Subgroups — C₂×D₁₁₈₄ #17996894

Order 4736.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₉₂	C₂	1	2	yes	maximal, complemented
2	D₁₁₈₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₉₆	—	2	2	no	—
5	D₅₉₂	—	2	2	no	—
6	D₅₉₂	C₂²	1	4	yes	complemented
7	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
8	C₃₂×C₃₇	C₂²	1	2	yes	complemented
9	C₂×D₁₄₈	—	4	2	no	—
10	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
11	D₂₉₆	—	2	4	no	—
12	D₂₉₆	—	4	2	no	—
13	C₁₆×C₃₇	D₄	1	1	yes	characteristic
14	C₁₆×C₃₇	C₂³	1	1	yes	characteristic
15	C₂²×D₃₇	—	8	2	no	—
16	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
17	D₁₄₈	—	4	4	no	—
18	D₁₄₈	—	8	2	no	—
19	C₈×C₃₇	D₈	1	1	yes	characteristic
20	C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₃₇	D₁₆	1	1	yes	characteristic
22	C₂×D₃₇	—	8	4	no	—
23	C₂×D₃₇	—	16	4	no	—
24	C₄×C₃₇	D₁₆	1	1	yes	characteristic
25	C₄×C₃₇	C₂×D₈	1	1	yes	characteristic
26	C₂×D₃₂	—	37	1	no	maximal, Sylow
27	C₂×C₃₇	D₃₂	1	2	yes	complemented
28	C₂×C₃₇	C₂×D₁₆	1	1	yes	characteristic
29	D₃₇	—	16	4	no	—
30	C₂×D₁₆	—	37	2	no	—
31	D₃₂	—	37	4	no	—
32	C₂×C₃₂	D₃₇	1	1	yes	characteristic, complemented
33	C₃₇	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₈	—	74	2	no	—
35	D₁₆	—	37	4	no	—
36	D₁₆	—	74	2	no	—
37	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
38	C₃₂	C₂×D₃₇	1	2	yes	complemented
39	C₂×D₄	—	148	2	no	—
40	D₈	—	74	4	no	—
41	D₈	—	148	2	no	—
42	C₂×C₈	D₁₄₈	1	1	yes	characteristic
43	C₁₆	D₁₄₈	1	1	yes	characteristic
44	C₁₆	C₂²×D₃₇	1	1	yes	characteristic
45	C₂³	—	296	2	no	—
46	D₄	—	296	2	no	—
47	D₄	—	148	4	no	—
48	C₂×C₄	D₂₉₆	1	1	yes	characteristic
49	C₈	D₂₉₆	1	1	yes	characteristic
50	C₈	C₂×D₁₄₈	1	1	yes	characteristic
51	C₂²	—	296	4	no	—
52	C₂²	—	592	4	no	—
53	C₂²	D₅₉₂	1	1	yes	characteristic
54	C₄	D₅₉₂	1	1	yes	characteristic
55	C₄	C₂×D₂₉₆	1	1	yes	characteristic
56	C₂	—	592	4	no	—
57	C₂	D₁₁₈₄	1	2	yes	direct product factor
58	C₂	C₂×D₅₉₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₅₉₂
commutator, cosocle	C₁₆×C₃₇	C₂³
Frattini	C₁₆	C₂²×D₃₇
Fitting	C₂×C₃₂×C₃₇	C₂
socle	C₂²×C₃₇	D₁₆
hypercenter	C₂×C₃₂	D₃₇
hypocenter	C₃₇	C₂×D₃₂
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
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×D₅₉₂	C₂	semidirect
2. D₁₁₈₄	C₂	direct (N × H)
3. C₂×C₃₂×C₃₇	C₂	semidirect
6. D₅₉₂	C₂²	semidirect
8. C₃₂×C₃₇	C₂²	semidirect
27. C₂×C₃₇	D₃₂	semidirect
32. C₂×C₃₂	D₃₇	semidirect
33. C₃₇	C₂×D₃₂	semidirect
38. C₃₂	C₂×D₃₇	semidirect
57. C₂	D₁₁₈₄	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×D₅₉₂	2
D₁₁₈₄	2
C₂×C₃₂×C₃₇	2
C₂×D₃₂	37

Subgroups — C2×D1184 #17996894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₁₈₄ #17996894