Group #11795907 — subgroups

Subgroups — #11795907

Order 1152.

218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 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	#10596481	C₂	1	1	yes	maximal, characteristic
2	C₂×#64213	C₂	1	1	yes	maximal, characteristic
3	#10593775	C₂	1	1	yes	maximal, characteristic
4	#10593255	C₂	1	2	yes	maximal, complemented
5	#10593254	C₂	1	2	yes	maximal, complemented
6	#64286	C₄	1	1	yes	characteristic
7	C₂×#3787	C₂²	1	1	yes	characteristic
8	#64218	C₄	1	2	yes	complemented
9	C₂×#3771	C₄	1	2	yes	complemented
10	#64214	C₄	1	2	yes	complemented
11	#64213	C₄	1	2	yes	complemented
12	#64213	C₂²	1	1	yes	characteristic
13	#64213	C₂²	1	1	yes	characteristic
14	#64213	C₂²	1	2	yes	—
15	M₁₆×C₃⋊D₃	C₄	1	1	yes	characteristic
16	#63767	C₄	1	2	yes	—
17	C₈×#157	C₂²	1	2	yes	—
18	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
19	C₂²⋊#157	C₈	1	2	yes	—
20	C₂×#622	C₂×C₄	1	1	yes	characteristic
21	C₂×#622	C₂×C₄	1	1	yes	characteristic
22	C₄⋊#157	C₈	1	2	yes	—
23	C₄×#157	C₂×C₄	1	2	yes	—
24	#3787	C₂×C₄	1	1	yes	characteristic
25	#3787	C₂×C₄	1	1	yes	characteristic
26	#3787	C₂×C₄	1	1	yes	characteristic
27	#3787	C₂³	1	1	yes	characteristic
28	#3771	C₂×C₄	1	2	yes	—
29	#3771	C₂×C₄	1	2	yes	—
30	#3771	C₂×C₄	1	4	yes	—
31	C₃²×M₁₆	C₈	1	1	yes	characteristic
32	#3748	C₈	1	1	yes	characteristic
33	#3743	C₈	1	2	yes	—
34	C₈×C₃⋊D₃	C₂×C₄	1	2	yes	—
35	#2108	—	9	1	no	maximal, Sylow
36	D₃×M₁₆	—	12	1	no	—
37	C₂²×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
38	C₂×#157	C₂×C₈	1	4	yes	—
39	C₂×C₃²×C₄	C₂×C₈	1	1	yes	characteristic
40	C₂×C₃⋊Dic₃	C₄²	1	1	yes	characteristic
41	C₄×C₃⋊D₃	C₄²	1	1	yes	characteristic
42	C₄×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
43	C₄×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
44	C₄×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
45	#622	C₄²	1	1	yes	characteristic
46	#622	C₄²	1	1	yes	characteristic
47	#622	C₂²×C₄	1	1	yes	characteristic
48	#622	C₂²×C₄	1	1	yes	characteristic
49	C₃²×C₈	C₂×C₈	1	2	yes	—
50	C₃⋊(C₃⋊C₈)	C₂×C₈	1	2	yes	—
51	C₂×M₃₂	—	9	1	no	—
52	C₂²×C₁₆	—	9	1	no	—
53	#405	—	9	1	no	—
54	#346	—	9	2	no	—
55	C₄×C₁₆	—	9	2	no	—
56	C₂×C₄×D₃	—	12	1	no	—
57	C₃×M₁₆	—	4	1	no	—
58	#208	—	12	1	no	—
59	ΓL(1,𝔽₂₅)	—	12	2	no	—
60	D₃×C₈	—	12	2	no	—
61	C₂²×C₃²	C₄×C₈	1	1	yes	characteristic
