Subgroups — #14520980

Order 1984.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃₁⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₃₁⋊C₄	C₂	1	2	yes	maximal
4	C₃₁⋊#95	C₂	1	2	yes	maximal
5	C₃₁⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₃₁	C₂²	1	2	yes	—
7	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃₁	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₁	C₂²	1	1	yes	characteristic
10	C₂²×Dic₃₁	C₂²	1	2	yes	—
11	C₄⋊C₄×C₃₁	—	2	2	no	—
12	Dic₃₁⋊C₄	—	2	2	no	—
13	Dic₃₁⋊C₄	—	2	4	no	—
14	C₂³×C₃₁	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₃₁	—	2	2	no	—
16	C₂×C₄×C₃₁	—	2	2	no	—
17	C₂×C₄×C₃₁	—	2	2	no	—
18	C₂×C₄×C₃₁	—	2	2	no	—
19	C₂×C₄×C₃₁	D₄	1	2	yes	—
20	C₂×Dic₃₁	—	2	2	no	—
21	C₂×Dic₃₁	—	2	1	no	—
22	C₂×Dic₃₁	—	2	2	no	—
23	C₂×Dic₃₁	—	2	1	no	—
24	C₂×Dic₃₁	—	2	1	no	—
25	C₂×Dic₃₁	—	2	2	no	—
26	C₂×Dic₃₁	D₄	1	2	yes	—
27	C₂×Dic₃₁	Q₈	1	4	yes	—
28	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
29	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
30	C₂²×C₃₁	C₂×Q₈	1	2	yes	—
31	C₂²×C₃₁	#41	1	2	yes	—
32	C₂²×C₃₁	#41	1	1	yes	characteristic
33	C₄×C₃₁	—	2	2	no	—
34	C₄×C₃₁	—	4	2	no	—
35	Dic₃₁	—	2	2	no	—
36	Dic₃₁	—	2	4	no	—
37	Dic₃₁	—	4	1	no	—
38	#398	—	31	1	no	maximal, Sylow
39	C₂×C₃₁	#121	1	1	yes	characteristic
40	C₂×C₃₁	C₂²⋊Q₈	1	2	yes	—
41	C₂×C₃₁	#123	1	1	yes	characteristic
42	C₂×C₃₁	#125	1	2	yes	—
43	C₂×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
44	C₂×C₄⋊C₄	—	31	2	no	—
45	C₂×C₄⋊C₄	—	31	1	no	—
46	C₂×C₄⋊C₄	D₃₁	1	1	yes	characteristic
47	#95	—	31	1	no	—
48	#95	—	31	2	no	—
49	C₃₁	#398	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	31	2	no	—
51	C₂²×C₄	—	31	1	no	—
52	C₂²×C₄	—	31	1	no	—
53	C₂²×C₄	C₂×D₃₁	1	2	yes	—
54	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
55	C₄⋊C₄	—	2	2	no	—
56	C₄⋊C₄	—	62	4	no	—
57	C₄⋊C₄	—	62	2	no	—
58	C₂³	C₂²×D₃₁	1	1	yes	characteristic
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	31	2	no	—
64	C₂×C₄	—	31	4	no	—
65	C₂×C₄	—	62	2	no	—
66	C₂×C₄	—	62	2	no	—
67	C₂×C₄	—	62	1	no	—
68	C₂×C₄	—	62	1	no	—
69	C₂×C₄	—	62	2	no	—
70	C₂×C₄	—	62	1	no	—
71	C₂×C₄	C₂²⋊D₃₁	1	2	yes	—
72	C₂²	#92495	1	2	yes	—
73	C₂²	D₄×D₃₁	1	1	yes	characteristic
74	C₂²	#92497	1	1	yes	characteristic
75	C₂²	Q₈×D₃₁	1	2	yes	—
76	C₂²	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	4	2	no	—
79	C₄	—	62	4	no	—
80	C₄	—	62	2	no	—
81	C₄	—	124	1	no	—
82	C₂	#11758466	1	2	yes	—
83	C₂	#11758473	1	2	yes	—
84	C₂	#11758506	1	1	yes	characteristic
85	C₂	#11758515	1	1	yes	characteristic
86	C₂	#11758521	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃₁
commutator, socle, prime radical, cosocle	C₂³×C₃₁	C₂³
Fitting	C₂×C₄⋊C₄×C₃₁	C₂
hypercenter	C₂×C₄⋊C₄	D₃₁
hypocenter	C₃₁	#398
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
49. C₃₁	#398	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×C₃₁	2
C₂×Dic₃₁⋊C₄	2
C₃₁⋊#95	2
#398	31