Group #24983939 — subgroups

Subgroups — #24983939

Order 11008.

170 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 45 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	#19136205	C₂	1	1	yes	maximal, characteristic
2	#19132735	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#1400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₈×D₄₃	C₄	1	1	yes	characteristic
5	C₂×#13063265	C₄	1	1	yes	characteristic
6	#14582733	—	2	1	no	—
7	(C₂×D₄₃)⋊C₁₆	—	2	1	no	—
8	(C₂×D₄₃)⋊C₁₆	—	2	1	no	—
9	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
10	C₄₃×M₆₄	—	2	1	no	—
11	C₂²×C₄×D₄₃	C₈	1	1	yes	characteristic
12	C₂²×C₄₃⋊C₈	C₈	1	1	yes	characteristic
13	C₂×C₈×D₄₃	—	2	1	no	—
14	C₂×C₈×D₄₃	—	2	1	no	—
15	C₂×C₈×D₄₃	—	4	1	no	—
16	C₂×C₈×D₄₃	—	4	1	no	—
17	#13063265	—	4	1	no	—
18	C₂×C₄₃⋊C₁₆	—	2	1	no	—
19	C₄₃⋊C₃₂	—	4	1	no	—
20	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
21	M₃₂×C₄₃	—	4	1	no	—
22	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
23	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
24	C₃₂×C₄₃	—	4	1	no	—
25	C₂³×D₄₃	C₁₆	1	1	yes	characteristic
26	C₂²×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
27	C₂²×Dic₄₃	C₁₆	1	1	yes	characteristic
28	C₂×C₄×D₄₃	—	2	1	no	—
29	C₂×C₄×D₄₃	—	2	1	no	—
30	C₂×C₄×D₄₃	—	4	1	no	—
31	C₂×C₄×D₄₃	—	4	1	no	—
32	C₂×C₈×C₄₃	—	2	1	no	—
33	C₂×C₈×C₄₃	—	2	1	no	—
34	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₄₃	M₁₆	1	1	yes	characteristic
36	C₂×C₄₃⋊C₈	—	2	1	no	—
37	C₂×C₄₃⋊C₈	—	4	1	no	—
38	C₈×D₄₃	—	4	2	no	—
39	C₈×D₄₃	—	4	1	no	—
40	C₈×D₄₃	—	4	1	no	—
41	C₁₆×C₄₃	—	2	1	no	—
42	C₁₆×C₄₃	—	2	1	no	—
43	C₄₃⋊C₁₆	—	4	1	no	—
44	C₂³×C₄₃	C₂×C₁₆	1	1	yes	characteristic
45	C₂²×D₄₃	—	2	1	no	—
46	C₂²×D₄₃	—	4	2	no	—
47	C₂²×D₄₃	—	4	1	no	—
48	C₂×C₄×C₄₃	—	2	1	no	—
49	C₂×C₄×C₄₃	—	2	1	no	—
50	C₂×C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
51	C₂×C₄×C₄₃	M₃₂	1	1	yes	characteristic
52	C₂×Dic₄₃	—	2	1	no	—
53	C₂×Dic₄₃	—	4	1	no	—
54	C₄×D₄₃	—	4	2	no	—
55	C₄×D₄₃	—	4	1	no	—
56	C₄×D₄₃	—	4	1	no	—
57	C₈×C₄₃	—	2	1	no	—
58	C₈×C₄₃	#99	1	1	yes	characteristic
59	C₈×C₄₃	#100	1	1	yes	characteristic
60	C₄₃⋊C₈	—	4	1	no	—
61	#7336	—	43	1	no	maximal, Sylow
62	C₂²×C₄₃	—	2	1	no	—
63	C₂²×C₄₃	—	4	1	no	—
64	C₂²×C₄₃	C₂²⋊C₁₆	1	1	yes	characteristic
65	C₂×D₄₃	—	2	2	no	—
66	C₂×D₄₃	—	4	1	no	—
67	C₂×D₄₃	—	4	2	no	—
68	C₂×D₄₃	—	4	1	no	—
69	C₂×D₄₃	—	4	2	no	—
70	C₄×C₄₃	—	2	1	no	—
71	C₄×C₄₃	#323	1	1	yes	characteristic