62	C₂×C₃⋊D₃	—	2	2	no	—
63	C₂×C₃⋊D₃	C₄×C₈	1	1	yes	characteristic
64	C₂×C₃⋊D₃	C₂²×C₈	1	1	yes	characteristic
65	#157	—	2	4	no	—
66	C₃²×C₄	C₄×C₈	1	1	yes	characteristic
67	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
68	C₃⋊Dic₃	C₄×C₈	1	1	yes	characteristic
69	C₃⋊Dic₃	C₂×C₄²	1	1	yes	characteristic
70	C₂×M₁₆	—	9	1	no	—
71	C₂²×C₈	—	9	1	no	—
72	#117	—	9	1	no	—
73	M₃₂	—	9	2	no	—
74	M₃₂	—	9	2	no	—
75	C₂×C₁₆	—	9	1	no	—
76	C₂×C₁₆	—	9	2	no	—
77	C₂×C₁₆	—	9	1	no	—
78	C₂×C₁₆	—	9	2	no	—
79	C₂×C₁₆	—	9	2	no	—
80	#97	—	9	2	no	—
81	C₄×C₈	—	9	2	no	—
82	C₂²×D₃	—	12	1	no	—
83	C₂×C₃×C₄	—	4	1	no	—
84	C₂×Dic₃	—	12	1	no	—
85	C₄×D₃	—	12	1	no	—
86	C₄×D₃	—	12	1	no	—
87	C₄×D₃	—	12	1	no	—
88	C₄×D₃	—	12	1	no	—
89	C₃×C₈	—	4	2	no	—
90	C₃⋊C₈	—	12	2	no	—
91	C₂×C₃²	—	2	1	no	—
92	C₂×C₃²	C₂×C₄×C₈	1	1	yes	characteristic
93	C₃⋊D₃	—	2	1	no	—
94	C₃⋊D₃	#504	1	2	yes	—
95	C₂²×C₄	—	9	1	no	—
96	M₁₆	—	9	1	no	—
97	M₁₆	—	9	2	no	—
98	M₁₆	AGL(1,𝔽₉)	1	1	yes	characteristic
99	C₂×C₈	—	9	1	no	—
100	C₂×C₈	—	9	1	no	—
101	C₂×C₈	—	9	1	no	—
102	C₂×C₈	—	9	1	no	—
103	C₂×C₈	—	9	1	no	—
104	C₂×C₈	—	9	1	no	—
105	C₂×C₈	—	9	2	no	—
106	C₄⋊C₄	—	9	2	no	—
107	C₂²⋊C₄	—	9	2	no	—
108	C₄²	—	9	2	no	—
109	C₁₆	—	9	2	no	—
110	C₁₆	—	9	2	no	—
111	C₁₆	—	9	4	no	—
112	C₂²×C₃	—	4	1	no	—
113	C₂×D₃	—	12	1	no	—
114	C₂×D₃	—	12	1	no	—
115	C₂×D₃	—	24	2	no	—
116	C₃×C₄	—	4	1	no	—
117	C₃×C₄	—	4	1	no	—
118	Dic₃	—	12	1	no	—
119	Dic₃	—	12	1	no	—
120	C₃²	#2108	1	1	yes	characteristic, complemented, Sylow
121	C₂³	—	9	1	no	—
122	C₂×C₄	—	9	1	no	—
123	C₂×C₄	—	9	1	no	—
124	C₂×C₄	—	9	1	no	—
125	C₂×C₄	—	9	1	no	—
126	C₂×C₄	—	9	1	no	—
127	C₂×C₄	—	9	4	no	—
128	C₂×C₄	C₂×AGL(1,𝔽₉)	1	1	yes	characteristic
129	C₈	—	9	1	no	—
130	C₈	—	9	1	no	—
131	C₈	—	9	1	no	—
132	C₈	—	9	1	no	—
133	C₈	—	9	2	no	—
134	C₈	C₂×AGL(1,𝔽₉)	1	2	yes	—
135	C₂×C₃	—	4	1	no	—
136	C₂×C₃	—	8	1	no	—
137	D₃	—	12	2	no	—
138	D₃	—	24	1	no	—
139	C₂²	—	9	1	no	—
140	C₂²	—	9	1	no	—
141	C₂²	—	18	2	no	—
142	C₂²	C₄×AGL(1,𝔽₉)	1	1	yes	characteristic
143	C₄	—	9	1	no	—
144	C₄	—	9	1	no	—
145	C₄	—	18	4	no	—
146	C₄	C₄×AGL(1,𝔽₉)	1	1	yes	characteristic
147	C₄	C₂²×AGL(1,𝔽₉)	1	1	yes	characteristic
148	C₃	—	4	1	no	—
149	C₂	—	2	1	no	—
150	C₂	—	9	2	no	—
151	C₂	—	18	1	no	—
152	C₂	C₂×C₄×AGL(1,𝔽₉)	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10596481

