Subgroups — C₂₃⋊#11725077 #35202575

Order 20286.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#89204	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇⋊D₁₆₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇²×C₂₃	C₂×C₃	1	1	yes	characteristic
4	C₂₃⋊(D₇⋊C₉)	—	7	1	no	maximal
5	C₂₃⋊(D₇⋊C₉)	—	7	1	no	maximal
6	C₂₃⋊(D₇⋊C₉)	—	7	6	no	maximal
7	C₇⋊D₁₆₁	C₉	1	1	yes	characteristic, complemented, Hall
8	C₂₃×C₇⋊C₉	—	7	1	no	—
9	C₂₃×C₇⋊C₉	—	7	1	no	—
10	C₂₃×C₇⋊C₉	—	7	6	no	—
11	C₇²×C₂₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
12	C₃×D₁₆₁	—	7	1	no	—
13	C₃×D₁₆₁	—	21	1	no	—
14	C₃×D₁₆₁	—	21	6	no	—
15	#11725077	—	23	1	no	maximal, Hall
16	C₃×C₇×C₂₃	AGL(1,𝔽₇)	1	1	yes	characteristic
17	C₃×C₇×C₂₃	AGL(1,𝔽₇)	1	1	yes	characteristic
18	C₃×C₇×C₂₃	AGL(1,𝔽₇)	1	6	yes	—
19	#89204	D₂₃	1	1	yes	characteristic, complemented, Hall
20	C₉×D₂₃	—	49	1	no	Hall
21	D₁₆₁	—	7	1	no	—
22	D₁₆₁	—	21	1	no	—
23	D₁₆₁	—	21	6	no	—
24	C₃×C₇⋊D₇	—	23	1	no	—
25	C₉×C₂₃	—	49	1	no	Hall
26	C₇×C₂₃	D₇⋊C₉	1	1	yes	characteristic, complemented
27	C₇×C₂₃	D₇⋊C₉	1	1	yes	characteristic, complemented
28	C₇×C₂₃	D₇⋊C₉	1	6	yes	complemented
29	C₃×C₇²	C₃×D₂₃	1	1	yes	characteristic
30	C₃×D₂₃	—	147	1	no	—
31	D₇⋊C₉	—	161	1	no	—
32	D₇⋊C₉	—	161	1	no	—
33	D₇⋊C₉	—	161	6	no	—
34	C₇⋊D₇	—	23	1	no	Hall
35	C₃×C₂₃	#64424	1	1	yes	characteristic
36	C₇⋊C₉	—	7	1	no	—
37	C₇⋊C₉	—	7	1	no	—
38	C₇⋊C₉	—	7	6	no	—
39	C₇²	C₉×D₂₃	1	1	yes	characteristic, complemented, Sylow
40	D₂₃	—	147	1	no	Hall
41	C₃×D₇	—	161	1	no	—
42	C₃×D₇	—	483	1	no	—
43	C₃×D₇	—	483	6	no	—
44	C₂₃	#11725077	1	1	yes	characteristic, complemented, Sylow
45	C₃×C₇	ΓL(1,𝔽₈)⋊D₂₃	1	1	yes	characteristic
46	C₃×C₇	ΓL(1,𝔽₈)⋊D₂₃	1	1	yes	characteristic
47	C₃×C₇	ΓL(1,𝔽₈)⋊D₂₃	1	6	yes	—
48	C₂×C₉	—	1127	1	no	Hall
49	D₇	—	161	1	no	—
50	D₇	—	483	1	no	—
51	D₇	—	483	6	no	—
52	C₉	—	49	1	no	Sylow
53	C₇	C₂₃⋊(D₇⋊C₉)	1	1	yes	characteristic, complemented
54	C₇	C₂₃⋊(D₇⋊C₉)	1	1	yes	characteristic, complemented
55	C₇	C₂₃⋊(D₇⋊C₉)	1	6	yes	complemented
56	C₂×C₃	—	3381	1	no	—
57	C₃	C₂₃⋊#64424	1	1	yes	characteristic
58	C₂	—	3381	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₂₃⋊#64424
commutator, hypocenter	C₇²×C₂₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₇²×C₂₃	C₂×C₃
prime radical	C₃×C₇⋊D₁₆₁	C₃
LCS	G ▷ C₇²×C₂₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×#89204	C₂	semidirect
7. C₇⋊D₁₆₁	C₉	semidirect
11. C₇²×C₂₃	C₂×C₉	semidirect
19. #89204	D₂₃	semidirect
26. C₇×C₂₃	D₇⋊C₉	semidirect
27. C₇×C₂₃	D₇⋊C₉	semidirect
28. C₇×C₂₃	D₇⋊C₉	semidirect
39. C₇²	C₉×D₂₃	semidirect
44. C₂₃	#11725077	semidirect
53. C₇	C₂₃⋊(D₇⋊C₉)	semidirect
54. C₇	C₂₃⋊(D₇⋊C₉)	semidirect
55. C₇	C₂₃⋊(D₇⋊C₉)	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#89204	2
C₃×C₇⋊D₁₆₁	3
C₂₃⋊(D₇⋊C₉)	7
#11725077	23

Subgroups — C23⋊#11725077 #35202575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃⋊#11725077 #35202575