Group #19137147 — subgroups

Subgroups — #126×Dic₄₃ #19137147

Order 5504.

516 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 229 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	#14582792	C₂	1	3	yes	maximal
2	#14582785	C₂	1	3	yes	maximal, complemented
3	#14582767	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊C₄×Dic₄₃	C₂	1	3	yes	maximal, complemented
5	C₂²⋊C₄×Dic₄₃	C₂	1	3	yes	maximal
6	C₄²×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#126×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂³×Dic₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
10	C₂×C₂²⋊Dic₄₃	C₂²	1	3	yes	—
11	C₂×C₄×Dic₄₃	C₂²	1	3	yes	—
12	C₂×C₄×Dic₄₃	C₂²	1	3	yes	—
13	C₂×C₄×Dic₄₃	C₂²	1	3	yes	—
14	C₄₃⋊#95	C₂²	1	3	yes	—
15	C₄₃⋊#95	C₂²	1	3	yes	—
16	C₄₃⋊#95	C₂²	1	3	yes	—
17	C₄₃⋊#95	C₂²	1	3	yes	—
18	#126×C₄₃	C₄	1	8	yes	complemented
19	C₂×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
20	C₂×C₂²⋊C₄×C₄₃	C₂²	1	3	yes	—
21	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
25	C₂²×Dic₄₃	—	2	6	no	—
26	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₃	C₂³	1	3	yes	—
28	C₂²×Dic₄₃	C₂³	1	3	yes	—
29	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
30	C₄⋊C₄×C₄₃	C₂×C₄	1	12	yes	complemented
31	C₂²⋊C₄×C₄₃	C₂×C₄	1	12	yes	—
32	C₄²×C₄₃	C₂×C₄	1	4	yes	complemented
33	C₂²⋊Dic₄₃	—	2	6	no	—
34	C₄⋊Dic₄₃	—	2	6	no	—
35	C₄×Dic₄₃	—	2	6	no	—
36	C₄×Dic₄₃	—	2	6	no	—
37	C₄×Dic₄₃	—	2	6	no	—
38	C₂³×C₄₃	—	2	3	no	—
39	C₂³×C₄₃	—	2	3	no	—
40	C₂³×C₄₃	C₂²×C₄	1	2	yes	—
41	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
42	C₂×C₄×C₄₃	—	2	3	no	—
43	C₂×C₄×C₄₃	—	2	3	no	—
44	C₂×C₄×C₄₃	—	2	3	no	—
45	C₂×C₄×C₄₃	—	2	3	no	—
46	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
47	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
48	C₂×Dic₄₃	—	2	3	no	—
49	C₂×Dic₄₃	—	2	3	no	—
50	C₂×Dic₄₃	—	2	3	no	—
51	C₂×Dic₄₃	—	2	3	no	—
52	C₂×Dic₄₃	—	2	3	no	—
53	C₂×Dic₄₃	—	2	3	no	—
54	C₂×Dic₄₃	—	4	4	no	—
55	C₂×Dic₄₃	#41	1	6	yes	—
56	C₂×Dic₄₃	#41	1	6	yes	—
57	C₂²×C₄₃	—	2	6	no	—
58	C₂²×C₄₃	—	4	1	no	—
59	C₂²×C₄₃	—	4	3	no	—
60	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
61	C₂²×C₄₃	C₂×#41	1	3	yes	—
62	C₂²×C₄₃	C₂×#41	1	3	yes	—
63	C₄×C₄₃	—	2	6	no	—
64	C₄×C₄₃	—	2	6	no	—
65	Dic₄₃	—	2	6	no	—
66	Dic₄₃	—	4	1	no	—
