Group #19136473 — subgroups

Subgroups — #19136473

Order 5504.

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

normal subgroups only

This group has 146 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	#14583329	C₂	1	1	yes	maximal, characteristic
2	#14583016	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583015	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582728	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582707	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#359	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063347	C₂²	1	1	yes	characteristic
9	#13063333	—	2	1	no	—
10	#13063332	—	2	1	no	—
11	#13063271	C₄	1	1	yes	characteristic, complemented
12	#13063269	C₄	1	1	yes	characteristic, complemented
13	#13063268	C₄	1	1	yes	characteristic, complemented
14	#13063266	C₄	1	1	yes	characteristic, complemented
15	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
16	#13063261	C₂²	1	1	yes	characteristic
17	#13063252	—	2	1	no	—
18	#13063251	—	2	1	no	—
19	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
20	#135×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
22	#108×C₄₃	C₂²	1	1	yes	characteristic
23	#41×C₄₃	—	2	1	no	—
24	#10621898	—	2	1	no	—
25	Q₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
26	SD₁₆×C₄₃	—	2	1	no	—
27	D₈×C₄₃	C₂×C₄	1	1	yes	characteristic
28	M₁₆×C₄₃	—	2	1	no	—
29	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
30	C₄×Dic₄₃	D₄	1	1	yes	characteristic
31	#10621877	—	2	1	no	—
32	#10621877	—	4	1	no	—
33	C₂×C₄₃⋊C₈	—	4	1	no	—
34	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
35	Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
36	D₃₄₄	C₂×C₄	1	1	yes	characteristic
37	#10621873	—	2	1	no	—
38	#10621872	—	4	1	no	—
39	C₈×D₄₃	—	4	1	no	—
40	C₁₆×C₄₃	—	2	1	no	—
41	C₄₃⋊C₁₆	C₂×C₄	1	1	yes	characteristic
42	C₄₃⋊C₁₆	C₂×C₄	1	1	yes	characteristic
43	Q₈×C₄₃	—	2	1	no	—
44	D₄×C₄₃	—	2	1	no	—
45	D₄×C₄₃	—	4	1	no	—
46	C₂×C₄×C₄₃	—	4	1	no	—
47	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂²⋊D₄₃	—	4	1	no	—
49	C₂×Dic₄₃	—	2	1	no	—
50	D₁₇₂	—	2	1	no	—
51	C₄×D₄₃	—	4	1	no	—
52	Dic₈₆	—	2	1	no	—
53	C₈×C₄₃	—	4	1	no	—
54	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
55	C₈×C₄₃	#41	1	1	yes	characteristic
56	C₄₃⋊C₈	—	4	1	no	—
57	C₄₃⋊C₈	D₈	1	1	yes	characteristic
58	C₄₃⋊C₈	D₈	1	1	yes	characteristic
59	C₂²×C₄₃	—	4	1	no	—
60	C₂²×C₄₃	#135	1	1	yes	characteristic
61	C₂×D₄₃	—	4	1	no	—
62	C₄×C₄₃	—	4	1	no	—
63	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
64	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
65	Dic₄₃	—	2	2	no	—
66	Dic₄₃	—	4	1	no	—
67	#2178	—	43	1	no	maximal, Sylow
68	C₂×C₄₃	—	2	1	no	—
69	C₂×C₄₃	—	8	1	no	—
70	C₂×C₄₃	C₄×D₈	1	1	yes	characteristic
71	D₄₃	—	8	1	no	—
72	#508	—	43	1	no	—
73	#443	—	43	1	no	—
74	#443	—	43	1	no	—
75	#368	—	43	1	no	—
76	#359	—	43	1	no	—
77	#359	D₄₃	1	1	yes	characteristic, complemented
78	C₄×C₁₆	—	43	1	no	—
79	C₄₃	#2178	1	1	yes	characteristic, complemented, Sylow
80	#135	—	43	1	no	—
81	#135	C₂×D₄₃	1	1	yes	characteristic
82	#131	—	86	1	no	—
83	#131	—	86	1	no	—
84	Q₃₂	—	43	1	no	—
85	SD₃₂	—	43	1	no	—
86	SD₃₂	—	43	1	no	—
87	D₁₆	—	43	1	no	—
88	C₂×C₁₆	—	43	1	no	—
89	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
90	#108	—	43	1	no	—
91	#108	C₂×D₄₃	1	1	yes	characteristic
92	#104	—	86	1	no	—
93	#104	—	86	1	no	—
94	C₄×C₈	—	43	1	no	—
95	#41	—	2	1	no	—
96	#41	—	86	1	no	—
97	Q₁₆	—	43	1	no	—
98	Q₁₆	C₄×D₄₃	1	1	yes	characteristic
99	SD₁₆	—	2	1	no	—
100	SD₁₆	—	86	1	no	—
101	D₈	—	43	1	no	—
102	D₈	C₄×D₄₃	1	1	yes	characteristic
103	M₁₆	—	2	1	no	—
104	M₁₆	—	86	1	no	—
105	M₁₆	—	172	1	no	—
106	M₁₆	—	172	1	no	—
107	C₂×C₈	—	43	1	no	—
108	C₂×C₈	—	172	1	no	—
109	C₂×C₈	—	172	1	no	—
110	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
111	C₄²	—	43	1	no	—
112	C₁₆	—	2	1	no	—
113	C₁₆	—	43	1	no	—
114	C₁₆	—	43	1	no	—
115	Q₈	—	2	1	no	—
116	Q₈	—	86	1	no	—
117	D₄	—	2	1	no	—
118	D₄	—	4	1	no	—
119	D₄	—	86	1	no	—
120	D₄	—	172	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	86	1	no	—
123	C₂×C₄	—	172	1	no	—
124	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
125	C₈	—	4	1	no	—
126	C₈	—	43	1	no	—
127	C₈	—	43	1	no	—
128	C₈	—	172	1	no	—
129	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
130	C₈	#10621900	1	1	yes	characteristic
131	C₂²	—	4	1	no	—
132	C₂²	—	172	1	no	—
133	C₂²	#13063346	1	1	yes	characteristic
134	C₄	—	4	1	no	—
135	C₄	—	86	2	no	—
136	C₄	—	172	1	no	—
137	C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
138	C₄	D₈×D₄₃	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	8	1	no	—
141	C₂	—	344	1	no	—
142	C₂	#14582979	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583329

