Group #19136702 — subgroups

Subgroups — #19136702

Order 5504.

150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 47 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×#13063271	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063264	C₂	1	1	yes	maximal, characteristic
3	#14583141	C₂	1	1	yes	maximal, characteristic
4	#14583137	C₂	1	1	yes	maximal, characteristic
5	#14582726	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582704	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#358	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
10	#13063305	—	2	1	no	—
11	#13063301	—	2	1	no	—
12	#13063271	—	2	2	no	—
13	#13063264	—	2	2	no	—
14	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
15	#13063259	C₂²	1	1	yes	characteristic
16	#13063249	—	2	1	no	—
17	#13063248	—	2	1	no	—
18	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	#107×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₄₃	—	2	1	no	—
22	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
23	C₂×Dic₈₆	—	2	1	no	—
24	Q₁₆×C₄₃	—	2	1	no	—
25	Q₁₆×C₄₃	—	2	1	no	—
26	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
27	C₄⋊C₄×C₄₃	—	2	1	no	—
28	(C₂×D₄₃)⋊C₄	—	4	1	no	—
29	(C₂×D₄₃)⋊C₄	—	4	1	no	—
30	C₄⋊Dic₄₃	—	2	1	no	—
31	C₄⋊Dic₄₃	—	4	1	no	—
32	Dic₄₃⋊C₄	—	4	1	no	—
33	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
34	Dic₁₇₂	—	2	1	no	—
35	Dic₁₇₂	—	2	1	no	—
36	C₈×D₄₃	—	2	1	no	—
37	C₈×D₄₃	—	2	1	no	—
38	C₁₆×C₄₃	—	2	1	no	—
39	C₄₃⋊C₁₆	D₄	1	2	yes	—
40	C₂²×D₄₃	D₈	1	1	yes	characteristic
41	Q₈×C₄₃	—	4	1	no	—
42	Q₈×C₄₃	—	4	1	no	—
43	C₂×C₄×C₄₃	—	4	1	no	—
44	C₂×C₄×C₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂×Dic₄₃	—	4	1	no	—
47	C₂×Dic₄₃	—	4	1	no	—
48	C₂×Dic₄₃	D₈	1	1	yes	characteristic
49	C₄×D₄₃	—	2	1	no	—
50	C₄×D₄₃	—	2	1	no	—
51	Dic₈₆	—	4	1	no	—
52	Dic₈₆	—	4	1	no	—
53	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
54	C₈×C₄₃	#41	1	1	yes	characteristic
55	C₄₃⋊C₈	—	2	1	no	—
56	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
57	C₂×D₄₃	—	2	1	no	—
58	C₂×D₄₃	—	2	1	no	—
59	C₂×D₄₃	—	2	1	no	—
60	C₄×C₄₃	—	8	1	no	—
61	C₄×C₄₃	—	8	1	no	—
62	C₄×C₄₃	#121	1	1	yes	characteristic
63	C₄×C₄₃	#135	1	1	yes	characteristic
64	Dic₄₃	—	2	1	no	—
65	Dic₄₃	—	8	1	no	—
66	Dic₄₃	—	8	1	no	—
67	#2219	—	43	1	no	maximal, Sylow
68	C₂×C₄₃	#466	1	1	yes	characteristic
69	C₂×C₄₃	#510	1	1	yes	characteristic
70	C₂×C₄₃	#510	1	1	yes	characteristic
71	D₄₃	—	4	1	no	—
72	C₂×Q₃₂	—	43	1	no	—
73	C₂×M₃₂	—	43	1	no	—
74	#467	—	43	1	no	—
75	#467	—	43	1	no	—
76	#367	—	43	1	no	—
77	#358	—	43	1	no	—
78	#358	D₄₃	1	1	yes	characteristic, complemented
79	C₄₃	#2219	1	1	yes	characteristic, complemented, Sylow
80	C₂×Q₁₆	—	43	1	no	—
81	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
82	C₂²×C₈	—	43	1	no	—
83	C₂²⋊Q₈	—	86	1	no	—
84	C₂²⋊Q₈	—	86	1	no	—
85	Q₃₂	—	86	2	no	—
86	M₃₂	—	86	2	no	—
87	C₂×C₁₆	—	43	1	no	—
88	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
89	#107	—	43	1	no	—
90	#107	C₂×D₄₃	1	1	yes	characteristic
91	#103	—	86	1	no	—
92	#103	—	86	1	no	—
93	C₂×Q₈	—	2	1	no	—
94	C₂×Q₈	—	86	1	no	—
95	C₂²×C₄	—	43	1	no	—
96	Q₁₆	—	2	1	no	—
97	Q₁₆	—	2	1	no	—
98	Q₁₆	—	86	1	no	—
99	Q₁₆	—	86	1	no	—
100	C₂×C₈	—	43	1	no	—
101	C₂×C₈	—	86	1	no	—
102	C₂×C₈	—	86	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	C₄⋊C₄	—	172	1	no	—
108	C₂²⋊C₄	—	172	1	no	—
109	C₂²⋊C₄	—	172	1	no	—
110	C₁₆	—	2	1	no	—
111	C₁₆	—	43	2	no	—
112	C₂³	—	43	1	no	—
113	Q₈	—	4	1	no	—
114	Q₈	—	4	1	no	—
115	Q₈	—	172	1	no	—
116	Q₈	—	172	1	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	43	1	no	—
120	C₂×C₄	—	86	1	no	—
121	C₂×C₄	—	86	1	no	—
122	C₂×C₄	—	172	1	no	—
123	C₂×C₄	—	172	1	no	—
124	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
125	C₈	—	86	1	no	—
126	C₈	#10621898	1	1	yes	characteristic
127	C₈	D₄×D₄₃	1	1	yes	characteristic
128	C₂²	—	86	1	no	—
129	C₂²	—	86	1	no	—
130	C₂²	—	86	1	no	—
131	C₂²	D₈×D₄₃	1	1	yes	characteristic
132	C₄	—	8	1	no	—
133	C₄	—	8	1	no	—
134	C₄	—	86	1	no	—
135	C₄	—	344	1	no	—
136	C₄	—	344	1	no	—
137	C₄	#13063298	1	1	yes	characteristic
138	C₄	#13063346	1	1	yes	characteristic
139	C₂	—	172	1	no	—
140	C₂	#14583134	1	1	yes	characteristic
141	C₂	#14583338	1	1	yes	characteristic
142	C₂	#14583341	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063271

