Group #25249108 — subgroups

Subgroups — #25249108

Order 11008.

662 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 219 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	#19142958	C₂	1	1	yes	maximal, characteristic
2	#19135565	C₂	1	4	yes	maximal
3	#19135563	C₂	1	4	yes	maximal
4	#19134725	C₂	1	4	yes	maximal
5	C₄×#13063236	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#2859	C₂	1	1	yes	maximal, characteristic
7	C₂×#13063317	C₂²	1	2	yes	—
8	C₂×#13063236	C₂²	1	2	yes	—
9	C₂×#13063236	C₂²	1	2	yes	—
10	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
11	#14582797	—	2	4	no	—
12	#14582769	C₂²	1	2	yes	—
13	#14582765	C₂²	1	2	yes	—
14	#14582661	C₂²	1	16	yes	—
15	C₂×#125×C₄₃	C₂²	1	2	yes	—
16	C₄₃×#389	—	2	4	no	—
17	C₄₃×#384	C₂²	1	2	yes	—
18	C₄₃×#382	C₂²	1	2	yes	—
19	C₄³×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
21	#13063317	—	2	8	no	—
22	C₂×C₄⋊Dic₄₃	—	2	4	no	—
23	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
24	C₂×Dic₄₃⋊C₄	—	2	4	no	—
25	#13063236	—	2	4	no	—
26	#13063236	—	2	4	no	—
27	C₄×C₄₃⋊C₈	Q₈	1	8	yes	—
28	C₄₃⋊#95	—	2	4	no	—
29	#125×C₄₃	—	2	8	no	—
30	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
31	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
32	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
33	C₂×C₄²×C₄₃	D₄	1	4	yes	—
34	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
35	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
36	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
37	#95×C₄₃	—	2	4	no	—
38	C₂²×C₄×C₄₃	—	2	4	no	—
39	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
40	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
41	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
42	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
43	C₂²×Dic₄₃	—	2	4	no	—
44	C₄⋊C₄×C₄₃	—	2	8	no	—
45	C₄⋊C₄×C₄₃	—	4	8	no	—
46	C₄⋊C₄×C₄₃	—	4	8	no	—
47	C₄²×C₄₃	—	4	4	no	—
48	C₄²×C₄₃	C₂×Q₈	1	4	yes	—
49	C₄²×C₄₃	#41	1	4	yes	—
50	C₄²×C₄₃	#41	1	4	yes	—
51	C₄⋊Dic₄₃	—	2	8	no	—
52	C₄⋊Dic₄₃	—	4	8	no	—
53	Dic₄₃⋊C₄	—	4	8	no	—
54	C₂×C₄₃⋊C₈	—	2	4	no	—
55	C₂×C₄₃⋊C₈	—	2	4	no	—
56	C₂×C₄₃⋊C₈	C₂×Q₈	1	8	yes	—
57	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
58	C₂×C₄×C₄₃	—	2	4	no	—
59	C₂×C₄×C₄₃	—	2	4	no	—
60	C₂×C₄×C₄₃	—	2	4	no	—
61	C₂×C₄×C₄₃	—	4	4	no	—
62	C₂×C₄×C₄₃	—	4	8	no	—
63	C₂×C₄×C₄₃	#124	1	4	yes	—
64	C₂×C₄×C₄₃	#124	1	4	yes	—
65	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
66	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
67	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
68	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
69	C₂×Dic₄₃	—	4	4	no	—
70	C₂×Dic₄₃	—	4	8	no	—
71	C₄₃⋊C₈	—	2	8	no	—
72	#33299	—	43	1	no	maximal, Sylow
73	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
74	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
75	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
