Finite Group Databasebeta

← #29646846

Subgroups — #29646846

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#21454936C211yesmaximal, characteristic, complemented
2#21454786C211yesmaximal, characteristic, complemented
3#21444288C211yesmaximal, characteristic, complemented
4#21444284C211yesmaximal, characteristic, complemented
5#21444279C211yesmaximal, characteristic, complemented
6#21444270C211yesmaximal, characteristic, complemented
7#21444262C211yesmaximal, characteristic, complemented
8#21444258C211yesmaximal, characteristic, complemented
9#21444253C211yesmaximal, characteristic, complemented
10#21444244C211yesmaximal, characteristic, complemented
11#21444236C211yesmaximal, characteristic, complemented
12#21444232C211yesmaximal, characteristic, complemented
13#21444227C211yesmaximal, characteristic, complemented
14#21444218C211yesmaximal, characteristic, complemented
15C61×#3460C211yesmaximal, characteristic
16#16839893—21no—
17#16839893—21no—
18#16839840—21no—
19#16839840—21no—
20#16839834—21no—
21#16839834—21no—
22#16839834—21no—
23#16839834—21no—
24#16839819C2211yescharacteristic
25#16839819C2211yescharacteristic, complemented
26#16839815C2211yescharacteristic
27#16839815C2211yescharacteristic, complemented
28#16839815C2211yescharacteristic, complemented
29#16839815C2211yescharacteristic, complemented
30#16839786C2211yescharacteristic
31#16839786C2211yescharacteristic, complemented
32C2×C4⋊#92418C2211yescharacteristic, complemented
33C4×#11758194C2211yescharacteristic
34C4×#11758194C2211yescharacteristic, complemented
35C2×C4×#92418C2211yescharacteristic, complemented
36Q8⋊#92418C2211yescharacteristic, complemented
37Q8⋊#92418C2211yescharacteristic, complemented
38Q8⋊#92418C2211yescharacteristic, complemented
39Q8⋊#92418C2211yescharacteristic, complemented
40D4⋊#92418C2211yescharacteristic
41D4⋊#92418C2211yescharacteristic
42D4⋊#92418C2211yescharacteristic
43D4⋊#92418C2211yescharacteristic
44D4⋊#92418C2211yescharacteristic
45D4⋊#92418C2211yescharacteristic
46D4⋊#92418C2211yescharacteristic
47D4⋊#92418C2211yescharacteristic
48D4⋊#92418C2211yescharacteristic, complemented
49D4⋊#92418C2211yescharacteristic, complemented
50D4⋊#92418C2211yescharacteristic, complemented
51D4⋊#92418C2211yescharacteristic, complemented
52C61×#544C411yescharacteristic
53C61×#542—21no—
54C61×#542C411yescharacteristic
55C61×#542C411yescharacteristic
56C61×#540—21no—
57C61×#540C411yescharacteristic
58C61×#540C411yescharacteristic
59C61×#538—21no—
60C61×#538—21no—
61C61×#537C411yescharacteristic
62C61×#535C411yescharacteristic
63C61×#535C411yescharacteristic
64C61×#532—21no—
65C61×#532C2211yescharacteristic
66C61×#532C2211yescharacteristic
67C61×#529—21no—
68C61×#529C2211yescharacteristic
69C61×#529C2211yescharacteristic
70C61×#525—21no—
71C61×#525—21no—
72C4×#41×C61C2211yescharacteristic
73C4×#41×C61C2211yescharacteristic
74C2×C4×D4×C61C2211yescharacteristic
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C2×#11758194—21no—
