Group #19136122 — subgroups

Subgroups — #19136122

Order 5504.

290 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 95 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×#13063259	C₂	1	2	yes	maximal, complemented
2	C₂×#13063247	C₂	1	2	yes	maximal
3	#14582801	C₂	1	1	yes	maximal, characteristic
4	#14582769	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₄₃	—	2	2	no	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
10	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
11	#13063259	—	2	4	no	—
12	#13063247	—	2	4	no	—
13	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄₃	—	2	1	no	—
16	C₂²×C₄×C₄₃	D₄	1	2	yes	—
17	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₃	—	2	1	no	—
19	C₂²×Dic₄₃	—	2	2	no	—
20	C₂×D₁₇₂	—	2	1	no	—
21	C₂×D₁₇₂	—	2	2	no	—
22	C₂×D₁₇₂	—	2	2	no	—
23	C₂×D₁₇₂	Q₈	1	2	yes	—
24	C₂×C₈×C₄₃	—	2	2	no	—
25	C₂×C₈×C₄₃	—	2	2	no	—
26	C₂×C₈×C₄₃	D₄	1	4	yes	—
27	C₄²×C₄₃	—	2	2	no	—
28	(C₂×D₄₃)⋊C₄	—	4	4	no	—
29	C₄⋊Dic₄₃	—	2	2	no	—
30	C₄⋊Dic₄₃	—	2	2	no	—
31	C₄⋊Dic₄₃	—	2	2	no	—
32	C₄⋊Dic₄₃	—	4	4	no	—
33	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
34	C₂²×D₄₃	—	2	2	no	—
35	C₂²×D₄₃	—	4	1	no	—
36	C₂²×D₄₃	—	4	1	no	—
37	C₂²×D₄₃	—	4	2	no	—
38	C₂²×D₄₃	—	4	2	no	—
39	C₂×C₄×C₄₃	—	2	2	no	—
40	C₂×C₄×C₄₃	—	2	2	no	—
41	C₂×C₄×C₄₃	D₈	1	4	yes	—
42	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
44	C₂×C₄×C₄₃	#41	1	2	yes	—
45	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
46	C₂×Dic₄₃	—	4	2	no	—
47	C₂×Dic₄₃	—	4	1	no	—
48	C₂×Dic₄₃	—	4	4	no	—
49	C₂×Dic₄₃	—	4	2	no	—
50	D₁₇₂	—	2	4	no	—
51	D₁₇₂	—	4	2	no	—
52	C₈×C₄₃	—	2	4	no	—
53	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
54	C₂²×C₄₃	#123	1	1	yes	characteristic
55	C₂²×C₄₃	#127	1	1	yes	characteristic
56	C₂²×C₄₃	C₂×D₈	1	2	yes	—
57	C₂²×C₄₃	#137	1	2	yes	—
58	C₂×D₄₃	—	4	2	no	—
59	C₂×D₄₃	—	4	4	no	—
60	C₂×D₄₃	—	8	2	no	—
61	C₂×D₄₃	—	8	1	no	—
62	C₂×D₄₃	—	8	1	no	—
63	C₄×C₄₃	—	2	4	no	—
64	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
65	C₄×C₄₃	#123	1	2	yes	—
66	Dic₄₃	—	8	2	no	—
67	Dic₄₃	—	8	1	no	—
68	#2093	—	43	1	no	maximal, Sylow
69	C₂×C₄₃	#399	1	1	yes	characteristic
70	C₂×C₄₃	#474	1	2	yes	—
71	C₂×C₄₃	#480	1	2	yes	—
72	C₂×C₄₃	#493	1	1	yes	characteristic
73	C₂×C₄₃	#497	1	1	yes	characteristic
74	D₄₃	—	8	2	no	—
75	C₂×#107	—	43	2	no	—
76	C₂×#102	—	43	2	no	—
77	#390	—	43	1	no	—
78	#384	—	43	1	no	—
79	#336	D₄₃	1	1	yes	characteristic, complemented
80	C₄₃	#2093	1	1	yes	characteristic, complemented, Sylow
81	C₂²×D₄	—	43	1	no	—
82	C₂²×C₈	C₂×D₄₃	1	2	yes	—
83	C₂×C₄⋊C₄	—	43	2	no	—
84	C₂×C₄⋊C₄	—	43	1	no	—
85	C₂×C₄⋊C₄	—	86	2	no	—
86	C₂×C₂²⋊C₄	—	86	2	no	—
87	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
88	#107	—	86	4	no	—
89	#102	—	86	4	no	—
90	C₂⁴	—	86	1	no	—
91	C₂×D₄	—	43	2	no	—
92	C₂×D₄	—	86	2	no	—
93	C₂×D₄	—	86	2	no	—
94	C₂×D₄	—	86	1	no	—
95	C₂²×C₄	—	86	1	no	—
96	C₂²×C₄	—	86	2	no	—
97	C₂²×C₄	D₁₇₂	1	2	yes	—
98	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	D₁₇₂	1	4	yes	—
102	C₄⋊C₄	—	86	2	no	—
103	C₄⋊C₄	—	86	2	no	—
104	C₄⋊C₄	—	86	2	no	—
105	C₄⋊C₄	—	172	4	no	—
106	C₂²⋊C₄	—	172	4	no	—
107	C₄²	—	2	2	no	—
108	C₂³	—	86	2	no	—
109	C₂³	—	172	1	no	—
110	C₂³	—	172	1	no	—
111	C₂³	—	172	2	no	—
112	C₂³	—	172	2	no	—
113	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
114	D₄	—	86	4	no	—
115	D₄	—	172	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	172	2	no	—
119	C₂×C₄	—	172	1	no	—
120	C₂×C₄	—	172	2	no	—
121	C₂×C₄	—	172	4	no	—
122	C₂×C₄	D₃₄₄	1	4	yes	—
123	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
124	C₂×C₄	#10621900	1	2	yes	—
125	C₂×C₄	#10621900	1	1	yes	characteristic
126	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
127	C₈	—	2	4	no	—
128	C₂²	—	344	2	no	—
129	C₂²	—	344	1	no	—
130	C₂²	—	344	1	no	—
131	C₂²	—	172	2	no	—
132	C₂²	—	172	4	no	—
133	C₂²	#13063305	1	1	yes	characteristic
134	C₂²	#13063309	1	1	yes	characteristic
135	C₂²	#13063322	1	1	yes	characteristic
136	C₂²	C₂×D₃₄₄	1	2	yes	—
137	C₂²	#13063358	1	2	yes	—
138	C₄	—	2	4	no	—
139	C₄	—	344	1	no	—
140	C₄	—	344	2	no	—
141	C₄	#13063305	1	2	yes	—
142	C₄	#13063309	1	2	yes	—
143	C₂	—	344	2	no	—
144	C₂	#14582836	1	1	yes	characteristic
145	C₂	#14583180	1	2	yes	—
146	C₂	#14583213	1	2	yes	—
147	C₂	#14583276	1	1	yes	characteristic
148	C₂	#14583293	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063259

