Finite Group Databasebeta

← #29646934

Subgroups — #29646934

Order 15616.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454786C211yesmaximal, characteristic, complemented
2#21454485C211yesmaximal, characteristic, complemented
3#21444292C211yesmaximal, characteristic, complemented
4#21444284C211yesmaximal, characteristic, complemented
5#21444279C211yesmaximal, characteristic, complemented
6#21444262C211yesmaximal, characteristic, complemented
7#21444258C211yesmaximal, characteristic, complemented
8#21444253C211yesmaximal, characteristic, complemented
9#21444240C211yesmaximal, characteristic, complemented
10#21444232C211yesmaximal, characteristic, complemented
11#21444227C211yesmaximal, characteristic, complemented
12#21444210C211yesmaximal, characteristic, complemented
13#21444206C211yesmaximal, characteristic, complemented
14#21444201C211yesmaximal, characteristic, complemented
15C61×#3475C211yesmaximal, characteristic
16#16839893—21no—
17#16839840—21no—
18#16839834—21no—
19#16839834—21no—
20#16839823—21no—
21#16839823—21no—
22#16839819C2211yescharacteristic
23#16839819C2211yescharacteristic, complemented
24#16839815C2211yescharacteristic
25#16839815C2211yescharacteristic
26#16839815C2211yescharacteristic, complemented
27#16839815C2211yescharacteristic, complemented
28#16839815C2211yescharacteristic, complemented
29#16839786C2211yescharacteristic, complemented
30C2×C4⋊#92418C2211yescharacteristic, complemented
31#16839729—21no—
32#16839718—21no—
33C4×#11758194C2211yescharacteristic
34C4×#11758194C2211yescharacteristic, complemented
35C2×C4×#92418C2211yescharacteristic, complemented
36Q8⋊#92418C2211yescharacteristic, complemented
37Q8⋊#92418C2211yescharacteristic, complemented
38Q8⋊#92418C2211yescharacteristic, complemented
39Q8⋊#92418C2211yescharacteristic, complemented
40Q8⋊#92418C2211yescharacteristic, complemented
41Q8⋊#92418C2211yescharacteristic, complemented
42Q8⋊#92418C2211yescharacteristic, complemented
43Q8⋊#92418C2211yescharacteristic, complemented
44D4⋊#92418C2211yescharacteristic
45D4⋊#92418C2211yescharacteristic
46D4⋊#92418C2211yescharacteristic
47D4⋊#92418C2211yescharacteristic
48D4⋊#92418C2211yescharacteristic
49D4⋊#92418C2211yescharacteristic
50D4⋊#92418C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52C61×#556C411yescharacteristic
53C61×#555C411yescharacteristic
54C61×#554C411yescharacteristic
55C61×#553—21no—
56C61×#552—21no—
57C61×#552C411yescharacteristic
58C61×#552C411yescharacteristic
59C61×#551—21no—
60C61×#551—21no—
61C61×#547C411yescharacteristic
62C61×#546C411yescharacteristic
63C61×#546C411yescharacteristic
64C61×#533C2211yescharacteristic
65C61×#529—21no—
66C61×#529—21no—
67C61×#529C2211yescharacteristic
68C61×#529C2211yescharacteristic
69C61×#525—21no—
70C4×#41×C61C2211yescharacteristic
71C4×#41×C61C2211yescharacteristic
72C4×#41×C61C2211yescharacteristic
73C2×C4×D4×C61C2211yescharacteristic
74C2×#117×C61—21no—
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C22×#92418—21no—
79C22×#92418—21no—
80C4⋊#92418—21no—
81C4⋊#92418—21no—
82C4⋊#92418—21no—
83C4⋊#92418—21no—
84C4⋊#92418—21no—
85C4⋊#92418C2311yescharacteristic