79C22×#92418—21no—
80C22×#92418—21no—
81C4⋊#92418—21no—
82C4⋊#92418—21no—
83C4⋊#92418—21no—
84C4⋊#92418—21no—
85C4⋊#92418—21no—
86C4⋊#92418—21no—
87C4⋊#92418C2311yescharacteristic
88C4⋊#92418C2311yescharacteristic
89C4⋊#92418C2311yescharacteristic
90C4⋊#92418C2311yescharacteristic
91C22⋊#92418—21no—
92C22⋊#92418—21no—
93C22⋊#92418—21no—
94C22⋊#92418—21no—
95C22⋊#92418—21no—
96C22⋊#92418—21no—
97#14519688—21no—
98#14519688—21no—
99#14519688—21no—
100#14519688—21no—
101C4×#92418—21no—
102C4×#92418—21no—
103C4×#92418C2311yescharacteristic
104C4×#92418C2311yescharacteristic
105C4×#92418C2311yescharacteristic
106C4×#92418C2311yescharacteristic
107C2×#41×C61—21no—
108C2×#41×C61—21no—
109C2×#41×C61C2×C411yescharacteristic
110C2×#41×C61C2×C411yescharacteristic
111C22×D4×C61C2×C411yescharacteristic
112C23×C4×C61—21no—
113C4⋊Q8×C61—21no—
114C4⋊Q8×C61C2×C411yescharacteristic
115C4⋊Q8×C61C2×C411yescharacteristic
116#127×C61—21no—
117#127×C61C2×C411yescharacteristic
118#127×C61C2×C411yescharacteristic
119#126×C61—21no—
120#126×C61—21no—
121#126×C61—21no—
122#126×C61—21no—
123#125×C61—21no—
124#125×C61C2×C411yescharacteristic
125#125×C61C2×C411yescharacteristic
126#124×C61—21no—
127#124×C61—21no—
128#124×C61—21no—
129#124×C61—21no—
130#124×C61—21no—
131#124×C61C2×C411yescharacteristic
132#124×C61C2×C411yescharacteristic
133#123×C61—21no—
134#123×C61—21no—
135#123×C61—21no—
136#123×C61—21no—
137#123×C61—21no—
138#123×C61—21no—
139#123×C61—21no—
140#123×C61—21no—
141C22⋊Q8×C61—21no—
142C22⋊Q8×C61—21no—
143C22⋊Q8×C61—21no—
144C22⋊Q8×C61—21no—
145C22⋊Q8×C61—21no—
146C22⋊Q8×C61C2×C411yescharacteristic
147C22⋊Q8×C61C2×C411yescharacteristic
148#121×C61—21no—
149#121×C61—21no—
150#121×C61—21no—
151#121×C61—21no—
152#121×C61—21no—
153#121×C61—21no—
154#121×C61—21no—
155#121×C61—21no—
156#121×C61—21no—
157#121×C61—21no—
158#121×C61—21no—
159#121×C61C2×C411yescharacteristic
160#121×C61C2×C411yescharacteristic
161#121×C61C2×C411yescharacteristic
162#121×C61C2×C411yescharacteristic
163#121×C61C2×C411yescharacteristic
164#121×C61C2×C411yescharacteristic
165#120×C61—21no—
166#120×C61—21no—
167#120×C61—21no—
168#120×C61—21no—
169C4×Q8×C61C2×C411yescharacteristic
170C4×Q8×C61D411yescharacteristic
171C4×Q8×C61D411yescharacteristic
172C4×Q8×C61C2311yescharacteristic
173C4×D4×C61—21no—
174C4×D4×C61—21no—
175C4×D4×C61—21no—
176C4×D4×C61—21no—
177C4×D4×C61—21no—
178C4×D4×C61—21no—
179C4×D4×C61—21no—
180C4×D4×C61—21no—
181C4×D4×C61C2×C411yescharacteristic
182C4×D4×C61C2×C411yescharacteristic
183C4×D4×C61C2×C411yescharacteristic
184C4×D4×C61D411yescharacteristic
185C4×D4×C61D411yescharacteristic
186C4×D4×C61D411yescharacteristic
187C4×D4×C61D411yescharacteristic
188C4×D4×C61D411yescharacteristic
189C4×D4×C61D411yescharacteristic
190C4×D4×C61C2311yescharacteristic
191C4×D4×C61C2311yescharacteristic
192C4×D4×C61C2311yescharacteristic
193#117×C61—21no—
194#117×C61—21no—
195#117×C61—21no—
196#117×C61C2×C411yescharacteristic
197#117×C61C2×C411yescharacteristic
