Finite Group Databasebeta

← #29646702

Subgroups — #29646702

Order 15616.

920 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#21459250C211yesmaximal, characteristic
2#21454938C211yesmaximal, characteristic, complemented
3#21454775C211yesmaximal, characteristic, complemented
4#21444290C211yesmaximal, characteristic, complemented
5#21444285C211yesmaximal, characteristic, complemented
6#21444283C211yesmaximal, characteristic, complemented
7#21444278C211yesmaximal, characteristic, complemented
8#21444277C211yesmaximal, characteristic, complemented
9#21444274C211yesmaximal, characteristic, complemented
10#21444272C211yesmaximal, characteristic, complemented
11#21444212C211yesmaximal, characteristic, complemented
12#21444205C211yesmaximal, characteristic, complemented
13#21444200C211yesmaximal, characteristic, complemented
14Q8⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#1497C211yesmaximal, characteristic, complemented
16#16840389C411yescharacteristic
17#16840386C411yescharacteristic
18#16840385C411yescharacteristic
19#16840382—21no—
20#16840373C411yescharacteristic
21#16840372C411yescharacteristic
22#16840371—21no—
23#16840360—21no—
24#16840358—21no—
25#16840342C411yescharacteristic
26#16840337C411yescharacteristic
27#16840335C411yescharacteristic
28#16840316—21no—
29#16840316C2211yescharacteristic
30#16840299—21no—
31#16840299C2211yescharacteristic
32#16840296C2211yescharacteristic
33#16840290—21no—
34#16840290—21no—
35C4×#11758226C2211yescharacteristic
36C4×#11758222C2211yescharacteristic
37C4×Q8×D61C2211yescharacteristic
38#16839890—21no—
39#16839886—21no—
40#16839837—21no—
41#16839836—21no—
42#16839835—21no—
43#16839827—21no—
44#16839825—21no—
45#16839825—21no—
46#16839818C2211yescharacteristic
47#16839814C2211yescharacteristic
48#16839813C2211yescharacteristic
49#16839813C2211yescharacteristic
50#16839786C2211yescharacteristic
51#16839784C2211yescharacteristic
52C4⋊C8×D61C2211yescharacteristic
53C2×C4×#92418C2211yescharacteristic
54C4×C8×D61C2211yescharacteristic
55C4×C8×D61C2211yescharacteristic
56#16839494C2211yescharacteristic
57#16839494C2211yescharacteristic
58Q8⋊#92418C2211yescharacteristic
59Q8⋊#92418C2211yescharacteristic
60Q8⋊#92418C2211yescharacteristic
61Q8⋊#92418C2211yescharacteristic
62#16839492C2211yescharacteristic
63#16839492C2211yescharacteristic
64#16839491C2211yescharacteristic
65#16839491C2211yescharacteristic
66#16839489C2211yescharacteristic
67#16839489C2211yescharacteristic
68C61×#533C2211yescharacteristic
69C61×#432C2211yescharacteristic
70C61×#431C2211yescharacteristic
71C61×Q8⋊C8C2211yescharacteristic
72C61×Q8⋊C8C2211yescharacteristic
73C61×Q8⋊C8C2211yescharacteristic
74C61×Q8⋊C8C2211yescharacteristic
75C2×#11758226C2×C411yescharacteristic
76C2×#11758222C2×C411yescharacteristic
77C2×Q8×D61C2×C411yescharacteristic
78C2×#11758194—21no—
79C2×#11758189—21no—
80C22×#92418—21no—
81C2×C8×D61—21no—
82C2×C8×D61—21no—
83C2×C8×D61—21no—
84#14519776—21no—
85#14519776C2×C411yescharacteristic
86#14519775—21no—
87#14519775C2×C411yescharacteristic
88#14519772—21no—
89#14519772—21no—
90#14519772—21no—
91#14519772—21no—
92#14519772—21no—
93#14519771—21no—
94#14519770—21no—
95#14519770—21no—
96#14519769C2×C411yescharacteristic
97#14519768—21no—
98#14519768C2×C411yescharacteristic
99#14519767—21no—
100#14519767—21no—
101#14519767—21no—
102#14519767—21no—
