Finite Group Databasebeta

← #30613405

Subgroups — #30613405

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462766C211yesmaximal, characteristic, complemented
2#21462751C211yesmaximal, characteristic, complemented
3#21461460C211yesmaximal, characteristic, complemented
4#21461452C211yesmaximal, characteristic, complemented
5#21461449C211yesmaximal, characteristic, complemented
6#21461448C211yesmaximal, characteristic, complemented
7#21461430C211yesmaximal, characteristic, complemented
8#21461420C211yesmaximal, characteristic, complemented
9SD16⋊#92420C211yesmaximal, characteristic, complemented
10#21461406C211yesmaximal, characteristic, complemented
11#21461388C211yesmaximal, characteristic, complemented
12#21461174C211yesmaximal, characteristic, complemented
13#21461114C211yesmaximal, characteristic, complemented
14#21461040C211yesmaximal, characteristic, complemented
15#21455830C211yesmaximal, characteristic
16#16840812C2211yescharacteristic
17#16840811C2211yescharacteristic
18Q8×#92420C2211yescharacteristic
19Q8×#92420C2211yescharacteristic
20#16840797—21no—
21#16840797—21no—
22#16840797C2211yescharacteristic
23#16840797C2211yescharacteristic
24#16840797C2211yescharacteristic
25#16840793—21no—
26D4×#92420—21no—
27D4×#92420C2211yescharacteristic
28#16840786—21no—
29#16840779—21no—
30#16840779C2211yescharacteristic
31#16840778C2211yescharacteristic
32#16840768—21no—
33#16840765—21no—
34#16840765C2211yescharacteristic
35C2×C4⋊#92420C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840626C2211yescharacteristic
38#16840625C2211yescharacteristic
39#16840625C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51C8×#92420C2211yescharacteristic
52#16840293C2211yescharacteristic
53#41×Dic61C2211yescharacteristic
54#16840104C411yescharacteristic
55#16840083C411yescharacteristic
56#16840071C411yescharacteristic
57#16840064C411yescharacteristic
58#16839982C411yescharacteristic
59#16839975C411yescharacteristic
60#16839924C411yescharacteristic
61#16839854C2211yescharacteristic
62#16839853C2211yescharacteristic
63SD16×Dic61C2211yescharacteristic
64D8×Dic61C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#449C411yescharacteristic
67C2×#11758217—21no—
68C2×#11758217—21no—
69C2×#11758217—21no—
70C2×#11758217—21no—
71C22×#92420—21no—
72C22×#92420—21no—
73#14519844—21no—
74#14519844—21no—
75#14519844D411yescharacteristic
76#14519844D411yescharacteristic
77C4⋊#92420—21no—
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420—21no—
81C4⋊#92420—21no—
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84C4⋊#92420C2311yescharacteristic
85C4⋊#92420C2311yescharacteristic
86C22⋊#92420—21no—
87C22⋊#92420—21no—
88C22⋊#92420—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91C22⋊#92420D411yescharacteristic
92C22⋊#92420D411yescharacteristic
93#14519832—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758202C2×C411yescharacteristic
102C2×#11758200C2×C411yescharacteristic
103#14519770—21no—
104#14519768C2×C411yescharacteristic
105#14519764C2×C411yescharacteristic
106#14519758—21no—
107#14519756C2×C411yescharacteristic
108Q8×Dic61C2×C411yescharacteristic
109Q8×Dic61C2311yescharacteristic
110#14519742C2311yescharacteristic
111D4×Dic61—21no—
112D4×Dic61—21no—
113D4×Dic61—21no—
114D4×Dic61C2×C411yescharacteristic
115D4×Dic61C2311yescharacteristic
116D4×Dic61C2311yescharacteristic
117#14519736—21no—
118#14519736C2×C411yescharacteristic
119#14519733—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61C2311yescharacteristic
122#14519711C2×C411yescharacteristic
123#14519710C2×C411yescharacteristic
124#14519709C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126#14519706C2×C411yescharacteristic
127#14519706C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519702C2×C411yescharacteristic
130#14519701C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519698C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×#41×C61C2×C411yescharacteristic
138C2×SD16×C61C2×C411yescharacteristic
139C2×D8×C61C2×C411yescharacteristic
140#121×C61C2×C411yescharacteristic
