Group #14521776 — subgroups

Subgroups — #14521776

Order 1984.

200 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 105 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	C₃₁×#125	C₂	1	1	yes	maximal, characteristic
2	#11758467	C₂	1	1	yes	maximal, characteristic
3	#11758466	C₂	1	2	yes	maximal
4	#11758466	C₂	1	2	yes	maximal
5	#11758465	C₂	1	1	yes	maximal, characteristic
6	#11758465	C₂	1	2	yes	maximal
7	#11758464	C₂	1	1	yes	maximal, characteristic
8	#11758464	C₂	1	2	yes	maximal
9	#11758464	C₂	1	1	yes	maximal, characteristic
10	C₄×Dic₆₂	C₂	1	1	yes	maximal, characteristic
11	C₄×Dic₆₂	C₂	1	1	yes	maximal, characteristic
12	C₂×Dic₆₂	C₂²	1	1	yes	characteristic
13	C₂×Dic₆₂	C₂²	1	2	yes	—
14	C₂×Dic₆₂	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
16	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
17	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
19	C₄²×C₃₁	C₂²	1	1	yes	characteristic
20	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
21	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
22	C₄⋊Dic₃₁	C₂²	1	2	yes	—
23	Dic₃₁⋊C₄	C₂²	1	1	yes	characteristic
24	Dic₃₁⋊C₄	C₂²	1	2	yes	—
25	Dic₃₁⋊C₄	C₂²	1	1	yes	characteristic
26	Dic₃₁⋊C₄	C₂²	1	2	yes	—
27	Dic₃₁⋊C₄	C₂²	1	2	yes	—
28	Dic₃₁⋊C₄	C₂²	1	2	yes	—
29	Dic₃₁⋊C₄	C₂²	1	2	yes	—
30	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
31	C₄×Dic₃₁	C₂²	1	2	yes	—
32	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
33	C₄×Dic₃₁	C₂²	1	2	yes	—
34	C₄×Dic₃₁	C₂²	1	2	yes	—
35	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
36	C₂×C₄×C₃₁	C₂³	1	2	yes	—
37	C₂×C₄×C₃₁	C₂³	1	2	yes	—
38	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
39	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
40	C₂×Dic₃₁	C₂³	1	1	yes	characteristic
41	C₂×Dic₃₁	C₂³	1	1	yes	characteristic
42	C₂×Dic₃₁	C₂³	1	2	yes	—
43	C₂×Dic₃₁	C₂³	1	1	yes	characteristic
44	C₂×Dic₃₁	C₂³	1	2	yes	—
45	C₂×Dic₃₁	C₂³	1	1	yes	characteristic
46	Dic₆₂	—	2	2	no	—
47	Dic₆₂	—	2	4	no	—
48	Dic₆₂	Q₈	1	4	yes	complemented
49	C₂²×C₃₁	C₂⁴	1	1	yes	characteristic
50	C₄×C₃₁	—	2	2	no	—
51	C₄×C₃₁	—	2	1	no	—
52	C₄×C₃₁	—	2	1	no	—