76	C₂²×C₄₃	#575	1	4	yes	—
77	C₄×C₄₃	—	2	4	no	—
78	C₄×C₄₃	—	2	4	no	—
79	C₄×C₄₃	—	2	4	no	—
80	C₄×C₄₃	—	8	4	no	—
81	C₄×C₄₃	#533	1	4	yes	—
82	Dic₄₃	—	8	4	no	—
83	#2859	—	43	1	no	—
84	#2859	D₄₃	1	1	yes	characteristic
85	#1992	—	43	4	no	—
86	#1992	—	43	4	no	—
87	#1835	—	43	4	no	—
88	C₄×#97	—	43	1	no	—
89	C₂×C₄₃	#2862	1	1	yes	characteristic
90	C₂×C₄₃	#3142	1	2	yes	—
91	C₂×C₄₃	#3142	1	2	yes	—
92	C₂×C₄₃	#3162	1	2	yes	—
93	C₂×#125	—	43	2	no	—
94	C₂×#125	C₂×D₄₃	1	2	yes	—
95	C₂×#97	—	43	2	no	—
96	C₂×#97	—	43	2	no	—
97	C₂×C₄×C₈	—	43	2	no	—
98	#389	—	2	4	no	—
99	#389	—	86	4	no	—
100	#384	—	43	2	no	—
101	#384	C₂×D₄₃	1	2	yes	—
102	#382	—	43	2	no	—
103	#382	C₂×D₄₃	1	2	yes	—
104	C₄³	C₂×D₄₃	1	1	yes	characteristic
105	#340	—	43	16	no	—
106	C₄₃	#33299	1	1	yes	characteristic, complemented, Sylow
107	C₂²×C₈	—	43	4	no	—
108	#125	—	2	8	no	—
109	#125	—	86	8	no	—
110	C₂×C₄⋊C₄	—	2	4	no	—
111	C₂×C₄⋊C₄	—	2	4	no	—
112	C₂×C₄⋊C₄	—	43	4	no	—
113	C₂×C₄⋊C₄	—	86	4	no	—
114	C₂×C₄⋊C₄	—	86	4	no	—
115	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
116	C₂×C₄²	C₂²⋊D₄₃	1	4	yes	—
117	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
118	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
119	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
120	#97	—	86	4	no	—
121	#97	—	86	4	no	—
122	C₄×C₈	—	43	8	no	—
123	#95	—	2	4	no	—
124	#95	—	86	4	no	—
125	C₂²×C₄	—	2	4	no	—
126	C₂²×C₄	—	86	4	no	—
127	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
128	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
129	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
130	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
131	C₂×C₈	—	43	8	no	—
132	C₂×C₈	—	86	4	no	—
133	C₂×C₈	—	86	4	no	—
134	C₄⋊C₄	—	2	8	no	—
135	C₄⋊C₄	—	4	8	no	—
136	C₄⋊C₄	—	4	8	no	—
137	C₄⋊C₄	—	86	8	no	—
138	C₄⋊C₄	—	172	8	no	—
139	C₄⋊C₄	—	172	8	no	—
140	C₄²	—	4	4	no	—
141	C₄²	#10621900	1	4	yes	—
142	C₄²	Q₈×D₄₃	1	4	yes	—
143	C₄²	#10621902	1	4	yes	—
144	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
145	C₂×C₄	—	2	4	no	—
146	C₂×C₄	—	2	4	no	—
147	C₂×C₄	—	2	4	no	—
148	C₂×C₄	—	4	4	no	—
149	C₂×C₄	—	4	8	no	—
150	C₂×C₄	—	172	4	no	—
151	C₂×C₄	—	172	8	no	—
152	C₂×C₄	#13063312	1	4	yes	—
153	C₂×C₄	#13063314	1	4	yes	—
154	C₂×C₄	#13063323	1	4	yes	—
155	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
156	C₂×C₄	C₂×#10621900	1	2	yes	—
157	C₂×C₄	C₂×#10621902	1	2	yes	—
158	C₈	—	86	8	no	—
159	C₂²	C₂×#13063312	1	1	yes	characteristic
160	C₂²	C₂×#13063314	1	1	yes	characteristic
161	C₂²	C₂×#13063323	1	1	yes	characteristic
162	C₂²	#14583697	1	4	yes	—
163	C₄	—	2	4	no	—
164	C₄	—	2	4	no	—
165	C₄	—	2	4	no	—
166	C₄	—	8	4	no	—
167	C₄	—	344	4	no	—
168	C₄	#14583454	1	4	yes	—
169	C₂	#19142972	1	1	yes	characteristic
170	C₂	#19144995	1	2	yes	—
171	C₂	#19144998	1	2	yes	—
172	C₂	#19145117	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19142958

