Subgroups — #16845325

Order 3968.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521426	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521425	C₂	1	4	yes	maximal, complemented
3	C₈×C₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₃₁	—	2	2	no	—
6	C₃₁×#127	C₂²	1	2	yes	—
7	C₂×#92479	—	2	8	no	—
8	C₂×D₂₄₈	—	2	2	no	—
9	#11758451	C₂²	1	2	yes	—
10	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₄×C₃₁⋊C₈	C₂²	1	2	yes	—
12	C₂×D₄×C₃₁	—	2	4	no	—
13	C₂×D₄×C₃₁	—	2	2	no	—
14	C₂×D₁₂₄	—	2	2	no	—
15	C₂×D₁₂₄	—	2	4	no	—
16	D₈×C₃₁	—	4	4	no	—
17	C₂×C₈×C₃₁	D₄	1	2	yes	—
18	C₄²×C₃₁	C₂³	1	1	yes	characteristic
19	#92479	—	4	16	no	—
20	C₂×C₃₁⋊C₈	D₄	1	4	yes	—
21	D₂₄₈	—	4	4	no	—
22	C₂³×C₃₁	—	4	2	no	—
23	C₂²×D₃₁	—	4	2	no	—
24	D₄×C₃₁	—	4	8	no	—
25	D₄×C₃₁	—	4	4	no	—
26	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
27	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
28	D₁₂₄	—	4	4	no	—
29	D₁₂₄	—	4	8	no	—
30	C₈×C₃₁	D₈	1	4	yes	complemented
31	C₃₁⋊C₈	D₈	1	8	yes	complemented
32	#1712	—	31	1	no	maximal, Sylow
33	C₂²×C₃₁	—	8	4	no	—
34	C₂²×C₃₁	—	8	2	no	—
35	C₂²×C₃₁	#127	1	1	yes	characteristic
36	C₂×D₃₁	—	8	4	no	—
37	C₂×D₃₁	—	8	2	no	—
38	C₄×C₃₁	C₂×D₈	1	4	yes	—
39	C₄×C₃₁	C₂×D₈	1	2	yes	—
40	#493	—	31	4	no	—
41	#493	—	31	1	no	—
42	#493	D₃₁	1	1	yes	characteristic, complemented
43	C₈²	—	31	1	no	—
44	C₂×C₃₁	—	16	2	no	—
45	C₂×C₃₁	#493	1	2	yes	—
46	C₂×C₃₁	#493	1	1	yes	characteristic
47	D₃₁	—	16	2	no	—
48	C₂×D₈	—	2	2	no	—
49	C₂×D₈	—	62	8	no	—
50	C₂×D₈	—	62	2	no	—
51	#127	—	31	2	no	—
52	#127	C₂×D₃₁	1	2	yes	—
53	C₄×C₈	—	31	2	no	—
54	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
55	C₃₁	#1712	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₄	—	2	4	no	—
57	C₂×D₄	—	2	2	no	—
58	C₂×D₄	—	62	4	no	—
59	C₂×D₄	—	62	2	no	—
60	D₈	—	4	4	no	—
61	D₈	—	124	16	no	—
62	D₈	—	124	4	no	—
63	C₂×C₈	—	31	4	no	—
64	C₂×C₈	C₂²⋊D₃₁	1	2	yes	—
65	C₄²	C₂²×D₃₁	1	1	yes	characteristic
66	C₂³	—	4	2	no	—
67	C₂³	—	124	2	no	—
68	D₄	—	4	8	no	—
69	D₄	—	4	4	no	—
70	D₄	—	124	8	no	—
71	D₄	—	124	4	no	—
72	C₂×C₄	D₄×D₃₁	1	2	yes	—
73	C₂×C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
74	C₈	—	31	8	no	—
75	C₈	#92479	1	4	yes	complemented
76	C₂²	—	8	4	no	—
77	C₂²	—	8	2	no	—
78	C₂²	—	248	4	no	—
79	C₂²	—	248	2	no	—
80	C₂²	#11758517	1	1	yes	characteristic
81	C₄	D₈×D₃₁	1	4	yes	—
82	C₄	C₂×#92479	1	2	yes	—
83	C₂	—	16	2	no	—
84	C₂	—	496	2	no	—
85	C₂	#14521424	1	2	yes	—
86	C₂	#14521425	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11758517
commutator, cosocle	C₄²×C₃₁	C₂³
Frattini	C₄²	C₂²×D₃₁
Fitting	C₃₁×#493	C₂
socle	C₂²×C₃₁	#127
hypercenter	#493	D₃₁
hypocenter	C₃₁	#1712
LCS	G ▷ C₄²×C₃₁ ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

Complements

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

N	H ≅ G/N	type
1. #14521426	C₂	semidirect
2. #14521425	C₂	semidirect
3. C₈×C₃₁⋊C₈	C₂	semidirect
4. C₃₁×#493	C₂	semidirect
30. C₈×C₃₁	D₈	semidirect
31. C₃₁⋊C₈	D₈	semidirect
42. #493	D₃₁	semidirect
55. C₃₁	#1712	semidirect
75. C₈	#92479	semidirect

Maximal subgroups

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

subgroup	index
#14521426	2
#14521425	2
C₈×C₃₁⋊C₈	2
C₃₁×#493	2
#1712	31