Group #19134810 — subgroups

Subgroups — #19134810

Order 5504.

272 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14582942	C₂	1	2	yes	maximal
2	C₂×#13063244	C₂	1	1	yes	maximal, characteristic
3	#14582806	C₂	1	1	yes	maximal, characteristic
4	#14582658	C₂	1	2	yes	maximal
5	C₄₃×#519	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621877	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
9	#13063258	—	2	2	no	—
10	#13063256	—	2	2	no	—
11	#13063244	C₄	1	4	yes	complemented
12	C₄₃⋊#95	—	2	2	no	—
13	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₄×Q₈×C₄₃	—	2	2	no	—
15	C₄×Q₈×C₄₃	—	2	2	no	—
16	#117×C₄₃	—	2	2	no	—
17	#117×C₄₃	C₂²	1	2	yes	—
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	Q₈	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	C₄⋊C₄×C₄₃	—	2	2	no	—
27	C₄⋊C₄×C₄₃	—	2	2	no	—
28	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
29	C₄⋊C₄×C₄₃	D₄	1	2	yes	—
30	C₂²⋊C₄×C₄₃	—	2	2	no	—
31	C₄²×C₄₃	—	2	4	no	—
32	C₄²×C₄₃	—	2	2	no	—
33	C₄⋊Dic₄₃	—	2	2	no	—
34	C₄×Dic₄₃	—	2	2	no	—
35	#10621877	—	2	2	no	—
36	#10621877	C₂×C₄	1	4	yes	—
37	C₂×C₄₃⋊C₈	—	2	2	no	—
38	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
39	Q₈×C₄₃	—	2	4	no	—
40	Q₈×C₄₃	—	2	4	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	C₄⋊C₄	1	4	yes	—
46	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
48	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
49	C₂×C₄×C₄₃	#41	1	2	yes	—
50	C₂×Dic₄₃	—	2	2	no	—
51	C₂×Dic₄₃	—	4	1	no	—
52	C₂×Dic₄₃	—	4	1	no	—
53	C₂×Dic₄₃	—	4	2	no	—
54	C₂×Dic₄₃	—	4	1	no	—
55	C₄₃⋊C₈	—	2	4	no	—
56	C₂²×C₄₃	—	2	1	no	—
57	C₂²×C₄₃	—	2	1	no	—
58	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂²×C₄₃	#120	1	1	yes	characteristic
60	C₂²×C₄₃	#123	1	1	yes	characteristic
61	C₄×C₄₃	—	2	4	no	—
62	C₄×C₄₃	—	4	2	no	—
63	C₄×C₄₃	—	4	2	no	—
64	C₄×C₄₃	C₄×D₄	1	2	yes	—
65	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
66	Dic₄₃	—	4	2	no	—
67	Dic₄₃	—	8	1	no	—
68	#1857	—	43	1	no	maximal, Sylow
69	C₂×C₄₃	—	2	1	no	—
70	C₂×C₄₃	—	2	1	no	—
71	C₂×C₄₃	#385	1	1	yes	characteristic
72	C₂×C₄₃	#454	1	1	yes	characteristic
73	C₂×C₄₃	#456	1	1	yes	characteristic
74	#519	D₄₃	1	1	yes	characteristic
75	#428	—	43	2	no	—
76	C₂×#101	—	43	1	no	—
77	#391	—	43	1	no	—
78	#339	—	43	2	no	—
79	C₄₃	#1857	1	1	yes	characteristic, complemented, Sylow
80	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
81	C₂×M₁₆	—	43	2	no	—
82	C₄×Q₈	—	2	2	no	—
83	C₄×Q₈	—	2	2	no	—
84	#117	—	2	2	no	—
85	#117	C₂×D₄₃	1	2	yes	—
86	C₂×C₄⋊C₄	—	43	1	no	—
87	C₂×C₄²	—	43	1	no	—
88	#107	—	86	2	no	—
89	#106	—	86	2	no	—
90	#101	—	43	4	no	—
91	#95	—	86	2	no	—
92	C₂×Q₈	—	2	2	no	—
93	C₂×Q₈	—	2	2	no	—
94	C₂×Q₈	Dic₈₆	1	2	yes	—
95	C₂×Q₈	C₄×D₄₃	1	2	yes	—
96	C₂²×C₄	—	86	1	no	—
97	C₂²×C₄	—	86	1	no	—
98	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
99	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
100	M₁₆	—	43	4	no	—
101	M₁₆	—	86	2	no	—
102	C₂×C₈	—	86	2	no	—
103	C₄⋊C₄	—	2	2	no	—
104	C₄⋊C₄	—	2	2	no	—
105	C₄⋊C₄	—	86	2	no	—
106	C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
107	C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
108	C₂²⋊C₄	—	2	2	no	—
109	C₄²	—	2	4	no	—
110	C₄²	—	2	2	no	—
111	C₄²	—	86	2	no	—
112	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
113	Q₈	—	2	4	no	—
114	Q₈	—	2	4	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	—	86	2	no	—
120	C₂×C₄	—	172	2	no	—
121	C₂×C₄	—	172	1	no	—
122	C₂×C₄	—	172	1	no	—
123	C₂×C₄	—	172	1	no	—
124	C₂×C₄	Dic₄₃⋊C₄	1	4	yes	—
125	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
126	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
127	C₂×C₄	#10621898	1	2	yes	—
128	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
129	C₈	—	86	4	no	—
130	C₂²	—	2	1	no	—
131	C₂²	—	2	1	no	—
132	C₂²	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
133	C₂²	#13063294	1	1	yes	characteristic
134	C₂²	#13063308	1	1	yes	characteristic
135	C₄	—	2	4	no	—
136	C₄	—	4	2	no	—
137	C₄	—	4	2	no	—
138	C₄	—	344	1	no	—
139	C₄	—	172	2	no	—
140	C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
141	C₄	#13063304	1	2	yes	—
142	C₂	—	2	1	no	—
143	C₂	—	2	1	no	—
144	C₂	#14582772	1	1	yes	characteristic
145	C₂	#14583072	1	1	yes	characteristic
146	C₂	#14583082	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582942

