic
45Q8⋊#92420C2211yescharacteristic
46Q8⋊#92420C2211yescharacteristic
47Q8⋊#92420C2211yescharacteristic
48D4⋊#92420C2211yescharacteristic
49D4⋊#92420C2211yescharacteristic
50D4⋊#92420C2211yescharacteristic
51D4⋊#92420C2211yescharacteristic
52#16840393C411yescharacteristic
53#16840379—21no—
54#16840379C411yescharacteristic
55#16840379C411yescharacteristic
56#16840372—21no—
57#16840372C411yescharacteristic
58#16840372C411yescharacteristic
59#16840357—21no—
60#16840357—21no—
61#16840333C411yescharacteristic
62#16840333C411yescharacteristic
63#16840314—21no—
64#16840314C2211yescharacteristic
65#16840314C2211yescharacteristic
66#16840293—21no—
67#16840293—21no—
68#16840293—21no—
69#16840293C2211yescharacteristic
70#16840293C2211yescharacteristic
71#41×Dic61C2211yescharacteristic
72#41×Dic61C2211yescharacteristic
73C2×#14519742C2211yescharacteristic
74C61×#537C411yescharacteristic
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
107C22×Dic122C2×C411yescharacteristic
108#14519776—21no—
109#14519776C2×C411yescharacteristic
110#14519776C2×C411yescharacteristic
111#14519775—21no—
112#14519775C2×C411yescharacteristic
113#14519775C2×C411yescharacteristic
114#14519770—21no—
115#14519770—21no—
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519770—21no—
120#14519770—21no—
121#14519770—21no—
122#14519768—21no—
123#14519768—21no—
124#14519768—21no—
125#14519768C2×C411yescharacteristic
126#14519768C2×C411yescharacteristic
127#14519767—21no—
128#14519767—21no—
129#14519767—21no—
130#14519767—21no—
131#14519764—21no—
132#14519764—21no—
133#14519764—21no—
134#14519764C2×C411yescharacteristic
135#14519764C2×C411yescharacteristic
136#14519758—21no—
137#14519758—21no—
138#14519758—21no—
139#14519758—21no—
140#14519758—21no—
141#14519758—21no—
142#14519758—21no—
143#14519758—21no—
144#14519756—21no—
145#14519756—21no—
146#14519756—21no—
147#14519756—21no—
148#14519756C2×C411yescharacteristic
149#14519756C2×C411yescharacteristic
150#14519756C2×C411yescharacteristic
151#14519756C2×C411yescharacteristic
152#14519754—21no—
153#14519754—21no—
154#14519754—21no—
155#14519754—21no—
156Q8×Dic61C2×C411yescharacteristic
157Q8×Dic61D411yescharacteristic
158Q8×Dic61D411yescharacteristic
159Q8×Dic61C2311yescharacteristic
160#14519742—21no—
161#14519742—21no—
162#14519742—21no—
163#14519742—21no—
164#14519742C2×C411yescharacteristic
165#14519742C2×C411yescharacteristic
166#14519742C2311yescharacteristic
167#14519742C2311yescharacteristic
168D4×Dic61—21no—
169D4×Dic61—21no—
170D4×Dic61—21no—
171D4×Dic61—21no—
172D4×Dic61C2×C411yescharacteristic
173D4×Dic61D411yescharacteristic
174D4×Dic61D411yescharacteristic
175D4×Dic61D411yescharacteristic
176D4×Dic61D411yescharacteristic
177D4×Dic61D411yescharacteristic
178D4×Dic61D411yescharacteristic
179D4×Dic61C2311yescharacteristic
180#14519736—21no—
181#14519736C2×C411yescharacteristic
182#14519736C2×C411yescharacteristic
183#14519736C2×C411yescharacteristic
184#14519736C2×C411yescharacteristic
185#14519733—21no—
186#14519733—21no—
187#14519733—21no—
188#14519733—21no—
189C2×#11758196—21no—
190C2×C4×Dic61—21no—
191C2×C4×Dic61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C2×C4×Dic61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C2×#41×C61C2×C411yescharacteristic
197C22⋊Q8×C61—21no—
198C22⋊Q8×C61C2×C411yescharacteristic
199C22⋊Q8×C61C2×C411yescharacteristic
200#121×C61—21no—
201#121×C61—21no—
202#121×C61—21no—
203#121×C61C2×C411yescharacteristic
204#121×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61C2×C411yescharacteristic
206#41×C61—42no—
207#41×C61—42no—