86C4⋊#92418C2311yescharacteristic
87C4⋊#92418C2311yescharacteristic
88C4⋊#92418C2311yescharacteristic
89C22⋊#92418—21no—
90C22⋊#92418—21no—
91C22⋊#92418—21no—
92C22⋊#92418—21no—
93C22⋊#92418—21no—
94C22⋊#92418—21no—
95C22⋊#92418—21no—
96#14519688—21no—
97#14519688—21no—
98#14519688—21no—
99#14519688—21no—
100C4×#92418—21no—
101C4×#92418—21no—
102C4×#92418—21no—
103C4×#92418C2311yescharacteristic
104C4×#92418C2311yescharacteristic
105C4×#92418C2311yescharacteristic
106C4×#92418C2311yescharacteristic
107C2×#41×C61C2×C411yescharacteristic
108C2×#41×C61C2×C411yescharacteristic
109C2×#41×C61D411yescharacteristic
110C22×D4×C61C2×C411yescharacteristic
111C23×C4×C61—21no—
112C4⋊Q8×C61C2×C411yescharacteristic
113C4⋊Q8×C61C2×C411yescharacteristic
114#126×C61—21no—
115#126×C61—21no—
116#126×C61—21no—
117#126×C61—21no—
118#126×C61—21no—
119#126×C61—21no—
120#125×C61—21no—
121#125×C61—21no—
122#125×C61—21no—
123#125×C61C2×C411yescharacteristic
124#125×C61C2×C411yescharacteristic
125#124×C61—21no—
126#124×C61—21no—
127#124×C61C2×C411yescharacteristic
128#124×C61C2×C411yescharacteristic
129#123×C61—21no—
130#123×C61—21no—
131#123×C61—21no—
132#123×C61—21no—
133#123×C61—21no—
134#123×C61—21no—
135#123×C61—21no—
136#123×C61—21no—
137C22⋊Q8×C61—21no—
138C22⋊Q8×C61—21no—
139C22⋊Q8×C61—21no—
140C22⋊Q8×C61—21no—
141C22⋊Q8×C61—21no—
142C22⋊Q8×C61C2×C411yescharacteristic
143C22⋊Q8×C61C2×C411yescharacteristic
144C22⋊Q8×C61C2×C411yescharacteristic
145C22⋊Q8×C61C2×C411yescharacteristic
146#121×C61—21no—
147#121×C61—21no—
148#121×C61—21no—
149#121×C61—21no—
150#121×C61C2×C411yescharacteristic
151#121×C61C2×C411yescharacteristic
152#120×C61—21no—
153#120×C61—21no—
154C4×Q8×C61—21no—
155C4×Q8×C61C2×C411yescharacteristic
156C4×Q8×C61C2×C411yescharacteristic
157C4×Q8×C61C2×C411yescharacteristic
158C4×Q8×C61D411yescharacteristic
159C4×Q8×C61C2311yescharacteristic
160C4×Q8×C61C2311yescharacteristic
161C4×D4×C61—21no—
162C4×D4×C61—21no—
163C4×D4×C61—21no—
164C4×D4×C61—21no—
165C4×D4×C61—21no—
166C4×D4×C61—21no—
167C4×D4×C61—21no—
168C4×D4×C61—21no—
169C4×D4×C61C2×C411yescharacteristic
170C4×D4×C61C2×C411yescharacteristic
171C4×D4×C61C2×C411yescharacteristic
172C4×D4×C61C2×C411yescharacteristic
173C4×D4×C61C2×C411yescharacteristic
174C4×D4×C61C2×C411yescharacteristic
175C4×D4×C61C2×C411yescharacteristic
176C4×D4×C61D411yescharacteristic
177C4×D4×C61D411yescharacteristic
178C4×D4×C61D411yescharacteristic
179C4×D4×C61C2311yescharacteristic
180C4×D4×C61C2311yescharacteristic
181#117×C61—21no—
182#117×C61—21no—
183#117×C61—21no—
184#117×C61—21no—
185#117×C61—21no—
186#117×C61—21no—
187#117×C61—21no—
188#117×C61—21no—
189#117×C61—21no—
190#117×C61C2×C411yescharacteristic
191#117×C61C2×C411yescharacteristic
192#117×C61D411yescharacteristic
193#117×C61D411yescharacteristic
194#117×C61D411yescharacteristic
195C2×C4⋊C4×C61—21no—
196C2×C4⋊C4×C61—21no—
197C2×C4⋊C4×C61C2×C411yescharacteristic
198C2×C22⋊C4×C61—21no—
199C2×C22⋊C4×C61—21no—
200C2×C22⋊C4×C61—21no—
201C2×C42×C61—21no—
202C2×C42×C61—21no—
203C2×C42×C61C2311yescharacteristic
204C2×C42×C61C2311yescharacteristic
205C2×C42×C61C2311yescharacteristic
206C24×C61—21no—
