Group #11777961 — subgroups

Subgroups — #11777961

Order 1152.

310 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 56 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	#10593752	C₂	1	2	yes	maximal, complemented
2	#10592571	C₂	1	1	yes	maximal, characteristic
3	#10590170	C₂	1	1	yes	maximal, characteristic, complemented
4	#10590168	C₂	1	1	yes	maximal, characteristic, complemented
5	#10590160	C₂	1	2	yes	maximal, complemented
6	C₂×#3788	—	2	2	no	—
7	C₂×#3745	C₄	1	1	yes	characteristic
8	#64102	C₂²	1	2	yes	—
9	#63778	—	2	2	no	—
10	C₄⋊#622	C₂²	1	2	yes	—
11	C₄×#622	C₂²	1	1	yes	characteristic
12	C₄×#622	C₂²	1	1	yes	characteristic
13	C₃²×#107	C₄	1	1	yes	characteristic
14	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
15	#63636	C₄	1	2	yes	—
16	#4872	—	6	2	no	—
17	C₂×C₄⋊(C₃⋊D₃)	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₃⋊D₃	—	2	2	no	—
19	C₂×#622	—	2	2	no	—
20	C₂×#622	—	2	1	no	—
21	C₂×#622	D₄	1	2	yes	—
22	#3788	—	4	4	no	—
23	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
24	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
25	#3752	—	2	2	no	—
26	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
27	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
28	#3745	—	2	2	no	—
29	#1594	—	9	1	no	maximal, Sylow
30	C₂×D₂₄	—	6	2	no	—
31	#893	—	6	4	no	—
32	C₃×#107	—	2	2	no	—
33	C₈×Dic₃	—	6	2	no	—
34	#809	—	6	4	no	—
35	C₂²×C₃⋊D₃	—	2	2	no	—
36	C₂×C₃²×C₄	—	2	2	no	—
37	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₃⋊Dic₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₃⋊Dic₃	#41	1	1	yes	characteristic
40	C₄⋊(C₃⋊D₃)	—	2	2	no	—
41	C₄⋊(C₃⋊D₃)	—	2	2	no	—
42	C₄×C₃⋊D₃	—	4	2	no	—
43	C₄×C₃⋊D₃	—	4	2	no	—
44	#622	—	2	2	no	—
45	#622	—	4	1	no	—
46	#622	—	4	2	no	—
47	C₃²×C₈	M₁₆	1	2	yes	complemented
48	C₃⋊(C₃⋊C₈)	—	2	1	no	—
49	C₄×D₈	—	9	1	no	—
50	#436	—	9	2	no	—
51	#334	—	9	1	no	—
52	D₄⋊C₈	—	9	2	no	—
53	#322	—	9	1	no	—
54	C₂×D₁₂	—	6	4	no	—
55	C₂×C₄×D₃	—	12	4	no	—
56	C₂×C₃×C₈	—	2	2	no	—
57	C₃×C₄⋊C₄	—	2	4	no	—
58	(C₂×D₃)⋊C₄	—	12	4	no	—
59	C₄×Dic₃	—	6	2	no	—
60	C₂×C₃⋊C₈	—	6	2	no	—
61	D₂₄	—	6	8	no	—
62	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
63	C₂×C₃⋊D₃	—	4	2	no	—
64	C₂×C₃⋊D₃	—	4	2	no	—
65	C₂×C₃⋊D₃	—	4	2	no	—
66	C₃²×C₄	—	4	2	no	—
67	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
68	C₃²×C₄	#131	1	1	yes	characteristic
69	C₃⋊Dic₃	—	2	1	no	—
70	C₃⋊Dic₃	AGL(1,ℤ/8)	1	2	yes	—
71	C₂×D₈	—	9	1	no	—
72	C₂×M₁₆	—	18	2	no	—
73	C₄×D₄	—	9	2	no	—
74	#107	#157	1	1	yes	characteristic
75	C₄⋊C₈	—	9	2	no	—
76	#102	—	9	2	no	—
77	C₂²⋊C₈	—	18	2	no	—
78	C₄×C₈	—	9	1	no	—
79	C₄×C₈	—	9	1	no	—
80	C₄×C₈	—	9	1	no	—
81	C₂²×D₃	—	12	4	no	—
82	C₂×C₃×C₄	—	2	2	no	—
83	C₂×C₃×C₄	—	4	4	no	—
84	C₂×Dic₃	—	6	2	no	—
85	C₂×Dic₃	—	6	2	no	—
86	D₁₂	—	6	8	no	—
87	D₁₂	—	12	4	no	—
88	C₄×D₃	—	24	4	no	—
89	C₄×D₃	—	24	4	no	—
90	C₃×C₈	—	2	4	no	—
91	C₃⋊C₈	—	12	2	no	—
92	C₂×C₃²	#436	1	1	yes	characteristic
93	C₂×C₃²	#442	1	1	yes	characteristic
94	C₂×C₃²	#444	1	1	yes	characteristic
95	C₃⋊D₃	—	8	2	no	—
96	C₂×D₄	—	9	2	no	—
97	C₂²×C₄	—	18	2	no	—
98	D₈	—	18	2	no	—
99	M₁₆	—	36	4	no	—
100	C₂×C₈	—	9	2	no	—
101	C₂×C₈	—	9	1	no	—
102	C₂×C₈	—	18	1	no	—
103	C₂×C₈	—	18	2	no	—
104	C₂×C₈	C₂×#157	1	1	yes	characteristic
105	C₄⋊C₄	C₂×#157	1	2	yes	—
106	C₂²⋊C₄	—	18	2	no	—
107	C₄²	—	9	1	no	—
108	C₂²×C₃	—	2	2	no	—
109	C₂×D₃	—	12	8	no	—
110	C₂×D₃	—	24	4	no	—
111	C₂×D₃	—	24	4	no	—
112	C₃×C₄	—	2	2	no	—
113	C₃×C₄	—	2	2	no	—
114	C₃×C₄	—	8	4	no	—
115	Dic₃	—	6	4	no	—
116	Dic₃	—	12	2	no	—
117	C₃²	#1594	1	1	yes	characteristic, complemented, Sylow
118	C₂³	—	18	2	no	—
119	D₄	—	18	2	no	—
120	D₄	—	18	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	9	1	no	—
123	C₂×C₄	—	9	1	no	—
124	C₂×C₄	—	36	2	no	—
125	C₂×C₄	—	36	2	no	—
126	C₂×C₄	C₂²×#157	1	1	yes	characteristic
127	C₈	—	18	2	no	—
128	C₈	—	18	1	no	—
129	C₈	—	36	2	no	—
130	C₈	—	36	1	no	—
131	C₈	#3788	1	2	yes	complemented
132	C₂×C₃	—	2	2	no	—
133	C₂×C₃	—	2	2	no	—
134	C₂×C₃	—	2	2	no	—
135	D₃	—	24	8	no	—
136	C₂²	—	36	2	no	—
137	C₂²	—	36	2	no	—
138	C₂²	—	36	2	no	—
139	C₂²	D₄×#157	1	1	yes	characteristic
140	C₄	—	4	2	no	—
141	C₄	—	9	2	no	—
142	C₄	—	18	1	no	—
143	C₄	C₂×#3788	1	1	yes	characteristic
144	C₄	#64289	1	1	yes	characteristic
145	C₃	—	2	2	no	—
146	C₂	—	72	2	no	—
147	C₂	#10593752	1	1	yes	characteristic
148	C₂	#10593778	1	1	yes	characteristic
149	C₂	#10593788	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10593752

