Subgroups — C₇×C₃⋊(C₂₃⋊#261) #38737416

Order 25116.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₂₃×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂₃⋊#261	—	3	1	no	maximal, Hall
3	C₃×C₇×C₁₃×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×C₂₃×D₁₃	D₃	1	1	yes	characteristic
5	C₃⋊(C₂₃⋊#261)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₃×C₂₃	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₇×Dic₆₉	—	13	1	no	maximal, Hall
8	C₃×C₂₃×D₁₃	C₂×C₇	1	1	yes	characteristic
9	C₂₃⋊#261	—	3	1	no	Hall
10	C₇×C₃⋊#261	—	23	1	no	maximal, Hall
11	C₂×C₃×C₇×C₂₃	—	13	1	no	—
12	C₃×C₁₃×C₂₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
13	C₇×Dic₂₃	—	39	1	no	Hall
14	C₂₃×D₁₃	D₃×C₇	1	1	yes	characteristic
15	C₃×C₇×D₁₃	D₂₃	1	1	yes	characteristic
16	C₃×C₇×C₂₃	#261	1	1	yes	characteristic, complemented, Hall
17	C₇×#261	—	69	1	no	Hall
18	C₂×C₇×C₂₃	—	13	1	no	—
19	C₁₃×C₂₃	C₇×Dic₃	1	1	yes	characteristic, complemented, Hall
20	Dic₆₉	—	13	1	no	Hall
21	C₃×C₇×C₁₃	Dic₂₃	1	1	yes	characteristic, complemented, Hall
22	C₇×D₁₃	D₆₉	1	1	yes	characteristic
23	C₇×C₂₃	C₃⋊#261	1	1	yes	characteristic, complemented, Hall
24	C₃⋊#261	—	23	1	no	Hall
25	C₂×C₃×C₂₃	—	13	1	no	—
26	Dic₂₃	—	39	1	no	Hall
27	C₇×C₁₃	Dic₆₉	1	1	yes	characteristic, complemented, Hall
28	C₇×Dic₃	—	299	1	no	Hall
29	C₃×D₁₃	C₇×D₂₃	1	1	yes	characteristic
30	C₃×C₂₃	C₇×#261	1	1	yes	characteristic, complemented, Hall
31	#261	—	69	1	no	Hall
32	C₂×C₂₃	—	13	1	no	—
33	C₂×C₃×C₇	—	13	1	no	—
34	C₃×C₁₃	C₇×Dic₂₃	1	1	yes	characteristic, complemented, Hall
35	C₄×C₇	—	897	1	no	Hall
36	D₁₃	C₇×D₆₉	1	1	yes	characteristic
37	C₂₃	C₇×C₃⋊#261	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₇	C₂₃⋊#261	1	1	yes	characteristic, complemented, Hall
39	C₂×C₇	—	13	1	no	—
40	C₁₃	C₇×Dic₆₉	1	1	yes	characteristic, complemented, Sylow
41	Dic₃	—	299	1	no	Hall
42	C₇	C₃⋊(C₂₃⋊#261)	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	13	1	no	—
44	C₄	—	897	1	no	Sylow
45	C₃	C₇×C₂₃⋊#261	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₇	C₃⋊(C₂₃⋊#261)
commutator, hypocenter	C₃×C₁₃×C₂₃	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₂₃	C₄
prime radical	C₃×C₇×C₂₃×D₁₃	C₂
cosocle	C₃×C₂₃×D₁₃	C₂×C₇
LCS	G ▷ C₃×C₁₃×C₂₃
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
3. C₃×C₇×C₁₃×C₂₃	C₄	semidirect
5. C₃⋊(C₂₃⋊#261)	C₇	direct (N × H)
6. C₇×C₁₃×C₂₃	Dic₃	semidirect
12. C₃×C₁₃×C₂₃	C₄×C₇	semidirect
16. C₃×C₇×C₂₃	#261	semidirect
19. C₁₃×C₂₃	C₇×Dic₃	semidirect
21. C₃×C₇×C₁₃	Dic₂₃	semidirect
23. C₇×C₂₃	C₃⋊#261	semidirect
27. C₇×C₁₃	Dic₆₉	semidirect
30. C₃×C₂₃	C₇×#261	semidirect
34. C₃×C₁₃	C₇×Dic₂₃	semidirect
37. C₂₃	C₇×C₃⋊#261	semidirect
38. C₃×C₇	C₂₃⋊#261	semidirect
40. C₁₃	C₇×Dic₆₉	semidirect
42. C₇	C₃⋊(C₂₃⋊#261)	direct (N × H)
45. C₃	C₇×C₂₃⋊#261	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₂₃×D₁₃	2
C₇×C₂₃⋊#261	3
C₃⋊(C₂₃⋊#261)	7
C₇×Dic₆₉	13
C₇×C₃⋊#261	23

Subgroups — C7×C3⋊(C23⋊#261) #38737416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊(C₂₃⋊#261) #38737416