Group #24995989 — subgroups

Subgroups — #24995989

Order 11008.

370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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	#19145109	C₂	1	1	yes	maximal, characteristic
2	#19134726	C₂	1	1	yes	maximal, characteristic
3	#19133160	C₂	1	4	yes	maximal
4	C₄₃×#1452	C₂	1	1	yes	maximal, characteristic
5	#14583456	C₂²	1	2	yes	—
6	#14583304	C₄	1	2	yes	complemented
7	#14583301	—	2	2	no	—
8	#14583297	C₄	1	2	yes	complemented
9	#14582937	—	2	2	no	—
10	#14582765	C₂²	1	2	yes	—
11	#14582662	—	2	2	no	—
12	#14582637	—	2	8	no	—
13	C₄₃×#431	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₄₃×#322	—	2	2	no	—
16	#13063325	C₂×C₄	1	4	yes	—
17	#13063317	—	2	2	no	—
18	#13063304	—	2	4	no	—
19	C₄×Dic₈₆	—	2	4	no	—
20	#13063284	—	2	2	no	—
21	C₂×C₄⋊Dic₄₃	—	2	2	no	—
22	#13063259	—	2	4	no	—
23	#13063257	—	2	4	no	—
24	C₄₃⋊#95	—	2	4	no	—
25	C₂²×C₈×C₄₃	D₄	1	2	yes	—
26	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
27	C₄⋊C₈×C₄₃	—	2	2	no	—
28	C₂²⋊C₈×C₄₃	D₄	1	4	yes	—
29	C₄×C₈×C₄₃	—	2	2	no	—
30	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
32	C₄×C₈×C₄₃	D₄	1	2	yes	—
33	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
34	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂²×Dic₄₃	—	4	2	no	—
36	C₂×Dic₈₆	—	2	4	no	—
37	C₂×C₈×C₄₃	—	2	4	no	—
38	C₂×C₈×C₄₃	—	2	4	no	—
39	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
40	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
41	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
42	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₄²×C₄₃	#41	1	2	yes	—
44	C₂²⋊Dic₄₃	—	4	2	no	—
45	C₄⋊Dic₄₃	—	2	4	no	—
46	C₄⋊Dic₄₃	—	2	4	no	—
47	C₄⋊Dic₄₃	—	4	4	no	—
48	Dic₄₃⋊C₄	—	4	4	no	—
49	C₄×Dic₄₃	—	4	2	no	—
50	C₂³×C₄₃	#127	1	1	yes	characteristic
51	C₂×C₄×C₄₃	—	4	2	no	—
52	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
54	C₂×C₄×C₄₃	#121	1	2	yes	—
55	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
56	C₂×C₄×C₄₃	#137	1	4	yes	—
57	C₂×Dic₄₃	—	4	4	no	—
58	C₂×Dic₄₃	—	8	4	no	—
59	C₂×Dic₄₃	—	8	2	no	—
60	Dic₈₆	—	8	4	no	—
61	C₈×C₄₃	—	2	2	no	—
62	C₈×C₄₃	—	2	2	no	—
63	C₈×C₄₃	—	4	4	no	—
64	#9759	—	43	1	no	maximal, Sylow
65	C₂²×C₄₃	—	2	2	no	—
66	C₂²×C₄₃	#390	1	1	yes	characteristic
67	C₂²×C₄₃	#497	1	2	yes	—
68	C₄×C₄₃	—	2	2	no	—
69	C₄×C₄₃	—	2	2	no	—
70	C₄×C₄₃	#419	1	2	yes	—
71	C₄×C₄₃	#491	1	2	yes	—
72	Dic₄₃	—	8	4	no	—
73	Dic₄₃	—	16	2	no	—
74	#3160	—	43	1	no	—
75	#1835	—	43	1	no	—
76	#1518	—	43	4	no	—
77	#1452	D₄₃	1	1	yes	characteristic
78	C₂×C₄₃	—	2	2	no	—
79	C₂×C₄₃	#1960	1	1	yes	characteristic
80	C₂×C₄₃	#1976	1	2	yes	—
81	#533	—	43	2	no	—
82	#500	—	43	2	no	—
83	#499	—	86	2	no	—
84	#498	—	43	2	no	—
85	#431	C₂×D₄₃	1	2	yes	—
86	#427	—	86	2	no	—
87	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
88	#382	—	43	2	no	—
89	#340	—	86	2	no	—
90	#328	—	86	8	no	—
91	#322	—	2	2	no	—
92	C₄₃	#9759	1	1	yes	characteristic, complemented, Sylow
93	C₂²×C₈	D₁₇₂	1	2	yes	—
94	C₄⋊Q₈	—	43	4	no	—
95	#125	—	86	2	no	—
96	C₂²⋊Q₈	—	86	4	no	—
97	C₄×Q₈	—	86	4	no	—
98	#117	—	86	2	no	—
99	C₂×C₄⋊C₄	—	86	2	no	—
100	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
101	#107	—	86	4	no	—
102	#106	—	86	4	no	—
103	C₄⋊C₈	—	2	2	no	—
104	C₂²⋊C₈	D₁₇₂	1	4	yes	—
105	C₄×C₈	—	2	2	no	—
106	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
107	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
108	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
109	#95	—	86	4	no	—
110	C₂×Q₈	—	86	4	no	—
111	C₂²×C₄	—	172	2	no	—
112	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
113	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
114	C₂×C₈	—	2	4	no	—
115	C₂×C₈	—	2	4	no	—
116	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
117	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
118	C₄⋊C₄	—	86	4	no	—
119	C₄⋊C₄	—	86	4	no	—
120	C₄⋊C₄	—	172	4	no	—
121	C₄⋊C₄	—	172	4	no	—
122	C₂²⋊C₄	—	172	2	no	—
123	C₄²	—	172	2	no	—
124	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
125	C₄²	#10621898	1	2	yes	—
126	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
127	C₂³	#13063322	1	1	yes	characteristic
128	Q₈	—	344	4	no	—
129	C₂×C₄	—	4	2	no	—
130	C₂×C₄	—	344	4	no	—
131	C₂×C₄	—	344	2	no	—
132	C₂×C₄	—	172	4	no	—
133	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
134	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
135	C₂×C₄	#13063299	1	2	yes	—
136	C₂×C₄	#13063313	1	1	yes	characteristic
137	C₂×C₄	#13063358	1	4	yes	—
138	C₈	—	2	2	no	—
139	C₈	—	2	2	no	—
140	C₈	—	4	4	no	—
141	C₂²	—	2	2	no	—
142	C₂²	#14582801	1	1	yes	characteristic
143	C₂²	#14583293	1	2	yes	—
144	C₄	—	2	2	no	—
145	C₄	—	2	2	no	—
146	C₄	—	344	4	no	—
147	C₄	—	688	2	no	—
148	C₄	#14582909	1	2	yes	—
149	C₄	#14583268	1	2	yes	—
150	C₂	—	2	2	no	—
151	C₂	#19135415	1	1	yes	characteristic
152	C₂	#19135493	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19145109

