Group #19145022 — subgroups

Subgroups — #19145022

Order 5504.

572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13063344	C₂	1	4	yes	maximal, complemented
2	#14583447	C₂	1	2	yes	maximal, complemented
3	#14583282	C₂	1	4	yes	maximal, complemented
4	#14583279	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583271	C₂	1	2	yes	maximal, complemented
6	C₄×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621900	C₂²	1	4	yes	—
9	#13063344	—	2	16	no	—
10	C₂×Dic₁₇₂	C₂²	1	4	yes	—
11	C₂×#10621883	C₂²	1	8	yes	—
12	C₂×C₈×D₄₃	C₂²	1	2	yes	—
13	#13063325	C₂²	1	2	yes	—
14	#13063312	C₂²	1	4	yes	—
15	#13063296	—	2	4	no	—
16	D₄×Dic₄₃	—	2	4	no	—
17	C₄²×D₄₃	C₂²	1	1	yes	characteristic
18	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₈×Dic₄₃	C₂²	1	2	yes	—
20	C₂×D₈×C₄₃	C₂²	1	4	yes	—
21	#127×C₄₃	C₂²	1	2	yes	—
22	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×D₄×C₄₃	—	2	4	no	—
24	C₂×D₄×C₄₃	C₂³	1	4	yes	—
25	C₂×C₂²⋊D₄₃	—	2	4	no	—
26	C₂²×Dic₄₃	—	2	4	no	—
27	#10621900	—	2	16	no	—
28	C₂×C₄×D₄₃	D₄	1	2	yes	—
29	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
30	C₂×Dic₈₆	C₂³	1	4	yes	—
31	D₈×C₄₃	—	2	8	no	—
32	C₂×C₈×C₄₃	C₂³	1	2	yes	—
33	C₄²×C₄₃	C₂³	1	1	yes	characteristic
34	C₂²⋊Dic₄₃	—	2	8	no	—
35	#10621883	—	2	16	no	—
36	C₄⋊Dic₄₃	—	2	4	no	—
37	C₄×Dic₄₃	D₄	1	2	yes	—
38	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
39	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
40	Dic₁₇₂	—	2	8	no	—
41	C₈×D₄₃	D₄	1	8	yes	complemented
42	C₂³×C₄₃	—	2	4	no	—
43	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
44	D₄×C₄₃	—	2	8	no	—
45	D₄×C₄₃	—	4	8	no	—
46	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
48	C₂²⋊D₄₃	—	4	8	no	—
49	C₂×Dic₄₃	—	2	4	no	—
50	C₂×Dic₄₃	—	4	8	no	—
51	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
52	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
53	C₄×D₄₃	—	2	4	no	—
54	C₄×D₄₃	C₂×D₄	1	4	yes	—
55	Dic₈₆	—	2	8	no	—
56	C₈×C₄₃	C₂×D₄	1	4	yes	—
57	C₄₃⋊C₈	C₂×D₄	1	4	yes	—
58	C₂²×C₄₃	—	4	4	no	—
59	C₂²×C₄₃	—	4	8	no	—
60	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
61	C₂×D₄₃	—	2	2	no	—
62	C₂×D₄₃	#127	1	2	yes	—