C₂

yes

maximal, complemented

C₂×#13063247

C₂

yes

maximal

#14582801

C₂

yes

maximal, characteristic

#14582769

C₂

yes

maximal, characteristic, complemented

C₄₃×#336

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₇₂

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

—

#13063259

—

#13063247

—

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂³×D₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

Q₈

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

—

C₄²×C₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₂²×C₄₃

C₂²⋊Q₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×D₈

yes

—

C₂²×C₄₃

#137

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

—

C₄×C₄₃

#123

yes

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#480

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2093

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×C₈

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#107

—

#102

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

D₁₇₂

yes

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

172

—

106

C₂²⋊C₄

—

172

—

107

C₄²

—

108

C₂³

—

109

C₂³

—

172

—

110

C₂³

—

172

—

111

C₂³

—

172

—

112

C₂³

—

172

—

113

C₂³

C₂×D₁₇₂

yes

characteristic

114

D₄

—

115

D₄

—

172

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

172

—

119

C₂×C₄

—

172

—

120

C₂×C₄

—

172

—

121

C₂×C₄

—

172

—

122

C₂×C₄

D₃₄₄

yes

—

123

C₂×C₄

C₂×D₁₇₂

yes

—

124

C₂×C₄

#10621900

yes

—

125

C₂×C₄

#10621900

yes

characteristic

126

C₂×C₄

Q₈×D₄₃

yes

characteristic

127

C₈

—

128

C₂²

—

344

—

129

C₂²

—

344

—

130

C₂²

—

344

—

131

C₂²

—

172

—

132

C₂²

—

172

—

133

C₂²

#13063305

yes

characteristic

134

C₂²

#13063309

yes

characteristic

135

C₂²

#13063322

yes

characteristic

136

C₂²

C₂×D₃₄₄

yes

—

137

C₂²

#13063358

yes

—

138

C₄

—

139

C₄

—

344

—

140

C₄

—

344

—

141

C₄

#13063305

yes

—

142

C₄

#13063309

yes

—

143

C₂

—

344

—

144

C₂

#14582836

yes

characteristic

145

C₂

#14583180

yes

—

146

C₂

#14583213

yes

—

147

C₂

#14583276

yes

characteristic

148

C₂

#14583293

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₇₂
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#336	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	#336	D₄₃
hypocenter	C₄₃	#2093
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₁₇₂

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#336

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
1. C₂×#13063259	C₂	semidirect
4. #14582769	C₂	semidirect
5. C₄₃×#336	C₂	semidirect
79. #336	D₄₃	semidirect
80. C₄₃	#2093	semidirect

H ≅ G/N

type

1. C₂×#13063259

C₂

semidirect

4. #14582769

C₂

semidirect

5. C₄₃×#336

C₂

semidirect

79. #336

D₄₃

semidirect

80. C₄₃

#2093

semidirect

Subgroups — #19136122

Conjugacy classes of subgroups

Complements