Subgroups — C₂×D₅₇₉₂ #37536019

Order 23168.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₈₉₆	C₂	1	2	yes	maximal, complemented
2	D₅₇₉₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₄₄₈	—	2	2	no	—
5	D₂₈₉₆	—	2	2	no	—
6	D₂₈₉₆	C₂²	1	4	yes	complemented
7	C₂×C₁₆×C₁₈₁	C₂²	1	1	yes	characteristic
8	C₃₂×C₁₈₁	C₂²	1	2	yes	complemented
9	C₂×D₇₂₄	—	4	2	no	—
10	D₁₄₄₈	—	2	4	no	—
11	D₁₄₄₈	—	4	2	no	—
12	C₂×C₈×C₁₈₁	D₄	1	1	yes	characteristic
13	C₁₆×C₁₈₁	D₄	1	1	yes	characteristic
14	C₁₆×C₁₈₁	C₂³	1	1	yes	characteristic
15	C₂²×D₁₈₁	—	8	2	no	—
16	D₇₂₄	—	4	4	no	—
17	D₇₂₄	—	8	2	no	—
18	C₂×C₄×C₁₈₁	D₈	1	1	yes	characteristic
19	C₈×C₁₈₁	D₈	1	1	yes	characteristic
20	C₈×C₁₈₁	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₁₈₁	D₁₆	1	1	yes	characteristic
22	C₂×D₁₈₁	—	8	4	no	—
23	C₂×D₁₈₁	—	16	4	no	—
24	C₄×C₁₈₁	D₁₆	1	1	yes	characteristic
25	C₄×C₁₈₁	C₂×D₈	1	1	yes	characteristic
26	C₂×C₁₈₁	D₃₂	1	2	yes	complemented
27	C₂×C₁₈₁	C₂×D₁₆	1	1	yes	characteristic
28	D₁₈₁	—	16	4	no	—
29	C₁₈₁	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃₂	—	181	1	no	maximal, Sylow
31	C₂×D₁₆	—	181	2	no	—
32	D₃₂	—	181	4	no	—
33	C₂×C₃₂	D₁₈₁	1	1	yes	characteristic, complemented
34	C₂×D₈	—	362	2	no	—
35	D₁₆	—	362	2	no	—
36	D₁₆	—	181	4	no	—
37	C₂×C₁₆	C₂×D₁₈₁	1	1	yes	characteristic
38	C₃₂	C₂×D₁₈₁	1	2	yes	complemented
39	C₂×D₄	—	724	2	no	—
40	D₈	—	362	4	no	—
41	D₈	—	724	2	no	—
42	C₂×C₈	D₇₂₄	1	1	yes	characteristic
43	C₁₆	D₇₂₄	1	1	yes	characteristic
44	C₁₆	C₂²×D₁₈₁	1	1	yes	characteristic
45	C₂³	—	1448	2	no	—
46	D₄	—	1448	2	no	—
47	D₄	—	724	4	no	—
48	C₂×C₄	D₁₄₄₈	1	1	yes	characteristic
49	C₈	D₁₄₄₈	1	1	yes	characteristic
50	C₈	C₂×D₇₂₄	1	1	yes	characteristic
51	C₂²	—	2896	4	no	—
52	C₂²	—	1448	4	no	—
53	C₂²	D₂₈₉₆	1	1	yes	characteristic
54	C₄	D₂₈₉₆	1	1	yes	characteristic
55	C₄	C₂×D₁₄₄₈	1	1	yes	characteristic
56	C₂	—	2896	4	no	—
57	C₂	D₅₇₉₂	1	2	yes	direct product factor
58	C₂	C₂×D₂₈₉₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₈₉₆
commutator, cosocle	C₁₆×C₁₈₁	C₂³
Frattini	C₁₆	C₂²×D₁₈₁
Fitting	C₂×C₃₂×C₁₈₁	C₂
socle	C₂²×C₁₈₁	D₁₆
hypercenter	C₂×C₃₂	D₁₈₁
hypocenter	C₁₈₁	C₂×D₃₂
LCS	G ▷ C₁₆×C₁₈₁ ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
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×D₂₈₉₆	C₂	semidirect
2. D₅₇₉₂	C₂	direct (N × H)
3. C₂×C₃₂×C₁₈₁	C₂	semidirect
6. D₂₈₉₆	C₂²	semidirect
8. C₃₂×C₁₈₁	C₂²	semidirect
26. C₂×C₁₈₁	D₃₂	semidirect
29. C₁₈₁	C₂×D₃₂	semidirect
33. C₂×C₃₂	D₁₈₁	semidirect
38. C₃₂	C₂×D₁₈₁	semidirect
57. C₂	D₅₇₉₂	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×D₂₈₉₆	2
D₅₇₉₂	2
C₂×C₃₂×C₁₈₁	2
C₂×D₃₂	181

Subgroups — C2×D5792 #37536019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅₇₉₂ #37536019