C₂

yes

maximal, complemented

#10592571

C₂

yes

maximal, characteristic

#10590170

C₂

yes

maximal, characteristic, complemented

#10590168

C₂

yes

maximal, characteristic, complemented

#10590160

C₂

yes

maximal, complemented

C₂×#3788

—

C₂×#3745

C₄

yes

characteristic

#64102

C₂²

yes

—

#63778

—

C₄⋊#622

C₂²

yes

—

C₄×#622

C₂²

yes

characteristic

C₄×#622

C₂²

yes

characteristic

C₃²×#107

C₄

yes

characteristic

C₈×C₃⋊Dic₃

C₂²

yes

characteristic

#63636

C₄

yes

—

#4872

—

C₂×C₄⋊(C₃⋊D₃)

C₂×C₄

yes

—

C₂×C₄×C₃⋊D₃

—

C₂×#622

—

C₂×#622

—

C₂×#622

D₄

yes

—

#3788

—

C₂×C₃²×C₈

C₂×C₄

yes

characteristic

C₃²×C₄⋊C₄

C₂×C₄

yes

—

#3752

—

C₄×C₃⋊Dic₃

C₂³

yes

characteristic

C₂×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

—

—

C₂×D₂₄

—

#893

—

C₃×#107

—

C₈×Dic₃

—

#809

—

C₂²×C₃⋊D₃

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₂²×C₄

yes

characteristic

C₂×C₃⋊Dic₃

C₂×D₄

yes

characteristic

C₂×C₃⋊Dic₃

#41

yes

characteristic

C₄⋊(C₃⋊D₃)

