Group #19135338 — subgroups

Subgroups — #19135338

Order 5504.

240 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 109 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×#13063259	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063257	C₂	1	1	yes	maximal, characteristic
3	#14582797	C₂	1	2	yes	maximal
4	#14582662	C₂	1	2	yes	maximal
5	C₂×#97×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
8	C₂×Dic₄₃⋊C₄	—	2	2	no	—
9	#13063259	—	2	2	no	—
10	#13063257	C₄	1	4	yes	complemented
11	C₄₃⋊#95	—	2	2	no	—
12	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	#97×C₄₃	—	2	2	no	—
16	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂²×Dic₄₃	—	2	2	no	—
20	C₂²×Dic₄₃	—	2	2	no	—
21	C₂×C₈×C₄₃	—	2	1	no	—
22	C₂×C₈×C₄₃	—	2	1	no	—
23	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₄₃	D₄	1	2	yes	—
25	C₂×C₈×C₄₃	Q₈	1	2	yes	—
26	C₂×C₈×C₄₃	Q₈	1	2	yes	—
27	C₄²×C₄₃	—	2	1	no	—
28	C₄²×C₄₃	—	2	1	no	—
29	C₄⋊Dic₄₃	—	2	2	no	—
30	C₄⋊Dic₄₃	—	2	2	no	—
31	C₄⋊Dic₄₃	—	2	2	no	—
32	C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
33	Dic₄₃⋊C₄	—	4	4	no	—
34	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	—	2	1	no	—
36	C₂×C₄×C₄₃	—	2	1	no	—
37	C₂×C₄×C₄₃	—	2	2	no	—
38	C₂×C₄×C₄₃	—	2	2	no	—
39	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
44	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
45	C₂×Dic₄₃	—	2	4	no	—
46	C₂×Dic₄₃	—	4	2	no	—
47	C₂×Dic₄₃	—	4	2	no	—
48	C₂×Dic₄₃	—	4	2	no	—
49	C₂×Dic₄₃	—	4	2	no	—
50	C₂×Dic₄₃	—	4	2	no	—
51	C₈×C₄₃	—	2	2	no	—
52	C₈×C₄₃	C₄⋊C₄	1	4	yes	complemented
53	C₂²×C₄₃	C₄×D₄	1	1	yes	characteristic
54	C₂²×C₄₃	#121	1	1	yes	characteristic
55	C₂²×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
56	C₂²×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
57	C₂²×C₄₃	#137	1	2	yes	—
58	C₄×C₄₃	—	4	1	no	—
59	C₄×C₄₃	—	4	1	no	—
60	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
62	C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
63	C₄×C₄₃	#125	1	1	yes	characteristic
64	Dic₄₃	—	4	4	no	—
65	Dic₄₃	—	8	2	no	—
66	#1944	—	43	1	no	maximal, Sylow
67	C₂×C₄₃	#389	1	1	yes	characteristic
68	C₂×C₄₃	#440	1	2	yes	—
69	C₂×C₄₃	#469	1	1	yes	characteristic
70	C₂×C₄₃	#470	1	1	yes	characteristic
71	C₂×C₄₃	#501	1	2	yes	—
72	C₂×#107	—	43	1	no	—
73	C₂×#106	—	43	1	no	—
74	C₂×#97	D₄₃	1	1	yes	characteristic
75	#389	—	43	2	no	—
76	#340	—	43	2	no	—
77	C₄₃	#1944	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
79	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
80	C₂×C₄⋊C₄	—	43	2	no	—
81	C₂×C₄⋊C₄	—	43	2	no	—
82	C₂×C₄⋊C₄	—	86	2	no	—
83	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
84	#107	—	86	2	no	—
85	#106	—	43	4	no	—
86	#97	—	2	2	no	—
87	#95	—	86	2	no	—
88	C₂²×C₄	—	86	2	no	—
89	C₂²×C₄	—	86	2	no	—
90	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
91	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
92	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
93	C₂×C₈	—	2	1	no	—
94	C₂×C₈	—	2	1	no	—
95	C₂×C₈	Dic₈₆	1	2	yes	—
96	C₂×C₈	Dic₈₆	1	2	yes	—
97	C₂×C₈	C₄×D₄₃	1	2	yes	—
98	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
99	C₄⋊C₄	—	43	4	no	—
100	C₄⋊C₄	—	86	2	no	—
101	C₄⋊C₄	—	86	2	no	—
102	C₄⋊C₄	—	86	2	no	—
103	C₄⋊C₄	—	172	4	no	—
104	C₄²	—	2	1	no	—
105	C₄²	—	2	1	no	—
106	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
107	C₂×C₄	—	2	1	no	—
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	86	4	no	—
112	C₂×C₄	—	172	2	no	—
113	C₂×C₄	—	172	2	no	—
114	C₂×C₄	—	172	2	no	—
115	C₂×C₄	—	172	2	no	—
116	C₂×C₄	—	172	2	no	—
117	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
118	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
119	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
120	C₂×C₄	#10621898	1	1	yes	characteristic
121	C₂×C₄	#10621898	1	1	yes	characteristic
122	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	Dic₄₃⋊C₄	1	4	yes	complemented
125	C₂²	C₄×D₁₇₂	1	1	yes	characteristic
126	C₂²	#13063299	1	1	yes	characteristic
127	C₂²	#13063325	1	1	yes	characteristic
128	C₂²	#13063353	1	2	yes	—
129	C₂²	#13063358	1	2	yes	—
130	C₄	—	4	1	no	—
131	C₄	—	4	1	no	—
132	C₄	—	344	2	no	—
133	C₄	—	172	4	no	—
134	C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
135	C₄	C₄×Dic₈₆	1	1	yes	characteristic
136	C₄	#13063304	1	1	yes	characteristic
137	C₄	#13063317	1	1	yes	characteristic
138	C₂	#14582797	1	1	yes	characteristic
139	C₂	#14583001	1	2	yes	—
140	C₂	#14583152	1	1	yes	characteristic
141	C₂	#14583157	1	1	yes	characteristic
142	C₂	#14583308	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063259

