Group #19136817 — subgroups

Subgroups — #19136817

Order 5504.

160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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	#14583303	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583274	C₂	1	1	yes	maximal, characteristic
3	#14582701	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582700	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582699	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
9	C₂×#10621882	—	2	1	no	—
10	#13063324	—	2	1	no	—
11	#13063321	—	2	1	no	—
12	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
13	#13063259	C₂²	1	1	yes	characteristic
14	#13063258	—	2	1	no	—
15	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
16	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	#107×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×D₄×C₄₃	—	2	1	no	—
20	C₂×C₂²⋊D₄₃	—	4	1	no	—
21	C₂×C₂²⋊D₄₃	—	4	1	no	—
22	C₂×D₁₇₂	—	2	1	no	—
23	C₂×Dic₈₆	—	4	1	no	—
24	D₈×C₄₃	—	2	1	no	—
25	D₈×C₄₃	—	2	1	no	—
26	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
27	C₄⋊C₄×C₄₃	—	2	1	no	—
28	#10621882	—	4	2	no	—
29	C₄⋊Dic₄₃	—	2	1	no	—
30	Dic₄₃⋊C₄	—	4	1	no	—
31	C₄×Dic₄₃	D₄	1	1	yes	characteristic
32	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
33	D₃₄₄	—	2	1	no	—
34	D₃₄₄	—	2	1	no	—
35	C₁₆×C₄₃	—	2	1	no	—
36	C₄₃⋊C₁₆	—	2	1	no	—
37	C₂³×C₄₃	—	4	1	no	—
38	C₂²×D₄₃	—	4	1	no	—
39	D₄×C₄₃	—	4	1	no	—
40	D₄×C₄₃	—	4	1	no	—
41	C₂×C₄×C₄₃	—	4	1	no	—
42	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂²⋊D₄₃	—	8	2	no	—
44	C₂²⋊D₄₃	—	8	2	no	—
45	C₂×Dic₄₃	—	4	1	no	—
46	C₂×Dic₄₃	D₈	1	1	yes	characteristic
47	C₂×Dic₄₃	D₈	1	1	yes	characteristic
48	D₁₇₂	—	4	1	no	—
49	D₁₇₂	—	4	1	no	—
50	Dic₈₆	—	8	2	no	—
51	C₈×C₄₃	#41	1	1	yes	characteristic
52	C₈×C₄₃	#41	1	1	yes	characteristic
53	C₄₃⋊C₈	SD₁₆	1	2	yes	—
54	C₂²×C₄₃	—	8	1	no	—
55	C₂²×C₄₃	—	8	1	no	—
56	C₂²×C₄₃	—	8	1	no	—
57	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
58	C₂×D₄₃	—	8	1	no	—
59	C₂×D₄₃	—	8	1	no	—
60	C₂×D₄₃	—	8	1	no	—
61	C₄×C₄₃	—	8	1	no	—
62	C₄×C₄₃	#124	1	1	yes	characteristic
63	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
64	Dic₄₃	—	8	1	no	—
65	Dic₄₃	D₁₆	1	2	yes	—
66	Dic₄₃	SD₃₂	1	2	yes	—
67	#2240	—	43	1	no	maximal, Sylow
68	C₂×C₄₃	—	16	1	no	—
69	C₂×C₄₃	#486	1	1	yes	characteristic
70	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
71	C₂×C₄₃	C₂×SD₃₂	1	1	yes	characteristic
72	D₄₃	—	16	1	no	—
73	#500	—	43	1	no	—
74	#493	—	43	1	no	—
75	#357	—	43	1	no	—
76	#357	—	43	1	no	—
77	#357	—	43	1	no	—
78	#357	D₄₃	1	1	yes	characteristic, complemented
79	C₄×C₁₆	—	43	1	no	—
80	C₄₃	#2240	1	1	yes	characteristic, complemented, Sylow
81	C₂×D₈	—	43	1	no	—
82	C₂×D₈	—	86	1	no	—
83	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
84	C₄⋊Q₈	—	86	1	no	—
85	#127	—	86	1	no	—
86	C₂×C₁₆	—	43	1	no	—
87	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
88	#107	—	43	1	no	—
89	#107	—	86	1	no	—
90	#107	C₂×D₄₃	1	1	yes	characteristic
91	C₄×C₈	—	43	1	no	—
92	C₂×Q₈	—	172	1	no	—
93	C₂×D₄	—	2	1	no	—
94	C₂×D₄	—	86	1	no	—
95	C₂×D₄	—	172	1	no	—
96	C₂×D₄	—	172	1	no	—
97	D₈	—	2	1	no	—
98	D₈	—	2	1	no	—
99	D₈	—	86	1	no	—
100	D₈	—	86	1	no	—
101	D₈	—	172	2	no	—
102	C₂×C₈	—	43	1	no	—
103	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	86	1	no	—
106	C₄⋊C₄	—	172	1	no	—
107	C₄²	—	43	1	no	—
108	C₁₆	—	2	1	no	—
109	C₁₆	—	86	1	no	—
110	C₂³	—	4	1	no	—
111	C₂³	—	172	1	no	—
112	Q₈	—	344	2	no	—
113	D₄	—	4	1	no	—
114	D₄	—	4	1	no	—
115	D₄	—	344	2	no	—
116	D₄	—	344	2	no	—
117	D₄	—	172	1	no	—
118	D₄	—	172	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	43	1	no	—
121	C₂×C₄	—	43	1	no	—
122	C₂×C₄	—	172	1	no	—
123	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
124	C₈	—	43	2	no	—
125	C₈	#10621898	1	1	yes	characteristic
126	C₈	#10621900	1	1	yes	characteristic
127	C₂²	—	8	1	no	—
128	C₂²	—	8	1	no	—
129	C₂²	—	8	1	no	—
130	C₂²	—	344	1	no	—
131	C₂²	—	344	1	no	—
132	C₂²	—	344	1	no	—
133	C₂²	D₈×D₄₃	1	1	yes	characteristic
134	C₄	—	8	1	no	—
135	C₄	—	43	2	no	—
136	C₄	—	43	2	no	—
137	C₄	—	344	1	no	—
138	C₄	#13063311	1	1	yes	characteristic
139	C₄	SD₁₆×D₄₃	1	1	yes	characteristic
140	C₂	—	16	1	no	—
141	C₂	—	688	1	no	—
142	C₂	#14583244	1	1	yes	characteristic
143	C₂	D₁₆×D₄₃	1	1	yes	characteristic
144	C₂	SD₃₂×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583303

