Group #19145976 — subgroups

Subgroups — #19145976

Order 5504.

430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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	#14583449	C₂	1	2	yes	maximal, complemented
2	#14583190	C₂	1	4	yes	maximal, complemented
3	#14583152	C₂	1	4	yes	maximal, complemented
4	#14583095	C₂	1	4	yes	maximal, complemented
5	C₄₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10621898	—	2	2	no	—
7	C₂×D₃₄₄	C₂²	1	4	yes	—
8	#13063325	C₂²	1	2	yes	—
9	#13063322	C₂²	1	2	yes	—
10	#13063313	—	2	2	no	—
11	#13063299	—	2	2	no	—
12	#13063299	C₂²	1	4	yes	—
13	C₄×D₁₇₂	—	2	2	no	—
14	C₄×D₁₇₂	C₂²	1	4	yes	—
15	#13063257	C₂²	1	4	yes	—
16	#13063247	C₂²	1	8	yes	—
17	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₄⋊C₈×C₄₃	C₂²	1	4	yes	—
20	C₂²×C₄×C₄₃	D₄	1	2	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂×C₂²⋊D₄₃	—	2	4	no	—
23	#10621898	—	4	8	no	—
24	C₂×D₁₇₂	—	2	2	no	—
25	C₂×D₁₇₂	—	2	2	no	—
26	C₂×D₁₇₂	C₂³	1	4	yes	—
27	C₂×C₄×D₄₃	—	2	4	no	—
28	C₂×Dic₈₆	—	2	2	no	—
29	M₁₆×C₄₃	—	4	2	no	—
30	C₂×C₈×C₄₃	C₂³	1	4	yes	—
31	C₄²×C₄₃	D₄	1	1	yes	characteristic
32	C₄²×C₄₃	D₄	1	1	yes	characteristic
33	C₄²×C₄₃	C₂³	1	2	yes	—
34	(C₂×D₄₃)⋊C₄	—	2	4	no	—
35	(C₂×D₄₃)⋊C₄	—	2	4	no	—
36	C₄⋊Dic₄₃	—	2	2	no	—
37	C₄⋊Dic₄₃	C₂³	1	4	yes	—
38	D₃₄₄	—	4	4	no	—
39	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₂²×D₄₃	—	2	4	no	—
41	C₂×C₄×C₄₃	—	2	4	no	—
42	C₂×C₄×C₄₃	—	2	1	no	—
43	C₂×C₄×C₄₃	—	2	1	no	—
44	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
48	C₂²⋊D₄₃	—	4	8	no	—
49	C₂×Dic₄₃	—	2	4	no	—
50	D₁₇₂	—	2	4	no	—
51	D₁₇₂	—	2	4	no	—
52	D₁₇₂	—	4	4	no	—
53	D₁₇₂	—	4	4	no	—
54	C₄×D₄₃	—	4	8	no	—
55	Dic₈₆	—	4	4	no	—
56	C₈×C₄₃	—	2	4	no	—
57	C₂²×C₄₃	—	2	1	no	—
58	C₂²×C₄₃	—	2	2	no	—
59	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
60	C₂×D₄₃	—	4	4	no	—
61	C₂×D₄₃	—	4	4	no	—
62	C₂×D₄₃	—	4	4	no	—
63	C₄×C₄₃	—	2	1	no	—
64	C₄×C₄₃	—	2	2	no	—
65	C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
66	C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
67	C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
68	Dic₄₃	—	4	4	no	—
69	#3253	—	43	1	no	maximal, Sylow
70	C₂×C₄₃	—	4	1	no	—
71	C₂×C₄₃	#537	1	1	yes	characteristic
72	C₂×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
73	D₄₃	—	8	4	no	—
74	#532	—	43	2	no	—
75	#476	—	43	4	no	—
76	#469	—	43	4	no	—
77	#459	—	43	4	no	—
78	#423	D₄₃	1	1	yes	characteristic, complemented
79	C₄₃	#3253	1	1	yes	characteristic, complemented, Sylow
80	C₂×#41	—	86	2	no	—
81	C₂×D₈	—	43	4	no	—
82	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
83	C₄⋊Q₈	—	43	2	no	—
84	#127	—	43	2	no	—
85	#124	—	86	2	no	—
86	#121	—	43	4	no	—
87	#121	—	86	2	no	—
88	C₄×D₄	—	43	4	no	—
89	C₄×D₄	—	86	2	no	—
90	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
91	#106	—	43	4	no	—
92	C₄⋊C₈	C₂×D₄₃	1	4	yes	—
93	#102	—	43	8	no	—
94	#41	—	172	8	no	—
95	C₂×Q₈	—	86	2	no	—
96	C₂×D₄	—	43	4	no	—
97	C₂×D₄	—	86	4	no	—
98	C₂×D₄	—	86	2	no	—
99	C₂×D₄	—	86	2	no	—
100	C₂²×C₄	—	86	4	no	—
101	C₂²×C₄	D₁₇₂	1	2	yes	—
102	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
103	D₈	—	172	4	no	—
104	M₁₆	—	4	2	no	—
105	C₂×C₈	C₂²×D₄₃	1	4	yes	—
106	C₄⋊C₄	—	43	4	no	—
107	C₄⋊C₄	—	86	2	no	—
108	C₂²⋊C₄	—	86	4	no	—
109	C₂²⋊C₄	—	86	4	no	—
110	C₄²	D₁₇₂	1	1	yes	characteristic
111	C₄²	D₁₇₂	1	1	yes	characteristic
112	C₄²	C₂²×D₄₃	1	2	yes	—
113	C₂³	—	86	4	no	—
114	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
115	Q₈	—	172	4	no	—
116	D₄	—	86	4	no	—
117	D₄	—	86	4	no	—
118	D₄	—	172	4	no	—
119	D₄	—	172	8	no	—
120	D₄	—	172	4	no	—
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	86	4	no	—
125	C₂×C₄	—	172	8	no	—
126	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
127	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
128	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
129	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
130	C₈	—	2	4	no	—
131	C₂²	—	2	2	no	—
132	C₂²	—	2	1	no	—
133	C₂²	—	172	4	no	—
134	C₂²	—	172	4	no	—
135	C₂²	—	172	4	no	—
136	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
137	C₄	—	2	2	no	—
138	C₄	—	2	1	no	—
139	C₄	—	172	4	no	—
140	C₄	#13063353	1	4	yes	—
141	C₄	#13063370	1	1	yes	characteristic
142	C₄	#13063373	1	1	yes	characteristic
143	C₂	—	4	1	no	—
144	C₂	—	344	4	no	—
145	C₂	#14583480	1	1	yes	characteristic
146	C₂	C₂×#13063353	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583449

