Group #19136288 — subgroups

Subgroups — #19136288

Order 5504.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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	#14583474	C₂	1	1	yes	maximal, characteristic
2	#14582882	C₂	1	2	yes	maximal
3	#14582698	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582697	C₂	1	2	yes	maximal, complemented
5	C₄₃×#356	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621902	C₂²	1	1	yes	characteristic
7	C₂×Q₈×D₄₃	C₄	1	1	yes	characteristic
8	M₁₆×D₄₃	—	2	2	no	—
9	#13063323	C₂²	1	1	yes	characteristic
10	#13063314	C₄	1	1	yes	characteristic
11	#13063313	C₄	1	1	yes	characteristic
12	#13063310	—	2	2	no	—
13	#13063303	—	2	2	no	—
14	#13063282	C₄	1	1	yes	characteristic
15	#13063244	C₂²	1	2	yes	—
16	#13063241	—	2	2	no	—
17	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	#101×C₄₃	C₂²	1	2	yes	—
19	C₂×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
21	#10621902	—	4	2	no	—
22	Q₈×D₄₃	—	4	2	no	—
23	C₂×D₁₇₂	C₂×C₄	1	1	yes	characteristic
24	C₂×D₁₇₂	D₄	1	2	yes	—
25	C₂×C₄×D₄₃	—	2	1	no	—
26	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×D₄₃	D₄	1	2	yes	—
28	C₂×Dic₈₆	—	2	1	no	—
29	C₂×Dic₈₆	C₂×C₄	1	1	yes	characteristic
30	M₁₆×C₄₃	—	2	2	no	—
31	C₄⋊C₄×C₄₃	—	2	2	no	—
32	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
33	(C₂×D₄₃)⋊C₄	—	2	1	no	—
34	(C₂×D₄₃)⋊C₄	—	2	2	no	—
35	(C₂×D₄₃)⋊C₄	—	2	2	no	—
36	Dic₄₃⋊C₄	—	2	2	no	—
37	Dic₄₃⋊C₄	—	2	1	no	—
38	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
39	#10621877	—	2	2	no	—
40	#10621872	—	4	2	no	—
41	C₈×D₄₃	—	4	2	no	—
42	C₂²×D₄₃	C₂²⋊C₄	1	2	yes	—
43	C₂²×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
44	Q₈×C₄₃	—	4	1	no	—
45	Q₈×C₄₃	—	4	1	no	—
46	C₂×C₄×C₄₃	—	2	1	no	—
47	C₂×C₄×C₄₃	—	2	1	no	—
48	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
50	C₂×Dic₄₃	—	2	1	no	—
51	C₂×Dic₄₃	—	2	1	no	—
52	C₂×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
53	D₁₇₂	—	4	1	no	—
54	D₁₇₂	—	4	2	no	—
55	C₄×D₄₃	—	2	2	no	—
56	C₄×D₄₃	—	2	2	no	—
57	C₄×D₄₃	—	2	2	no	—
58	C₄×D₄₃	—	4	2	no	—
59	Dic₈₆	—	4	2	no	—
60	Dic₈₆	—	4	1	no	—
61	C₈×C₄₃	—	4	2	no	—
62	C₄₃⋊C₈	—	4	2	no	—
63	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₂×D₄₃	—	2	1	no	—
65	C₂×D₄₃	—	2	2	no	—
66	C₂×D₄₃	—	4	2	no	—
67	C₂×D₄₃	—	4	1	no	—
68	C₄×C₄₃	—	2	2	no	—
69	C₄×C₄₃	—	2	1	no	—
70	C₄×C₄₃	—	4	1	no	—
71	C₄×C₄₃	—	4	1	no	—
72	Dic₄₃	—	4	1	no	—
73	Dic₄₃	—	4	1	no	—
74	Dic₄₃	#99	1	2	yes	—
75	#2135	—	43	1	no	maximal, Sylow
76	C₂×C₄₃	—	2	1	no	—
77	C₂×C₄₃	C₂×#99	1	1	yes	characteristic
78	D₄₃	—	4	1	no	—
79	D₄₃	—	4	2	no	—
80	#536	—	43	1	no	—
81	#413	—	43	2	no	—
82	#356	—	43	1	no	—
83	#356	—	43	2	no	—
84	#356	D₄₃	1	1	yes	characteristic, complemented
85	C₄₃	#2135	1	1	yes	characteristic, complemented, Sylow
86	C₂×#41	—	43	1	no	—
87	C₂²×Q₈	—	43	1	no	—
88	C₂×M₁₆	—	86	2	no	—
89	C₄⋊Q₈	—	43	1	no	—
90	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
91	#124	—	43	1	no	—
92	#124	—	43	1	no	—
93	#123	—	86	2	no	—
94	C₂²⋊Q₈	—	86	2	no	—
95	#117	—	43	1	no	—
96	#101	—	43	2	no	—
97	#101	C₂×D₄₃	1	2	yes	—
98	#100	—	86	2	no	—
99	#41	—	172	2	no	—
100	C₂×Q₈	—	43	1	no	—
101	C₂×Q₈	—	86	1	no	—
102	C₂×Q₈	—	172	2	no	—
103	C₂×Q₈	C₄×D₄₃	1	1	yes	characteristic
104	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
105	C₂×D₄	—	43	1	no	—
106	C₂×D₄	—	43	2	no	—
107	C₂²×C₄	—	43	1	no	—
108	C₂²×C₄	—	43	2	no	—
109	C₂²×C₄	—	86	1	no	—
110	M₁₆	—	2	2	no	—
111	M₁₆	—	86	2	no	—
112	M₁₆	—	172	2	no	—
113	C₂×C₈	—	172	2	no	—
114	C₄⋊C₄	—	2	2	no	—
115	C₄⋊C₄	—	86	1	no	—
116	C₄⋊C₄	—	86	2	no	—
117	C₂²⋊C₄	—	86	1	no	—
118	C₂²⋊C₄	—	86	2	no	—
119	C₂²⋊C₄	—	86	2	no	—
120	C₄²	—	43	1	no	—
121	C₄²	C₄×D₄₃	1	1	yes	characteristic
122	C₂³	—	43	2	no	—
123	C₂³	—	43	1	no	—
124	Q₈	—	4	1	no	—
125	Q₈	—	4	1	no	—
126	Q₈	—	172	1	no	—
127	Q₈	—	172	2	no	—
128	D₄	—	172	2	no	—
129	D₄	—	172	1	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	43	1	no	—
133	C₂×C₄	—	86	2	no	—
134	C₂×C₄	—	86	2	no	—
135	C₂×C₄	—	86	2	no	—
136	C₂×C₄	—	86	1	no	—
137	C₂×C₄	—	86	1	no	—
138	C₂×C₄	—	172	2	no	—
139	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
140	C₂×C₄	D₄×D₄₃	1	2	yes	—
141	C₈	—	4	2	no	—
142	C₈	—	172	2	no	—
143	C₂²	—	86	1	no	—
144	C₂²	—	86	2	no	—
145	C₂²	—	172	2	no	—
146	C₂²	—	172	1	no	—
147	C₂²	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
148	C₄	—	2	2	no	—
149	C₄	—	2	1	no	—
150	C₄	—	4	1	no	—
151	C₄	—	4	1	no	—
152	C₄	—	43	2	no	—
153	C₄	—	172	1	no	—
154	C₄	—	172	1	no	—
155	C₂	—	2	1	no	—
156	C₂	—	172	1	no	—
157	C₂	—	172	2	no	—
158	C₂	#99×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583474