208C2×Q8×C61C22⋊C411yescharacteristic
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61C22⋊C411yescharacteristic
214C2×D4×C61C22⋊C411yescharacteristic
215C2×D4×C61C22⋊C411yescharacteristic
216C2×D4×C61C22×C411yescharacteristic
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—42no—
235C2×Dic122C22×C411yescharacteristic
236C2×Dic122C22×C411yescharacteristic
237#11758217—42no—
238#11758217—42no—
239#11758217—81no—
240#11758217—81no—
241C2×#92420—21no—
242C2×#92420—21no—
243C2×#92420—21no—
244C2×#92420—21no—
245C2×#92420—21no—
246C2×#92420—21no—
247C2×#92420—21no—
248C2×#92420—21no—
249C2×#92420—42no—
250C2×#92420—81no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61C22×C411yescharacteristic
255C4⋊C4×C61C22×C411yescharacteristic
256C22⋊C4×C61—21no—
257C22⋊C4×C61—21no—
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—21no—
265C22⋊Dic61—21no—
266C22⋊Dic61—21no—
267C22⋊Dic61—21no—
268C22⋊Dic61—21no—
269C22⋊Dic61—21no—
270C22⋊Dic61—21no—
271C22⋊Dic61C22⋊C411yescharacteristic
272C22⋊Dic61C22⋊C411yescharacteristic
273C22⋊Dic61C22⋊C411yescharacteristic
274C22⋊Dic61C22⋊C411yescharacteristic
275C22⋊Dic61C22⋊C411yescharacteristic
276C22⋊Dic61C22⋊C411yescharacteristic
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61C22⋊C411yescharacteristic
282C4⋊Dic61C22⋊C411yescharacteristic
283C4⋊Dic61C22⋊C411yescharacteristic
284C4⋊Dic61C22⋊C411yescharacteristic
285C4⋊Dic61C22⋊C411yescharacteristic
286C4⋊Dic61C22⋊C411yescharacteristic
287C4⋊Dic61C22×C411yescharacteristic
288C4⋊Dic61C22×C411yescharacteristic
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305C4×Dic61—21no—
306C4×Dic61—21no—
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61C22×C411yescharacteristic
313C4×Dic61C22×C411yescharacteristic
314C4×Dic61C22×C411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2411yescharacteristic
322C23×C61—21no—
323C23×C61C2×C22⋊C411yescharacteristic
324C23×C61C2×C22⋊C411yescharacteristic
325C23×C61C2×C22⋊C411yescharacteristic
326Q8×C61—22no—
327Q8×C61—41no—
328D4×C61—22no—
329D4×C61—41no—
330D4×C61—41no—
331D4×C61—41no—
332D4×C61—42no—
333D4×C61—81no—
334D4×C61—81no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—42no—
342C2×C4×C61—81no—
343C2×C4×C61C2×C22⋊C411yescharacteristic
344C2×C4×C61C2×C22⋊C411yescharacteristic
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C23×C411yescharacteristic
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—42no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—81no—
364C2×Dic61C2×C22⋊C411yescharacteristic
365C2×Dic61C2×C22⋊C411yescharacteristic
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C22×D411yescharacteristic
371C2×Dic61C22×D411yescharacteristic
372Dic122—22no—
373Dic122—22no—
374Dic122—42no—
375Dic122—81no—
376Dic122—81no—
377#92420—22no—
378#92420—41no—
379#92420—41no—
380#92420—41no—
381#92420—41no—
382#92420—41no—
383#92420—41no—
384#92420—41no—
385#17506—611nomaximal, Sylow
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—21no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61C22×C22⋊C411yescharacteristic
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61—41no—
405C4×C61#56812yes—
406Dic61—21no—
407Dic61—21no—
408Dic61—21no—
409Dic61—21no—
410Dic61—21no—
411Dic61—21no—
412Dic61—21no—
413Dic61—41no—
414Dic61—41no—
415Dic61—41no—
416Dic61—41no—
417Dic61#57711yescharacteristic
418Dic61#57811yescharacteristic
419#3461—611no—
420#2989—611no—
421#2965—611no—
422#1497—611no—
423#1495—611no—
424#1494—611no—
425#1493—611no—
426#1491—611no—
427#1489—611no—
428#1488—611no—
429#1487—611no—
430#1485—611no—