63	C₄×C₄₃	#135	1	4	yes	complemented
64	C₄×C₄₃	C₂²×D₄	1	2	yes	—
65	Dic₄₃	—	2	2	no	—
66	Dic₄₃	—	4	4	no	—
67	Dic₄₃	#127	1	2	yes	—
68	#3147	—	43	1	no	maximal, Sylow
69	C₂×C₄₃	—	8	4	no	—
70	C₂×C₄₃	C₂×#127	1	1	yes	characteristic
71	C₂×C₄₃	C₂×#135	1	2	yes	—
72	D₄₃	—	2	2	no	—
73	C₂×#135	—	43	4	no	—
74	#532	—	43	2	no	—
75	#495	—	43	4	no	—
76	#494	—	43	1	no	—
77	#493	D₄₃	1	1	yes	characteristic, complemented
78	#492	—	43	2	no	—
79	C₂×C₄×C₈	—	43	1	no	—
80	C₄₃	#3147	1	1	yes	characteristic, complemented, Sylow
81	C₂×#41	—	43	4	no	—
82	#135	—	86	16	no	—
83	C₂×Q₁₆	—	43	4	no	—
84	C₂×SD₁₆	—	43	8	no	—
85	C₂×D₈	C₂×D₄₃	1	4	yes	—
86	C₂²×C₈	—	43	2	no	—
87	C₄⋊Q₈	—	43	2	no	—
88	#127	C₂×D₄₃	1	2	yes	—
89	#124	—	43	4	no	—
90	#121	—	86	4	no	—
91	C₄×D₄	—	86	4	no	—
92	C₂×C₄²	—	43	1	no	—
93	C₄×C₈	—	43	2	no	—
94	C₄×C₈	—	43	1	no	—
95	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
96	#41	—	86	16	no	—
97	C₂×Q₈	—	43	4	no	—
98	C₂×D₄	—	2	4	no	—
99	C₂×D₄	—	86	4	no	—
100	C₂×D₄	C₂²×D₄₃	1	4	yes	—
101	C₂²×C₄	—	43	1	no	—
102	C₂²×C₄	—	43	2	no	—
103	C₂²×C₄	—	86	4	no	—
104	Q₁₆	—	86	8	no	—
105	SD₁₆	—	86	16	no	—
106	D₈	—	2	8	no	—
107	C₂×C₈	—	43	2	no	—
108	C₂×C₈	—	43	8	no	—
109	C₂×C₈	C₂²×D₄₃	1	2	yes	—
110	C₄⋊C₄	—	86	4	no	—
111	C₂²⋊C₄	—	86	8	no	—
112	C₄²	—	43	2	no	—
113	C₄²	—	43	1	no	—
114	C₄²	C₂²×D₄₃	1	1	yes	characteristic
115	C₂³	—	2	4	no	—
116	C₂³	—	43	1	no	—
117	Q₈	—	86	8	no	—
118	D₄	—	2	8	no	—
119	D₄	—	4	8	no	—
120	D₄	—	172	8	no	—
121	C₂×C₄	—	43	1	no	—
122	C₂×C₄	—	43	4	no	—
123	C₂×C₄	—	43	2	no	—
124	C₂×C₄	—	86	4	no	—
125	C₂×C₄	—	86	4	no	—
126	C₂×C₄	—	172	8	no	—
127	C₂×C₄	D₄×D₄₃	1	2	yes	—
128	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
129	C₈	—	43	4	no	—
130	C₈	D₄×D₄₃	1	4	yes	—
131	C₂²	—	4	8	no	—
132	C₂²	—	4	4	no	—
133	C₂²	—	43	2	no	—
134	C₂²	—	86	2	no	—
135	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
136	C₄	—	43	2	no	—
137	C₄	—	86	2	no	—
138	C₄	—	172	4	no	—
139	C₄	#13063344	1	4	yes	complemented
140	C₄	C₂×D₄×D₄₃	1	2	yes	—
141	C₂	—	8	4	no	—
142	C₂	—	86	2	no	—
143	C₂	#127×D₄₃	1	1	yes	characteristic
144	C₂	C₂×#13063344	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063344

