Group #19140260 — subgroups

Subgroups — #19140260

Order 5504.

444 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 141 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	#14582835	C₂	1	2	yes	maximal
2	#14582811	C₂	1	2	yes	maximal
3	#14582803	C₂	1	4	yes	maximal, complemented
4	#14582786	C₂	1	4	yes	maximal, complemented
5	C₄×C₂²⋊Dic₄₃	C₂	1	2	yes	maximal
6	C₄₃×#381	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₈₆	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
9	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
10	C₂×C₂²⋊Dic₄₃	C₂²	1	4	yes	—
11	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
12	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
13	C₄₃⋊#95	C₂²	1	2	yes	—
14	C₄₃⋊#95	C₂²	1	4	yes	—
15	C₄₃⋊#95	C₂²	1	4	yes	—
16	C₄₃⋊#95	C₂²	1	2	yes	—
17	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
20	#95×C₄₃	C₂²	1	4	yes	—
21	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	—	4	1	no	—
23	C₂²×C₄×C₄₃	—	4	1	no	—
24	C₂²×C₄×C₄₃	Q₈	1	4	yes	complemented
25	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
26	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
27	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
28	C₂²×Dic₄₃	C₂³	1	4	yes	—
29	C₂²×Dic₄₃	C₂³	1	4	yes	—
30	C₂×Dic₈₆	—	2	8	no	—
31	C₂×Dic₈₆	—	4	2	no	—
32	C₂²⋊C₄×C₄₃	—	4	1	no	—
33	C₂²⋊C₄×C₄₃	—	4	1	no	—
34	C₂²⋊Dic₄₃	—	2	8	no	—
35	C₄⋊Dic₄₃	—	4	2	no	—
36	Dic₄₃⋊C₄	—	2	8	no	—
37	C₄×Dic₄₃	—	4	2	no	—
38	C₄×Dic₄₃	—	4	2	no	—
39	C₂³×C₄₃	—	2	4	no	—
40	C₂³×C₄₃	—	2	1	no	—
41	C₂³×C₄₃	—	2	1	no	—
42	C₂³×C₄₃	C₂×Q₈	1	2	yes	—
43	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
44	C₂×C₄×C₄₃	—	2	2	no	—
45	C₂×C₄×C₄₃	—	2	2	no	—
46	C₂×C₄×C₄₃	—	2	4	no	—
47	C₂×C₄×C₄₃	—	2	4	no	—
48	C₂×C₄×C₄₃	—	2	2	no	—
49	C₂×C₄×C₄₃	—	2	2	no	—
50	C₂×C₄×C₄₃	—	4	4	no	—
51	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
52	C₂×Dic₄₃	—	2	4	no	—
53	C₂×Dic₄₃	—	2	4	no	—
54	C₂×Dic₄₃	—	2	4	no	—
55	C₂×Dic₄₃	—	2	4	no	—
56	C₂×Dic₄₃	—	2	4	no	—
57	C₂×Dic₄₃	#41	1	8	yes	—
58	Dic₈₆	—	4	8	no	—
59	C₂²×C₄₃	—	2	4	no	—
60	C₂²×C₄₃	—	2	2	no	—
61	C₂²×C₄₃	—	4	2	no	—
62	C₂²×C₄₃	—	4	2	no	—
63	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
64	C₂²×C₄₃	C₂×#41	1	4	yes	—
65	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
66	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
67	C₄×C₄₃	—	2	4	no	—
68	C₄×C₄₃	—	4	2	no	—
69	C₄×C₄₃	—	4	2	no	—
70	Dic₄₃	—	2	8	no	—
71	Dic₄₃	—	4	4	no	—
72	#2607	—	43	1	no	maximal, Sylow
73	C₂×C₄₃	—	4	2	no	—
74	C₂×C₄₃	#533	1	2	yes	—
75	C₂×C₄₃	#543	1	1	yes	characteristic
76	C₂×C₄₃	#551	1	2	yes	—
77	C₂×C₄₃	#559	1	2	yes	—
78	#399	—	43	2	no	—
79	#393	—	43	2	no	—
80	#391	—	43	4	no	—
81	#387	—	43	4	no	—
82	#381	D₄₃	1	1	yes	characteristic
83	C₄×C₂²⋊C₄	—	43	2	no	—
84	C₄₃	#2607	1	1	yes	characteristic, complemented, Sylow
85	C₂²×Q₈	—	43	2	no	—
86	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
87	C₂×C₄⋊C₄	—	43	4	no	—
88	C₂×C₄⋊C₄	—	43	2	no	—
89	C₂×C₂²⋊C₄	—	43	4	no	—
90	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
91	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
92	C₂×C₄²	—	43	2	no	—
93	C₂×C₄²	—	43	2	no	—
94	#95	—	43	4	no	—
95	#95	—	43	2	no	—
96	#95	—	43	4	no	—
97	#95	—	43	2	no	—
98	#95	C₂×D₄₃	1	4	yes	—
99	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
100	C₂×Q₈	—	86	8	no	—
101	C₂×Q₈	—	172	2	no	—
102	C₂²×C₄	—	4	1	no	—
103	C₂²×C₄	—	4	1	no	—
104	C₂²×C₄	—	43	4	no	—
105	C₂²×C₄	—	43	4	no	—
106	C₂²×C₄	Dic₈₆	1	4	yes	complemented
107	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
108	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
109	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
110	C₄⋊C₄	—	86	8	no	—
111	C₄⋊C₄	—	172	2	no	—
112	C₂²⋊C₄	—	4	1	no	—
113	C₂²⋊C₄	—	4	1	no	—
114	C₂²⋊C₄	—	86	8	no	—
115	C₄²	—	172	2	no	—
116	C₄²	—	172	2	no	—
117	C₂³	—	2	4	no	—
118	C₂³	—	2	1	no	—
119	C₂³	—	2	1	no	—
120	C₂³	C₂×Dic₈₆	1	2	yes	—
121	C₂³	C₂³×D₄₃	1	1	yes	characteristic
122	Q₈	—	172	8	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	4	no	—
126	C₂×C₄	—	2	4	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	4	4	no	—
130	C₂×C₄	—	43	8	no	—
131	C₂×C₄	—	86	4	no	—
132	C₂×C₄	—	86	4	no	—
133	C₂×C₄	—	86	4	no	—
134	C₂×C₄	—	86	4	no	—
135	C₂×C₄	—	86	4	no	—
136	C₂×C₄	C₂×Dic₈₆	1	4	yes	—
137	C₂²	—	2	4	no	—
138	C₂²	—	2	2	no	—
139	C₂²	—	4	2	no	—
140	C₂²	—	4	2	no	—
141	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
142	C₂²	#41×D₄₃	1	4	yes	—
143	C₂²	#13063370	1	1	yes	characteristic
144	C₂²	#13063370	1	1	yes	characteristic
145	C₄	—	2	4	no	—
146	C₄	—	4	2	no	—
147	C₄	—	4	2	no	—
148	C₄	—	86	8	no	—
149	C₄	—	172	4	no	—
150	C₂	—	4	2	no	—
151	C₂	#14583452	1	2	yes	—
152	C₂	#14583525	1	1	yes	characteristic
153	C₂	#14583577	1	2	yes	—
154	C₂	#14583633	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14582835

