Subgroups — C₇²×C₁₁×Dic₁₅ #44568521

Order 32340.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₇²×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₇²×C₁₁×Dic₅	—	3	1	no	maximal, Hall
3	C₃×C₅×C₇²×C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇²×C₁₁×Dic₃	—	5	1	no	maximal, Hall
5	C₂×C₅×C₇²×C₁₁	D₃	1	1	yes	characteristic
6	C₇×C₁₁×Dic₁₅	C₇	1	8	yes	maximal, direct product factor
7	C₂×C₃×C₇²×C₁₁	D₅	1	1	yes	characteristic
8	C₇²×Dic₁₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₇²×C₁₁	Dic₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₅×C₇×C₁₁	C₂×C₇	1	8	yes	—
11	C₄×C₇²×C₁₁	—	15	1	no	Hall
12	C₃×C₇²×C₁₁	Dic₅	1	1	yes	characteristic, complemented, Hall
13	C₇×C₁₁×Dic₅	—	3	8	no	—
14	C₂×C₃×C₅×C₇²	C₂×C₁₁	1	1	yes	characteristic
15	C₃×C₅×C₇×C₁₁	C₄×C₇	1	8	yes	complemented
16	C₂×C₇²×C₁₁	D₁₅	1	1	yes	characteristic
17	C₇²×Dic₅	—	3	1	no	Hall
18	C₇×C₁₁×Dic₃	—	5	8	no	—
19	C₂×C₅×C₇×C₁₁	D₃×C₇	1	8	yes	—
20	C₃×C₅×C₇²	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₁₁×Dic₁₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
22	C₇²×Dic₃	—	5	1	no	Hall
23	C₇²×C₁₁	Dic₁₅	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₅×C₇²	D₃×C₁₁	1	1	yes	characteristic
25	C₂×C₃×C₇×C₁₁	C₇×D₅	1	8	yes	—
26	C₇×Dic₁₅	C₇×C₁₁	1	8	yes	direct product factor
27	C₅×C₇×C₁₁	C₇×Dic₃	1	8	yes	complemented
28	C₂×C₃×C₅×C₁₁	C₂×C₇²	1	1	yes	characteristic
29	C₄×C₇×C₁₁	—	15	8	no	—
30	C₂×C₃×C₇²	D₅×C₁₁	1	1	yes	characteristic
31	C₅×C₇²	C₁₁×Dic₃	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₁	C₇×Dic₅	1	8	yes	complemented
33	C₁₁×Dic₅	—	3	1	no	Hall
34	C₂×C₃×C₅×C₇	C₂×C₇×C₁₁	1	8	yes	—
35	C₄×C₇²	—	15	1	no	Hall
36	C₃×C₅×C₁₁	C₄×C₇²	1	1	yes	characteristic, complemented, Hall
37	C₂×C₇×C₁₁	C₇×D₁₅	1	8	yes	—
38	C₃×C₇²	C₁₁×Dic₅	1	1	yes	characteristic, complemented, Hall
39	C₇×Dic₅	—	3	8	no	—
40	C₁₁×Dic₃	—	5	1	no	Hall
41	C₂×C₅×C₁₁	D₃×C₇²	1	1	yes	characteristic
42	C₃×C₅×C₇	C₄×C₇×C₁₁	1	8	yes	complemented
43	C₂×C₇²	C₁₁×D₁₅	1	1	yes	characteristic
44	C₇×Dic₃	—	5	8	no	—
45	C₇×C₁₁	C₇×Dic₁₅	1	8	yes	direct product factor
46	C₂×C₅×C₇	D₃×C₇×C₁₁	1	8	yes	—
47	C₂×C₃×C₁₁	C₇²×D₅	1	1	yes	characteristic
48	Dic₁₅	C₇²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
49	C₅×C₁₁	C₇²×Dic₃	1	1	yes	characteristic, complemented, Hall
50	C₇²	C₁₁×Dic₁₅	1	1	yes	characteristic, direct product factor, Sylow
