Group #11797025 — subgroups

Subgroups — #11797025

Order 1152.

290 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 76 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	C₂×#63765	C₂	1	1	yes	maximal, characteristic
2	C₂×#63764	C₂	1	1	yes	maximal, characteristic
3	#10592407	C₂	1	1	yes	maximal, characteristic
4	#10590177	C₂	1	2	yes	maximal, complemented
5	C₄⋊#3708	C₂	1	2	yes	maximal, complemented
6	C₂×#3743	C₄	1	1	yes	characteristic
7	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
8	#64081	C₄	1	1	yes	characteristic
9	C₂×#3708	C₂²	1	2	yes	—
10	C₂×#3708	C₂²	1	2	yes	—
11	#63765	—	2	2	no	—
12	#63764	—	2	2	no	—
13	C₃²×#97	C₄	1	1	yes	characteristic
14	#63642	C₄	1	1	yes	characteristic
15	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
16	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
17	#4708	—	6	2	no	—
18	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
20	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
21	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
22	#3752	C₈	1	2	yes	—
23	#3750	C₈	1	2	yes	—
24	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
26	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
27	#3743	—	2	2	no	—
28	C₈×C₃⋊D₃	D₄	1	2	yes	—
29	C₈×C₃⋊D₃	Q₈	1	2	yes	—
30	#3708	—	2	2	no	—
31	#3708	—	2	2	no	—
32	#2151	—	9	1	no	maximal, Sylow
33	C₂×ΓL(1,𝔽₂₅)	—	6	2	no	—
34	C₂×D₃×C₈	—	6	2	no	—
35	#872	—	6	2	no	—
36	C₃×#97	—	2	2	no	—
37	#815	—	6	2	no	—
38	C₈×Dic₃	—	6	2	no	—
39	C₄×C₃⋊C₈	—	6	2	no	—
40	C₂²×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
41	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
42	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₃⋊Dic₃	C₂×C₈	1	2	yes	—
44	C₂×C₃⋊Dic₃	C₂×C₈	1	1	yes	characteristic
45	C₄×C₃⋊D₃	C₄⋊C₄	1	2	yes	—
46	C₄×C₃⋊D₃	M₁₆	1	2	yes	—
47	C₃²×C₈	—	2	1	no	—
48	C₃²×C₈	C₄⋊C₄	1	2	yes	—
49	C₃⋊(C₃⋊C₈)	—	2	1	no	—
50	C₃⋊(C₃⋊C₈)	C₂×D₄	1	1	yes	characteristic
51	C₃⋊(C₃⋊C₈)	C₂×Q₈	1	1	yes	characteristic
52	C₂×M₃₂	—	9	1	no	—
53	C₂²×C₁₆	—	9	1	no	—
54	#405	—	9	1	no	—
55	C₄⋊C₁₆	—	9	2	no	—
56	C₄⋊C₁₆	—	9	2	no	—
57	C₂×C₄×D₃	—	6	2	no	—
58	C₂×C₃×C₈	—	2	2	no	—
59	C₂×C₃×C₈	—	2	2	no	—
60	C₃×C₄²	—	2	2	no	—
61	(C₂×D₃)⋊C₄	—	6	4	no	—
62	Dic₃⋊C₄	—	6	4	no	—
63	C₄×Dic₃	—	6	2	no	—
64	C₂×C₃⋊C₈	—	6	2	no	—
65	C₂×C₃⋊C₈	—	6	2	no	—
66	ΓL(1,𝔽₂₅)	—	6	8	no	—
67	D₃×C₈	—	6	4	no	—
68	D₃×C₈	—	6	4	no	—
69	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
70	C₂×C₃⋊D₃	—	2	2	no	—
71	C₂×C₃⋊D₃	C₄⋊C₈	1	2	yes	—
72	C₃²×C₄	—	2	2	no	—
73	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
74	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
75	C₃⋊Dic₃	—	2	2	no	—
76	C₃⋊Dic₃	C₄⋊C₈	1	2	yes	—
77	C₂×M₁₆	—	9	1	no	—
78	C₂²×C₈	—	9	1	no	—
79	#117	—	9	1	no	—
80	M₃₂	—	18	2	no	—
81	C₂×C₁₆	—	9	2	no	—
82	C₂×C₁₆	—	9	2	no	—
83	C₂×C₁₆	—	18	2	no	—
84	#97	—	9	1	no	—
85	#97	#157	1	1	yes	characteristic
86	C₄×C₈	—	9	1	no	—
87	C₄×C₈	—	9	1	no	—
88	C₂²×D₃	—	6	2	no	—
89	C₂×C₃×C₄	—	2	2	no	—
90	C₂×C₃×C₄	—	2	4	no	—
91	C₂×Dic₃	—	6	2	no	—
92	C₂×Dic₃	—	6	4	no	—
93	C₄×D₃	—	6	4	no	—
94	C₄×D₃	—	6	4	no	—
95	C₃×C₈	—	2	4	no	—
96	C₃×C₈	—	2	4	no	—
97	C₃⋊C₈	—	6	2	no	—
98	C₃⋊C₈	—	6	2	no	—
99	C₃⋊C₈	—	6	4	no	—
100	C₂×C₃²	C₂×C₄⋊C₈	1	1	yes	characteristic
101	C₂×C₃²	#504	1	2	yes	—
102	C₃⋊D₃	—	2	2	no	—
103	C₂²×C₄	—	9	1	no	—
104	M₁₆	—	18	2	no	—
105	C₂×C₈	—	9	1	no	—
106	C₂×C₈	—	9	2	no	—
107	C₂×C₈	—	9	2	no	—
108	C₂×C₈	—	9	1	no	—
109	C₂×C₈	C₂×#157	1	1	yes	characteristic
110	C₂×C₈	C₂×#157	1	1	yes	characteristic
111	C₄⋊C₄	—	9	2	no	—
112	C₂²⋊C₄	—	9	2	no	—
113	C₄²	—	9	1	no	—
114	C₄²	C₂×#157	1	1	yes	characteristic
115	C₁₆	—	18	2	no	—
116	C₁₆	—	18	2	no	—
117	C₂²×C₃	—	2	2	no	—
118	C₂×D₃	—	6	4	no	—
119	C₂×D₃	—	12	4	no	—
120	C₃×C₄	—	2	2	no	—
121	C₃×C₄	—	2	2	no	—
122	C₃×C₄	—	4	4	no	—
123	Dic₃	—	6	4	no	—
124	Dic₃	—	12	4	no	—
125	C₃²	#2151	1	1	yes	characteristic, complemented, Sylow
126	C₂³	—	9	1	no	—
127	C₂×C₄	—	9	1	no	—
128	C₂×C₄	—	9	2	no	—
129	C₂×C₄	—	9	2	no	—
130	C₂×C₄	—	9	2	no	—
131	C₂×C₄	#3787	1	2	yes	—
132	C₂×C₄	C₂²×#157	1	1	yes	characteristic
133	C₈	—	2	1	no	—
134	C₈	—	9	1	no	—
135	C₈	—	9	1	no	—
136	C₈	—	18	1	no	—
137	C₈	C₄⋊#157	1	2	yes	—
138	C₂×C₃	—	2	2	no	—
139	C₂×C₃	—	2	4	no	—
140	D₃	—	12	4	no	—
141	C₂²	—	9	2	no	—
142	C₂²	—	18	2	no	—
143	C₂²	C₂×#3787	1	1	yes	characteristic
144	C₄	—	2	2	no	—
145	C₄	—	9	2	no	—
146	C₄	—	18	2	no	—
147	C₄	#64283	1	1	yes	characteristic
148	C₄	C₂×C₄⋊#157	1	1	yes	characteristic
149	C₃	—	2	2	no	—
150	C₂	—	18	2	no	—
151	C₂	#10593726	1	1	yes	characteristic
152	C₂	#10593772	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#63765

