Group #19136548 — subgroups

Subgroups — #19136548

Order 5504.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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	#14583699	C₂	1	1	yes	maximal, characteristic
2	#14583342	C₂	1	2	yes	maximal, complemented
3	#14583157	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582710	C₂	1	2	yes	maximal, complemented
5	C₄₃×#349	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621898	—	2	1	no	—
7	#13063358	—	2	2	no	—
8	#13063353	—	2	2	no	—
9	#13063347	—	2	1	no	—
10	#13063347	C₂²	1	2	yes	—
11	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
12	#13063304	—	2	1	no	—
13	Dic₃₄₄	—	2	2	no	—
14	#13063270	—	2	2	no	—
15	#13063257	C₂²	1	1	yes	characteristic, complemented
16	#13063250	—	2	1	no	—
17	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	M₃₂×C₄₃	C₂²	1	2	yes	complemented
19	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
20	C₂×C₂²⋊D₄₃	—	4	1	no	—
21	#10621898	—	2	2	no	—
22	#10621898	—	2	2	no	—
23	#10621898	—	4	1	no	—
24	#10621898	—	4	1	no	—
25	C₂×D₁₇₂	—	2	1	no	—
26	C₂×C₄×D₄₃	—	4	1	no	—
27	C₂×Dic₈₆	—	2	1	no	—
28	C₂×Dic₈₆	—	2	1	no	—
29	M₁₆×C₄₃	—	2	2	no	—
30	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
31	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
32	C₂²⋊Dic₄₃	—	4	1	no	—
33	C₄⋊Dic₄₃	—	2	1	no	—
34	Dic₄₃⋊C₄	—	4	1	no	—
35	Dic₁₇₂	—	2	1	no	—
36	Dic₁₇₂	—	2	2	no	—
37	Dic₁₇₂	D₄	1	2	yes	—
38	D₃₄₄	—	2	1	no	—
39	D₃₄₄	D₄	1	2	yes	—
40	#10621873	—	2	2	no	—
41	#10621873	—	2	2	no	—
42	C₁₆×C₄₃	—	2	2	no	—
43	C₂³×C₄₃	D₈	1	1	yes	characteristic
44	C₂²×D₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	—	2	1	no	—
46	C₂×C₄×C₄₃	—	2	1	no	—
47	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
48	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂²⋊D₄₃	—	4	2	no	—
50	C₂²⋊D₄₃	—	4	2	no	—
51	C₂×Dic₄₃	—	4	1	no	—
52	C₂×Dic₄₃	—	4	1	no	—
53	C₂×Dic₄₃	—	4	1	no	—
54	D₁₇₂	—	2	2	no	—
55	D₁₇₂	—	4	1	no	—
56	C₄×D₄₃	—	4	2	no	—
57	C₄×D₄₃	—	4	2	no	—
58	Dic₈₆	—	2	2	no	—
59	Dic₈₆	—	4	1	no	—
60	Dic₈₆	—	4	1	no	—
61	Dic₈₆	—	4	1	no	—
62	C₈×C₄₃	—	2	1	no	—
63	C₈×C₄₃	C₂×D₄	1	2	yes	—
64	C₂²×C₄₃	—	2	1	no	—
65	C₂²×C₄₃	—	4	1	no	—
66	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
67	C₂×D₄₃	—	4	2	no	—
68	C₂×D₄₃	—	8	2	no	—
69	C₄×C₄₃	—	2	1	no	—
70	C₄×C₄₃	#120	1	1	yes	characteristic
