Subgroups — #14521446

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×#106	C₂	1	1	yes	maximal, characteristic
3	#11758405	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₃₁	C₂	1	1	yes	maximal, characteristic
5	#11758396	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	2	yes	—
17	Dic₆₂	—	4	4	no	—
18	C₈×C₃₁	Q₈	1	2	yes	complemented
19	C₃₁⋊C₈	Q₈	1	2	yes	complemented
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	—	4	2	no	—
25	Dic₃₁	SD₁₆	1	4	yes	—
26	#498	—	31	1	no	maximal, Sylow
27	C₂×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
28	C₂×C₃₁	C₂×SD₁₆	1	2	yes	—
29	C₄⋊Q₈	—	31	2	no	—
30	#106	—	31	1	no	—
31	#106	—	31	2	no	—
32	#106	D₃₁	1	1	yes	characteristic
33	C₄×C₈	—	31	1	no	—
34	C₃₁	#498	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₈	—	62	2	no	—
36	C₂×C₈	—	31	1	no	—
37	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
38	C₄⋊C₄	—	31	2	no	—
39	C₄⋊C₄	—	62	2	no	—
40	C₄⋊C₄	C₂×D₃₁	1	2	yes	—
41	C₄²	—	31	1	no	—
42	Q₈	—	124	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	31	2	no	—
45	C₂×C₄	—	62	2	no	—
46	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
47	C₈	—	31	2	no	—
48	C₈	Dic₆₂	1	2	yes	complemented
49	C₂²	D₄×D₃₁	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	31	4	no	—
52	C₄	—	124	2	no	—
53	C₄	C₂×Dic₆₂	1	1	yes	characteristic
54	C₄	Q₈×D₃₁	1	1	yes	characteristic
55	C₂	#11758465	1	1	yes	characteristic
56	C₂	SD₁₆×D₃₁	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#106	C₂
socle, prime radical	C₂²×C₃₁	C₂×D₄
hypercenter	#106	D₃₁
hypocenter	C₃₁	#498
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
18. C₈×C₃₁	Q₈	semidirect
19. C₃₁⋊C₈	Q₈	semidirect
34. C₃₁	#498	semidirect
48. 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×#106	2
#11758405	2
C₈×Dic₃₁	2
#11758396	2
#498	31