Group #2524 — subgroups

Subgroups — #2524

Order 128.

182 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 92 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	#400	C₂	1	1	yes	maximal, characteristic
2	#400	C₂	1	1	yes	maximal, characteristic
3	#398	C₂	1	1	yes	maximal, characteristic
4	#398	C₂	1	1	yes	maximal, characteristic
5	#387	C₂	1	1	yes	maximal, characteristic
6	#387	C₂	1	1	yes	maximal, characteristic
7	#387	C₂	1	1	yes	maximal, characteristic
8	#387	C₂	1	1	yes	maximal, characteristic
9	#387	C₂	1	1	yes	maximal, characteristic
10	#387	C₂	1	1	yes	maximal, characteristic
11	#383	C₂	1	1	yes	maximal, characteristic
12	#383	C₂	1	1	yes	maximal, characteristic
13	#382	C₂	1	1	yes	maximal, characteristic
14	C₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
15	C₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₄²	C₂²	1	1	yes	characteristic
27	C₂×C₄²	C₂²	1	1	yes	characteristic
28	C₂×C₄²	C₂²	1	1	yes	characteristic
29	C₂×C₄²	C₂²	1	1	yes	characteristic
30	C₂×C₄²	C₂²	1	1	yes	characteristic
31	#95	C₂²	1	1	yes	characteristic
32	#95	C₂²	1	1	yes	characteristic
33	#95	C₂²	1	1	yes	characteristic
34	#95	C₂²	1	1	yes	characteristic
35	#95	C₂²	1	1	yes	characteristic
36	#95	C₂²	1	1	yes	characteristic
37	#95	C₂²	1	1	yes	characteristic
38	#95	C₂²	1	1	yes	characteristic
39	#95	C₂²	1	1	yes	characteristic
40	#95	C₂²	1	1	yes	characteristic
41	#95	C₂²	1	1	yes	characteristic
42	#95	C₂²	1	1	yes	characteristic
43	#95	C₂²	1	1	yes	characteristic
44	#95	C₂²	1	1	yes	characteristic
45	#95	C₂²	1	1	yes	characteristic
46	#95	C₂²	1	1	yes	characteristic
47	#95	C₂²	1	1	yes	characteristic
48	#95	C₂²	1	1	yes	characteristic
49	#95	C₂²	1	1	yes	characteristic
50	#95	C₂²	1	1	yes	characteristic
51	C₂²×C₄	C₂³	1	1	yes	characteristic
52	C₂²×C₄	C₂³	1	1	yes	characteristic
53	C₂²×C₄	C₂³	1	1	yes	characteristic
54	C₂²×C₄	C₂³	1	1	yes	characteristic
55	C₂²×C₄	C₂³	1	1	yes	characteristic
56	C₂²×C₄	C₂³	1	1	yes	characteristic
57	C₂²×C₄	C₂³	1	1	yes	characteristic
58	C₂²×C₄	C₂³	1	1	yes	characteristic
59	C₂²×C₄	C₂³	1	1	yes	characteristic
60	C₂²×C₄	C₂³	1	1	yes	characteristic
61	C₂²×C₄	C₂³	1	1	yes	characteristic
62	C₂²×C₄	C₂³	1	1	yes	characteristic
63	C₂²×C₄	C₂³	1	1	yes	characteristic
64	C₂²×C₄	C₂³	1	1	yes	characteristic
65	C₂²×C₄	C₂³	1	1	yes	characteristic
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	2	2	no	—
68	C₄⋊C₄	—	2	2	no	—
69	C₄⋊C₄	—	2	2	no	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	2	2	no	—
74	C₄⋊C₄	—	2	2	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄²	—	2	2	no	—
77	C₄²	—	2	2	no	—
78	C₄²	—	2	2	no	—
79	C₄²	—	2	2	no	—
80	C₄²	—	2	2	no	—
81	C₂³	C₂⁴	1	1	yes	characteristic
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	2	1	no	—
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	2	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	2	1	no	—
105	C₂×C₄	—	2	1	no	—
106	C₂×C₄	—	2	1	no	—
107	C₂×C₄	—	2	1	no	—
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	#41	1	2	yes	—
123	C₂×C₄	#41	1	2	yes	—
124	C₂×C₄	#41	1	2	yes	—
125	C₂×C₄	#41	1	2	yes	—
126	C₂×C₄	#41	1	2	yes	—
127	C₂²	C₂×#41	1	1	yes	characteristic
128	C₂²	C₂×#41	1	1	yes	characteristic
129	C₂²	C₂×#41	1	1	yes	characteristic
130	C₂²	C₂×#41	1	1	yes	characteristic
131	C₂²	C₂×#41	1	1	yes	characteristic
132	C₂²	2₋¹⁺⁴	1	1	yes	characteristic
133	C₂²	2₋¹⁺⁴	1	1	yes	characteristic
134	C₄	—	2	2	no	—
135	C₄	—	2	2	no	—
136	C₄	—	2	2	no	—
137	C₄	—	2	2	no	—
138	C₄	—	2	2	no	—
139	C₄	—	4	1	no	—
140	C₄	—	4	1	no	—
141	C₄	—	4	1	no	—
142	C₄	—	4	1	no	—
143	C₄	—	4	1	no	—
144	C₄	—	4	1	no	—
145	C₄	—	4	1	no	—
146	C₄	—	4	1	no	—
147	C₄	—	4	1	no	—
148	C₄	—	4	1	no	—
149	C₂	#529	1	1	yes	characteristic
150	C₂	#529	1	1	yes	characteristic
151	C₂	#541	1	1	yes	characteristic
152	C₂	#552	1	1	yes	characteristic
153	C₂	#552	1	1	yes	characteristic
154	C₂	#552	1	1	yes	characteristic
155	C₂	#556	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#400

