Group #24983401 — subgroups

Subgroups — #24983401

Order 11008.

182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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	#19135348	C₂	1	1	yes	maximal, characteristic
2	#19132440	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1375	C₂	1	1	yes	maximal, characteristic
4	#14582952	—	2	1	no	—
5	C₂×#13063261	C₄	1	1	yes	characteristic
6	#14582937	C₄	1	1	yes	characteristic
7	#14582925	—	2	1	no	—
8	#14582659	—	2	1	no	—
9	C₂×M₃₂×C₄₃	—	2	1	no	—
10	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×#10621877	—	2	1	no	—
12	#13063284	—	2	1	no	—
13	#13063261	—	4	1	no	—
14	#13063259	—	2	1	no	—
15	#13063257	C₈	1	2	yes	complemented
16	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
17	Dic₄₃⋊C₈	—	4	1	no	—
18	Dic₄₃⋊C₈	—	4	1	no	—
19	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
20	C₄×C₄₃⋊C₈	—	4	1	no	—
21	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
24	M₃₂×C₄₃	—	4	1	no	—
25	M₃₂×C₄₃	—	4	1	no	—
26	C₂×C₁₆×C₄₃	—	2	2	no	—
27	#97×C₄₃	—	4	1	no	—
28	C₂²×C₄×C₄₃	—	2	1	no	—
29	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₈×C₄₃	—	2	1	no	—
31	C₂×C₈×C₄₃	—	2	1	no	—
32	C₂×C₈×C₄₃	—	2	1	no	—
33	C₂×C₈×C₄₃	—	2	1	no	—
34	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈×C₄₃	M₁₆	1	1	yes	characteristic
36	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
37	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
38	C₄²×C₄₃	—	2	1	no	—
39	C₄²×C₄₃	SD₁₆	1	1	yes	characteristic
40	C₄²×C₄₃	Q₁₆	1	1	yes	characteristic
41	C₂²⋊Dic₄₃	—	4	1	no	—
42	C₄⋊Dic₄₃	—	2	2	no	—
43	C₄×Dic₄₃	—	4	1	no	—
44	#10621877	—	4	1	no	—
45	#10621877	—	4	1	no	—
46	C₂×C₄₃⋊C₈	—	4	2	no	—
47	C₂×C₄₃⋊C₈	—	4	1	no	—
48	C₁₆×C₄₃	—	4	2	no	—
49	C₂³×C₄₃	#104	1	1	yes	characteristic
50	C₂×C₄×C₄₃	—	2	1	no	—
51	C₂×C₄×C₄₃	—	2	1	no	—
52	C₂×C₄×C₄₃	—	8	1	no	—
53	C₂×C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
54	C₂×C₄×C₄₃	#99	1	1	yes	characteristic
55	C₂×C₄×C₄₃	#101	1	1	yes	characteristic
56	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
57	C₂×C₄×C₄₃	#103	1	1	yes	characteristic
58	C₂×C₄×C₄₃	#104	1	1	yes	characteristic
59	C₂×Dic₄₃	—	4	2	no	—
60	C₈×C₄₃	—	2	1	no	—
61	C₈×C₄₃	—	2	1	no	—
62	C₈×C₄₃	—	2	1	no	—
63	C₈×C₄₃	—	2	1	no	—
64	C₄₃⋊C₈	—	8	2	no	—
65	C₄₃⋊C₈	—	8	1	no	—
66	#7125	—	43	1	no	maximal, Sylow
67	C₂²×C₄₃	—	4	1	no	—
68	C₂²×C₄₃	D₄⋊C₈	1	1	yes	characteristic
69	C₂²×C₄₃	#328	1	1	yes	characteristic
70	C₂²×C₄₃	#330	1	1	yes	characteristic
71	C₄×C₄₃	—	4	1	no	—
72	C₄×C₄₃	—	4	1	no	—
73	C₄×C₄₃	#324	1	1	yes	characteristic
74	C₄×C₄₃	Q₈⋊C₈	1	1	yes	characteristic
75	C₄×C₄₃	#327	1	1	yes	characteristic
