Group #19137001 — subgroups

Subgroups — #19137001

Order 5504.

656 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 245 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×#13063283	C₂	1	2	yes	maximal
2	C₂×C₄²×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582768	C₂	1	2	yes	maximal, complemented
4	#14582765	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582758	C₂	1	4	yes	maximal
6	#14582750	C₂	1	4	yes	maximal, complemented
7	C₄₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄₃	C₂²	1	2	yes	—
9	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
10	#13063283	—	2	8	no	—
11	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
12	C₂×Dic₄₃⋊C₄	C₂²	1	8	yes	—
13	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
14	C₂×C₄×Dic₄₃	C₂²	1	4	yes	—
15	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
16	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
17	C₄²×D₄₃	C₄	1	8	yes	complemented
18	C₄₃⋊#95	C₂²	1	4	yes	—
19	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
20	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	#95×C₄₃	C₂²	1	4	yes	—
22	C₂³×D₄₃	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
25	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₃	C₂³	1	4	yes	—
27	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
28	C₂²×Dic₄₃	C₂³	1	2	yes	—
29	C₂×C₄×D₄₃	—	2	8	no	—
30	C₂×C₄×D₄₃	C₂×C₄	1	8	yes	—
31	C₂×C₄×D₄₃	C₂×C₄	1	4	yes	—
32	C₂×C₄×D₄₃	D₄	1	4	yes	—
33	C₂×C₄×D₄₃	Q₈	1	4	yes	—
34	C₄⋊C₄×C₄₃	—	2	4	no	—
35	C₄²×C₄₃	C₂×C₄	1	4	yes	—
36	(C₂×D₄₃)⋊C₄	—	2	8	no	—
37	C₄⋊Dic₄₃	—	2	4	no	—
38	Dic₄₃⋊C₄	—	2	16	no	—
39	C₄×Dic₄₃	—	2	8	no	—
40	C₄×Dic₄₃	C₂×C₄	1	8	yes	—
41	C₄×Dic₄₃	C₂×C₄	1	4	yes	—
42	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
43	C₂²×D₄₃	—	2	4	no	—
44	C₂²×D₄₃	C₂²×C₄	1	2	yes	—
45	C₂²×D₄₃	C₂×D₄	1	2	yes	—
46	C₂²×D₄₃	C₂×Q₈	1	2	yes	—
47	C₂×C₄×C₄₃	—	2	4	no	—
48	C₂×C₄×C₄₃	—	2	4	no	—
49	C₂×C₄×C₄₃	—	2	8	no	—
50	C₂×C₄×C₄₃	C₂²×C₄	1	4	yes	—
51	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
52	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
53	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
54	C₂×Dic₄₃	—	2	4	no	—
55	C₂×Dic₄₃	—	2	8	no	—
56	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
57	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
58	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
59	C₂×Dic₄₃	C₂×Q₈	1	2	yes	—
60	C₂×Dic₄₃	#41	1	8	yes	—
61	C₄×D₄₃	—	2	16	no	—
62	C₄×D₄₃	C₄⋊C₄	1	16	yes	complemented
63	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
64	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
65	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
66	C₂²×C₄₃	C₂×#41	1	4	yes	—
67	C₂×D₄₃	—	2	4	no	—
68	C₂×D₄₃	—	2	4	no	—
69	C₂×D₄₃	—	2	4	no	—
70	C₂×D₄₃	C₂×C₄⋊C₄	1	4	yes	—
