Subgroups — C₂×C₃₁×D₆₄ #21470497

Order 7936.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×D₃₂	C₂	1	2	yes	maximal, complemented
2	C₃₁×D₆₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₁×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×D₁₆	—	2	2	no	—
5	C₃₁×D₃₂	—	2	2	no	—
6	C₃₁×D₃₂	C₂²	1	4	yes	complemented
7	C₂×C₃₁×C₃₂	C₂²	1	1	yes	characteristic
8	C₃₁×C₆₄	C₂²	1	2	yes	complemented
9	C₂×D₈×C₃₁	—	4	2	no	—
10	C₃₁×D₁₆	—	2	4	no	—
11	C₃₁×D₁₆	—	4	2	no	—
12	C₂×C₁₆×C₃₁	D₄	1	1	yes	characteristic
13	C₃₁×C₃₂	D₄	1	1	yes	characteristic
14	C₃₁×C₃₂	C₂³	1	1	yes	characteristic
15	C₂×D₄×C₃₁	—	8	2	no	—
16	D₈×C₃₁	—	4	4	no	—
17	D₈×C₃₁	—	8	2	no	—
18	C₂×C₈×C₃₁	D₈	1	1	yes	characteristic
19	C₁₆×C₃₁	D₈	1	1	yes	characteristic
20	C₁₆×C₃₁	C₂×D₄	1	1	yes	characteristic
21	C₂×D₆₄	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂³×C₃₁	—	16	2	no	—
23	D₄×C₃₁	—	8	4	no	—
24	D₄×C₃₁	—	16	2	no	—
25	C₂×C₄×C₃₁	D₁₆	1	1	yes	characteristic
26	C₈×C₃₁	D₁₆	1	1	yes	characteristic
27	C₈×C₃₁	C₂×D₈	1	1	yes	characteristic
28	C₂×D₃₂	C₂×C₃₁	1	2	yes	complemented
29	D₆₄	C₂×C₃₁	1	4	yes	direct product factor
30	C₂×C₆₄	C₂×C₃₁	1	1	yes	characteristic, complemented
31	C₂²×C₃₁	—	16	4	no	—
32	C₂²×C₃₁	—	32	4	no	—
33	C₂²×C₃₁	D₃₂	1	1	yes	characteristic
34	C₄×C₃₁	D₃₂	1	1	yes	characteristic
35	C₄×C₃₁	C₂×D₁₆	1	1	yes	characteristic
36	C₂×D₁₆	—	2	2	no	—
37	D₃₂	—	2	2	no	—
38	D₃₂	C₂²×C₃₁	1	4	yes	complemented
39	C₂×C₃₂	C₂²×C₃₁	1	1	yes	characteristic
40	C₆₄	C₂²×C₃₁	1	2	yes	complemented
41	C₂×C₃₁	—	32	4	no	—
42	C₂×C₃₁	D₆₄	1	2	yes	direct product factor
43	C₂×C₃₁	C₂×D₃₂	1	1	yes	characteristic
44	C₂×D₈	—	4	2	no	—
45	D₁₆	—	2	4	no	—
46	D₁₆	—	4	2	no	—
47	C₂×C₁₆	D₄×C₃₁	1	1	yes	characteristic
48	C₃₂	D₄×C₃₁	1	1	yes	characteristic
49	C₃₂	C₂³×C₃₁	1	1	yes	characteristic
50	C₃₁	C₂×D₆₄	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×D₄	—	8	2	no	—
52	D₈	—	4	4	no	—
53	D₈	—	8	2	no	—
54	C₂×C₈	D₈×C₃₁	1	1	yes	characteristic
55	C₁₆	D₈×C₃₁	1	1	yes	characteristic
56	C₁₆	C₂×D₄×C₃₁	1	1	yes	characteristic
57	C₂³	—	16	2	no	—
58	D₄	—	8	4	no	—
59	D₄	—	16	2	no	—
60	C₂×C₄	C₃₁×D₁₆	1	1	yes	characteristic
61	C₈	C₃₁×D₁₆	1	1	yes	characteristic
62	C₈	C₂×D₈×C₃₁	1	1	yes	characteristic
63	C₂²	—	16	4	no	—
64	C₂²	—	32	4	no	—
65	C₂²	C₃₁×D₃₂	1	1	yes	characteristic
66	C₄	C₃₁×D₃₂	1	1	yes	characteristic
67	C₄	C₂×C₃₁×D₁₆	1	1	yes	characteristic
68	C₂	—	32	4	no	—
69	C₂	C₃₁×D₆₄	1	2	yes	direct product factor
70	C₂	C₂×C₃₁×D₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂³×C₃₁
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₈×C₃₁ ◁ C₂×C₁₆×C₃₁ ◁ C₂×C₃₁×C₃₂ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×D₃₂	C₂	semidirect
2. C₃₁×D₆₄	C₂	direct (N × H)
3. C₂×C₃₁×C₆₄	C₂	semidirect
6. C₃₁×D₃₂	C₂²	semidirect
8. C₃₁×C₆₄	C₂²	semidirect
21. C₂×D₆₄	C₃₁	direct (N × H)
28. C₂×D₃₂	C₂×C₃₁	semidirect
29. D₆₄	C₂×C₃₁	direct (N × H)
30. C₂×C₆₄	C₂×C₃₁	semidirect
38. D₃₂	C₂²×C₃₁	semidirect
40. C₆₄	C₂²×C₃₁	semidirect
42. C₂×C₃₁	D₆₄	direct (N × H)
50. C₃₁	C₂×D₆₄	direct (N × H)
69. C₂	C₃₁×D₆₄	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×C₃₁×D₃₂	2
C₃₁×D₆₄	2
C₂×C₃₁×C₆₄	2
C₂×D₆₄	31

Subgroups — C2×C31×D64 #21470497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×D₆₄ #21470497