Group #33941 — subgroups

Subgroups — #33941

Order 256.

231 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 231 conjugacy classes of subgroups — too many to draw. Only its 101 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	#3395	C₂	1	1	yes	maximal, characteristic
2	#3383	C₂	1	1	yes	maximal, characteristic
3	#2245	C₂	1	2	yes	maximal
4	#2241	C₂	1	1	yes	maximal, characteristic
5	#2229	C₂	1	2	yes	maximal
6	#2225	C₂	1	1	yes	maximal, characteristic
7	#2209	C₂	1	2	yes	maximal
8	#2209	C₂	1	1	yes	maximal, characteristic
9	#2183	C₂	1	1	yes	maximal, characteristic
10	#2176	C₂	1	2	yes	maximal
11	C₄×Q₃₂	C₂	1	1	yes	maximal, characteristic
12	#557	—	2	1	no	—
13	#557	—	2	1	no	—
14	C₂×Q₃₂	C₂²	1	1	yes	characteristic
15	C₂×Q₃₂	C₂²	1	2	yes	—
16	#500	C₂²	1	1	yes	characteristic
17	#499	C₂²	1	2	yes	—
18	#494	C₂²	1	1	yes	characteristic
19	#494	C₂²	1	2	yes	—
20	#479	—	2	2	no	—
21	#475	—	2	1	no	—
22	#462	—	2	1	no	—
23	#462	—	2	2	no	—
24	C₈×Q₈	C₂²	1	1	yes	characteristic
25	C₄×Q₁₆	C₂²	1	1	yes	characteristic
26	C₄×Q₁₆	C₂²	1	2	yes	—
27	C₄×Q₁₆	C₂²	1	1	yes	characteristic
28	C₄×Q₁₆	C₂²	1	2	yes	—
29	#367	C₂²	1	2	yes	—
30	#366	C₂²	1	1	yes	characteristic
31	C₄⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₄⋊C₁₆	C₂²	1	2	yes	—
33	#358	C₂²	1	1	yes	characteristic
34	#358	C₂²	1	1	yes	characteristic
35	#358	C₂²	1	2	yes	—
36	#358	C₂²	1	2	yes	—
37	#358	C₂²	1	2	yes	—
38	#358	C₂²	1	2	yes	—
39	#346	C₂²	1	2	yes	—
40	C₄×C₁₆	C₂²	1	1	yes	characteristic
41	C₂×Q₁₆	—	2	2	no	—
42	C₂×Q₁₆	—	2	1	no	—
43	C₂×Q₁₆	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆	C₂³	1	2	yes	—
45	C₂×Q₁₆	C₂³	1	1	yes	characteristic
46	C₄⋊Q₈	—	2	1	no	—
47	C₄⋊Q₈	—	2	2	no	—
48	C₄⋊Q₈	—	2	1	no	—
49	C₄⋊Q₈	—	4	1	no	—
50	#125	—	2	2	no	—
51	#125	—	4	1	no	—
52	#125	—	4	2	no	—
53	#125	—	4	2	no	—
54	C₄×Q₈	—	2	2	no	—
55	C₄×Q₈	—	2	1	no	—
56	C₄×Q₈	—	2	1	no	—
57	C₄×Q₈	—	2	2	no	—
58	C₄×Q₈	—	4	1	no	—
59	C₄×Q₈	—	4	1	no	—
60	C₄×Q₈	D₄	1	1	yes	characteristic
61	Q₃₂	—	2	2	no	—
62	Q₃₂	—	2	4	no	—
63	C₂×C₁₆	C₂³	1	1	yes	characteristic
64	C₂×C₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₁₆	C₂³	1	2	yes	—
66	#107	—	2	1	no	—
67	#107	C₂³	1	1	yes	characteristic
68	#107	C₂³	1	2	yes	—
69	#107	C₂³	1	1	yes	characteristic
