Subgroups — #14521234

Order 1984.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758564	C₂	1	1	yes	maximal, characteristic
2	#11758521	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758486	C₂	1	2	yes	maximal, complemented
4	C₃₁×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	#11758413	C₂	1	2	yes	maximal, complemented
6	C₂×Q₈×C₃₁	C₂²	1	1	yes	characteristic
7	#92499	—	2	2	no	—
8	Q₈×D₃₁	—	2	2	no	—
9	#92495	—	2	2	no	—
10	#92495	C₂²	1	2	yes	—
11	C₂×Dic₆₂	C₂²	1	1	yes	characteristic
12	M₁₆×C₃₁	C₂²	1	2	yes	—
13	Dic₃₁⋊C₄	—	2	2	no	—
14	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
15	Dic₁₂₄	—	2	2	no	—
16	#92470	—	2	2	no	—
17	Q₈×C₃₁	—	2	2	no	—
18	C₂×C₄×C₃₁	D₄	1	2	yes	—
19	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
20	C₂²⋊D₃₁	—	2	2	no	—
21	C₂×Dic₃₁	—	2	1	no	—
22	C₂×Dic₃₁	—	2	1	no	—
23	D₁₂₄	—	2	2	no	—
24	D₁₂₄	D₄	1	2	yes	—
25	C₄×D₃₁	—	2	4	no	—
26	C₄×D₃₁	—	2	2	no	—
27	Dic₆₂	—	2	2	no	—
28	Dic₆₂	—	2	2	no	—
29	Dic₆₂	D₄	1	2	yes	—
30	C₈×C₃₁	—	2	2	no	—
31	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
32	C₂×D₃₁	—	2	2	no	—
33	C₄×C₃₁	—	2	2	no	—
34	C₄×C₃₁	C₂×D₄	1	2	yes	—
35	Dic₃₁	—	2	2	no	—
36	Dic₃₁	—	2	2	no	—
37	Dic₃₁	—	4	1	no	—
38	#456	—	31	1	no	maximal, Sylow
39	C₂×C₃₁	—	2	1	no	—
40	C₂×C₃₁	#120	1	1	yes	characteristic
41	D₃₁	—	4	2	no	—
42	2₋¹⁺⁴	—	31	1	no	—
43	#137	—	31	2	no	—
44	C₄⋊Q₈	—	31	1	no	—
45	#104	—	31	2	no	—
46	#101	D₃₁	1	1	yes	characteristic, complemented
47	C₃₁	#456	1	1	yes	characteristic, complemented, Sylow
48	#41	—	31	2	no	—
49	#41	—	62	2	no	—
50	#41	—	62	2	no	—
51	C₂×Q₈	—	31	1	no	—
52	C₂×Q₈	—	62	2	no	—
53	C₂×Q₈	C₂×D₃₁	1	1	yes	characteristic
54	Q₁₆	—	62	2	no	—
55	SD₁₆	—	62	2	no	—
56	M₁₆	C₂×D₃₁	1	2	yes	—
57	C₄⋊C₄	—	62	2	no	—
58	C₄²	—	31	1	no	—
59	Q₈	—	2	2	no	—
60	Q₈	—	31	2	no	—
61	Q₈	—	62	2	no	—
62	Q₈	—	62	2	no	—
63	D₄	—	31	2	no	—
64	D₄	—	62	2	no	—
65	D₄	—	62	2	no	—
66	C₂×C₄	—	62	4	no	—
67	C₂×C₄	—	62	1	no	—
68	C₂×C₄	—	62	2	no	—
69	C₂×C₄	—	62	1	no	—
70	C₂×C₄	D₁₂₄	1	2	yes	—
71	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₂²	—	62	2	no	—
74	C₂²	C₂×D₁₂₄	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	62	2	no	—
77	C₄	—	62	2	no	—
78	C₄	—	124	1	no	—
79	C₄	D₄×D₃₁	1	2	yes	—
80	C₂	—	2	1	no	—
81	C₂	—	124	2	no	—
82	C₂	#11758459	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11758459
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#101	C₂
socle	C₂×C₃₁	#120
prime radical	#11758564	C₂
hypercenter	#101	D₃₁
hypocenter	C₃₁	#456
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

Complements

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

N	H ≅ G/N	type
2. #11758521	C₂	semidirect
3. #11758486	C₂	semidirect
4. C₃₁×#101	C₂	semidirect
5. #11758413	C₂	semidirect
46. #101	D₃₁	semidirect
47. C₃₁	#456	semidirect

Maximal subgroups

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

subgroup	index
#11758564	2
#11758521	2
#11758486	2
C₃₁×#101	2
#11758413	2
#456	31