Finite Group Databasebeta

← #29646865

Subgroups — #29646865

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#21459246C211yesmaximal, characteristic
2#21454936C211yesmaximal, characteristic, complemented
3#21444293C211yesmaximal, characteristic, complemented
4#21444285C211yesmaximal, characteristic, complemented
5#21444280C211yesmaximal, characteristic, complemented
6#21444275C211yesmaximal, characteristic, complemented
7#21444267C211yesmaximal, characteristic, complemented
8#21444259C211yesmaximal, characteristic, complemented
9#21444254C211yesmaximal, characteristic, complemented
10#21444249C211yesmaximal, characteristic, complemented
11#21444241C211yesmaximal, characteristic, complemented
12#21444233C211yesmaximal, characteristic, complemented
13#21444228C211yesmaximal, characteristic, complemented
14#21444223C211yesmaximal, characteristic, complemented
15C61×#2965C211yesmaximal, characteristic, complemented
16#16840390C411yescharacteristic
17#16840383C411yescharacteristic
18#16840383C411yescharacteristic
19#16840377—21no—
20#16840374C411yescharacteristic
21#16840374C411yescharacteristic
22#16840370—21no—
23#16840354—21no—
24#16840354—21no—
25#16840340C411yescharacteristic
26#16840338C411yescharacteristic
27#16840333C411yescharacteristic
28#16840319C2211yescharacteristic
29#16840319C2211yescharacteristic
30#16840316—21no—
31#16840296C2211yescharacteristic
32#16840296C2211yescharacteristic
33#16840294—21no—
34#16840292—21no—
35#16840292—21no—
36C4×#11758222C2211yescharacteristic
37C2×C4×Dic122C2211yescharacteristic
38#16839893—21no—
39#16839840—21no—
40#16839834—21no—
41#16839834—21no—
42#16839819C2211yescharacteristic
43#16839819C2211yescharacteristic
44#16839815C2211yescharacteristic
45#16839786C2211yescharacteristic
46#16839786C2211yescharacteristic
47C2×C4⋊#92418C2211yescharacteristic
48#16839494C2211yescharacteristic
49#16839494C2211yescharacteristic
50#16839494C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839494C2211yescharacteristic
55#16839494C2211yescharacteristic
56#16839494C2211yescharacteristic
57#16839494C2211yescharacteristic
58#16839494C2211yescharacteristic
59#16839494C2211yescharacteristic
60#16839491C2211yescharacteristic
61#16839491C2211yescharacteristic
62#16839491C2211yescharacteristic
63#16839491C2211yescharacteristic
64C4×#41×C61C2211yescharacteristic
65C61×#446—21no—
66C61×#436—21no—
67C61×#435—21no—
68C61×#435—21no—
69C61×#431C2211yescharacteristic
70C61×#431C2211yescharacteristic
71C61×#431C2211yescharacteristic
72C4×M16×C61C2211yescharacteristic
73C4×M16×C61C2211yescharacteristic
74C2×C4×C8×C61C2211yescharacteristic
75C2×#11758222C2×C411yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C2×#11758194—21no—
78C2×#11758194—21no—
79C22×#92418—21no—
80#14519777C2×C411yescharacteristic
81#14519777C2×C411yescharacteristic
82#14519777C2×C411yescharacteristic
83#14519777C2×C411yescharacteristic
84#14519776—21no—
85#14519775—21no—
86#14519772—21no—
87#14519772—21no—
88#14519771—21no—
89#14519771—21no—
90#14519770—21no—
91#14519770—21no—
92#14519770—21no—
93#14519770—21no—
94#14519769—21no—
95#14519769—21no—
96#14519769C2×C411yescharacteristic
97#14519769C2×C411yescharacteristic
98#14519768—21no—
99#14519767—21no—
100#14519767—21no—
101#14519767—21no—
102#14519767—21no—