C₂

yes

maximal, characteristic

#19135565

C₂

yes

maximal

#19135563

C₂

yes

maximal

#19134725

C₂

yes

maximal

C₄×#13063236

C₂

yes

maximal, characteristic

C₄₃×#2859

C₂

yes

maximal, characteristic

C₂×#13063317

C₂²

yes

—

C₂×#13063236

C₂²

yes

—

C₂×#13063236

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

#14582797

—

#14582769

C₂²

yes

—

#14582765

C₂²

yes

—

#14582661

C₂²

yes

—

C₂×#125×C₄₃

C₂²

yes

—

C₄₃×#389

—

C₄₃×#384

C₂²

yes

—

C₄₃×#382

C₂²

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂³

yes

—

#13063317

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂³

yes

—

C₂×Dic₄₃⋊C₄

—

#13063236

—

#13063236

—

C₄×C₄₃⋊C₈

Q₈

yes

—

C₄₃⋊#95

—

#125×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂³

yes

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#95×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×Q₈

yes

—

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×Q₈

yes

—

C₂³×C₄₃

C₂²×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#124

yes

—

C₂×C₄×C₄₃

#124

yes

—

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂²×Q₈

yes

—

C₂×C₄×C₄₃

C₂×#41

yes

—

C₂×C₄×C₄₃

C₂×#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂²×C₄₃

#575

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#533

yes

—

Dic₄₃

—

#2859

—

#2859

D₄₃

yes

—

—

—

C₄×#97

—

C₂×C₄₃

#2862

yes

characteristic

C₂×C₄₃

#3142

yes

—

C₂×C₄₃

#3142

yes

—

C₂×C₄₃

#3162

yes

—

C₂×#125

—

C₂×#125

C₂×D₄₃

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

#389

—

#389

—

100

#384

—

101

#384

C₂×D₄₃

yes

—

102

#382

—

103

#382

C₂×D₄₃

yes

—

104

C₄³

C₂×D₄₃

yes

characteristic

105

#340

—

106

C₄₃

#33299

yes

characteristic, complemented, Sylow

107

C₂²×C₈

—

108

#125

—

109

#125

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

C₂²×D₄₃

yes

—

116

C₂×C₄²

C₂²⋊D₄₃

yes

—

117

C₂×C₄²

C₂²×D₄₃

yes

characteristic

118

C₂×C₄²

C₂²×D₄₃

yes

characteristic

119

C₂×C₄²

C₂²×D₄₃

yes

characteristic

120

#97

—

121

#97

—

122

C₄×C₈

—

123

#95

—

124

#95

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

128

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

129

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

130

C₂²×C₄

C₂³×D₄₃

yes

characteristic

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

172

—

139

C₄⋊C₄

—

172

—

140

C₄²

—

141

C₄²

#10621900

yes

—

142

C₄²

Q₈×D₄₃

yes

—

143

C₄²

#10621902

yes

—

144

C₂³

C₂²×C₂²⋊D₄₃

yes

characteristic

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

172

—

151

C₂×C₄

—

172

—

152

C₂×C₄

#13063312

yes

—

153

C₂×C₄

#13063314

yes

—

154

C₂×C₄

#13063323

yes

—

155

C₂×C₄

C₂×Q₈×D₄₃

yes

—

156

C₂×C₄

C₂×#10621900

yes

—

157

C₂×C₄

C₂×#10621902

yes

—

158

C₈

—

159

C₂²

C₂×#13063312

yes

characteristic

160

C₂²

C₂×#13063314

yes

characteristic

161

C₂²

C₂×#13063323

yes

characteristic

162

C₂²

#14583697

yes

—

163

C₄

—

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

—

344

—

168

C₄

#14583454

yes

—

169

C₂

#19142972

yes

characteristic

170

C₂

#19144995

yes

—

171

C₂

#19144998

yes

—

172

C₂

#19145117

yes

—

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₃
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2859	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
hypercenter	#2859	D₄₃
hypocenter	C₄₃	#33299
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2859

subgroup

G/H

center

C₂³

C₂²×C₂²⋊D₄₃

commutator, cosocle

C₂²×C₄×C₄₃

C₂⁴

Frattini

C₂²×C₄

C₂³×D₄₃

Fitting

C₄₃×#2859

C₂

socle, prime radical

C₂³×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #2859

N	H ≅ G/N	type
106. C₄₃	#33299	semidirect

H ≅ G/N

type

106. C₄₃

#33299

semidirect

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

subgroup	index
#19142958	2
#19135565	2
#19135563	2
#19134725	2
C₄×#13063236	2
C₄₃×#2859	2
#33299	43

subgroup

index

C₄₃×#2859

Subgroups — #25249108

Conjugacy classes of subgroups

Complements

Maximal subgroups