Group #19136152 — subgroups

Subgroups — #19136152

Order 5504.

214 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 87 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	#14582797	C₂	1	1	yes	maximal, characteristic
2	#14582661	C₂	1	2	yes	maximal
3	#14582661	C₂	1	2	yes	maximal
4	#14582654	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#384	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₄₃⋊C₄	—	2	1	no	—
10	C₄₃⋊#95	—	2	1	no	—
11	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
12	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
13	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	—	2	2	no	—
16	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂²×Dic₄₃	—	2	1	no	—
20	C₂²×Dic₄₃	—	2	1	no	—
21	C₄⋊C₄×C₄₃	—	2	4	no	—
22	C₄⋊C₄×C₄₃	—	4	2	no	—
23	C₄⋊C₄×C₄₃	—	4	2	no	—
24	C₄²×C₄₃	—	2	2	no	—
25	C₄⋊Dic₄₃	—	2	1	no	—
26	C₄⋊Dic₄₃	—	2	2	no	—
27	C₄⋊Dic₄₃	Q₈	1	2	yes	—
28	Dic₄₃⋊C₄	—	4	2	no	—
29	C₂×C₄₃⋊C₈	—	2	2	no	—
30	C₂×C₄₃⋊C₈	—	2	2	no	—
31	C₂×C₄₃⋊C₈	—	2	2	no	—
32	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	—	2	1	no	—
34	C₂×C₄×C₄₃	—	2	1	no	—
35	C₂×C₄×C₄₃	—	2	1	no	—
36	C₂×C₄×C₄₃	—	2	1	no	—
37	C₂×C₄×C₄₃	—	4	2	no	—
38	C₂×C₄×C₄₃	—	4	2	no	—
39	C₂×C₄×C₄₃	—	4	2	no	—
40	C₂×C₄×C₄₃	D₈	1	2	yes	—
41	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
42	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₄×C₄₃	#41	1	2	yes	—
44	C₂×C₄×C₄₃	#41	1	2	yes	—
45	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
46	C₂×Dic₄₃	—	2	2	no	—
47	C₂×Dic₄₃	—	4	1	no	—
48	C₂×Dic₄₃	—	4	1	no	—
49	C₂×Dic₄₃	—	4	1	no	—
50	C₂×Dic₄₃	—	4	1	no	—
51	C₂×Dic₄₃	—	4	1	no	—
52	C₄₃⋊C₈	—	4	2	no	—
53	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
54	C₂²×C₄₃	#123	1	1	yes	characteristic
55	C₂²×C₄₃	#124	1	1	yes	characteristic
56	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
57	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
58	C₂²×C₄₃	#137	1	1	yes	characteristic
59	C₂²×C₄₃	#137	1	1	yes	characteristic
60	C₄×C₄₃	—	2	2	no	—
61	C₄×C₄₃	—	2	2	no	—
62	C₄×C₄₃	—	8	2	no	—
63	C₄×C₄₃	#125	1	2	yes	—
64	C₄×C₄₃	#126	1	2	yes	—
65	Dic₄₃	—	4	2	no	—
66	Dic₄₃	—	8	1	no	—
67	#2099	—	43	1	no	maximal, Sylow
68	C₂×C₄₃	#400	1	1	yes	characteristic
69	C₂×C₄₃	#474	1	1	yes	characteristic
70	C₂×C₄₃	#475	1	1	yes	characteristic
71	C₂×C₄₃	#480	1	1	yes	characteristic
72	C₂×C₄₃	#483	1	1	yes	characteristic
73	C₂×C₄₃	#486	1	1	yes	characteristic
74	C₂×C₄₃	#491	1	1	yes	characteristic
75	#389	—	43	1	no	—
76	#384	D₄₃	1	1	yes	characteristic
77	#340	—	43	2	no	—
78	#340	—	43	2	no	—
79	#336	—	43	1	no	—
80	C₄₃	#2099	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₈	—	43	2	no	—
82	C₂×C₄⋊C₄	—	2	1	no	—
83	C₂×C₄⋊C₄	—	2	1	no	—
84	C₂×C₄⋊C₄	—	43	1	no	—
85	C₂×C₄⋊C₄	—	43	1	no	—
86	C₂×C₄⋊C₄	—	86	1	no	—
87	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
88	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
89	#95	—	86	1	no	—
90	C₂²×C₄	—	2	2	no	—
91	C₂²×C₄	—	86	1	no	—
92	C₂²×C₄	—	86	1	no	—
93	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
94	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
95	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
96	C₂×C₈	—	86	2	no	—
97	C₂×C₈	—	86	2	no	—
98	C₂×C₈	—	86	2	no	—
99	C₄⋊C₄	—	2	4	no	—
100	C₄⋊C₄	—	4	2	no	—
101	C₄⋊C₄	—	4	2	no	—
102	C₄⋊C₄	—	43	2	no	—
103	C₄⋊C₄	—	86	1	no	—
104	C₄⋊C₄	—	86	2	no	—
105	C₄⋊C₄	—	172	2	no	—
106	C₄²	—	2	2	no	—
107	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	4	2	no	—
113	C₂×C₄	—	4	2	no	—
114	C₂×C₄	—	4	2	no	—
115	C₂×C₄	—	86	2	no	—
116	C₂×C₄	—	172	1	no	—
117	C₂×C₄	—	172	1	no	—
118	C₂×C₄	—	172	1	no	—
119	C₂×C₄	—	172	1	no	—
120	C₂×C₄	—	172	1	no	—
121	C₂×C₄	#10621882	1	2	yes	—
122	C₂×C₄	#10621883	1	2	yes	—
123	C₂×C₄	#10621898	1	2	yes	—
124	C₂×C₄	#10621900	1	2	yes	—
125	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
126	C₂×C₄	#10621902	1	1	yes	characteristic
127	C₈	—	172	2	no	—
128	C₂²	#13063301	1	1	yes	characteristic
129	C₂²	#13063308	1	1	yes	characteristic
130	C₂²	#13063312	1	1	yes	characteristic
131	C₂²	C₂×#10621882	1	1	yes	characteristic
132	C₂²	C₂×#10621883	1	1	yes	characteristic
133	C₂²	#13063356	1	1	yes	characteristic
134	C₂²	#13063356	1	1	yes	characteristic
135	C₄	—	2	2	no	—
136	C₄	—	2	2	no	—
137	C₄	—	8	2	no	—
138	C₄	—	344	1	no	—
139	C₄	—	172	2	no	—
140	C₄	#13063315	1	2	yes	—
141	C₄	#13063320	1	2	yes	—
142	C₂	#14582837	1	1	yes	characteristic
143	C₂	#14583176	1	1	yes	characteristic
144	C₂	#14583181	1	1	yes	characteristic
145	C₂	#14583212	1	1	yes	characteristic
146	C₂	#14583229	1	1	yes	characteristic
147	C₂	#14583245	1	1	yes	characteristic
148	C₂	#14583267	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582797

