Group #19140570 — subgroups

Subgroups — #19140570

Order 5504.

360 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 149 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	#14582841	C₂	1	4	yes	maximal
2	#14582833	C₂	1	4	yes	maximal
3	#14582797	C₂	1	2	yes	maximal
4	#14582797	C₂	1	2	yes	maximal
5	#14582769	C₂	1	1	yes	maximal, characteristic
6	#14582765	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#376	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
11	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
12	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
13	C₄₃⋊#95	C₂²	1	4	yes	—
14	C₄₃⋊#95	C₂²	1	4	yes	—
15	C₄₃⋊#95	C₂²	1	4	yes	—
16	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	#95×C₄₃	C₂²	1	2	yes	—
20	#95×C₄₃	C₂²	1	2	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
23	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
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	4	yes	—
28	C₄²×C₄₃	—	2	2	no	—
29	C₄²×C₄₃	—	2	2	no	—
30	C₄²×C₄₃	Q₈	1	4	yes	—
31	C₄⋊Dic₄₃	—	2	4	no	—
32	C₄⋊Dic₄₃	—	2	4	no	—
33	C₄⋊Dic₄₃	—	4	4	no	—
34	Dic₄₃⋊C₄	—	4	4	no	—
35	Dic₄₃⋊C₄	—	4	4	no	—
36	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
37	C₂×C₄×C₄₃	—	2	2	no	—
38	C₂×C₄×C₄₃	—	2	2	no	—
39	C₂×C₄×C₄₃	—	2	1	no	—
40	C₂×C₄×C₄₃	—	2	1	no	—
41	C₂×C₄×C₄₃	—	2	2	no	—
42	C₂×C₄×C₄₃	—	2	2	no	—
43	C₂×C₄×C₄₃	—	2	2	no	—
44	C₂×C₄×C₄₃	—	2	2	no	—
45	C₂×C₄×C₄₃	—	2	2	no	—
46	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
47	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
48	C₂×C₄×C₄₃	#41	1	2	yes	—
49	C₂×C₄×C₄₃	#41	1	2	yes	—
50	C₂×Dic₄₃	—	2	4	no	—
51	C₂×Dic₄₃	—	2	4	no	—
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	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
57	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
58	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
59	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
60	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
61	C₄×C₄₃	—	2	4	no	—
62	C₄×C₄₃	—	4	1	no	—
63	C₄×C₄₃	—	4	1	no	—
64	C₄×C₄₃	—	4	2	no	—
65	C₄×C₄₃	#125	1	4	yes	—
66	Dic₄₃	—	4	4	no	—
67	Dic₄₃	—	4	4	no	—
68	#2647	—	43	1	no	maximal, Sylow
69	C₂×C₄₃	C₂×#125	1	1	yes	characteristic
70	C₂×C₄₃	#540	1	1	yes	characteristic
71	C₂×C₄₃	#541	1	1	yes	characteristic
72	C₂×C₄₃	#542	1	2	yes	—
73	C₂×C₄₃	#544	1	2	yes	—
74	#400	—	43	4	no	—
75	#398	—	43	4	no	—
76	#389	—	43	2	no	—
77	#389	—	43	2	no	—
78	#384	—	43	1	no	—
79	#382	—	43	1	no	—
80	#376	D₄₃	1	1	yes	characteristic
81	C₄₃	#2647	1	1	yes	characteristic, complemented, Sylow
82	C₂×C₄⋊C₄	—	43	2	no	—
83	C₂×C₄⋊C₄	—	43	2	no	—
84	C₂×C₄⋊C₄	—	43	4	no	—
85	C₂×C₄⋊C₄	—	43	4	no	—
86	C₂×C₄⋊C₄	—	43	4	no	—
87	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
88	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
89	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
90	#95	—	43	4	no	—
91	#95	—	43	4	no	—
92	#95	—	43	4	no	—
93	#95	C₂×D₄₃	1	2	yes	—
94	#95	C₂×D₄₃	1	2	yes	—
95	C₂²×C₄	—	43	4	no	—
96	C₂²×C₄	—	43	4	no	—
97	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
99	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
100	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
101	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
102	C₄⋊C₄	—	86	4	no	—
103	C₄⋊C₄	—	86	4	no	—
104	C₄⋊C₄	—	172	4	no	—
105	C₄⋊C₄	—	172	4	no	—
106	C₄⋊C₄	—	172	4	no	—
107	C₄²	—	2	2	no	—
108	C₄²	—	2	2	no	—
109	C₄²	Dic₈₆	1	4	yes	—
110	C₂³	C₂³×D₄₃	1	1	yes	characteristic
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	86	4	no	—
121	C₂×C₄	—	86	4	no	—
122	C₂×C₄	—	86	4	no	—
123	C₂×C₄	—	86	4	no	—
124	C₂×C₄	—	86	4	no	—
125	C₂×C₄	—	86	4	no	—
126	C₂×C₄	C₂×Dic₈₆	1	4	yes	—
127	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
128	C₂×C₄	#10621898	1	2	yes	—
129	C₂×C₄	#10621898	1	2	yes	—
130	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
131	C₂²	C₂×#10621898	1	1	yes	characteristic
132	C₂²	C₂×#10621898	1	1	yes	characteristic
133	C₂²	#13063371	1	2	yes	—
134	C₂²	#13063372	1	2	yes	—
135	C₄	—	2	4	no	—
136	C₄	—	4	1	no	—
137	C₄	—	4	1	no	—
138	C₄	—	4	2	no	—
139	C₄	—	172	4	no	—
140	C₄	—	172	4	no	—
141	C₄	#13063317	1	4	yes	—
142	C₂	C₂×#13063317	1	1	yes	characteristic
143	C₂	#14583504	1	1	yes	characteristic
144	C₂	#14583511	1	1	yes	characteristic
145	C₂	#14583520	1	2	yes	—
146	C₂	#14583527	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14582841

