Group #11777764 — subgroups

Subgroups — #11777764

Order 1152.

314 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 58 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	#10593821	C₂	1	2	yes	maximal, complemented
2	D₈×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	D₄⋊#622	C₂	1	2	yes	maximal, complemented
4	#10590171	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×#622	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#3792	—	2	2	no	—
7	C₂×C₃²×D₈	C₄	1	1	yes	characteristic
8	D₄×C₃⋊Dic₃	C₂²	1	2	yes	—
9	C₂²⋊#622	—	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	#63659	C₄	1	2	yes	—
14	#63645	C₄	1	1	yes	characteristic
15	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
16	Dic₃×D₈	—	6	2	no	—
17	C₂×C₃²×D₄	C₂×C₄	1	2	yes	—
18	C₂²×C₃⋊Dic₃	—	2	2	no	—
19	#3792	—	4	4	no	—
20	C₂×#622	—	2	1	no	—
21	C₂×#622	—	2	2	no	—
22	C₂×#622	D₄	1	1	yes	characteristic
23	C₂×#622	D₄	1	1	yes	characteristic
24	C₃²×D₈	—	2	2	no	—
25	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
26	#3757	—	2	2	no	—
27	C₄⋊(C₃⋊Dic₃)	C₂×C₄	1	2	yes	—
28	C₄×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
29	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
30	#1589	—	9	1	no	maximal, Sylow
31	C₂×C₃×D₈	—	2	2	no	—
32	D₄×Dic₃	—	6	4	no	—
33	#832	—	6	4	no	—
34	#818	—	6	2	no	—
35	C₈×Dic₃	—	6	2	no	—
36	C₂³×C₃²	—	2	2	no	—
37	C₃²×D₄	—	2	2	no	—
38	C₃²×D₄	—	2	2	no	—
39	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₃⋊Dic₃	—	2	2	no	—
41	C₂×C₃⋊Dic₃	—	4	2	no	—
42	C₂×C₃⋊Dic₃	—	4	2	no	—
43	C₂×C₃⋊Dic₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₃⋊Dic₃	#41	1	1	yes	characteristic
45	#622	—	2	2	no	—
46	#622	—	2	1	no	—
47	#622	—	4	2	no	—
48	#622	D₈	1	2	yes	complemented
49	C₃²×C₈	M₁₆	1	2	yes	complemented
50	C₃⋊(C₃⋊C₈)	—	2	1	no	—
51	C₄×D₈	—	9	1	no	—
52	#436	—	9	2	no	—
53	#335	—	9	1	no	—
54	D₄⋊C₈	—	9	2	no	—
55	C₈²	—	9	1	no	—
56	C₂×C₃×D₄	—	2	4	no	—
57	C₂²×Dic₃	—	12	4	no	—
58	C₃×D₈	—	2	8	no	—
59	C₂×C₃×C₈	—	2	2	no	—
60	#217	—	12	4	no	—
61	C₄⋊Dic₃	—	6	4	no	—
62	C₄×Dic₃	—	6	2	no	—
63	C₂×C₃⋊C₈	—	6	2	no	—
64	C₂²×C₃²	—	4	2	no	—
65	C₂²×C₃²	—	4	2	no	—
66	C₂²×C₃²	—	4	2	no	—
67	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
68	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