141#103×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144#41×C61—22no—
145#41×C61—41no—
146C2×Q8×C61C22×C411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61C22×C411yescharacteristic
150C2×D4×C61C22×C411yescharacteristic
151C22×C4×C61—21no—
152C22×C4×C61C22×C411yescharacteristic
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61#4111yescharacteristic
158C2×Dic122C22×C411yescharacteristic
159#11758217—81no—
160#11758217—81no—
161#11758217—81no—
162#11758217—81no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—81no—
170C2×#92420—81no—
171C2×#92420C2×D411yescharacteristic
172C2×#92420C2×D411yescharacteristic
173C2×#92420C2×D411yescharacteristic
174C2×#92420C2×D411yescharacteristic
175SD16×C61—22no—
176D8×C61—41no—
177C2×C8×C61C22×C411yescharacteristic
178C2×C8×C61C22×C411yescharacteristic
179C4⋊C4×C61C22×C411yescharacteristic
180C22⋊C4×C61—21no—
181C22⋊Dic61—21no—
182C22⋊Dic61—21no—
183C22⋊Dic61—21no—
184C22⋊Dic61—21no—
185C22⋊Dic61—21no—
186C22⋊Dic61—21no—
187C22⋊Dic61—21no—
188#11758202—22no—
189#11758200—41no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61C22×C411yescharacteristic
194C4⋊Dic61C22×C411yescharacteristic
195C4⋊Dic61C22×C411yescharacteristic
196#11758196—21no—
197#11758196—21no—
198#11758196—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61C22×C411yescharacteristic
204C4×Dic61C2×D411yescharacteristic
205C4×Dic61#4111yescharacteristic
206C4×Dic61C2411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209C23×C61—21no—
210C23×C61—21no—
211C23×C61C4×D411yescharacteristic
212Q8×C61—21no—
213Q8×C61#13112yes—
214D4×C61—21no—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—21no—
218D4×C61—42no—
219D4×C61—42no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—42no—
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C23×C411yescharacteristic
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—41no—
234C2×Dic61—42no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61C4×D411yescharacteristic
240C2×Dic61C4×D411yescharacteristic
241C2×Dic61C22×D411yescharacteristic
242C2×Dic61C2×#4111yescharacteristic
243Dic122—21no—
244Dic122—21no—
245#92420—21no—
246#92420—21no—
247#92420—21no—
248#92420—21no—
249#92420—41no—
250#92420—41no—
251#92420—41no—
252#92420—41no—
253#92420—41no—
254#92420—41no—
255C8×C61—21no—
256C8×C61—21no—
257#92418—21no—
258#92418—21no—
259#18033—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61C2×C4×D411yescharacteristic
270C4×C61—21no—
271C4×C61—22no—
272C4×C61—41no—
273C4×C61C2×#13111yescharacteristic
274C4×C61#56811yescharacteristic
275Dic61—21no—
276Dic61—21no—
277Dic61—21no—
278Dic61—41no—
279Dic61—41no—
280Dic61—41no—
281Dic61—41no—
282Dic61#57611yescharacteristic
283Dic61#57811yescharacteristic
284#3102—611no—
285#2994—611no—
286#2991—611no—
287#1592—611no—
288#1589—611no—
289#1588—611no—
290#1588—611no—
291#1584—611no—
292#1581—611no—
293SD16⋊C8—611no—
294C8×Q16—611no—
295#1571—611no—
296#1495—611no—
297#1477—611no—
298#1454—611no—
299C2×C61—41no—
300C2×C61—81no—
301C2×C61—81no—
302C2×C61#293311yescharacteristic
303C2×C61#295111yescharacteristic
304C2×C61#295511yescharacteristic
305#529—611no—
306C4×#41—611no—
307#485—611no—
308#482—611no—
309#479—611no—
310#478—611no—
311#464—611no—
312#463—611no—
313#452—611no—
314#449#692311yescharacteristic
315#446—611no—
316C8×Q8—611no—
317C8×Q8—611no—
318C8×Q8—611no—
319C4×Q16—611no—
320C4×SD16—611no—
321C4×SD16—611no—
322C4×D8—611no—
323#436—611no—
324#436—611no—
325#436—611no—
326#436—1221no—
327#436—1221no—
328#435—1221no—
329C8×D4—611no—
330C8×D4—1221no—
331#433—1221no—
332#431—611no—
333#431—611no—
334#431—611no—
335#431—1221no—
336#424—1221no—
337#423—611no—
338#423—1221no—
339C2×C4⋊C8—611no—
340#335—611no—
341#335—611no—
342#335—611no—
343#335—611no—
344Q8⋊C8—611no—
345Q8⋊C8—611no—
346Q8⋊C8—611no—
347Q8⋊C8—611no—
348D4⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351D4⋊C8—611no—
352#322—611no—
353#322—611no—
354#322—611no—
355C82—611no—
356C61#1803311yescharacteristic, complemented, Sylow
357C2×#41C2×#692311yescharacteristic
