Subgroups — #37524487

Order 22932.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#89205	C₂	1	1	yes	maximal, characteristic
2	C₇×C₃⋊(C₇⋊#261)	—	3	1	no	maximal
3	C₁₃×#89205	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇²×D₁₃	D₃	1	1	yes	characteristic
5	C₇×C₇⋊#261	—	9	1	no	Hall
6	C₃×C₇²×C₁₃	Dic₃	1	1	yes	characteristic
7	#13183527	—	13	1	no	maximal, Hall
8	D₁₃×C₇⋊C₉	—	14	1	no	—
9	C₇²×D₁₃	D₉	1	1	yes	characteristic
10	C₃⋊(C₇⋊#261)	—	3	1	no	—
11	C₇×C₃⋊#261	—	21	1	no	—
12	C₂×#89205	—	13	1	no	—
13	C₁₃×C₇⋊C₉	—	14	1	no	—
14	C₇²×C₁₃	Dic₉	1	1	yes	characteristic, complemented, Hall
15	C₇×Dic₂₁	—	39	1	no	—
16	C₃×C₇×D₁₃	—	2	1	no	—
17	C₃×C₇×D₁₃	—	6	1	no	—
18	C₃×C₇×D₁₃	—	6	1	no	—
19	C₉⋊#261	—	49	1	no	maximal, Hall
20	#89205	#261	1	1	yes	characteristic, complemented, Hall
21	C₇⋊#261	—	9	1	no	—
22	C₇×#261	—	63	1	no	—
23	C₂×C₃×C₇²	—	13	1	no	—
24	C₃×C₇×C₁₃	—	2	1	no	—
25	C₃×C₇×C₁₃	—	6	1	no	—
26	C₃×C₇×C₁₃	—	6	1	no	—
27	C₉×D₁₃	—	98	1	no	—
28	C₇×Dic₇	—	117	1	no	Hall
29	C₇×D₁₃	—	2	1	no	—
30	C₇×D₁₃	—	3	1	no	—
31	C₇×D₁₃	—	6	1	no	—
32	C₃⋊#261	—	21	1	no	—
33	C₃×C₇²	C₃⋊#261	1	1	yes	characteristic
34	C₂×C₇⋊C₉	—	182	1	no	—
35	C₉×C₁₃	—	98	1	no	Hall
36	C₂×C₇²	—	13	1	no	—
37	C₇×C₁₃	—	2	1	no	—
38	C₇×C₁₃	—	3	1	no	—
39	C₇×C₁₃	—	6	1	no	—
40	Dic₂₁	—	39	1	no	—
41	C₇×Dic₃	—	273	1	no	—
42	C₃×D₁₃	#64418	1	1	yes	characteristic
43	C₇⋊C₉	—	14	1	no	—
44	#261	—	63	1	no	Hall
45	C₇²	C₉⋊#261	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃×C₇	—	26	1	no	—
47	C₂×C₃×C₇	—	39	1	no	—
48	C₂×C₃×C₇	—	78	1	no	—
49	C₃×C₁₃	#10596868	1	1	yes	characteristic
50	Dic₉	—	637	1	no	Hall
51	C₄×C₇	—	819	1	no	—
52	Dic₇	—	117	1	no	—
53	D₁₃	#11725071	1	1	yes	characteristic
54	C₃×C₇	—	2	1	no	—
55	C₃×C₇	—	3	1	no	—
56	C₃×C₇	—	6	1	no	—
57	C₂×C₉	—	1274	1	no	—
58	C₂×C₇	—	26	1	no	—
59	C₂×C₇	—	78	1	no	—
60	C₂×C₇	—	78	1	no	—
61	C₁₃	#13183527	1	1	yes	characteristic, complemented, Sylow
62	Dic₃	—	273	1	no	—
63	C₉	—	98	1	no	Sylow
64	C₇	—	2	1	no	—
65	C₇	—	6	1	no	—
66	C₇	—	6	1	no	—
67	C₂×C₃	—	13	1	no	—
68	C₄	—	819	1	no	Sylow
69	C₃	#21439672	1	1	yes	characteristic
70	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, hypocenter	C₁₃×#89205	C₄
Frattini	C₃	#21439672
Fitting, socle	C₃×C₇²×C₁₃	Dic₃
prime radical	C₃×C₇²×D₁₃	D₃
cosocle	D₁₃×#89205	C₂
LCS	G ▷ C₁₃×#89205
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₁₃×#89205	C₄	semidirect
14. C₇²×C₁₃	Dic₉	semidirect
20. #89205	#261	semidirect
45. C₇²	C₉⋊#261	semidirect
61. C₁₃	#13183527	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#89205	2
C₇×C₃⋊(C₇⋊#261)	3
#13183527	13
C₉⋊#261	49