C₂

yes

maximal, complemented

#14583190

C₂

yes

maximal, complemented

#14583152

C₂

yes

maximal, complemented

#14583095

C₂

yes

maximal, complemented

C₄₃×#423

C₂

yes

maximal, characteristic, complemented

C₂×#10621898

—

C₂×D₃₄₄

C₂²

yes

—

#13063325

C₂²

yes

—

#13063322

C₂²

yes

—

#13063313

—

#13063299

—

#13063299

C₂²

yes

—

C₄×D₁₇₂

—

C₄×D₁₇₂

C₂²

yes

—

#13063257

C₂²

yes

—

#13063247

C₂²

yes

—

C₂×M₁₆×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₂²⋊D₄₃

—

#10621898

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

C₂³

yes

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

—

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

D₃₄₄

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₄×C₄₃

H(5,𝔽₂)

yes

characteristic

C₄×C₄₃

2₋¹⁺⁴

yes

characteristic

Dic₄₃

—

#3253

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#537

yes

characteristic

C₂×C₄₃

C₂×AGL(1,ℤ/8)

yes

—

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#3253

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂×D₈

—

C₂×M₁₆

C₂×D₄₃

yes

—

C₄⋊Q₈

—

—

—

—

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#106

—

C₄⋊C₈

C₂×D₄₃

yes

—

#102

—

#41

—

172

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

100

C₂²×C₄

—

101

C₂²×C₄

D₁₇₂

yes

—

102

C₂²×C₄

C₂²×D₄₃

yes

characteristic

103

D₈

—

172

—

104

M₁₆

—

105

C₂×C₈

C₂²×D₄₃

yes

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

110

C₄²

D₁₇₂

yes

characteristic

111

C₄²

D₁₇₂

yes

characteristic

112

C₄²

C₂²×D₄₃

yes

—

113

C₂³

—

114

C₂³

C₂×D₁₇₂

yes

characteristic

115

Q₈

—

172

—

116

D₄

—

117

D₄

—

118

D₄

—

172

—

119

D₄

—

172

—

120

D₄

—

172

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

172

—

126

C₂×C₄

C₂×D₁₇₂

yes

—

127

C₂×C₄

C₂×D₁₇₂

yes

characteristic

128

C₂×C₄

C₂×D₁₇₂

yes

—

129

C₂×C₄

C₂³×D₄₃

yes

characteristic

130

C₈

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

172

—

134

C₂²

—

172

—

135

C₂²

—

172

—

136

C₂²

C₂²×D₁₇₂

yes

characteristic

137

C₄

—

138

C₄

—

139

C₄

—

172

—

140

C₄

#13063353

yes

—

141

C₄

#13063370

yes

characteristic

142

C₄

#13063373

yes

characteristic

143

C₂

—

144

C₂

—

344

—

145

C₂

#14583480

yes

characteristic

146

C₂

C₂×#13063353

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#423	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#423	D₄₃
hypocenter	C₄₃	#3253
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂²

C₂²×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#423

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
1. #14583449	C₂	semidirect
2. #14583190	C₂	semidirect
3. #14583152	C₂	semidirect
4. #14583095	C₂	semidirect
5. C₄₃×#423	C₂	semidirect
78. #423	D₄₃	semidirect
79. C₄₃	#3253	semidirect

H ≅ G/N

type

1. #14583449

C₂

semidirect

2. #14583190

C₂

semidirect

3. #14583152

C₂

semidirect

4. #14583095

C₂

semidirect

5. C₄₃×#423

C₂

semidirect

78. #423

D₄₃

semidirect

79. C₄₃

#3253

semidirect

Subgroups — #19145976

Conjugacy classes of subgroups

Complements