76	C₄×C₄₃	#332	1	1	yes	characteristic
77	Dic₄₃	—	8	2	no	—
78	#1946	—	43	1	no	—
79	#1375	D₄₃	1	1	yes	characteristic
80	#1281	—	43	1	no	—
81	C₂×C₄₃	—	2	1	no	—
82	C₂×C₄₃	—	2	1	no	—
83	C₂×C₄₃	—	2	1	no	—
84	C₂×C₄₃	#1271	1	1	yes	characteristic
85	C₂×M₃₂	—	2	1	no	—
86	#431	—	86	1	no	—
87	C₂×#108	—	43	1	no	—
88	#427	—	43	1	no	—
89	#424	—	86	1	no	—
90	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
91	#339	—	86	1	no	—
92	C₄₃	#7125	1	1	yes	characteristic, complemented, Sylow
93	C₂×M₁₆	—	86	1	no	—
94	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
95	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
96	#117	—	86	1	no	—
97	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
98	M₃₂	—	4	1	no	—
99	M₃₂	—	4	1	no	—
100	C₂×C₁₆	—	2	2	no	—
101	#108	—	172	1	no	—
102	#107	—	86	1	no	—
103	#106	—	43	2	no	—
104	C₄⋊C₈	—	172	1	no	—
105	C₄⋊C₈	—	172	1	no	—
106	C₄⋊C₈	—	172	1	no	—
107	C₂²⋊C₈	—	86	2	no	—
108	#97	—	4	1	no	—
109	C₄×C₈	—	172	1	no	—
110	C₂²×C₄	—	2	1	no	—
111	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
112	M₁₆	—	172	1	no	—
113	M₁₆	—	172	1	no	—
114	C₂×C₈	—	2	1	no	—
115	C₂×C₈	—	2	1	no	—
116	C₂×C₈	—	2	1	no	—
117	C₂×C₈	—	2	1	no	—
118	C₂×C₈	—	172	2	no	—
119	C₂×C₈	—	172	1	no	—
120	C₂×C₈	C₈×D₄₃	1	1	yes	characteristic
121	C₂×C₈	#10621872	1	1	yes	characteristic
122	C₂×C₈	#10621882	1	1	yes	characteristic
123	C₂×C₈	#10621884	1	1	yes	characteristic
124	C₄⋊C₄	—	86	2	no	—
125	C₂²⋊C₄	—	172	1	no	—
126	C₄²	—	2	1	no	—
127	C₄²	—	172	1	no	—
128	C₄²	#10621873	1	1	yes	characteristic
129	C₄²	Dic₁₇₂	1	1	yes	characteristic
130	C₁₆	—	4	2	no	—
131	C₂³	#13063251	1	1	yes	characteristic
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	8	1	no	—
135	C₂×C₄	—	172	2	no	—
136	C₂×C₄	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
137	C₂×C₄	#13063239	1	1	yes	characteristic
138	C₂×C₄	#13063243	1	1	yes	characteristic
139	C₂×C₄	#13063245	1	1	yes	characteristic
140	C₂×C₄	#13063250	1	1	yes	characteristic
141	C₂×C₄	#13063253	1	1	yes	characteristic
142	C₈	—	2	1	no	—
143	C₈	—	2	1	no	—
144	C₈	—	2	1	no	—
145	C₈	—	2	1	no	—
146	C₈	—	344	2	no	—
147	C₈	—	344	1	no	—
148	C₂²	—	4	1	no	—
149	C₂²	#14582626	1	1	yes	characteristic
150	C₂²	#14582637	1	1	yes	characteristic
151	C₂²	#14582640	1	1	yes	characteristic
152	C₄	—	4	1	no	—
153	C₄	—	4	1	no	—
154	C₄	—	344	2	no	—
155	C₄	#14582624	1	1	yes	characteristic
156	C₄	#14582631	1	1	yes	characteristic
157	C₄	#14582632	1	1	yes	characteristic
158	C₄	#14582646	1	1	yes	characteristic
159	C₂	—	2	1	no	—
160	C₂	—	2	1	no	—
161	C₂	—	2	1	no	—
162	C₂	#19132419	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19135348