207#41×C61—22no—
208#41×C61—22no—
209#41×C61—41no—
210#41×C61—41no—
211#41×C61—41no—
212#41×C61—41no—
213C2×Q8×C61—21no—
214C2×Q8×C61C22⋊C411yescharacteristic
215C2×Q8×C61C22×C411yescharacteristic
216C2×Q8×C61C22×C411yescharacteristic
217C2×D4×C61—22no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—41no—
224C2×D4×C61C22⋊C411yescharacteristic
225C2×D4×C61C22⋊C411yescharacteristic
226C2×D4×C61C22⋊C411yescharacteristic
227C2×D4×C61C22×C411yescharacteristic
228C2×D4×C61C22×C411yescharacteristic
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—42no—
239C22×C4×C61—42no—
240C22×C4×C61C22×C411yescharacteristic
241C22×C4×C61C22×C411yescharacteristic
242C22×C4×C61C22×C411yescharacteristic
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
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×C61C22⋊C411yescharacteristic
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
275C22⋊C4×C61—21no—
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×C61C22⋊C411yescharacteristic
294C22⋊C4×C61C22⋊C411yescharacteristic
295C22⋊C4×C61C22⋊C411yescharacteristic
296C22⋊C4×C61C22⋊C411yescharacteristic
297C22⋊C4×C61C22⋊C411yescharacteristic
298C22⋊C4×C61C22⋊C411yescharacteristic
299C42×C61—21no—
300C42×C61—21no—
301C42×C61—21no—
302C42×C61—21no—
303C42×C61—21no—
304C42×C61—21no—
305C42×C61C22×C411yescharacteristic
306C42×C61C22×C411yescharacteristic
307C42×C61C22×C411yescharacteristic
308C42×C61C2×D411yescharacteristic
309C42×C61C2×D411yescharacteristic
310C42×C61C2×D411yescharacteristic
311C42×C61C2×D411yescharacteristic
312C42×C61C2×D411yescharacteristic
313C42×C61C2×D411yescharacteristic
314C42×C61C2411yescharacteristic
315#11758194—42no—
316#11758194—42no—
317#11758194—42no—
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—42no—
328C23×C61—21no—
329C23×C61—21no—
330C23×C61—42no—
331C23×C61—42no—
332C23×C61—81no—
333C23×C61C2×C22⋊C411yescharacteristic
334C23×C61C2×C22⋊C411yescharacteristic
335C23×C61C2×C22⋊C411yescharacteristic
336Q8×C61—21no—
337Q8×C61—21no—
338Q8×C61—21no—
339Q8×C61—21no—
340Q8×C61—41no—
341Q8×C61—81no—
342D4×C61—21no—
343D4×C61—21no—
344D4×C61—21no—
345D4×C61—41no—
346D4×C61—41no—
347D4×C61—41no—
348D4×C61—42no—
349D4×C61—42no—
350D4×C61—42no—
351D4×C61—81no—
352D4×C61—81no—
353D4×C61#13112yes—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
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—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—42no—
376C2×C4×C61—42no—
377C2×C4×C61—42no—
378C2×C4×C61—42no—
379C2×C4×C61—42no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—81no—
385C2×C4×C61—81no—
386C2×C4×C61C2×C22⋊C411yescharacteristic
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×C61C23×C411yescharacteristic
396C2×C4×C61C22×D411yescharacteristic
397C2×C4×C61C22×D411yescharacteristic
398#92418—22no—
399#92418—41no—
400#92418—41no—
401#92418—41no—
402#92418—41no—
403#92418—41no—
404#92418—41no—
405#92418—41no—
406#17513—611nomaximal, Sylow
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—22no—
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—84no—
423C22×C61C22×C22⋊C411yescharacteristic
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—21no—
