Subgroups — C₂×C₃₁×#103 #14520596

Order 1984.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#103	C₂	1	4	yes	maximal, direct product factor
5	C₂×Q₈×C₃₁	—	2	2	no	—
6	C₂×Q₈×C₃₁	—	2	1	no	—
7	C₂×Q₈×C₃₁	C₄	1	4	yes	complemented
8	C₂×Q₈×C₃₁	C₂²	1	2	yes	—
9	C₂²×C₄×C₃₁	—	2	1	no	—
10	C₂²×C₄×C₃₁	—	2	1	no	—
11	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₃₁	—	2	2	no	—
13	C₂×C₈×C₃₁	C₂²	1	2	yes	—
14	C₄⋊C₄×C₃₁	—	2	1	no	—
15	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
16	C₂³×C₃₁	D₄	1	1	yes	characteristic
17	Q₈×C₃₁	—	2	4	no	—
18	Q₈×C₃₁	—	2	2	no	—
19	Q₈×C₃₁	C₂×C₄	1	4	yes	complemented
20	C₂×C₄×C₃₁	—	2	4	no	—
21	C₂×C₄×C₃₁	—	2	2	no	—
22	C₂×C₄×C₃₁	—	2	2	no	—
23	C₂×C₄×C₃₁	—	4	2	no	—
24	C₂×C₄×C₃₁	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
26	C₂×C₄×C₃₁	D₄	1	2	yes	—
27	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
28	C₈×C₃₁	—	2	2	no	—
29	C₂²×C₃₁	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₃₁	SD₁₆	1	2	yes	—
31	C₂²×C₃₁	Q₁₆	1	2	yes	—
32	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
33	C₄×C₃₁	—	2	4	no	—
34	C₄×C₃₁	—	4	2	no	—
35	C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
36	C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
38	C₂×#103	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×C₃₁	#103	1	4	yes	direct product factor
40	C₂×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₃₁	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
43	C₂²×Q₈	C₂×C₃₁	1	1	yes	characteristic
44	C₂²×C₈	C₂×C₃₁	1	1	yes	characteristic
45	C₂×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
46	#103	C₂×C₃₁	1	4	yes	direct product factor
47	C₃₁	C₂×#103	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×Q₈	—	2	2	no	—
49	C₂×Q₈	—	2	1	no	—
50	C₂×Q₈	C₄×C₃₁	1	4	yes	complemented
51	C₂×Q₈	C₂²×C₃₁	1	2	yes	—
52	C₂²×C₄	—	2	1	no	—
53	C₂²×C₄	—	2	1	no	—
54	C₂²×C₄	C₂²×C₃₁	1	1	yes	characteristic
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	C₂²×C₃₁	1	2	yes	—
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
59	C₂³	D₄×C₃₁	1	1	yes	characteristic
60	Q₈	—	2	4	no	—
61	Q₈	—	2	2	no	—
62	Q₈	C₂×C₄×C₃₁	1	4	yes	complemented
63	C₂×C₄	—	2	4	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	4	2	no	—
67	C₂×C₄	C₂×C₄×C₃₁	1	2	yes	—
68	C₂×C₄	D₄×C₃₁	1	1	yes	characteristic
69	C₂×C₄	D₄×C₃₁	1	2	yes	—
70	C₂×C₄	C₂³×C₃₁	1	1	yes	characteristic
71	C₈	—	2	2	no	—
72	C₂²	C₂²⋊C₄×C₃₁	1	2	yes	—
73	C₂²	SD₁₆×C₃₁	1	2	yes	—
74	C₂²	Q₁₆×C₃₁	1	2	yes	—
75	C₂²	C₂×D₄×C₃₁	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	4	2	no	—
78	C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
79	C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
80	C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
81	C₂	C₃₁×#103	1	4	yes	direct product factor
82	C₂	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
83	C₂	C₂×SD₁₆×C₃₁	1	1	yes	characteristic
84	C₂	C₂×Q₁₆×C₃₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₃₁×#103	C₂	direct (N × H)
7. C₂×Q₈×C₃₁	C₄	semidirect
19. Q₈×C₃₁	C₂×C₄	semidirect
38. C₂×#103	C₃₁	direct (N × H)
39. C₂×C₃₁	#103	direct (N × H)
46. #103	C₂×C₃₁	direct (N × H)
47. C₃₁	C₂×#103	direct (N × H)
50. C₂×Q₈	C₄×C₃₁	semidirect
62. Q₈	C₂×C₄×C₃₁	semidirect
81. C₂	C₃₁×#103	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×Q₈×C₃₁	2
C₂²×C₈×C₃₁	2
C₂×C₄⋊C₄×C₃₁	2
C₃₁×#103	2
C₂×#103	31

Subgroups — C2×C31×#103 #14520596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#103 #14520596