198#117×C61C2×C411yescharacteristic
199#117×C61C2×C411yescharacteristic
200C2×C4⋊C4×C61C2×C411yescharacteristic
201C2×C22⋊C4×C61—21no—
202C2×C42×C61—21no—
203C2×C42×C61C2311yescharacteristic
204C2×C42×C61C2311yescharacteristic
205C2×C42×C61C2311yescharacteristic
206C24×C61—21no—
207#41×C61—42no—
208#41×C61—42no—
209#41×C61—81no—
210#41×C61—81no—
211#41×C61—81no—
212#41×C61—81no—
213C2×Q8×C61—21no—
214C2×Q8×C61—21no—
215C2×Q8×C61C22⋊C411yescharacteristic
216C2×Q8×C61C22×C411yescharacteristic
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61—42no—
230C2×D4×C61C22⋊C411yescharacteristic
231C2×D4×C61C22⋊C411yescharacteristic
232C2×D4×C61C22⋊C411yescharacteristic
233C2×D4×C61C22×C411yescharacteristic
234C2×D4×C61C22×C411yescharacteristic
235C2×D4×C61C22×C411yescharacteristic
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—81no—
245C22×C4×C61—81no—
246C22×C4×C61C22×C411yescharacteristic
247C22×C4×C61C22×C411yescharacteristic
248C22×C4×C61C22×C411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D411yescharacteristic
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61C22⋊C411yescharacteristic
267C4⋊C4×C61C22⋊C411yescharacteristic
268C4⋊C4×C61C22⋊C411yescharacteristic
269C4⋊C4×C61C22⋊C411yescharacteristic
270C4⋊C4×C61C22⋊C411yescharacteristic
271C4⋊C4×C61C22⋊C411yescharacteristic
272C4⋊C4×C61C22×C411yescharacteristic
273C4⋊C4×C61C22×C411yescharacteristic
274C4⋊C4×C61C22×C411yescharacteristic
275C4⋊C4×C61C22×C411yescharacteristic
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C22⋊C4×C61—21no—
295C22⋊C4×C61C22⋊C411yescharacteristic
296C22⋊C4×C61C22⋊C411yescharacteristic
297C22⋊C4×C61C22⋊C411yescharacteristic
298C22⋊C4×C61C22⋊C411yescharacteristic
299C22⋊C4×C61C22⋊C411yescharacteristic
300C22⋊C4×C61C22⋊C411yescharacteristic
301C42×C61—21no—
302C42×C61—21no—
303C42×C61—21no—
304C42×C61C22×C411yescharacteristic
305C42×C61C22×C411yescharacteristic
306C42×C61C22×C411yescharacteristic
307C42×C61C2×D411yescharacteristic
308C42×C61C2×D411yescharacteristic
309C42×C61C2×D411yescharacteristic
310C42×C61C2×D411yescharacteristic
311C42×C61C2×D411yescharacteristic
312C42×C61C2×D411yescharacteristic
313C42×C61C2411yescharacteristic
314#11758194—42no—
315#11758194—42no—
316#11758194—81no—
317#11758194—81no—
318C2×#92418—21no—
319C2×#92418—21no—
320C2×#92418—21no—
321C2×#92418—21no—
322C2×#92418—21no—
323C2×#92418—21no—
324C2×#92418—21no—
325C2×#92418—21no—
326C2×#92418—42no—
327C2×#92418—81no—
328C23×C61—21no—
329C23×C61—21no—
330C23×C61—21no—
331C23×C61—42no—
332C23×C61—81no—
333C23×C61—81no—
334C23×C61C2×C22⋊C411yescharacteristic
335C23×C61C2×C22⋊C411yescharacteristic
336C23×C61C2×C22⋊C411yescharacteristic
337Q8×C61—22no—
338Q8×C61—41no—
339Q8×C61—81no—
340Q8×C61—81no—
341D4×C61—22no—
342D4×C61—22no—
343D4×C61—22no—
344D4×C61—41no—
345D4×C61—41no—
346D4×C61—41no—
347D4×C61—42no—
348D4×C61—42no—
349D4×C61—81no—
350D4×C61—81no—
351D4×C61—81no—
352D4×C61—81no—
353D4×C61—81no—
354D4×C61—81no—
355D4×C61—81no—
356D4×C61—81no—