434C4×C61—41no—
435C4×C61—41no—
436C4×C61—41no—
437C4×C61—41no—
438C4×C61—41no—
439C4×C61—41no—
440C4×C61C2×#13111yescharacteristic
441C4×C61#56811yescharacteristic
442C4×C61#57511yescharacteristic
443C4×C61#57511yescharacteristic
444#3475D6111yescharacteristic
445#2965—611no—
446#2925—611no—
447#1497—611no—
448#1495—611no—
449#1494—611no—
450#1490—611no—
451#1489—611no—
452#1488—611no—
453#1485—611no—
454#1483—611no—
455#1482—611no—
456#1478—611no—
457#1477—611no—
458#1476—611no—
459C2×C61—41no—
460C2×C61—41no—
461C2×C61—41no—
462C2×C61—42no—
463C2×C61—81no—
464C2×C61#288011yescharacteristic
465C2×C61#289611yescharacteristic
466C2×C61#290111yescharacteristic
467#556Dic6111yescharacteristic
468#555Dic6111yescharacteristic
469#554Dic6111yescharacteristic
470#553—21no—
471#552—21no—
472#552Dic6111yescharacteristic
473#552Dic6111yescharacteristic
474#551—21no—
475#551—21no—
476#547Dic6111yescharacteristic
477#546Dic6111yescharacteristic
478#546Dic6111yescharacteristic
479#533C2×D6111yescharacteristic
480#529—21no—
481#529—21no—
482#529C2×D6111yescharacteristic
483#529C2×D6111yescharacteristic
484#525—21no—
485C4×#41C2×D6111yescharacteristic
486C4×#41C2×D6111yescharacteristic
487C4×#41C2×D6111yescharacteristic
488C2×C4×D4C2×D6111yescharacteristic
489C2×#117—21no—
490#446—1221no—
491#436—1221no—
492#435—1221no—
493#435—1221no—
494#433—1221no—
495#433—1221no—
496#432—611no—
497#432—611no—
498#431—611no—
499#431—611no—
500#431—611no—
501#431—611no—
502#431—611no—
503#423—611no—
504C2×C4⋊C8—611no—
505#408—1221no—
506#405—1221no—
507C4×M16—611no—
508C4×M16—611no—
509C2×C4×C8—611no—
510Q8⋊C8—611no—
511Q8⋊C8—611no—
512Q8⋊C8—611no—
513Q8⋊C8—611no—
514Q8⋊C8—611no—
515Q8⋊C8—611no—
516Q8⋊C8—611no—
517Q8⋊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—
526C61#1751311yescharacteristic, complemented, Sylow
527C2×#41C2×Dic6111yescharacteristic
528C2×#41C2×Dic6111yescharacteristic
529C2×#41C22⋊D6111yescharacteristic
530C22×D4C2×Dic6111yescharacteristic
531C23×C4—21no—
532C2×M16—1221no—
533C2×M16—1221no—
534C2×M16—1221no—
535C22×C8—1221no—
536C22×C8—1221no—
537C4⋊Q8C2×Dic6111yescharacteristic
538C4⋊Q8C2×Dic6111yescharacteristic
539#126—21no—
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#125—21no—
546#125—21no—
547#125—21no—
548#125C2×Dic6111yescharacteristic
549#125C2×Dic6111yescharacteristic
550#124—21no—
551#124—21no—
552#124C2×Dic6111yescharacteristic
553#124C2×Dic6111yescharacteristic
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8C2×Dic6111yescharacteristic
568C22⋊Q8C2×Dic6111yescharacteristic
569C22⋊Q8C2×Dic6111yescharacteristic
570C22⋊Q8C2×Dic6111yescharacteristic
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121C2×Dic6111yescharacteristic
576#121C2×Dic6111yescharacteristic
577#120—21no—
578#120—21no—
579C4×Q8—21no—
580C4×Q8C2×Dic6111yescharacteristic
581C4×Q8C2×Dic6111yescharacteristic
582C4×Q8C2×Dic6111yescharacteristic
583C4×Q8C22⋊D6111yescharacteristic
584C4×Q8C22×D6111yescharacteristic
585C4×Q8C22×D6111yescharacteristic
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4C2×Dic6111yescharacteristic
595C4×D4C2×Dic6111yescharacteristic
