Subgroups — #14521205

Order 1984.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#92482	C₂	1	2	yes	maximal, complemented
3	#11758501	C₂	1	1	yes	maximal, characteristic
4	#11758423	C₂	1	2	yes	maximal, complemented
5	C₂²⋊(C₃₁⋊C₈)	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₃₁	—	2	4	no	—
7	C₂×Q₈×C₃₁	—	2	1	no	—
8	C₂×Q₈×C₃₁	C₂²	1	2	yes	—
9	C₂²×C₄×C₃₁	—	2	1	no	—
10	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₆₂	C₂²	1	1	yes	characteristic
12	C₂²⋊Dic₃₁	—	2	1	no	—
13	#92482	—	2	4	no	—
14	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
15	Dic₃₁⋊C₄	—	2	1	no	—
16	C₂×C₃₁⋊C₈	C₂²	1	2	yes	—
17	C₂³×C₃₁	D₄	1	1	yes	characteristic
18	Q₈×C₃₁	—	2	4	no	—
19	Q₈×C₃₁	—	2	2	no	—
20	Q₈×C₃₁	D₄	1	4	yes	—
21	C₂×C₄×C₃₁	—	2	4	no	—
22	C₂×C₄×C₃₁	—	2	2	no	—
23	C₂×C₄×C₃₁	—	2	2	no	—
24	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
25	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
26	C₂×Dic₃₁	—	2	1	no	—
27	C₂×Dic₃₁	—	2	1	no	—
28	Dic₆₂	—	2	2	no	—
29	C₃₁⋊C₈	—	2	2	no	—
30	C₂²×C₃₁	—	2	1	no	—
31	C₂²×C₃₁	—	2	1	no	—
32	C₂²×C₃₁	Q₁₆	1	2	yes	complemented
33	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
34	C₄×C₃₁	—	2	4	no	—
35	C₄×C₃₁	—	2	1	no	—
36	C₄×C₃₁	C₂×D₄	1	2	yes	—
37	Dic₃₁	—	4	1	no	—
38	Dic₃₁	—	4	1	no	—
39	#451	—	31	1	no	maximal, Sylow
40	C₂×C₃₁	—	2	2	no	—
41	C₂×C₃₁	#120	1	1	yes	characteristic
42	C₂×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
43	C₂×C₃₁	#137	1	1	yes	characteristic
44	C₂²×Q₈	D₃₁	1	1	yes	characteristic
45	C₂×Q₁₆	—	31	2	no	—
46	C₂²⋊Q₈	—	31	1	no	—
47	#103	—	31	2	no	—
48	C₂²⋊C₈	—	31	1	no	—
49	C₃₁	#451	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₈	—	2	4	no	—
51	C₂×Q₈	—	2	1	no	—
52	C₂×Q₈	—	31	1	no	—
53	C₂×Q₈	C₂×D₃₁	1	2	yes	—
54	C₂²×C₄	—	2	1	no	—
55	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
56	Q₁₆	—	62	4	no	—
57	C₂×C₈	—	31	2	no	—
58	C₄⋊C₄	—	31	1	no	—
59	C₄⋊C₄	—	62	1	no	—
60	C₂²⋊C₄	—	62	1	no	—
61	C₂³	C₂²⋊D₃₁	1	1	yes	characteristic
62	Q₈	—	2	4	no	—
63	Q₈	—	2	2	no	—
64	Q₈	—	62	2	no	—
65	Q₈	C₂²⋊D₃₁	1	4	yes	—
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	2	2	no	—
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	—	62	1	no	—
70	C₂×C₄	—	62	1	no	—
71	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
72	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
73	C₈	—	62	2	no	—
74	C₂²	—	2	1	no	—
75	C₂²	—	2	1	no	—
76	C₂²	#92482	1	2	yes	complemented
77	C₂²	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
78	C₄	—	2	4	no	—
79	C₄	—	2	1	no	—
80	C₄	—	124	1	no	—
81	C₄	—	124	1	no	—
82	C₄	C₂×C₂²⋊D₃₁	1	2	yes	—
83	C₂	—	2	2	no	—
84	C₂	#11758519	1	1	yes	characteristic
85	C₂	C₂×#92482	1	1	yes	characteristic
86	C₂	#11758530	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₂²×Q₈×C₃₁	C₂
socle	C₂²×C₃₁	C₂×D₄
prime radical	C₂³×C₃₁	D₄
hypercenter	C₂²×Q₈	D₃₁
hypocenter	C₃₁	#451
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×#92482	C₂	semidirect
4. #11758423	C₂	semidirect
32. C₂²×C₃₁	Q₁₆	semidirect
49. C₃₁	#451	semidirect
76. C₂²	#92482	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Q₈×C₃₁	2
C₂×#92482	2
#11758501	2
#11758423	2
C₂²⋊(C₃₁⋊C₈)	2
#451	31