53	C₄×C₃₁	—	2	2	no	—
54	C₄×C₃₁	C₂×Q₈	1	2	yes	—
55	Dic₃₁	—	2	1	no	—
56	Dic₃₁	—	2	2	no	—
57	Dic₃₁	—	2	1	no	—
58	Dic₃₁	—	2	1	no	—
59	Dic₃₁	C₂×Q₈	1	4	yes	—
60	Dic₃₁	#41	1	2	yes	—
61	#557	—	31	1	no	maximal, Sylow
62	C₂×C₃₁	C₂²×Q₈	1	1	yes	characteristic
63	C₂×C₃₁	C₂×#41	1	1	yes	characteristic
64	C₂×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
65	C₄⋊Q₈	—	31	2	no	—
66	C₄⋊Q₈	—	31	1	no	—
67	#125	—	31	2	no	—
68	#125	—	31	2	no	—
69	#125	—	31	1	no	—
70	#125	D₃₁	1	1	yes	characteristic
71	C₄×Q₈	—	31	1	no	—
72	C₄×Q₈	—	31	2	no	—
73	C₄×Q₈	—	31	1	no	—
74	C₄×Q₈	—	31	1	no	—
75	C₄×Q₈	—	31	1	no	—
76	C₃₁	#557	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₈	—	31	1	no	—
78	C₂×Q₈	—	31	2	no	—
79	C₂×Q₈	—	31	1	no	—
80	C₄⋊C₄	—	31	1	no	—
81	C₄⋊C₄	—	31	2	no	—
82	C₄⋊C₄	—	31	2	no	—
83	C₄⋊C₄	—	31	1	no	—
84	C₄⋊C₄	—	31	2	no	—
85	C₄⋊C₄	—	31	2	no	—
86	C₄⋊C₄	—	31	2	no	—
87	C₄⋊C₄	—	31	1	no	—
88	C₄⋊C₄	—	31	1	no	—
89	C₄⋊C₄	—	31	2	no	—
90	C₄⋊C₄	C₂×D₃₁	1	2	yes	—
91	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
92	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
93	C₄⋊C₄	C₂×D₃₁	1	2	yes	—
94	C₄²	—	31	2	no	—
95	C₄²	—	31	2	no	—
96	C₄²	—	31	1	no	—
97	C₄²	—	31	2	no	—
98	C₄²	—	31	1	no	—
99	C₄²	C₂×D₃₁	1	1	yes	characteristic
100	Q₈	—	31	4	no	—
101	Q₈	—	62	4	no	—
102	Q₈	—	62	2	no	—
103	C₂×C₄	—	31	2	no	—
104	C₂×C₄	—	31	1	no	—
105	C₂×C₄	—	31	1	no	—
106	C₂×C₄	—	31	1	no	—
107	C₂×C₄	—	31	1	no	—
108	C₂×C₄	—	31	2	no	—
109	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
110	C₂×C₄	C₂²×D₃₁	1	2	yes	—
111	C₂×C₄	C₂²×D₃₁	1	2	yes	—
112	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
113	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
114	C₂²	C₂³×D₃₁	1	1	yes	characteristic
115	C₄	—	2	2	no	—
116	C₄	—	2	1	no	—
117	C₄	—	2	1	no	—
118	C₄	—	2	2	no	—
119	C₄	—	31	4	no	—
120	C₄	—	31	2	no	—
121	C₄	—	62	1	no	—
122	C₄	—	62	2	no	—
123	C₄	—	62	1	no	—
124	C₄	—	62	1	no	—
125	C₄	Q₈×D₃₁	1	2	yes	—
126	C₂	C₂×Q₈×D₃₁	1	1	yes	characteristic
127	C₂	#41×D₃₁	1	1	yes	characteristic
128	C₂	#11758567	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃₁×#125

