Group #19142779 — subgroups

Subgroups — #19142779

Order 5504.

372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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	C₄₃⋊#401	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582836	C₂	1	1	yes	maximal, characteristic
3	#14582833	C₂	1	3	yes	maximal, complemented
4	#14582831	C₂	1	3	yes	maximal, complemented
5	#14582828	C₂	1	3	yes	maximal
6	#14582773	C₂	1	3	yes	maximal
7	C₄₃×#401	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
11	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
12	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
13	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
14	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
15	C₄₃⋊#95	C₂²	1	3	yes	—
16	C₄₃⋊#95	C₂²	1	3	yes	—
17	C₄₃⋊#95	C₂²	1	3	yes	—
18	#95×C₄₃	C₂²	1	3	yes	—
19	#95×C₄₃	C₂²	1	3	yes	—
20	#95×C₄₃	C₂²	1	1	yes	characteristic
21	C₂³×D₄₃	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
23	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂²×Dic₄₃	C₂³	1	3	yes	—
26	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₃	C₂³	1	3	yes	—
28	C₂×C₄×D₄₃	—	4	3	no	—
29	(C₂×D₄₃)⋊C₄	—	2	6	no	—
30	(C₂×D₄₃)⋊C₄	—	4	3	no	—
31	C₄⋊Dic₄₃	—	4	3	no	—
32	C₄⋊Dic₄₃	—	4	3	no	—
33	Dic₄₃⋊C₄	—	4	3	no	—
34	Dic₄₃⋊C₄	—	4	3	no	—
35	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
36	C₂²×D₄₃	—	2	3	no	—
37	C₂²×D₄₃	—	2	3	no	—
38	C₂²×D₄₃	#41	1	2	yes	—
39	C₂×C₄×C₄₃	—	2	3	no	—
40	C₂×C₄×C₄₃	—	2	3	no	—
41	C₂×C₄×C₄₃	—	2	3	no	—
42	C₂×C₄×C₄₃	—	2	3	no	—
43	C₂×C₄×C₄₃	—	2	3	no	—
44	C₂×C₄×C₄₃	—	2	6	no	—
45	C₂×Dic₄₃	—	2	3	no	—
46	C₂×Dic₄₃	—	2	3	no	—
47	C₂×Dic₄₃	—	2	3	no	—
48	C₂×Dic₄₃	—	2	3	no	—
49	C₂×Dic₄₃	—	2	3	no	—
50	C₂×Dic₄₃	—	2	3	no	—
51	C₂×Dic₄₃	—	2	3	no	—
52	C₄×D₄₃	—	4	4	no	—
53	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
54	C₂²×C₄₃	H(5,𝔽₂)	1	3	yes	—
55	C₂²×C₄₃	2₋¹⁺⁴	1	3	yes	—
56	C₂×D₄₃	—	2	6	no	—
57	C₂×D₄₃	—	4	1	no	—
58	C₂×D₄₃	—	4	3	no	—
59	C₄×C₄₃	—	4	3	no	—
60	C₄×C₄₃	—	4	1	no	—
61	C₄×C₄₃	—	4	3	no	—
62	Dic₄₃	—	4	3	no	—
63	Dic₄₃	—	4	1	no	—
64	Dic₄₃	—	4	3	no	—
65	#2834	—	43	1	no	maximal, Sylow
66	C₂×C₄₃	#539	1	3	yes	—
67	C₂×C₄₃	#560	1	1	yes	characteristic
68	C₂×C₄₃	#563	1	3	yes	—
69	D₄₃	—	4	2	no	—
70	#401	—	43	1	no	—
71	#401	D₄₃	1	1	yes	characteristic, complemented
72	#399	—	43	1	no	—
73	#398	—	43	3	no	—
74	#398	—	43	3	no	—
75	#397	—	43	3	no	—
76	#385	—	43	3	no	—
77	C₄₃	#2834	1	1	yes	characteristic, complemented, Sylow
78	C₂³×C₄	—	43	1	no	—
79	C₂×C₄⋊C₄	—	43	3	no	—
80	C₂×C₄⋊C₄	—	43	3	no	—
81	C₂×C₄⋊C₄	—	43	3	no	—
82	C₂×C₄⋊C₄	—	43	3	no	—
83	C₂×C₂²⋊C₄	—	43	3	no	—
84	C₂×C₂²⋊C₄	—	43	3	no	—
85	#95	—	43	3	no	—
86	#95	—	43	3	no	—
87	#95	—	43	3	no	—
88	#95	C₂×D₄₃	1	3	yes	—
89	#95	C₂×D₄₃	1	3	yes	—
90	#95	C₂×D₄₃	1	1	yes	characteristic
91	C₂⁴	—	43	1	no	—
92	C₂²×C₄	—	43	3	no	—
93	C₂²×C₄	—	43	1	no	—
94	C₂²×C₄	—	43	3	no	—
95	C₂²×C₄	—	172	3	no	—
96	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
97	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
98	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
99	C₄⋊C₄	—	172	3	no	—
100	C₄⋊C₄	—	172	3	no	—
101	C₄⋊C₄	—	172	3	no	—
102	C₄⋊C₄	—	172	3	no	—
103	C₂²⋊C₄	—	86	6	no	—
104	C₂²⋊C₄	—	172	3	no	—
105	C₂³	—	43	2	no	—
106	C₂³	—	86	3	no	—
107	C₂³	—	86	3	no	—
108	C₂³	C₂³×D₄₃	1	1	yes	characteristic
109	C₂×C₄	—	2	3	no	—
110	C₂×C₄	—	2	3	no	—
111	C₂×C₄	—	2	3	no	—
112	C₂×C₄	—	2	3	no	—
113	C₂×C₄	—	2	6	no	—
114	C₂×C₄	—	2	3	no	—
115	C₂×C₄	—	86	3	no	—
116	C₂×C₄	—	86	3	no	—
117	C₂×C₄	—	86	3	no	—
118	C₂×C₄	—	86	3	no	—
119	C₂×C₄	—	86	3	no	—
120	C₂×C₄	—	86	3	no	—
121	C₂×C₄	—	86	3	no	—
122	C₂×C₄	—	172	4	no	—
123	C₂²	—	86	6	no	—
124	C₂²	—	172	1	no	—
125	C₂²	—	172	3	no	—
126	C₂²	#41×D₄₃	1	1	yes	characteristic
127	C₂²	#13063371	1	3	yes	—
128	C₂²	#13063372	1	3	yes	—
129	C₄	—	4	1	no	—
130	C₄	—	4	3	no	—
131	C₄	—	4	3	no	—
132	C₄	—	172	1	no	—
133	C₄	—	172	3	no	—
134	C₄	—	172	3	no	—
135	C₂	—	172	2	no	—
136	C₂	#14583490	1	3	yes	—
137	C₂	#14583640	1	1	yes	characteristic
138	C₂	#14583651	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₃⋊#401

