Group #24999849 — subgroups

Subgroups — #24999849

Order 11008.

542 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 77 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	#19134667	C₂	1	3	yes	maximal
2	C₄₃⋊#1304	C₂	1	3	yes	maximal
3	C₄₃×#2840	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
5	#14582755	C₂²	1	3	yes	—
6	#14582665	—	2	6	no	—
7	C₄₃×#393	—	2	6	no	—
8	C₄₃×#379	C₂²	1	3	yes	—
9	C₂³×Dic₄₃	Q₈	1	2	yes	complemented
10	C₂×C₂²⋊Dic₄₃	—	2	3	no	—
11	C₂×C₂²⋊Dic₄₃	—	2	3	no	—
12	C₂×C₂²⋊Dic₄₃	—	2	3	no	—
13	C₂×C₂²⋊Dic₄₃	—	2	6	no	—
14	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
15	C₂²×Q₈×C₄₃	—	2	2	no	—
16	C₂×C₂²⋊C₄×C₄₃	—	2	6	no	—
17	C₂×C₂²⋊C₄×C₄₃	D₄	1	6	yes	—
18	#95×C₄₃	—	2	6	no	—
19	C₂⁴×C₄₃	—	4	2	no	—
20	C₂⁴×C₄₃	—	8	2	no	—
21	C₂⁴×C₄₃	C₂×D₄	1	3	yes	—
22	C₂⁴×C₄₃	C₂×Q₈	1	1	yes	characteristic
23	C₂⁴×C₄₃	#41	1	3	yes	—
24	C₂×Q₈×C₄₃	—	8	4	no	—
25	C₂×Q₈×C₄₃	—	8	2	no	—
26	C₂²×C₄×C₄₃	—	2	6	no	—
27	C₂²×Dic₄₃	—	2	6	no	—
28	C₂²×Dic₄₃	—	4	3	no	—
29	C₂²×Dic₄₃	—	8	2	no	—
30	C₂²⋊C₄×C₄₃	—	4	6	no	—
31	C₂²⋊C₄×C₄₃	—	8	6	no	—
32	C₂²⋊Dic₄₃	—	4	6	no	—
33	C₂²⋊Dic₄₃	—	4	1	no	—
34	C₂²⋊Dic₄₃	—	4	3	no	—
35	C₂²⋊Dic₄₃	—	8	6	no	—
36	C₂³×C₄₃	—	2	6	no	—
37	C₂³×C₄₃	—	4	2	no	—
38	C₂³×C₄₃	—	4	1	no	—
39	C₂³×C₄₃	—	4	6	no	—
40	C₂³×C₄₃	—	4	6	no	—
41	C₂³×C₄₃	—	4	3	no	—
42	C₂³×C₄₃	—	8	8	no	—
43	C₂³×C₄₃	#120	1	1	yes	characteristic
44	C₂³×C₄₃	C₂²⋊Q₈	1	3	yes	—
45	C₂³×C₄₃	#124	1	3	yes	—
46	Q₈×C₄₃	—	8	8	no	—
47	C₂×C₄×C₄₃	—	4	12	no	—
48	C₂×C₄×C₄₃	—	4	6	no	—
49	C₂×Dic₄₃	—	4	2	no	—
50	C₂×Dic₄₃	—	8	6	no	—
51	C₂×Dic₄₃	—	8	3	no	—
52	C₂×Dic₄₃	—	8	6	no	—
53	#10391	—	43	1	no	maximal, Sylow
54	C₂²×C₄₃	—	2	2	no	—
55	C₂²×C₄₃	—	2	3	no	—
56	C₂²×C₄₃	—	2	3	no	—
57	C₂²×C₄₃	—	2	6	no	—
58	C₂²×C₄₃	—	2	6	no	—
59	C₂²×C₄₃	—	4	4	no	—
60	C₂²×C₄₃	—	8	6	no	—
61	C₂²×C₄₃	—	8	6	no	—
62	C₂²×C₄₃	#393	1	1	yes	characteristic
63	C₂²×C₄₃	#458	1	2	yes	—
64	C₄×C₄₃	—	8	6	no	—
65	Dic₄₃	—	8	2	no	—
