Group #24990249 — subgroups

Subgroups — #24990249

Order 11008.

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

normal subgroups only

This group has 262 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	#19134347	C₂	1	1	yes	maximal, characteristic
2	#19133341	C₂	1	2	yes	maximal
3	#19132439	C₂	1	2	yes	maximal
4	#19132424	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1274	C₂	1	1	yes	maximal, characteristic
6	#14582952	C₂²	1	2	yes	—
7	C₂×#13063236	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	#14582654	C₄	1	2	yes	—
10	#14582654	C₄	1	2	yes	—
11	#14582651	—	2	2	no	—
12	#14582649	—	2	2	no	—
13	C₄₃×#431	C₂²	1	2	yes	—
14	C₄₃×#376	C₂²	1	1	yes	characteristic
15	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
18	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
19	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
20	#13063236	—	2	2	no	—
21	C₄×C₄₃⋊C₈	—	2	2	no	—
22	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
23	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
24	C₄×C₄₃⋊C₈	Q₈	1	2	yes	—
25	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
27	C₄⋊C₈×C₄₃	—	2	2	no	—
28	C₂²⋊C₈×C₄₃	—	2	2	no	—
29	C₄×C₈×C₄₃	—	2	2	no	—
30	#95×C₄₃	—	2	2	no	—
31	C₂²×C₄×C₄₃	—	2	2	no	—
32	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₄₃	#41	1	2	yes	—
34	C₂×C₈×C₄₃	—	4	2	no	—
35	C₄²×C₄₃	—	2	2	no	—
36	C₄²×C₄₃	—	2	2	no	—
37	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
39	C₄²×C₄₃	#41	1	2	yes	—
40	C₂×C₄₃⋊C₈	—	2	2	no	—
41	C₂×C₄₃⋊C₈	—	2	2	no	—
42	C₂×C₄₃⋊C₈	—	2	1	no	—
43	C₂×C₄₃⋊C₈	—	2	1	no	—
44	C₂×C₄₃⋊C₈	—	2	2	no	—
45	C₂×C₄₃⋊C₈	—	2	2	no	—
46	C₂×C₄₃⋊C₈	—	4	2	no	—
47	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
48	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
49	C₂³×C₄₃	#117	1	1	yes	characteristic
50	C₂×C₄×C₄₃	—	4	2	no	—
51	C₂×C₄×C₄₃	—	4	4	no	—
52	C₂×C₄×C₄₃	—	4	2	no	—
53	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
55	C₂×C₄×C₄₃	#124	1	2	yes	—
56	C₂×C₄×C₄₃	#125	1	2	yes	—
57	C₂×C₄×C₄₃	#131	1	2	yes	—
58	C₂×C₄×C₄₃	#131	1	2	yes	—
59	C₈×C₄₃	—	8	2	no	—
60	C₄₃⋊C₈	—	2	2	no	—
61	C₄₃⋊C₈	—	2	2	no	—
62	C₄₃⋊C₈	—	4	1	no	—
63	C₄₃⋊C₈	—	4	1	no	—
64	C₄₃⋊C₈	—	8	2	no	—
65	#8782	—	43	1	no	maximal, Sylow
66	C₂²×C₄₃	—	2	2	no	—
67	C₂²×C₄₃	#382	1	1	yes	characteristic
68	C₂²×C₄₃	#433	1	2	yes	—
69	C₄×C₄₃	—	2	2	no	—
70	C₄×C₄₃	—	2	2	no	—
71	C₄×C₄₃	—	8	2	no	—
72	C₄×C₄₃	#424	1	2	yes	—
73	C₄×C₄₃	#433	1	1	yes	characteristic
74	C₄×C₄₃	#433	1	1	yes	characteristic
75	#1746	—	43	1	no	—
76	#1564	—	43	2	no	—
77	#1281	—	43	2	no	—
78	#1274	—	43	1	no	—
79	#1274	D₄₃	1	1	yes	characteristic
80	C₂×C₄₃	—	2	2	no	—
81	C₂×C₄₃	#1832	1	1	yes	characteristic
82	C₂×C₄₃	#1833	1	2	yes	—
83	#431	—	43	2	no	—
84	#431	C₂×D₄₃	1	2	yes	—
85	C₂×#97	—	43	1	no	—
86	C₂×C₄×C₈	—	43	1	no	—
87	#376	C₂×D₄₃	1	1	yes	characteristic
88	#336	—	43	2	no	—
89	#336	—	43	2	no	—
90	#335	—	86	2	no	—
91	#334	—	86	2	no	—
92	C₄₃	#8782	1	1	yes	characteristic, complemented, Sylow
93	C₂²×C₈	—	43	2	no	—
94	C₂²×C₈	—	43	1	no	—
95	C₂²×C₈	—	43	1	no	—
96	C₂×C₄²	C₄×D₄₃	1	2	yes	—
97	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
98	C₄⋊C₈	—	2	2	no	—
99	C₄⋊C₈	—	86	2	no	—
100	C₂²⋊C₈	—	2	2	no	—
101	C₂²⋊C₈	—	86	2	no	—
102	#97	—	86	2	no	—
103	C₄×C₈	—	2	2	no	—
104	C₄×C₈	—	43	1	no	—
105	C₄×C₈	—	43	1	no	—
106	C₄×C₈	—	43	2	no	—
107	C₄×C₈	—	86	2	no	—
108	#95	—	2	2	no	—
109	C₂²×C₄	—	2	2	no	—
110	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
111	C₂²×C₄	#10621900	1	2	yes	—
112	C₂×C₈	—	4	2	no	—
113	C₂×C₈	—	43	2	no	—
114	C₂×C₈	—	43	2	no	—
115	C₂×C₈	—	86	2	no	—
116	C₂×C₈	—	86	2	no	—
117	C₂×C₈	—	86	1	no	—
118	C₂×C₈	—	86	1	no	—
119	C₂×C₈	—	86	2	no	—
120	C₂×C₈	—	86	2	no	—
121	C₂×C₈	—	172	2	no	—
122	C₄²	—	2	2	no	—
123	C₄²	—	2	2	no	—
124	C₄²	#10621898	1	2	yes	—
125	C₄²	D₄×D₄₃	1	1	yes	characteristic
126	C₄²	Q₈×D₄₃	1	1	yes	characteristic
127	C₂³	#13063281	1	1	yes	characteristic
128	C₂×C₄	—	4	2	no	—
129	C₂×C₄	—	4	4	no	—
130	C₂×C₄	—	4	2	no	—
131	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
132	C₂×C₄	#13063282	1	1	yes	characteristic
133	C₂×C₄	#13063311	1	2	yes	—
134	C₂×C₄	#13063315	1	2	yes	—
135	C₂×C₄	#13063331	1	2	yes	—
136	C₂×C₄	#13063333	1	2	yes	—
137	C₈	—	8	2	no	—
138	C₈	—	86	2	no	—
139	C₈	—	86	2	no	—
140	C₈	—	344	2	no	—
141	C₈	—	172	1	no	—
142	C₈	—	172	1	no	—
143	C₂²	—	2	2	no	—
144	C₂²	#14582763	1	1	yes	characteristic
145	C₂²	#14582957	1	2	yes	—
146	C₄	—	2	2	no	—
147	C₄	—	2	2	no	—
148	C₄	—	8	2	no	—
149	C₄	#14582924	1	2	yes	—
150	C₄	#14582958	1	1	yes	characteristic
151	C₄	#14582961	1	1	yes	characteristic
152	C₂	—	2	2	no	—
153	C₂	#19134713	1	1	yes	characteristic
154	C₂	#19134717	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134347

