Group #11769691 — subgroups

Subgroups — C₃²×#2642 #11769691

Order 1152.

1248 conjugacy classes of subgroups; only the 600 normal subgroups are shown.

normal subgroups only

This group has 1248 conjugacy classes of subgroups — too many to draw. Only its 600 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×C₃²×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×#125	C₂	1	1	yes	maximal, characteristic
3	C₃²×#400	C₂	1	8	yes	maximal
4	C₃²×#391	C₂	1	4	yes	maximal
5	C₃²×#376	C₂	1	1	yes	maximal, characteristic
6	C₃×#2642	C₃	1	4	yes	maximal, direct product factor
7	C₂²×C₃²×Q₈	C₂²	1	2	yes	—
8	C₃²×C₄⋊Q₈	—	2	4	no	—
9	C₃²×#125	—	2	4	no	—
10	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₃²×C₄⋊C₄	C₂²	1	4	yes	—
12	C₂×C₃²×C₄⋊C₄	C₂²	1	4	yes	—
13	C₂×C₃²×C₄²	C₂²	1	2	yes	—
14	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
15	C₃²×#95	C₂²	1	4	yes	—
16	C₃²×#95	C₂²	1	16	yes	—
17	C₂×C₃×C₄⋊Q₈	C₂×C₃	1	4	yes	—
18	C₂×C₃×#125	C₂×C₃	1	4	yes	—
19	C₃×#400	C₂×C₃	1	32	yes	—
20	C₃×#391	C₂×C₃	1	16	yes	—
21	C₃×#376	C₂×C₃	1	4	yes	—
22	C₂×C₃²×Q₈	—	2	4	no	—
23	C₂×C₃²×Q₈	—	2	8	no	—
24	C₂²×C₃²×C₄	C₂³	1	4	yes	—
25	C₂²×C₃²×C₄	C₂³	1	4	yes	—
26	C₂²×C₃²×C₄	C₂³	1	4	yes	—
27	C₂²×C₃²×C₄	C₂³	1	2	yes	—
28	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
29	C₃²×C₄⋊C₄	—	2	8	no	—
30	C₃²×C₄⋊C₄	—	2	4	no	—
31	C₃²×C₄⋊C₄	—	2	8	no	—
32	C₃²×C₄²	—	2	4	no	—
33	C₃²×C₄²	D₄	1	4	yes	—
34	#2642	C₃²	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²×C₃×Q₈	C₂²×C₃	1	8	yes	—
36	C₃×C₄⋊Q₈	—	2	16	no	—
37	C₃×#125	—	2	16	no	—
38	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
39	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	16	yes	—
40	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	16	yes	—
41	C₂×C₃×C₄²	C₂²×C₃	1	8	yes	—
42	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
43	C₃×#95	C₂²×C₃	1	16	yes	—
44	C₃×#95	C₂²×C₃	1	64	yes	—
45	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
46	C₃²×Q₈	—	4	8	no	—
47	C₂×C₃²×C₄	—	2	4	no	—
48	C₂×C₃²×C₄	—	2	4	no	—
49	C₂×C₃²×C₄	—	2	4	no	—
50	C₂×C₃²×C₄	—	2	4	no	—
51	C₂×C₃²×C₄	—	2	8	no	—
52	C₂×C₃²×C₄	—	2	8	no	—
53	C₂×C₃²×C₄	—	2	8	no	—
54	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
55	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
56	C₂×C₃²×C₄	#41	1	4	yes	—
57	C₂×C₄⋊Q₈	C₂×C₃²	1	1	yes	characteristic
58	C₂×#125	C₂×C₃²	1	1	yes	characteristic
59	#400	C₂×C₃²	1	8	yes	—
60	#391	C₂×C₃²	1	4	yes	—
61	#376	C₂×C₃²	1	1	yes	characteristic
62	C₂×C₃×Q₈	—	2	16	no	—
63	C₂×C₃×Q₈	—	2	32	no	—
64	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
65	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
66	C₂²×C₃×C₄	C₂³×C₃	1	16	yes	—
67	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
