Group #25127535 — subgroups

Subgroups — #25127535

Order 11008.

662 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 211 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	C₄×#13063317	C₂	1	2	yes	maximal
2	#19136078	C₂	1	4	yes	maximal
3	#19135934	C₂	1	4	yes	maximal
4	#19134492	C₂	1	4	yes	maximal
5	C₄₃×#1745	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063317	C₂²	1	2	yes	—
7	C₂×#13063259	C₂²	1	4	yes	—
8	C₂×#13063257	C₂²	1	4	yes	—
9	#14582797	C₂²	1	4	yes	—
10	#14582783	—	2	4	no	—
11	#14582765	C₂²	1	2	yes	—
12	C₄×Dic₄₃⋊C₄	—	2	4	no	—
13	C₄×C₄⋊Dic₄₃	C₂²	1	4	yes	—
14	#14582662	C₂²	1	4	yes	—
15	#14582662	C₂²	1	4	yes	—
16	C₂×#97×C₄₃	C₂²	1	2	yes	—
17	C₄³×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#336	C₂²	1	4	yes	—
19	#13063317	—	2	8	no	—
20	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
21	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
22	C₂×Dic₄₃⋊C₄	—	2	4	no	—
23	C₂×Dic₄₃⋊C₄	—	2	4	no	—
24	C₂×C₄×Dic₄₃	—	2	4	no	—
25	#13063259	—	2	8	no	—
26	#13063257	—	2	8	no	—
27	C₄₃⋊#95	—	2	4	no	—
28	C₄₃⋊#95	—	2	4	no	—
29	C₄₃⋊#95	—	2	4	no	—
30	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
31	C₂×C₄²×C₄₃	D₄	1	4	yes	—
32	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
33	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
34	#97×C₄₃	Q₈	1	8	yes	—
35	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
36	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
37	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
38	C₂²×Dic₄₃	—	2	4	no	—
39	C₂²×Dic₄₃	—	2	4	no	—
40	C₂×C₈×C₄₃	—	2	4	no	—
41	C₂×C₈×C₄₃	—	2	4	no	—
42	C₂×C₈×C₄₃	C₂×Q₈	1	8	yes	—
43	C₄²×C₄₃	—	2	4	no	—
44	C₄²×C₄₃	—	4	4	no	—
45	C₄²×C₄₃	C₂×Q₈	1	4	yes	—
46	C₄⋊Dic₄₃	—	2	4	no	—
47	C₄⋊Dic₄₃	—	2	4	no	—
48	C₄⋊Dic₄₃	—	2	4	no	—
49	C₄⋊Dic₄₃	#41	1	8	yes	—
50	Dic₄₃⋊C₄	—	2	16	no	—
51	Dic₄₃⋊C₄	—	4	8	no	—
52	C₄×Dic₄₃	—	4	8	no	—
53	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
54	C₂×C₄×C₄₃	—	2	4	no	—
55	C₂×C₄×C₄₃	—	2	4	no	—
56	C₂×C₄×C₄₃	—	2	4	no	—
57	C₂×C₄×C₄₃	—	2	4	no	—
58	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
59	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
60	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
61	C₂×Dic₄₃	—	2	8	no	—
62	C₂×Dic₄₃	—	4	4	no	—
63	C₂×Dic₄₃	—	4	4	no	—
64	C₂×Dic₄₃	—	4	4	no	—
65	C₂×Dic₄₃	—	4	4	no	—
66	C₂×Dic₄₃	—	4	4	no	—
67	C₈×C₄₃	—	2	8	no	—
68	#23840	—	43	1	no	maximal, Sylow
69	C₂²×C₄₃	#525	1	2	yes	—
70	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