357D4×C61—81no—
358D4×C61—81no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—42no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—81no—
384C2×C4×C61—81no—
385C2×C4×C61—81no—
386C2×C4×C61—81no—
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C2×C22⋊C411yescharacteristic
390C2×C4×C61C2×C22⋊C411yescharacteristic
391C2×C4×C61C2×C22⋊C411yescharacteristic
392C2×C4×C61C2×C22⋊C411yescharacteristic
393C2×C4×C61C2×C22⋊C411yescharacteristic
394C2×C4×C61C2×C22⋊C411yescharacteristic
395C2×C4×C61C2×C22⋊C411yescharacteristic
396C2×C4×C61C23×C411yescharacteristic
397C2×C4×C61C22×D411yescharacteristic
398C2×C4×C61C22×D411yescharacteristic
399#92418—22no—
400#92418—41no—
401#92418—41no—
402#92418—41no—
403#92418—41no—
404#92418—41no—
405#92418—41no—
406#92418—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—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—84no—
427C22×C61C22×C22⋊C411yescharacteristic
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—21no—
434C4×C61—21no—
435C4×C61—21no—
436C4×C61—21no—
437C4×C61—21no—
438C4×C61—41no—
439C4×C61—41no—
440C4×C61—41no—
441C4×C61—41no—
442C4×C61—41no—
443C4×C61#56812yes—
444C4×C61#57611yescharacteristic
445C4×C61#57711yescharacteristic
446#3460D6111yescharacteristic
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—81no—
467C2×C61#287911yescharacteristic
468C2×C61#289711yescharacteristic
469C2×C61#290111yescharacteristic
470#544Dic6111yescharacteristic
471#542—21no—
472#542Dic6111yescharacteristic
473#542Dic6111yescharacteristic
474#540—21no—
475#540Dic6111yescharacteristic
476#540Dic6111yescharacteristic
477#538—21no—
478#538—21no—
479#537Dic6111yescharacteristic
480#535Dic6111yescharacteristic
481#535Dic6111yescharacteristic
482#532—21no—
483#532C2×D6111yescharacteristic
484#532C2×D6111yescharacteristic
485#529—21no—
486#529C2×D6111yescharacteristic
487#529C2×D6111yescharacteristic
488#525—21no—
489#525—21no—
490C4×#41C2×D6111yescharacteristic
491C4×#41C2×D6111yescharacteristic
492C2×C4×D4C2×D6111yescharacteristic
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—21no—
531C2×#41—21no—
532C2×#41C2×Dic6111yescharacteristic
533C2×#41C2×Dic6111yescharacteristic
534C22×D4C2×Dic6111yescharacteristic
535C23×C4—21no—
536C2×M16—1221no—
537C2×M16—1221no—
538C2×M16—1221no—
539C2×M16—1221no—
540C22×C8—1221no—
541C22×C8—1221no—
542C4⋊Q8—21no—
543C4⋊Q8C2×Dic6111yescharacteristic
544C4⋊Q8C2×Dic6111yescharacteristic
545#127—21no—
546#127C2×Dic6111yescharacteristic
547#127C2×Dic6111yescharacteristic
548#126—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#125—21no—
553#125C2×Dic6111yescharacteristic
554#125C2×Dic6111yescharacteristic
555#124—21no—
556#124—21no—
557#124—21no—
558#124—21no—
559#124—21no—
560#124C2×Dic6111yescharacteristic
561#124C2×Dic6111yescharacteristic
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8C2×Dic6111yescharacteristic
576C22⋊Q8C2×Dic6111yescharacteristic
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121C2×Dic6111yescharacteristic