71	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
72	Dic₄₃	—	4	2	no	—
73	Dic₄₃	—	8	1	no	—
74	Dic₄₃	—	8	1	no	—
75	#2191	—	43	1	no	maximal, Sylow
76	C₂×C₄₃	—	2	1	no	—
77	C₂×C₄₃	—	4	1	no	—
78	C₂×C₄₃	#447	1	1	yes	characteristic
79	D₄₃	—	8	2	no	—
80	#575	—	43	1	no	—
81	#510	—	43	2	no	—
82	#470	—	43	1	no	—
83	#360	—	43	2	no	—
84	#349	D₄₃	1	1	yes	characteristic, complemented
85	C₄₃	#2191	1	1	yes	characteristic, complemented, Sylow
86	C₂×#41	—	86	1	no	—
87	#137	—	86	2	no	—
88	AGL(1,ℤ/8)	—	86	2	no	—
89	#135	—	43	2	no	—
90	#135	—	86	1	no	—
91	C₂×Q₁₆	—	43	1	no	—
92	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
93	C₂²⋊Q₈	—	86	1	no	—
94	Q₃₂	—	86	2	no	—
95	SD₃₂	—	86	2	no	—
96	M₃₂	C₂×D₄₃	1	2	yes	complemented
97	#106	—	43	1	no	—
98	#103	—	86	1	no	—
99	#41	—	86	2	no	—
100	#41	—	86	2	no	—
101	#41	—	172	1	no	—
102	#41	—	172	1	no	—
103	C₂×Q₈	—	86	1	no	—
104	C₂×Q₈	—	86	1	no	—
105	C₂×D₄	—	86	1	no	—
106	C₂×D₄	—	172	1	no	—
107	C₂²×C₄	—	172	1	no	—
108	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
109	Q₁₆	—	43	2	no	—
110	Q₁₆	—	86	1	no	—
111	Q₁₆	—	86	2	no	—
112	SD₁₆	—	86	2	no	—
113	SD₁₆	—	86	2	no	—
114	D₈	—	43	2	no	—
115	D₈	—	86	1	no	—
116	M₁₆	—	2	2	no	—
117	C₂×C₈	D₁₇₂	1	1	yes	characteristic
118	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
119	C₄⋊C₄	—	86	1	no	—
120	C₄⋊C₄	—	172	1	no	—
121	C₂²⋊C₄	—	172	1	no	—
122	C₁₆	—	2	2	no	—
123	C₂³	—	172	1	no	—
124	C₂³	D₃₄₄	1	1	yes	characteristic
125	Q₈	—	86	2	no	—
126	Q₈	—	172	1	no	—
127	Q₈	—	172	1	no	—
128	Q₈	—	172	1	no	—
129	D₄	—	86	2	no	—
130	D₄	—	172	1	no	—
131	D₄	—	172	2	no	—
132	D₄	—	172	2	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	2	1	no	—
135	C₂×C₄	—	172	2	no	—
136	C₂×C₄	—	172	1	no	—
137	C₂×C₄	—	172	1	no	—
138	C₂×C₄	—	172	1	no	—
139	C₂×C₄	—	172	2	no	—
140	C₂×C₄	D₃₄₄	1	1	yes	characteristic
141	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
142	C₈	—	2	1	no	—
143	C₈	D₄×D₄₃	1	2	yes	—
144	C₂²	—	2	1	no	—
145	C₂²	—	4	1	no	—
146	C₂²	—	344	2	no	—
147	C₂²	—	172	2	no	—
148	C₂²	C₂×D₃₄₄	1	1	yes	characteristic
149	C₄	—	2	1	no	—
150	C₄	—	344	1	no	—
151	C₄	—	344	1	no	—
152	C₄	—	172	2	no	—
153	C₄	#13063295	1	1	yes	characteristic
154	C₄	#13063353	1	1	yes	characteristic
155	C₂	—	2	1	no	—
156	C₂	—	4	1	no	—
157	C₂	—	344	2	no	—
158	C₂	#14583035	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583699

