Subgroups — C₃⋊(C₇⋊(C₂₃⋊#261)) #38737424

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)	—	7	1	no	maximal, Hall
6	C₇×C₁₃×C₂₃	Dic₃	1	1	yes	characteristic, complemented, Hall
7	Dic₄₈₃	—	13	1	no	maximal, Hall
8	C₃×C₂₃×D₁₃	D₇	1	1	yes	characteristic
9	C₂₃⋊#261	—	21	1	no	Hall
10	C₃⋊(C₇⋊#261)	—	23	1	no	maximal, Hall
11	C₂×C₃×C₇×C₂₃	—	13	1	no	—
12	C₃×C₁₃×C₂₃	Dic₇	1	1	yes	characteristic, complemented, Hall
13	Dic₁₆₁	—	39	1	no	Hall
14	C₂₃×D₁₃	D₂₁	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	Dic₂₁	1	1	yes	characteristic, complemented, Hall
20	Dic₆₉	—	91	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	—	161	1	no	Hall
25	C₂×C₃×C₂₃	—	13	1	no	—
26	Dic₂₃	—	273	1	no	Hall
27	C₇×C₁₃	Dic₆₉	1	1	yes	characteristic, complemented, Hall
28	Dic₂₁	—	299	1	no	Hall
29	C₃×D₁₃	D₁₆₁	1	1	yes	characteristic
30	C₃×C₂₃	C₇⋊#261	1	1	yes	characteristic, complemented, Hall
31	#261	—	483	1	no	Hall
32	C₂×C₂₃	—	13	1	no	—
33	C₂×C₃×C₇	—	13	1	no	—
34	C₃×C₁₃	Dic₁₆₁	1	1	yes	characteristic, complemented, Hall
35	Dic₇	—	897	1	no	Hall
36	D₁₃	D₄₈₃	1	1	yes	characteristic
37	C₂₃	C₃⋊(C₇⋊#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	Dic₄₈₃	1	1	yes	characteristic, complemented, Sylow
41	Dic₃	—	2093	1	no	Hall
42	C₇	C₃⋊(C₂₃⋊#261)	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	13	1	no	—
44	C₄	—	6279	1	no	Sylow
45	C₃	C₇⋊(C₂₃⋊#261)	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	13	1	no	—

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₇×C₁₃×C₂₃	C₄	semidirect
6. C₇×C₁₃×C₂₃	Dic₃	semidirect
12. C₃×C₁₃×C₂₃	Dic₇	semidirect
16. C₃×C₇×C₂₃	#261	semidirect
19. C₁₃×C₂₃	Dic₂₁	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	Dic₁₆₁	semidirect
37. C₂₃	C₃⋊(C₇⋊#261)	semidirect
38. C₃×C₇	C₂₃⋊#261	semidirect
40. C₁₃	Dic₄₈₃	semidirect
42. C₇	C₃⋊(C₂₃⋊#261)	semidirect
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
Dic₄₈₃	13
C₃⋊(C₇⋊#261)	23

Subgroups — C3⋊(C7⋊(C23⋊#261)) #38737424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₇⋊(C₂₃⋊#261)) #38737424