70	#106	—	2	2	no	—
71	C₄⋊C₈	D₄	1	1	yes	characteristic
72	C₄⋊C₈	D₄	1	2	yes	—
73	#103	—	2	2	no	—
74	#103	—	2	1	no	—
75	#103	—	2	2	no	—
76	#103	—	2	1	no	—
77	C₄×C₈	C₂³	1	1	yes	characteristic
78	C₄×C₈	C₂³	1	2	yes	—
79	C₂×Q₈	—	2	1	no	—
80	C₂×Q₈	—	2	2	no	—
81	C₂×Q₈	—	2	1	no	—
82	C₂×Q₈	—	4	1	no	—
83	C₂×Q₈	D₈	1	1	yes	characteristic
84	Q₁₆	—	2	1	no	—
85	Q₁₆	—	2	2	no	—
86	Q₁₆	—	2	1	no	—
87	Q₁₆	—	2	1	no	—
88	Q₁₆	—	2	2	no	—
89	Q₁₆	—	8	2	no	—
90	Q₁₆	—	8	1	no	—
91	Q₁₆	#41	1	2	yes	—
92	C₂×C₈	C₂×D₄	1	2	yes	—
93	C₂×C₈	C₂×D₄	1	1	yes	characteristic
94	C₂×C₈	C₂⁴	1	1	yes	characteristic
95	C₄⋊C₄	—	2	1	no	—
96	C₄⋊C₄	—	2	1	no	—
97	C₄⋊C₄	—	2	2	no	—
98	C₄⋊C₄	—	4	1	no	—
99	C₄⋊C₄	—	4	2	no	—
100	C₄⋊C₄	—	4	1	no	—
101	C₄⋊C₄	—	4	2	no	—
102	C₄⋊C₄	—	4	2	no	—
103	C₄⋊C₄	—	4	2	no	—
104	C₄⋊C₄	—	4	1	no	—
105	C₄⋊C₄	—	4	2	no	—
106	C₄⋊C₄	—	4	1	no	—
107	C₄⋊C₄	—	4	2	no	—
108	C₄⋊C₄	—	4	1	no	—
109	C₄⋊C₄	D₈	1	1	yes	characteristic
110	C₄⋊C₄	D₈	1	2	yes	—
111	C₄²	—	4	2	no	—
112	C₄²	—	4	2	no	—
113	C₄²	—	4	1	no	—
114	C₄²	—	4	1	no	—
115	C₄²	C₂×D₄	1	2	yes	—
116	C₄²	C₂×D₄	1	1	yes	characteristic
117	C₁₆	—	2	1	no	—
118	C₁₆	—	2	2	no	—
119	C₁₆	—	2	1	no	—
120	Q₈	—	2	2	no	—
121	Q₈	—	2	2	no	—
122	Q₈	—	4	1	no	—
123	Q₈	—	4	1	no	—
124	Q₈	—	4	2	no	—
125	Q₈	—	4	1	no	—
126	Q₈	—	4	2	no	—
127	Q₈	—	8	2	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	—	4	1	no	—
130	C₂×C₄	—	4	1	no	—
131	C₂×C₄	—	4	2	no	—
132	C₂×C₄	—	4	2	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	C₂×D₈	1	2	yes	—
135	C₂×C₄	C₂×D₈	1	2	yes	—
136	C₂×C₄	C₂×D₈	1	1	yes	characteristic
137	C₂×C₄	C₂×D₈	1	1	yes	characteristic
138	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
139	C₈	—	2	2	no	—
140	C₈	—	2	1	no	—
141	C₈	C₂×#41	1	1	yes	characteristic
142	C₈	2₋¹⁺⁴	1	1	yes	characteristic
143	C₂²	C₂²×D₈	1	1	yes	characteristic
144	C₄	—	2	2	no	—
145	C₄	—	2	2	no	—
146	C₄	—	2	1	no	—
147	C₄	—	4	2	no	—
148	C₄	—	8	2	no	—
149	C₄	—	8	1	no	—
150	C₄	—	8	2	no	—
151	C₄	—	8	1	no	—
152	C₄	—	8	1	no	—
153	C₄	#510	1	2	yes	—
154	C₄	#548	1	1	yes	characteristic
155	C₄	#577	1	1	yes	characteristic
156	C₂	#3358	1	1	yes	characteristic
157	C₂	C₂×#510	1	1	yes	characteristic
158	C₂	#3417	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#3395

