Subgroups — C₂²×Q₈×Dic₃₁ #16858887

Order 3968.

1664 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×Dic₃₁	C₂	1	24	yes	maximal, direct product factor
2	C₂²×C₄⋊Dic₃₁	C₂	1	3	yes	maximal
3	C₂²×C₄×Dic₃₁	C₂	1	3	yes	maximal
4	C₂³×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₃₁	C₄	1	16	yes	complemented
6	C₂²×Q₈×C₃₁	C₂²	1	12	yes	—
7	C₂³×C₄×C₃₁	C₂²	1	3	yes	—
8	C₂³×Dic₃₁	C₂²	1	3	yes	—
9	C₂³×Dic₃₁	C₂²	1	1	yes	characteristic
10	Q₈×Dic₃₁	C₂²	1	64	yes	direct product factor
11	C₂×C₄⋊Dic₃₁	C₂²	1	36	yes	—
12	C₂×C₄×Dic₃₁	C₂²	1	36	yes	—
13	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
14	C₂×Q₈×C₃₁	C₂×C₄	1	96	yes	complemented
15	C₂×Q₈×C₃₁	C₂³	1	16	yes	—
16	C₂²×C₄×C₃₁	C₂×C₄	1	24	yes	—
17	C₂²×C₄×C₃₁	C₂³	1	18	yes	—
18	C₂²×Dic₃₁	—	2	12	no	—
19	C₂²×Dic₃₁	Q₈	1	8	yes	direct product factor
20	C₂²×Dic₃₁	C₂³	1	18	yes	—
21	C₂²×Dic₃₁	C₂³	1	6	yes	—
22	C₄⋊Dic₃₁	C₂³	1	48	yes	—
23	C₄×Dic₃₁	C₂³	1	48	yes	—
24	C₂³×C₃₁	C₂²×C₄	1	4	yes	—
25	C₂³×C₃₁	C₂×Q₈	1	4	yes	—
26	C₂³×C₃₁	#41	1	4	yes	—
27	C₂³×C₃₁	C₂⁴	1	3	yes	—
28	Q₈×C₃₁	C₂²×C₄	1	64	yes	complemented
29	C₂×C₄×C₃₁	C₂²×C₄	1	72	yes	—
30	C₂×C₄×C₃₁	C₂⁴	1	12	yes	—
31	C₂×Dic₃₁	—	2	36	no	—
32	C₂×Dic₃₁	C₂×Q₈	1	24	yes	direct product factor
33	C₂×Dic₃₁	C₂⁴	1	12	yes	—
34	C₂×Dic₃₁	C₂⁴	1	4	yes	—
35	C₂²×C₄×Q₈	—	31	1	no	maximal, Sylow
36	C₂²×C₃₁	C₄×Q₈	1	16	yes	complemented
37	C₂²×C₃₁	C₂³×C₄	1	6	yes	—
38	C₂²×C₃₁	C₂²×Q₈	1	6	yes	—
39	C₂²×C₃₁	C₂×#41	1	6	yes	—
40	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
41	C₄×C₃₁	C₂³×C₄	1	24	yes	—
42	Dic₃₁	—	2	12	no	—
43	Dic₃₁	C₂²×Q₈	1	8	yes	direct product factor
44	C₂³×Q₈	D₃₁	1	1	yes	characteristic
45	C₂×C₄×Q₈	—	31	24	no	—
46	C₂²×C₄⋊C₄	—	31	3	no	—
47	C₂²×C₄²	—	31	3	no	—
48	C₂×C₃₁	C₂×C₄×Q₈	1	12	yes	complemented
49	C₂×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
50	C₂×C₃₁	C₂³×Q₈	1	1	yes	characteristic
51	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
52	C₂²×Q₈	Dic₃₁	1	16	yes	direct product factor
53	C₂²×Q₈	C₂×D₃₁	1	12	yes	—
54	C₂³×C₄	—	31	1	no	—
55	C₂³×C₄	—	31	3	no	—
56	C₂³×C₄	C₂×D₃₁	1	3	yes	—
57	C₄×Q₈	—	31	64	no	—
58	C₂×C₄⋊C₄	—	31	36	no	—
59	C₂×C₄²	—	31	36	no	—
