Group #19134390 — subgroups

Subgroups — #19134390

Order 5504.

296 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 107 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×#13063290	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063243	C₂	1	2	yes	maximal
3	M₁₆×Dic₄₃	C₂	1	2	yes	maximal
4	#14582668	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#343	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
7	C₂×#10621877	C₂²	1	2	yes	—
8	#13063290	—	2	2	no	—
9	#13063290	—	2	2	no	—
10	C₂×Dic₄₃⋊C₄	C₄	1	2	yes	—
11	C₂×C₄×Dic₄₃	C₄	1	2	yes	—
12	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
13	#13063243	C₄	1	8	yes	complemented
14	#13063235	—	2	2	no	—
15	C₈×Dic₄₃	—	2	2	no	—
16	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
17	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
19	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
20	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
21	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₈₆	—	2	2	no	—
24	C₂×Dic₈₆	—	2	1	no	—
25	C₂×Dic₈₆	—	2	1	no	—
26	C₂×Dic₈₆	C₂×C₄	1	4	yes	—
27	M₁₆×C₄₃	—	2	2	no	—
28	M₁₆×C₄₃	C₂×C₄	1	4	yes	—
29	C₂×C₈×C₄₃	—	2	2	no	—
30	C₄⋊C₄×C₄₃	—	2	2	no	—
31	Dic₄₃⋊C₄	—	2	4	no	—
32	C₄×Dic₄₃	—	2	2	no	—
33	C₄×Dic₄₃	—	2	2	no	—
34	C₄×Dic₄₃	D₄	1	2	yes	—
35	C₄×Dic₄₃	D₄	1	2	yes	—
36	#10621877	—	2	2	no	—
37	#10621877	C₂×C₄	1	4	yes	—
38	C₂×C₄₃⋊C₈	—	2	2	no	—
39	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₄₃	—	2	2	no	—
41	C₂×C₄×C₄₃	—	4	2	no	—
42	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
43	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
45	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
46	C₂×Dic₄₃	—	2	2	no	—
47	C₂×Dic₄₃	—	2	2	no	—
48	C₂×Dic₄₃	—	2	2	no	—
49	C₂×Dic₄₃	—	4	1	no	—
50	C₂×Dic₄₃	C₄²	1	4	yes	—
51	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×Dic₄₃	C₂²⋊C₄	1	2	yes	—
53	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
54	Dic₈₆	—	2	4	no	—
55	Dic₈₆	—	2	4	no	—
56	C₈×C₄₃	—	2	4	no	—
57	C₄₃⋊C₈	—	2	4	no	—
58	C₂²×C₄₃	—	2	1	no	—
59	C₂²×C₄₃	—	2	1	no	—
60	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
61	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄₃	#117	1	1	yes	characteristic
63	C₄×C₄₃	—	4	2	no	—
64	C₄×C₄₃	C₄×D₄	1	2	yes	—
65	C₄×C₄₃	C₄×D₄	1	2	yes	—
66	Dic₄₃	—	2	4	no	—
67	Dic₄₃	—	2	1	no	—
68	Dic₄₃	—	2	2	no	—
69	Dic₄₃	#101	1	2	yes	complemented
70	C₄×#101	—	43	1	no	maximal, Sylow
71	C₂×C₄₃	—	2	1	no	—
72	C₂×C₄₃	—	2	1	no	—
73	C₂×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₄₃	C₂×#101	1	1	yes	characteristic
75	C₂×C₄₃	#413	1	1	yes	characteristic
76	C₂×C₄×Q₈	—	43	1	no	—
77	C₂×#101	—	43	2	no	—
78	C₄×M₁₆	—	43	2	no	—
79	#343	—	43	1	no	—
80	#343	D₄₃	1	1	yes	characteristic
81	C₄₃	C₄×#101	1	1	yes	characteristic, complemented, Sylow
82	C₂²×Q₈	—	43	1	no	—
83	C₂×M₁₆	—	43	2	no	—
84	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
85	C₄×Q₈	—	86	2	no	—
86	C₄×Q₈	—	86	2	no	—
87	C₂×C₄⋊C₄	—	43	2	no	—
88	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
89	C₂×C₄²	—	43	1	no	—
90	C₂×C₄²	—	43	2	no	—
91	#101	—	43	8	no	—
92	#97	—	86	2	no	—
93	C₄×C₈	—	86	2	no	—
94	C₂×Q₈	—	43	4	no	—
95	C₂×Q₈	—	86	2	no	—
96	C₂×Q₈	—	86	1	no	—
97	C₂×Q₈	—	86	1	no	—
98	C₂²×C₄	—	43	1	no	—
99	C₂²×C₄	—	43	2	no	—
100	C₂²×C₄	—	43	1	no	—
101	C₂²×C₄	C₄×D₄₃	1	2	yes	—
102	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
103	M₁₆	—	2	2	no	—
104	M₁₆	—	43	4	no	—
105	M₁₆	—	86	2	no	—
106	M₁₆	C₄×D₄₃	1	4	yes	—
107	C₂×C₈	—	2	2	no	—
108	C₂×C₈	—	86	2	no	—
109	C₄⋊C₄	—	2	2	no	—
110	C₄⋊C₄	—	86	4	no	—
111	C₄²	—	43	2	no	—
112	C₄²	—	43	2	no	—
113	C₄²	—	86	2	no	—
114	C₄²	—	86	2	no	—
115	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
116	Q₈	—	86	4	no	—
117	Q₈	—	86	4	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	43	1	no	—
121	C₂×C₄	—	43	4	no	—
122	C₂×C₄	—	43	1	no	—
123	C₂×C₄	—	43	2	no	—
124	C₂×C₄	—	86	2	no	—
125	C₂×C₄	—	86	2	no	—
126	C₂×C₄	—	86	2	no	—
127	C₂×C₄	—	172	1	no	—
128	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
129	C₂×C₄	D₄×D₄₃	1	2	yes	—
130	C₂×C₄	#10621900	1	1	yes	characteristic
131	C₂×C₄	#10621902	1	1	yes	characteristic
132	C₈	—	2	4	no	—
133	C₈	—	86	4	no	—
134	C₂²	—	2	1	no	—
135	C₂²	—	2	1	no	—
136	C₂²	C₄²×D₄₃	1	1	yes	characteristic
137	C₂²	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
138	C₂²	#13063283	1	1	yes	characteristic
139	C₄	—	4	2	no	—
140	C₄	—	43	2	no	—
141	C₄	—	86	1	no	—
142	C₄	—	86	2	no	—
143	C₄	—	86	4	no	—
144	C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
145	C₄	#13063287	1	2	yes	—
146	C₂	—	2	1	no	—
147	C₂	—	2	1	no	—
148	C₂	#14582746	1	1	yes	characteristic
149	C₂	#101×D₄₃	1	1	yes	characteristic
150	C₂	#14582880	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063290