51	C₄×C₁₁	—	15	1	no	Hall
52	C₂×C₃×C₇	C₇×D₅×C₁₁	1	8	yes	—
53	C₅×C₇	C₇×C₁₁×Dic₃	1	8	yes	complemented
54	C₃×C₁₁	C₇²×Dic₅	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₅	C₂×C₇²×C₁₁	1	1	yes	characteristic
56	C₄×C₇	—	15	8	no	—
57	C₂×C₁₁	C₇²×D₁₅	1	1	yes	characteristic
58	C₃×C₇	C₇×C₁₁×Dic₅	1	8	yes	complemented
59	Dic₅	—	3	1	no	Hall
60	C₃×C₅	C₄×C₇²×C₁₁	1	1	yes	characteristic, complemented, Hall
61	C₂×C₇	C₇×C₁₁×D₁₅	1	8	yes	—
62	Dic₃	—	5	1	no	Hall
63	C₁₁	C₇²×Dic₁₅	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₅	D₃×C₇²×C₁₁	1	1	yes	characteristic
65	C₇	C₇×C₁₁×Dic₁₅	1	8	yes	direct product factor
66	C₂×C₃	C₇²×D₅×C₁₁	1	1	yes	characteristic
67	C₅	C₇²×C₁₁×Dic₃	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	15	1	no	Sylow
69	C₃	C₇²×C₁₁×Dic₅	1	1	yes	characteristic, complemented, Sylow
70	C₂	C₇²×C₁₁×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇²×C₁₁	D₁₅
commutator, hypocenter	C₃×C₅	C₄×C₇²×C₁₁
Frattini	C₂	C₇²×C₁₁×D₁₅
Fitting, socle, prime radical	C₂×C₃×C₅×C₇²×C₁₁	C₂
cosocle	C₂×C₃×C₅	C₂×C₇²×C₁₁
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₇²×C₁₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₇²×C₁₁	C₄	semidirect
6. C₇×C₁₁×Dic₁₅	C₇	direct (N × H)
8. C₇²×Dic₁₅	C₁₁	direct (N × H)
9. C₅×C₇²×C₁₁	Dic₃	semidirect
12. C₃×C₇²×C₁₁	Dic₅	semidirect
15. C₃×C₅×C₇×C₁₁	C₄×C₇	semidirect
20. C₃×C₅×C₇²	C₄×C₁₁	semidirect
21. C₁₁×Dic₁₅	C₇²	direct (N × H)
23. C₇²×C₁₁	Dic₁₅	direct (N × H)
26. C₇×Dic₁₅	C₇×C₁₁	direct (N × H)
27. C₅×C₇×C₁₁	C₇×Dic₃	semidirect
31. C₅×C₇²	C₁₁×Dic₃	semidirect
32. C₃×C₇×C₁₁	C₇×Dic₅	semidirect
36. C₃×C₅×C₁₁	C₄×C₇²	semidirect
38. C₃×C₇²	C₁₁×Dic₅	semidirect
42. C₃×C₅×C₇	C₄×C₇×C₁₁	semidirect
45. C₇×C₁₁	C₇×Dic₁₅	direct (N × H)
48. Dic₁₅	C₇²×C₁₁	direct (N × H)
49. C₅×C₁₁	C₇²×Dic₃	semidirect
50. C₇²	C₁₁×Dic₁₅	direct (N × H)
53. C₅×C₇	C₇×C₁₁×Dic₃	semidirect
54. C₃×C₁₁	C₇²×Dic₅	semidirect
58. C₃×C₇	C₇×C₁₁×Dic₅	semidirect
60. C₃×C₅	C₄×C₇²×C₁₁	semidirect
63. C₁₁	C₇²×Dic₁₅	direct (N × H)
65. C₇	C₇×C₁₁×Dic₁₅	direct (N × H)
67. C₅	C₇²×C₁₁×Dic₃	semidirect
69. C₃	C₇²×C₁₁×Dic₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₇²×C₁₁	2
C₇²×C₁₁×Dic₅	3
C₇²×C₁₁×Dic₃	5
C₇×C₁₁×Dic₁₅	7
C₇²×Dic₁₅	11

Subgroups — C72×C11×Dic15 #44568521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×C₁₁×Dic₁₅ #44568521