66	Dic₄₃	—	16	3	no	—
67	#2840	D₄₃	1	1	yes	characteristic
68	#1819	—	43	3	no	—
69	#1304	—	43	3	no	—
70	C₂×C₄₃	—	2	2	no	—
71	C₂×C₄₃	—	4	3	no	—
72	C₂×C₄₃	—	4	3	no	—
73	C₂×C₄₃	#2030	1	1	yes	characteristic
74	C₂×C₄₃	#2032	1	2	yes	—
75	C₂²×C₂²⋊C₄	—	43	1	no	—
76	#393	—	2	6	no	—
77	#379	—	43	3	no	—
78	#379	C₂×D₄₃	1	3	yes	—
79	#342	—	86	6	no	—
80	C₄₃	#10391	1	1	yes	characteristic, complemented, Sylow
81	C₂⁵	C₂²×D₄₃	1	1	yes	characteristic
82	C₂²×Q₈	—	2	2	no	—
83	C₂³×C₄	—	43	2	no	—
84	C₂×C₂²⋊C₄	—	2	6	no	—
85	C₂×C₂²⋊C₄	—	86	6	no	—
86	C₂×C₂²⋊C₄	—	86	3	no	—
87	C₂×C₂²⋊C₄	—	86	3	no	—
88	C₂×C₂²⋊C₄	—	86	3	no	—
89	C₂×C₂²⋊C₄	C₂²⋊D₄₃	1	6	yes	—
90	#95	—	2	6	no	—
91	C₂⁴	—	4	2	no	—
92	C₂⁴	—	8	2	no	—
93	C₂⁴	Q₈×D₄₃	1	1	yes	characteristic
94	C₂⁴	#10621902	1	3	yes	—
95	C₂⁴	C₂×C₂²⋊D₄₃	1	3	yes	—
96	C₂×Q₈	—	8	4	no	—
97	C₂×Q₈	—	8	2	no	—
98	C₂²×C₄	—	2	6	no	—
99	C₂²×C₄	—	86	6	no	—
100	C₂²×C₄	—	344	2	no	—
101	C₂²×C₄	—	172	3	no	—
102	C₂²⋊C₄	—	4	6	no	—
103	C₂²⋊C₄	—	8	6	no	—
104	C₂²⋊C₄	—	344	6	no	—
105	C₂²⋊C₄	—	172	6	no	—
106	C₂²⋊C₄	—	172	1	no	—
107	C₂²⋊C₄	—	172	3	no	—
108	C₂³	—	2	6	no	—
109	C₂³	—	4	2	no	—
110	C₂³	—	4	1	no	—
111	C₂³	—	4	6	no	—
112	C₂³	—	4	6	no	—
113	C₂³	—	4	3	no	—
114	C₂³	—	8	8	no	—
115	C₂³	#13063294	1	1	yes	characteristic
116	C₂³	#13063301	1	3	yes	—
117	C₂³	#13063314	1	3	yes	—
118	Q₈	—	8	8	no	—
119	C₂×C₄	—	4	12	no	—
120	C₂×C₄	—	4	6	no	—
121	C₂×C₄	—	344	6	no	—
122	C₂×C₄	—	344	6	no	—
123	C₂×C₄	—	344	3	no	—
124	C₂×C₄	—	172	2	no	—
125	C₂²	—	2	2	no	—
126	C₂²	—	2	3	no	—
127	C₂²	—	2	3	no	—
128	C₂²	—	2	6	no	—
129	C₂²	—	2	6	no	—
130	C₂²	—	4	4	no	—
131	C₂²	—	8	6	no	—
132	C₂²	—	8	6	no	—
133	C₂²	#14582810	1	1	yes	characteristic
134	C₂²	#14583089	1	2	yes	—
135	C₄	—	8	6	no	—
136	C₄	—	344	2	no	—
137	C₄	—	688	3	no	—
138	C₂	—	2	2	no	—
139	C₂	—	4	3	no	—
140	C₂	—	4	3	no	—
141	C₂	#19135761	1	1	yes	characteristic
142	C₂	#19135771	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134667