103#14519767—21no—
104#14519766—21no—
105#14519766C2×C411yescharacteristic
106#14519765C2×C411yescharacteristic
107#14519763—21no—
108#14519763—21no—
109#14519762—21no—
110#14519762—21no—
111#14519762—21no—
112#14519762—21no—
113#14519762—21no—
114#14519760—21no—
115#14519759—21no—
116#14519759—21no—
117#14519757—21no—
118#14519757C2×C411yescharacteristic
119#14519756C2×C411yescharacteristic
120#14519755—21no—
121#14519755—21no—
122#14519755—21no—
123#14519755—21no—
124#14519755—21no—
125#14519753—21no—
126#14519753—21no—
127#14519753C2×C411yescharacteristic
128#14519753C2×C411yescharacteristic
129#14519752—21no—
130#14519752C2×C411yescharacteristic
131#14519751C2×C411yescharacteristic
132#14519750—21no—
133#14519750—21no—
134Q8×Dic61C2×C411yescharacteristic
135Q8×Dic61C2×C411yescharacteristic
136C4×Dic122—21no—
137C4×Dic122—21no—
138C4×Dic122D411yescharacteristic
139C4×Dic122D411yescharacteristic
140C4×Dic122C2311yescharacteristic
141#14519742—21no—
142#14519742C2×C411yescharacteristic
143C4×D244—21no—
144C4×D244—21no—
145C4×D244D411yescharacteristic
146C4×D244D411yescharacteristic
147C4×D244C2311yescharacteristic
148#14519739—21no—
149#14519739C2×C411yescharacteristic
150C4×C22⋊D61—21no—
151C4×C22⋊D61D411yescharacteristic
152C4×C22⋊D61D411yescharacteristic
153C4×C22⋊D61D411yescharacteristic
154C4×C22⋊D61D411yescharacteristic
155#14519736C2×C411yescharacteristic
156#14519735—21no—
157#14519735C2×C411yescharacteristic
158#14519734—21no—
159#14519734—21no—
160#14519734—21no—
161#14519734C2×C411yescharacteristic
162#14519734C2×C411yescharacteristic
163C4⋊C4×D61—21no—
164C4⋊C4×D61C2×C411yescharacteristic
165C42×D61—21no—
166C42×D61—21no—
167C42×D61C2311yescharacteristic
168C42×D61C2311yescharacteristic
169C4⋊#92418—21no—
170C4⋊#92418C2311yescharacteristic
171C4⋊#92418C2311yescharacteristic
172#14519706—21no—
173#14519706—21no—
174#14519706—21no—
175#14519706—21no—
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519687—21no—
181C4×#92418—21no—
182C4×#92418C2311yescharacteristic
183C4×#92418C2311yescharacteristic
184C8×Dic61—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187C4⋊Q8×C61C2×C411yescharacteristic
188C4⋊Q8×C61C2×C411yescharacteristic
189#125×C61—21no—
190C22⋊Q8×C61—21no—
191C22⋊Q8×C61C2×C411yescharacteristic
192C22⋊Q8×C61C2×C411yescharacteristic
193C4×Q8×C61—21no—
194C4×Q8×C61C2311yescharacteristic
195C4×Q8×C61C2311yescharacteristic
196#117×C61—21no—
197C2×C42×C61C2311yescharacteristic
198C4⋊C8×C61—21no—
199C4⋊C8×C61C2311yescharacteristic
200C4⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61—21no—
202C22⋊C8×C61—21no—
203#97×C61—21no—
204C4×C8×C61C2311yescharacteristic
205C4×C8×C61C2311yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61C22×C411yescharacteristic
208C2×Q8×C61C22×C411yescharacteristic
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C2×C22⋊D61—21no—
213C2×C22⋊D61C22⋊C411yescharacteristic
214C2×C22⋊D61C22⋊C411yescharacteristic
215#11758226—24no—
216Q8×D61—24no—
217#11758222—24no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244C22⋊C411yescharacteristic
221C2×D244C22×C411yescharacteristic
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61C22×C411yescharacteristic
228C2×C4×D61C22×C411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122C22⋊C411yescharacteristic
236C2×Dic122C22×C411yescharacteristic
