Subgroups — #37524486

Order 22932.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊#11725071	C₂	1	2	yes	maximal, complemented
2	C₁₃×#11725078	C₂	1	1	yes	maximal, characteristic, complemented
3	#21439774	—	3	1	no	maximal
4	C₁₃×#89205	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₂₇₃	—	3	2	no	—
6	C₃×C₁₃×C₇⋊D₇	D₃	1	1	yes	characteristic
7	(C₇⋊D₇)⋊D₁₃	—	9	1	no	Hall
8	C₃×C₇²×C₁₃	C₂×D₃	1	1	yes	characteristic
9	#11725071⋊C₂	—	13	1	no	maximal, Hall
10	C₁₃×D₇⋊C₉	—	14	1	no	—
11	C₁₃×C₇⋊D₇	D₉	1	1	yes	characteristic, complemented
12	C₇×D₉₁	—	9	2	no	—
13	D₇×D₃₉	—	21	2	no	—
14	#11725078	D₁₃	1	1	yes	characteristic, complemented
15	#11725071	—	13	2	no	—
16	C₁₃×C₇⋊C₉	—	28	1	no	—
17	C₇²×C₁₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
18	D₂₁⋊D₇	—	39	1	no	—
19	D₂₇₃	—	3	2	no	—
20	C₇×D₃₉	—	21	2	no	—
21	C₃×C₁₃×D₇	—	14	1	no	—
22	C₃×C₁₃×D₇	—	21	2	no	—
23	C₂×D₁₁₇	—	49	1	no	maximal, Hall
24	#89205	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
25	D₇×D₁₃	—	63	2	no	—
26	C₇×D₂₁	—	39	2	no	—
27	C₃×C₇⋊D₇	D₃₉	1	1	yes	characteristic
28	C₃×C₇×C₁₃	—	2	1	no	—
29	C₃×C₇×C₁₃	—	3	2	no	—
30	C₂×C₉×C₁₃	—	49	1	no	—
31	D₁₁₇	—	98	2	no	—
32	D₇²	—	117	1	no	Hall
33	D₉₁	—	9	2	no	—
34	C₇×D₁₃	—	63	2	no	—
35	C₁₃×D₇	—	14	1	no	—
36	C₁₃×D₇	—	42	2	no	—
37	C₂×D₃₉	—	147	1	no	—
38	C₃×C₇²	C₂×D₃₉	1	1	yes	characteristic
39	D₇⋊C₉	—	14	1	no	—
40	C₉×C₁₃	—	196	1	no	Hall
41	C₇⋊D₇	D₁₁₇	1	1	yes	characteristic, complemented
42	C₇×D₇	—	117	2	no	—
43	C₇×C₁₃	—	2	1	no	—
44	C₇×C₁₃	—	6	2	no	—
45	D₃×D₇	—	273	2	no	—
46	C₂×C₃×C₁₃	—	49	1	no	—
47	D₃₉	—	21	2	no	—
48	C₇⋊C₉	—	28	1	no	—
49	C₂×D₁₃	—	441	1	no	Hall
50	C₇²	C₂×D₁₁₇	1	1	yes	characteristic, complemented, Sylow
51	D₂₁	—	39	2	no	—
52	C₃×D₇	—	14	1	no	—
53	C₃×D₇	—	42	2	no	—
54	D₃×C₇	—	273	2	no	—
55	C₃×C₁₃	#64418⋊C₂	1	1	yes	characteristic
56	C₂×D₉	—	637	1	no	Hall
57	C₂×D₇	—	819	2	no	—
58	C₂×C₁₃	—	49	1	no	—
59	D₁₃	—	63	2	no	—
60	C₃×C₇	—	2	1	no	—
61	C₃×C₇	—	6	2	no	—
62	C₂×C₉	—	49	1	no	—
63	D₉	—	1274	2	no	—
64	C₂×C₇	—	819	2	no	—
65	D₇	—	14	1	no	—
66	D₇	—	21	2	no	—
67	D₇	—	117	2	no	—
68	C₁₃	#11725071⋊C₂	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	1911	1	no	—
70	C₉	—	98	1	no	Sylow
71	C₇	—	2	1	no	—
72	C₇	—	3	2	no	—
73	C₂×C₃	—	49	1	no	—
74	D₃	—	273	2	no	—
75	C₂²	—	5733	1	no	Sylow
76	C₃	#21439671	1	1	yes	characteristic
77	C₂	—	49	1	no	—
78	C₂	—	819	2	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₁₃×#89205	C₂²
Frattini	C₃	#21439671
Fitting, socle	C₃×C₇²×C₁₃	C₂×D₃
LCS	G ▷ C₁₃×#89205
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₃⋊#11725071	C₂	semidirect
2. C₁₃×#11725078	C₂	semidirect
4. C₁₃×#89205	C₂²	semidirect
11. C₁₃×C₇⋊D₇	D₉	semidirect
14. #11725078	D₁₃	semidirect
17. C₇²×C₁₃	C₂×D₉	semidirect
24. #89205	C₂×D₁₃	semidirect
41. C₇⋊D₇	D₁₁₇	semidirect
50. C₇²	C₂×D₁₁₇	semidirect
68. C₁₃	#11725071⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
C₁₃⋊#11725071	2
C₁₃×#11725078	2
#21439774	3
#11725071⋊C₂	13
C₂×D₁₁₇	49