Subgroups — #14521456

Order 1984.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758467	C₂	1	1	yes	maximal, characteristic
2	#11758465	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#106	C₂	1	1	yes	maximal, characteristic
4	#11758406	C₂	1	1	yes	maximal, characteristic
5	#11758403	C₂	1	1	yes	maximal, characteristic
6	#11758396	C₂	1	1	yes	maximal, characteristic
7	#11758395	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₆₂	—	2	1	no	—
9	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₃₁	—	2	1	no	—
13	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
15	Dic₃₁⋊C₄	—	2	1	no	—
16	Dic₃₁⋊C₄	—	2	1	no	—
17	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₃₁	—	2	1	no	—
20	C₂×C₄×C₃₁	—	2	1	no	—
21	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
22	C₂×Dic₃₁	—	2	1	no	—
23	C₂×Dic₃₁	—	2	1	no	—
24	C₂×Dic₃₁	D₄	1	1	yes	characteristic
25	C₂×Dic₃₁	D₄	1	1	yes	characteristic
26	Dic₆₂	—	4	2	no	—
27	C₈×C₃₁	Q₈	1	2	yes	complemented
28	C₃₁⋊C₈	Q₈	1	2	yes	complemented
29	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
30	C₄×C₃₁	—	4	1	no	—
31	C₄×C₃₁	—	4	1	no	—
32	C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
34	Dic₃₁	—	2	1	no	—
35	Dic₃₁	—	2	1	no	—
36	Dic₃₁	—	4	1	no	—
37	Dic₃₁	—	4	1	no	—
38	#501	—	31	1	no	maximal, Sylow
39	C₂×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
40	C₂×C₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
41	C₂×C₃₁	#137	1	1	yes	characteristic
42	C₄⋊Q₈	—	31	1	no	—
43	#125	—	31	1	no	—
44	#107	—	31	1	no	—
45	#107	—	31	1	no	—
46	#106	—	31	1	no	—
47	#106	D₃₁	1	1	yes	characteristic
48	#97	—	31	1	no	—
49	C₃₁	#501	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₈	—	62	1	no	—
51	C₂×C₈	—	31	1	no	—
52	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
53	C₄⋊C₄	—	31	1	no	—
54	C₄⋊C₄	—	31	1	no	—
55	C₄⋊C₄	—	62	1	no	—
56	C₄⋊C₄	—	62	1	no	—
57	C₄⋊C₄	—	62	1	no	—
58	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
60	C₄²	—	31	1	no	—
61	Q₈	—	124	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	31	1	no	—
65	C₂×C₄	—	31	1	no	—
66	C₂×C₄	—	62	1	no	—
67	C₂×C₄	—	62	1	no	—
68	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
69	C₈	—	31	2	no	—
70	C₈	Dic₆₂	1	2	yes	complemented
71	C₂²	D₄×D₃₁	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	62	1	no	—
75	C₄	—	62	1	no	—
76	C₄	—	124	1	no	—
77	C₄	—	124	1	no	—
78	C₄	C₂×Dic₆₂	1	1	yes	characteristic
79	C₄	Q₈×D₃₁	1	1	yes	characteristic
80	C₂	#11758465	1	1	yes	characteristic
81	C₂	#11758491	1	1	yes	characteristic
82	C₂	#11758492	1	1	yes	characteristic

	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	#501
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
27. C₈×C₃₁	Q₈	semidirect
28. C₃₁⋊C₈	Q₈	semidirect
49. C₃₁	#501	semidirect
70. C₈	Dic₆₂	semidirect

Maximal subgroups

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

subgroup	index
#11758467	2
#11758465	2
C₃₁×#106	2
#11758406	2
#11758403	2
#11758396	2
#11758395	2
#501	31