Group #19134986 — subgroups

Subgroups — #19134986

Order 5504.

324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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	1	yes	maximal, characteristic
2	#14583377	C₂	1	1	yes	maximal, characteristic
3	#14582909	C₂	1	2	yes	maximal
4	#14582660	C₂	1	2	yes	maximal
5	C₂×#101×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
7	#13063323	—	2	2	no	—
8	#13063323	C₄	1	4	yes	complemented
9	Q₈×Dic₄₃	—	2	4	no	—
10	#13063284	—	2	2	no	—
11	#13063284	C₂²	1	2	yes	—
12	C₂×Dic₄₃⋊C₄	—	2	2	no	—
13	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
14	#13063250	—	2	4	no	—
15	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
17	#101×C₄₃	—	2	2	no	—
18	C₂×Q₈×C₄₃	—	2	2	no	—
19	C₂×Q₈×C₄₃	—	2	2	no	—
20	C₂×Q₈×C₄₃	C₂×C₄	1	2	yes	—
21	C₂×Q₈×C₄₃	D₄	1	2	yes	—
22	C₂²×C₄×C₄₃	D₄	1	2	yes	—
23	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
24	C₂²×Dic₄₃	—	2	1	no	—
25	C₂²×Dic₄₃	—	2	1	no	—
26	C₂×Dic₈₆	—	2	2	no	—
27	C₂×Dic₈₆	—	2	2	no	—
28	C₂×Dic₈₆	—	2	1	no	—
29	C₂×Dic₈₆	C₂×C₄	1	2	yes	—
30	M₁₆×C₄₃	—	2	2	no	—
31	M₁₆×C₄₃	—	2	2	no	—
32	C₂×C₈×C₄₃	—	2	2	no	—
33	C₂²⋊Dic₄₃	—	2	2	no	—
34	C₄⋊Dic₄₃	—	2	4	no	—
35	C₄⋊Dic₄₃	D₄	1	4	yes	—
36	Dic₄₃⋊C₄	—	2	8	no	—
37	C₄×Dic₄₃	—	2	4	no	—
38	C₄×Dic₄₃	—	2	1	no	—
39	C₄×Dic₄₃	—	2	2	no	—
40	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
41	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
42	Q₈×C₄₃	—	2	4	no	—
43	Q₈×C₄₃	—	2	4	no	—
44	C₂×C₄×C₄₃	—	2	2	no	—
45	C₂×C₄×C₄₃	—	2	2	no	—
46	C₂×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
47	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₄₃	#41	1	2	yes	—
51	C₂×Dic₄₃	—	2	4	no	—
52	C₂×Dic₄₃	—	2	2	no	—
53	C₂×Dic₄₃	—	2	2	no	—
54	C₂×Dic₄₃	—	2	4	no	—
55	C₂×Dic₄₃	—	4	1	no	—
56	C₂×Dic₄₃	—	4	1	no	—
57	Dic₈₆	—	2	4	no	—
58	Dic₈₆	—	4	2	no	—
59	C₈×C₄₃	—	4	2	no	—
60	C₂²×C₄₃	—	2	2	no	—
61	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄₃	#120	1	1	yes	characteristic
63	C₂²×C₄₃	#123	1	1	yes	characteristic
64	C₄×C₄₃	—	2	4	no	—
65	C₄×C₄₃	C₄×D₄	1	2	yes	—
66	C₄×C₄₃	#121	1	2	yes	—
67	Dic₄₃	—	2	4	no	—
68	Dic₄₃	—	4	2	no	—
69	Dic₄₃	—	4	4	no	—
70	#1886	—	43	1	no	maximal, Sylow
71	C₂×C₄₃	—	2	1	no	—
72	C₂×C₄₃	—	2	1	no	—
73	C₂×C₄₃	#386	1	1	yes	characteristic
74	C₂×C₄₃	#456	1	2	yes	—
75	C₂×C₄⋊Q₈	—	43	1	no	—
76	#519	—	43	1	no	—
77	#419	—	43	2	no	—
78	C₂×#101	D₄₃	1	1	yes	characteristic
79	#339	—	43	2	no	—
80	C₄₃	#1886	1	1	yes	characteristic, complemented, Sylow
81	C₂²×Q₈	—	43	1	no	—
82	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
83	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
84	C₄⋊Q₈	—	43	4	no	—
85	C₄⋊Q₈	—	86	2	no	—
86	C₄×Q₈	—	86	4	no	—
87	#117	—	43	2	no	—
88	#117	—	86	2	no	—
89	C₂×C₄⋊C₄	—	86	2	no	—
90	C₂×C₄²	—	43	1	no	—
91	#103	—	86	4	no	—
92	#101	—	2	2	no	—
93	C₂×Q₈	—	2	2	no	—
94	C₂×Q₈	—	2	2	no	—
95	C₂×Q₈	—	43	2	no	—
96	C₂×Q₈	—	86	1	no	—
97	C₂×Q₈	—	86	2	no	—
98	C₂×Q₈	—	86	2	no	—
99	C₂×Q₈	C₄×D₄₃	1	2	yes	—
100	C₂×Q₈	C₂²⋊D₄₃	1	2	yes	—
101	C₂²×C₄	—	86	1	no	—
102	C₂²×C₄	—	86	1	no	—
103	C₂²×C₄	D₁₇₂	1	2	yes	—
104	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
105	M₁₆	—	2	2	no	—
106	M₁₆	—	2	2	no	—
107	C₂×C₈	—	2	2	no	—
108	C₄⋊C₄	—	43	4	no	—
109	C₄⋊C₄	—	86	4	no	—
110	C₄⋊C₄	—	86	8	no	—
111	C₂²⋊C₄	—	86	2	no	—
112	C₄²	—	43	2	no	—
113	C₄²	—	86	4	no	—
114	C₄²	—	86	2	no	—
115	C₄²	—	86	1	no	—
116	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
117	Q₈	—	2	4	no	—
118	Q₈	—	2	4	no	—
119	Q₈	—	86	4	no	—
120	Q₈	—	172	2	no	—
121	C₂×C₄	—	2	2	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	86	4	no	—
124	C₂×C₄	—	86	2	no	—
125	C₂×C₄	—	86	2	no	—
126	C₂×C₄	—	86	4	no	—
127	C₂×C₄	—	172	1	no	—
128	C₂×C₄	—	172	1	no	—
129	C₂×C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
130	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
131	C₂×C₄	D₄×D₄₃	1	2	yes	—
132	C₂×C₄	#10621900	1	2	yes	—
133	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
134	C₈	—	4	2	no	—
135	C₂²	—	2	2	no	—
136	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
137	C₂²	#13063295	1	1	yes	characteristic
138	C₂²	#13063309	1	1	yes	characteristic
139	C₄	—	2	4	no	—
140	C₄	—	86	4	no	—
141	C₄	—	172	4	no	—
142	C₄	—	172	2	no	—
143	C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
144	C₄	#13063297	1	2	yes	—
145	C₂	—	2	1	no	—
146	C₂	—	2	1	no	—
147	C₂	#14582776	1	1	yes	characteristic
148	C₂	#14583084	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063323

