Subgroups — C₃₁×#461 #14520642

Order 1984.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×C₃₁	C₂	1	2	yes	maximal
2	C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#103	C₂	1	2	yes	maximal, complemented
6	C₂×Q₈×C₃₁	C₂²	1	2	yes	—
7	C₂×D₄×C₃₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₃₁	—	2	1	no	—
9	SD₁₆×C₃₁	—	2	4	no	—
10	C₂×C₈×C₃₁	C₂²	1	2	yes	—
11	C₄⋊C₄×C₃₁	—	2	1	no	—
12	C₄⋊C₄×C₃₁	—	2	1	no	—
13	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
14	C₂²⋊C₄×C₃₁	—	2	1	no	—
15	C₄²×C₃₁	C₂²	1	1	yes	characteristic
16	C₂³×C₃₁	—	2	1	no	—
17	Q₈×C₃₁	—	2	2	no	—
18	Q₈×C₃₁	—	2	2	no	—
19	D₄×C₃₁	—	2	1	no	—
20	D₄×C₃₁	D₄	1	2	yes	—
21	C₂×C₄×C₃₁	—	2	1	no	—
22	C₂×C₄×C₃₁	—	2	2	no	—
23	C₂×C₄×C₃₁	—	4	2	no	—
24	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
25	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
26	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
27	C₈×C₃₁	—	2	2	no	—
28	C₂²×C₃₁	—	2	2	no	—
29	C₂²×C₃₁	—	4	1	no	—
30	C₂²×C₃₁	—	4	1	no	—
31	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
32	C₄×C₃₁	—	2	1	no	—
33	C₄×C₃₁	—	4	2	no	—
34	C₄×C₃₁	—	4	1	no	—
35	C₄×C₃₁	SD₁₆	1	2	yes	complemented
36	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
37	C₄×C₃₁	#41	1	1	yes	characteristic
38	#461	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×C₃₁	—	4	2	no	—
40	C₂×C₃₁	#121	1	1	yes	characteristic
41	C₂×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₃₁	#137	1	1	yes	characteristic
43	C₂×SD₁₆	C₂×C₃₁	1	2	yes	—
44	C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
45	C₄×D₄	C₂×C₃₁	1	1	yes	characteristic
46	C₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
47	#103	C₂×C₃₁	1	2	yes	complemented
48	C₃₁	#461	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×Q₈	C₂²×C₃₁	1	2	yes	—
50	C₂×D₄	C₂²×C₃₁	1	1	yes	characteristic
51	C₂²×C₄	—	2	1	no	—
52	SD₁₆	—	2	4	no	—
53	C₂×C₈	C₂²×C₃₁	1	2	yes	—
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	2	1	no	—
56	C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
57	C₂²⋊C₄	—	2	1	no	—
58	C₄²	C₂²×C₃₁	1	1	yes	characteristic
59	C₂³	—	2	1	no	—
60	Q₈	—	2	2	no	—
61	Q₈	—	2	2	no	—
62	D₄	—	2	1	no	—
63	D₄	D₄×C₃₁	1	2	yes	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	4	2	no	—
67	C₂×C₄	D₄×C₃₁	1	1	yes	characteristic
68	C₂×C₄	D₄×C₃₁	1	1	yes	characteristic
69	C₂×C₄	C₂³×C₃₁	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₂²	—	2	2	no	—
72	C₂²	—	4	1	no	—
73	C₂²	—	4	1	no	—
74	C₂²	C₂×D₄×C₃₁	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	2	no	—
77	C₄	—	4	1	no	—
78	C₄	SD₁₆×C₃₁	1	2	yes	complemented
79	C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
80	C₄	#41×C₃₁	1	1	yes	characteristic
81	C₂	—	4	2	no	—
82	C₂	C₃₁×#121	1	1	yes	characteristic
83	C₂	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
84	C₂	C₃₁×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃₁
prime radical	C₂×D₄×C₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×C₄⋊Q₈	C₂	semidirect
4. C₃₁×C₄⋊C₈	C₂	semidirect
5. C₃₁×#103	C₂	semidirect
35. C₄×C₃₁	SD₁₆	semidirect
38. #461	C₃₁	direct (N × H)
44. C₄⋊Q₈	C₂×C₃₁	semidirect
46. C₄⋊C₈	C₂×C₃₁	semidirect
47. #103	C₂×C₃₁	semidirect
48. C₃₁	#461	direct (N × H)
78. C₄	SD₁₆×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×C₃₁	2
C₃₁×C₄⋊Q₈	2
C₄×D₄×C₃₁	2
C₃₁×C₄⋊C₈	2
C₃₁×#103	2
#461	31

Subgroups — C31×#461 #14520642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#461 #14520642