Group #19134170 — subgroups

Subgroups — #19134170

Order 5504.

154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14583250	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583189	C₂	1	1	yes	maximal, characteristic
3	#14583179	C₂	1	1	yes	maximal, characteristic
4	#14582650	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582647	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582646	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#436	C₂	1	1	yes	maximal, characteristic
8	#13063325	C₂²	1	1	yes	characteristic
9	#13063325	C₂²	1	1	yes	characteristic
10	#13063258	—	2	1	no	—
11	#13063256	—	2	1	no	—
12	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
13	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	#13063250	—	2	1	no	—
15	#13063250	—	2	1	no	—
16	#13063246	—	2	1	no	—
17	#13063246	—	2	1	no	—
18	C₂×M₁₆×C₄₃	—	2	1	no	—
19	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²⋊C₈×C₄₃	—	2	1	no	—
22	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₄₃	—	2	1	no	—
25	C₂×Dic₈₆	—	2	1	no	—
26	C₂×Dic₈₆	—	2	1	no	—
27	M₁₆×C₄₃	—	4	2	no	—
28	C₂×C₈×C₄₃	—	2	1	no	—
29	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
30	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
31	C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
32	C₂²⋊C₄×C₄₃	—	2	1	no	—
33	C₄²×C₄₃	C₂³	1	1	yes	characteristic
34	C₄⋊Dic₄₃	—	2	1	no	—
35	C₄⋊Dic₄₃	—	2	1	no	—
36	C₄⋊Dic₄₃	—	2	1	no	—
37	C₄⋊Dic₄₃	—	2	1	no	—
38	C₂×C₄₃⋊C₈	—	2	1	no	—
39	C₂×C₄₃⋊C₈	—	2	1	no	—
40	C₂³×C₄₃	—	2	1	no	—
41	D₄×C₄₃	—	2	1	no	—
42	D₄×C₄₃	—	2	1	no	—
43	C₂×C₄×C₄₃	—	2	1	no	—
44	C₂×C₄×C₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	—	4	1	no	—
46	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
49	C₂×Dic₄₃	—	4	1	no	—
50	C₂×Dic₄₃	—	4	1	no	—
51	Dic₈₆	—	4	1	no	—
52	Dic₈₆	—	4	1	no	—
53	Dic₈₆	—	8	1	no	—
54	C₈×C₄₃	—	2	1	no	—
55	C₈×C₄₃	—	2	1	no	—
56	C₈×C₄₃	—	4	1	no	—
57	C₄₃⋊C₈	—	4	1	no	—
58	C₄₃⋊C₈	—	4	1	no	—
59	C₂²×C₄₃	—	4	1	no	—
60	C₂²×C₄₃	—	4	1	no	—
61	C₂²×C₄₃	—	4	1	no	—
62	C₂²×C₄₃	#121	1	1	yes	characteristic
63	C₄×C₄₃	—	2	1	no	—
64	C₄×C₄₃	—	4	1	no	—
65	C₄×C₄₃	#135	1	1	yes	characteristic
66	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
67	C₄×C₄₃	#137	1	1	yes	characteristic
68	C₄×C₄₃	#137	1	1	yes	characteristic
69	Dic₄₃	—	8	1	no	—
70	Dic₄₃	—	8	1	no	—
71	#1703	—	43	1	no	maximal, Sylow
72	C₂×C₄₃	—	8	1	no	—
73	C₂×C₄₃	#463	1	1	yes	characteristic
74	C₂×C₄₃	#470	1	1	yes	characteristic
75	C₂×C₄₃	#471	1	1	yes	characteristic
76	#487	—	43	1	no	—
77	#476	—	43	1	no	—
78	#474	—	43	1	no	—
79	#436	D₄₃	1	1	yes	characteristic
80	#334	—	43	1	no	—
81	#333	—	43	1	no	—
82	#332	—	43	1	no	—
83	C₄₃	#1703	1	1	yes	characteristic, complemented, Sylow
84	C₂×M₁₆	—	2	1	no	—
85	C₄⋊Q₈	—	43	1	no	—
86	C₄⋊Q₈	—	43	1	no	—
87	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
88	#107	—	86	1	no	—
89	#106	—	86	1	no	—
90	C₄⋊C₈	—	43	1	no	—
91	C₄⋊C₈	—	43	1	no	—
92	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
93	#103	—	86	1	no	—
94	#103	—	86	1	no	—
95	#102	—	86	1	no	—
96	#102	—	86	1	no	—
97	C₂²⋊C₈	—	2	1	no	—
98	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
99	C₂×Q₈	—	86	1	no	—
100	C₂×Q₈	—	86	1	no	—
101	C₂×D₄	D₁₇₂	1	1	yes	characteristic
102	C₂²×C₄	—	2	1	no	—
103	M₁₆	—	4	2	no	—
104	C₂×C₈	—	2	1	no	—
105	C₂×C₈	—	86	1	no	—
106	C₂×C₈	—	86	1	no	—
107	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
108	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
109	C₄⋊C₄	—	86	1	no	—
110	C₄⋊C₄	—	86	1	no	—
111	C₄⋊C₄	—	86	1	no	—
112	C₄⋊C₄	—	86	1	no	—
113	C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
114	C₂²⋊C₄	—	2	1	no	—
115	C₄²	C₂²×D₄₃	1	1	yes	characteristic
116	C₂³	—	2	1	no	—
117	Q₈	—	344	1	no	—
118	Q₈	—	172	1	no	—
119	Q₈	—	172	1	no	—
120	D₄	—	2	1	no	—
121	D₄	—	2	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	4	1	no	—
125	C₂×C₄	—	172	1	no	—
126	C₂×C₄	—	172	1	no	—
127	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
128	C₂×C₄	#10621898	1	1	yes	characteristic
129	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
130	C₈	—	2	1	no	—
131	C₈	—	2	1	no	—
132	C₈	—	4	1	no	—
133	C₈	—	172	1	no	—
134	C₈	—	172	1	no	—
135	C₂²	—	4	1	no	—
136	C₂²	—	4	1	no	—
137	C₂²	—	4	1	no	—
138	C₂²	#13063299	1	1	yes	characteristic
139	C₄	—	2	1	no	—
140	C₄	—	4	1	no	—
141	C₄	—	344	1	no	—
142	C₄	—	344	1	no	—
143	C₄	#13063345	1	1	yes	characteristic
144	C₄	#13063351	1	1	yes	characteristic
145	C₄	#13063358	1	1	yes	characteristic
146	C₄	#13063358	1	1	yes	characteristic
147	C₂	—	8	1	no	—
148	C₂	#14583114	1	1	yes	characteristic
149	C₂	#14583157	1	1	yes	characteristic
150	C₂	#14583162	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583250