C₂

yes

maximal, characteristic

#11758467

C₂

yes

maximal, characteristic

#11758466

C₂

yes

maximal

#11758466

C₂

yes

maximal

#11758465

C₂

yes

maximal, characteristic

#11758465

C₂

yes

maximal

#11758464

C₂

yes

maximal, characteristic

#11758464

C₂

yes

maximal

#11758464

C₂

yes

maximal, characteristic

C₄×Dic₆₂

C₂

yes

maximal, characteristic

C₄×Dic₆₂

C₂

yes

maximal, characteristic

C₂×Dic₆₂

C₂²

yes

characteristic

C₂×Dic₆₂

C₂²

yes

—

C₂×Dic₆₂

C₂²

yes

characteristic

C₄⋊C₄×C₃₁

C₂²

yes

characteristic

C₄⋊C₄×C₃₁

C₂²

yes

—

C₄⋊C₄×C₃₁

C₂²

yes

characteristic

C₄⋊C₄×C₃₁

C₂²

yes

—

C₄²×C₃₁

C₂²

yes

characteristic

C₄⋊Dic₃₁

C₂²

yes

characteristic

C₄⋊Dic₃₁

C₂²

yes

characteristic

C₄⋊Dic₃₁

C₂²

yes

—

Dic₃₁⋊C₄

C₂²

yes

characteristic

Dic₃₁⋊C₄

C₂²

yes

—

Dic₃₁⋊C₄

C₂²

yes

characteristic

Dic₃₁⋊C₄

C₂²

yes

—

Dic₃₁⋊C₄

C₂²

yes

—

Dic₃₁⋊C₄

C₂²

yes

—

Dic₃₁⋊C₄

C₂²

yes

—

C₄×Dic₃₁

C₂²

yes

characteristic

C₄×Dic₃₁

C₂²

yes

—

C₄×Dic₃₁

C₂²

yes

characteristic

C₄×Dic₃₁

C₂²

yes

—

C₄×Dic₃₁

C₂²

yes

—

C₂×C₄×C₃₁

C₂³

yes

characteristic

C₂×C₄×C₃₁

C₂³

yes

—

C₂×C₄×C₃₁

C₂³

yes

—

C₂×C₄×C₃₁

C₂³

yes

characteristic

C₂×C₄×C₃₁

C₂³

yes

characteristic

C₂×Dic₃₁

C₂³

yes

characteristic

C₂×Dic₃₁

C₂³

yes

characteristic

C₂×Dic₃₁

C₂³

yes

—

C₂×Dic₃₁

C₂³

yes

characteristic

C₂×Dic₃₁

C₂³

yes

—

C₂×Dic₃₁

C₂³

yes

characteristic

Dic₆₂

—

Dic₆₂

—

Dic₆₂

Q₈

yes

complemented

C₂²×C₃₁

C₂⁴

yes

characteristic

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

—

C₄×C₃₁

C₂×Q₈

yes

—

Dic₃₁

—

Dic₃₁

—

Dic₃₁

—

Dic₃₁

—

Dic₃₁

C₂×Q₈

yes

—

Dic₃₁

#41

yes

—

#557

—

maximal, Sylow

C₂×C₃₁

C₂²×Q₈

yes

characteristic

C₂×C₃₁

C₂×#41

yes

characteristic

C₂×C₃₁

2₋¹⁺⁴

yes

characteristic

C₄⋊Q₈

—

C₄⋊Q₈

—

—

—

—

D₃₁

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₃₁

#557

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×D₃₁

yes

—

C₄⋊C₄

C₂×D₃₁

yes

characteristic

C₄⋊C₄

C₂×D₃₁

yes

characteristic

C₄⋊C₄

C₂×D₃₁

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×D₃₁

yes

characteristic

100

Q₈

—

101

Q₈

—

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₂²×D₃₁

yes

characteristic

110

C₂×C₄

C₂²×D₃₁

yes

—

111

C₂×C₄

C₂²×D₃₁

yes

—

112

C₂×C₄

C₂²×D₃₁

yes

characteristic

113

C₂×C₄

C₂²×D₃₁

yes

characteristic

114

C₂²

C₂³×D₃₁

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

Q₈×D₃₁

yes

—

126

C₂

C₂×Q₈×D₃₁

yes

characteristic

127

C₂

#41×D₃₁

yes

characteristic

128

C₂

#11758567

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃₁
commutator, socle, prime radical, cosocle	C₂²×C₃₁	C₂⁴
Fitting	C₃₁×#125	C₂
hypercenter	#125	D₃₁
hypocenter	C₃₁	#557
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ #125

subgroup

G/H

center, Frattini

C₂²

C₂³×D₃₁

commutator, socle, prime radical, cosocle

C₂²×C₃₁

C₂⁴

Fitting

C₃₁×#125

C₂

D₃₁

C₃₁

G ▷ C₂²×C₃₁ ▷ C₃₁

C₁ ◁ C₂² ◁ #125

N	H ≅ G/N	type
48. Dic₆₂	Q₈	semidirect
76. C₃₁	#557	semidirect

H ≅ G/N

type

48. Dic₆₂

Q₈

semidirect

76. C₃₁

#557

semidirect

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

subgroup	index
C₃₁×#125	2
#11758467	2
#11758466	2
#11758465	2
#11758464	2
C₄×Dic₆₂	2
#557	31

subgroup

index

C₃₁×#125

C₄×Dic₆₂

Subgroups — #14521776

Conjugacy classes of subgroups

Complements

Maximal subgroups