431#1483—611no—
432#1482—611no—
433#1481—611no—
434C2×C61—41no—
435C2×C61—41no—
436C2×C61—41no—
437C2×C61—81no—
438C2×C61#287911yescharacteristic
439C2×C61#289811yescharacteristic
440C2×C61#290111yescharacteristic
441#544—611no—
442#542—611no—
443#542—611no—
444#542—1221no—
445#541—611no—
446#541—611no—
447#541—1221no—
448#539—1221no—
449#539—1221no—
450#537#692311yescharacteristic
451#536—611no—
452#536—611no—
453#533—611no—
454#533—611no—
455#533—1221no—
456#529—611no—
457#529—611no—
458#529—1221no—
459#529—1221no—
460#529—1221no—
461C4×#41—611no—
462C4×#41—611no—
463C2×C4×Q8—611no—
464#446—1221no—
465#446—1221no—
466#436—1221no—
467#436—1221no—
468#435—1221no—
469#435—1221no—
470#435—1221no—
471#435—1221no—
472#432—611no—
473#432—611no—
474#431—611no—
475#431—611no—
476#431—611no—
477#431—611no—
478#423—611no—
479#423—611no—
480C2×C4⋊C8—611no—
481C4×M16—611no—
482C4×M16—611no—
483C2×C4×C8—611no—
484Q8⋊C8—611no—
485Q8⋊C8—611no—
486Q8⋊C8—611no—
487Q8⋊C8—611no—
488Q8⋊C8—611no—
489Q8⋊C8—611no—
490Q8⋊C8—611no—
491Q8⋊C8—611no—
492Q8⋊C8—611no—
493Q8⋊C8—611no—
494Q8⋊C8—611no—
495Q8⋊C8—611no—
496D4⋊C8—611no—
497D4⋊C8—611no—
498D4⋊C8—611no—
499D4⋊C8—611no—
500C61#1750611yescharacteristic, complemented, Sylow
501C2×#41C2×#692311yescharacteristic
502C2×#41C2×#692311yescharacteristic
503C22×Q8—611no—
504C2×M16—1221no—
505C2×M16—1221no—
506C2×M16—1221no—
507C2×M16—1221no—
508C22×C8—1221no—
509C22×C8—1221no—
510C4⋊Q8—611no—
511C4⋊Q8—611no—
512C4⋊Q8—611no—
513C4⋊Q8—611no—
514C4⋊Q8—1221no—
515C4⋊Q8—1221no—
516#126—1221no—
517#126—1221no—
518#126—1221no—
519#126—1221no—
520#126—1221no—
521#126—1221no—
522#126—1221no—
523#126—1221no—
524#125—611no—
525#125—611no—
526#125—1221no—
527#125—1221no—
528#125—1221no—
529#125—1221no—
530#125—1221no—
531#125—1221no—
532#125—1221no—
533#124—611no—
534#124—611no—
535#124—1221no—
536#124—1221no—
537#124—1221no—
538#123—1221no—
539#123—1221no—
540#123—1221no—
541#123—1221no—
542#123—1221no—
543#123—1221no—
544#123—1221no—
545#123—1221no—
546C22⋊Q8—21no—
547C22⋊Q8—611no—
548C22⋊Q8—611no—
549C22⋊Q8—611no—
550C22⋊Q8—611no—
551C22⋊Q8—1221no—
552C22⋊Q8—1221no—
553C22⋊Q8—1221no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8C2×#692311yescharacteristic
560C22⋊Q8C2×#692311yescharacteristic
561#121—21no—
562#121—21no—
563#121—21no—
564#121C2×#692311yescharacteristic
565#121C2×#692311yescharacteristic
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1221no—
577C4×Q8—1221no—
578C4×D4—611no—
579C4×D4—611no—
580C4×D4—611no—
581C4×D4—611no—
582C4×D4—611no—
583C4×D4—611no—
584C4×D4—611no—
585C4×D4—611no—
586C4×D4—1221no—
587C4×D4—1221no—
588C4×D4—1221no—
589C4×D4—1221no—
590#117—611no—
591#117—611no—
592#117—611no—
593#117—611no—
594#117—1221no—
595#117—1221no—
596#117—1221no—
597#117—1221no—
598#117—1221no—
599C2×C4⋊C4—1221no—
600C2×C4⋊C4C2×#692311yescharacteristic
601C2×C42—611no—
602C2×C42—611no—
603C2×C42—611no—
604C2×C42—1221no—
605C2×C42—1221no—
606C4⋊C8—611no—
607C4⋊C8—611no—
608C4⋊C8—611no—
609C4⋊C8—611no—
610C4⋊C8—1221no—
611C4⋊C8—1221no—
612C4⋊C8—1221no—
613C4⋊C8—1221no—
614C4⋊C8—1221no—
615C4⋊C8—1221no—
616C22⋊C8—1221no—
617C22⋊C8—1221no—
618C22⋊C8—1221no—
619C22⋊C8—1221no—
620C22⋊C8—1221no—
621C22⋊C8—1221no—
622#97—1221no—
623#97—1221no—
624#97—1221no—
625#97—1221no—
626C4×C8—611no—
627C4×C8—611no—
628C4×C8—611no—
629C4×C8—611no—
630C4×C8—1221no—
631C4×C8—1221no—
632#41—42no—
633#41—42no—
634C2×Q8—611no—
635C2×Q8—611no—
636C2×Q8—1221no—
637C2×Q8—1221no—
638C2×Q8—1221no—
639C2×Q8—2442no—
640C2×Q8C22⋊#692311yescharacteristic
641C2×Q8C22×#692311yescharacteristic
