Group #24937119 — subgroups

Subgroups — C₄₃×#17102 #24937119

Order 11008.

2966 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 2966 conjugacy classes of subgroups — too many to draw. Only its 366 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	C₂×C₄₃×#392	C₂	1	10	yes	maximal, complemented
2	C₄₃×#1440	C₂	1	5	yes	maximal, complemented
3	C₂³×D₄×C₄₃	C₂²	1	10	yes	—
4	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	10	yes	—
5	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	5	yes	—
6	C₄₃×#392	—	2	40	no	—
7	C₂×#95×C₄₃	C₂²	1	10	yes	—
8	C₂⁵×C₄₃	C₂³	1	5	yes	—
9	C₂²×D₄×C₄₃	—	2	40	no	—
10	C₂²×D₄×C₄₃	—	2	20	no	—
11	C₂²×D₄×C₄₃	—	4	10	no	—
12	C₂²×D₄×C₄₃	—	4	20	no	—
13	C₂²×D₄×C₄₃	—	4	10	no	—
14	C₂³×C₄×C₄₃	C₂³	1	10	yes	—
15	C₂×C₂²⋊C₄×C₄₃	—	2	40	no	—
16	C₂×C₂²⋊C₄×C₄₃	—	4	10	no	—
17	C₂×C₂²⋊C₄×C₄₃	—	4	10	no	—
18	C₂×C₂²⋊C₄×C₄₃	D₄	1	20	yes	complemented
19	#95×C₄₃	—	2	20	no	—
20	C₂⁴×C₄₃	—	2	20	no	—
21	C₂⁴×C₄₃	—	2	10	no	—
22	C₂⁴×C₄₃	—	2	20	no	—
23	C₂⁴×C₄₃	—	2	20	no	—
24	C₂⁴×C₄₃	C₂×D₄	1	10	yes	—
25	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
26	C₂×D₄×C₄₃	—	4	40	no	—
27	C₂×D₄×C₄₃	—	4	80	no	—
28	C₂×D₄×C₄₃	—	4	80	no	—
29	C₂×D₄×C₄₃	—	4	40	no	—
30	C₂×D₄×C₄₃	—	4	40	no	—
31	C₂²×C₄×C₄₃	—	2	20	no	—
32	C₂²×C₄×C₄₃	—	2	10	no	—
33	C₂²×C₄×C₄₃	—	2	10	no	—
34	C₂²×C₄×C₄₃	—	2	20	no	—
35	C₂²×C₄×C₄₃	C₂×D₄	1	20	yes	—
36	C₂²⋊C₄×C₄₃	—	4	20	no	—
37	C₂²⋊C₄×C₄₃	—	4	40	no	—
38	C₂³×C₄₃	—	2	10	no	—
39	C₂³×C₄₃	—	2	20	no	—
40	C₂³×C₄₃	—	2	40	no	—
41	C₂³×C₄₃	—	4	20	no	—
42	C₂³×C₄₃	—	4	20	no	—
43	C₂³×C₄₃	—	4	20	no	—
44	C₂³×C₄₃	—	4	10	no	—
45	C₂³×C₄₃	—	4	20	no	—
46	C₂³×C₄₃	—	4	20	no	—
47	C₂³×C₄₃	—	4	10	no	—
48	C₂³×C₄₃	—	4	20	no	—
49	C₂³×C₄₃	C₂²×D₄	1	5	yes	—
50	C₂³×C₄₃	H(5,𝔽₂)	1	10	yes	—
51	D₄×C₄₃	—	4	160	no	—
52	C₂×C₄×C₄₃	—	2	20	no	—
53	C₂×C₄×C₄₃	—	2	40	no	—
54	C₂×C₄×C₄₃	—	4	20	no	—
55	C₂×C₄×C₄₃	—	4	10	no	—
56	C₂×C₄×C₄₃	—	4	10	no	—
57	#17102	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂²×C₄₃	—	4	20	no	—
59	C₂²×C₄₃	—	4	40	no	—
60	C₂²×C₄₃	—	4	10	no	—
61	C₂²×C₄₃	—	8	20	no	—
62	C₂²×C₄₃	—	8	20	no	—
63	C₂²×C₄₃	#534	1	5	yes	—