69	C₃²×C₄	#131	1	1	yes	characteristic
70	C₃⋊Dic₃	—	2	1	no	—
71	C₃⋊Dic₃	—	4	2	no	—
72	C₃⋊Dic₃	C₂×D₈	1	1	yes	characteristic
73	C₃⋊Dic₃	#135	1	1	yes	characteristic
74	C₂×D₈	#157	1	1	yes	characteristic
75	C₂×M₁₆	—	18	2	no	—
76	C₄×D₄	—	9	2	no	—
77	#107	—	9	1	no	—
78	C₄⋊C₈	—	9	2	no	—
79	#102	—	9	2	no	—
80	C₂²⋊C₈	—	18	2	no	—
81	C₄×C₈	—	9	1	no	—
82	C₄×C₈	—	9	1	no	—
83	C₄×C₈	—	9	1	no	—
84	C₂³×C₃	—	4	4	no	—
85	C₃×D₄	—	2	8	no	—
86	C₃×D₄	—	4	4	no	—
87	C₂×C₃×C₄	—	2	2	no	—
88	C₂×Dic₃	—	6	2	no	—
89	C₂×Dic₃	—	6	2	no	—
90	C₂×Dic₃	—	12	4	no	—
91	C₂×Dic₃	—	24	4	no	—
92	C₂×Dic₃	—	24	4	no	—
93	C₃×C₈	—	2	4	no	—
94	C₃⋊C₈	—	12	2	no	—
95	C₂×C₃²	—	8	2	no	—
96	C₂×C₃²	#436	1	1	yes	characteristic
97	C₂×C₃²	C₄×D₈	1	1	yes	characteristic
98	C₂×C₃²	#443	1	1	yes	characteristic
99	C₂×D₄	C₂×#157	1	2	yes	—
100	C₂²×C₄	—	18	2	no	—
101	D₈	—	2	2	no	—
102	M₁₆	—	36	4	no	—
103	C₂×C₈	—	9	1	no	—
104	C₂×C₈	—	9	1	no	—
105	C₂×C₈	—	9	1	no	—
106	C₂×C₈	—	18	1	no	—
107	C₂×C₈	—	18	2	no	—
108	C₂×C₈	C₂×#157	1	1	yes	characteristic
109	C₄⋊C₄	—	9	2	no	—
110	C₂²⋊C₄	—	18	2	no	—
111	C₄²	—	9	1	no	—
112	C₂²×C₃	—	2	2	no	—
113	C₂²×C₃	—	4	8	no	—
114	C₂²×C₃	—	8	4	no	—
115	C₂²×C₃	—	8	4	no	—
116	C₃×C₄	—	2	2	no	—
117	C₃×C₄	—	2	2	no	—
118	Dic₃	—	6	2	no	—
119	Dic₃	—	6	2	no	—
120	Dic₃	—	12	2	no	—
121	Dic₃	—	24	4	no	—
122	C₃²	#1589	1	1	yes	characteristic, complemented, Sylow
123	C₂³	—	2	2	no	—
124	D₄	—	2	2	no	—
125	D₄	—	2	2	no	—
126	C₂×C₄	—	9	1	no	—
127	C₂×C₄	—	9	1	no	—
128	C₂×C₄	—	18	2	no	—
129	C₂×C₄	—	36	2	no	—
130	C₂×C₄	—	36	2	no	—
131	C₂×C₄	C₂²×#157	1	1	yes	characteristic
132	C₈	—	9	2	no	—
133	C₈	—	18	1	no	—
134	C₈	—	18	2	no	—
135	C₈	—	18	1	no	—
136	C₈	—	36	2	no	—
137	C₈	#3792	1	2	yes	complemented
138	C₂×C₃	—	2	2	no	—
139	C₂×C₃	—	2	2	no	—
140	C₂×C₃	—	2	2	no	—
141	C₂×C₃	—	8	8	no	—
142	C₂²	—	4	2	no	—
143	C₂²	—	4	2	no	—
144	C₂²	—	4	2	no	—
145	C₂²	D₄×#157	1	1	yes	characteristic
146	C₄	—	9	1	no	—
147	C₄	—	9	1	no	—
148	C₄	—	18	1	no	—
149	C₄	—	36	2	no	—
150	C₄	#64287	1	1	yes	characteristic
151	C₄	C₂×#3792	1	1	yes	characteristic
152	C₃	—	2	2	no	—
153	C₂	—	8	2	no	—
154	C₂	D₈×#157	1	1	yes	characteristic
155	C₂	#10593779	1	1	yes	characteristic
156	C₂	#10593821	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#10593821

