Group #16853986 — subgroups

Subgroups — #16853986

Order 3968.

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14520983	C₂	1	4	yes	maximal
2	#14520982	C₂	1	4	yes	maximal
3	#14520981	C₂	1	4	yes	maximal
4	#14520915	C₂	1	2	yes	maximal
5	C₃₁×#382	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
7	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₃₁	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₃₁	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₃₁	C₂²	1	4	yes	—
11	C₂×Dic₃₁⋊C₄	C₂²	1	4	yes	—
12	C₂×Dic₃₁⋊C₄	C₂²	1	4	yes	—
13	C₃₁×#95	C₂²	1	4	yes	—
14	C₃₁⋊#95	C₂²	1	4	yes	—
15	C₃₁⋊#95	C₂²	1	4	yes	—
16	C₃₁⋊#95	C₂²	1	4	yes	—
17	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
18	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
20	C₂²×Dic₃₁	C₂³	1	4	yes	—
21	C₂²×Dic₃₁	C₂³	1	4	yes	—
22	C₄⋊C₄×C₃₁	—	4	2	no	—
23	C₄²×C₃₁	Q₈	1	4	yes	—
24	C₄⋊Dic₃₁	—	4	2	no	—
25	C₄⋊Dic₃₁	—	4	4	no	—
26	C₄⋊Dic₃₁	—	4	2	no	—
27	Dic₃₁⋊C₄	—	4	4	no	—
28	Dic₃₁⋊C₄	—	4	4	no	—
29	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₃₁	—	2	2	no	—
31	C₂×C₄×C₃₁	—	2	1	no	—
32	C₂×C₄×C₃₁	—	2	1	no	—
33	C₂×C₄×C₃₁	—	2	2	no	—
34	C₂×C₄×C₃₁	—	2	4	no	—
35	C₂×C₄×C₃₁	—	2	4	no	—
36	C₂×C₄×C₃₁	—	2	4	no	—
37	C₂×C₄×C₃₁	C₂×Q₈	1	2	yes	—
38	C₂×C₄×C₃₁	C₂×Q₈	1	4	yes	—
39	C₂×Dic₃₁	—	2	4	no	—
40	C₂×Dic₃₁	—	2	4	no	—
41	C₂×Dic₃₁	—	2	4	no	—
42	C₂×Dic₃₁	—	2	4	no	—
43	C₂×Dic₃₁	—	2	4	no	—
44	C₂×Dic₃₁	—	2	4	no	—
45	#2845	—	31	1	no	maximal, Sylow
46	C₂²×C₃₁	C₂²×Q₈	1	1	yes	characteristic
47	C₂²×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
48	C₂²×C₃₁	H(5,𝔽₂)	1	2	yes	—
49	C₂²×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
50	C₂²×C₃₁	2₋¹⁺⁴	1	2	yes	—
51	C₄×C₃₁	—	2	4	no	—
52	C₄×C₃₁	—	2	2	no	—
53	C₄×C₃₁	—	4	4	no	—
54	Dic₃₁	—	4	4	no	—
55	Dic₃₁	—	4	4	no	—
56	#398	—	31	4	no	—
57	#398	—	31	4	no	—
58	#398	—	31	4	no	—
59	#382	—	31	2	no	—
60	#382	D₃₁	1	1	yes	characteristic
61	C₂×C₃₁	#544	1	2	yes	—
62	C₂×C₃₁	#544	1	1	yes	characteristic
63	C₂×C₃₁	#562	1	2	yes	—
64	C₂×C₃₁	#562	1	1	yes	characteristic
65	C₂×C₃₁	#564	1	1	yes	characteristic
66	C₂×C₄⋊C₄	—	31	2	no	—
67	C₂×C₄⋊C₄	—	31	2	no	—
68	C₂×C₄⋊C₄	—	31	4	no	—
69	C₂×C₄⋊C₄	—	31	4	no	—
70	C₂×C₄⋊C₄	—	31	4	no	—
71	C₂×C₄⋊C₄	C₂×D₃₁	1	2	yes	—
72	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
73	#95	—	31	4	no	—
74	#95	—	31	4	no	—
75	#95	—	31	4	no	—
76	#95	C₂×D₃₁	1	4	yes	—
77	C₃₁	#2845	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₄	—	31	4	no	—
79	C₂²×C₄	—	31	4	no	—
80	C₂²×C₄	C₂²×D₃₁	1	4	yes	—
81	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
82	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
83	C₄⋊C₄	—	4	2	no	—
84	C₄⋊C₄	—	124	4	no	—
85	C₄⋊C₄	—	124	4	no	—
86	C₄⋊C₄	—	124	2	no	—
87	C₄⋊C₄	—	124	2	no	—
88	C₄⋊C₄	—	124	4	no	—
89	C₄²	Dic₆₂	1	4	yes	—
90	C₂³	C₂³×D₃₁	1	1	yes	characteristic
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	2	4	no	—
98	C₂×C₄	—	62	4	no	—
99	C₂×C₄	—	62	4	no	—
100	C₂×C₄	—	62	4	no	—
101	C₂×C₄	—	62	4	no	—
102	C₂×C₄	—	62	4	no	—
103	C₂×C₄	—	62	4	no	—
104	C₂×C₄	C₂×Dic₆₂	1	4	yes	—
105	C₂×C₄	C₂×Dic₆₂	1	2	yes	—
106	C₂²	C₂²×Dic₆₂	1	1	yes	characteristic
107	C₂²	#11758561	1	1	yes	characteristic
108	C₂²	#11758564	1	1	yes	characteristic
109	C₂²	#11758566	1	2	yes	—
110	C₂²	#11758567	1	2	yes	—
111	C₄	—	2	4	no	—
112	C₄	—	2	2	no	—
113	C₄	—	4	4	no	—
114	C₄	—	124	4	no	—
115	C₄	—	124	4	no	—
116	C₂	#14521677	1	2	yes	—
117	C₂	#14521680	1	1	yes	characteristic
118	C₂	#14521793	1	2	yes	—
119	C₂	#14521797	1	1	yes	characteristic
120	C₂	C₃₁⋊#564	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14520983