71	C₄×C₄₃	—	2	4	no	—
72	C₄×C₄₃	—	4	4	no	—
73	C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
74	Dic₄₃	—	4	4	no	—
75	Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
76	Dic₄₃	#117	1	8	yes	complemented
77	#2285	—	43	1	no	maximal, Sylow
78	C₂×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄₃	C₂×#117	1	2	yes	—
80	C₂×C₄₃	#532	1	2	yes	—
81	C₂×C₄₃	#533	1	2	yes	—
82	D₄₃	—	2	4	no	—
83	C₂×#117	—	43	2	no	—
84	C₂²×C₄²	—	43	1	no	—
85	#384	—	43	2	no	—
86	#382	—	43	1	no	—
87	#382	D₄₃	1	1	yes	characteristic, complemented
88	#380	—	43	4	no	—
89	C₄×C₄⋊C₄	—	43	4	no	—
90	C₄₃	#2285	1	1	yes	characteristic, complemented, Sylow
91	C₂³×C₄	—	43	1	no	—
92	C₂³×C₄	—	43	2	no	—
93	#117	—	86	8	no	—
94	C₂×C₄⋊C₄	—	43	2	no	—
95	C₂×C₄⋊C₄	—	43	8	no	—
96	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
97	C₂×C₂²⋊C₄	—	43	4	no	—
98	C₂×C₄²	—	43	2	no	—
99	C₂×C₄²	—	43	1	no	—
100	C₂×C₄²	—	43	8	no	—
101	C₂×C₄²	—	43	4	no	—
102	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
103	#95	—	43	4	no	—
104	#95	C₂×D₄₃	1	4	yes	—
105	C₂⁴	—	43	1	no	—
106	C₂²×C₄	—	43	1	no	—
107	C₂²×C₄	—	43	2	no	—
108	C₂²×C₄	—	43	4	no	—
109	C₂²×C₄	—	43	4	no	—
110	C₂²×C₄	—	43	4	no	—
111	C₂²×C₄	—	43	8	no	—
112	C₂²×C₄	—	43	4	no	—
113	C₂²×C₄	—	86	8	no	—
114	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
115	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
116	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
117	C₄⋊C₄	—	2	4	no	—
118	C₄⋊C₄	—	86	16	no	—
119	C₄⋊C₄	—	86	4	no	—
120	C₂²⋊C₄	—	86	8	no	—
121	C₄²	—	43	8	no	—
122	C₄²	—	43	4	no	—
123	C₄²	—	86	8	no	—
124	C₄²	C₄×D₄₃	1	4	yes	—
125	C₂³	—	43	2	no	—
126	C₂³	—	43	2	no	—
127	C₂³	—	43	2	no	—
128	C₂³	—	86	4	no	—
129	C₂³	C₂³×D₄₃	1	1	yes	characteristic
130	C₂×C₄	—	2	4	no	—
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	—	2	8	no	—
133	C₂×C₄	—	43	2	no	—
134	C₂×C₄	—	43	4	no	—
135	C₂×C₄	—	43	2	no	—
136	C₂×C₄	—	43	2	no	—
137	C₂×C₄	—	43	8	no	—
138	C₂×C₄	—	43	16	no	—
139	C₂×C₄	—	86	16	no	—
140	C₂×C₄	—	86	4	no	—
141	C₂×C₄	—	86	8	no	—
142	C₂×C₄	C₂×C₄×D₄₃	1	4	yes	—
143	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
144	C₂×C₄	D₄×D₄₃	1	2	yes	—
145	C₂×C₄	Q₈×D₄₃	1	2	yes	—
146	C₂²	—	43	4	no	—
147	C₂²	—	86	4	no	—
148	C₂²	—	86	4	no	—
149	C₂²	—	86	4	no	—
150	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
151	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
152	C₂²	C₂×Q₈×D₄₃	1	1	yes	characteristic
153	C₂²	#41×D₄₃	1	4	yes	—
154	C₄	—	2	4	no	—
155	C₄	—	4	4	no	—
156	C₄	—	43	4	no	—
157	C₄	—	43	8	no	—
158	C₄	—	172	4	no	—
159	C₄	C₄⋊C₄×D₄₃	1	4	yes	—
160	C₂	—	86	4	no	—
161	C₂	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
162	C₂	#117×D₄₃	1	2	yes	—
163	C₂	#14583448	1	2	yes	—
164	C₂	#14583455	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063283