67	Dic₄₃	—	4	3	no	—
68	Dic₄₃	#126	1	4	yes	direct product factor
69	C₄×#126	—	43	1	no	maximal, Sylow
70	C₂×C₄₃	—	4	2	no	—
71	C₂×C₄₃	C₄×#41	1	3	yes	—
72	C₂×C₄₃	C₂×#126	1	1	yes	characteristic
73	C₂×C₄₃	#529	1	3	yes	—
74	C₂×#126	D₄₃	1	1	yes	characteristic
75	#388	—	43	3	no	—
76	#387	—	43	3	no	—
77	#383	—	43	1	no	—
78	C₄×C₄⋊C₄	—	43	3	no	—
79	C₄×C₂²⋊C₄	—	43	3	no	—
80	C₄³	—	43	1	no	—
81	C₄₃	C₄×#126	1	1	yes	characteristic, complemented, Sylow
82	C₂³×C₄	—	43	1	no	—
83	#126	Dic₄₃	1	8	yes	direct product factor
84	C₂×C₄⋊C₄	—	43	3	no	—
85	C₂×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
86	C₂×C₂²⋊C₄	—	43	3	no	—
87	C₂×C₂²⋊C₄	C₂×D₄₃	1	3	yes	—
88	C₂×C₄²	—	43	3	no	—
89	C₂×C₄²	—	43	3	no	—
90	C₂×C₄²	—	43	3	no	—
91	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
92	#95	—	43	3	no	—
93	#95	—	43	3	no	—
94	#95	—	43	3	no	—
95	#95	—	43	3	no	—
96	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
97	C₂²×C₄	—	43	1	no	—
98	C₂²×C₄	—	43	3	no	—
99	C₂²×C₄	—	43	1	no	—
100	C₂²×C₄	—	43	3	no	—
101	C₂²×C₄	—	86	6	no	—
102	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
103	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
104	C₄⋊C₄	—	86	6	no	—
105	C₄⋊C₄	C₂×Dic₄₃	1	12	yes	complemented
106	C₂²⋊C₄	—	86	6	no	—
107	C₂²⋊C₄	C₂×Dic₄₃	1	12	yes	—
108	C₄²	—	86	6	no	—
109	C₄²	—	86	6	no	—
110	C₄²	—	86	6	no	—
111	C₄²	C₂×Dic₄₃	1	4	yes	complemented
112	C₂³	—	2	3	no	—
113	C₂³	—	2	3	no	—
114	C₂³	C₂²×Dic₄₃	1	2	yes	—
115	C₂³	C₂³×D₄₃	1	1	yes	characteristic
116	C₂×C₄	—	2	3	no	—
117	C₂×C₄	—	2	3	no	—
118	C₂×C₄	—	2	3	no	—
119	C₂×C₄	—	2	3	no	—
120	C₂×C₄	—	43	6	no	—
121	C₂×C₄	—	43	6	no	—
122	C₂×C₄	—	86	3	no	—
123	C₂×C₄	—	86	3	no	—
124	C₂×C₄	—	86	3	no	—
125	C₂×C₄	—	86	3	no	—
126	C₂×C₄	—	86	3	no	—
127	C₂×C₄	—	86	3	no	—
128	C₂×C₄	—	172	4	no	—
129	C₂×C₄	C₂²×Dic₄₃	1	6	yes	—
130	C₂×C₄	C₂²×Dic₄₃	1	6	yes	—
131	C₂²	—	2	6	no	—
132	C₂²	—	4	1	no	—
133	C₂²	—	4	3	no	—
134	C₂²	C₂³×Dic₄₃	1	1	yes	characteristic
135	C₂²	#41×D₄₃	1	3	yes	—
136	C₂²	#41×D₄₃	1	3	yes	—
137	C₄	—	2	6	no	—
138	C₄	—	2	6	no	—
139	C₄	—	43	4	no	—
140	C₄	—	86	6	no	—
141	C₄	—	172	1	no	—
142	C₄	—	172	3	no	—
143	C₂	—	4	2	no	—
144	C₂	#41×Dic₄₃	1	3	yes	—
145	C₂	#126×D₄₃	1	1	yes	characteristic
146	C₂	#14583432	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14582792

