Group #10582 — subgroups

Subgroups — #10582

Order 256.

213 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 213 conjugacy classes of subgroups — too many to draw. Only its 77 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	#2552	C₂	1	1	yes	maximal, characteristic
2	#1948	C₂	1	1	yes	maximal, characteristic
3	#1948	C₂	1	1	yes	maximal, characteristic
4	#1834	C₂	1	1	yes	maximal, characteristic
5	#1296	C₂	1	1	yes	maximal, characteristic
6	#1279	C₂	1	1	yes	maximal, characteristic
7	#1279	C₂	1	1	yes	maximal, characteristic
8	C₂×#125	—	2	1	no	—
9	C₂×#106	—	2	1	no	—
10	C₂×#106	—	2	1	no	—
11	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
14	#398	—	2	2	no	—
15	#389	—	2	1	no	—
16	#389	—	2	1	no	—
17	#384	—	2	1	no	—
18	#384	C₂²	1	1	yes	characteristic
19	#384	C₂²	1	1	yes	characteristic
20	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	#340	—	2	2	no	—
23	#340	—	2	1	no	—
24	#340	—	2	1	no	—
25	C₂²×C₈	—	2	1	no	—
26	C₂²×C₈	—	2	1	no	—
27	C₂²×C₈	—	2	1	no	—
28	#125	—	4	2	no	—
29	#125	—	4	2	no	—
30	C₂×C₄⋊C₄	—	2	2	no	—
31	C₂×C₄⋊C₄	—	2	2	no	—
32	C₂×C₄⋊C₄	—	2	1	no	—
33	C₂×C₄⋊C₄	—	2	1	no	—
34	C₂×C₄⋊C₄	—	2	1	no	—
35	C₂×C₄⋊C₄	—	2	1	no	—
36	C₂×C₄⋊C₄	—	2	1	no	—
37	C₂×C₄⋊C₄	—	2	2	no	—
38	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄	D₄	1	2	yes	—
43	C₂×C₄²	—	2	1	no	—
44	C₂×C₄²	—	2	1	no	—
45	C₂×C₄²	C₂³	1	1	yes	characteristic
46	#106	—	4	2	no	—
47	#106	—	4	2	no	—
48	C₄⋊C₈	—	2	1	no	—
49	C₄⋊C₈	—	2	1	no	—
50	C₄⋊C₈	Q₈	1	2	yes	—
51	C₄⋊C₈	Q₈	1	2	yes	—
52	C₄×C₈	—	2	1	no	—
53	C₄×C₈	Q₈	1	2	yes	—
54	#95	—	2	2	no	—
55	#95	—	2	1	no	—
56	#95	—	2	1	no	—
57	C₂²×C₄	—	2	1	no	—
58	C₂²×C₄	—	2	1	no	—
59	C₂²×C₄	—	2	1	no	—
60	C₂²×C₄	—	2	1	no	—
61	C₂²×C₄	—	2	2	no	—
62	C₂²×C₄	—	4	1	no	—
63	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈	—	2	2	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	4	1	no	—
70	C₂×C₈	—	4	1	no	—
71	C₂×C₈	—	4	1	no	—
72	C₂×C₈	—	4	1	no	—
73	C₂×C₈	—	4	1	no	—
74	C₂×C₈	—	4	1	no	—
75	C₄⋊C₄	—	2	1	no	—
76	C₄⋊C₄	—	2	1	no	—
77	C₄⋊C₄	—	2	1	no	—
78	C₄⋊C₄	—	2	1	no	—
79	C₄⋊C₄	—	2	1	no	—
80	C₄⋊C₄	—	2	1	no	—
81	C₄⋊C₄	—	4	2	no	—
82	C₄⋊C₄	—	4	4	no	—
83	C₄⋊C₄	—	4	4	no	—
84	C₄⋊C₄	—	4	2	no	—
85	C₄⋊C₄	—	4	1	no	—
86	C₄⋊C₄	—	4	1	no	—
87	C₄⋊C₄	—	4	1	no	—
88	C₄⋊C₄	—	4	1	no	—
89	C₄⋊C₄	—	4	1	no	—
90	C₄⋊C₄	—	4	1	no	—
91	C₄⋊C₄	—	4	1	no	—
92	C₄⋊C₄	—	4	1	no	—
93	C₄⋊C₄	—	8	2	no	—
94	C₄⋊C₄	SD₁₆	1	2	yes	—
