Group #19141627 — subgroups

Subgroups — #19141627

Order 5504.

456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13063323	C₂	1	2	yes	maximal
2	#14582829	C₂	1	2	yes	maximal
3	#14582820	C₂	1	4	yes	maximal
4	#14582797	C₂	1	2	yes	maximal
5	#14582784	C₂	1	4	yes	maximal
6	C₄₃×#391	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₈₆	C₂²	1	2	yes	—
8	#13063323	—	2	8	no	—
9	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
12	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
13	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
14	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
15	C₄₃⋊#95	C₂²	1	2	yes	—
16	C₄₃⋊#95	C₂²	1	4	yes	—
17	C₄₃⋊#95	C₂²	1	4	yes	—
18	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	#95×C₄₃	C₂²	1	4	yes	—
22	C₂×Q₈×C₄₃	—	4	1	no	—
23	C₂×Q₈×C₄₃	—	4	1	no	—
24	C₂×Q₈×C₄₃	D₄	1	4	yes	—
25	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
26	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
27	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
29	C₂²×Dic₄₃	C₂³	1	4	yes	—
30	C₂²×Dic₄₃	C₂³	1	4	yes	—
31	C₂×Dic₈₆	—	2	4	no	—
32	C₂×Dic₈₆	—	4	2	no	—
33	C₂×Dic₈₆	—	4	2	no	—
34	C₄⋊C₄×C₄₃	—	4	1	no	—
35	C₄²×C₄₃	—	4	1	no	—
36	C₄⋊Dic₄₃	—	4	2	no	—
37	C₄⋊Dic₄₃	—	4	2	no	—
38	C₄⋊Dic₄₃	Q₈	1	8	yes	complemented
39	Dic₄₃⋊C₄	—	2	8	no	—
40	Dic₄₃⋊C₄	—	2	8	no	—
41	C₄×Dic₄₃	—	2	4	no	—
42	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
43	Q₈×C₄₃	—	4	4	no	—
44	C₂×C₄×C₄₃	—	2	2	no	—
45	C₂×C₄×C₄₃	—	2	1	no	—
46	C₂×C₄×C₄₃	—	2	1	no	—
47	C₂×C₄×C₄₃	—	2	2	no	—
48	C₂×C₄×C₄₃	—	2	2	no	—
49	C₂×C₄×C₄₃	—	2	2	no	—
50	C₂×C₄×C₄₃	—	2	2	no	—
51	C₂×C₄×C₄₃	—	2	4	no	—
52	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
53	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
55	C₂×Dic₄₃	—	2	4	no	—
56	C₂×Dic₄₃	—	2	4	no	—
57	C₂×Dic₄₃	—	2	4	no	—
58	C₂×Dic₄₃	—	2	4	no	—
59	C₂×Dic₄₃	—	2	4	no	—
60	C₂×Dic₄₃	C₂×Q₈	1	8	yes	—
61	Dic₈₆	—	4	8	no	—
62	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
63	C₂²×C₄₃	C₂²×Q₈	1	2	yes	—
64	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
65	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
66	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
67	C₄×C₄₃	—	2	4	no	—
68	C₄×C₄₃	—	2	2	no	—
69	C₄×C₄₃	—	2	4	no	—
70	C₄×C₄₃	—	4	2	no	—
71	Dic₄₃	—	2	8	no	—
72	Dic₄₃	—	4	4	no	—
73	#2734	—	43	1	no	maximal, Sylow
74	C₂×C₄₃	#534	1	1	yes	characteristic
75	C₂×C₄₃	#544	1	2	yes	—
76	C₂×C₄₃	D₄×Q₈	1	2	yes	—
77	C₂×C₄₃	Q₈²	1	1	yes	characteristic
78	C₂×C₄₃	#563	1	1	yes	characteristic
79	C₂×C₄⋊Q₈	—	43	2	no	—
80	#398	—	43	2	no	—
81	#395	—	43	4	no	—
82	#391	D₄₃	1	1	yes	characteristic
83	#389	—	43	2	no	—
84	#387	—	43	4	no	—
85	C₄₃	#2734	1	1	yes	characteristic, complemented, Sylow
86	C₂²×Q₈	—	43	2	no	—
87	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
88	C₄⋊Q₈	—	86	8	no	—
89	C₂×C₄⋊C₄	—	43	2	no	—
90	C₂×C₄⋊C₄	—	43	4	no	—
91	C₂×C₄⋊C₄	—	43	4	no	—
92	C₂×C₄⋊C₄	—	43	2	no	—
93	C₂×C₄⋊C₄	—	43	2	no	—
94	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
95	C₂×C₄²	—	43	2	no	—
96	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
97	#95	—	43	2	no	—
98	#95	—	43	4	no	—
99	#95	—	43	4	no	—
100	#95	C₂×D₄₃	1	4	yes	—
101	C₂×Q₈	—	4	1	no	—
102	C₂×Q₈	—	4	1	no	—
103	C₂×Q₈	—	86	4	no	—
104	C₂×Q₈	—	172	2	no	—
105	C₂×Q₈	—	172	2	no	—
106	C₂×Q₈	D₁₇₂	1	4	yes	—
107	C₂²×C₄	—	43	4	no	—
108	C₂²×C₄	—	43	4	no	—
109	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
110	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
111	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
112	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
113	C₄⋊C₄	—	4	1	no	—
114	C₄⋊C₄	—	43	8	no	—
115	C₄⋊C₄	—	86	8	no	—
116	C₄⋊C₄	—	86	8	no	—
117	C₄⋊C₄	—	172	2	no	—
118	C₄⋊C₄	—	172	2	no	—
119	C₄²	—	4	1	no	—
120	C₄²	—	86	4	no	—
121	C₂³	C₂³×D₄₃	1	1	yes	characteristic
122	Q₈	—	4	4	no	—
123	Q₈	—	172	8	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	—	43	8	no	—
133	C₂×C₄	—	86	4	no	—
134	C₂×C₄	—	86	4	no	—
135	C₂×C₄	—	86	4	no	—
136	C₂×C₄	—	86	4	no	—
137	C₂×C₄	—	86	4	no	—
138	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
139	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
140	C₂×C₄	Q₈×D₄₃	1	4	yes	—
141	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
142	C₂²	C₂×Q₈×D₄₃	1	2	yes	—
143	C₂²	#13063370	1	1	yes	characteristic
144	C₂²	#13063370	1	1	yes	characteristic
145	C₂²	#13063372	1	2	yes	—
146	C₄	—	2	4	no	—
147	C₄	—	2	2	no	—
148	C₄	—	2	4	no	—
149	C₄	—	4	2	no	—
150	C₄	—	86	8	no	—
151	C₄	—	172	4	no	—
152	C₂	#14583461	1	1	yes	characteristic
153	C₂	#14583528	1	2	yes	—
154	C₂	Q₈×D₁₇₂	1	2	yes	—
155	C₂	#14583629	1	1	yes	characteristic
156	C₂	#14583649	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063323