C₂

yes

maximal

#14582811

C₂

yes

maximal

#14582803

C₂

yes

maximal, complemented

#14582786

C₂

yes

maximal, complemented

C₄×C₂²⋊Dic₄₃

C₂

yes

maximal

C₄₃×#381

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

characteristic

#95×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

Q₈

yes

complemented

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂²⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×Q₈

yes

—

C₂³×C₄₃

C₂⁴

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

C₂×Q₈

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

#41

yes

—

Dic₈₆

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#2607

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#533

yes

—

C₂×C₄₃

#543

yes

characteristic

C₂×C₄₃

#551

yes

—

C₂×C₄₃

#559

yes

—

—

—

—

—

D₄₃

yes

characteristic

C₄×C₂²⋊C₄

—

C₄₃

#2607

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₂²⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

—

—

—

—

C₂×D₄₃

yes

—

C₂⁴

C₂²×D₄₃

yes

characteristic

100

C₂×Q₈

—

101

C₂×Q₈

—

172

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

Dic₈₆

yes

complemented

107

C₂²×C₄

C₂²×D₄₃

yes

—

108

C₂²×C₄

C₂²×D₄₃

yes

—

109

C₂²×C₄

C₂²×D₄₃

yes

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

172

—

112

C₂²⋊C₄

—

113

C₂²⋊C₄

—

114

C₂²⋊C₄

—

115

C₄²

—

172

—

116

C₄²

—

172

—

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

C₂×Dic₈₆

yes

—

121

C₂³

C₂³×D₄₃

yes

characteristic

122

Q₈

—

172

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

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

C₂×Dic₈₆

yes

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

C₂²×Dic₈₆

yes

characteristic

142

C₂²

#41×D₄₃

yes

—

143

C₂²

#13063370

yes

characteristic

144

C₂²

#13063370

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

172

—

150

C₂

—

151

C₂

#14583452

yes

—

152

C₂

#14583525

yes

characteristic

153

C₂

#14583577

yes

—

154

C₂

#14583633

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#381	C₂
hypercenter	#381	D₄₃
hypocenter	C₄₃	#2607
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #381

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#381

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #381

N	H ≅ G/N	type
3. #14582803	C₂	semidirect
4. #14582786	C₂	semidirect
24. C₂²×C₄×C₄₃	Q₈	semidirect
84. C₄₃	#2607	semidirect
106. C₂²×C₄	Dic₈₆	semidirect

H ≅ G/N

type

3. #14582803

C₂

semidirect

4. #14582786

C₂

semidirect

24. C₂²×C₄×C₄₃

Q₈

semidirect

84. C₄₃

#2607

semidirect

106. C₂²×C₄

Dic₈₆

semidirect

Subgroups — #19140260

Conjugacy classes of subgroups

Complements