95	C₄⋊C₄	SD₁₆	1	2	yes	—
96	C₄²	—	4	1	no	—
97	C₄²	—	4	1	no	—
98	C₄²	—	4	1	no	—
99	C₄²	—	4	1	no	—
100	C₄²	C₂×Q₈	1	1	yes	characteristic
101	C₄²	C₂×Q₈	1	1	yes	characteristic
102	C₄²	C₂×Q₈	1	1	yes	characteristic
103	C₄²	#41	1	1	yes	characteristic
104	C₂³	#120	1	1	yes	characteristic
105	C₂×C₄	—	2	1	no	—
106	C₂×C₄	—	2	1	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	4	1	no	—
110	C₂×C₄	—	4	1	no	—
111	C₂×C₄	—	4	1	no	—
112	C₂×C₄	—	4	1	no	—
113	C₂×C₄	—	4	1	no	—
114	C₂×C₄	—	4	2	no	—
115	C₂×C₄	—	4	1	no	—
116	C₂×C₄	—	4	1	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	4	2	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	8	1	no	—
123	C₂×C₄	—	8	1	no	—
124	C₂×C₄	—	8	1	no	—
125	C₂×C₄	C₂²⋊Q₈	1	1	yes	characteristic
126	C₂×C₄	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂×C₄	C₂²⋊Q₈	1	1	yes	characteristic
128	C₂×C₄	C₄⋊Q₈	1	1	yes	characteristic
129	C₂×C₄	C₄⋊Q₈	1	1	yes	characteristic
130	C₂×C₄	C₄⋊Q₈	1	1	yes	characteristic
131	C₂×C₄	C₂×SD₁₆	1	1	yes	characteristic
132	C₂×C₄	C₂×SD₁₆	1	1	yes	characteristic
133	C₂×C₄	#135	1	1	yes	characteristic
134	C₂×C₄	#135	1	1	yes	characteristic
135	C₂×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
136	C₂×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
137	C₂×C₄	#137	1	1	yes	characteristic
138	C₂×C₄	#137	1	1	yes	characteristic
139	C₈	—	4	2	no	—
140	C₈	—	4	2	no	—
141	C₈	—	4	2	no	—
142	C₂²	#395	1	1	yes	characteristic
143	C₂²	#448	1	1	yes	characteristic
144	C₂²	#449	1	1	yes	characteristic
145	C₂²	#450	1	1	yes	characteristic
146	C₂²	#452	1	1	yes	characteristic
147	C₂²	#454	1	1	yes	characteristic
148	C₂²	#455	1	1	yes	characteristic
149	C₄	—	2	1	no	—
150	C₄	—	2	1	no	—
151	C₄	—	4	2	no	—
152	C₄	—	4	2	no	—
153	C₄	—	8	1	no	—
154	C₄	—	8	1	no	—
155	C₄	—	8	2	no	—
156	C₄	—	16	1	no	—
157	C₄	#475	1	1	yes	characteristic
158	C₄	#476	1	1	yes	characteristic
159	C₄	#478	1	1	yes	characteristic
160	C₄	#479	1	1	yes	characteristic
161	C₄	#498	1	1	yes	characteristic
162	C₄	#499	1	1	yes	characteristic
163	C₄	#501	1	1	yes	characteristic
164	C₄	#501	1	1	yes	characteristic
165	C₂	#1626	1	1	yes	characteristic
166	C₂	#1635	1	1	yes	characteristic
167	C₂	#1642	1	1	yes	characteristic
168	C₂	#1643	1	1	yes	characteristic
169	C₂	#2058	1	1	yes	characteristic
170	C₂	#2059	1	1	yes	characteristic
171	C₂	#2061	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#2552