C₂

yes

maximal, characteristic

#19132440

C₂

yes

maximal, characteristic

C₄₃×#1375

C₂

yes

maximal, characteristic

#14582952

—

C₂×#13063261

C₄

yes

characteristic

#14582937

C₄

yes

characteristic

#14582925

—

#14582659

—

C₂×M₃₂×C₄₃

—

C₂×#97×C₄₃

C₂²

yes

—

—

—

—

C₈

yes

complemented

C₄⋊(C₄₃⋊C₈)

—

Dic₄₃⋊C₈

—

Dic₄₃⋊C₈

—

C₂²⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

—

C₂²×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

M₃₂×C₄₃

—

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

#97×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₈

yes

characteristic

C₂×C₈×C₄₃

M₁₆

yes

characteristic

C₂×C₈×C₄₃

D₈

yes

characteristic

C₂×C₈×C₄₃

SD₁₆

yes

characteristic

C₄²×C₄₃

—

C₄²×C₄₃

SD₁₆

yes

characteristic

C₄²×C₄₃

Q₁₆

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₂³×C₄₃

#104

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#7125

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

D₄⋊C₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#324

yes

characteristic

C₄×C₄₃

Q₈⋊C₈

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#1946

—

#1375

D₄₃

yes

characteristic

#1281

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#1271

yes

characteristic

C₂×M₃₂

—

—

—

—

—

C₂×#97

C₂×D₄₃

yes

characteristic

#339

—

C₄₃

#7125

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

C₄×D₄₃

yes

characteristic

C₂²×C₈

C₂²⋊D₄₃

yes

characteristic

#117

—

C₂×C₄²

D₁₇₂

yes

characteristic

M₃₂

—

M₃₂

—

100

C₂×C₁₆

—

101

#108

—

172

—

102

#107

—

103

#106

—

104

C₄⋊C₈

—

172

—

105

C₄⋊C₈

—

172

—

106

C₄⋊C₈

—

172

—

107

C₂²⋊C₈

—

108

#97

—

109

C₄×C₈

—

172

—

110

C₂²×C₄

—

111

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

112

M₁₆

—

172

—

113

M₁₆

—

172

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

172

—

119

C₂×C₈

—

172

—

120

C₂×C₈

C₈×D₄₃

yes

characteristic

121

C₂×C₈

#10621872

yes

characteristic

122

C₂×C₈

#10621882

yes

characteristic

123

C₂×C₈

#10621884

yes

characteristic

124

C₄⋊C₄

—

125

C₂²⋊C₄

—

172

—

126

C₄²

—

127

C₄²

—

172

—

128

C₄²

#10621873

yes

characteristic

129

C₄²

Dic₁₇₂

yes

characteristic

130

C₁₆

—

131

C₂³

#13063251

yes

characteristic

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

172

—

136

C₂×C₄

(C₂×D₄₃)⋊C₈

yes

characteristic

137

C₂×C₄

#13063239

yes

characteristic

138

C₂×C₄

#13063243

yes

characteristic

139

C₂×C₄

#13063245

yes

characteristic

140

C₂×C₄

#13063250

yes

characteristic

141

C₂×C₄

#13063253

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

344

—

147

C₈

—

344

—

148

C₂²

—

149

C₂²

#14582626

yes

characteristic

150

C₂²

#14582637

yes

characteristic

151

C₂²

#14582640

yes

characteristic

152

C₄

—

153

C₄

—

154

C₄

—

344

—

155

C₄

#14582624

yes

characteristic

156

C₄

#14582631

yes

characteristic

157

C₄

#14582632

yes

characteristic

158

C₄

#14582646

yes

characteristic

159

C₂

—

160

C₂

—

161

C₂

—

162

C₂

#19132419

yes

characteristic

	subgroup	G/H
center	C₄	#14582632
commutator	C₂×C₈×C₄₃	C₂×C₈
Frattini	C₂×#97	C₂×D₄₃
Fitting	C₄₃×#1375	C₂
socle	C₂×C₄₃	#1271
prime radical	C₂³×C₄₃	#104
cosocle	C₂×#97×C₄₃	C₂²
hypercenter	#1375	D₄₃
hypocenter	C₄₃	#7125
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1375

subgroup

G/H

center

C₄

#14582632

commutator

C₂×C₈×C₄₃

C₂×C₈

Frattini

C₂×#97

C₂×D₄₃

Fitting

C₄₃×#1375

C₂

C₂×C₄₃

C₂³×C₄₃

C₂×#97×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1375

N	H ≅ G/N	type
15. #13063257	C₈	semidirect
92. C₄₃	#7125	semidirect

H ≅ G/N

type

15. #13063257

C₈

semidirect

92. C₄₃

#7125

semidirect

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

subgroup	index
#19135348	2
#19132440	2
C₄₃×#1375	2
#7125	43

subgroup

index

#19135348

#19132440

C₄₃×#1375

#7125

Subgroups — #24983401

Conjugacy classes of subgroups

Complements

Maximal subgroups