—

C₄⋊(C₃⋊D₃)

—

C₄×C₃⋊D₃

—

C₄×C₃⋊D₃

—

#622

—

#622

—

#622

—

C₃²×C₈

M₁₆

yes

complemented

C₃⋊(C₃⋊C₈)

—

C₄×D₈

—

#436

—

#334

—

D₄⋊C₈

—

#322

—

C₂×D₁₂

—

C₂×C₄×D₃

—

C₂×C₃×C₈

—

C₃×C₄⋊C₄

—

(C₂×D₃)⋊C₄

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

D₂₄

—

C₂²×C₃²

C₄×D₄

yes

characteristic

C₂×C₃⋊D₃

—

C₂×C₃⋊D₃

—

C₂×C₃⋊D₃

—

C₃²×C₄

—

C₃²×C₄

C₂×M₁₆

yes

characteristic

C₃²×C₄

#131

yes

characteristic

C₃⋊Dic₃

—

C₃⋊Dic₃

AGL(1,ℤ/8)

yes

—

C₂×D₈

—

C₂×M₁₆

—

C₄×D₄

—

#107

#157

yes

characteristic

C₄⋊C₈

—

#102

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×D₃

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×Dic₃

—

C₂×Dic₃

—

D₁₂

—

D₁₂

—

C₄×D₃

—

C₄×D₃

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₃²

yes

C₂×C₃²

yes

C₂×C₃²

yes

C₃⋊D₃

—

C₂×D₄

—

C₂²×C₄

—

D₈

—

M₁₆

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

C₂×#157

yes

characteristic

105

C₄⋊C₄

C₂×#157

yes

—

106

C₂²⋊C₄

—

107

C₄²

—

108

C₂²×C₃

—

109

C₂×D₃

—

110

C₂×D₃

—

111

C₂×D₃

—

112

C₃×C₄

—

113

C₃×C₄

—

114

C₃×C₄

—

115

Dic₃

—

116

Dic₃

—

117

C₃²

#1594

yes

characteristic, complemented, Sylow

118

C₂³

—

119

D₄

—

120

D₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

C₂²×#157

yes

characteristic

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

—

131

C₈

#3788

yes

complemented

132

C₂×C₃

—

133

C₂×C₃

—

134

C₂×C₃

—

135

D₃

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

D₄×#157

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

C₂×#3788

yes

characteristic

144

C₄

#64289

yes

characteristic

145

C₃

—

146

C₂

—

147

C₂

#10593752

yes

characteristic

148

C₂

#10593778

yes

characteristic

149

C₂

#10593788

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#157
commutator	C₂×C₃²×C₄	C₂²×C₄
Frattini	C₂×C₄	C₂²×#157
Fitting	C₃²×#107	C₄
socle	C₂²×C₃²	C₄×D₄
prime radical	C₂×#3745	C₄
cosocle	C₄×C₃⋊Dic₃	C₂³
hypercenter	#107	#157
hypocenter	C₃²	#1594
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

subgroup

G/H

center

C₂²

D₄×#157

commutator

C₂×C₃²×C₄

C₂²×C₄

Frattini

C₂×C₄

C₂²×#157

Fitting

C₃²×#107

C₄

socle

C₂²×C₃²

C₄×D₄

prime radical

C₂×#3745

C₄

cosocle

C₄×C₃⋊Dic₃

C₂³

C₃²

G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

N	H ≅ G/N	type
1. #10593752	C₂	semidirect
3. #10590170	C₂	semidirect
4. #10590168	C₂	semidirect
5. #10590160	C₂	semidirect
47. C₃²×C₈	M₁₆	semidirect
117. C₃²	#1594	semidirect
131. C₈	#3788	semidirect

H ≅ G/N

type

1. #10593752

C₂

semidirect

3. #10590170

C₂

semidirect

4. #10590168

C₂

semidirect

5. #10590160

C₂

semidirect

47. C₃²×C₈

M₁₆

semidirect

117. C₃²

#1594

semidirect

131. C₈

#3788

semidirect

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

subgroup	index
#10593752	2
#10592571	2
#10590170	2
#10590168	2
#10590160	2
#1594	9

subgroup

index

Subgroups — #11777961

Conjugacy classes of subgroups

Complements

Maximal subgroups