C₂

yes

maximal

C₄₃⋊#1304

C₂

yes

maximal

C₄₃×#2840

C₂

yes

maximal, characteristic

C₂²×C₂²⋊Dic₄₃

C₂²

yes

characteristic

#14582755

C₂²

yes

—

#14582665

—

C₄₃×#393

—

C₄₃×#379

C₂²

yes

—

C₂³×Dic₄₃

Q₈

yes

complemented

C₂×C₂²⋊Dic₄₃

—

C₂×C₂²⋊Dic₄₃

—

C₂×C₂²⋊Dic₄₃

—

C₂×C₂²⋊Dic₄₃

—

C₂⁵×C₄₃

C₂³

yes

characteristic

C₂²×Q₈×C₄₃

—

C₂×C₂²⋊C₄×C₄₃

—

C₂×C₂²⋊C₄×C₄₃

D₄

yes

—

#95×C₄₃

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

C₂×D₄

yes

—

C₂⁴×C₄₃

C₂×Q₈

yes

characteristic

C₂⁴×C₄₃

#41

yes

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

#120

yes

characteristic

C₂³×C₄₃

C₂²⋊Q₈

yes

—

C₂³×C₄₃

#124

yes

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

#10391

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#393

yes

characteristic

C₂²×C₄₃

#458

yes

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#2840

D₄₃

yes

characteristic

#1819

—

#1304

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#2030

yes

characteristic

C₂×C₄₃

#2032

yes

—

C₂²×C₂²⋊C₄

—

#393

—

#379

—

#379

C₂×D₄₃

yes

—

#342

—

C₄₃

#10391

yes

characteristic, complemented, Sylow

C₂⁵

C₂²×D₄₃

yes

characteristic

C₂²×Q₈

—

C₂³×C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂²⋊D₄₃

yes

—

#95

—

C₂⁴

—

C₂⁴

—

C₂⁴

Q₈×D₄₃

yes

characteristic

C₂⁴

#10621902

yes

—

C₂⁴

C₂×C₂²⋊D₄₃

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

344

—

101

C₂²×C₄

—

172

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

—

344

—

105

C₂²⋊C₄

—

172

—

106

C₂²⋊C₄

—

172

—

107

C₂²⋊C₄

—

172

—

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

—

112

C₂³

—

113

C₂³

—

114

C₂³

—

115

C₂³

#13063294

yes

characteristic

116

C₂³

#13063301

yes

—

117

C₂³

#13063314

yes

—

118

Q₈

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

344

—

122

C₂×C₄

—

344

—

123

C₂×C₄

—

344

—

124

C₂×C₄

—

172

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

#14582810

yes

characteristic

134

C₂²

#14583089

yes

—

135

C₄

—

136

C₄

—

344

—

137

C₄

—

688

—

138

C₂

—

139

C₂

—

140

C₂

—

141

C₂

#19135761

yes

characteristic

142

C₂

#19135771

yes

—

	subgroup	G/H
center	C₂²	#14582810
commutator, prime radical, cosocle	C₂⁵×C₄₃	C₂³
Frattini	C₂⁵	C₂²×D₄₃
Fitting	C₄₃×#2840	C₂
socle	C₂²×C₄₃	#393
hypercenter	#2840	D₄₃
hypocenter	C₄₃	#10391
LCS	G ▷ C₂⁵×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #2840

subgroup

G/H

center

C₂²

#14582810

commutator, prime radical, cosocle

C₂⁵×C₄₃

C₂³

Frattini

C₂⁵

C₂²×D₄₃

Fitting

C₄₃×#2840

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂⁵×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂⁵ ◁ #2840

N	H ≅ G/N	type
9. C₂³×Dic₄₃	Q₈	semidirect
80. C₄₃	#10391	semidirect

H ≅ G/N

type

9. C₂³×Dic₄₃

Q₈

semidirect

80. C₄₃

#10391

semidirect

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

subgroup	index
#19134667	2
C₄₃⋊#1304	2
C₄₃×#2840	2
#10391	43

subgroup

index

#19134667

C₄₃⋊#1304

C₄₃×#2840

#10391

Subgroups — #24999849

Conjugacy classes of subgroups

Complements

Maximal subgroups