C₂

yes

maximal, complemented

#14583447

C₂

yes

maximal, complemented

#14583282

C₂

yes

maximal, complemented

#14583279

C₂

yes

maximal, characteristic, complemented

#14583271

C₂

yes

maximal, complemented

C₄×C₈×D₄₃

C₂

yes

maximal, characteristic, complemented

C₄₃×#493

C₂

yes

maximal, characteristic, complemented

C₂×#10621900

C₂²

yes

—

#13063344

—

C₂×Dic₁₇₂

C₂²

yes

—

C₂×#10621883

C₂²

yes

—

C₂×C₈×D₄₃

C₂²

yes

—

#13063325

C₂²

yes

—

#13063312

C₂²

yes

—

#13063296

—

D₄×Dic₄₃

—

C₄²×D₄₃

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₈×Dic₄₃

C₂²

yes

—

C₂×D₈×C₄₃

C₂²

yes

—

#127×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

C₂³

yes

—

C₂×C₂²⋊D₄₃

—

C₂²×Dic₄₃

—

#10621900

—

C₂×C₄×D₄₃

D₄

yes

—

C₂×C₄×D₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

C₂³

yes

—

D₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

#10621883

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

D₄

yes

—

C₄×Dic₄₃

C₂³

yes

characteristic

C₂×C₄₃⋊C₈

C₂³

yes

—

Dic₁₇₂

—

C₈×D₄₃

D₄

yes

complemented

C₂³×C₄₃

—

C₂²×D₄₃

C₂×D₄

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

C₂×D₄

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

C₂×D₄

yes

—

Dic₈₆

—

C₈×C₄₃

C₂×D₄

yes

—

C₄₃⋊C₈

C₂×D₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

#127

yes

—

C₄×C₄₃

#135

yes

complemented

C₄×C₄₃

C₂²×D₄

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

#127

yes

—

#3147

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#127

yes

characteristic

C₂×C₄₃

C₂×#135

yes

—

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

#492

—

C₂×C₄×C₈

—

C₄₃

#3147

yes

characteristic, complemented, Sylow

C₂×#41

—

#135

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

C₂×D₄₃

yes

—

C₂²×C₈

—

C₄⋊Q₈

—

#127

C₂×D₄₃

yes

—

#124

—

#121

—

C₄×D₄

—

C₂×C₄²

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

100

C₂×D₄

C₂²×D₄₃

yes

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

Q₁₆

—

105

SD₁₆

—

106

D₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₂²×D₄₃

yes

—

110

C₄⋊C₄

—

111

C₂²⋊C₄

—

112

C₄²

—

113

C₄²

—

114

C₄²

C₂²×D₄₃

yes

characteristic

115

C₂³

—

116

C₂³

—

117

Q₈

—

118

D₄

—

119

D₄

—

120

D₄

—

172

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

172

—

127

C₂×C₄

D₄×D₄₃

yes

—

128

C₂×C₄

C₂³×D₄₃

yes

characteristic

129

C₈

—

130

C₈

D₄×D₄₃

yes

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

C₂×D₄×D₄₃

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

172

—

139

C₄

#13063344

yes

complemented

140

C₄

C₂×D₄×D₄₃

yes

—

141

C₂

—

142

C₂

—

143

C₂

#127×D₄₃

yes

characteristic

144

C₂

C₂×#13063344

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#493	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#493	D₄₃
hypocenter	C₄₃	#3147
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

C₂×D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#493

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. C₂×#13063344	C₂	semidirect
2. #14583447	C₂	semidirect
3. #14583282	C₂	semidirect
4. #14583279	C₂	semidirect
5. #14583271	C₂	semidirect
6. C₄×C₈×D₄₃	C₂	semidirect
7. C₄₃×#493	C₂	semidirect
41. C₈×D₄₃	D₄	semidirect
63. C₄×C₄₃	#135	semidirect
77. #493	D₄₃	semidirect
80. C₄₃	#3147	semidirect
139. C₄	#13063344	semidirect

H ≅ G/N

type

1. C₂×#13063344

C₂

semidirect

2. #14583447

C₂

semidirect

3. #14583282

C₂

semidirect

4. #14583279

C₂

semidirect

5. #14583271

C₂

semidirect

6. C₄×C₈×D₄₃

C₂

semidirect

7. C₄₃×#493

C₂

semidirect

41. C₈×D₄₃

D₄

semidirect

63. C₄×C₄₃

#135

semidirect

77. #493

D₄₃

semidirect

80. C₄₃

#3147

semidirect

139. C₄

#13063344

semidirect

Subgroups — #19145022

Conjugacy classes of subgroups

Complements