C₂

yes

maximal

C₂×#13063244

C₂

yes

maximal, characteristic

#14582806

C₂

yes

maximal, characteristic

#14582658

C₂

yes

maximal

C₄₃×#519

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄×Dic₄₃

C₂²

yes

—

—

C₄

yes

complemented

C₄₃⋊#95

—

C₂²×Q₈×C₄₃

C₂²

yes

characteristic

C₄×Q₈×C₄₃

—

C₄×Q₈×C₄₃

—

#117×C₄₃

—

#117×C₄₃

C₂²

yes

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂×C₄

yes

—

C₂×Q₈×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄⋊C₄

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

C₂²⋊Q₈

yes

—

Dic₄₃

—

Dic₄₃

—

#1857

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

—

—

—

—

C₄₃

#1857

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₃

yes

characteristic

C₂×M₁₆

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

#117

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

—

—

—

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₈₆

yes

—

C₂×Q₈

C₄×D₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

100

M₁₆

—

101

M₁₆

—

102

C₂×C₈

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

C₂²⋊D₄₃

yes

—

107

C₄⋊C₄

C₂²⋊D₄₃

yes

—

108

C₂²⋊C₄

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

113

Q₈

—

114

Q₈

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

172

—

121

C₂×C₄

—

172

—

122

C₂×C₄

—

172

—

123

C₂×C₄

—

172

—

124

C₂×C₄

Dic₄₃⋊C₄

yes

—

125

C₂×C₄

C₂×Dic₈₆

yes

characteristic

126

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

127

C₂×C₄

#10621898

yes

—

128

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

129

C₈

—

130

C₂²

—

131

C₂²

—

132

C₂²

C₂×Dic₄₃⋊C₄

yes

characteristic

133

C₂²

#13063294

yes

characteristic

134

C₂²

#13063308

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

344

—

139

C₄

—

172

—

140

C₄

C₄×C₂²⋊D₄₃

yes

—

141

C₄

#13063304

yes

—

142

C₂

—

143

C₂

—

144

C₂

#14582772

yes

characteristic

145

C₂

#14583072

yes

characteristic

146

C₂

#14583082

yes

characteristic

	subgroup	G/H
center	C₂²	#13063294
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#519	C₂
socle	C₂²×C₄₃	#120
hypercenter	#519	D₄₃
hypocenter	C₄₃	#1857
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #519

subgroup

G/H

center

C₂²

#13063294

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#519

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #519

N	H ≅ G/N	type
11. #13063244	C₄	semidirect
79. C₄₃	#1857	semidirect

H ≅ G/N

type

11. #13063244

C₄

semidirect

79. C₄₃

#1857

semidirect

Subgroups — #19134810

Conjugacy classes of subgroups

Complements