C₂

yes

maximal

#14582833

C₂

yes

maximal

#14582797

C₂

yes

maximal

#14582797

C₂

yes

maximal

#14582769

C₂

yes

maximal, characteristic

#14582765

C₂

yes

maximal, characteristic

C₄₃×#376

C₂

yes

maximal, characteristic

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

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

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×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

characteristic

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#125

yes

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#544

yes

—

—

—

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#2647

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

—

—

—

C₂×D₄₃

yes

—

#95

C₂×D₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

100

C₂²×C₄

C₂²×D₄₃

yes

—

101

C₂²×C₄

C₂²×D₄₃

yes

characteristic

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

172

—

105

C₄⋊C₄

—

172

—

106

C₄⋊C₄

—

172

—

107

C₄²

—

108

C₄²

—

109

C₄²

Dic₈₆

yes

—

110

C₂³

C₂³×D₄₃

yes

characteristic

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

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

C₂×Dic₈₆

yes

—

127

C₂×C₄

C₂×Dic₈₆

yes

—

128

C₂×C₄

#10621898

yes

—

129

C₂×C₄

#10621898

yes

—

130

C₂²

C₂²×Dic₈₆

yes

characteristic

131

C₂²

C₂×#10621898

yes

characteristic

132

C₂²

C₂×#10621898

yes

characteristic

133

C₂²

#13063371

yes

—

134

C₂²

#13063372

yes

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

172

—

140

C₄

—

172

—

141

C₄

#13063317

yes

—

142

C₂

C₂×#13063317

yes

characteristic

143

C₂

#14583504

yes

characteristic

144

C₂

#14583511

yes

characteristic

145

C₂

#14583520

yes

—

146

C₂

#14583527

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#376	C₂
hypercenter	#376	D₄₃
hypocenter	C₄₃	#2647
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#376

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
81. C₄₃	#2647	semidirect

H ≅ G/N

type

81. C₄₃

#2647

semidirect

Subgroups — #19140570

Conjugacy classes of subgroups

Complements