Subgroups — C₂×D₇₃₆ #15675695

Order 2944.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₆₈	C₂	1	2	yes	maximal, complemented
2	D₇₃₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₂₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₈₄	—	2	2	no	—
5	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
6	D₃₆₈	—	2	2	no	—
7	D₃₆₈	C₂²	1	4	yes	complemented
8	C₂₃×C₃₂	C₂²	1	2	yes	complemented
9	C₂×D₉₂	—	4	2	no	—
10	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
11	D₁₈₄	—	2	4	no	—
12	D₁₈₄	—	4	2	no	—
13	C₁₆×C₂₃	D₄	1	1	yes	characteristic
14	C₁₆×C₂₃	C₂³	1	1	yes	characteristic
15	C₂²×D₂₃	—	8	2	no	—
16	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
17	D₉₂	—	4	4	no	—
18	D₉₂	—	8	2	no	—
19	C₈×C₂₃	D₈	1	1	yes	characteristic
20	C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
21	C₂×D₃₂	—	23	1	no	maximal, Sylow
22	C₂²×C₂₃	D₁₆	1	1	yes	characteristic
23	C₂×D₂₃	—	8	4	no	—
24	C₂×D₂₃	—	16	4	no	—
25	C₄×C₂₃	D₁₆	1	1	yes	characteristic
26	C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
27	C₂×D₁₆	—	23	2	no	—
28	D₃₂	—	23	4	no	—
29	C₂×C₃₂	D₂₃	1	1	yes	characteristic, complemented
30	C₂×C₂₃	D₃₂	1	2	yes	complemented
31	C₂×C₂₃	C₂×D₁₆	1	1	yes	characteristic
32	D₂₃	—	16	4	no	—
33	C₂×D₈	—	46	2	no	—
34	D₁₆	—	23	4	no	—
35	D₁₆	—	46	2	no	—
36	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
37	C₃₂	C₂×D₂₃	1	2	yes	complemented
38	C₂₃	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₄	—	92	2	no	—
40	D₈	—	46	4	no	—
41	D₈	—	92	2	no	—
42	C₂×C₈	D₉₂	1	1	yes	characteristic
43	C₁₆	D₉₂	1	1	yes	characteristic
44	C₁₆	C₂²×D₂₃	1	1	yes	characteristic
45	C₂³	—	184	2	no	—
46	D₄	—	92	4	no	—
47	D₄	—	184	2	no	—
48	C₂×C₄	D₁₈₄	1	1	yes	characteristic
49	C₈	D₁₈₄	1	1	yes	characteristic
50	C₈	C₂×D₉₂	1	1	yes	characteristic
51	C₂²	—	368	4	no	—
52	C₂²	—	184	4	no	—
53	C₂²	D₃₆₈	1	1	yes	characteristic
54	C₄	D₃₆₈	1	1	yes	characteristic
55	C₄	C₂×D₁₈₄	1	1	yes	characteristic
56	C₂	—	368	4	no	—
57	C₂	D₇₃₆	1	2	yes	direct product factor
58	C₂	C₂×D₃₆₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₆₈
commutator, cosocle	C₁₆×C₂₃	C₂³
Frattini	C₁₆	C₂²×D₂₃
Fitting	C₂×C₂₃×C₃₂	C₂
socle	C₂²×C₂₃	D₁₆
hypercenter	C₂×C₃₂	D₂₃
hypocenter	C₂₃	C₂×D₃₂
LCS	G ▷ C₁₆×C₂₃ ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×D₃₆₈	C₂	semidirect
2. D₇₃₆	C₂	direct (N × H)
3. C₂×C₂₃×C₃₂	C₂	semidirect
7. D₃₆₈	C₂²	semidirect
8. C₂₃×C₃₂	C₂²	semidirect
29. C₂×C₃₂	D₂₃	semidirect
30. C₂×C₂₃	D₃₂	semidirect
37. C₃₂	C₂×D₂₃	semidirect
38. C₂₃	C₂×D₃₂	semidirect
57. C₂	D₇₃₆	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×D₃₆₈	2
D₇₃₆	2
C₂×C₂₃×C₃₂	2
C₂×D₃₂	23

Subgroups — C2×D736 #15675695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₇₃₆ #15675695