68	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
69	C₃×C₄⋊C₄	—	2	32	no	—
70	C₃×C₄⋊C₄	—	2	16	no	—
71	C₃×C₄⋊C₄	—	2	32	no	—
72	C₃×C₄²	—	2	16	no	—
73	C₃×C₄²	C₃×D₄	1	16	yes	—
74	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
75	C₂²×C₃²	C₂×#41	1	2	yes	—
76	C₂²×C₃²	2₋¹⁺⁴	1	4	yes	—
77	C₃²×C₄	—	2	4	no	—
78	C₃²×C₄	—	4	4	no	—
79	C₃²×C₄	—	4	4	no	—
80	C₃²×C₄	—	4	4	no	—
81	C₃²×C₄	#124	1	4	yes	—
82	C₂²×Q₈	C₂²×C₃²	1	2	yes	—
83	C₄⋊Q₈	—	2	4	no	—
84	#125	—	2	4	no	—
85	C₂×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
86	C₂×C₄⋊C₄	C₂²×C₃²	1	4	yes	—
87	C₂×C₄⋊C₄	C₂²×C₃²	1	4	yes	—
88	C₂×C₄²	C₂²×C₃²	1	2	yes	—
89	C₂×C₄²	C₂²×C₃²	1	1	yes	characteristic
90	#95	C₂²×C₃²	1	4	yes	—
91	#95	C₂²×C₃²	1	16	yes	—
92	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
93	C₃×Q₈	—	4	32	no	—
94	C₂×C₃×C₄	—	2	16	no	—
95	C₂×C₃×C₄	—	2	16	no	—
96	C₂×C₃×C₄	—	2	16	no	—
97	C₂×C₃×C₄	—	2	16	no	—
98	C₂×C₃×C₄	—	2	32	no	—
99	C₂×C₃×C₄	—	2	32	no	—
100	C₂×C₃×C₄	—	2	32	no	—
101	C₂×C₃×C₄	C₂×C₃×D₄	1	16	yes	—
102	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
103	C₂×C₃×C₄	C₃×#41	1	16	yes	—
104	C₂×C₃²	C₂×#124	1	1	yes	characteristic
105	C₂×C₃²	#536	1	2	yes	—
106	C₂×C₃²	#541	1	4	yes	—
107	C₂×Q₈	—	2	4	no	—
108	C₂×Q₈	—	2	8	no	—
109	C₂²×C₄	C₂³×C₃²	1	4	yes	—
110	C₂²×C₄	C₂³×C₃²	1	4	yes	—
111	C₂²×C₄	C₂³×C₃²	1	4	yes	—
112	C₂²×C₄	C₂³×C₃²	1	2	yes	—
113	C₂²×C₄	C₂³×C₃²	1	1	yes	characteristic
114	C₄⋊C₄	—	2	8	no	—
115	C₄⋊C₄	—	2	4	no	—
116	C₄⋊C₄	—	2	8	no	—
117	C₄²	—	2	4	no	—
118	C₄²	C₃²×D₄	1	4	yes	—
119	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
120	C₂²×C₃	C₂×C₃×#41	1	8	yes	—
121	C₂²×C₃	C₃×2₋¹⁺⁴	1	16	yes	—
122	C₃×C₄	—	2	16	no	—
123	C₃×C₄	—	4	16	no	—
124	C₃×C₄	—	4	16	no	—
125	C₃×C₄	—	4	16	no	—
126	C₃×C₄	C₃×#124	1	16	yes	—
127	C₃²	#2642	1	1	yes	characteristic, direct product factor, Sylow
128	C₂³	C₂⁴×C₃²	1	1	yes	characteristic
129	Q₈	—	4	8	no	—
130	C₂×C₄	—	2	4	no	—
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	—	2	4	no	—
133	C₂×C₄	—	2	4	no	—
134	C₂×C₄	—	2	8	no	—
135	C₂×C₄	—	2	8	no	—
136	C₂×C₄	—	2	8	no	—
137	C₂×C₄	C₂×C₃²×D₄	1	4	yes	—
138	C₂×C₄	C₂×C₃²×D₄	1	2	yes	—
139	C₂×C₄	C₃²×#41	1	4	yes	—
140	C₂×C₃	C₂×C₃×#124	1	4	yes	—
141	C₂×C₃	C₃×#536	1	8	yes	—
142	C₂×C₃	C₃×#541	1	16	yes	—
143	C₂²	C₂²×C₃²×D₄	1	1	yes	characteristic
144	C₂²	C₂×C₃²×#41	1	2	yes	—
145	C₂²	C₃²×2₋¹⁺⁴	1	4	yes	—
146	C₄	—	2	4	no	—
147	C₄	—	4	4	no	—
148	C₄	—	4	4	no	—
149	C₄	—	4	4	no	—
150	C₄	C₃²×#124	1	4	yes	—
151	C₃	C₃×#2642	1	4	yes	direct product factor
152	C₂	C₂×C₃²×#124	1	1	yes	characteristic
153	C₂	C₃²×#536	1	2	yes	—
154	C₂	C₃²×#541	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃²×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂×C₃²×#125