C₂

yes

maximal, characteristic

#14583016

C₂

yes

maximal, characteristic, complemented

#14583015

C₂

yes

maximal, characteristic, complemented

#14582728

C₂

yes

maximal, characteristic, complemented

#14582707

C₂

yes

maximal, characteristic, complemented

C₁₆×Dic₄₃

C₂

yes

maximal, characteristic, complemented

C₄₃×#359

C₂

yes

maximal, characteristic, complemented

#13063347

C₂²

yes

—

—

C₄

yes

characteristic, complemented

#13063269

C₄

yes

characteristic, complemented

#13063268

C₄

yes

characteristic, complemented

#13063266

C₄

yes

characteristic, complemented

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063261

C₂²

yes

characteristic

#13063252

—

#13063251

—

C₈×Dic₄₃

C₂²

yes

characteristic

#135×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#108×C₄₃

C₂²

yes

characteristic

#41×C₄₃

—

#10621898

—

Q₁₆×C₄₃

C₂×C₄

yes

characteristic

SD₁₆×C₄₃

—

D₈×C₄₃

C₂×C₄

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄×Dic₄₃

D₄

yes

characteristic

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Dic₁₇₂

C₂×C₄

yes

characteristic

D₃₄₄

C₂×C₄

yes

characteristic

#10621873

—

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

C₂×C₄

yes

characteristic

C₄₃⋊C₁₆

C₂×C₄

yes

characteristic

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

D₈

yes

characteristic

C₄₃⋊C₈

D₈

yes

characteristic

C₂²×C₄₃

—

C₂²×C₄₃

#135

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#2178

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

C₄×D₈

yes

characteristic

D₄₃

—

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄×C₁₆

—

C₄₃

#2178

yes

characteristic, complemented, Sylow

#135

—

#135

C₂×D₄₃

yes

characteristic

#131

—

#131

—

Q₃₂

—

SD₃₂

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

#108

—

#108

C₂×D₄₃

yes

characteristic

#104

—

#104

—

C₄×C₈

—

#41

—

#41

—

Q₁₆

—

Q₁₆

C₄×D₄₃

yes

characteristic

SD₁₆

—

100

SD₁₆

—

101

D₈

—

102

D₈

C₄×D₄₃

yes

characteristic

103

M₁₆

—

104

M₁₆

—

105

M₁₆

—

172

—

106

M₁₆

—

172

—

107

C₂×C₈

—

108

C₂×C₈

—

172

—

109

C₂×C₈

—

172

—

110

C₂×C₈

C₂²×D₄₃

yes

characteristic

111

C₄²

—

112

C₁₆

—

113

C₁₆

—

114

C₁₆

—

115

Q₈

—

116

Q₈

—

117

D₄

—

118

D₄

—

119

D₄

—

120

D₄

—

172

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

172

—

124

C₂×C₄

D₄×D₄₃

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

172

—

129

C₈

C₂×C₄×D₄₃

yes

characteristic

130

C₈

#10621900

yes

characteristic

131

C₂²

—

132

C₂²

—

172

—

133

C₂²

#13063346

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

172

—

137

C₄

(C₂²⋊D₄₃)⋊C₄

yes

characteristic

138

C₄

D₈×D₄₃

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

344

—

142

C₂

#14582979

yes

characteristic

	subgroup	G/H
center	C₄	D₈×D₄₃
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#359	C₂
socle	C₂×C₄₃	C₄×D₈
hypercenter	#359	D₄₃
hypocenter	C₄₃	#2178
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #359

subgroup

G/H

center

C₄

D₈×D₄₃

commutator

C₈×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#359

C₂

socle

C₂×C₄₃

C₄×D₈

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #359

N	H ≅ G/N	type
2. #14583016	C₂	semidirect
3. #14583015	C₂	semidirect
4. #14582728	C₂	semidirect
5. #14582707	C₂	semidirect
6. C₁₆×Dic₄₃	C₂	semidirect
7. C₄₃×#359	C₂	semidirect
11. #13063271	C₄	semidirect
12. #13063269	C₄	semidirect
13. #13063268	C₄	semidirect
14. #13063266	C₄	semidirect
77. #359	D₄₃	semidirect
79. C₄₃	#2178	semidirect

H ≅ G/N

type

2. #14583016

C₂

semidirect

3. #14583015

C₂

semidirect

4. #14582728

C₂

semidirect

5. #14582707

C₂

semidirect

6. C₁₆×Dic₄₃

C₂

semidirect

7. C₄₃×#359

C₂

semidirect

11. #13063271

C₄

semidirect

12. #13063269

C₄

semidirect

13. #13063268

C₄

semidirect

14. #13063266

C₄

semidirect

77. #359

D₄₃

semidirect

79. C₄₃

#2178

semidirect

Subgroups — #19136473

Conjugacy classes of subgroups

Complements