C₂

yes

maximal, characteristic

#19133341

C₂

yes

maximal

#19132439

C₂

yes

maximal

#19132424

C₂

yes

maximal, characteristic

C₄₃×#1274

C₂

yes

maximal, characteristic

#14582952

C₂²

yes

—

C₂×#13063236

C₂²

yes

characteristic

C₂×C₄×C₄₃⋊C₈

C₂²

yes

characteristic

#14582654

C₄

yes

—

#14582654

C₄

yes

—

#14582651

—

#14582649

—

C₄₃×#431

C₂²

yes

—

C₄₃×#376

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₃⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₄₃⋊C₈

C₂×C₄

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

D₄

yes

characteristic

C₄×C₄₃⋊C₈

D₄

yes

characteristic

C₄×C₄₃⋊C₈

Q₈

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

—

#95×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

C₂×Q₈

yes

characteristic

C₄²×C₄₃

#41

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

—

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

—

C₂³×C₄₃

#117

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×C₄×C₄₃

#125

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#8782

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#382

yes

characteristic

C₂²×C₄₃

#433

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#424

yes

—

C₄×C₄₃

yes

C₄×C₄₃

yes

—

—

—

—

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

#1832

yes

characteristic

C₂×C₄₃

#1833

yes

—

#431

—

#431

C₂×D₄₃

yes

—

C₂×#97

—

C₂×C₄×C₈

—

#376

C₂×D₄₃

yes

—

—

—

—

C₄₃

#8782

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

C₄×D₄₃

yes

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

100

C₂²⋊C₈

—

101

C₂²⋊C₈

—

102

#97

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₄×C₈

—

106

C₄×C₈

—

107

C₄×C₈

—

108

#95

—

109

C₂²×C₄

—

110

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

111

C₂²×C₄

#10621900

yes

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

172

—

122

C₄²

—

123

C₄²

—

124

C₄²

#10621898

yes

—

125

C₄²

D₄×D₄₃

yes

characteristic

126

C₄²

Q₈×D₄₃

yes

characteristic

127

C₂³

#13063281

yes

characteristic

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

C₄⋊C₄×D₄₃

yes

characteristic

132

C₂×C₄

#13063282

yes

characteristic

133

C₂×C₄

#13063311

yes

—

134

C₂×C₄

#13063315

yes

—

135

C₂×C₄

#13063331

yes

—

136

C₂×C₄

#13063333

yes

—

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

344

—

141

C₈

—

172

—

142

C₈

—

172

—

143

C₂²

—

144

C₂²

#14582763

yes

characteristic

145

C₂²

#14582957

yes

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

#14582924

yes

—

150

C₄

#14582958

yes

characteristic

151

C₄

#14582961

yes

characteristic

152

C₂

—

153

C₂

#19134713

yes

characteristic

154

C₂

#19134717

yes

—

	subgroup	G/H
center	C₂×C₄	#13063282
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1274	C₂
socle	C₂²×C₄₃	#382
prime radical	C₂³×C₄₃	#117
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1274	D₄₃
hypocenter	C₄₃	#8782
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #376 ◁ #1274

subgroup

G/H

center

C₂×C₄

#13063282

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1274

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ #376 ◁ #1274

N	H ≅ G/N	type
92. C₄₃	#8782	semidirect

H ≅ G/N

type

92. C₄₃

#8782

semidirect

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

subgroup	index
#19134347	2
#19133341	2
#19132439	2
#19132424	2
C₄₃×#1274	2
#8782	43

subgroup

index

C₄₃×#1274

Subgroups — #24990249

Conjugacy classes of subgroups

Complements

Maximal subgroups