Subgroups — C₂×C₃₁×#2867 #21493401

Order 7936.

8094 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#127	C₂	1	14	yes	maximal, complemented
2	C₃₁×#2867	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₄×C₃₁	C₂²	1	28	yes	—
5	C₂×C₃₁×#127	—	2	112	no	—
6	C₂×C₃₁×#127	C₂²	1	112	yes	complemented
7	C₂²×C₄²×C₃₁	C₂²	1	7	yes	—
8	C₄³×C₃₁	C₂²	1	8	yes	complemented
9	C₂⁵×C₃₁	C₂³	1	8	yes	—
10	C₂²×D₄×C₃₁	—	2	336	no	—
11	C₂²×D₄×C₃₁	C₂³	1	112	yes	—
12	C₂³×C₄×C₃₁	C₂³	1	7	yes	—
13	C₃₁×#127	—	2	448	no	—
14	C₂×C₄²×C₃₁	D₄	1	56	yes	complemented
15	C₂×C₄²×C₃₁	C₂³	1	28	yes	—
16	C₂⁴×C₃₁	—	2	112	no	—
17	C₂⁴×C₃₁	C₂⁴	1	16	yes	—
18	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
19	C₂×D₄×C₃₁	—	2	672	no	—
20	C₂×D₄×C₃₁	—	4	448	no	—
21	C₂²×C₄×C₃₁	C₂×D₄	1	84	yes	—
22	C₂²×C₄×C₃₁	C₂⁴	1	14	yes	—
23	C₄²×C₃₁	C₂×D₄	1	112	yes	complemented
24	C₂×#2867	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₃₁	—	2	112	no	—
26	C₂³×C₃₁	—	4	224	no	—
27	C₂³×C₃₁	C₂²×D₄	1	14	yes	—
28	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
29	D₄×C₃₁	—	4	448	no	—
30	C₂×C₄×C₃₁	#127	1	112	yes	complemented
31	C₂×C₄×C₃₁	C₂²×D₄	1	84	yes	—
32	C₂²×#127	C₂×C₃₁	1	14	yes	complemented
33	#2867	C₂×C₃₁	1	16	yes	direct product factor
34	C₂×C₄³	C₂×C₃₁	1	1	yes	characteristic, complemented
35	C₂²×C₃₁	—	4	112	no	—
36	C₂²×C₃₁	—	8	64	no	—
37	C₂²×C₃₁	C₂×#127	1	28	yes	—
38	C₂²×C₃₁	C₂³×D₄	1	7	yes	—
39	C₄×C₃₁	C₂×#127	1	56	yes	complemented
40	C₂³×D₄	C₂²×C₃₁	1	28	yes	—
41	C₂×#127	—	2	112	no	—
42	C₂×#127	C₂²×C₃₁	1	112	yes	complemented
43	C₂²×C₄²	C₂²×C₃₁	1	7	yes	—
44	C₄³	C₂²×C₃₁	1	8	yes	complemented
45	C₂×C₃₁	—	8	16	no	—
46	C₂×C₃₁	#2867	1	8	yes	direct product factor
47	C₂×C₃₁	C₂²×#127	1	7	yes	—
48	C₂⁵	C₂³×C₃₁	1	8	yes	—
49	C₂²×D₄	—	2	336	no	—
50	C₂²×D₄	C₂³×C₃₁	1	112	yes	—
51	C₂³×C₄	C₂³×C₃₁	1	7	yes	—
52	#127	—	2	448	no	—
53	C₂×C₄²	D₄×C₃₁	1	56	yes	complemented
54	C₂×C₄²	C₂³×C₃₁	1	28	yes	—
55	C₃₁	C₂×#2867	1	1	yes	characteristic, direct product factor, Sylow
56	C₂⁴	—	2	112	no	—
57	C₂⁴	C₂⁴×C₃₁	1	16	yes	—
58	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
59	C₂×D₄	—	2	672	no	—
60	C₂×D₄	—	4	448	no	—
61	C₂²×C₄	C₂×D₄×C₃₁	1	84	yes	—
62	C₂²×C₄	C₂⁴×C₃₁	1	14	yes	—
63	C₄²	C₂×D₄×C₃₁	1	112	yes	complemented
64	C₂³	—	2	112	no	—
65	C₂³	—	4	224	no	—
66	C₂³	C₂²×D₄×C₃₁	1	14	yes	—
67	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
68	D₄	—	4	448	no	—
69	C₂×C₄	C₃₁×#127	1	112	yes	complemented
70	C₂×C₄	C₂²×D₄×C₃₁	1	84	yes	—
71	C₂²	—	4	112	no	—
72	C₂²	—	8	64	no	—
73	C₂²	C₂×C₃₁×#127	1	28	yes	—
74	C₂²	C₂³×D₄×C₃₁	1	7	yes	—
75	C₄	C₂×C₃₁×#127	1	56	yes	complemented
76	C₂	—	8	16	no	—
77	C₂	C₃₁×#2867	1	8	yes	direct product factor
78	C₂	C₂²×C₃₁×#127	1	7	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×#127	C₂	semidirect
2. C₃₁×#2867	C₂	direct (N × H)
3. C₂×C₄³×C₃₁	C₂	semidirect
6. C₂×C₃₁×#127	C₂²	semidirect
8. C₄³×C₃₁	C₂²	semidirect
14. C₂×C₄²×C₃₁	D₄	semidirect
23. C₄²×C₃₁	C₂×D₄	semidirect
24. C₂×#2867	C₃₁	direct (N × H)
30. C₂×C₄×C₃₁	#127	semidirect
32. C₂²×#127	C₂×C₃₁	semidirect
33. #2867	C₂×C₃₁	direct (N × H)
34. C₂×C₄³	C₂×C₃₁	semidirect
39. C₄×C₃₁	C₂×#127	semidirect
42. C₂×#127	C₂²×C₃₁	semidirect
44. C₄³	C₂²×C₃₁	semidirect
46. C₂×C₃₁	#2867	direct (N × H)
53. C₂×C₄²	D₄×C₃₁	semidirect
55. C₃₁	C₂×#2867	direct (N × H)
63. C₄²	C₂×D₄×C₃₁	semidirect
69. C₂×C₄	C₃₁×#127	semidirect
75. C₄	C₂×C₃₁×#127	semidirect
77. C₂	C₃₁×#2867	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃₁×#127	2
C₃₁×#2867	2
C₂×C₄³×C₃₁	2
C₂×#2867	31

Subgroups — C2×C31×#2867 #21493401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2867 #21493401