Subgroups — #493×C₃₆₇ #37553811

Order 23488.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×C₃₆₇	C₂	1	4	yes	maximal, complemented
2	#127×C₃₆₇	C₂	1	2	yes	maximal, complemented
3	C₄×C₈×C₃₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₃₆₇	—	2	4	no	—
5	C₂×D₄×C₃₆₇	C₂²	1	4	yes	—
6	D₈×C₃₆₇	—	2	8	no	—
7	C₂×C₈×C₃₆₇	C₂²	1	2	yes	—
8	C₄²×C₃₆₇	C₂²	1	1	yes	characteristic
9	C₂³×C₃₆₇	—	2	4	no	—
10	D₄×C₃₆₇	—	2	8	no	—
11	D₄×C₃₆₇	—	4	8	no	—
12	C₂×C₄×C₃₆₇	D₄	1	2	yes	—
13	C₂×C₄×C₃₆₇	C₂³	1	1	yes	characteristic
14	C₈×C₃₆₇	D₄	1	4	yes	complemented
15	C₂²×C₃₆₇	—	4	4	no	—
16	C₂²×C₃₆₇	—	4	8	no	—
17	C₂²×C₃₆₇	C₂×D₄	1	1	yes	characteristic
18	C₄×C₃₆₇	D₈	1	4	yes	complemented
19	C₄×C₃₆₇	C₂×D₄	1	2	yes	—
20	C₂×C₃₆₇	—	8	4	no	—
21	C₂×C₃₆₇	#127	1	1	yes	characteristic
22	C₂×C₃₆₇	C₂×D₈	1	2	yes	—
23	C₃₆₇	#493	1	1	yes	characteristic, direct product factor, Sylow
24	#493	C₃₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×D₈	C₂×C₃₆₇	1	4	yes	complemented
26	#127	C₂×C₃₆₇	1	2	yes	complemented
27	C₄×C₈	C₂×C₃₆₇	1	1	yes	characteristic, complemented
28	C₂×D₄	—	2	4	no	—
29	C₂×D₄	C₂²×C₃₆₇	1	4	yes	—
30	D₈	—	2	8	no	—
31	C₂×C₈	C₂²×C₃₆₇	1	2	yes	—
32	C₄²	C₂²×C₃₆₇	1	1	yes	characteristic
33	C₂³	—	2	4	no	—
34	D₄	—	2	8	no	—
35	D₄	—	4	8	no	—
36	C₂×C₄	D₄×C₃₆₇	1	2	yes	—
37	C₂×C₄	C₂³×C₃₆₇	1	1	yes	characteristic
38	C₈	D₄×C₃₆₇	1	4	yes	complemented
39	C₂²	—	4	4	no	—
40	C₂²	—	4	8	no	—
41	C₂²	C₂×D₄×C₃₆₇	1	1	yes	characteristic
42	C₄	D₈×C₃₆₇	1	4	yes	complemented
43	C₄	C₂×D₄×C₃₆₇	1	2	yes	—
44	C₂	—	8	4	no	—
45	C₂	#127×C₃₆₇	1	1	yes	characteristic
46	C₂	C₂×D₈×C₃₆₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₆₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₆₇ ◁ C₄²×C₃₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₈×C₃₆₇	C₂	semidirect
2. #127×C₃₆₇	C₂	semidirect
3. C₄×C₈×C₃₆₇	C₂	semidirect
14. C₈×C₃₆₇	D₄	semidirect
18. C₄×C₃₆₇	D₈	semidirect
23. C₃₆₇	#493	direct (N × H)
24. #493	C₃₆₇	direct (N × H)
25. C₂×D₈	C₂×C₃₆₇	semidirect
26. #127	C₂×C₃₆₇	semidirect
27. C₄×C₈	C₂×C₃₆₇	semidirect
38. C₈	D₄×C₃₆₇	semidirect
42. C₄	D₈×C₃₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₈×C₃₆₇	2
#127×C₃₆₇	2
C₄×C₈×C₃₆₇	2
#493	367

Subgroups — #493×C367 #37553811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #493×C₃₆₇ #37553811