64	C₂²×C₄₃	#535	1	10	yes	—
65	C₂²×C₄₃	D₄²	1	10	yes	—
66	C₂²×C₄₃	#560	1	10	yes	—
67	C₄×C₄₃	—	4	20	no	—
68	C₂×#392	C₂×C₄₃	1	10	yes	complemented
69	#1440	C₂×C₄₃	1	5	yes	complemented
70	C₂×C₄₃	—	8	10	no	—
71	C₂×C₄₃	#2669	1	10	yes	—
72	C₂×C₄₃	#2815	1	5	yes	—
73	C₂³×D₄	C₂²×C₄₃	1	10	yes	—
74	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	10	yes	—
75	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	5	yes	—
76	#392	—	2	40	no	—
77	C₂×#95	C₂²×C₄₃	1	10	yes	—
78	C₄₃	#17102	1	1	yes	characteristic, direct product factor, Sylow
79	C₂⁵	C₂³×C₄₃	1	5	yes	—
80	C₂²×D₄	—	2	40	no	—
81	C₂²×D₄	—	2	20	no	—
82	C₂²×D₄	—	4	20	no	—
83	C₂²×D₄	—	4	10	no	—
84	C₂²×D₄	—	4	10	no	—
85	C₂³×C₄	C₂³×C₄₃	1	10	yes	—
86	C₂×C₂²⋊C₄	—	2	40	no	—
87	C₂×C₂²⋊C₄	—	4	10	no	—
88	C₂×C₂²⋊C₄	—	4	10	no	—
89	C₂×C₂²⋊C₄	D₄×C₄₃	1	20	yes	complemented
90	#95	—	2	20	no	—
91	C₂⁴	—	2	20	no	—
92	C₂⁴	—	2	10	no	—
93	C₂⁴	—	2	20	no	—
94	C₂⁴	—	2	20	no	—
95	C₂⁴	C₂×D₄×C₄₃	1	10	yes	—
96	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
97	C₂×D₄	—	4	80	no	—
98	C₂×D₄	—	4	40	no	—
99	C₂×D₄	—	4	40	no	—
100	C₂×D₄	—	4	80	no	—
101	C₂×D₄	—	4	40	no	—
102	C₂²×C₄	—	2	20	no	—
103	C₂²×C₄	—	2	10	no	—
104	C₂²×C₄	—	2	10	no	—
105	C₂²×C₄	—	2	20	no	—
106	C₂²×C₄	C₂×D₄×C₄₃	1	20	yes	—
107	C₂²⋊C₄	—	4	20	no	—
108	C₂²⋊C₄	—	4	40	no	—
109	C₂³	—	2	10	no	—
110	C₂³	—	2	20	no	—
111	C₂³	—	2	40	no	—
112	C₂³	—	4	20	no	—
113	C₂³	—	4	20	no	—
114	C₂³	—	4	20	no	—
115	C₂³	—	4	10	no	—
116	C₂³	—	4	20	no	—
117	C₂³	—	4	20	no	—
118	C₂³	—	4	10	no	—
119	C₂³	—	4	20	no	—
120	C₂³	C₂²×D₄×C₄₃	1	5	yes	—
121	C₂³	H(5,𝔽₂)×C₄₃	1	10	yes	—
122	D₄	—	4	160	no	—
123	C₂×C₄	—	2	20	no	—
124	C₂×C₄	—	2	40	no	—
125	C₂×C₄	—	4	20	no	—
126	C₂×C₄	—	4	10	no	—
127	C₂×C₄	—	4	10	no	—
128	C₂²	—	4	40	no	—
129	C₂²	—	4	20	no	—
130	C₂²	—	4	10	no	—
131	C₂²	—	8	20	no	—
132	C₂²	—	8	20	no	—
133	C₂²	C₄₃×#534	1	5	yes	—
134	C₂²	C₄₃×#535	1	10	yes	—
135	C₂²	D₄²×C₄₃	1	10	yes	—
136	C₂²	C₄₃×#560	1	10	yes	—
137	C₄	—	4	20	no	—
138	C₂	—	8	10	no	—
139	C₂	C₄₃×#2669	1	10	yes	—
140	C₂	C₄₃×#2815	1	5	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄₃×#392