C₂

yes

maximal, characteristic

C₂×#63764

C₂

yes

maximal, characteristic

#10592407

C₂

yes

maximal, characteristic

#10590177

C₂

yes

maximal, complemented

C₄⋊#3708

C₂

yes

maximal, complemented

C₂×#3743

C₄

yes

characteristic

C₂×C₈×C₃⋊D₃

C₂²

yes

characteristic

#64081

C₄

yes

characteristic

C₂×#3708

C₂²

yes

—

C₂×#3708

C₂²

yes

—

#63765

—

#63764

—

C₃²×#97

C₄

yes

characteristic

#63642

C₄

yes

characteristic

C₈×C₃⋊Dic₃

C₂²

yes

characteristic

C₄×C₃⋊(C₃⋊C₈)

C₂²

yes

characteristic

#4708

—

C₂×C₄×C₃⋊D₃

C₂×C₄

yes

characteristic

C₂×C₃²×C₈

C₂×C₄

yes

characteristic

C₂×C₃²×C₈

C₂×C₄

yes

characteristic

C₃²×C₄²

C₂×C₄

yes

characteristic

#3752

C₈

yes

—

#3750

C₈

yes

—

C₄×C₃⋊Dic₃

C₂×C₄

yes

characteristic

C₂×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

characteristic

C₂×C₃⋊(C₃⋊C₈)

