Subgroups — #14521453

Order 1984.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758465	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	#11758395	C₂	1	2	yes	maximal
6	C₂×Dic₆₂	—	2	2	no	—
7	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
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	Dic₆₂	—	4	4	no	—
19	C₈×C₃₁	Q₈	1	2	yes	complemented
20	C₃₁⋊C₈	Q₈	1	2	yes	complemented
21	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
22	C₄×C₃₁	—	4	2	no	—
23	C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
25	Dic₃₁	—	4	2	no	—
26	Dic₃₁	D₈	1	2	yes	—
27	Dic₃₁	Q₁₆	1	2	yes	—
28	#500	—	31	1	no	maximal, Sylow
29	C₂×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
30	C₂×C₃₁	C₂×D₈	1	1	yes	characteristic
31	C₂×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
32	C₄⋊Q₈	—	31	2	no	—
33	#107	—	31	1	no	—
34	#107	—	31	2	no	—
35	#107	D₃₁	1	1	yes	characteristic
36	C₄×C₈	—	31	1	no	—
37	C₃₁	#500	1	1	yes	characteristic, complemented, Sylow
38	C₂×Q₈	—	62	2	no	—
39	C₂×C₈	—	31	1	no	—
40	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
41	C₄⋊C₄	—	31	2	no	—
42	C₄⋊C₄	—	62	2	no	—
43	C₄⋊C₄	C₂×D₃₁	1	2	yes	—
44	C₄²	—	31	1	no	—
45	Q₈	—	124	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	31	1	no	—
48	C₂×C₄	—	31	1	no	—
49	C₂×C₄	—	62	2	no	—
50	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
51	C₈	—	31	2	no	—
52	C₈	Dic₆₂	1	2	yes	complemented
53	C₂²	D₄×D₃₁	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	31	2	no	—
56	C₄	—	31	2	no	—
57	C₄	—	124	2	no	—
58	C₄	C₂×Dic₆₂	1	1	yes	characteristic
59	C₄	Q₈×D₃₁	1	1	yes	characteristic
60	C₂	#11758465	1	1	yes	characteristic
61	C₂	D₈×D₃₁	1	1	yes	characteristic
62	C₂	Q₁₆×D₃₁	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	#500
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
19. C₈×C₃₁	Q₈	semidirect
20. C₃₁⋊C₈	Q₈	semidirect
37. C₃₁	#500	semidirect
52. C₈	Dic₆₂	semidirect

Maximal subgroups

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

subgroup	index
#11758465	2
C₃₁×#107	2
#11758406	2
C₈×Dic₃₁	2
#11758395	2
#500	31