71	C₂²×C₄₃	#575	1	4	yes	—
72	C₄×C₄₃	—	2	4	no	—
73	C₄×C₄₃	—	4	4	no	—
74	C₄×C₄₃	#533	1	4	yes	—
75	Dic₄₃	—	4	8	no	—
76	Dic₄₃	—	8	4	no	—
77	C₄×#125	—	43	2	no	—
78	#2085	—	43	4	no	—
79	#2059	—	43	4	no	—
80	#1776	—	43	4	no	—
81	#1745	D₄₃	1	1	yes	characteristic
82	C₂×C₄₃	#2399	1	1	yes	characteristic
83	C₂×C₄₃	#3111	1	4	yes	—
84	C₂×C₄₃	#3166	1	2	yes	—
85	C₂×#125	—	43	2	no	—
86	C₂×#107	—	43	4	no	—
87	C₂×#106	—	43	4	no	—
88	C₂×#97	C₂×D₄₃	1	2	yes	—
89	#389	—	43	4	no	—
90	#387	—	86	4	no	—
91	#382	—	43	2	no	—
92	C₄×C₄⋊C₄	—	43	4	no	—
93	C₄×C₄⋊C₄	—	86	4	no	—
94	C₄³	C₂×D₄₃	1	1	yes	characteristic
95	#340	—	43	4	no	—
96	#340	—	43	4	no	—
97	#336	C₂×D₄₃	1	4	yes	—
98	C₄₃	#23840	1	1	yes	characteristic, complemented, Sylow
99	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
100	#125	—	86	8	no	—
101	C₂×C₄⋊C₄	—	43	4	no	—
102	C₂×C₄⋊C₄	—	43	4	no	—
103	C₂×C₄⋊C₄	—	86	4	no	—
104	C₂×C₄⋊C₄	—	86	4	no	—
105	C₂×C₄²	—	86	4	no	—
106	C₂×C₄²	D₁₇₂	1	4	yes	—
107	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
108	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
109	#107	—	86	8	no	—
110	#106	—	86	8	no	—
111	#97	Dic₈₆	1	8	yes	—
112	#95	—	86	4	no	—
113	#95	—	86	4	no	—
114	#95	—	86	4	no	—
115	C₂²×C₄	—	86	4	no	—
116	C₂²×C₄	—	86	4	no	—
117	C₂²×C₄	C₂×D₁₇₂	1	4	yes	—
118	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
119	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
120	C₂×C₈	—	2	4	no	—
121	C₂×C₈	—	2	4	no	—
122	C₂×C₈	C₂×Dic₈₆	1	8	yes	—
123	C₄⋊C₄	—	43	8	no	—
124	C₄⋊C₄	—	86	16	no	—
125	C₄⋊C₄	—	86	4	no	—
126	C₄⋊C₄	—	86	4	no	—
127	C₄⋊C₄	—	86	4	no	—
128	C₄⋊C₄	—	172	8	no	—
129	C₄²	—	2	4	no	—
130	C₄²	—	4	4	no	—
131	C₄²	—	172	8	no	—
132	C₄²	C₂×Dic₈₆	1	4	yes	—
133	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
134	C₂×C₄	—	2	4	no	—
135	C₂×C₄	—	2	4	no	—
136	C₂×C₄	—	2	4	no	—
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	86	8	no	—
139	C₂×C₄	—	172	4	no	—
140	C₂×C₄	—	172	4	no	—
141	C₂×C₄	—	172	4	no	—
142	C₂×C₄	—	172	4	no	—
143	C₂×C₄	—	172	4	no	—
144	C₂×C₄	#13063325	1	4	yes	—
145	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
146	C₂×C₄	#41×D₄₃	1	4	yes	—
147	C₈	—	2	8	no	—
148	C₂²	#14583411	1	2	yes	—
149	C₂²	C₂×#13063325	1	1	yes	characteristic
150	C₂²	#14583699	1	4	yes	—
151	C₄	—	2	4	no	—
152	C₄	—	4	4	no	—
153	C₄	—	344	4	no	—
154	C₄	—	172	8	no	—
155	C₄	#14583452	1	4	yes	—
156	C₂	#19137888	1	1	yes	characteristic
157	C₂	#19144706	1	4	yes	—
158	C₂	#19145147	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#13063317

