Subgroups — #37524499

Order 22932.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26039447	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×#5997	C₃	1	1	yes	maximal, characteristic
3	#19153199	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
5	C₁₃×#5997	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic
7	#5997⋊C₉	—	13	1	no	maximal, Hall
8	#13109901	—	14	2	no	—
9	#13109901	—	14	2	no	—
10	C₁₃×C₇⋊D₇	C₂×C₉	1	1	yes	characteristic
11	#11725077	—	13	1	no	—
12	#11717942	—	14	2	no	—
13	#11717942	—	14	2	no	—
14	C₇²×C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
15	C₃×#5997	C₁₃⋊C₃	1	1	yes	characteristic
16	C₃×C₁₃×D₇	—	42	2	no	—
17	C₃×C₁₃×D₇	—	42	2	no	—
18	C₄×C₁₃⋊C₉	—	49	1	no	maximal, Hall
19	#89204	—	13	1	no	Hall
20	C₃×C₇⋊D₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic
21	C₃×C₇×C₁₃	—	2	2	no	—
22	C₃×C₇×C₁₃	—	2	2	no	—
23	C₂×C₁₃⋊C₉	—	49	1	no	—
24	#5997	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
25	C₁₃×D₇	—	42	2	no	—
26	C₁₃×D₇	—	42	2	no	—
27	C₃×C₄×C₁₃	—	147	1	no	—
28	C₃×C₇²	C₄×C₁₃⋊C₃	1	1	yes	characteristic
29	D₇⋊C₉	—	182	2	no	—
30	D₇⋊C₉	—	182	2	no	—
31	C₁₃⋊C₉	—	49	1	no	Hall
32	C₇⋊D₇	C₂×C₁₃⋊C₉	1	1	yes	characteristic
33	C₇×C₁₃	—	2	2	no	—
34	C₇×C₁₃	—	2	2	no	—
35	C₂×C₃×C₁₃	—	147	1	no	—
36	C₇⋊C₉	—	182	2	no	—
37	C₇⋊C₉	—	182	2	no	—
38	C₄×C₁₃	—	147	1	no	Hall
39	C₇²	C₄×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
40	C₃×D₇	—	14	2	no	—
41	C₃×D₇	—	42	2	no	—
42	C₃×C₁₃	#5997⋊C₃	1	1	yes	characteristic
43	C₄×C₉	—	637	1	no	Hall
44	C₂×C₁₃	—	147	1	no	—
45	C₃×C₇	—	2	2	no	—
46	C₃×C₇	—	2	2	no	—
47	C₂×C₉	—	637	1	no	—
48	D₇	—	14	2	no	—
49	D₇	—	42	2	no	—
50	C₁₃	#5997⋊C₉	1	1	yes	characteristic, complemented, Sylow
51	C₃×C₄	—	147	1	no	—
52	C₉	—	637	1	no	Sylow
53	C₇	—	2	2	no	—
54	C₇	—	2	2	no	—
55	C₂×C₃	—	147	1	no	—
56	C₄	—	147	1	no	Sylow
57	C₃	#21439684	1	1	yes	characteristic
58	C₂	—	147	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#21439684
commutator, hypocenter	C₇²×C₁₃	C₄×C₉
Fitting, socle	C₃×C₇²×C₁₃	C₃×C₄
prime radical, cosocle	C₃×C₁₃×C₇⋊D₇	C₂×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. #19153199	C₄	semidirect
5. C₁₃×#5997	C₉	semidirect
14. C₇²×C₁₃	C₄×C₉	semidirect
24. #5997	C₁₃⋊C₉	semidirect
39. C₇²	C₄×C₁₃⋊C₉	semidirect
50. C₁₃	#5997⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
#26039447	2
C₃×C₁₃×#5997	3
#5997⋊C₉	13
C₄×C₁₃⋊C₉	49