Subgroups — #14521450

Order 1984.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758467	C₂	1	2	yes	maximal
2	C₃₁×#107	C₂	1	1	yes	maximal, characteristic
3	#11758406	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₃₁	C₂	1	1	yes	maximal, characteristic
5	#11758396	C₂	1	2	yes	maximal
6	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
8	C₄⋊Dic₃₁	—	2	2	no	—
9	C₄⋊Dic₃₁	C₂²	1	2	yes	—
10	Dic₃₁⋊C₄	—	2	2	no	—
11	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₃₁	—	2	2	no	—
14	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
15	C₂×Dic₃₁	—	2	2	no	—
16	C₂×Dic₃₁	D₄	1	1	yes	characteristic
17	C₂×Dic₃₁	D₄	1	1	yes	characteristic
18	C₈×C₃₁	Q₈	1	2	yes	—
19	C₃₁⋊C₈	Q₈	1	2	yes	—
20	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
21	C₄×C₃₁	—	4	2	no	—
22	C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
24	Dic₃₁	—	2	1	no	—
25	Dic₃₁	—	2	1	no	—
26	Dic₃₁	—	4	2	no	—
27	#499	—	31	1	no	maximal, Sylow
28	C₂×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
29	C₂×C₃₁	#135	1	1	yes	characteristic
30	C₂×C₃₁	#135	1	1	yes	characteristic
31	#125	—	31	2	no	—
32	#107	—	31	1	no	—
33	#107	D₃₁	1	1	yes	characteristic
34	#106	—	31	2	no	—
35	C₄×C₈	—	31	1	no	—
36	C₃₁	#499	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₈	—	31	1	no	—
38	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
39	C₄⋊C₄	—	31	2	no	—
40	C₄⋊C₄	—	62	2	no	—
41	C₄⋊C₄	—	62	2	no	—
42	C₄⋊C₄	C₂×D₃₁	1	2	yes	—
43	C₄²	—	31	1	no	—
44	C₂×C₄	—	2	2	no	—
45	C₂×C₄	—	31	1	no	—
46	C₂×C₄	—	31	1	no	—
47	C₂×C₄	—	62	2	no	—
48	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
49	C₈	—	31	2	no	—
50	C₈	Dic₆₂	1	2	yes	—
51	C₂²	D₄×D₃₁	1	1	yes	characteristic
52	C₄	—	4	2	no	—
53	C₄	—	62	1	no	—
54	C₄	—	62	1	no	—
55	C₄	—	124	2	no	—
56	C₄	C₂×Dic₆₂	1	1	yes	characteristic
57	C₄	Q₈×D₃₁	1	1	yes	characteristic
58	C₂	#11758465	1	1	yes	characteristic
59	C₂	#11758489	1	1	yes	characteristic
60	C₂	#11758496	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#107	C₂
socle, prime radical	C₂²×C₃₁	C₂×D₄
hypercenter	#107	D₃₁
hypocenter	C₃₁	#499
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
36. C₃₁	#499	semidirect

Maximal subgroups

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

subgroup	index
#11758467	2
C₃₁×#107	2
#11758406	2
C₈×Dic₃₁	2
#11758396	2
#499	31