358C2×Q16—611no—
359C2×SD16—611no—
360C2×SD16C2×#692311yescharacteristic
361C2×D8C2×#692311yescharacteristic
362C2×M16—1221no—
363C2×M16—1221no—
364C2×M16—1221no—
365C2×M16—1221no—
366C22×C8—1221no—
367C22×C8—1221no—
368#126—1221no—
369#125—611no—
370#124—611no—
371#123—1221no—
372C22⋊Q8—611no—
373#121C2×#692311yescharacteristic
374C4×Q8—611no—
375C4×Q8—611no—
376C4×Q8—611no—
377C4×D4—611no—
378C4×D4—611no—
379C4×D4—611no—
380C4×D4—1221no—
381C4×D4—1221no—
382C4×D4—1221no—
383#117—611no—
384#117—1221no—
385#117—1221no—
386C2×C42—611no—
387C2×C42—1221no—
388#107—611no—
389#107—611no—
390#106—611no—
391#106—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8—1221no—
407#103—611no—
408#103—611no—
409#103—611no—
410#103C2×#692311yescharacteristic
411#102—611no—
412#102—611no—
413#102—611no—
414#102C2×#692311yescharacteristic
415C22⋊C8—611no—
416C22⋊C8—611no—
417C22⋊C8—611no—
418C22⋊C8—1221no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8C2×#692311yescharacteristic
424#97—1221no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—1221no—
432C4×C8—1221no—
433C4×C8—1221no—
434#41—22no—
435#41—41no—
436C2×Q8—611no—
437C2×Q8C22×#692311yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C22×#692311yescharacteristic
441C2×D4C22×#692311yescharacteristic
442C22×C4—21no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4C22×#692311yescharacteristic
449Q16—1222no—
450SD16—22no—
451SD16—2441no—
452D8—41no—
453M16—4881no—
454M16—4881no—
455M16—4881no—
456M16—4881no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—4881no—
470C2×C8—4881no—
471C2×C8C22×#692311yescharacteristic
472C2×C8C22×#692311yescharacteristic
473C4⋊C4—611no—
474C4⋊C4—611no—
475C4⋊C4—611no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4C22×#692311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—1221no—
485C22⋊C4—1221no—
486C22⋊C4—1221no—
487C22⋊C4—1221no—
488C22⋊C4—1221no—
489C22⋊C4—1221no—
490C22⋊C4—1221no—
491C42—611no—
492C42—611no—
493C42—611no—
494C42—611no—
495C42—1221no—
496C42—1221no—
497C42—1221no—
498C42—1221no—
499C23—21no—
500C23—21no—
501C23D4×#692311yescharacteristic
502Q8—21no—
503Q8—1221no—
504Q8—1221no—
505Q8#1451986412yes—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—42no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—42no—
517C2×C4—611no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—611no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—2441no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2442no—
533C2×C4D4×#692311yescharacteristic
534C2×C4C23×#692311yescharacteristic
535C8—21no—
536C8—21no—
537C8—1221no—
538C8—1221no—
539C8—1221no—
540C8—1221no—
541C8—1221no—
542C8—1221no—
543C8—2441no—
544C8—2441no—
545C8—2441no—
546C8—2441no—
547C8—2441no—
548C8—2441no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22C2×D4×#692311yescharacteristic
559C4—21no—
560C4—22no—
561C4—41no—
562C4—611no—
563C4—611no—
564C4—1221no—
565C4—1221no—
566C4—1221no—
567C4—2441no—
568C4—2441no—
569C4—2441no—
570C4—2441no—
571C4C2×#1451986411yescharacteristic
572C4#1684084011yescharacteristic
573C2—41no—
574C2—81no—
575C2—81no—
576C2#2146255111yescharacteristic
577C2#2146258111yescharacteristic
578C2#2146259111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
Fitting, prime radicalC61×#449C4
socleC22×C61C2×C4×D4
cosocleC4×Dic61C24
hypercenter#449#6923
hypocenterC61#18033
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #21462766C2semidirect
2. #21462751C2semidirect
3. #21461460C2semidirect
4. #21461452C2semidirect
5. #21461449C2semidirect
6. #21461448C2semidirect
7. #21461430C2semidirect
8. #21461420C2semidirect
9. SD16⋊#92420C2semidirect
10. #21461406C2semidirect
11. #21461388C2semidirect
12. #21461174C2semidirect
13. #21461114C2semidirect
14. #21461040C2semidirect
356. C61#18033semidirect

Maximal subgroups

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

subgroupindex
#214627662
#214627512
#214614602
#214614522
#214614492
#214614482
#214614302
#214614202
SD16⋊#924202
#214614062
#214613882
#214611742
#214611142
#214610402
#214558302
#1803361