Group #24995990 — subgroups

Subgroups — #24995990

Order 11008.

370 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 119 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	#19134726	C₂	1	1	yes	maximal, characteristic
2	#19133159	C₂	1	4	yes	maximal
3	#19132887	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#3160	C₂	1	1	yes	maximal, characteristic
5	#14582952	C₂²	1	2	yes	—
6	#14582765	C₂²	1	2	yes	—
7	#14582662	—	2	2	no	—
8	#14582636	—	2	8	no	—
9	#14582621	—	2	2	no	—
10	C₄₃×#533	C₂²	1	2	yes	—
11	C₄₃×#500	C₄	1	2	yes	complemented
12	C₄₃×#499	—	2	2	no	—
13	C₄₃×#498	C₄	1	2	yes	complemented
14	C₄₃×#427	—	2	2	no	—
15	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Dic₄₃	—	2	2	no	—
17	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
18	C₂²⋊(C₄₃⋊C₈)	D₄	1	4	yes	—
19	C₄×C₄₃⋊C₈	—	2	2	no	—
20	C₄₃⋊#95	—	2	4	no	—
21	C₂²×C₈×C₄₃	D₄	1	2	yes	—
22	C₄⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
23	#125×C₄₃	—	2	2	no	—
24	C₂²⋊Q₈×C₄₃	—	2	4	no	—
25	C₄×Q₈×C₄₃	—	2	4	no	—
26	#117×C₄₃	—	2	2	no	—
27	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
28	#107×C₄₃	—	2	4	no	—
29	#106×C₄₃	—	2	4	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	C₂×Q₈×C₄₃	—	2	4	no	—
34	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
35	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
36	C₂²×Dic₄₃	—	4	2	no	—
37	C₂×C₈×C₄₃	—	2	4	no	—
38	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
39	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
40	C₄⋊C₄×C₄₃	—	2	4	no	—
41	C₄⋊C₄×C₄₃	—	2	4	no	—
42	C₄⋊C₄×C₄₃	—	4	4	no	—
43	C₂²⋊C₄×C₄₃	—	4	2	no	—
44	C₄²×C₄₃	—	4	2	no	—
45	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
46	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₄²×C₄₃	#41	1	2	yes	—
48	C₄⋊Dic₄₃	—	4	4	no	—
49	C₂×C₄₃⋊C₈	—	2	4	no	—
50	C₂³×C₄₃	#127	1	1	yes	characteristic
51	Q₈×C₄₃	—	8	4	no	—
52	C₂×C₄×C₄₃	—	4	2	no	—
53	C₂×C₄×C₄₃	—	4	4	no	—
54	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
56	C₂×C₄×C₄₃	#121	1	2	yes	—
57	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
58	C₂×C₄×C₄₃	#137	1	4	yes	—
59	C₂×Dic₄₃	—	8	4	no	—
60	C₂×Dic₄₃	—	8	2	no	—
61	C₈×C₄₃	—	2	2	no	—
62	C₈×C₄₃	—	2	2	no	—
63	C₄₃⋊C₈	—	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	—	8	4	no	—
71	C₄×C₄₃	#419	1	2	yes	—
72	C₄×C₄₃	#491	1	2	yes	—
73	Dic₄₃	—	16	2	no	—
74	#3160	D₄₃	1	1	yes	characteristic
75	#1835	—	43	1	no	—
76	#1518	—	43	4	no	—
77	#1452	—	43	1	no	—
78	C₂×C₄₃	—	2	2	no	—
79	C₂×C₄₃	#1960	1	1	yes	characteristic
80	C₂×C₄₃	#1976	1	2	yes	—
81	#533	C₂×D₄₃	1	2	yes	—
82	#500	Dic₄₃	1	2	yes	complemented
83	#499	—	2	2	no	—
84	#498	Dic₄₃	1	2	yes	complemented
85	#431	—	43	2	no	—
86	#427	—	2	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	—	86	2	no	—
92	C₄₃	#9759	1	1	yes	characteristic, complemented, Sylow
93	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
94	C₄⋊Q₈	C₂×Dic₄₃	1	4	yes	—
95	#125	—	2	2	no	—
96	C₂²⋊Q₈	—	2	4	no	—
97	C₄×Q₈	—	2	4	no	—
98	#117	—	2	2	no	—
99	C₂×C₄⋊C₄	—	86	2	no	—
100	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
101	#107	—	2	4	no	—
102	#106	—	2	4	no	—
103	C₄⋊C₈	—	86	2	no	—
104	C₂²⋊C₈	—	43	4	no	—
105	C₄×C₈	—	86	2	no	—
106	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
107	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
108	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
109	#95	—	86	4	no	—
110	C₂×Q₈	—	2	4	no	—
111	C₂²×C₄	—	172	2	no	—
112	C₂²×C₄	D₄×D₄₃	1	2	yes	—
113	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
114	C₂×C₈	—	2	4	no	—
115	C₂×C₈	—	86	4	no	—
116	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
117	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
118	C₄⋊C₄	—	2	4	no	—
119	C₄⋊C₄	—	2	4	no	—
120	C₄⋊C₄	—	4	4	no	—
121	C₄⋊C₄	—	172	4	no	—
122	C₂²⋊C₄	—	4	2	no	—
123	C₄²	—	4	2	no	—
124	C₄²	#10621900	1	2	yes	—
125	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
126	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
127	C₂³	#13063321	1	1	yes	characteristic
128	Q₈	—	8	4	no	—
129	C₂×C₄	—	4	2	no	—
130	C₂×C₄	—	4	4	no	—
131	C₂×C₄	—	344	4	no	—
132	C₂×C₄	—	344	2	no	—
133	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
134	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
135	C₂×C₄	#13063296	1	2	yes	—
136	C₂×C₄	#13063312	1	1	yes	characteristic
137	C₂×C₄	#13063356	1	4	yes	—
138	C₈	—	2	2	no	—
139	C₈	—	2	2	no	—
140	C₈	—	172	4	no	—
141	C₂²	—	2	2	no	—
142	C₂²	#14582802	1	1	yes	characteristic
143	C₂²	#14583291	1	2	yes	—
144	C₄	—	2	2	no	—
145	C₄	—	2	2	no	—
146	C₄	—	8	4	no	—
147	C₄	—	688	2	no	—
148	C₄	#14582908	1	2	yes	—
149	C₄	#14583267	1	2	yes	—
150	C₂	—	2	2	no	—
151	C₂	#19135416	1	1	yes	characteristic
152	C₂	#19135494	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134726