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61C22×C411yescharacteristic
249C4⋊C4×C61C22×C411yescharacteristic
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C42×C61—21no—
253C42×C61—21no—
254C42×C61C22×C411yescharacteristic
255C42×C61C2×D411yescharacteristic
256C42×C61C2×D411yescharacteristic
257C42×C61C2411yescharacteristic
258C22⋊Dic61—21no—
259C22⋊Dic61C22⋊C411yescharacteristic
260C22⋊Dic61C22⋊C411yescharacteristic
261#11758198—21no—
262#11758198—21no—
263#11758198—21no—
264#11758198—21no—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198C22⋊C411yescharacteristic
274#11758198C22⋊C411yescharacteristic
275#11758198C22⋊C411yescharacteristic
276#11758198C22⋊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
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
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#11758196C22⋊C411yescharacteristic
298#11758196C22⋊C411yescharacteristic
299#11758196C22⋊C411yescharacteristic
300#11758196C22⋊C411yescharacteristic
301C4×Dic61—21no—
302C4×Dic61—21no—
303C4×Dic61—21no—
304C4×Dic61—21no—
305C4×Dic61—21no—
306C4×Dic61C22×C411yescharacteristic
307C4×Dic61C22×C411yescharacteristic
308C4×Dic61C2×D411yescharacteristic
309C4×Dic61C2×D411yescharacteristic
310C4×Dic61C2×D411yescharacteristic
311C4×Dic61C2×D411yescharacteristic
312#11758194—81no—
313C2×#92418—21no—
314C2×#92418—21no—
315C2×#92418—21no—
316C2×#92418—21no—
317C2×#92418—42no—
318#11758189—81no—
319C8×D61—42no—
320C8×D61—42no—
321C8×D61—81no—
322C23×C61C2×C22⋊C411yescharacteristic
323C22×D61—21no—
324C22×D61C2×C22⋊C411yescharacteristic
325C22×D61C2×C22⋊C411yescharacteristic
326Q8×C61—22no—
327Q8×C61—22no—
328Q8×C61—81no—
329C2×C4×C61—22no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—41no—
337C2×C4×C61C2×C22⋊C411yescharacteristic
338C2×C4×C61C2×C22⋊C411yescharacteristic
339C2×C4×C61C2×C22⋊C411yescharacteristic
340C2×C4×C61C23×C411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C22⋊D61—22no—
344C22⋊D61—22no—
345C22⋊D61—81no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61C2×C22⋊C411yescharacteristic
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C2×C22⋊C411yescharacteristic
352C2×Dic61C2×C22⋊C411yescharacteristic
353C2×Dic61C2×C22⋊C411yescharacteristic
354C2×Dic61C2×C22⋊C411yescharacteristic
355D244—22no—
356D244—22no—
357D244—42no—
358D244—81no—
359C4×D61—22no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—21no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61—42no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—42no—
370C4×D61—81no—
371C4×D61—81no—
372C4×D61#13114yes—
373Dic122—22no—
374Dic122—22no—
375Dic122—42no—
376Dic122—81no—
377C8×C61—41no—
378C8×C61—41no—
379C8×C61—41no—
380C8×C61—41no—
381#92418—22no—
382#92418—41no—
383#92418—41no—
384#92418—41no—
385#17484—611nomaximal, Sylow
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61C22×C22⋊C411yescharacteristic
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—41no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61#40812yes—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—41no—
404C4×C61—41no—
405C4×C61—41no—
406C4×C61—41no—
407C4×C61C2×#13112yes—
408C4×C61#57711yescharacteristic
409C4×C61#57811yescharacteristic
410Dic61—21no—
411Dic61—21no—
412Dic61—21no—
413Dic61—21no—
414Dic61—21no—
415Dic61—41no—
416Dic61—41no—
417Dic61—41no—
418Dic61#40812yes—
419#3461—611no—