C₂

yes

maximal, characteristic, complemented

C₂×#13063264

C₂

yes

maximal, characteristic

#14583141

C₂

yes

maximal, characteristic

#14583137

C₂

yes

maximal, characteristic

#14582726

C₂

yes

maximal, characteristic, complemented

#14582704

C₂

yes

maximal, characteristic, complemented

C₄₃×#358

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₂×C₈×D₄₃

C₂²

yes

—

—

—

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063249

—

#13063248

—

C₂×Q₁₆×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#107×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×Dic₈₆

—

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Dic₁₇₂

—

Dic₁₇₂

—

C₈×D₄₃

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

D₄

yes

—

C₂²×D₄₃

D₈

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

D₈

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

C₂×Q₃₂

—

C₂×M₃₂

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2219

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₃

yes

characteristic

C₂²×C₈

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

Q₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

#107

—

#107

C₂×D₄₃

yes

characteristic

#103

—

#103

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

C₂²×D₄₃

yes

characteristic

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

172

—

107

C₄⋊C₄

—

172

—

108

C₂²⋊C₄

—

172

—

109

C₂²⋊C₄

—

172

—

110

C₁₆

—

111

C₁₆

—

112

C₂³

—

113

Q₈

—

114

Q₈

—

115

Q₈

—

172

—

116

Q₈

—

172

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

172

—

123

C₂×C₄

—

172

—

124

C₂×C₄

D₄×D₄₃

yes

characteristic

125

C₈

—

126

C₈

#10621898

yes

characteristic

127

C₈

D₄×D₄₃

yes

characteristic

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

D₈×D₄₃

yes

characteristic

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

344

—

136

C₄

—

344

—

137

C₄

#13063298

yes

characteristic

138

C₄

#13063346

yes

characteristic

139

C₂

—

172

—

140

C₂

#14583134

yes

characteristic

141

C₂

#14583338

yes

characteristic

142

C₂

#14583341

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#358	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#358	D₄₃
hypocenter	C₄₃	#2219
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#358

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
1. C₂×#13063271	C₂	semidirect
5. #14582726	C₂	semidirect
6. #14582704	C₂	semidirect
7. C₄₃×#358	C₂	semidirect
78. #358	D₄₃	semidirect
79. C₄₃	#2219	semidirect

H ≅ G/N

type

1. C₂×#13063271

C₂

semidirect

5. #14582726

C₂

semidirect

6. #14582704

C₂

semidirect

7. C₄₃×#358

C₂

semidirect

78. #358

D₄₃

semidirect

79. C₄₃

#2219

semidirect

Subgroups — #19136702

Conjugacy classes of subgroups

Complements