Subgroups — #16853964

Order 3968.

580 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14520961	C₂	1	12	yes	maximal, complemented
2	#14520905	C₂	1	2	yes	maximal
3	C₃₁×#379	C₂	1	1	yes	maximal, characteristic
4	C₂⁵×C₃₁	C₂²	1	1	yes	characteristic
5	C₂²×Dic₆₂	C₂²	1	4	yes	complemented
6	C₂×C₂²⋊C₄×C₃₁	C₂²	1	6	yes	—
7	C₂×C₂²⋊Dic₃₁	C₂²	1	12	yes	—
8	C₃₁⋊#95	C₂²	1	12	yes	complemented
9	C₂⁴×C₃₁	—	4	6	no	—
10	C₂⁴×C₃₁	Q₈	1	4	yes	complemented
11	C₂⁴×C₃₁	C₂³	1	3	yes	—
12	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
13	C₂²×Dic₃₁	C₂³	1	8	yes	—
14	C₂×Dic₆₂	—	4	12	no	—
15	C₂²⋊C₄×C₃₁	—	4	6	no	—
16	C₂²⋊Dic₃₁	—	4	12	no	—
17	C₂³×C₃₁	—	2	12	no	—
18	C₂³×C₃₁	—	2	6	no	—
19	C₂³×C₃₁	—	4	12	no	—
20	C₂³×C₃₁	—	4	16	no	—
21	C₂³×C₃₁	C₂×Q₈	1	6	yes	—
22	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
23	C₂×C₄×C₃₁	—	2	12	no	—
24	C₂×Dic₃₁	—	2	24	no	—
25	Dic₆₂	—	4	16	no	—
26	#2840	—	31	1	no	maximal, Sylow
27	C₂²×C₃₁	—	2	12	no	—
28	C₂²×C₃₁	—	2	6	no	—
29	C₂²×C₃₁	—	4	16	no	—
30	C₂²×C₃₁	—	4	12	no	—
31	C₂²×C₃₁	C₂²×Q₈	1	1	yes	characteristic
32	C₂²×C₃₁	H(5,𝔽₂)	1	6	yes	—
33	C₄×C₃₁	—	4	4	no	—
34	Dic₃₁	—	4	8	no	—
35	#393	—	31	12	no	—
36	#379	—	31	2	no	—
37	#379	D₃₁	1	1	yes	characteristic
38	C₂×C₃₁	—	4	6	no	—
39	C₂×C₃₁	#543	1	3	yes	—
40	C₂×C₃₁	H(3,𝔽₄)	1	4	yes	—
41	C₂⁵	C₂×D₃₁	1	1	yes	characteristic
42	C₂²×Q₈	—	31	4	no	—
43	C₂×C₂²⋊C₄	—	31	12	no	—
44	C₂×C₂²⋊C₄	C₂×D₃₁	1	6	yes	—
45	#95	—	31	12	no	—
46	C₃₁	#2840	1	1	yes	characteristic, complemented, Sylow
47	C₂⁴	—	4	6	no	—
48	C₂⁴	Dic₆₂	1	4	yes	complemented
49	C₂⁴	C₂²×D₃₁	1	3	yes	—
50	C₂×Q₈	—	124	12	no	—
51	C₂²×C₄	—	31	8	no	—
52	C₂²×C₄	C₂²×D₃₁	1	4	yes	—
53	C₂²⋊C₄	—	4	6	no	—
54	C₂²⋊C₄	—	124	12	no	—
55	C₂³	—	2	6	no	—
56	C₂³	—	2	12	no	—
57	C₂³	—	4	12	no	—
58	C₂³	—	4	16	no	—
59	C₂³	C₂×Dic₆₂	1	6	yes	—
60	C₂³	C₂³×D₃₁	1	1	yes	characteristic
61	Q₈	—	124	16	no	—
62	C₂×C₄	—	2	12	no	—
63	C₂×C₄	—	62	24	no	—
64	C₂²	—	2	6	no	—
65	C₂²	—	2	12	no	—
66	C₂²	—	4	16	no	—
67	C₂²	—	4	12	no	—
68	C₂²	C₂²×Dic₆₂	1	1	yes	characteristic
69	C₂²	#11758561	1	6	yes	—
70	C₄	—	4	4	no	—
71	C₄	—	124	8	no	—
72	C₂	—	4	6	no	—
73	C₂	#14521675	1	3	yes	—
74	C₂	#14521792	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃₁
commutator, socle, cosocle	C₂³×C₃₁	C₂⁴
Fitting	C₃₁×#379	C₂
prime radical	C₂⁵×C₃₁	C₂²
hypercenter	#379	D₃₁
hypocenter	C₃₁	#2840
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ #379

Complements

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

N	H ≅ G/N	type
1. #14520961	C₂	semidirect
5. C₂²×Dic₆₂	C₂²	semidirect
8. C₃₁⋊#95	C₂²	semidirect
10. C₂⁴×C₃₁	Q₈	semidirect
46. C₃₁	#2840	semidirect
48. C₂⁴	Dic₆₂	semidirect

Maximal subgroups

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

subgroup	index
#14520961	2
#14520905	2
C₃₁×#379	2
#2840	31