420#2989—611no—
421C8×#41—611no—
422#1497—611no—
423#1497D6111yescharacteristic, complemented
424#1495—611no—
425#1495—611no—
426#1494—611no—
427#1494—611no—
428#1493—611no—
429#1493—611no—
430#1479—611no—
431#1477—611no—
432#1476—611no—
433C2×Q8⋊C8—611no—
434C2×C61—41no—
435C2×C61C2×#40811yescharacteristic
436C2×C61#289811yescharacteristic
437C2×C61#290111yescharacteristic
438D61—22no—
439D61—41no—
440D61—81no—
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—611no—
451#536—611no—
452#536—611no—
453#533—611no—
454#533—1221no—
455#533C2×D6111yescharacteristic
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—
465C8×Q8—1221no—
466#436—1221no—
467#435—1221no—
468#435—1221no—
469C8×D4—1221no—
470C8×D4—1221no—
471C8×D4—1221no—
472#432—611no—
473#432C2×D6111yescharacteristic
474#431—611no—
475#431—611no—
476#431—611no—
477#431C2×D6111yescharacteristic
478#423—611no—
479#423—611no—
480C2×C4⋊C8—611no—
481C2×C4×C8—611no—
482C2×C4×C8—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⋊C8C2×D6111yescharacteristic
493Q8⋊C8C2×D6111yescharacteristic
494Q8⋊C8C2×D6111yescharacteristic
495Q8⋊C8C2×D6111yescharacteristic
496D4⋊C8—611no—
497D4⋊C8—611no—
498D4⋊C8—611no—
499D4⋊C8—611no—
500C61#1748411yescharacteristic, complemented, Sylow
501C2×#41—611no—
502C2×#41—611no—
503C22×Q8—611no—
504C2×M16—1221no—
505C2×M16—1221no—
506C22×C8—1221no—
507C22×C8—1221no—
508C22×C8—1221no—
509C22×C8—1221no—
510C4⋊Q8—611no—
511C4⋊Q8—611no—
512C4⋊Q8—1221no—
513C4⋊Q8—1221no—
514C4⋊Q8C4×D6111yescharacteristic
515C4⋊Q8C4×D6111yescharacteristic
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—21no—
525#125—611no—
526#125—611no—
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⋊Q8C4×D6111yescharacteristic
560C22⋊Q8C4×D6111yescharacteristic
561#121—611no—
562#121—611no—
563#121—1221no—
564#121—1221no—
565#121—1221no—
566C4×Q8—21no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—1221no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8C22×D6111yescharacteristic
577C4×Q8C22×D6111yescharacteristic
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—21no—
591#117—611no—
592#117—611no—
593#117—611no—
594#117—611no—
595#117—1221no—
596#117—1221no—
597#117—1221no—
598#117—1221no—
599C2×C4⋊C4—611no—
600C2×C4⋊C4—1221no—
601C2×C42—611no—
602C2×C42—611no—
603C2×C42—1221no—
604C2×C42—1221no—
605C2×C42C22×D6111yescharacteristic
606C4⋊C8—21no—
607C4⋊C8—611no—
608C4⋊C8—611no—
609C4⋊C8—1221no—
610C4⋊C8—1221no—
611C4⋊C8—1221no—
612C4⋊C8—1221no—
613C4⋊C8—1221no—
614C4⋊C8C22×D6111yescharacteristic
615C4⋊C8C22×D6111yescharacteristic
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—1221no—
619C22⋊C8—1221no—
620C22⋊C8—1221no—
621C22⋊C8—1221no—
622#97—21no—
623#97—1221no—
624C4×C8—611no—
625C4×C8—611no—
626C4×C8—1221no—
627C4×C8—1221no—
628C4×C8—1221no—
629C4×C8—1221no—
630C4×C8C22×D6111yescharacteristic
631C4×C8C22×D6111yescharacteristic
632#41—1224no—
633#41—1224no—
634C2×Q8—21no—
635C2×Q8—611no—
636C2×Q8—611no—
637C2×Q8—1221no—
638C2×Q8—1221no—
639C2×Q8—1224no—
640C2×Q8C2×C4×D6111yescharacteristic
641C2×Q8C2×C4×D6111yescharacteristic
642C2×D4—611no—
643C2×D4—611no—
644C2×D4—611no—
645C2×D4—611no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4C2×C4×D6111yescharacteristic
661C22×C4D4×D6111yescharacteristic
662C22×C4D4×D6111yescharacteristic
663M16—4881no—
664M16—4881no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—4881no—