C₂

yes

maximal, characteristic

#14583342

C₂

yes

maximal, complemented

#14583157

C₂

yes

maximal, characteristic, complemented

#14582710

C₂

yes

maximal, complemented

C₄₃×#349

C₂

yes

maximal, characteristic, complemented

—

—

—

—

C₂²

yes

—

C₂×Dic₁₇₂

C₂²

yes

characteristic, complemented

#13063304

—

Dic₃₄₄

—

#13063270

—

#13063257

C₂²

yes

characteristic, complemented

#13063250

—

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

complemented

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

—

—

—

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

D₄

yes

—

D₃₄₄

—

D₃₄₄

D₄

yes

—

#10621873

—

#10621873

—

C₁₆×C₄₃

—

C₂³×C₄₃

D₈

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂×D₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2191

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#447

yes

characteristic

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2191

yes

characteristic, complemented, Sylow

C₂×#41

—

—

—

—

—

C₂×Q₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂²⋊Q₈

—

Q₃₂

—

SD₃₂

—

M₃₂

C₂×D₄₃

yes

—

—

—

100

#41

—

101

#41

—

172

—

102

#41

—

172

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×D₄

—

106

C₂×D₄

—

172

—

107

C₂²×C₄

—

172

—

108

C₂²×C₄

D₁₇₂

yes

characteristic

109

Q₁₆

—

110

Q₁₆

—

111

Q₁₆

—

112

SD₁₆

—

113

SD₁₆

—

114

D₈

—

115

D₈

—

116

M₁₆

—

117

C₂×C₈

D₁₇₂

yes

characteristic

118

C₂×C₈

C₂²×D₄₃

yes

characteristic

119

C₄⋊C₄

—

120

C₄⋊C₄

—

172

—

121

C₂²⋊C₄

—

172

—

122

C₁₆

—

123

C₂³

—

172

—

124

C₂³

D₃₄₄

yes

characteristic

125

Q₈

—

126

Q₈

—

172

—

127

Q₈

—

172

—

128

Q₈

—

172

—

129

D₄

—

130

D₄

—

172

—

131

D₄

—

172

—

132

D₄

—

172

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

172

—

136

C₂×C₄

—

172

—

137

C₂×C₄

—

172

—

138

C₂×C₄

—

172

—

139

C₂×C₄

—

172

—

140

C₂×C₄

D₃₄₄

yes

characteristic

141

C₂×C₄

C₂×D₁₇₂

yes

characteristic

142

C₈

—

143

C₈

D₄×D₄₃

yes

—

144

C₂²

—

145

C₂²

—

146

C₂²

—

344

—

147

C₂²

—

172

—

148

C₂²

C₂×D₃₄₄

yes

characteristic

149

C₄

—

150

C₄

—

344

—

151

C₄

—

344

—

152

C₄

—

172

—

153

C₄

#13063295

yes

characteristic

154

C₄

#13063353

yes

characteristic

155

C₂

—

156

C₂

—

157

C₂

—

344

—

158

C₂

#14583035

yes

characteristic

	subgroup	G/H
center	C₂	#14583035
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#349	C₂
socle	C₂×C₄₃	#447
hypercenter	#349	D₄₃
hypocenter	C₄₃	#2191
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

subgroup

G/H

center

C₂

#14583035

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#349

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

N	H ≅ G/N	type
2. #14583342	C₂	semidirect
3. #14583157	C₂	semidirect
4. #14582710	C₂	semidirect
5. C₄₃×#349	C₂	semidirect
11. C₂×Dic₁₇₂	C₂²	semidirect
15. #13063257	C₂²	semidirect
18. M₃₂×C₄₃	C₂²	semidirect
84. #349	D₄₃	semidirect
85. C₄₃	#2191	semidirect
96. M₃₂	C₂×D₄₃	semidirect

H ≅ G/N

type

2. #14583342

C₂

semidirect

3. #14583157

C₂

semidirect

4. #14582710

C₂

semidirect

5. C₄₃×#349

C₂

semidirect

11. C₂×Dic₁₇₂

C₂²

semidirect

15. #13063257

C₂²

semidirect

18. M₃₂×C₄₃

C₂²

semidirect

84. #349

D₄₃

semidirect

85. C₄₃

#2191

semidirect

96. M₃₂

C₂×D₄₃

semidirect

Subgroups — #19136548

Conjugacy classes of subgroups

Complements