Group #24990126 — subgroups

Subgroups — #24990126

Order 11008.

398 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 99 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	#19134675	C₂	1	2	yes	maximal
2	#19132503	C₂	1	4	yes	maximal
3	C₄₃×#2313	C₂	1	1	yes	maximal, characteristic
4	#14582863	C₂²	1	4	yes	—
5	#14582668	—	2	4	no	—
6	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
7	C₄₃×#387	—	2	4	no	—
8	C₄₃×#381	C₂²	1	2	yes	—
9	C₄₃×#380	C₄	1	2	yes	—
10	C₄×C₂²⋊C₄×C₄₃	C₄	1	2	yes	—
11	C₂×#10621877	—	2	4	no	—
12	C₂²⋊(C₄₃⋊C₈)	—	2	8	no	—
13	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
17	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
18	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
19	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
20	C₂×C₄²×C₄₃	—	2	2	no	—
21	#95×C₄₃	—	2	2	no	—
22	#95×C₄₃	—	2	2	no	—
23	#95×C₄₃	—	2	4	no	—
24	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₄₃	—	2	4	no	—
26	C₂²×C₄×C₄₃	—	2	2	no	—
27	C₂²×C₄×C₄₃	—	2	2	no	—
28	C₂²×C₄×C₄₃	—	4	2	no	—
29	C₂²×C₄×C₄₃	—	8	1	no	—
30	C₂²×C₄×C₄₃	—	8	1	no	—
31	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
32	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
33	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
34	C₂²×C₄×C₄₃	#41	1	4	yes	—
35	C₄⋊C₄×C₄₃	—	2	8	no	—
36	C₄⋊C₄×C₄₃	—	8	2	no	—
37	C₂²⋊C₄×C₄₃	—	4	4	no	—
38	C₄²×C₄₃	—	8	2	no	—
39	#10621877	—	4	8	no	—
40	C₂×C₄₃⋊C₈	—	4	4	no	—
41	C₂³×C₄₃	—	2	2	no	—
42	C₂³×C₄₃	—	4	1	no	—
43	C₂³×C₄₃	—	4	1	no	—
44	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂³×C₄₃	#117	1	2	yes	—
46	C₂×C₄×C₄₃	—	2	4	no	—
47	C₂×C₄×C₄₃	—	2	2	no	—
48	C₂×C₄×C₄₃	—	2	2	no	—
49	C₂×C₄×C₄₃	—	4	4	no	—
50	C₂×C₄×C₄₃	—	4	2	no	—
51	C₂×C₄×C₄₃	—	4	2	no	—
52	C₂×C₄×C₄₃	—	4	4	no	—
53	C₂×C₄×C₄₃	—	4	4	no	—
54	C₂×C₄×C₄₃	—	4	4	no	—
55	C₂×C₄×C₄₃	—	8	2	no	—
56	C₂×C₄×C₄₃	—	8	2	no	—
57	C₂×C₄×C₄₃	#123	1	4	yes	—
58	C₄₃⋊C₈	—	8	4	no	—
59	#8755	—	43	1	no	maximal, Sylow
60	C₂²×C₄₃	—	2	1	no	—
61	C₂²×C₄₃	—	2	1	no	—
62	C₂²×C₄₃	—	2	2	no	—
63	C₂²×C₄₃	—	2	2	no	—
64	C₂²×C₄₃	—	2	2	no	—
65	C₂²×C₄₃	—	4	4	no	—
66	C₂²×C₄₃	#381	1	1	yes	characteristic
67	C₂²×C₄₃	#410	1	2	yes	—
68	C₄×C₄₃	—	2	4	no	—
69	C₄×C₄₃	—	4	2	no	—
70	C₄×C₄₃	—	4	2	no	—
71	C₄×C₄₃	—	8	4	no	—
72	#2313	D₄₃	1	1	yes	characteristic
73	#1821	—	43	2	no	—
74	#1306	—	43	4	no	—
75	C₂×C₄₃	—	2	2	no	—
76	C₂×C₄₃	—	4	2	no	—
77	C₂×C₄₃	#1820	1	1	yes	characteristic
78	C₂×C₄₃	#1829	1	1	yes	characteristic
79	C₂×C₄₃	#1830	1	1	yes	characteristic
80	C₂²×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
81	#407	—	43	4	no	—
82	#387	—	2	4	no	—
83	#381	C₂×D₄₃	1	2	yes	—
84	#380	Dic₄₃	1	2	yes	—
85	C₄×C₂²⋊C₄	Dic₄₃	1	2	yes	—
86	#343	—	86	4	no	—
87	C₄₃	#8755	1	1	yes	characteristic, complemented, Sylow
88	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
89	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
90	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
91	C₂×M₁₆	—	86	4	no	—
92	C₂×C₄⋊C₄	—	2	4	no	—
93	C₂×C₄⋊C₄	—	2	2	no	—
94	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	4	yes	—
95	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	4	yes	—
96	C₂×C₄²	—	2	2	no	—
97	C₂²⋊C₈	—	86	8	no	—
98	#95	—	2	2	no	—
99	#95	—	2	2	no	—
100	#95	—	2	4	no	—
101	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
102	C₂²×C₄	—	2	2	no	—
103	C₂²×C₄	—	2	2	no	—
104	C₂²×C₄	—	2	4	no	—
105	C₂²×C₄	—	4	2	no	—
106	C₂²×C₄	—	8	1	no	—
107	C₂²×C₄	—	8	1	no	—
108	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
109	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
110	C₂²×C₄	#10621898	1	4	yes	—
111	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
112	M₁₆	—	172	8	no	—
113	C₂×C₈	—	172	4	no	—
114	C₄⋊C₄	—	2	8	no	—
115	C₄⋊C₄	—	8	2	no	—
116	C₂²⋊C₄	—	4	4	no	—
117	C₄²	—	8	2	no	—
118	C₂³	—	2	2	no	—
119	C₂³	—	4	1	no	—
120	C₂³	—	4	1	no	—
121	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
122	C₂³	#13063284	1	2	yes	—
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	4	4	no	—
127	C₂×C₄	—	4	2	no	—
128	C₂×C₄	—	4	2	no	—
129	C₂×C₄	—	4	4	no	—
130	C₂×C₄	—	4	4	no	—
131	C₂×C₄	—	4	4	no	—
132	C₂×C₄	—	8	2	no	—
133	C₂×C₄	—	8	2	no	—
134	C₂×C₄	#13063308	1	4	yes	—
135	C₈	—	344	4	no	—
136	C₂²	—	2	1	no	—
137	C₂²	—	2	1	no	—
138	C₂²	—	2	2	no	—
139	C₂²	—	2	2	no	—
140	C₂²	—	2	2	no	—
141	C₂²	—	4	4	no	—
142	C₂²	#14582762	1	1	yes	characteristic
143	C₂²	#14582873	1	2	yes	—
144	C₄	—	2	4	no	—
145	C₄	—	4	2	no	—
146	C₄	—	4	2	no	—
147	C₄	—	8	4	no	—
148	C₂	—	2	2	no	—
149	C₂	—	4	2	no	—
150	C₂	#19134672	1	1	yes	characteristic
151	C₂	#19134706	1	1	yes	characteristic
152	C₂	#19134709	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134675