C₂

yes

maximal, characteristic

#14583377

C₂

yes

maximal, characteristic

#14582909

C₂

yes

maximal

#14582660

C₂

yes

maximal

C₂×#101×C₄₃

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

characteristic

#13063323

—

#13063323

C₄

yes

complemented

Q₈×Dic₄₃

—

#13063284

—

#13063284

C₂²

yes

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

#13063250

—

C₂²×Q₈×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₂²

yes

—

#101×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂×C₄

yes

—

C₂×Q₈×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂×C₄

yes

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

#121

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#1886

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#386

yes

characteristic

C₂×C₄₃

#456

yes

—

C₂×C₄⋊Q₈

—

#519

—

#419

—

C₂×#101

D₄₃

yes

characteristic

#339

—

C₄₃

#1886

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

C₂×D₄₃

yes

characteristic

C₂×M₁₆

C₂×D₄₃

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄×Q₈

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

#103

—

#101

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₄×D₄₃

yes

—

100

C₂×Q₈

C₂²⋊D₄₃

yes

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

D₁₇₂

yes

—

104

C₂²×C₄

C₂²×D₄₃

yes

characteristic

105

M₁₆

—

106

M₁₆

—

107

C₂×C₈

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₂²⋊C₄

—

112

C₄²

—

113

C₄²

—

114

C₄²

—

115

C₄²

—

116

C₂³

C₂×D₁₇₂

yes

characteristic

117

Q₈

—

118

Q₈

—

119

Q₈

—

120

Q₈

—

172

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

172

—

128

C₂×C₄

—

172

—

129

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

130

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

131

C₂×C₄

D₄×D₄₃

yes

—

132

C₂×C₄

#10621900

yes

—

133

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

134

C₈

—

135

C₂²

—

136

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

137

C₂²

#13063295

yes

characteristic

138

C₂²

#13063309

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

172

—

142

C₄

—

172

—

143

C₄

(C₂²⋊D₄₃)⋊C₄

yes

—

144

C₄

#13063297

yes

—

145

C₂

—

146

C₂

—

147

C₂

#14582776

yes

characteristic

148

C₂

#14583084

yes

—

	subgroup	G/H
center	C₂²	#13063295
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#101×C₄₃	C₂
socle	C₂²×C₄₃	#120
hypercenter	C₂×#101	D₄₃
hypocenter	C₄₃	#1886
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

subgroup

G/H

center

C₂²

#13063295

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#101×C₄₃

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#101

N	H ≅ G/N	type
8. #13063323	C₄	semidirect
80. C₄₃	#1886	semidirect

H ≅ G/N

type

8. #13063323

C₄

semidirect

80. C₄₃

#1886

semidirect

Subgroups — #19134986

Conjugacy classes of subgroups

Complements