Subgroups — #14521105

Order 1984.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₃₁)⋊C₈	C₂	1	2	yes	maximal
4	#11758403	C₂	1	2	yes	maximal, complemented
5	C₄⋊(C₃₁⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₃₁	C₄	1	1	yes	characteristic
7	C₂×C₄×D₃₁	C₄	1	1	yes	characteristic
8	C₂×C₄×D₃₁	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₃₁	C₂²	1	2	yes	—
10	C₄²×C₃₁	C₂²	1	1	yes	characteristic
11	C₄×Dic₃₁	C₄	1	1	yes	characteristic
12	C₄×Dic₃₁	C₄	1	1	yes	characteristic
13	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₃₁⋊C₈	C₂²	1	2	yes	—
15	C₂²×D₃₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₃₁	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₃₁	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₃₁	C₂×C₄	1	1	yes	characteristic
22	C₄×D₃₁	—	2	2	no	—
23	C₄×D₃₁	—	2	2	no	—
24	C₄×D₃₁	—	2	1	no	—
25	C₄×D₃₁	—	2	1	no	—
26	C₈×C₃₁	—	2	2	no	—
27	C₃₁⋊C₈	—	2	2	no	—
28	C₂²×C₃₁	C₂²×C₄	1	1	yes	characteristic
29	C₂×D₃₁	—	2	1	no	—
30	C₂×D₃₁	—	2	1	no	—
31	C₂×D₃₁	M₁₆	1	2	yes	—
32	C₄×C₃₁	—	2	1	no	—
33	C₄×C₃₁	M₁₆	1	2	yes	—
34	C₄×C₃₁	#41	1	1	yes	characteristic
35	C₄×C₃₁	#41	1	1	yes	characteristic
36	Dic₃₁	—	2	1	no	—
37	Dic₃₁	—	2	1	no	—
38	Dic₃₁	—	2	1	no	—
39	#432	—	31	1	no	maximal, Sylow
40	C₂×C₃₁	#117	1	1	yes	characteristic
41	C₂×C₃₁	C₂×M₁₆	1	1	yes	characteristic
42	C₂×C₃₁	C₂×M₁₆	1	1	yes	characteristic
43	D₃₁	—	2	2	no	—
44	C₂×C₄²	—	31	1	no	—
45	C₄⋊C₈	—	31	1	no	—
46	C₄⋊C₈	D₃₁	1	1	yes	characteristic, complemented
47	C₂²⋊C₈	—	31	2	no	—
48	#97	—	31	2	no	—
49	C₃₁	#432	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	31	1	no	—
51	C₂²×C₄	—	31	1	no	—
52	C₂²×C₄	—	31	1	no	—
53	C₂×C₈	—	31	2	no	—
54	C₂×C₈	C₂×D₃₁	1	2	yes	—
55	C₄²	—	31	1	no	—
56	C₄²	—	31	1	no	—
57	C₄²	—	31	1	no	—
58	C₄²	C₂×D₃₁	1	1	yes	characteristic
59	C₂³	—	31	1	no	—
60	C₂×C₄	—	31	1	no	—
61	C₂×C₄	—	31	1	no	—
62	C₂×C₄	—	31	1	no	—
63	C₂×C₄	—	62	2	no	—
64	C₂×C₄	—	62	2	no	—
65	C₂×C₄	—	62	1	no	—
66	C₂×C₄	—	62	1	no	—
67	C₂×C₄	C₄×D₃₁	1	1	yes	characteristic
68	C₂×C₄	C₄×D₃₁	1	1	yes	characteristic
69	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₈	—	62	2	no	—
72	C₂²	—	31	2	no	—
73	C₂²	—	62	1	no	—
74	C₂²	—	62	1	no	—
75	C₂²	C₂×C₄×D₃₁	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	62	1	no	—
78	C₄	—	62	1	no	—
79	C₄	—	62	1	no	—
80	C₄	#92469	1	2	yes	—
81	C₄	#92497	1	1	yes	characteristic
82	C₄	#92499	1	1	yes	characteristic
83	C₂	—	62	2	no	—
84	C₂	#11758469	1	1	yes	characteristic
85	C₂	C₂×#92469	1	1	yes	characteristic
86	C₂	M₁₆×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃₁
commutator, socle	C₂²×C₃₁	C₂²×C₄
Fitting	C₃₁×C₄⋊C₈	C₂
prime radical	C₂²×D₃₁	C₂×C₄
cosocle	C₂×C₄×C₃₁	C₂³
hypercenter	C₄⋊C₈	D₃₁
hypocenter	C₃₁	#432
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₃₁×C₄⋊C₈	C₂	semidirect
4. #11758403	C₂	semidirect
5. C₄⋊(C₃₁⋊C₈)	C₂	semidirect
46. C₄⋊C₈	D₃₁	semidirect
49. C₃₁	#432	semidirect

Maximal subgroups

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

subgroup	index
C₄²×D₃₁	2
C₃₁×C₄⋊C₈	2
(C₂×D₃₁)⋊C₈	2
#11758403	2
C₄⋊(C₃₁⋊C₈)	2
#432	31