C₂

yes

maximal

#19132503

C₂

yes

maximal

C₄₃×#2313

C₂

yes

maximal, characteristic

#14582863

C₂²

yes

—

#14582668

—

C₂²×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₄₃×#387

—

C₄₃×#381

C₂²

yes

—

C₄₃×#380

C₄

yes

—

C₄×C₂²⋊C₄×C₄₃

C₄

yes

—

C₂×#10621877

—

C₂²⋊(C₄₃⋊C₈)

—

C₂³×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₂²⋊C₄×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

—

#95×C₄₃

—

#95×C₄₃

—

#95×C₄₃

—

C₂⁴×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

#41

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₄₃

#117

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#123

yes

—

C₄₃⋊C₈

—

#8755

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#381

yes

characteristic

C₂²×C₄₃

#410

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

#2313

D₄₃

yes

characteristic

#1821

—

#1306

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂²×C₄⋊C₄

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

—

#380

Dic₄₃

yes

—

C₄×C₂²⋊C₄

Dic₄₃

yes

—

#343

—

C₄₃

#8755

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×Dic₄₃

yes

characteristic

C₂³×C₄

C₂×Dic₄₃

yes

characteristic

C₂³×C₄

C₂²×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

C₂×C₂²⋊C₄

C₂×Dic₄₃

yes

—

C₂×C₄²

—

C₂²⋊C₈

—

#95

—

#95

—

100

#95

—

101

C₂⁴

C₂²×Dic₄₃

yes

characteristic

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₂²⋊Dic₄₃

yes

—

109

C₂²×C₄

C₂²⋊Dic₄₃

yes

—

110

C₂²×C₄

#10621898

yes

—

111

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

112

M₁₆

—

172

—

113

C₂×C₈

—

172

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₄²

—

118

C₂³

—

119

C₂³

—

120

C₂³

—

121

C₂³

C₂×C₂²⋊Dic₄₃

yes

characteristic

122

C₂³

#13063284

yes

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

#13063308

yes

—

135

C₈

—

344

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

#14582762

yes

characteristic

143

C₂²

#14582873

yes

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₂

—

149

C₂

—

150

C₂

#19134672

yes

characteristic

151

C₂

#19134706

yes

characteristic

152

C₂

#19134709

yes

characteristic

	subgroup	G/H
center	C₂²	#14582762
commutator, prime radical	C₂⁴×C₄₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₄₃×#2313	C₂
socle	C₂²×C₄₃	#381
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	#2313	D₄₃
hypocenter	C₄₃	#8755
LCS	G ▷ C₂⁴×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2313

subgroup

G/H

center

C₂²

#14582762

commutator, prime radical

C₂⁴×C₄₃

C₂²×C₄

Frattini

C₂³×C₄

C₂²×D₄₃

Fitting

C₄₃×#2313

C₂

socle

C₂²×C₄₃

#381

cosocle

C₂³×C₄×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂⁴×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2313

N	H ≅ G/N	type
87. C₄₃	#8755	semidirect

H ≅ G/N

type

87. C₄₃

#8755

semidirect

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

subgroup	index
#19134675	2
#19132503	2
C₄₃×#2313	2
#8755	43

subgroup

index

#19134675

#19132503

C₄₃×#2313

#8755

Subgroups — #24990126

Conjugacy classes of subgroups

Complements

Maximal subgroups