72	C₄×C₄₃	#349	1	1	yes	characteristic
73	Dic₄₃	—	4	1	no	—
74	#2112	—	43	1	no	—
75	#1400	—	43	1	no	—
76	#1400	D₄₃	1	1	yes	characteristic, complemented
77	C₂×C₄₃	—	2	1	no	—
78	C₂×C₄₃	—	4	1	no	—
79	C₂×C₄₃	#1314	1	1	yes	characteristic
80	D₄₃	—	4	2	no	—
81	C₂³×C₈	—	43	1	no	—
82	C₂×M₃₂	—	43	1	no	—
83	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
84	M₆₄	—	2	1	no	—
85	M₆₄	—	86	1	no	—
86	C₂²⋊C₁₆	—	86	1	no	—
87	C₂²⋊C₁₆	—	86	1	no	—
88	C₄₃	#7336	1	1	yes	characteristic, complemented, Sylow
89	C₂³×C₄	—	43	1	no	—
90	C₂²×C₈	—	43	1	no	—
91	C₂²×C₈	—	86	1	no	—
92	C₂²×C₈	—	86	1	no	—
93	C₂²×C₈	—	172	1	no	—
94	C₂²×C₈	—	172	1	no	—
95	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
96	M₃₂	—	4	1	no	—
97	M₃₂	—	172	1	no	—
98	C₂×C₁₆	—	86	1	no	—
99	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
100	C₂×C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
101	C₃₂	—	4	1	no	—
102	C₃₂	—	172	1	no	—
103	C₂⁴	—	43	1	no	—
104	C₂²×C₄	—	43	1	no	—
105	C₂²×C₄	—	86	1	no	—
106	C₂²×C₄	—	86	1	no	—
107	C₂²×C₄	—	172	1	no	—
108	C₂²×C₄	—	172	1	no	—
109	C₂²×C₄	C₈×D₄₃	1	1	yes	characteristic
110	C₂×C₈	—	2	1	no	—
111	C₂×C₈	—	2	1	no	—
112	C₂×C₈	—	86	1	no	—
113	C₂×C₈	—	172	2	no	—
114	C₂×C₈	—	172	1	no	—
115	C₂×C₈	—	172	1	no	—
116	C₂×C₈	—	172	1	no	—
117	C₂×C₈	#10621872	1	1	yes	characteristic
118	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
119	C₁₆	—	2	1	no	—
120	C₁₆	—	2	1	no	—
121	C₁₆	—	172	1	no	—
122	C₂³	—	86	1	no	—
123	C₂³	—	172	1	no	—
124	C₂³	—	172	2	no	—
125	C₂³	C₁₆×D₄₃	1	1	yes	characteristic
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	86	1	no	—
129	C₂×C₄	—	172	2	no	—
130	C₂×C₄	—	172	1	no	—
131	C₂×C₄	—	172	1	no	—
132	C₂×C₄	—	172	1	no	—
133	C₂×C₄	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
134	C₂×C₄	#13063264	1	1	yes	characteristic
135	C₈	—	2	1	no	—
136	C₈	—	172	1	no	—
137	C₈	#13063239	1	1	yes	characteristic
138	C₈	#13063241	1	1	yes	characteristic
139	C₂²	—	2	1	no	—
140	C₂²	—	4	1	no	—
141	C₂²	—	86	2	no	—
142	C₂²	—	172	1	no	—
143	C₂²	—	172	2	no	—
144	C₂²	—	172	2	no	—
145	C₂²	—	172	1	no	—
146	C₂²	(C₂×D₄₃)⋊C₁₆	1	1	yes	characteristic
147	C₄	—	2	1	no	—
148	C₄	—	172	1	no	—
149	C₄	#14582622	1	1	yes	characteristic
150	C₄	#14582680	1	1	yes	characteristic
151	C₂	—	2	1	no	—
152	C₂	—	4	1	no	—
153	C₂	—	172	2	no	—
154	C₂	#19132518	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136205

