Group #19140704 — subgroups

Subgroups — #19140704

Order 5504.

612 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13063324	C₂	1	3	yes	maximal, complemented
2	C₂×#13063311	C₂	1	3	yes	maximal
3	#14582836	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582835	C₂	1	3	yes	maximal, complemented
5	#14582834	C₂	1	3	yes	maximal, complemented
6	#14582744	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#399	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₈₆	C₂²	1	3	yes	—
9	C₂²×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
10	#13063324	—	2	12	no	—
11	#13063311	—	2	12	no	—
12	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
13	C₂×Dic₄₃⋊C₄	C₂²	1	6	yes	—
14	C₂×C₂²⋊Dic₄₃	C₂²	1	3	yes	—
15	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
16	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
17	C₂×C₄×Dic₄₃	C₂²	1	3	yes	—
18	C₄₃⋊#95	C₂²	1	3	yes	—
19	C₂×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
20	C₂×C₂²⋊C₄×C₄₃	C₂²	1	3	yes	—
21	#95×C₄₃	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
23	C₂³×D₄₃	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
25	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
26	C₂×C₂²⋊D₄₃	—	2	6	no	—
27	C₂²×Dic₄₃	C₂³	1	3	yes	—
28	C₂²×Dic₄₃	C₂³	1	3	yes	—
29	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
30	C₂×Dic₈₆	—	2	6	no	—
31	C₂×Dic₈₆	—	2	12	no	—
32	C₄⋊C₄×C₄₃	—	2	6	no	—
33	C₂²⋊C₄×C₄₃	—	2	6	no	—
34	C₂²⋊Dic₄₃	—	2	6	no	—
35	(C₂×D₄₃)⋊C₄	—	2	6	no	—
36	(C₂×D₄₃)⋊C₄	—	2	6	no	—
37	C₄⋊Dic₄₃	—	2	6	no	—
38	Dic₄₃⋊C₄	—	2	12	no	—
39	C₄×Dic₄₃	D₄	1	12	yes	—
40	C₂³×C₄₃	—	2	3	no	—
41	C₂³×C₄₃	—	2	3	no	—
42	C₂³×C₄₃	—	2	1	no	—
43	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
44	C₂²×D₄₃	—	2	3	no	—
45	C₂²×D₄₃	—	2	3	no	—
46	C₂²×D₄₃	—	2	1	no	—
47	C₂×C₄×C₄₃	—	2	6	no	—
48	C₂×C₄×C₄₃	—	2	6	no	—
49	C₂×C₄×C₄₃	—	2	3	no	—
50	C₂×C₄×C₄₃	C₂×D₄	1	6	yes	—
51	C₂²⋊D₄₃	—	4	4	no	—
52	C₂×Dic₄₃	—	2	3	no	—
53	C₂×Dic₄₃	—	2	3	no	—
54	C₂×Dic₄₃	—	2	6	no	—
55	C₂×Dic₄₃	—	2	3	no	—
56	C₂×Dic₄₃	C₂×D₄	1	6	yes	—
57	C₂×Dic₄₃	C₂×D₄	1	6	yes	—
58	Dic₈₆	—	4	12	no	—
59	C₂²×C₄₃	—	4	1	no	—
60	C₂²×C₄₃	—	4	3	no	—
61	C₂²×C₄₃	—	4	3	no	—
62	C₂²×C₄₃	C₂²×D₄	1	3	yes	—
63	C₂²×C₄₃	2₋¹⁺⁴	1	3	yes	—
64	C₂²×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
65	C₂×D₄₃	—	4	1	no	—
66	C₂×D₄₃	—	4	3	no	—
67	C₂×D₄₃	—	4	3	no	—
68	C₄×C₄₃	—	2	6	no	—
69	C₄×C₄₃	—	4	3	no	—
70	Dic₄₃	—	2	6	no	—
71	Dic₄₃	—	4	3	no	—
72	Dic₄₃	#127	1	4	yes	—
73	#2658	—	43	1	no	maximal, Sylow
74	C₂×C₄₃	—	8	1	no	—
75	C₂×C₄₃	C₂×#127	1	1	yes	characteristic
76	C₂×C₄₃	#536	1	3	yes	—
77	C₂×C₄₃	#536	1	3	yes	—
78	D₄₃	—	8	1	no	—
79	C₂×C₄⋊Q₈	—	43	3	no	—
80	C₂×#124	—	43	3	no	—
81	#399	—	43	3	no	—
82	#399	—	43	3	no	—
83	#399	—	43	1	no	—
84	#399	D₄₃	1	1	yes	characteristic, complemented
85	#376	—	43	1	no	—
86	C₄₃	#2658	1	1	yes	characteristic, complemented, Sylow
87	C₂²×Q₈	—	43	3	no	—
88	C₂²×D₄	—	43	1	no	—
89	C₄⋊Q₈	—	86	12	no	—
90	#124	—	86	12	no	—
91	C₂×C₄⋊C₄	—	43	6	no	—
92	C₂×C₄⋊C₄	—	43	3	no	—
93	C₂×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
94	C₂×C₂²⋊C₄	—	43	3	no	—
95	C₂×C₂²⋊C₄	—	43	3	no	—
96	C₂×C₂²⋊C₄	—	43	3	no	—
97	C₂×C₂²⋊C₄	C₂×D₄₃	1	3	yes	—
98	C₂×C₄²	—	43	3	no	—
99	#95	—	43	3	no	—
100	#95	C₂×D₄₃	1	1	yes	characteristic
101	C₂⁴	—	43	1	no	—
102	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
103	C₂×Q₈	—	86	6	no	—
104	C₂×Q₈	—	86	12	no	—
105	C₂×D₄	—	86	6	no	—
106	C₂²×C₄	—	43	1	no	—
107	C₂²×C₄	—	43	3	no	—
108	C₂²×C₄	—	43	3	no	—
109	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
110	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
111	C₄⋊C₄	—	2	6	no	—
112	C₄⋊C₄	—	86	12	no	—
113	C₄⋊C₄	—	86	6	no	—
114	C₂²⋊C₄	—	2	6	no	—
115	C₂²⋊C₄	—	86	6	no	—
116	C₂²⋊C₄	—	86	6	no	—
117	C₂²⋊C₄	—	86	6	no	—
118	C₄²	—	43	12	no	—
119	C₂³	—	2	3	no	—
120	C₂³	—	2	3	no	—
121	C₂³	—	2	1	no	—
122	C₂³	—	86	3	no	—
123	C₂³	—	86	3	no	—
124	C₂³	—	86	1	no	—
125	C₂³	C₂³×D₄₃	1	1	yes	characteristic
126	Q₈	—	172	12	no	—
127	D₄	—	172	4	no	—
128	C₂×C₄	—	2	6	no	—
129	C₂×C₄	—	2	3	no	—
130	C₂×C₄	—	2	6	no	—
131	C₂×C₄	—	43	6	no	—
132	C₂×C₄	—	43	6	no	—
133	C₂×C₄	—	86	3	no	—
134	C₂×C₄	—	86	3	no	—
135	C₂×C₄	—	86	3	no	—
136	C₂×C₄	—	86	6	no	—
137	C₂×C₄	D₄×D₄₃	1	6	yes	—
138	C₂²	—	4	1	no	—
139	C₂²	—	4	3	no	—
140	C₂²	—	4	3	no	—
141	C₂²	—	172	1	no	—
142	C₂²	—	172	3	no	—
143	C₂²	—	172	3	no	—
144	C₂²	C₂×D₄×D₄₃	1	3	yes	—
145	C₂²	#13063372	1	3	yes	—
146	C₂²	#13063373	1	1	yes	characteristic
147	C₄	—	2	6	no	—
148	C₄	—	4	3	no	—
149	C₄	—	43	4	no	—
150	C₄	—	86	6	no	—
151	C₄	—	172	3	no	—
152	C₂	—	8	1	no	—
153	C₂	—	344	1	no	—
154	C₂	#127×D₄₃	1	1	yes	characteristic
155	C₂	#14583471	1	3	yes	—
156	C₂	#14583472	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063324