C₂

yes

maximal, complemented

D₈×C₃⋊Dic₃

C₂

yes

maximal, characteristic

D₄⋊#622

C₂

yes

maximal, complemented

#10590171

C₂

yes

maximal, characteristic, complemented

C₈×#622

C₂

yes

maximal, characteristic, complemented

C₂×#3792

—

C₂×C₃²×D₈

C₄

yes

characteristic

D₄×C₃⋊Dic₃

C₂²

yes

—

C₂²⋊#622

—

C₄⋊#622

C₂²

yes

—

C₄×#622

C₂²

yes

characteristic

C₄×#622

C₂²

yes

characteristic

#63659

C₄

yes

—

#63645

C₄

yes

characteristic

C₈×C₃⋊Dic₃

C₂²

yes

characteristic

Dic₃×D₈

—

C₂×C₃²×D₄

C₂×C₄

yes

—

C₂²×C₃⋊Dic₃

—

—

—

—

D₄

yes

characteristic

C₂×#622

D₄

yes

characteristic

C₃²×D₈

—

C₂×C₃²×C₈

C₂×C₄

yes

characteristic

#3757

—

C₄⋊(C₃⋊Dic₃)

C₂×C₄

yes

—

C₄×C₃⋊Dic₃

C₂³

yes

characteristic

C₂×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

characteristic

#1589

—

maximal, Sylow

C₂×C₃×D₈

—

D₄×Dic₃

—

#832

—

#818

—

C₈×Dic₃

—

C₂³×C₃²

—

C₃²×D₄

—

C₃²×D₄

—

C₂×C₃²×C₄

C₂²×C₄

yes

characteristic

C₂×C₃⋊Dic₃

—

C₂×C₃⋊Dic₃

—

C₂×C₃⋊Dic₃

—

C₂×C₃⋊Dic₃

C₂×D₄

yes

C₂×C₃⋊Dic₃

yes

—

—

—

D₈

yes

complemented

C₃²×C₈

M₁₆

yes

complemented

C₃⋊(C₃⋊C₈)

—

C₄×D₈

—

#436

—

#335

—

D₄⋊C₈

—

C₈²

—

C₂×C₃×D₄

—

C₂²×Dic₃

—

C₃×D₈

—

C₂×C₃×C₈

—

#217

—

C₄⋊Dic₃

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

—

C₂²×C₃²

C₄×D₄

yes

characteristic

C₃²×C₄

C₂×M₁₆

yes

characteristic

C₃²×C₄

#131

yes

characteristic

C₃⋊Dic₃

—

C₃⋊Dic₃

—

C₃⋊Dic₃

C₂×D₈

yes

C₃⋊Dic₃

yes

C₂×D₈

yes

C₂×M₁₆

—

C₄×D₄

—

#107

—

C₄⋊C₈

—

#102

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂³×C₃

—

C₃×D₄

—

C₃×D₄

—

C₂×C₃×C₄

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₂×Dic₃

—

C₃×C₈

—

C₃⋊C₈

—

C₂×C₃²

—

C₂×C₃²

#436

yes

characteristic

C₂×C₃²

C₄×D₈

yes

C₂×C₃²

yes

C₂×D₄

yes

—

100

C₂²×C₄

—

101

D₈

—

102

M₁₆

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

C₂×#157

yes

characteristic

109

C₄⋊C₄

—

110

C₂²⋊C₄

—

111

C₄²

—

112

C₂²×C₃

—

113

C₂²×C₃

—

114

C₂²×C₃

—

115

C₂²×C₃

—

116

C₃×C₄

—

117

C₃×C₄

—

118

Dic₃

—

119

Dic₃

—

120

Dic₃

—

121

Dic₃

—

122

C₃²

#1589

yes

characteristic, complemented, Sylow

123

C₂³

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

C₂²×#157

yes

characteristic

132

C₈

—

133

C₈

—

134

C₈

—

135

C₈

—

136

C₈

—

137

C₈

#3792

yes

complemented

138

C₂×C₃

—

139

C₂×C₃

—

140

C₂×C₃

—

141

C₂×C₃

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

D₄×#157

yes

characteristic

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

#64287

yes

characteristic

151

C₄

C₂×#3792

yes

characteristic

152

C₃

—

153

C₂

—

154

C₂

D₈×#157

yes

characteristic

155

C₂

#10593779

yes

characteristic

156

C₂

#10593821

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×#157
commutator	C₂×C₃²×C₄	C₂²×C₄
Frattini	C₂×C₄	C₂²×#157
Fitting, prime radical	C₂×C₃²×D₈	C₄
socle	C₂²×C₃²	C₄×D₄
cosocle	C₄×C₃⋊Dic₃	C₂³
hypercenter	C₂×D₈	#157
hypocenter	C₃²	#1589
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

subgroup

G/H

center

C₂²

D₄×#157

commutator

C₂×C₃²×C₄

C₂²×C₄

Frattini

C₂×C₄

C₂²×#157

Fitting, prime radical

C₂×C₃²×D₈

C₄

socle

C₂²×C₃²

C₄×D₄

cosocle

C₄×C₃⋊Dic₃

C₂³

C₂×D₈

C₃²

G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

N	H ≅ G/N	type
1. #10593821	C₂	semidirect
3. D₄⋊#622	C₂	semidirect
4. #10590171	C₂	semidirect
5. C₈×#622	C₂	semidirect
48. #622	D₈	semidirect
49. C₃²×C₈	M₁₆	semidirect
122. C₃²	#1589	semidirect
137. C₈	#3792	semidirect

H ≅ G/N

type

1. #10593821

C₂

semidirect

3. D₄⋊#622

C₂

semidirect

4. #10590171

C₂

semidirect

5. C₈×#622

C₂

semidirect

48. #622

D₈

semidirect

49. C₃²×C₈

M₁₆

semidirect

122. C₃²

#1589

semidirect

137. C₈

#3792

semidirect

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

subgroup	index
#10593821	2
D₈×C₃⋊Dic₃	2
D₄⋊#622	2
#10590171	2
C₈×#622	2
#1589	9

subgroup

index

D₈×C₃⋊Dic₃

Subgroups — #11777764

Conjugacy classes of subgroups

Complements

Maximal subgroups