C₂

yes

maximal, characteristic

#400

C₂

yes

maximal, characteristic

#398

C₂

yes

maximal, characteristic

#398

C₂

yes

maximal, characteristic

#387

C₂

yes

maximal, characteristic

#387

C₂

yes

maximal, characteristic

#387

C₂

yes

maximal, characteristic

#387

C₂

yes

maximal, characteristic

#387

C₂

yes

maximal, characteristic

#387

C₂

yes

maximal, characteristic

#383

C₂

yes

maximal, characteristic

#383

C₂

yes

maximal, characteristic

#382

C₂

yes

maximal, characteristic

C₄×C₄⋊C₄

C₂

yes

maximal, characteristic

C₄×C₄⋊C₄

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄²

C₂²

yes

characteristic

C₂×C₄²

C₂²

yes

characteristic

C₂×C₄²

C₂²

yes

characteristic

C₂×C₄²

C₂²

yes

characteristic

C₂×C₄²

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

#95

C₂²

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₂²×C₄

C₂³

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂⁴

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

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

#41

yes

—

123

C₂×C₄

#41

yes

—

124

C₂×C₄

#41

yes

—

125

C₂×C₄

#41

yes

—

126

C₂×C₄

#41

yes

—

127

C₂²

C₂×#41

yes

characteristic

128

C₂²

C₂×#41

yes

characteristic

129

C₂²

C₂×#41

yes

characteristic

130

C₂²

C₂×#41

yes

characteristic

131

C₂²

C₂×#41

yes

characteristic

132

C₂²

2₋¹⁺⁴

yes

characteristic

133

C₂²

2₋¹⁺⁴

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₂

#529

yes

characteristic

150

C₂

#529

yes

characteristic

151

C₂

#541

yes

characteristic

152

C₂

#552

yes

characteristic

153

C₂

#552

yes

characteristic

154

C₂

#552

yes

characteristic

155

C₂

#556

yes

characteristic

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

subgroup

G/H

center, commutator, Frattini, socle, prime radical, cosocle

C₂³

C₂⁴

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂³ ◁ G

LECS

G ▷ C₂³ ▷ C₁

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

subgroup	index
#400	2
#398	2
#387	2
#383	2
#382	2
C₄×C₄⋊C₄	2

subgroup

index

C₄×C₄⋊C₄

Subgroups — #2524

Conjugacy classes of subgroups

Maximal subgroups