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4C22⋊#692311yescharacteristic
646C2×D4C22⋊#692311yescharacteristic
647C2×D4C22⋊#692311yescharacteristic
648C2×D4C22×#692311yescharacteristic
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4C22×#692311yescharacteristic
661C22×C4C22×#692311yescharacteristic
662C22×C4C22×#692311yescharacteristic
663M16—4881no—
664M16—4881no—
665M16—2442no—
666M16—2442no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—4881no—
676C2×C8—2442no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—611no—
681C4⋊C4—611no—
682C4⋊C4—611no—
683C4⋊C4—611no—
684C4⋊C4—611no—
685C4⋊C4—611no—
686C4⋊C4—611no—
687C4⋊C4—611no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4C22×#692311yescharacteristic
709C4⋊C4C22×#692311yescharacteristic
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—611no—
715C22⋊C4—611no—
716C22⋊C4—611no—
717C22⋊C4—611no—
718C22⋊C4—611no—
719C22⋊C4—611no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—1221no—
723C22⋊C4—1221no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C42—611no—
732C42—611no—
733C42—611no—
734C42—611no—
735C42—611no—
736C42—611no—
737C42—611no—
738C42—611no—
739C42—611no—
740C42—611no—
741C42—1221no—
742C42—1221no—
743C42—1221no—
744C42—1221no—
745C42—1221no—
746C42—1221no—
747C42—1221no—
748C23—21no—
749C23C2×C22⋊#692311yescharacteristic
750C23C2×C22⋊#692311yescharacteristic
751C23C2×C22⋊#692311yescharacteristic
752Q8—22no—
753Q8—41no—
754Q8—1222no—
755Q8—1222no—
756Q8—4881no—
757Q8—4881no—
758Q8—2442no—
759D4—22no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—42no—
764D4—81no—
765D4—81no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—42no—
773C2×C4—81no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—611no—
777C2×C4—611no—
778C2×C4—611no—
779C2×C4—611no—
780C2×C4—611no—
781C2×C4—611no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—4881no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2442no—
799C2×C4C2×C22⋊#692311yescharacteristic
800C2×C4C2×C22⋊#692311yescharacteristic
801C2×C4C2×C22⋊#692311yescharacteristic
802C2×C4C23×#692311yescharacteristic
803C8—1222no—
804C8—2441no—
805C8—2441no—
806C8—2441no—
807C8—2441no—
808C8—2441no—
809C8—2441no—
810C8—2441no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22C22×C22⋊#692311yescharacteristic
824C4—21no—
825C4—21no—
826C4—21no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—611no—
831C4—611no—
832C4—1221no—
833C4—1221no—
834C4—1221no—
835C4—1221no—
836C4—1221no—
837C4—1221no—
838C4—1221no—
839C4—2441no—
840C4—2441no—
841C4—2441no—
842C4—2441no—
843C4#1684084012yes—
844C2—41no—
845C2—41no—
846C2—41no—
847C2—81no—
848C2#2146240311yescharacteristic
849C2#2146244111yescharacteristic
850C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
Fitting, prime radicalC61×#537C4
socleC22×C61C22×C22⋊C4
cosocleC4×Dic61C24
hypercenter#537#6923
hypocenterC61#17506
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #21462738C2semidirect
2. #21462628C2semidirect
3. #21461181C2semidirect
4. #21461174C2semidirect
5. #21461170C2semidirect
6. #21461167C2semidirect
7. #21461163C2semidirect
8. #21461154C2semidirect
9. #21461150C2semidirect
10. #21461149C2semidirect
11. #21461141C2semidirect
12. #21461134C2semidirect
13. #21461130C2semidirect
14. #21461127C2semidirect
500. C61#17506semidirect

Maximal subgroups

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

subgroupindex
#214627382
#214626282
#214611812
#214611742
#214611702
#214611672
#214611632
#214611542
#214611502
#214611492
#214611412
#214611342
#214611302
#214611272
#214592472
#1750661