C₂

yes

maximal, complemented

C₄₃×#1440

C₂

yes

maximal, complemented

C₂³×D₄×C₄₃

C₂²

yes

—

C₂²×C₂²⋊C₄×C₄₃

C₂²

yes

—

C₂²×C₂²⋊C₄×C₄₃

C₂²

yes

—

C₄₃×#392

—

C₂×#95×C₄₃

C₂²

yes

—

C₂⁵×C₄₃

C₂³

yes

—

C₂²×D₄×C₄₃

—

C₂²×D₄×C₄₃

—

C₂²×D₄×C₄₃

—

C₂²×D₄×C₄₃

—

C₂²×D₄×C₄₃

—

C₂³×C₄×C₄₃

C₂³

yes

—

C₂×C₂²⋊C₄×C₄₃

—

C₂×C₂²⋊C₄×C₄₃

—

C₂×C₂²⋊C₄×C₄₃

—

C₂×C₂²⋊C₄×C₄₃

D₄

yes

complemented

#95×C₄₃

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

—

C₂⁴×C₄₃

C₂×D₄

yes

—

C₂⁴×C₄₃

C₂⁴

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²×D₄

yes

—

C₂³×C₄₃

H(5,𝔽₂)

yes

—

D₄×C₄₃

—

160

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

#17102

C₄₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#534

yes

—

C₂²×C₄₃

#535

yes

—

C₂²×C₄₃

D₄²

yes

—

C₂²×C₄₃

#560

yes

—

C₄×C₄₃

—

C₂×#392

C₂×C₄₃

yes

complemented

#1440

C₂×C₄₃

yes

complemented

C₂×C₄₃

—

C₂×C₄₃

#2669

yes

—

C₂×C₄₃

#2815

yes

—

C₂³×D₄

C₂²×C₄₃

yes

—

C₂²×C₂²⋊C₄

C₂²×C₄₃

yes

—

C₂²×C₂²⋊C₄

C₂²×C₄₃

yes

—

#392

—

C₂×#95

C₂²×C₄₃

yes

—

C₄₃

#17102

yes

characteristic, direct product factor, Sylow

C₂⁵

C₂³×C₄₃

yes

—

C₂²×D₄

—

C₂²×D₄

—

C₂²×D₄

—

C₂²×D₄

—

C₂²×D₄

—

C₂³×C₄

C₂³×C₄₃

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

D₄×C₄₃

yes

complemented

#95

—

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

C₂×D₄×C₄₃

yes

—

C₂⁴

C₂⁴×C₄₃

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

C₂×D₄×C₄₃

yes

—

107

C₂²⋊C₄

—

108

C₂²⋊C₄

—

109

C₂³

—

110

C₂³

—

111

C₂³

—

112

C₂³

—

113

C₂³

—

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

C₂²×D₄×C₄₃

yes

—

121

C₂³

H(5,𝔽₂)×C₄₃

yes

—

122

D₄

—

160

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

C₄₃×#534

yes

—

134

C₂²

C₄₃×#535

yes

—

135

C₂²

D₄²×C₄₃

yes

—

136

C₂²

C₄₃×#560

yes

—

137

C₄

—

138

C₂

—

139

C₂

C₄₃×#2669

yes

—

140

C₂

C₄₃×#2815

yes

—

	subgroup	G/H
center, socle	C₂⁴×C₄₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ G

subgroup

G/H

center, socle

C₂⁴×C₄₃

C₂⁴

commutator, Frattini, cosocle

C₂⁴

C₂⁴×C₄₃

LCS

G ▷ C₂⁴ ▷ C₁

UCS

C₁ ◁ C₂⁴×C₄₃ ◁ G

N	H ≅ G/N	type
1. C₂×C₄₃×#392	C₂	semidirect
2. C₄₃×#1440	C₂	semidirect
18. C₂×C₂²⋊C₄×C₄₃	D₄	semidirect
57. #17102	C₄₃	direct (N × H)
68. C₂×#392	C₂×C₄₃	semidirect
69. #1440	C₂×C₄₃	semidirect
78. C₄₃	#17102	direct (N × H)
89. C₂×C₂²⋊C₄	D₄×C₄₃	semidirect

H ≅ G/N

type

1. C₂×C₄₃×#392

C₂

semidirect

2. C₄₃×#1440

C₂

semidirect

18. C₂×C₂²⋊C₄×C₄₃

D₄

semidirect

57. #17102

C₄₃

direct (N × H)

68. C₂×#392

C₂×C₄₃

semidirect

69. #1440

C₂×C₄₃

semidirect

78. C₄₃

#17102

direct (N × H)

89. C₂×C₂²⋊C₄

D₄×C₄₃

semidirect

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

subgroup	index
C₂×C₄₃×#392	2
C₄₃×#1440	2
#17102	43

subgroup

index

C₂×C₄₃×#392

C₄₃×#1440

#17102

Subgroups — C₄₃×#17102 #24937119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C43×#17102 #24937119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17102 #24937119