C₂

yes

maximal, characteristic, complemented

#14583189

C₂

yes

maximal, characteristic

#14583179

C₂

yes

maximal, characteristic

#14582650

C₂

yes

maximal, characteristic, complemented

#14582647

C₂

yes

maximal, characteristic, complemented

#14582646

C₂

yes

maximal, characteristic, complemented

C₄₃×#436

C₂

yes

maximal, characteristic

#13063325

C₂²

yes

characteristic

#13063325

C₂²

yes

characteristic

#13063258

—

#13063256

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

—

—

—

C₂×M₁₆×C₄₃

—

C₄×D₄×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄⋊C₄×C₄₃

D₄

yes

characteristic

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#121

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#1703

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

D₄₃

yes

—

—

—

C₄₃

#1703

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄×D₄

C₂×D₄₃

yes

characteristic

#107

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

—

—

—

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×D₄

D₁₇₂

yes

characteristic

102

C₂²×C₄

—

103

M₁₆

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

108

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

D₁₇₂

yes

characteristic

114

C₂²⋊C₄

—

115

C₄²

C₂²×D₄₃

yes

characteristic

116

C₂³

—

117

Q₈

—

344

—

118

Q₈

—

172

—

119

Q₈

—

172

—

120

D₄

—

121

D₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

172

—

126

C₂×C₄

—

172

—

127

C₂×C₄

C₂×D₁₇₂

yes

characteristic

128

C₂×C₄

#10621898

yes

characteristic

129

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

—

172

—

134

C₈

—

172

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

#13063299

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

344

—

142

C₄

—

344

—

143

C₄

#13063345

yes

characteristic

144

C₄

#13063351

yes

characteristic

145

C₄

#13063358

yes

characteristic

146

C₄

#13063358

yes

characteristic

147

C₂

—

148

C₂

#14583114

yes

characteristic

149

C₂

#14583157

yes

characteristic

150

C₂

#14583162

yes

characteristic

	subgroup	G/H
center	C₂²	#13063299
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#436	C₂
socle	C₂²×C₄₃	#121
hypercenter	#436	D₄₃
hypocenter	C₄₃	#1703
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #436

subgroup

G/H

center

C₂²

#13063299

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#436

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #436

N	H ≅ G/N	type
1. #14583250	C₂	semidirect
4. #14582650	C₂	semidirect
5. #14582647	C₂	semidirect
6. #14582646	C₂	semidirect
83. C₄₃	#1703	semidirect

H ≅ G/N

type

1. #14583250

C₂

semidirect

4. #14582650

C₂

semidirect

5. #14582647

C₂

semidirect

6. #14582646

C₂

semidirect

83. C₄₃

#1703

semidirect

Subgroups — #19134170

Conjugacy classes of subgroups

Complements