C₂

yes

maximal, characteristic

#19132735

C₂

yes

maximal, characteristic, complemented

C₄₃×#1400

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₄₃

C₄

yes

characteristic

C₂×#13063265

C₄

yes

characteristic

#14582733

—

(C₂×D₄₃)⋊C₁₆

—

(C₂×D₄₃)⋊C₁₆

—

C₂×M₃₂×C₄₃

C₂²

yes

characteristic

C₄₃×M₆₄

—

C₂²×C₄×D₄₃

C₈

yes

characteristic

C₂²×C₄₃⋊C₈

C₈

yes

characteristic

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

—

#13063265

—

C₂×C₄₃⋊C₁₆

—

C₄₃⋊C₃₂

—

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

D₄

yes

characteristic

C₃₂×C₄₃

—

C₂³×D₄₃

C₁₆

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂²×Dic₄₃

C₁₆

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

M₁₆

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₈×D₄₃

—

C₈×D₄₃

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

C₂×C₁₆

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₄₃

M₃₂

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

—

#7336

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊C₁₆

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#2112

—

#1400

—

#1400

D₄₃

yes

characteristic, complemented

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#1314

yes

characteristic

D₄₃

—

C₂³×C₈

—

C₂×M₃₂

—

C₂×M₃₂

C₂×D₄₃

yes

characteristic

M₆₄

—

M₆₄

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

—

C₄₃

#7336

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

172

—

C₂²×C₈

—

172

—

C₂²×C₈

C₄×D₄₃

yes

characteristic

M₃₂

—

M₃₂

—

172

—

C₂×C₁₆

—

C₂×C₁₆

D₁₇₂

yes

characteristic

100

C₂×C₁₆

C₂²⋊D₄₃

yes

characteristic

101

C₃₂

—

102

C₃₂

—

172

—

103

C₂⁴

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

172

—

108

C₂²×C₄

—

172

—

109

C₂²×C₄

C₈×D₄₃

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

172

—

114

C₂×C₈

—

172

—

115

C₂×C₈

—

172

—

116

C₂×C₈

—

172

—

117

C₂×C₈

#10621872

yes

characteristic

118

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

characteristic

119

C₁₆

—

120

C₁₆

—

121

C₁₆

—

172

—

122

C₂³

—

123

C₂³

—

172

—

124

C₂³

—

172

—

125

C₂³

C₁₆×D₄₃

yes

characteristic

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

172

—

130

C₂×C₄

—

172

—

131

C₂×C₄

—

172

—

132

C₂×C₄

—

172

—

133

C₂×C₄

(C₂×D₄₃)⋊C₈

yes

characteristic

134

C₂×C₄

#13063264

yes

characteristic

135

C₈

—

136

C₈

—

172

—

137

C₈

#13063239

yes

characteristic

138

C₈

#13063241

yes

characteristic

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

172

—

143

C₂²

—

172

—

144

C₂²

—

172

—

145

C₂²

—

172

—

146

C₂²

(C₂×D₄₃)⋊C₁₆

yes

characteristic

147

C₄

—

148

C₄

—

172

—

149

C₄

#14582622

yes

characteristic

150

C₄

#14582680

yes

characteristic

151

C₂

—

152

C₂

—

153

C₂

—

172

—

154

C₂

#19132518

yes

characteristic

	subgroup	G/H
center	C₈	#13063239
commutator	C₂³×C₄₃	C₂×C₁₆
Frattini	C₂×M₃₂	C₂×D₄₃
Fitting	C₄₃×#1400	C₂
socle	C₂×C₄₃	#1314
prime radical	C₂³×D₄₃	C₁₆
cosocle	C₂×M₃₂×C₄₃	C₂²
hypercenter	#1400	D₄₃
hypocenter	C₄₃	#7336
LCS	G ▷ C₂³×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×M₃₂ ◁ #1400

subgroup

G/H

center

C₈

#13063239

commutator

C₂³×C₄₃

C₂×C₁₆

Frattini

C₂×M₃₂

C₂×D₄₃

Fitting

C₄₃×#1400

C₂

socle

C₂×C₄₃

#1314

prime radical

C₂³×D₄₃

C₁₆

cosocle

C₂×M₃₂×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×M₃₂ ◁ #1400

N	H ≅ G/N	type
2. #19132735	C₂	semidirect
3. C₄₃×#1400	C₂	semidirect
76. #1400	D₄₃	semidirect
88. C₄₃	#7336	semidirect

H ≅ G/N

type

2. #19132735

C₂

semidirect

3. C₄₃×#1400

C₂

semidirect

76. #1400

D₄₃

semidirect

88. C₄₃

#7336

semidirect

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

subgroup	index
#19136205	2
#19132735	2
C₄₃×#1400	2
#7336	43

subgroup

index

#19136205

#19132735

C₄₃×#1400

#7336

Subgroups — #24983939

Conjugacy classes of subgroups

Complements

Maximal subgroups