Subgroups — #27133641⋊C₂ #37587608

Order 24492.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27133649	C₂	1	1	yes	maximal, characteristic, complemented
2	#27133645	C₂	1	1	yes	maximal, characteristic, complemented
3	#27133641	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₁₅₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	#20259404	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₀₄₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₁₅₇	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₃×C₁₅₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₃×C₁₅₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×D₁₅₇⋊C₃	—	13	1	no	maximal, Hall
11	C₂×C₁₅₇⋊C₃	—	13	1	no	—
12	D₁₅₇⋊C₃	—	13	1	no	—
13	D₁₅₇⋊C₃	—	13	1	no	—
14	C₂×D₁₅₇	—	13	1	no	Hall
15	C₁₅₇⋊C₃	—	13	1	no	Hall
16	C₂×C₁₅₇	—	13	1	no	—
17	D₁₅₇	—	13	1	no	—
18	D₁₅₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
19	C₁₅₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₁₃⋊C₃	—	157	1	no	maximal, Hall
21	C₂×C₁₃⋊C₃	—	157	1	no	—
22	D₁₃⋊C₃	—	157	1	no	—
23	D₁₃⋊C₃	—	157	1	no	—
24	C₂×D₁₃	—	157	1	no	Hall
25	C₁₃⋊C₃	—	157	1	no	Hall
26	C₂×C₁₃	—	157	1	no	—
27	D₁₃	—	157	1	no	—
28	D₁₃	D₁₅₇⋊C₃	1	1	yes	characteristic, complemented
29	C₁₃	C₂×D₁₅₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	—	2041	1	no	Hall
31	C₂×C₃	—	2041	1	no	—
32	C₂×C₃	—	2041	1	no	—
33	C₂×C₃	—	2041	1	no	—
34	C₂²	—	2041	1	no	Sylow
35	C₃	—	2041	1	no	Sylow
36	C₂	—	13	1	no	—
37	C₂	—	157	1	no	—
38	C₂	—	2041	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₅₇	C₂²×C₃
LCS	G ▷ C₁₃×C₁₅₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #27133649	C₂	semidirect
2. #27133645	C₂	semidirect
3. #27133641	C₂	semidirect
4. D₁₃×D₁₅₇	C₃	semidirect
5. #20259404	C₂²	semidirect
6. D₂₀₄₁	C₂×C₃	semidirect
7. C₁₃×D₁₅₇	C₂×C₃	semidirect
8. D₁₃×C₁₅₇	C₂×C₃	semidirect
9. C₁₃×C₁₅₇	C₂²×C₃	semidirect
18. D₁₅₇	D₁₃⋊C₃	semidirect
19. C₁₅₇	C₂×D₁₃⋊C₃	semidirect
28. D₁₃	D₁₅₇⋊C₃	semidirect
29. C₁₃	C₂×D₁₅₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#27133649	2
#27133645	2
#27133641	2
D₁₃×D₁₅₇	3
C₂×D₁₅₇⋊C₃	13
C₂×D₁₃⋊C₃	157

Subgroups — #27133641⋊C2 #37587608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #27133641⋊C₂ #37587608