596C4×D4C2×Dic6111yescharacteristic
597C4×D4C2×Dic6111yescharacteristic
598C4×D4C2×Dic6111yescharacteristic
599C4×D4C2×Dic6111yescharacteristic
600C4×D4C2×Dic6111yescharacteristic
601C4×D4C22⋊D6111yescharacteristic
602C4×D4C22⋊D6111yescharacteristic
603C4×D4C22⋊D6111yescharacteristic
604C4×D4C22×D6111yescharacteristic
605C4×D4C22×D6111yescharacteristic
606#117—21no—
607#117—21no—
608#117—21no—
609#117—21no—
610#117—21no—
611#117—21no—
612#117—21no—
613#117—21no—
614#117—21no—
615#117C2×Dic6111yescharacteristic
616#117C2×Dic6111yescharacteristic
617#117C22⋊D6111yescharacteristic
618#117C22⋊D6111yescharacteristic
619#117C22⋊D6111yescharacteristic
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4C2×Dic6111yescharacteristic
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42C22×D6111yescharacteristic
629C2×C42C22×D6111yescharacteristic
630C2×C42C22×D6111yescharacteristic
631C4⋊C8—611no—
632C4⋊C8—611no—
633C4⋊C8—611no—
634C4⋊C8—611no—
635C4⋊C8—1221no—
636C4⋊C8—1221no—
637C4⋊C8—1221no—
638C4⋊C8—1221no—
639C4⋊C8—1221no—
640C22⋊C8—1221no—
641C22⋊C8—1221no—
642C22⋊C8—1221no—
643C22⋊C8—1221no—
644C22⋊C8—1221no—
645C22⋊C8—1221no—
646C22⋊C8—1221no—
647#97—1221no—
648#97—1221no—
649#97—1221no—
650#97—1221no—
651C4×C8—611no—
652C4×C8—611no—
653C4×C8—611no—
654C4×C8—611no—
655C4×C8—1221no—
656C4×C8—1221no—
657C4×C8—1221no—
658C24—21no—
659#41—22no—
660#41—22no—
661#41—41no—
662#41—41no—
663#41—41no—
664#41—41no—
665C2×Q8—21no—
666C2×Q8C22⋊Dic6111yescharacteristic
667C2×Q8C22×Dic6111yescharacteristic
668C2×Q8C22×Dic6111yescharacteristic
669C2×D4—22no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—41no—
676C2×D4C22⋊Dic6111yescharacteristic
677C2×D4C22⋊Dic6111yescharacteristic
678C2×D4C22⋊Dic6111yescharacteristic
679C2×D4C22×Dic6111yescharacteristic
680C2×D4C22×Dic6111yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4C22×Dic6111yescharacteristic
693C22×C4C22×Dic6111yescharacteristic
694C22×C4C22×Dic6111yescharacteristic
695C22×C4C2×C22⋊D6111yescharacteristic
696C22×C4C2×C22⋊D6111yescharacteristic
697C22×C4C2×C22⋊D6111yescharacteristic
698C22×C4C2×C22⋊D6111yescharacteristic
699C22×C4C2×C22⋊D6111yescharacteristic
700C22×C4C2×C22⋊D6111yescharacteristic
701M16—2442no—
702M16—2442no—
703M16—2442no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—2442no—
713C2×C8—2442no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4C22⋊Dic6111yescharacteristic
731C4⋊C4C22⋊Dic6111yescharacteristic
732C4⋊C4C22⋊Dic6111yescharacteristic
733C4⋊C4C22⋊Dic6111yescharacteristic
734C4⋊C4C22⋊Dic6111yescharacteristic
735C4⋊C4C22⋊Dic6111yescharacteristic
736C4⋊C4C22×Dic6111yescharacteristic
737C4⋊C4C22×Dic6111yescharacteristic
738C4⋊C4C22×Dic6111yescharacteristic
739C4⋊C4C22×Dic6111yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
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⋊C4C22⋊Dic6111yescharacteristic
759C22⋊C4C22⋊Dic6111yescharacteristic
760C22⋊C4C22⋊Dic6111yescharacteristic
761C22⋊C4C22⋊Dic6111yescharacteristic
762C22⋊C4C22⋊Dic6111yescharacteristic
763C22⋊C4C22⋊Dic6111yescharacteristic
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42—21no—
