Subgroups — C₂×D₈₆₇₂ #46838662

Order 34688.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₃₃₆	C₂	1	2	yes	maximal, complemented
2	D₈₆₇₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₁₆₈	—	2	2	no	—
5	D₄₃₃₆	—	2	2	no	—
6	D₄₃₃₆	C₂²	1	4	yes	complemented
7	C₂×C₁₆×C₂₇₁	C₂²	1	1	yes	characteristic
8	C₃₂×C₂₇₁	C₂²	1	2	yes	complemented
9	C₂×D₁₀₈₄	—	4	2	no	—
10	D₂₁₆₈	—	2	4	no	—
11	D₂₁₆₈	—	4	2	no	—
12	C₂×C₈×C₂₇₁	D₄	1	1	yes	characteristic
13	C₁₆×C₂₇₁	D₄	1	1	yes	characteristic
14	C₁₆×C₂₇₁	C₂³	1	1	yes	characteristic
15	C₂²×D₂₇₁	—	8	2	no	—
16	D₁₀₈₄	—	4	4	no	—
17	D₁₀₈₄	—	8	2	no	—
18	C₂×C₄×C₂₇₁	D₈	1	1	yes	characteristic
19	C₈×C₂₇₁	D₈	1	1	yes	characteristic
20	C₈×C₂₇₁	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₂₇₁	D₁₆	1	1	yes	characteristic
22	C₂×D₂₇₁	—	8	4	no	—
23	C₂×D₂₇₁	—	16	4	no	—
24	C₄×C₂₇₁	D₁₆	1	1	yes	characteristic
25	C₄×C₂₇₁	C₂×D₈	1	1	yes	characteristic
26	C₂×C₂₇₁	D₃₂	1	2	yes	complemented
27	C₂×C₂₇₁	C₂×D₁₆	1	1	yes	characteristic
28	D₂₇₁	—	16	4	no	—
29	C₂₇₁	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₃₂	—	271	1	no	maximal, Sylow
31	C₂×D₁₆	—	271	2	no	—
32	D₃₂	—	271	4	no	—
33	C₂×C₃₂	D₂₇₁	1	1	yes	characteristic, complemented
34	C₂×D₈	—	542	2	no	—
35	D₁₆	—	271	4	no	—
36	D₁₆	—	542	2	no	—
37	C₂×C₁₆	C₂×D₂₇₁	1	1	yes	characteristic
38	C₃₂	C₂×D₂₇₁	1	2	yes	complemented
39	C₂×D₄	—	1084	2	no	—
40	D₈	—	542	4	no	—
41	D₈	—	1084	2	no	—
42	C₂×C₈	D₁₀₈₄	1	1	yes	characteristic
43	C₁₆	D₁₀₈₄	1	1	yes	characteristic
44	C₁₆	C₂²×D₂₇₁	1	1	yes	characteristic
45	C₂³	—	2168	2	no	—
46	D₄	—	1084	4	no	—
47	D₄	—	2168	2	no	—
48	C₂×C₄	D₂₁₆₈	1	1	yes	characteristic
49	C₈	D₂₁₆₈	1	1	yes	characteristic
50	C₈	C₂×D₁₀₈₄	1	1	yes	characteristic
51	C₂²	—	2168	4	no	—
52	C₂²	—	4336	4	no	—
53	C₂²	D₄₃₃₆	1	1	yes	characteristic
54	C₄	D₄₃₃₆	1	1	yes	characteristic
55	C₄	C₂×D₂₁₆₈	1	1	yes	characteristic
56	C₂	—	4336	4	no	—
57	C₂	D₈₆₇₂	1	2	yes	direct product factor
58	C₂	C₂×D₄₃₃₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄₃₃₆
commutator, cosocle	C₁₆×C₂₇₁	C₂³
Frattini	C₁₆	C₂²×D₂₇₁
Fitting	C₂×C₃₂×C₂₇₁	C₂
socle	C₂²×C₂₇₁	D₁₆
hypercenter	C₂×C₃₂	D₂₇₁
hypocenter	C₂₇₁	C₂×D₃₂
LCS	G ▷ C₁₆×C₂₇₁ ▷ C₈×C₂₇₁ ▷ C₄×C₂₇₁ ▷ C₂×C₂₇₁ ▷ C₂₇₁
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×D₄₃₃₆	C₂	semidirect
2. D₈₆₇₂	C₂	direct (N × H)
3. C₂×C₃₂×C₂₇₁	C₂	semidirect
6. D₄₃₃₆	C₂²	semidirect
8. C₃₂×C₂₇₁	C₂²	semidirect
26. C₂×C₂₇₁	D₃₂	semidirect
29. C₂₇₁	C₂×D₃₂	semidirect
33. C₂×C₃₂	D₂₇₁	semidirect
38. C₃₂	C₂×D₂₇₁	semidirect
57. C₂	D₈₆₇₂	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×D₄₃₃₆	2
D₈₆₇₂	2
C₂×C₃₂×C₂₇₁	2
C₂×D₃₂	271

Subgroups — C2×D8672 #46838662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₈₆₇₂ #46838662