C₂

yes

maximal, characteristic

#14582882

C₂

yes

maximal

#14582698

C₂

yes

maximal, characteristic, complemented

#14582697

C₂

yes

maximal, complemented

C₄₃×#356

C₂

yes

maximal, characteristic, complemented

C₂×#10621902

C₂²

yes

characteristic

C₂×Q₈×D₄₃

C₄

yes

characteristic

M₁₆×D₄₃

—

#13063323

C₂²

yes

characteristic

#13063314

C₄

yes

characteristic

#13063313

C₄

yes

—

—

C₄

yes

characteristic

#13063244

C₂²

yes

—

#13063241

—

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

#101×C₄₃

C₂²

yes

—

C₂×Q₈×C₄₃

C₂×C₄

yes

characteristic

C₂×Q₈×C₄₃

C₂³

yes

characteristic

#10621902

—

Q₈×D₄₃

—

C₂×D₁₇₂

C₂×C₄

yes

characteristic

C₂×D₁₇₂

D₄

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₂×C₄

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂×C₄

yes

characteristic

M₁₆×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

C₂×C₄

yes

characteristic

#10621877

—

#10621872

—

C₈×D₄₃

—

C₂²×D₄₃

C₂²⋊C₄

yes

—

C₂²×D₄₃

C₂²⋊C₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²⋊C₄

yes

characteristic

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

#99

yes

—

#2135

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#99

yes

characteristic

D₄₃

—

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2135

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂²×Q₈

—

C₂×M₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

—

—

—

C₂²⋊Q₈

—

#117

—

#101

—

#101

C₂×D₄₃

yes

—

#100

—

#41

—

172

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

172

—

103

C₂×Q₈

C₄×D₄₃

yes

characteristic

104

C₂×Q₈

C₂²×D₄₃

yes

characteristic

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

M₁₆

—

111

M₁₆

—

112

M₁₆

—

172

—

113

C₂×C₈

—

172

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₂²⋊C₄

—

118

C₂²⋊C₄

—

119

C₂²⋊C₄

—

120

C₄²

—

121

C₄²

C₄×D₄₃

yes

characteristic

122

C₂³

—

123

C₂³

—

124

Q₈

—

125

Q₈

—

126

Q₈

—

172

—

127

Q₈

—

172

—

128

D₄

—

172

—

129

D₄

—

172

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

172

—

139

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

140

C₂×C₄

D₄×D₄₃

yes

—

141

C₈

—

142

C₈

—

172

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

172

—

146

C₂²

—

172

—

147

C₂²

C₂²⋊C₄×D₄₃

yes

characteristic

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

172

—

154

C₄

—

172

—

155

C₂

—

156

C₂

—

172

—

157

C₂

—

172

—

158

C₂

#99×D₄₃

yes

characteristic

	subgroup	G/H
center	C₂	#99×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂×Q₈	C₂²×D₄₃
Fitting	C₄₃×#356	C₂
socle	C₂×C₄₃	C₂×#99
hypercenter	#356	D₄₃
hypocenter	C₄₃	#2135
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #356

subgroup

G/H

center

C₂

#99×D₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂×Q₈

C₂²×D₄₃

Fitting

C₄₃×#356

C₂

socle

C₂×C₄₃

C₂×#99

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #356

N	H ≅ G/N	type
3. #14582698	C₂	semidirect
4. #14582697	C₂	semidirect
5. C₄₃×#356	C₂	semidirect
84. #356	D₄₃	semidirect
85. C₄₃	#2135	semidirect

H ≅ G/N

type

3. #14582698

C₂

semidirect

4. #14582697

C₂

semidirect

5. C₄₃×#356

C₂

semidirect

84. #356

D₄₃

semidirect

85. C₄₃

#2135

semidirect

Subgroups — #19136288

Conjugacy classes of subgroups

Complements