Subgroups — #37524501

Order 22932.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₃⋊C₉)⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic
2	C₃×#14579330	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₁₃⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇⋊D₉₁	C₂×C₃	1	1	yes	characteristic
5	#14579330	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic
7	C₉×#5997	—	13	1	no	maximal, Hall
8	(C₁₃⋊C₉)⋊D₇	—	14	4	no	—
9	C₇⋊D₉₁	C₂×C₉	1	1	yes	characteristic
10	C₉×C₇⋊D₇	—	13	1	no	—
11	C₇×C₁₃⋊C₉	—	2	4	no	—
12	C₇²×C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₃×#5997	—	39	1	no	—
14	C₃×D₉₁	—	14	4	no	—
15	#261⋊C₉	—	49	1	no	maximal, Hall
16	C₇²×C₉	—	13	1	no	Hall
17	C₃×C₇⋊D₇	—	39	1	no	—
18	C₃×C₇×C₁₃	—	2	4	no	—
19	D₁₃⋊C₉	—	49	1	no	—
20	#5997	—	39	1	no	Hall
21	D₉₁	—	14	4	no	—
22	C₃×#261	—	49	1	no	—
23	C₃×C₇²	AGL(1,𝔽₁₃)	1	1	yes	characteristic
24	C₉×D₇	—	182	4	no	—
25	C₁₃⋊C₉	#5997	1	1	yes	characteristic, complemented, Hall
26	C₇⋊D₇	—	39	1	no	—
27	C₇×C₁₃	—	2	4	no	—
28	C₃×D₁₃	—	49	1	no	—
29	C₇×C₉	—	26	4	no	—
30	#261	—	49	1	no	Hall
31	C₇²	#261⋊C₉	1	1	yes	characteristic, complemented, Sylow
32	C₃×D₇	—	546	4	no	—
33	C₃×C₁₃	C₃×#5997	1	1	yes	characteristic
34	C₄×C₉	—	637	1	no	Hall
35	D₁₃	—	49	1	no	—
36	C₃×C₇	—	2	4	no	—
37	C₂×C₉	—	637	1	no	—
38	D₇	—	546	4	no	—
39	C₁₃	C₉×#5997	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	1911	1	no	—
41	C₉	—	13	1	no	Sylow
42	C₇	—	2	4	no	—
43	C₂×C₃	—	1911	1	no	—
44	C₄	—	1911	1	no	Sylow
45	C₃	#21439686	1	1	yes	characteristic
46	C₂	—	1911	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#21439686
commutator, hypocenter	C₇²×C₁₃	C₄×C₉
Fitting, socle	C₃×C₇²×C₁₃	C₃×C₄
prime radical, cosocle	C₃×C₇⋊D₉₁	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. C₇²×C₁₃⋊C₉	C₄	semidirect
5. #14579330	C₉	semidirect
12. C₇²×C₁₃	C₄×C₉	semidirect
25. C₁₃⋊C₉	#5997	semidirect
31. C₇²	#261⋊C₉	semidirect
39. C₁₃	C₉×#5997	semidirect

Maximal subgroups

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

subgroup	index
(C₁₃⋊C₉)⋊(C₇⋊D₇)	2
C₃×#14579330	3
C₉×#5997	13
#261⋊C₉	49