C₂

yes

maximal

#14520982

C₂

yes

maximal

#14520981

C₂

yes

maximal

#14520915

C₂

yes

maximal

C₃₁×#382

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₃₁

C₂²

yes

—

C₂×C₄²×C₃₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₃₁

C₂²

yes

—

C₂×C₄⋊Dic₃₁

C₂²

yes

—

C₂×C₄⋊Dic₃₁

C₂²

yes

—

C₂×Dic₃₁⋊C₄

C₂²

yes

—

C₂×Dic₃₁⋊C₄

C₂²

yes

—

C₃₁×#95

C₂²

yes

—

C₃₁⋊#95

C₂²

yes

—

C₃₁⋊#95

C₂²

yes

—

C₃₁⋊#95

C₂²

yes

—

C₂²×C₄×C₃₁

C₂³

yes

—

C₂²×C₄×C₃₁

C₂³

yes

characteristic

C₂²×C₄×C₃₁

C₂³

yes

—

C₂²×Dic₃₁

C₂³

yes

—

C₂²×Dic₃₁

C₂³

yes

—

C₄⋊C₄×C₃₁

—

C₄²×C₃₁

Q₈

yes

—

C₄⋊Dic₃₁

—

C₄⋊Dic₃₁

—

C₄⋊Dic₃₁

—

Dic₃₁⋊C₄

—

Dic₃₁⋊C₄

—

C₂³×C₃₁

C₂⁴

yes

characteristic

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

C₂×Q₈

yes

—

C₂×C₄×C₃₁

C₂×Q₈

yes

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

C₂×Dic₃₁

—

#2845

—

maximal, Sylow

C₂²×C₃₁

C₂²×Q₈

yes

C₂²×C₃₁

yes

C₂²×C₃₁

yes

—

C₂²×C₃₁

2₋¹⁺⁴

yes

characteristic

C₂²×C₃₁

2₋¹⁺⁴

yes

—

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

—

Dic₃₁

—

Dic₃₁

—

—

—

—

—

D₃₁

yes

characteristic

C₂×C₃₁

#544

yes

—

C₂×C₃₁

#544

yes

characteristic

C₂×C₃₁

#562

yes

—

C₂×C₃₁

yes

C₂×C₃₁

yes

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₃₁

yes

—

C₂×C₄²

C₂×D₃₁

yes

—

—

—

C₂×D₃₁

yes

—

C₃₁

#2845

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₃₁

yes

—

C₂²×C₄

C₂²×D₃₁

yes

characteristic

C₂²×C₄

C₂²×D₃₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

124

—

C₄⋊C₄

—

124

—

C₄⋊C₄

—

124

—

C₄⋊C₄

—

124

—

C₄⋊C₄

—

124

—

C₄²

Dic₆₂

yes

—

C₂³

C₂³×D₃₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂×Dic₆₂

yes

—

105

C₂×C₄

C₂×Dic₆₂

yes

—

106

C₂²

C₂²×Dic₆₂

yes

characteristic

107

C₂²

#11758561

yes

characteristic

108

C₂²

#11758564

yes

characteristic

109

C₂²

#11758566

yes

—

110

C₂²

#11758567

yes

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

124

—

115

C₄

—

124

—

116

C₂

#14521677

yes

—

117

C₂

#14521680

yes

characteristic

118

C₂

#14521793

yes

—

119

C₂

#14521797

yes

characteristic

120

C₂

C₃₁⋊#564

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃₁
commutator, socle, prime radical, cosocle	C₂³×C₃₁	C₂⁴
Fitting	C₃₁×#382	C₂
hypercenter	#382	D₃₁
hypocenter	C₃₁	#2845
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₃₁

commutator, socle, prime radical, cosocle

C₂³×C₃₁

C₂⁴

Fitting

C₃₁×#382

C₂

D₃₁

C₃₁

G ▷ C₂³×C₃₁ ▷ C₃₁

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
77. C₃₁	#2845	semidirect

H ≅ G/N

type

77. C₃₁

#2845

semidirect

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

subgroup	index
#14520983	2
#14520982	2
#14520981	2
#14520915	2
C₃₁×#382	2
#2845	31

subgroup

index

C₃₁×#382

Subgroups — #16853986

Conjugacy classes of subgroups

Complements

Maximal subgroups