C₂

yes

maximal, characteristic

C₂×#64213

C₂

yes

maximal, characteristic

#10593775

C₂

yes

maximal, characteristic

#10593255

C₂

yes

maximal, complemented

#10593254

C₂

yes

maximal, complemented

#64286

C₄

yes

characteristic

C₂×#3787

C₂²

yes

characteristic

#64218

C₄

yes

complemented

C₂×#3771

C₄

yes

complemented

#64214

C₄

yes

complemented

#64213

C₄

yes

complemented

#64213

C₂²

yes

characteristic

#64213

C₂²

yes

characteristic

#64213

C₂²

yes

—

M₁₆×C₃⋊D₃

C₄

yes

characteristic

#63767

C₄

yes

—

C₈×#157

C₂²

yes

—

C₂×C₄×C₃⋊D₃

C₂×C₄

yes

characteristic

C₂²⋊#157

C₈

yes

—

C₂×#622

C₂×C₄

yes

characteristic

C₂×#622

C₂×C₄

yes

characteristic

C₄⋊#157

C₈

yes

—

C₄×#157

C₂×C₄

yes

—

#3787

C₂×C₄

yes

characteristic

#3787

C₂×C₄

yes

characteristic

#3787

C₂×C₄

yes

characteristic

#3787

C₂³

yes

characteristic

#3771

C₂×C₄

yes

—

#3771

C₂×C₄

yes

—

#3771

C₂×C₄

yes

—

C₃²×M₁₆

C₈

yes

characteristic

#3748

C₈

yes

characteristic

#3743

C₈

yes

—

C₈×C₃⋊D₃

C₂×C₄

yes

—

#2108

—

maximal, Sylow

D₃×M₁₆

—

C₂²×C₃⋊D₃

C₂×C₈

yes

characteristic

C₂×#157

C₂×C₈

yes

—

C₂×C₃²×C₄

C₂×C₈

yes

characteristic

C₂×C₃⋊Dic₃

C₄²

yes

characteristic

C₄×C₃⋊D₃

C₄²

yes

characteristic

C₄×C₃⋊D₃

C₂×C₈

yes

characteristic

C₄×C₃⋊D₃

C₂×C₈

yes

characteristic

C₄×C₃⋊D₃

C₂²×C₄

yes

characteristic

#622

C₄²

yes

characteristic

#622

C₄²

yes

characteristic

#622

C₂²×C₄

yes

characteristic

#622

C₂²×C₄

yes

characteristic

C₃²×C₈

C₂×C₈

yes

—

C₃⋊(C₃⋊C₈)

C₂×C₈

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

C₄×C₁₆

—

C₂×C₄×D₃

—

C₃×M₁₆

—

#208

—

ΓL(1,𝔽₂₅)

—

D₃×C₈

—

C₂²×C₃²

C₄×C₈

yes

characteristic

C₂×C₃⋊D₃

—

C₂×C₃⋊D₃

C₄×C₈

yes

characteristic

C₂×C₃⋊D₃

C₂²×C₈

yes

characteristic

#157

—

C₃²×C₄

C₄×C₈

yes

characteristic

C₃²×C₄

C₂²×C₈

yes

characteristic

C₃⋊Dic₃

C₄×C₈

yes

characteristic

C₃⋊Dic₃

C₂×C₄²

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₂²×D₃

—

C₂×C₃×C₄

—

C₂×Dic₃

—

C₄×D₃

—

C₄×D₃

—

C₄×D₃

—

C₄×D₃

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₃²

—

C₂×C₃²

C₂×C₄×C₈

yes

characteristic

C₃⋊D₃

—

C₃⋊D₃

#504

yes

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

AGL(1,𝔽₉)

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₄⋊C₄

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₁₆

—

110

C₁₆

—

111

C₁₆

—

112

C₂²×C₃

—

113

C₂×D₃

—

114

C₂×D₃

—

115

C₂×D₃

—

116

C₃×C₄

—

117

C₃×C₄

—

118

Dic₃

—

119

Dic₃

—

120

C₃²

#2108

yes

characteristic, complemented, Sylow

121

C₂³

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₂×AGL(1,𝔽₉)

yes

characteristic

129

C₈

—

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

—

134

C₈

C₂×AGL(1,𝔽₉)

yes

—

135

C₂×C₃

—

136

C₂×C₃

—

137

D₃

—

138

D₃

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

C₄×AGL(1,𝔽₉)

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

C₄×AGL(1,𝔽₉)

yes

characteristic

147

C₄

C₂²×AGL(1,𝔽₉)

yes

characteristic

148

C₃

—

149

C₂

—

150

C₂

—

151

C₂

—

152

C₂

C₂×C₄×AGL(1,𝔽₉)

yes

characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×AGL(1,𝔽₉)
commutator, socle	C₂×C₃²	C₂×C₄×C₈
Fitting	C₃²×M₁₆	C₈
prime radical	C₂²×C₃⋊D₃	C₂×C₈
cosocle	#3787	C₂³
hypercenter	M₁₆	AGL(1,𝔽₉)
hypocenter	C₃²	#2108
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ M₁₆

subgroup

G/H

center, Frattini

C₄

C₂²×AGL(1,𝔽₉)

commutator, socle

C₂×C₃²

C₂×C₄×C₈

Fitting

C₃²×M₁₆

C₈

prime radical

C₂²×C₃⋊D₃

C₂×C₈

C₂³

M₁₆

C₃²

G ▷ C₂×C₃² ▷ C₃²

C₁ ◁ C₄ ◁ M₁₆

N	H ≅ G/N	type
4. #10593255	C₂	semidirect
5. #10593254	C₂	semidirect
8. #64218	C₄	semidirect
9. C₂×#3771	C₄	semidirect
10. #64214	C₄	semidirect
11. #64213	C₄	semidirect
120. C₃²	#2108	semidirect

H ≅ G/N

type

4. #10593255

C₂

semidirect

5. #10593254

C₂

semidirect

8. #64218

C₄

semidirect

9. C₂×#3771

C₄

semidirect

10. #64214

C₄

semidirect

11. #64213

C₄

semidirect

120. C₃²

#2108

semidirect

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

subgroup	index
#10596481	2
C₂×#64213	2
#10593775	2
#10593255	2
#10593254	2
#2108	9

subgroup

index

Subgroups — #11795907

Conjugacy classes of subgroups

Complements

Maximal subgroups