C₂

yes

maximal, characteristic

#1948

C₂

yes

maximal, characteristic

#1948

C₂

yes

maximal, characteristic

#1834

C₂

yes

maximal, characteristic

#1296

C₂

yes

maximal, characteristic

#1279

C₂

yes

maximal, characteristic

#1279

C₂

yes

maximal, characteristic

C₂×#125

—

C₂×#106

—

C₂×#106

—

C₂×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₄×C₈

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

#384

C₂²

yes

characteristic

C₄×C₄⋊C₄

C₂²

yes

characteristic

C₄×C₄⋊C₄

C₂²

yes

—

—

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₄

yes

characteristic

C₂×C₄⋊C₄

D₄

yes

characteristic

C₂×C₄⋊C₄

D₄

yes

characteristic

C₂×C₄⋊C₄

D₄

yes

characteristic

C₂×C₄⋊C₄

D₄

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂³

yes

characteristic

#106

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

Q₈

yes

—

C₄⋊C₈

Q₈

yes

—

C₄×C₈

—

C₄×C₈

Q₈

yes

—

#95

—

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄

yes

characteristic

C₂²×C₄

C₂×D₄

yes

characteristic

C₂²×C₄

C₂×D₄

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

SD₁₆

yes

—

C₄⋊C₄

SD₁₆

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

100

C₄²

C₂×Q₈

yes

characteristic

101

C₄²

C₂×Q₈

yes

characteristic

102

C₄²

C₂×Q₈

yes

characteristic

103

C₄²

#41

yes

characteristic

104

C₂³

#120

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

C₂²⋊Q₈

yes

characteristic

126

C₂×C₄

C₂²⋊Q₈

yes

characteristic

127

C₂×C₄

C₂²⋊Q₈

yes

characteristic

128

C₂×C₄

C₄⋊Q₈

yes

characteristic

129

C₂×C₄

C₄⋊Q₈

yes

characteristic

130

C₂×C₄

C₄⋊Q₈

yes

characteristic

131

C₂×C₄

C₂×SD₁₆

yes

characteristic

132

C₂×C₄

C₂×SD₁₆

yes

characteristic

133

C₂×C₄

#135

yes

characteristic

134

C₂×C₄

#135

yes

characteristic

135

C₂×C₄

AGL(1,ℤ/8)

yes

characteristic

136

C₂×C₄

AGL(1,ℤ/8)

yes

characteristic

137

C₂×C₄

#137

yes

characteristic

138

C₂×C₄

#137

yes

characteristic

139

C₈

—

140

C₈

—

141

C₈

—

142

C₂²

#395

yes

characteristic

143

C₂²

#448

yes

characteristic

144

C₂²

#449

yes

characteristic

145

C₂²

#450

yes

characteristic

146

C₂²

#452

yes

characteristic

147

C₂²

#454

yes

characteristic

148

C₂²

#455

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

#475

yes

characteristic

158

C₄

#476

yes

characteristic

159

C₄

#478

yes

characteristic

160

C₄

#479

yes

characteristic

161

C₄

#498

yes

characteristic

162

C₄

#499

yes

characteristic

163

C₄

#501

yes

characteristic

164

C₄

#501

yes

characteristic

165

C₂

#1626

yes

characteristic

166

C₂

#1635

yes

characteristic

167

C₂

#1642

yes

characteristic

168

C₂

#1643

yes

characteristic

169

C₂

#2058

yes

characteristic

170

C₂

#2059

yes

characteristic

171

C₂

#2061

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

subgroup

G/H

center, socle, prime radical

C₂³

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ G

LECS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

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

subgroup	index
#2552	2
#1948	2
#1834	2
#1296	2
#1279	2

subgroup

index

Subgroups — #10582

Conjugacy classes of subgroups

Maximal subgroups