674C2×C8—2442no—
675C2×C8—2442no—
676C2×C8—2442no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—611no—
685C4⋊C4—611no—
686C4⋊C4—611no—
687C4⋊C4—611no—
688C4⋊C4—611no—
689C4⋊C4—611no—
690C4⋊C4—611no—
691C4⋊C4—611no—
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⋊C4C2×C4×D6111yescharacteristic
709C4⋊C4C2×C4×D6111yescharacteristic
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—611no—
713C22⋊C4—611no—
714C22⋊C4—611no—
715C22⋊C4—611no—
716C22⋊C4—611no—
717C22⋊C4—611no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
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—21no—
732C42—21no—
733C42—611no—
734C42—611no—
735C42—611no—
736C42—611no—
737C42—611no—
738C42—611no—
739C42—1221no—
740C42—1221no—
741C42—1221no—
742C42—1221no—
743C42—1221no—
744C42C2×C4×D6111yescharacteristic
745C42D4×D6111yescharacteristic
746C42D4×D6111yescharacteristic
747C42C23×D6111yescharacteristic
748C23—611no—
749C23—611no—
750C23—1221no—
751C23C22⋊C4×D6111yescharacteristic
752Q8—22no—
753Q8—22no—
754Q8—81no—
755Q8—1222no—
756Q8—1222no—
757Q8—4881no—
758Q8—2442no—
759D4—1222no—
760D4—1222no—
761D4—1222no—
762D4—1222no—
763D4—4881no—
764D4—4881no—
765D4—2442no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—41no—
774C2×C4—611no—
775C2×C4—614no—
776C2×C4—611no—
777C2×C4—611no—
778C2×C4—611no—
779C2×C4—611no—
780C2×C4—611no—
781C2×C4—1222no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—4881no—
790C2×C4—4881no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4C22⋊C4×D6111yescharacteristic
798C2×C4C22⋊C4×D6111yescharacteristic
799C2×C4C22⋊C4×D6111yescharacteristic
800C2×C4C22×C4×D6111yescharacteristic
801C2×C4C2×D4×D6111yescharacteristic
802C2×C4C2×D4×D6111yescharacteristic
803C8—41no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—1222no—
808C8—2441no—
809C8—2441no—
810C8—2441no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—612no—
815C22—1221no—
816C22—1221no—
817C22—1221no—
818C22—1221no—
819C22—1221no—
820C22—2441no—
821C22—2441no—
822C22—2441no—
823C22C2×C22⋊C4×D6111yescharacteristic
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—612no—
833C4—1221no—
834C4—1221no—
835C4—1221no—
836C4—1221no—
837C4—1221no—
838C4—2441no—
839C4—2441no—
840C4—2441no—
841C4#131×D6112yes—
842C4#1684057111yescharacteristic
843C4#1684057811yescharacteristic
844C2—41no—
845C2—1222no—
846C2—4881no—
847C2—2441no—
848C2#408×D6111yescharacteristic
849C2#2145435111yescharacteristic
850C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1497C2
socleC22×C61C22×C22⋊C4
prime radical#16840342C4
cosocleC42×C61C24
hypercenter#1497D61
hypocenterC61#17484
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
2. #21454938C2semidirect
3. #21454775C2semidirect
4. #21444290C2semidirect
5. #21444285C2semidirect
6. #21444283C2semidirect
7. #21444278C2semidirect
8. #21444277C2semidirect
9. #21444274C2semidirect
10. #21444272C2semidirect
11. #21444212C2semidirect
12. #21444205C2semidirect
13. #21444200C2semidirect
14. Q8⋊C8×D61C2semidirect
15. C61×#1497C2semidirect
423. #1497D61semidirect
500. C61#17484semidirect

Maximal subgroups

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

subgroupindex
#214592502
#214549382
#214547752
#214442902
#214442852
#214442832
#214442782
#214442772
#214442742
#214442722
#214442122
#214442052
#214442002
Q8⋊C8×D612
C61×#14972
#1748461