770C42C22×Dic6111yescharacteristic
771C42C22×Dic6111yescharacteristic
772C42C22×Dic6111yescharacteristic
773C42C2×C22⋊D6111yescharacteristic
774C42C2×C22⋊D6111yescharacteristic
775C42C2×C22⋊D6111yescharacteristic
776C42C2×C22⋊D6111yescharacteristic
777C42C2×C22⋊D6111yescharacteristic
778C42C2×C22⋊D6111yescharacteristic
779C42C23×D6111yescharacteristic
780C23—21no—
781C23—21no—
782C23—42no—
783C23—42no—
784C23—81no—
785C23C2×C22⋊Dic6111yescharacteristic
786C23C2×C22⋊Dic6111yescharacteristic
787C23C2×C22⋊Dic6111yescharacteristic
788Q8—21no—
789Q8—21no—
790Q8—21no—
791Q8—21no—
792Q8—41no—
793Q8—81no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—42no—
801D4—42no—
802D4—42no—
803D4—81no—
804D4—81no—
805D4#1451978412yes—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4C2×C22⋊Dic6111yescharacteristic
839C2×C4C2×C22⋊Dic6111yescharacteristic
840C2×C4C2×C22⋊Dic6111yescharacteristic
841C2×C4C2×C22⋊Dic6111yescharacteristic
842C2×C4C2×C22⋊Dic6111yescharacteristic
843C2×C4C2×C22⋊Dic6111yescharacteristic
844C2×C4C2×C22⋊Dic6111yescharacteristic
845C2×C4C2×C22⋊Dic6111yescharacteristic
846C2×C4C2×C22⋊Dic6111yescharacteristic
847C2×C4C23×Dic6111yescharacteristic
848C2×C4C22×C22⋊D6111yescharacteristic
849C2×C4C22×C22⋊D6111yescharacteristic
850C8—1222no—
851C8—2441no—
852C8—2441no—
853C8—2441no—
854C8—2441no—
855C8—2441no—
856C8—2441no—
857C8—2441no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—22no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—84no—
874C22C22×C22⋊Dic6111yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4C2×#1451978411yescharacteristic
892C4#1684052911yescharacteristic
893C4#1684056011yescharacteristic
894C4#1684056011yescharacteristic
895C2—41no—
896C2—41no—
897C2—41no—
898C2—42no—
899C2—81no—
900C2#2145426811yescharacteristic
901C2#2145433811yescharacteristic
902C2#2145436611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
Fitting, prime radicalC61×#3475C2
socleC22×C61C22×C22⋊C4
cosocleC42×C61C24
hypercenter#3475D61
hypocenterC61#17513
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. #21454786C2semidirect
2. #21454485C2semidirect
3. #21444292C2semidirect
4. #21444284C2semidirect
5. #21444279C2semidirect
6. #21444262C2semidirect
7. #21444258C2semidirect
8. #21444253C2semidirect
9. #21444240C2semidirect
10. #21444232C2semidirect
11. #21444227C2semidirect
12. #21444210C2semidirect
13. #21444206C2semidirect
14. #21444201C2semidirect
23. #16839819C22semidirect
26. #16839815C22semidirect
27. #16839815C22semidirect
28. #16839815C22semidirect
29. #16839786C22semidirect
30. C2×C4⋊#92418C22semidirect
34. C4×#11758194C22semidirect
35. C2×C4×#92418C22semidirect
36. Q8⋊#92418C22semidirect
37. Q8⋊#92418C22semidirect
38. Q8⋊#92418C22semidirect
39. Q8⋊#92418C22semidirect
40. Q8⋊#92418C22semidirect
41. Q8⋊#92418C22semidirect
42. Q8⋊#92418C22semidirect
43. Q8⋊#92418C22semidirect
526. C61#17513semidirect

Maximal subgroups

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

subgroupindex
#214547862
#214544852
#214442922
#214442842
#214442792
#214442622
#214442582
#214442532
#214442402
#214442322
#214442272
#214442102
#214442062
#214442012
C61×#34752
#1751361