C₂

yes

maximal, characteristic

C₂×#13063257

C₂

yes

maximal, characteristic

#14582797

C₂

yes

maximal

#14582662

C₂

yes

maximal

C₂×#97×C₄₃

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

—

#13063259

—

#13063257

C₄

yes

complemented

C₄₃⋊#95

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#97×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

Q₈

yes

—

C₂×C₈×C₄₃

Q₈

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

C₄⋊C₄

yes

complemented

C₂²×C₄₃

C₄×D₄

yes

characteristic

C₂²×C₄₃

#121

yes

characteristic

C₂²×C₄₃

C₄⋊Q₈

yes

characteristic

C₂²×C₄₃

AGL(1,ℤ/8)

yes

—

C₂²×C₄₃

#137

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

C₄×Q₈

yes

characteristic

C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄×C₄₃

#125

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×#107

—

C₂×#106

—

C₂×#97

D₄₃

yes

characteristic

#389

—

#340

—

C₄₃

#1944

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

—

—

—

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₈₆

yes

—

C₂×C₈

Dic₈₆

yes

—

C₂×C₈

C₄×D₄₃

yes

—

C₂×C₈

C₂²⋊D₄₃

yes

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

172

—

104

C₄²

—

105

C₄²

—

106

C₂³

C₂×D₁₇₂

yes

characteristic

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

172

—

113

C₂×C₄

—

172

—

114

C₂×C₄

—

172

—

115

C₂×C₄

—

172

—

116

C₂×C₄

—

172

—

117

C₂×C₄

C₂×Dic₈₆

yes

characteristic

118

C₂×C₄

C₂×Dic₈₆

yes

characteristic

119

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

120

C₂×C₄

#10621898

yes

characteristic

121

C₂×C₄

#10621898

yes

characteristic

122

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

123

C₈

—

124

C₈

Dic₄₃⋊C₄

yes

complemented

125

C₂²

C₄×D₁₇₂

yes

characteristic

126

C₂²

#13063299

yes

characteristic

127

C₂²

#13063325

yes

characteristic

128

C₂²

#13063353

yes

—

129

C₂²

#13063358

yes

—

130

C₄

—

131

C₄

—

132

C₄

—

344

—

133

C₄

—

172

—

134

C₄

C₂×Dic₄₃⋊C₄

yes

characteristic

135

C₄

C₄×Dic₈₆

yes

characteristic

136

C₄

#13063304

yes

characteristic

137

C₄

#13063317

yes

characteristic

138

C₂

#14582797

yes

characteristic

139

C₂

#14583001

yes

—

140

C₂

#14583152

yes

characteristic

141

C₂

#14583157

yes

characteristic

142

C₂

#14583308

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#97×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#97	D₄₃
hypocenter	C₄₃	#1944
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#97×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

hypercenter

C₂×#97

D₄₃

hypocenter

C₄₃

#1944

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
10. #13063257	C₄	semidirect
52. C₈×C₄₃	C₄⋊C₄	semidirect
77. C₄₃	#1944	semidirect
124. C₈	Dic₄₃⋊C₄	semidirect

H ≅ G/N

type

10. #13063257

C₄

semidirect

52. C₈×C₄₃

C₄⋊C₄

semidirect

77. C₄₃

#1944

semidirect

124. C₈

Dic₄₃⋊C₄

semidirect

Subgroups — #19135338

Conjugacy classes of subgroups

Complements