Subgroups — C₂×D₁₆×C₃₆₇ #37553823

Order 23488.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×C₃₆₇	C₂	1	2	yes	maximal, complemented
2	D₁₆×C₃₆₇	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₃₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₃₆₇	—	2	2	no	—
5	D₈×C₃₆₇	—	2	2	no	—
6	D₈×C₃₆₇	C₂²	1	4	yes	complemented
7	C₂×C₈×C₃₆₇	C₂²	1	1	yes	characteristic
8	C₁₆×C₃₆₇	C₂²	1	2	yes	complemented
9	C₂³×C₃₆₇	—	4	2	no	—
10	D₄×C₃₆₇	—	2	4	no	—
11	D₄×C₃₆₇	—	4	2	no	—
12	C₂×C₄×C₃₆₇	D₄	1	1	yes	characteristic
13	C₈×C₃₆₇	D₄	1	1	yes	characteristic
14	C₈×C₃₆₇	C₂³	1	1	yes	characteristic
15	C₂²×C₃₆₇	—	4	4	no	—
16	C₂²×C₃₆₇	—	8	4	no	—
17	C₂²×C₃₆₇	D₈	1	1	yes	characteristic
18	C₄×C₃₆₇	D₈	1	1	yes	characteristic
19	C₄×C₃₆₇	C₂×D₄	1	1	yes	characteristic
20	C₂×C₃₆₇	—	8	4	no	—
21	C₂×C₃₆₇	D₁₆	1	2	yes	direct product factor
22	C₂×C₃₆₇	C₂×D₈	1	1	yes	characteristic
23	C₃₆₇	C₂×D₁₆	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₁₆	C₃₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×D₈	C₂×C₃₆₇	1	2	yes	complemented
26	D₁₆	C₂×C₃₆₇	1	4	yes	direct product factor
27	C₂×C₁₆	C₂×C₃₆₇	1	1	yes	characteristic, complemented
28	C₂×D₄	—	2	2	no	—
29	D₈	—	2	2	no	—
30	D₈	C₂²×C₃₆₇	1	4	yes	complemented
31	C₂×C₈	C₂²×C₃₆₇	1	1	yes	characteristic
32	C₁₆	C₂²×C₃₆₇	1	2	yes	complemented
33	C₂³	—	4	2	no	—
34	D₄	—	2	4	no	—
35	D₄	—	4	2	no	—
36	C₂×C₄	D₄×C₃₆₇	1	1	yes	characteristic
37	C₈	D₄×C₃₆₇	1	1	yes	characteristic
38	C₈	C₂³×C₃₆₇	1	1	yes	characteristic
39	C₂²	—	4	4	no	—
40	C₂²	—	8	4	no	—
41	C₂²	D₈×C₃₆₇	1	1	yes	characteristic
42	C₄	D₈×C₃₆₇	1	1	yes	characteristic
43	C₄	C₂×D₄×C₃₆₇	1	1	yes	characteristic
44	C₂	—	8	4	no	—
45	C₂	D₁₆×C₃₆₇	1	2	yes	direct product factor
46	C₂	C₂×D₈×C₃₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₆₇	D₈
commutator, Frattini, cosocle	C₈	C₂³×C₃₆₇
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₆₇ ◁ C₂×C₄×C₃₆₇ ◁ C₂×C₈×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. D₁₆×C₃₆₇	C₂	direct (N × H)
3. C₂×C₁₆×C₃₆₇	C₂	semidirect
6. D₈×C₃₆₇	C₂²	semidirect
8. C₁₆×C₃₆₇	C₂²	semidirect
21. C₂×C₃₆₇	D₁₆	direct (N × H)
23. C₃₆₇	C₂×D₁₆	direct (N × H)
24. C₂×D₁₆	C₃₆₇	direct (N × H)
25. C₂×D₈	C₂×C₃₆₇	semidirect
26. D₁₆	C₂×C₃₆₇	direct (N × H)
27. C₂×C₁₆	C₂×C₃₆₇	semidirect
30. D₈	C₂²×C₃₆₇	semidirect
32. C₁₆	C₂²×C₃₆₇	semidirect
45. C₂	D₁₆×C₃₆₇	direct (N × H)

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
D₁₆×C₃₆₇	2
C₂×C₁₆×C₃₆₇	2
C₂×D₁₆	367

Subgroups — C2×D16×C367 #37553823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₆×C₃₆₇ #37553823