C₂³

yes

characteristic

#3743

—

C₈×C₃⋊D₃

D₄

yes

—

C₈×C₃⋊D₃

Q₈

yes

—

—

—

—

C₂×ΓL(1,𝔽₂₅)

—

C₂×D₃×C₈

—

#872

—

C₃×#97

—

#815

—

C₈×Dic₃

—

C₄×C₃⋊C₈

—

C₂²×C₃⋊D₃

C₂×C₈

yes

characteristic

C₂×C₃²×C₄

C₂×C₈

yes

—

C₂×C₃²×C₄

C₂²×C₄

yes

characteristic

C₂×C₃⋊Dic₃

C₂×C₈

yes

—

C₂×C₃⋊Dic₃

C₂×C₈

yes

characteristic

C₄×C₃⋊D₃

C₄⋊C₄

yes

—

C₄×C₃⋊D₃

M₁₆

yes

—

C₃²×C₈

—

C₃²×C₈

C₄⋊C₄

yes

—

C₃⋊(C₃⋊C₈)

—

C₃⋊(C₃⋊C₈)

C₂×D₄

yes

characteristic

C₃⋊(C₃⋊C₈)

C₂×Q₈

yes

characteristic

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂×C₄×D₃

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₃×C₄²

—

(C₂×D₃)⋊C₄

—

Dic₃⋊C₄

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

ΓL(1,𝔽₂₅)

—

D₃×C₈

—

D₃×C₈

—

C₂²×C₃²

C₂²×C₈

yes

characteristic

C₂×C₃⋊D₃

—

C₂×C₃⋊D₃

C₄⋊C₈

yes

—

C₃²×C₄

—

C₃²×C₄

C₂×C₄⋊C₄

yes

characteristic

C₃²×C₄

C₂×M₁₆

yes

characteristic

C₃⋊Dic₃

—

C₃⋊Dic₃

C₄⋊C₈

yes

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₂²×D₃

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×Dic₃

—

C₂×Dic₃

—

C₄×D₃

—

C₄×D₃

—

C₃×C₈

—

C₃×C₈

—

C₃⋊C₈

—

C₃⋊C₈

—

C₃⋊C₈

—

100

C₂×C₃²

C₂×C₄⋊C₈

yes

characteristic

101

C₂×C₃²

#504

yes

—

102

C₃⋊D₃

—

103

C₂²×C₄

—

104

M₁₆

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₂×#157

yes

characteristic

110

C₂×C₈

C₂×#157

yes

characteristic

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

113

C₄²

—

114

C₄²

C₂×#157

yes

characteristic

115

C₁₆

—

116

C₁₆

—

117

C₂²×C₃

—

118

C₂×D₃

—

119

C₂×D₃

—

120

C₃×C₄

—

121

C₃×C₄

—

122

C₃×C₄

—

123

Dic₃

—

124

Dic₃

—

125

C₃²

#2151

yes

characteristic, complemented, Sylow

126

C₂³

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

#3787

yes

—

132

C₂×C₄

C₂²×#157

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

—

136

C₈

—

137

C₈

C₄⋊#157

yes

—

138

C₂×C₃

—

139

C₂×C₃

—

140

D₃

—

141

C₂²

—

142

C₂²

—

143

C₂²

C₂×#3787

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

#64283

yes

characteristic

148

C₄

C₂×C₄⋊#157

yes

characteristic

149

C₃

—

150

C₂

—

151

C₂

#10593726

yes

characteristic

152

C₂

#10593772

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#157
commutator, socle	C₂²×C₃²	C₂²×C₈
Fitting	C₃²×#97	C₄
prime radical	C₂²×C₃⋊D₃	C₂×C₈
cosocle	C₂×C₃⋊(C₃⋊C₈)	C₂³
hypercenter	#97	#157
hypocenter	C₃²	#2151
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#157

commutator, socle

C₂²×C₃²

C₂²×C₈

Fitting

C₃²×#97

C₄

prime radical

C₂²×C₃⋊D₃

C₂×C₈

cosocle

C₂×C₃⋊(C₃⋊C₈)

C₂³

C₃²

G ▷ C₂²×C₃² ▷ C₃²

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
4. #10590177	C₂	semidirect
5. C₄⋊#3708	C₂	semidirect
125. C₃²	#2151	semidirect

H ≅ G/N

type

4. #10590177

C₂

semidirect

5. C₄⋊#3708

C₂

semidirect

125. C₃²

#2151

semidirect

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

subgroup	index
C₂×#63765	2
C₂×#63764	2
#10592407	2
#10590177	2
C₄⋊#3708	2
#2151	9

subgroup

index

Subgroups — #11797025

Conjugacy classes of subgroups

Complements

Maximal subgroups