C₂

yes

maximal, complemented

C₂×#13063311

C₂

yes

maximal

#14582836

C₂

yes

maximal, characteristic, complemented

#14582835

C₂

yes

maximal, complemented

#14582834

C₂

yes

maximal, complemented

#14582744

C₂

yes

maximal, characteristic, complemented

C₄₃×#399

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₈₆

C₂²

yes

—

C₂²×C₂²⋊D₄₃

C₂²

yes

characteristic

#13063324

—

#13063311

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂³×D₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂×C₂²⋊D₄₃

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

D₄

yes

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

C₂×D₄

yes

—

Dic₈₆

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²×D₄

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

#127

yes

—

#2658

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×#127

yes

characteristic

C₂×C₄₃

#536

yes

—

C₂×C₄₃

#536

yes

—

D₄₃

—

C₂×C₄⋊Q₈

—

—

—

—

—

D₄₃

yes

characteristic, complemented

#376

—

C₄₃

#2658

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×D₄

—

C₄⋊Q₈

—

#124

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

#95

—

100

#95

C₂×D₄₃

yes

characteristic

101

C₂⁴

—

102

C₂⁴

C₂²×D₄₃

yes

characteristic

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×D₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

C₂²×D₄₃

yes

—

110

C₂²×C₄

C₂²×D₄₃

yes

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₂²⋊C₄

—

115

C₂²⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₂³

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

—

124

C₂³

—

125

C₂³

C₂³×D₄₃

yes

characteristic

126

Q₈

—

172

—

127

D₄

—

172

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

D₄×D₄₃

yes

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

172

—

142

C₂²

—

172

—

143

C₂²

—

172

—

144

C₂²

C₂×D₄×D₄₃

yes

—

145

C₂²

#13063372

yes

—

146

C₂²

#13063373

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

172

—

152

C₂

—

153

C₂

—

344

—

154

C₂

#127×D₄₃

yes

characteristic

155

C₂

#14583471

yes

—

156

C₂

#14583472

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#399	C₂
hypercenter	#399	D₄₃
hypocenter	C₄₃	#2658
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #399

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#399

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #399

N	H ≅ G/N	type
1. C₂×#13063324	C₂	semidirect
3. #14582836	C₂	semidirect
4. #14582835	C₂	semidirect
5. #14582834	C₂	semidirect
6. #14582744	C₂	semidirect
7. C₄₃×#399	C₂	semidirect
84. #399	D₄₃	semidirect
86. C₄₃	#2658	semidirect

H ≅ G/N

type

1. C₂×#13063324

C₂

semidirect

3. #14582836

C₂

semidirect

4. #14582835

C₂

semidirect

5. #14582834

C₂

semidirect

6. #14582744

C₂

semidirect

7. C₄₃×#399

C₂

semidirect

84. #399

D₄₃

semidirect

86. C₄₃

#2658

semidirect

Subgroups — #19140704

Conjugacy classes of subgroups

Complements