103#14519765C2×C411yescharacteristic
104#14519765C2×C411yescharacteristic
105#14519764—21no—
106#14519763—21no—
107#14519763—21no—
108#14519761—21no—
109#14519761—21no—
110#14519760—21no—
111#14519760—21no—
112#14519759—21no—
113#14519759—21no—
114#14519758—21no—
115#14519758—21no—
116#14519757—21no—
117#14519757—21no—
118#14519756—21no—
119#14519756—21no—
120#14519756C2×C411yescharacteristic
121#14519756C2×C411yescharacteristic
122#14519756C2×C411yescharacteristic
123#14519756C2×C411yescharacteristic
124#14519756C2×C411yescharacteristic
125#14519756C2×C411yescharacteristic
126#14519755—21no—
127#14519755—21no—
128#14519754—21no—
129#14519754—21no—
130#14519753—21no—
131#14519751C2×C411yescharacteristic
132#14519751C2×C411yescharacteristic
133#14519749—21no—
134#14519749—21no—
135#14519748—21no—
136C4×Dic122—21no—
137C4×Dic122—21no—
138C4×Dic122—21no—
139C4×Dic122—21no—
140C4×Dic122C2×C411yescharacteristic
141C4×Dic122C2×C411yescharacteristic
142C4×Dic122C2×C411yescharacteristic
143C4×Dic122C2311yescharacteristic
144C4×Dic122C2311yescharacteristic
145C4×Dic122C2311yescharacteristic
146C4×D244C2×C411yescharacteristic
147C4×D244C2311yescharacteristic
148C4×C22⋊D61—21no—
149C4×C22⋊D61—21no—
150C4×C22⋊D61—21no—
151C4×C22⋊D61—21no—
152#14519736—21no—
153#14519736—21no—
154#14519736C2×C411yescharacteristic
155#14519734—21no—
156#14519734—21no—
157#14519734—21no—
158C2×C4⋊Dic61C2×C411yescharacteristic
159C2×#11758196—21no—
160C2×C4×Dic61—21no—
161C42×D61—21no—
162C4⋊#92418—21no—
163C4⋊#92418—21no—
164C4⋊#92418—21no—
165C4⋊#92418C2311yescharacteristic
166C4⋊#92418C2311yescharacteristic
167C4⋊#92418C2311yescharacteristic
168C4⋊#92418C2311yescharacteristic
169C22⋊#92418—21no—
170C22⋊#92418—21no—
171C22⋊#92418—21no—
172#14519688—21no—
173#14519688—21no—
174C4×#92418—21no—
175C2×#41×C61C2×C411yescharacteristic
176C2×M16×C61—21no—
177C2×M16×C61—21no—
178C22×C8×C61—21no—
179C4×Q8×C61D411yescharacteristic
180C4×Q8×C61D411yescharacteristic
181C4×D4×C61D411yescharacteristic
182C4×D4×C61D411yescharacteristic
183C4×D4×C61D411yescharacteristic
184C4×D4×C61D411yescharacteristic
185C4×D4×C61D411yescharacteristic
186C4×D4×C61D411yescharacteristic
187#117×C61C2×C411yescharacteristic
188#117×C61C2×C411yescharacteristic
189#117×C61C2×C411yescharacteristic
190C2×C42×C61C2311yescharacteristic
191C2×C42×C61C2311yescharacteristic
192C2×C42×C61C2311yescharacteristic
193C4⋊C8×C61—21no—
194C4⋊C8×C61—21no—
195C4⋊C8×C61—21no—
196C22⋊C8×C61—21no—
197C22⋊C8×C61—21no—
198C22⋊C8×C61—21no—
199#97×C61—21no—
200#97×C61—21no—
201C4×C8×C61—21no—
202C4×C8×C61C2311yescharacteristic
203C4×C8×C61C2311yescharacteristic
204C4×C8×C61C2311yescharacteristic
205C4×C8×C61C2311yescharacteristic
206#41×C61—42no—
207C2×Q8×C61C22⋊C411yescharacteristic
208C2×D4×C61C22⋊C411yescharacteristic
209C2×D4×C61C22⋊C411yescharacteristic
210C2×D4×C61C22⋊C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225#11758222—42no—
226C2×D244C22×C411yescharacteristic
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—42no—
234C2×Dic122C22×C411yescharacteristic
235C2×Dic122C22×C411yescharacteristic
236C2×Dic122C22×C411yescharacteristic
237M16×C61—42no—
238M16×C61—42no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—42no—
244C4⋊C4×C61C22⋊C411yescharacteristic
245C4⋊C4×C61C22⋊C411yescharacteristic
