Subgroups — #14521360

Order 1984.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758420	C₂	1	2	yes	maximal, complemented
4	C₂²⋊(C₃₁⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#11758395	C₂	1	2	yes	maximal, complemented
6	C₂×D₄×C₃₁	—	2	1	no	—
7	C₂×D₄×C₃₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₁	—	2	1	no	—
10	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₂²⋊C₄×C₃₁	—	2	1	no	—
12	C₄⋊Dic₃₁	—	2	1	no	—
13	C₄⋊Dic₃₁	C₂²	1	2	yes	—
14	C₂×C₃₁⋊C₈	C₂²	1	2	yes	—
15	C₂³×C₃₁	—	2	1	no	—
16	C₂³×C₃₁	D₄	1	1	yes	characteristic
17	D₄×C₃₁	—	2	2	no	—
18	D₄×C₃₁	—	4	2	no	—
19	C₂×C₄×C₃₁	—	2	2	no	—
20	C₂×C₄×C₃₁	—	2	1	no	—
21	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
22	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
23	C₂×Dic₃₁	—	2	2	no	—
24	C₂×Dic₃₁	—	4	2	no	—
25	C₃₁⋊C₈	—	2	2	no	—
26	C₂²×C₃₁	—	2	1	no	—
27	C₂²×C₃₁	—	2	1	no	—
28	C₂²×C₃₁	—	4	1	no	—
29	C₂²×C₃₁	—	4	1	no	—
30	C₂²×C₃₁	—	4	1	no	—
31	C₂²×C₃₁	D₈	1	2	yes	—
32	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
33	C₄×C₃₁	—	2	1	no	—
34	C₄×C₃₁	—	4	1	no	—
35	C₄×C₃₁	#41	1	2	yes	—
36	Dic₃₁	—	4	2	no	—
37	#480	—	31	1	no	maximal, Sylow
38	C₂×C₃₁	—	2	2	no	—
39	C₂×C₃₁	—	8	1	no	—
40	C₂×C₃₁	#123	1	1	yes	characteristic
41	C₂×C₃₁	C₂×D₈	1	1	yes	characteristic
42	C₂×C₃₁	#137	1	1	yes	characteristic
43	#121	D₃₁	1	1	yes	characteristic
44	C₂×C₄⋊C₄	—	31	1	no	—
45	#107	—	31	2	no	—
46	#102	—	31	2	no	—
47	C₂²⋊C₈	—	31	1	no	—
48	C₃₁	#480	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₄	—	2	1	no	—
50	C₂×D₄	C₂×D₃₁	1	1	yes	characteristic
51	C₂²×C₄	—	62	1	no	—
52	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
53	C₂×C₈	—	31	2	no	—
54	C₄⋊C₄	—	31	2	no	—
55	C₄⋊C₄	—	62	1	no	—
56	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
57	C₂²⋊C₄	—	2	1	no	—
58	C₂³	—	2	1	no	—
59	C₂³	C₂²⋊D₃₁	1	1	yes	characteristic
60	D₄	—	2	2	no	—
61	D₄	—	4	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	62	2	no	—
65	C₂×C₄	—	124	2	no	—
66	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
67	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
68	C₈	—	62	2	no	—
69	C₂²	—	2	1	no	—
70	C₂²	—	2	1	no	—
71	C₂²	—	4	1	no	—
72	C₂²	—	4	1	no	—
73	C₂²	—	4	1	no	—
74	C₂²	#92479	1	2	yes	—
75	C₂²	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	124	2	no	—
79	C₄	#92497	1	2	yes	—
80	C₂	—	2	2	no	—
81	C₂	—	8	1	no	—
82	C₂	C₂×#92479	1	1	yes	characteristic
83	C₂	#11758512	1	1	yes	characteristic
84	C₂	#11758528	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting, prime radical	C₃₁×#121	C₂
socle	C₂²×C₃₁	C₂×D₄
hypercenter	#121	D₃₁
hypocenter	C₃₁	#480
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #121

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊Dic₃₁	C₂	semidirect
3. #11758420	C₂	semidirect
4. C₂²⋊(C₃₁⋊C₈)	C₂	semidirect
5. #11758395	C₂	semidirect
48. C₃₁	#480	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#121	2
C₂×C₄⋊Dic₃₁	2
#11758420	2
C₂²⋊(C₃₁⋊C₈)	2
#11758395	2
#480	31