C₂

yes

maximal

#14582785

C₂

yes

maximal, complemented

#14582767

C₂

yes

maximal, characteristic, complemented

C₄⋊C₄×Dic₄₃

C₂

yes

maximal, complemented

C₂²⋊C₄×Dic₄₃

C₂

yes

maximal

C₄²×Dic₄₃

C₂

yes

maximal, characteristic, complemented

C₂×#126×C₄₃

C₂

yes

maximal, characteristic

C₂³×Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

#126×C₄₃

C₄

yes

complemented

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

C₂×C₄

yes

complemented

C₂²⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

complemented

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²×C₄

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

#41

yes

—

C₂×Dic₄₃

#41

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

#126

yes

direct product factor

C₄×#126

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₄×#41

yes

—

C₂×C₄₃

C₂×#126

yes

characteristic

C₂×C₄₃

#529

yes

—

C₂×#126

D₄₃

yes

—

—

—

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

C₄³

—

C₄₃

C₄×#126

yes

characteristic, complemented, Sylow

C₂³×C₄

—

#126

Dic₄₃

yes

direct product factor

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

—

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

C₂²×D₄₃

yes

—

103

C₂²×C₄

C₂²×D₄₃

yes

—

104

C₄⋊C₄

—

105

C₄⋊C₄

C₂×Dic₄₃

yes

complemented

106

C₂²⋊C₄

—

107

C₂²⋊C₄

C₂×Dic₄₃

yes

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

C₂×Dic₄₃

yes

complemented

112

C₂³

—

113

C₂³

—

114

C₂³

C₂²×Dic₄₃

yes

—

115

C₂³

C₂³×D₄₃

yes

characteristic

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

172

—

129

C₂×C₄

C₂²×Dic₄₃

yes

—

130

C₂×C₄

C₂²×Dic₄₃

yes

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

C₂³×Dic₄₃

yes

characteristic

135

C₂²

#41×D₄₃

yes

—

136

C₂²

#41×D₄₃

yes

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

172

—

142

C₄

—

172

—

143

C₂

—

144

C₂

#41×Dic₄₃

yes

—

145

C₂

#126×D₄₃

yes

characteristic

146

C₂

#14583432

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Fitting	C₂×#126×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₂×#126	D₄₃
hypocenter	C₄₃	C₄×#126
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#126

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator

C₂²×C₄₃

C₂³×C₄

Fitting

C₂×#126×C₄₃

C₂

socle

C₂³×C₄₃

C₂⁴

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂×#126

N	H ≅ G/N	type
2. #14582785	C₂	semidirect
3. #14582767	C₂	semidirect
4. C₄⋊C₄×Dic₄₃	C₂	semidirect
6. C₄²×Dic₄₃	C₂	semidirect
18. #126×C₄₃	C₄	semidirect
30. C₄⋊C₄×C₄₃	C₂×C₄	semidirect
32. C₄²×C₄₃	C₂×C₄	semidirect
68. Dic₄₃	#126	direct (N × H)
81. C₄₃	C₄×#126	semidirect
83. #126	Dic₄₃	direct (N × H)
105. C₄⋊C₄	C₂×Dic₄₃	semidirect
111. C₄²	C₂×Dic₄₃	semidirect

H ≅ G/N

type

2. #14582785

C₂

semidirect

3. #14582767

C₂

semidirect

4. C₄⋊C₄×Dic₄₃

C₂

semidirect

6. C₄²×Dic₄₃

C₂

semidirect

18. #126×C₄₃

C₄

semidirect

30. C₄⋊C₄×C₄₃

C₂×C₄

semidirect

32. C₄²×C₄₃

C₂×C₄

semidirect

68. Dic₄₃

#126

direct (N × H)

81. C₄₃

C₄×#126

semidirect

83. #126

Dic₄₃

direct (N × H)

105. C₄⋊C₄

C₂×Dic₄₃

semidirect

111. C₄²

C₂×Dic₄₃

semidirect

Subgroups — #126×Dic₄₃ #19137147

Conjugacy classes of subgroups

Complements

Subgroups — #126×Dic43 #19137147

Conjugacy classes of subgroups

Complements

Subgroups — #126×Dic₄₃ #19137147