246C4⋊C4×C61C22⋊C411yescharacteristic
247C4⋊C4×C61C22⋊C411yescharacteristic
248C4⋊C4×C61C22⋊C411yescharacteristic
249C4⋊C4×C61C22⋊C411yescharacteristic
250C22⋊C4×C61C22⋊C411yescharacteristic
251C22⋊C4×C61C22⋊C411yescharacteristic
252C22⋊C4×C61C22⋊C411yescharacteristic
253C22⋊C4×C61C22⋊C411yescharacteristic
254C22⋊C4×C61C22⋊C411yescharacteristic
255C22⋊C4×C61C22⋊C411yescharacteristic
256C42×C61C22×C411yescharacteristic
257C42×C61C22×C411yescharacteristic
258C42×C61C22×C411yescharacteristic
259C42×C61C2×D411yescharacteristic
260C42×C61C2×D411yescharacteristic
261C42×C61C2×D411yescharacteristic
262C42×C61C2×D411yescharacteristic
263C42×C61C2×D411yescharacteristic
264C42×C61C2×D411yescharacteristic
265C42×C61C2411yescharacteristic
266C22⋊Dic61—21no—
267C22⋊Dic61—21no—
268C22⋊Dic61—21no—
269C22⋊Dic61—21no—
270C22⋊Dic61—21no—
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61C22×C411yescharacteristic
289C4⋊Dic61C22×C411yescharacteristic
290C4⋊Dic61C22×C411yescharacteristic
291C4⋊Dic61C22×C411yescharacteristic
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—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315#11758194—81no—
316#11758194—81no—
317C2×#92418—21no—
318C2×#92418—21no—
319C2×#92418—21no—
320C2×#92418—21no—
321C2×#92418—81no—
322C23×C61C2×C22⋊C411yescharacteristic
323C23×C61C2×C22⋊C411yescharacteristic
324C23×C61C2×C22⋊C411yescharacteristic
325C22×D61—21no—
326Q8×C61—41no—
327D4×C61—41no—
328D4×C61—41no—
329D4×C61—41no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61C2×C22⋊C411yescharacteristic
343C2×C4×C61C2×C22⋊C411yescharacteristic
344C2×C4×C61C2×C22⋊C411yescharacteristic
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C23×C411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C22⋊D61—42no—
355C22⋊D61—81no—
356C22⋊D61—81no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—42no—
365C2×Dic61—81no—
366D244—22no—
367C4×D61—42no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—81no—
371Dic122—22no—
372Dic122—22no—
373Dic122—22no—
374Dic122—42no—
375Dic122—81no—
376Dic122—81no—
377C8×C61—22no—
378C8×C61—41no—
379C8×C61—41no—
380C8×C61—41no—
381#92418—41no—
382#92418—41no—
383#92418—41no—
384#92418—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×C61C22×C22⋊C411yescharacteristic
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—41no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—21no—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—21no—
407C4×C61—21no—
408C4×C61—21no—
409C4×C61#56812yes—
410C4×C61#57711yescharacteristic
411C4×C61#57811yescharacteristic
412Dic61—41no—
413Dic61—41no—
414Dic61—41no—
415Dic61—41no—
416Dic61—41no—
417Dic61—41no—
418Dic61—41no—
419#3461—611no—
420#2989—611no—
421#2965D6111yescharacteristic, complemented
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#287911yescharacteristic
438C2×C61#289811yescharacteristic
439C2×C61#290111yescharacteristic
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—611no—
455#533—1221no—
456#529—611no—
457#529—611no—
458#529—1221no—
459#529—1221no—
460#529—1221no—
461C4×#41—611no—
462C4×#41C2×D6111yescharacteristic
463C2×C4×Q8—611no—
464#446—21no—
465#446—1221no—
466#436—21no—
467#436—1221no—
468#435—21no—
469#435—21no—
470#435—1221no—
471#435—1221no—
472#432—611no—
473#432—611no—
474#431—611no—
475#431C2×D6111yescharacteristic