C₂

yes

maximal

C₂×C₄²×D₄₃

C₂

yes

maximal, characteristic

#14582768

C₂

yes

maximal, complemented

#14582765

C₂

yes

maximal, characteristic, complemented

#14582758

C₂

yes

maximal

#14582750

C₂

yes

maximal, complemented

C₄₃×#382

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₃

C₂²

yes

—

C₂²×C₄×D₄₃

C₂²

yes

characteristic

#13063283

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₄²×D₄₃

C₄

yes

complemented

C₄₃⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

C₂²

yes

—

C₂³×D₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

D₄

yes

—

C₂×C₄×D₄₃

Q₈

yes

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

C₂²×C₄

yes

—

C₂²×D₄₃

C₂×D₄

yes

—

C₂²×D₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

C₂×Q₈

yes

—

C₂×Dic₄₃

#41

yes

—

C₄×D₄₃

—

C₄×D₄₃

C₄⋊C₄

yes

complemented

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

C₂×C₄⋊C₄

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄⋊C₄

yes

—

Dic₄₃

—

Dic₄₃

C₂×C₄⋊C₄

yes

—

Dic₄₃

yes

—

C₂×C₄₃

C₂²×C₄⋊C₄

yes

characteristic

C₂×C₄₃

C₂×#117

yes

—

C₂×C₄₃

#532

yes

—

C₂×C₄₃

#533

yes

—

D₄₃

—

C₂×#117

—

C₂²×C₄²

—

#384

—

#382

—

#382

D₄₃

yes

characteristic, complemented

#380

—

C₄×C₄⋊C₄

—

C₄₃

#2285

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

100

C₂×C₄²

—

101

C₂×C₄²

—

102

C₂×C₄²

C₂×D₄₃

yes

characteristic

103

#95

—

104

#95

C₂×D₄₃

yes

—

105

C₂⁴

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

C₂²×D₄₃

yes

—

115

C₂²×C₄

C₂²×D₄₃

yes

—

116

C₂²×C₄

C₂²×D₄₃

yes

characteristic

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₂²⋊C₄

—

121

C₄²

—

122

C₄²

—

123

C₄²

—

124

C₄²

C₄×D₄₃

yes

—

125

C₂³

—

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

C₂³×D₄₃

yes

characteristic

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

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

C₂×C₄×D₄₃

yes

—

143

C₂×C₄

C₂×C₄×D₄₃

yes

—

144

C₂×C₄

D₄×D₄₃

yes

—

145

C₂×C₄

Q₈×D₄₃

yes

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

C₂²×C₄×D₄₃

yes

characteristic

151

C₂²

C₂×D₄×D₄₃

yes

characteristic

152

C₂²

C₂×Q₈×D₄₃

yes

characteristic

153

C₂²

#41×D₄₃

yes

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

—

172

—

159

C₄

C₄⋊C₄×D₄₃

yes

—

160

C₂

—

161

C₂

C₂×C₄⋊C₄×D₄₃

yes

characteristic

162

C₂

#117×D₄₃

yes

—

163

C₂

#14583448

yes

—

164

C₂

#14583455

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Fitting	C₄₃×#382	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	#382	D₄₃
hypocenter	C₄₃	#2285
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator

C₂²×C₄₃

C₂³×C₄

Fitting

C₄₃×#382

C₂

socle

C₂³×C₄₃

C₂⁴

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
3. #14582768	C₂	semidirect
4. #14582765	C₂	semidirect
6. #14582750	C₂	semidirect
7. C₄₃×#382	C₂	semidirect
17. C₄²×D₄₃	C₄	semidirect
62. C₄×D₄₃	C₄⋊C₄	semidirect
76. Dic₄₃	#117	semidirect
87. #382	D₄₃	semidirect
90. C₄₃	#2285	semidirect

H ≅ G/N

type

3. #14582768

C₂

semidirect

4. #14582765

C₂

semidirect

6. #14582750

C₂

semidirect

7. C₄₃×#382

C₂

semidirect

17. C₄²×D₄₃

C₄

semidirect

62. C₄×D₄₃

C₄⋊C₄

semidirect

76. Dic₄₃

#117

semidirect

87. #382

D₄₃

semidirect

90. C₄₃

#2285

semidirect

Subgroups — #19137001

Conjugacy classes of subgroups

Complements