C₂

yes

maximal, characteristic

C₃²×#400

C₂

yes

maximal

C₃²×#391

C₂

yes

maximal

C₃²×#376

C₂

yes

maximal, characteristic

C₃×#2642

C₃

yes

maximal, direct product factor

C₂²×C₃²×Q₈

C₂²

yes

—

C₃²×C₄⋊Q₈

—

C₃²×#125

—

C₂×C₃²×C₄⋊C₄

C₂²

yes

—

C₂×C₃²×C₄⋊C₄

C₂²

yes

—

C₂×C₃²×C₄⋊C₄

C₂²

yes

—

C₂×C₃²×C₄²

C₂²

yes

—

C₂×C₃²×C₄²

C₂²

yes

characteristic

C₃²×#95

C₂²

yes

—

C₃²×#95

C₂²

yes

—

C₂×C₃×C₄⋊Q₈

C₂×C₃

yes

—

C₂×C₃×#125

C₂×C₃

yes

—

C₃×#400

C₂×C₃

yes

—

C₃×#391

C₂×C₃

yes

—

C₃×#376

C₂×C₃

yes

—

C₂×C₃²×Q₈

—

C₂×C₃²×Q₈

—

C₂²×C₃²×C₄

C₂³

yes

—

C₂²×C₃²×C₄

C₂³

yes

—

C₂²×C₃²×C₄

C₂³

yes

—

C₂²×C₃²×C₄

C₂³

yes

—

C₂²×C₃²×C₄

C₂³

yes

characteristic

C₃²×C₄⋊C₄

—

C₃²×C₄⋊C₄

—

C₃²×C₄⋊C₄

—

C₃²×C₄²

—

C₃²×C₄²

D₄

yes

—

#2642

C₃²

yes

characteristic, direct product factor, Sylow

C₂²×C₃×Q₈

C₂²×C₃

yes

—

C₃×C₄⋊Q₈

—

C₃×#125

—

C₂×C₃×C₄⋊C₄

C₂²×C₃

yes

—

C₂×C₃×C₄⋊C₄

C₂²×C₃

yes

—

C₂×C₃×C₄⋊C₄

C₂²×C₃

yes

—

C₂×C₃×C₄²

C₂²×C₃

yes

—

C₂×C₃×C₄²

C₂²×C₃

yes

—

C₃×#95

C₂²×C₃

yes

—

C₃×#95

C₂²×C₃

yes

—

C₂³×C₃²

C₂⁴

yes

characteristic

C₃²×Q₈

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₂×D₄

yes

—

C₂×C₃²×C₄

C₂×D₄

yes

—

C₂×C₃²×C₄

#41

yes

—

C₂×C₄⋊Q₈

C₂×C₃²

yes

characteristic

C₂×#125

C₂×C₃²

yes

characteristic

#400

C₂×C₃²

yes

—

#391

C₂×C₃²

yes

—

#376

C₂×C₃²

yes

characteristic

C₂×C₃×Q₈

—

C₂×C₃×Q₈

—

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₂²×C₃×C₄

C₂³×C₃

yes

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄²

—

C₃×C₄²

C₃×D₄

yes

—

C₂²×C₃²

C₂²×D₄

yes

characteristic

C₂²×C₃²

C₂×#41

yes

—

C₂²×C₃²

2₋¹⁺⁴

yes

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

#124

yes

—

C₂²×Q₈

C₂²×C₃²

yes

—

C₄⋊Q₈

—

#125

—

C₂×C₄⋊C₄

C₂²×C₃²

yes

—

C₂×C₄⋊C₄

C₂²×C₃²

yes

—

C₂×C₄⋊C₄

C₂²×C₃²

yes

—

C₂×C₄²

C₂²×C₃²

yes

—

C₂×C₄²

C₂²×C₃²

yes

characteristic

#95

C₂²×C₃²

yes

—

#95

C₂²×C₃²

yes

—

C₂³×C₃

C₂⁴×C₃

yes

—

C₃×Q₈

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

100

C₂×C₃×C₄

—

101

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

102

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