476#431C2×D6111yescharacteristic
477#431C2×D6111yescharacteristic
478#423—611no—
479#423—611no—
480C2×C4⋊C8—611no—
481C4×M16C2×D6111yescharacteristic
482C4×M16C2×D6111yescharacteristic
483C2×C4×C8C2×D6111yescharacteristic
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×#41—611no—
502C2×#41C4×D6111yescharacteristic
503C22×Q8—611no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—1221no—
507C2×M16—1221no—
508C22×C8—21no—
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—611no—
547C22⋊Q8—611no—
548C22⋊Q8—611no—
549C22⋊Q8—611no—
550C22⋊Q8—611no—
551C22⋊Q8—611no—
552C22⋊Q8—1221no—
553C22⋊Q8—1221no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561#121—611no—
562#121—611no—
563#121—1221no—
564#121—1221no—
565#121—1221no—
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8D24411yescharacteristic
577C4×Q8C22⋊D6111yescharacteristic
578C4×D4—611no—
579C4×D4—611no—
580C4×D4—1221no—
581C4×D4—1221no—
582C4×D4—1221no—
583C4×D4—1221no—
584C4×D4D24411yescharacteristic
585C4×D4D24411yescharacteristic
586C4×D4D24411yescharacteristic
587C4×D4C22⋊D6111yescharacteristic
588C4×D4C22⋊D6111yescharacteristic
589C4×D4C22⋊D6111yescharacteristic
590#117—611no—
591#117—1221no—
592#117—1221no—
593#117—1221no—
594#117—1221no—
595#117—1221no—
596#117C4×D6111yescharacteristic
597#117C4×D6111yescharacteristic
598#117C4×D6111yescharacteristic
599C2×C4⋊C4—611no—
600C2×C4⋊C4—1221no—
601C2×C42—1221no—
602C2×C42—1221no—
603C2×C42C22×D6111yescharacteristic
604C2×C42C22×D6111yescharacteristic
605C2×C42C22×D6111yescharacteristic
606C4⋊C8—21no—
607C4⋊C8—21no—
608C4⋊C8—21no—
609C4⋊C8—611no—
610C4⋊C8—611no—
611C4⋊C8—611no—
612C4⋊C8—611no—
613C4⋊C8—1221no—
614C4⋊C8—1221no—
615C4⋊C8—1221no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—21no—
619C22⋊C8—1221no—
620C22⋊C8—1221no—
621C22⋊C8—1221no—
622#97—21no—
623#97—21no—
624#97—1221no—
625#97—1221no—
626C4×C8—21no—
627C4×C8—1221no—
628C4×C8C22×D6111yescharacteristic
629C4×C8C22×D6111yescharacteristic
630C4×C8C22×D6111yescharacteristic
631C4×C8C22×D6111yescharacteristic
632#41—42no—
633#41—2442no—
634C2×Q8—611no—
635C2×Q8—611no—
636C2×Q8—611no—
637C2×Q8—1221no—
638C2×Q8—1221no—
639C2×Q8—1221no—
640C2×Q8—2442no—
641C2×Q8#1175819811yescharacteristic
642C2×D4—611no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4#1175819811yescharacteristic
647C2×D4#1175819811yescharacteristic
648C2×D4#1175819811yescharacteristic
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4C2×C4×D6111yescharacteristic
655C22×C4C2×C4×D6111yescharacteristic
656C22×C4C2×C4×D6111yescharacteristic
657C22×C4C2×D24411yescharacteristic
658C22×C4C2×D24411yescharacteristic
659C22×C4C2×D24411yescharacteristic
660C22×C4C2×C22⋊D6111yescharacteristic
661C22×C4C2×C22⋊D6111yescharacteristic
662C22×C4C2×C22⋊D6111yescharacteristic
663M16—42no—
664M16—42no—
665M16—4881no—
666M16—4881no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—42no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—4881no—
677C4⋊C4—611no—
678C4⋊C4—611no—
679C4⋊C4—611no—
680C4⋊C4—611no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
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#1175819811yescharacteristic
705C4⋊C4#1175819811yescharacteristic
706C4⋊C4#1175819811yescharacteristic
707C4⋊C4#1175819811yescharacteristic