C₂

yes

maximal, characteristic

#19133159

C₂

yes

maximal

#19132887

C₂

yes

maximal, characteristic

C₄₃×#3160

C₂

yes

maximal, characteristic

#14582952

C₂²

yes

—

#14582765

C₂²

yes

—

#14582662

—

#14582636

—

#14582621

—

C₄₃×#533

C₂²

yes

—

C₄₃×#500

C₄

yes

complemented

C₄₃×#499

—

C₄₃×#498

C₄

yes

complemented

C₄₃×#427

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

D₄

yes

—

C₄×C₄₃⋊C₈

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

D₄

yes

—

C₄⋊Q₈×C₄₃

C₂×C₄

yes

—

#125×C₄₃

—

C₂²⋊Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

#117×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#107×C₄₃

—

#106×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

#41

yes

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#127

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

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

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

#9759

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#390

yes

characteristic

C₂²×C₄₃

#497

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#419

yes

—

C₄×C₄₃

#491

yes

—

Dic₄₃

—

#3160

D₄₃

yes

—

—

—

C₂×C₄₃

—

C₂×C₄₃

#1960

yes

characteristic

C₂×C₄₃

#1976

yes

—

#533

C₂×D₄₃

yes

—

#500

Dic₄₃

yes

complemented

#499

—

#498

Dic₄₃

yes

complemented

#431

—

#427

—

C₂×C₄×C₈

C₂×D₄₃

yes

—

—

—

—

C₄₃

#9759

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂²⋊D₄₃

yes

—

C₄⋊Q₈

C₂×Dic₄₃

yes

—

#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

—

105

C₄×C₈

—

106

C₄×C₈

C₂×Dic₄₃

yes

characteristic

107

C₄×C₈

C₂×Dic₄₃

yes

characteristic

108

C₄×C₈

C₂²⋊D₄₃

yes

—

109

#95

—

110

C₂×Q₈

—

111

C₂²×C₄

—

172

—

112

C₂²×C₄

D₄×D₄₃

yes

—

113

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

C₂²⋊Dic₄₃

yes

—

117

C₂×C₈

C₂²⋊Dic₄₃

yes

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

172

—

122

C₂²⋊C₄

—

123

C₄²

—

124

C₄²

#10621900

yes

—

125

C₄²

C₂²×Dic₄₃

yes

characteristic

126

C₄²

C₂×C₂²⋊D₄₃

yes

characteristic

127

C₂³

#13063321

yes

characteristic

128

Q₈

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

344

—

132

C₂×C₄

—

344

—

133

C₂×C₄

C₂×C₂²⋊Dic₄₃

yes

characteristic

134

C₂×C₄

D₄×Dic₄₃

yes

—

135

C₂×C₄

#13063296

yes

—

136

C₂×C₄

#13063312

yes

characteristic

137

C₂×C₄

#13063356

yes

—

138

C₈

—

139

C₈

—

140

C₈

—

172

—

141

C₂²

—

142

C₂²

#14582802

yes

characteristic

143

C₂²

#14583291

yes

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

688

—

148

C₄

#14582908

yes

—

149

C₄

#14583267

yes

—

150

C₂

—

151

C₂

#19135416

yes

characteristic

152

C₂

#19135494

yes

—

	subgroup	G/H
center	C₂²	#14582802
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#3160	C₂
socle	C₂²×C₄₃	#390
prime radical	C₂³×C₄₃	#127
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#3160	D₄₃
hypocenter	C₄₃	#9759
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

subgroup

G/H

center

C₂²

#14582802

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#3160

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

N	H ≅ G/N	type
11. C₄₃×#500	C₄	semidirect
13. C₄₃×#498	C₄	semidirect
82. #500	Dic₄₃	semidirect
84. #498	Dic₄₃	semidirect
92. C₄₃	#9759	semidirect

H ≅ G/N

type

11. C₄₃×#500

C₄

semidirect

13. C₄₃×#498

C₄

semidirect

82. #500

Dic₄₃

semidirect

84. #498

Dic₄₃

semidirect

92. C₄₃

#9759

semidirect

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

subgroup	index
#19134726	2
#19133159	2
#19132887	2
C₄₃×#3160	2
#9759	43

subgroup

index

C₄₃×#3160

Subgroups — #24995990

Conjugacy classes of subgroups

Complements

Maximal subgroups