C₂

yes

maximal, characteristic, complemented

#14583274

C₂

yes

maximal, characteristic

#14582701

C₂

yes

maximal, characteristic, complemented

#14582700

C₂

yes

maximal, characteristic, complemented

#14582699

C₂

yes

maximal, characteristic, complemented

C₁₆×Dic₄₃

C₂

yes

maximal, characteristic, complemented

C₄₃×#357

C₂

yes

maximal, characteristic, complemented

C₂×D₃₄₄

C₂²

yes

—

—

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063258

—

C₈×Dic₄₃

C₂²

yes

characteristic

C₂×D₈×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#107×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂×C₂²⋊D₄₃

—

C₂×C₂²⋊D₄₃

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

D₈×C₄₃

—

D₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

#10621882

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

D₃₄₄

—

D₃₄₄

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

C₂²×D₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

D₈

yes

characteristic

C₂×Dic₄₃

D₈

yes

characteristic

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

SD₁₆

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#124

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

Dic₄₃

—

Dic₄₃

D₁₆

yes

—

Dic₄₃

SD₃₂

yes

—

#2240

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#486

yes

characteristic

C₂×C₄₃

C₂×D₁₆

yes

characteristic

C₂×C₄₃

C₂×SD₃₂

yes

characteristic

D₄₃

—

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄×C₁₆

—

C₄₃

#2240

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×D₈

—

C₂×D₈

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

—

#127

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

characteristic

C₄×C₈

—

C₂×Q₈

—

172

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

172

—

C₂×D₄

—

172

—

D₈

—

D₈

—

D₈

—

100

D₈

—

101

D₈

—

172

—

102

C₂×C₈

—

103

C₂×C₈

C₂²×D₄₃

yes

characteristic

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

172

—

107

C₄²

—

108

C₁₆

—

109

C₁₆

—

110

C₂³

—

111

C₂³

—

172

—

112

Q₈

—

344

—

113

D₄

—

114

D₄

—

115

D₄

—

344

—

116

D₄

—

344

—

117

D₄

—

172

—

118

D₄

—

172

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

172

—

123

C₂×C₄

D₄×D₄₃

yes

characteristic

124

C₈

—

125

C₈

#10621898

yes

characteristic

126

C₈

#10621900

yes

characteristic

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

344

—

131

C₂²

—

344

—

132

C₂²

—

344

—

133

C₂²

D₈×D₄₃

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

344

—

138

C₄

#13063311

yes

characteristic

139

C₄

SD₁₆×D₄₃

yes

characteristic

140

C₂

—

141

C₂

—

688

—

142

C₂

#14583244

yes

characteristic

143

C₂

D₁₆×D₄₃

yes

characteristic

144

C₂

SD₃₂×D₄₃

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#357	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#357	D₄₃
hypocenter	C₄₃	#2240
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#357

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. #14583303	C₂	semidirect
3. #14582701	C₂	semidirect
4. #14582700	C₂	semidirect
5. #14582699	C₂	semidirect
6. C₁₆×Dic₄₃	C₂	semidirect
7. C₄₃×#357	C₂	semidirect
78. #357	D₄₃	semidirect
80. C₄₃	#2240	semidirect

H ≅ G/N

type

1. #14583303

C₂

semidirect

3. #14582701

C₂

semidirect

4. #14582700

C₂

semidirect

5. #14582699

C₂

semidirect

6. C₁₆×Dic₄₃

C₂

semidirect

7. C₄₃×#357

C₂

semidirect

78. #357

D₄₃

semidirect

80. C₄₃

#2240

semidirect

Subgroups — #19136817

Conjugacy classes of subgroups

Complements