C₂

yes

maximal, characteristic

C₂×#13063243

C₂

yes

maximal

M₁₆×Dic₄₃

C₂

yes

maximal

#14582668

C₂

yes

maximal, characteristic

C₄₃×#343

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

—

#13063290

—

#13063290

—

C₂×Dic₄₃⋊C₄

C₄

yes

—

C₂×C₄×Dic₄₃

C₄

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

#13063243

C₄

yes

complemented

#13063235

—

C₈×Dic₄₃

—

C₂×M₁₆×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂²×Dic₄₃

C₂×C₄

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂×C₄

yes

—

M₁₆×C₄₃

—

M₁₆×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

D₄

yes

—

C₄×Dic₄₃

D₄

yes

—

#10621877

—

#10621877

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₄²

yes

—

C₂×Dic₄₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₃

C₂²⋊C₄

yes

—

C₂×Dic₄₃

C₂²⋊C₄

yes

characteristic

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄²

yes

characteristic

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

#117

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

C₄×D₄

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

yes

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

C₄×C₂²⋊C₄

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄×Q₈

—

C₂×#101

—

C₄×M₁₆

—

#343

—

#343

D₄₃

yes

characteristic

C₄₃

C₄×#101

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

#101

—

#97

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₄×D₄₃

yes

—

102

C₂²×C₄

C₂²×D₄₃

yes

characteristic

103

M₁₆

—

104

M₁₆

—

105

M₁₆

—

106

M₁₆

C₄×D₄₃

yes

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₄²

—

115

C₂³

C₂×C₄×D₄₃

yes

characteristic

116

Q₈

—

117

Q₈

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

172

—

128

C₂×C₄

C₂×C₄×D₄₃

yes

—

129

C₂×C₄

D₄×D₄₃

yes

—

130

C₂×C₄

#10621900

yes

characteristic

131

C₂×C₄

#10621902

yes

characteristic

132

C₈

—

133

C₈

—

134

C₂²

—

135

C₂²

—

136

C₂²

C₄²×D₄₃

yes

characteristic

137

C₂²

C₂²⋊C₄×D₄₃

yes

characteristic

138

C₂²

#13063283

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

(C₂²⋊D₄₃)⋊C₄

yes

—

145

C₄

#13063287

yes

—

146

C₂

—

147

C₂

—

148

C₂

#14582746

yes

characteristic

149

C₂

#101×D₄₃

yes

characteristic

150

C₂

#14582880

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₄₃
commutator	C₂²×C₄₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#343	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	#343	D₄₃
hypocenter	C₄₃	C₄×#101
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #343

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₄₃

commutator

C₂²×C₄₃

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#343

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #343

N	H ≅ G/N	type
13. #13063243	C₄	semidirect
69. Dic₄₃	#101	semidirect
81. C₄₃	C₄×#101	semidirect

H ≅ G/N

type

13. #13063243

C₄

semidirect

69. Dic₄₃

#101

semidirect

81. C₄₃

C₄×#101

semidirect

Subgroups — #19134390

Conjugacy classes of subgroups

Complements