C₂

yes

maximal, characteristic

#14582661

C₂

yes

maximal

#14582661

C₂

yes

maximal

#14582654

C₂

yes

maximal, characteristic

C₄₃×#384

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×Dic₄₃⋊C₄

—

C₄₃⋊#95

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

Q₈

yes

—

Dic₄₃⋊C₄

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

SD₁₆

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂²⋊Q₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂²×C₄₃

C₂×SD₁₆

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#125

yes

—

C₄×C₄₃

#126

yes

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

yes

—

—

—

C₄₃

#2099

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

172

—

106

C₄²

—

107

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

172

—

117

C₂×C₄

—

172

—

118

C₂×C₄

—

172

—

119

C₂×C₄

—

172

—

120

C₂×C₄

—

172

—

121

C₂×C₄

#10621882

yes

—

122

C₂×C₄

#10621883

yes

—

123

C₂×C₄

#10621898

yes

—

124

C₂×C₄

#10621900

yes

—

125

C₂×C₄

Q₈×D₄₃

yes

characteristic

126

C₂×C₄

#10621902

yes

characteristic

127

C₈

—

172

—

128

C₂²

#13063301

yes

characteristic

129

C₂²

#13063308

yes

characteristic

130

C₂²

#13063312

yes

characteristic

131

C₂²

C₂×#10621882

yes

characteristic

132

C₂²

C₂×#10621883

yes

characteristic

133

C₂²

#13063356

yes

characteristic

134

C₂²

#13063356

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

344

—

139

C₄

—

172

—

140

C₄

#13063315

yes

—

141

C₄

#13063320

yes

—

142

C₂

#14582837

yes

characteristic

143

C₂

#14583176

yes

characteristic

144

C₂

#14583181

yes

characteristic

145

C₂

#14583212

yes

characteristic

146

C₂

#14583229

yes

characteristic

147

C₂

#14583245

yes

characteristic

148

C₂

#14583267

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#384	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	#384	D₄₃
hypocenter	C₄₃	#2099
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#384

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
80. C₄₃	#2099	semidirect

H ≅ G/N

type

80. C₄₃

#2099

semidirect

Subgroups — #19136152

Conjugacy classes of subgroups

Complements