708C4⋊C4#1175819811yescharacteristic
709C4⋊C4#1175819811yescharacteristic
710C22⋊C4—1221no—
711C22⋊C4—1221no—
712C22⋊C4—1221no—
713C22⋊C4—1221no—
714C22⋊C4—1221no—
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—1221no—
725C22⋊C4#1175819811yescharacteristic
726C22⋊C4#1175819811yescharacteristic
727C22⋊C4#1175819811yescharacteristic
728C22⋊C4#1175819811yescharacteristic
729C22⋊C4#1175819811yescharacteristic
730C22⋊C4#1175819811yescharacteristic
731C42—1221no—
732C42—1221no—
733C42—1221no—
734C42—1221no—
735C42—1221no—
736C42—1221no—
737C42—1221no—
738C42C2×C4×D6111yescharacteristic
739C42C2×C4×D6111yescharacteristic
740C42C2×C4×D6111yescharacteristic
741C42C2×D24411yescharacteristic
742C42C2×D24411yescharacteristic
743C42C2×D24411yescharacteristic
744C42C2×C22⋊D6111yescharacteristic
745C42C2×C22⋊D6111yescharacteristic
746C42C2×C22⋊D6111yescharacteristic
747C42C23×D6111yescharacteristic
748C23—1221no—
749C23C2×#1175819811yescharacteristic
750C23C2×#1175819811yescharacteristic
751C23C2×#1175819811yescharacteristic
752Q8—41no—
753Q8—1222no—
754Q8—1222no—
755Q8—1222no—
756Q8—4881no—
757Q8—4881no—
758Q8—2442no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—1222no—
763D4—4881no—
764D4—4881no—
765D4—2442no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—4881no—
786C2×C4—4881no—
787C2×C4—2442no—
788C2×C4—2442no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4C2×#1175819811yescharacteristic
792C2×C4C2×#1175819811yescharacteristic
793C2×C4C2×#1175819811yescharacteristic
794C2×C4C2×#1175819811yescharacteristic
795C2×C4C2×#1175819811yescharacteristic
796C2×C4C2×#1175819811yescharacteristic
797C2×C4C2×#1175819811yescharacteristic
798C2×C4C2×#1175819811yescharacteristic
799C2×C4C2×#1175819811yescharacteristic
800C2×C4C22×C4×D6111yescharacteristic
801C2×C4C22×C22⋊D6111yescharacteristic
802C2×C4C22×D24411yescharacteristic
803C8—22no—
804C8—41no—
805C8—41no—
806C8—41no—
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—2441no—
821C22—2441no—
822C22—2441no—
823C22C22×#1175819811yescharacteristic
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—2441no—
835C4—2441no—
836C4—2441no—
837C4—2441no—
838C4—2441no—
839C4—2441no—
840C4—2441no—
841C4#1684052812yes—
842C4#1684057411yescharacteristic
843C4#1684057911yescharacteristic
844C2—41no—
845C2—41no—
846C2—41no—
847C2—4881no—
848C2#2145426311yescharacteristic
849C2#2145435311yescharacteristic
850C2#2145436711yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2965C2
socleC22×C61C22×C22⋊C4
prime radical#16840340C4
cosocleC42×C61C24
hypercenter#2965D61
hypocenterC61#17506
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #21454936C2semidirect
3. #21444293C2semidirect
4. #21444285C2semidirect
5. #21444280C2semidirect
6. #21444275C2semidirect
7. #21444267C2semidirect
8. #21444259C2semidirect
9. #21444254C2semidirect
10. #21444249C2semidirect
11. #21444241C2semidirect
12. #21444233C2semidirect
13. #21444228C2semidirect
14. #21444223C2semidirect
15. C61×#2965C2semidirect
421. #2965D61semidirect
500. C61#17506semidirect

Maximal subgroups

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

subgroupindex
#214592462
#214549362
#214442932
#214442852
#214442802
#214442752
#214442672
#214442592
#214442542
#214442492
#214442412
#214442332
#214442282
#214442232
C61×#29652
#1750661