589#121C2×Dic6111yescharacteristic
590#121C2×Dic6111yescharacteristic
591#121C2×Dic6111yescharacteristic
592#121C2×Dic6111yescharacteristic
593#121C2×Dic6111yescharacteristic
594#120—21no—
595#120—21no—
596#120—21no—
597#120—21no—
598C4×Q8C2×Dic6111yescharacteristic
599C4×Q8C22⋊D6111yescharacteristic
600C4×Q8C22⋊D6111yescharacteristic
601C4×Q8C22×D6111yescharacteristic
602C4×D4—21no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4C2×Dic6111yescharacteristic
611C4×D4C2×Dic6111yescharacteristic
612C4×D4C2×Dic6111yescharacteristic
613C4×D4C22⋊D6111yescharacteristic
614C4×D4C22⋊D6111yescharacteristic
615C4×D4C22⋊D6111yescharacteristic
616C4×D4C22⋊D6111yescharacteristic
617C4×D4C22⋊D6111yescharacteristic
618C4×D4C22⋊D6111yescharacteristic
619C4×D4C22×D6111yescharacteristic
620C4×D4C22×D6111yescharacteristic
621C4×D4C22×D6111yescharacteristic
622#117—21no—
623#117—21no—
624#117—21no—
625#117C2×Dic6111yescharacteristic
626#117C2×Dic6111yescharacteristic
627#117C2×Dic6111yescharacteristic
628#117C2×Dic6111yescharacteristic
629C2×C4⋊C4C2×Dic6111yescharacteristic
630C2×C22⋊C4—21no—
631C2×C42—21no—
632C2×C42C22×D6111yescharacteristic
633C2×C42C22×D6111yescharacteristic
634C2×C42C22×D6111yescharacteristic
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—42no—
664#41—81no—
665#41—81no—
666#41—81no—
667#41—81no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8C22⋊Dic6111yescharacteristic
671C2×Q8C22×Dic6111yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4C22⋊Dic6111yescharacteristic
686C2×D4C22⋊Dic6111yescharacteristic
687C2×D4C22⋊Dic6111yescharacteristic
688C2×D4C22×Dic6111yescharacteristic
689C2×D4C22×Dic6111yescharacteristic
690C2×D4C22×Dic6111yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—81no—
700C22×C4—81no—
701C22×C4C22×Dic6111yescharacteristic
702C22×C4C22×Dic6111yescharacteristic
703C22×C4C22×Dic6111yescharacteristic
704C22×C4C2×C22⋊D6111yescharacteristic
705C22×C4C2×C22⋊D6111yescharacteristic
706C22×C4C2×C22⋊D6111yescharacteristic
707C22×C4C2×C22⋊D6111yescharacteristic
708C22×C4C2×C22⋊D6111yescharacteristic
709C22×C4C2×C22⋊D6111yescharacteristic
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—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4C22⋊Dic6111yescharacteristic
736C4⋊C4C22⋊Dic6111yescharacteristic
737C4⋊C4C22⋊Dic6111yescharacteristic
738C4⋊C4C22⋊Dic6111yescharacteristic
739C4⋊C4C22⋊Dic6111yescharacteristic
740C4⋊C4C22⋊Dic6111yescharacteristic
741C4⋊C4C22×Dic6111yescharacteristic
742C4⋊C4C22×Dic6111yescharacteristic
743C4⋊C4C22×Dic6111yescharacteristic
744C4⋊C4C22×Dic6111yescharacteristic
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4C22⋊Dic6111yescharacteristic
765C22⋊C4C22⋊Dic6111yescharacteristic
766C22⋊C4C22⋊Dic6111yescharacteristic
767C22⋊C4C22⋊Dic6111yescharacteristic
768C22⋊C4C22⋊Dic6111yescharacteristic
769C22⋊C4C22⋊Dic6111yescharacteristic
770C42—21no—
771C42—21no—
772C42—21no—
773C42C22×Dic6111yescharacteristic
774C42C22×Dic6111yescharacteristic