C₂

yes

maximal, characteristic

#19134726

C₂

yes

maximal, characteristic

#19133160

C₂

yes

maximal

C₄₃×#1452

C₂

yes

maximal, characteristic

#14583456

C₂²

yes

—

#14583304

C₄

yes

complemented

#14583301

—

#14583297

C₄

yes

complemented

#14582937

—

#14582765

C₂²

yes

—

#14582662

—

#14582637

—

C₄₃×#431

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#322

—

#13063325

C₂×C₄

yes

—

#13063317

—

#13063304

—

C₄×Dic₈₆

—

#13063284

—

C₂×C₄⋊Dic₄₃

—

#13063259

—

#13063257

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

D₄

yes

—

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

#41

yes

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂³×C₄₃

#127

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄×D₄

yes

—

C₂×C₄×C₄₃

#121

yes

—

C₂×C₄×C₄₃

#124

yes

characteristic

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

#9759

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#390

yes

characteristic

C₂²×C₄₃

#497

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#419

yes

—

C₄×C₄₃

#491

yes

—

Dic₄₃

—

Dic₄₃

—

—

—

—

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

#1960

yes

characteristic

C₂×C₄₃

#1976

yes

—

—

—

—

—

C₂×D₄₃

yes

—

#427

—

C₂×C₄×C₈

C₂×D₄₃

yes

—

—

—

—

C₄₃

#9759

yes

characteristic, complemented, Sylow

C₂²×C₈

D₁₇₂

yes

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄⋊C₄

—

100

C₂×C₄²

C₂²×D₄₃

yes

characteristic

101

#107

—

102

#106

—

103

C₄⋊C₈

—

104

C₂²⋊C₈

D₁₇₂

yes

—

105

C₄×C₈

—

106

C₄×C₈

C₄×D₄₃

yes

characteristic

107

C₄×C₈

C₄×D₄₃

yes

characteristic

108

C₄×C₈

C₂²⋊D₄₃

yes

—

109

#95

—

110

C₂×Q₈

—

111

C₂²×C₄

—

172

—

112

C₂²×C₄

C₂×D₁₇₂

yes

—

113

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

117

C₂×C₈

(C₂×D₄₃)⋊C₄

yes

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

172

—

121

C₄⋊C₄

—

172

—

122

C₂²⋊C₄

—

172

—

123

C₄²

—

172

—

124

C₄²

C₂×C₄×D₄₃

yes

characteristic

125

C₄²

#10621898

yes

—

126

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

127

C₂³

#13063322

yes

characteristic

128

Q₈

—

344

—

129

C₂×C₄

—

130

C₂×C₄

—

344

—

131

C₂×C₄

—

344

—

132

C₂×C₄

—

172

—

133

C₂×C₄

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

134

C₂×C₄

C₄×D₁₇₂

yes

—

135

C₂×C₄

#13063299

yes

—

136

C₂×C₄

#13063313

yes

characteristic

137

C₂×C₄

#13063358

yes

—

138

C₈

—

139

C₈

—

140

C₈

—

141

C₂²

—

142

C₂²

#14582801

yes

characteristic

143

C₂²

#14583293

yes

—

144

C₄

—

145

C₄

—

146

C₄

—

344

—

147

C₄

—

688

—

148

C₄

#14582909

yes

—

149

C₄

#14583268

yes

—

150

C₂

—

151

C₂

#19135415

yes

characteristic

152

C₂

#19135493

yes

—

	subgroup	G/H
center	C₂²	#14582801
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1452	C₂
socle	C₂²×C₄₃	#390
prime radical	C₂³×C₄₃	#127
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1452	D₄₃
hypocenter	C₄₃	#9759
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

subgroup

G/H

center

C₂²

#14582801

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1452

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

N	H ≅ G/N	type
6. #14583304	C₄	semidirect
8. #14583297	C₄	semidirect
92. C₄₃	#9759	semidirect

H ≅ G/N

type

6. #14583304

C₄

semidirect

8. #14583297

C₄

semidirect

92. C₄₃

#9759

semidirect

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

subgroup	index
#19145109	2
#19134726	2
#19133160	2
C₄₃×#1452	2
#9759	43

subgroup

index

C₄₃×#1452

Subgroups — #24995989

Conjugacy classes of subgroups

Complements

Maximal subgroups