103

C₂×C₃×C₄

C₃×#41

yes

—

104

C₂×C₃²

C₂×#124

yes

characteristic

105

C₂×C₃²

#536

yes

—

106

C₂×C₃²

#541

yes

—

107

C₂×Q₈

—

108

C₂×Q₈

—

109

C₂²×C₄

C₂³×C₃²

yes

—

110

C₂²×C₄

C₂³×C₃²

yes

—

111

C₂²×C₄

C₂³×C₃²

yes

—

112

C₂²×C₄

C₂³×C₃²

yes

—

113

C₂²×C₄

C₂³×C₃²

yes

characteristic

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄²

—

118

C₄²

C₃²×D₄

yes

—

119

C₂²×C₃

C₂²×C₃×D₄

yes

—

120

C₂²×C₃

C₂×C₃×#41

yes

—

121

C₂²×C₃

C₃×2₋¹⁺⁴

yes

—

122

C₃×C₄

—

123

C₃×C₄

—

124

C₃×C₄

—

125

C₃×C₄

—

126

C₃×C₄

C₃×#124

yes

—

127

C₃²

#2642

yes

characteristic, direct product factor, Sylow

128

C₂³

C₂⁴×C₃²

yes

characteristic

129

Q₈

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

C₂×C₃²×D₄

yes

—

138

C₂×C₄

C₂×C₃²×D₄

yes

—

139

C₂×C₄

C₃²×#41

yes

—

140

C₂×C₃

C₂×C₃×#124

yes

—

141

C₂×C₃

C₃×#536

yes

—

142

C₂×C₃

C₃×#541

yes

—

143

C₂²

C₂²×C₃²×D₄

yes

characteristic

144

C₂²

C₂×C₃²×#41

yes

—

145

C₂²

C₃²×2₋¹⁺⁴

yes

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

C₃²×#124

yes

—

151

C₃

C₃×#2642

yes

direct product factor

152

C₂

C₂×C₃²×#124

yes

characteristic

153

C₂

C₃²×#536

yes

—

154

C₂

C₃²×#541

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃²	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃² ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₃²

C₂⁴

commutator, Frattini, cosocle

C₂³

C₂⁴×C₃²

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂³×C₃² ◁ G

N	H ≅ G/N	type
6. C₃×#2642	C₃	direct (N × H)
34. #2642	C₃²	direct (N × H)
127. C₃²	#2642	direct (N × H)
151. C₃	C₃×#2642	direct (N × H)

H ≅ G/N

type

6. C₃×#2642

C₃

direct (N × H)

34. #2642

C₃²

direct (N × H)

127. C₃²

#2642

direct (N × H)

151. C₃

C₃×#2642

direct (N × H)

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

subgroup	index
C₂×C₃²×C₄⋊Q₈	2
C₂×C₃²×#125	2
C₃²×#400	2
C₃²×#391	2
C₃²×#376	2
C₃×#2642	3

subgroup

index

C₂×C₃²×C₄⋊Q₈

C₂×C₃²×#125

C₃²×#400

C₃²×#391

C₃²×#376

C₃×#2642

Subgroups — C₃²×#2642 #11769691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C32×#2642 #11769691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#2642 #11769691