C₂

yes

maximal

#14582829

C₂

yes

maximal

#14582820

C₂

yes

maximal

#14582797

C₂

yes

maximal

#14582784

C₂

yes

maximal

C₄₃×#391

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

—

#13063323

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

C₂²

yes

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

Q₈

yes

complemented

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

Q₈×C₄₃

—

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×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×Q₈

yes

—

Dic₈₆

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

D₄×Q₈

yes

—

C₂×C₄₃

Q₈²

yes

characteristic

C₂×C₄₃

#563

yes

characteristic

C₂×C₄⋊Q₈

—

#398

—

#395

—

#391

D₄₃

yes

characteristic

#389

—

#387

—

C₄₃

#2734

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

100

#95

C₂×D₄₃

yes

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

172

—

105

C₂×Q₈

—

172

—

106

C₂×Q₈

D₁₇₂

yes

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

C₂²×D₄₃

yes

—

110

C₂²×C₄

C₂²×D₄₃

yes

—

111

C₂²×C₄

C₂²×D₄₃

yes

characteristic

112

C₂²×C₄

C₂²×D₄₃

yes

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

172

—

118

C₄⋊C₄

—

172

—

119

C₄²

—

120

C₄²

—

121

C₂³

C₂³×D₄₃

yes

characteristic

122

Q₈

—

123

Q₈

—

172

—

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

—

137

C₂×C₄

—

138

C₂×C₄

C₂×D₁₇₂

yes

—

139

C₂×C₄

C₂×D₁₇₂

yes

—

140

C₂×C₄

Q₈×D₄₃

yes

—

141

C₂²

C₂²×D₁₇₂

yes

characteristic

142

C₂²

C₂×Q₈×D₄₃

yes

—

143

C₂²

#13063370

yes

characteristic

144

C₂²

#13063370

yes

characteristic

145

C₂²

#13063372

yes

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

172

—

152

C₂

#14583461

yes

characteristic

153

C₂

#14583528

yes

—

154

C₂

Q₈×D₁₇₂

yes

—

155

C₂

#14583629

yes

characteristic

156

C₂

#14583649

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#391	C₂
hypercenter	#391	D₄₃
hypocenter	C₄₃	#2734
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #391

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#391

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #391

N	H ≅ G/N	type
38. C₄⋊Dic₄₃	Q₈	semidirect
85. C₄₃	#2734	semidirect

H ≅ G/N

type

38. C₄⋊Dic₄₃

Q₈

semidirect

85. C₄₃

#2734

semidirect

Subgroups — #19141627

Conjugacy classes of subgroups

Complements