C₂

yes

maximal

#19136078

C₂

yes

maximal

#19135934

C₂

yes

maximal

#19134492

C₂

yes

maximal

C₄₃×#1745

C₂

yes

maximal, characteristic

C₂×#13063317

C₂²

yes

—

C₂×#13063259

C₂²

yes

—

C₂×#13063257

C₂²

yes

—

#14582797

C₂²

yes

—

#14582783

—

#14582765

C₂²

yes

—

C₄×Dic₄₃⋊C₄

—

C₄×C₄⋊Dic₄₃

C₂²

yes

—

#14582662

C₂²

yes

—

#14582662

C₂²

yes

—

C₂×#97×C₄₃

C₂²

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₄₃×#336

C₂²

yes

—

#13063317

—

C₂×C₄⋊Dic₄₃

C₂³

yes

—

C₂×C₄⋊Dic₄₃

C₂³

yes

—

C₂×Dic₄₃⋊C₄

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

—

#13063259

—

#13063257

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

C₂³

yes

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#97×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×Q₈

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

#41

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂³×C₄₃

C₂²×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂²×Q₈

yes

—

C₂×C₄×C₄₃

C₂×#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

#23840

—

maximal, Sylow

C₂²×C₄₃

#525

yes

—

C₂²×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂²×C₄₃

#575

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#533

yes

—

Dic₄₃

—

Dic₄₃

—

—

—

—

—

D₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#3166

yes

—

C₂×#125

—

C₂×#107

—

C₂×#106

—

C₂×#97

C₂×D₄₃

yes

—

#389

—

#387

—

#382

—

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

—

C₄³

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

—

C₄₃

#23840

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂²×D₄₃

yes

—

100

#125

—

101

C₂×C₄⋊C₄

—

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

—

104

C₂×C₄⋊C₄

—

105

C₂×C₄²

—

106

C₂×C₄²

D₁₇₂

yes

—

107

C₂×C₄²

C₂²×D₄₃

yes

—

108

C₂×C₄²

C₂²×D₄₃

yes

characteristic

109

#107

—

110

#106

—

111

#97

Dic₈₆

yes

—

112

#95

—

113

#95

—

114

#95

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

C₂×D₁₇₂

yes

—

118

C₂²×C₄

C₂×D₁₇₂

yes

—

119

C₂²×C₄

C₂³×D₄₃

yes

characteristic

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

C₂×Dic₈₆

yes

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

172

—

129

C₄²

—

130

C₄²

—

131

C₄²

—

172

—

132

C₄²

C₂×Dic₈₆

yes

—

133

C₂³

C₂²×D₁₇₂

yes

characteristic

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

172

—

140

C₂×C₄

—

172

—

141

C₂×C₄

—

172

—

142

C₂×C₄

—

172

—

143

C₂×C₄

—

172

—

144

C₂×C₄

#13063325

yes

—

145

C₂×C₄

C₂²×Dic₈₆

yes

—

146

C₂×C₄

#41×D₄₃

yes

—

147

C₈

—

148

C₂²

#14583411

yes

—

149

C₂²

C₂×#13063325

yes

characteristic

150

C₂²

#14583699

yes

—

151

C₄

—

152

C₄

—

153

C₄

—

344

—

154

C₄

—

172

—

155

C₄

#14583452

yes

—

156

C₂

#19137888

yes

characteristic

157

C₂

#19144706

yes

—

158

C₂

#19145147

yes

—

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1745	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
hypercenter	#1745	D₄₃
hypocenter	C₄₃	#23840
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1745

subgroup

G/H

center

C₂³

C₂²×D₁₇₂

commutator, cosocle

C₂²×C₄×C₄₃

C₂⁴

Frattini

C₂²×C₄

C₂³×D₄₃

Fitting

C₄₃×#1745

C₂

socle, prime radical

C₂³×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1745

N	H ≅ G/N	type
98. C₄₃	#23840	semidirect

H ≅ G/N

type

98. C₄₃

#23840

semidirect

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

subgroup	index
C₄×#13063317	2
#19136078	2
#19135934	2
#19134492	2
C₄₃×#1745	2
#23840	43

subgroup

index

C₄₃×#1745

Subgroups — #25127535

Conjugacy classes of subgroups

Complements

Maximal subgroups