C₂

yes

maximal, characteristic

#3383

C₂

yes

maximal, characteristic

#2245

C₂

yes

maximal

#2241

C₂

yes

maximal, characteristic

#2229

C₂

yes

maximal

#2225

C₂

yes

maximal, characteristic

#2209

C₂

yes

maximal

#2209

C₂

yes

maximal, characteristic

#2183

C₂

yes

maximal, characteristic

#2176

C₂

yes

maximal

C₄×Q₃₂

C₂

yes

maximal, characteristic

#557

—

#557

—

C₂×Q₃₂

C₂²

yes

characteristic

C₂×Q₃₂

C₂²

yes

—

#500

C₂²

yes

characteristic

#499

C₂²

yes

—

#494

C₂²

yes

characteristic

#494

C₂²

yes

—

—

—

—

—

C₈×Q₈

C₂²

yes

characteristic

C₄×Q₁₆

C₂²

yes

characteristic

C₄×Q₁₆

C₂²

yes

—

C₄×Q₁₆

C₂²

yes

characteristic

C₄×Q₁₆

C₂²

yes

—

#367

C₂²

yes

—

#366

C₂²

yes

characteristic

C₄⋊C₁₆

C₂²

yes

characteristic

C₄⋊C₁₆

C₂²

yes

—

#358

C₂²

yes

characteristic

#358

C₂²

yes

characteristic

#358

C₂²

yes

—

#358

C₂²

yes

—

#358

C₂²

yes

—

#358

C₂²

yes

—

#346

C₂²

yes

—

C₄×C₁₆

C₂²

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂³

yes

characteristic

C₂×Q₁₆

C₂³

yes

—

C₂×Q₁₆

C₂³

yes

characteristic

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

—

—

—

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

D₄

yes

characteristic

Q₃₂

—

Q₃₂

—

C₂×C₁₆

C₂³

yes

characteristic

C₂×C₁₆

C₂³

yes

characteristic

C₂×C₁₆

C₂³

yes

—

#107

—

#107

C₂³

yes

characteristic

#107

C₂³

yes

—

#107

C₂³

yes

characteristic

#106

—

C₄⋊C₈

D₄

yes

characteristic

C₄⋊C₈

D₄

yes

—

—

—

—

—

C₄×C₈

C₂³

yes

characteristic

C₄×C₈

C₂³

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₈

yes

characteristic

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

#41

yes

—

C₂×C₈

C₂×D₄

yes

—

C₂×C₈

C₂×D₄

yes

characteristic

C₂×C₈

C₂⁴

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

D₈

yes

characteristic

110

C₄⋊C₄

D₈

yes

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

—

115

C₄²

C₂×D₄

yes

—

116

C₄²

C₂×D₄

yes

characteristic

117

C₁₆

—

118

C₁₆

—

119

C₁₆

—

120

Q₈

—

121

Q₈

—

122

Q₈

—

123

Q₈

—

124

Q₈

—

125

Q₈

—

126

Q₈

—

127

Q₈

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

C₂×D₈

yes

—

135

C₂×C₄

C₂×D₈

yes

—

136

C₂×C₄

C₂×D₈

yes

characteristic

137

C₂×C₄

C₂×D₈

yes

characteristic

138

C₂×C₄

C₂²×D₄

yes

characteristic

139

C₈

—

140

C₈

—

141

C₈

C₂×#41

yes

characteristic

142

C₈

2₋¹⁺⁴

yes

characteristic

143

C₂²

C₂²×D₈

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

#510

yes

—

154

C₄

#548

yes

characteristic

155

C₄

#577

yes

characteristic

156

C₂

#3358

yes

characteristic

157

C₂

C₂×#510

yes

characteristic

158

C₂

#3417

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂²	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ C₈×Q₈ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

subgroup

G/H

center, socle, prime radical

C₂²

C₂²×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂⁴

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ C₈×Q₈ ◁ G

LECS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

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

subgroup	index
#3395	2
#3383	2
#2245	2
#2241	2
#2229	2
#2225	2
#2209	2
#2183	2
#2176	2
C₄×Q₃₂	2

subgroup

index

C₄×Q₃₂

Subgroups — #33941

Conjugacy classes of subgroups

Maximal subgroups