775C42C22×Dic6111yescharacteristic
776C42C2×C22⋊D6111yescharacteristic
777C42C2×C22⋊D6111yescharacteristic
778C42C2×C22⋊D6111yescharacteristic
779C42C2×C22⋊D6111yescharacteristic
780C42C2×C22⋊D6111yescharacteristic
781C42C2×C22⋊D6111yescharacteristic
782C42C23×D6111yescharacteristic
783C23—21no—
784C23—21no—
785C23—21no—
786C23—42no—
787C23—81no—
788C23—81no—
789C23C2×C22⋊Dic6111yescharacteristic
790C23C2×C22⋊Dic6111yescharacteristic
791C23C2×C22⋊Dic6111yescharacteristic
792Q8—22no—
793Q8—41no—
794Q8—81no—
795Q8—81no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—81no—
813D4—81no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4C2×C22⋊Dic6111yescharacteristic
843C2×C4C2×C22⋊Dic6111yescharacteristic
844C2×C4C2×C22⋊Dic6111yescharacteristic
845C2×C4C2×C22⋊Dic6111yescharacteristic
846C2×C4C2×C22⋊Dic6111yescharacteristic
847C2×C4C2×C22⋊Dic6111yescharacteristic
848C2×C4C2×C22⋊Dic6111yescharacteristic
849C2×C4C2×C22⋊Dic6111yescharacteristic
850C2×C4C2×C22⋊Dic6111yescharacteristic
851C2×C4C23×Dic6111yescharacteristic
852C2×C4C22×C22⋊D6111yescharacteristic
853C2×C4C22×C22⋊D6111yescharacteristic
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—41no—
878C22—41no—
879C22—41no—
880C22—84no—
881C22C22×C22⋊Dic6111yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—21no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4#1684052912yes—
898C4#1684056511yescharacteristic
899C4#1684057311yescharacteristic
900C2—41no—
901C2—41no—
902C2—41no—
903C2—81no—
904C2—81no—
905C2—81no—
906C2#2145426411yescharacteristic
907C2#2145434511yescharacteristic
908C2#2145436611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
Fitting, prime radicalC61×#3460C2
socleC22×C61C22×C22⋊C4
cosocleC42×C61C24
hypercenter#3460D61
hypocenterC61#17505
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3460

Complements

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

NH ≅ G/Ntype
1. #21454936C2semidirect
2. #21454786C2semidirect
3. #21444288C2semidirect
4. #21444284C2semidirect
5. #21444279C2semidirect
6. #21444270C2semidirect
7. #21444262C2semidirect
8. #21444258C2semidirect
9. #21444253C2semidirect
10. #21444244C2semidirect
11. #21444236C2semidirect
12. #21444232C2semidirect
13. #21444227C2semidirect
14. #21444218C2semidirect
25. #16839819C22semidirect
27. #16839815C22semidirect
28. #16839815C22semidirect
29. #16839815C22semidirect
31. #16839786C22semidirect
32. C2×C4⋊#92418C22semidirect
34. C4×#11758194C22semidirect
35. C2×C4×#92418C22semidirect
36. Q8⋊#92418C22semidirect
37. Q8⋊#92418C22semidirect
38. Q8⋊#92418C22semidirect
39. Q8⋊#92418C22semidirect
48. D4⋊#92418C22semidirect
49. D4⋊#92418C22semidirect
50. D4⋊#92418C22semidirect
51. D4⋊#92418C22semidirect
529. C61#17505semidirect

Maximal subgroups

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

subgroupindex
#214549362
#214547862
#214442882
#214442842
#214442792
#214442702
#214442622
#214442582
#214442532
#214442442
#214442362
#214442322
#214442272
#214442182
C61×#34602
#1750561