C₂

yes

maximal, characteristic, complemented

#14582836

C₂

yes

maximal, characteristic

#14582833

C₂

yes

maximal, complemented

#14582831

C₂

yes

maximal, complemented

#14582828

C₂

yes

maximal

#14582773

C₂

yes

maximal

C₄₃×#401

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

#95×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

characteristic

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×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

#41

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄×D₄₃

—

C₂²×C₄₃

C₂×#41

yes

characteristic

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2834

—

maximal, Sylow

C₂×C₄₃

#539

yes

—

C₂×C₄₃

#560

yes

characteristic

C₂×C₄₃

#563

yes

—

D₄₃

—

#401

—

#401

D₄₃

yes

characteristic, complemented

—

—

—

—

—

C₄₃

#2834

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

—

—

—

C₂×D₄₃

yes

—

#95

C₂×D₄₃

yes

—

#95

C₂×D₄₃

yes

characteristic

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

172

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

172

—

100

C₄⋊C₄

—

172

—

101

C₄⋊C₄

—

172

—

102

C₄⋊C₄

—

172

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

—

172

—

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

C₂³×D₄₃

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

172

—

123

C₂²

—

124

C₂²

—

172

—

125

C₂²

—

172

—

126

C₂²

#41×D₄₃

yes

characteristic

127

C₂²

#13063371

yes

—

128

C₂²

#13063372

yes

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

172

—

133

C₄

—

172

—

134

C₄

—

172

—

135

C₂

—

172

—

136

C₂

#14583490

yes

—

137

C₂

#14583640

yes

characteristic

138

C₂

#14583651

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#401	C₂
hypercenter	#401	D₄₃
hypocenter	C₄₃	#2834
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #401

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#401

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #401

N	H ≅ G/N	type
1. C₄₃⋊#401	C₂	semidirect
3. #14582833	C₂	semidirect
4. #14582831	C₂	semidirect
7. C₄₃×#401	C₂	semidirect
71. #401	D₄₃	semidirect
77. C₄₃	#2834	semidirect

H ≅ G/N

type

1. C₄₃⋊#401

C₂

semidirect

3. #14582833

C₂

semidirect

4. #14582831

C₂

semidirect

7. C₄₃×#401

C₂

semidirect

71. #401

D₄₃

semidirect

77. C₄₃

#2834

semidirect

Subgroups — #19142779

Conjugacy classes of subgroups

Complements