60	C₃₁	C₂²×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
61	C₂⁴	C₂²×D₃₁	1	1	yes	characteristic
62	C₂×Q₈	C₂×Dic₃₁	1	96	yes	direct product factor
63	C₂×Q₈	C₂²×D₃₁	1	16	yes	—
64	C₂²×C₄	—	31	8	no	—
65	C₂²×C₄	—	31	6	no	—
66	C₂²×C₄	—	31	18	no	—
67	C₂²×C₄	—	62	12	no	—
68	C₂²×C₄	C₂×Dic₃₁	1	24	yes	—
69	C₂²×C₄	C₂²×D₃₁	1	18	yes	—
70	C₄⋊C₄	—	31	48	no	—
71	C₄²	—	31	48	no	—
72	C₂³	Q₈×D₃₁	1	4	yes	—
73	C₂³	#92499	1	4	yes	—
74	C₂³	C₂²×Dic₃₁	1	4	yes	—
75	C₂³	C₂³×D₃₁	1	3	yes	—
76	Q₈	C₂²×Dic₃₁	1	64	yes	direct product factor
77	C₂×C₄	—	31	24	no	—
78	C₂×C₄	—	31	4	no	—
79	C₂×C₄	—	31	12	no	—
80	C₂×C₄	—	62	36	no	—
81	C₂×C₄	C₂²×Dic₃₁	1	72	yes	—
82	C₂×C₄	C₂³×D₃₁	1	12	yes	—
83	C₂²	Q₈×Dic₃₁	1	16	yes	direct product factor
84	C₂²	C₂×Q₈×D₃₁	1	6	yes	—
85	C₂²	C₂×#92499	1	6	yes	—
86	C₂²	C₂³×Dic₃₁	1	6	yes	—
87	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
88	C₄	—	31	8	no	—
89	C₄	—	62	12	no	—
90	C₄	C₂³×Dic₃₁	1	24	yes	—
91	C₂	C₂×Q₈×Dic₃₁	1	12	yes	direct product factor
92	C₂	C₂⁴×Dic₃₁	1	1	yes	characteristic
93	C₂	C₂²×Q₈×D₃₁	1	1	yes	characteristic
94	C₂	C₂²×#92499	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²×D₃₁
commutator	C₂×C₃₁	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₂³×Q₈×C₃₁	C₂
socle, prime radical	C₂⁴×C₃₁	C₂³
cosocle	C₂²×C₃₁	C₂⁵
hypercenter	C₂³×Q₈	D₃₁
hypocenter	C₃₁	C₂²×C₄×Q₈
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×Dic₃₁	C₂	direct (N × H)
5. C₂²×Q₈×C₃₁	C₄	semidirect
10. Q₈×Dic₃₁	C₂²	direct (N × H)
14. C₂×Q₈×C₃₁	C₂×C₄	semidirect
19. C₂²×Dic₃₁	Q₈	direct (N × H)
28. Q₈×C₃₁	C₂²×C₄	semidirect
32. C₂×Dic₃₁	C₂×Q₈	direct (N × H)
36. C₂²×C₃₁	C₄×Q₈	semidirect
43. Dic₃₁	C₂²×Q₈	direct (N × H)
48. C₂×C₃₁	C₂×C₄×Q₈	semidirect
52. C₂²×Q₈	Dic₃₁	direct (N × H)
60. C₃₁	C₂²×C₄×Q₈	semidirect
62. C₂×Q₈	C₂×Dic₃₁	direct (N × H)
76. Q₈	C₂²×Dic₃₁	direct (N × H)
83. C₂²	Q₈×Dic₃₁	direct (N × H)
91. C₂	C₂×Q₈×Dic₃₁	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×Q₈×Dic₃₁	2
C₂²×C₄⋊Dic₃₁	2
C₂²×C₄×Dic₃₁	2
C₂³×Q₈×C₃₁	2
C₂²×C₄×Q₈	31

Subgroups — C22×Q8×Dic31 #16858887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Q₈×Dic₃₁ #16858887