Group #19135743 — subgroups

Subgroups — #19135743

Order 5504.

258 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13063248	C₂	1	2	yes	maximal
2	#14582805	C₂	1	1	yes	maximal, characteristic
3	#14582661	C₂	1	2	yes	maximal
4	#14582654	C₂	1	1	yes	maximal, characteristic
5	C₂×#125×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
7	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
9	#13063248	—	2	4	no	—
10	C₄₃⋊#95	—	2	2	no	—
11	#125×C₄₃	—	2	4	no	—
12	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
13	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	—	2	2	no	—
16	C₂²×C₄×C₄₃	D₄	1	2	yes	—
17	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₃	—	2	1	no	—
19	C₂²×Dic₄₃	—	2	1	no	—
20	C₂×Dic₈₆	—	2	2	no	—
21	C₂×Dic₈₆	—	2	2	no	—
22	C₂×Dic₈₆	—	2	1	no	—
23	C₂×Dic₈₆	Q₈	1	2	yes	—
24	C₄⋊C₄×C₄₃	—	2	8	no	—
25	C₄⋊C₄×C₄₃	—	2	2	no	—
26	C₄⋊C₄×C₄₃	D₄	1	4	yes	—
27	C₄²×C₄₃	—	2	2	no	—
28	C₄⋊Dic₄₃	—	2	2	no	—
29	C₂×C₄₃⋊C₈	—	2	2	no	—
30	C₂×C₄₃⋊C₈	—	2	2	no	—
31	C₂×C₄₃⋊C₈	—	2	2	no	—
32	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	—	2	2	no	—
34	C₂×C₄×C₄₃	—	2	4	no	—
35	C₂×C₄×C₄₃	—	2	2	no	—
36	C₂×C₄×C₄₃	—	2	2	no	—
37	C₂×C₄×C₄₃	—	4	2	no	—
38	C₂×C₄×C₄₃	—	4	2	no	—
39	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₄₃	#41	1	2	yes	—
42	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
43	C₂×Dic₄₃	—	2	2	no	—
44	C₂×Dic₄₃	—	4	1	no	—
45	C₂×Dic₄₃	—	4	1	no	—
46	C₂×Dic₄₃	—	4	1	no	—
47	C₂×Dic₄₃	—	4	2	no	—
48	Dic₈₆	—	2	4	no	—
49	Dic₈₆	—	4	2	no	—
50	C₄₃⋊C₈	—	4	2	no	—
51	C₂²×C₄₃	#120	1	1	yes	characteristic
52	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
53	C₂²×C₄₃	#124	1	1	yes	characteristic
54	C₂²×C₄₃	#135	1	2	yes	—
55	C₂²×C₄₃	#137	1	2	yes	—
56	C₄×C₄₃	—	4	2	no	—
57	C₄×C₄₃	—	4	4	no	—
58	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
59	C₄×C₄₃	#124	1	2	yes	—
60	Dic₄₃	—	4	2	no	—
61	Dic₄₃	—	8	1	no	—
62	#2026	—	43	1	no	maximal, Sylow
63	C₂×C₄₃	#393	1	1	yes	characteristic
64	C₂×C₄₃	#452	1	2	yes	—
65	C₂×C₄₃	#479	1	2	yes	—
66	C₂×C₄₃	#488	1	1	yes	characteristic
67	C₂×C₄₃	#491	1	1	yes	characteristic
68	C₂×#125	D₄₃	1	1	yes	characteristic
69	C₂×#103	—	43	2	no	—
70	#391	—	43	1	no	—
71	#340	—	43	2	no	—
72	#336	—	43	1	no	—
73	C₄₃	#2026	1	1	yes	characteristic, complemented, Sylow
74	C₂²×Q₈	—	43	1	no	—
75	C₂²×C₈	—	43	2	no	—
76	#125	—	2	4	no	—
77	C₂×C₄⋊C₄	—	2	2	no	—
78	C₂×C₄⋊C₄	—	43	1	no	—
79	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
80	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
81	#103	—	86	4	no	—
82	#95	—	86	2	no	—
83	C₂×Q₈	—	43	2	no	—
84	C₂×Q₈	—	86	1	no	—
85	C₂×Q₈	—	86	2	no	—
86	C₂×Q₈	—	86	2	no	—
87	C₂²×C₄	—	2	2	no	—
88	C₂²×C₄	—	86	1	no	—
89	C₂²×C₄	—	86	1	no	—
90	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
91	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
92	C₂×C₈	—	86	2	no	—
93	C₂×C₈	—	86	2	no	—
94	C₂×C₈	—	86	2	no	—
95	C₄⋊C₄	—	2	8	no	—
96	C₄⋊C₄	—	2	2	no	—
97	C₄⋊C₄	—	86	2	no	—
98	C₄⋊C₄	C₂²⋊D₄₃	1	4	yes	—
99	C₄²	—	2	2	no	—
100	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
101	Q₈	—	86	4	no	—
102	Q₈	—	172	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	2	2	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	86	2	no	—
110	C₂×C₄	—	172	1	no	—
111	C₂×C₄	—	172	2	no	—
112	C₂×C₄	—	172	1	no	—
113	C₂×C₄	—	172	1	no	—
114	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
115	C₂×C₄	#10621902	1	2	yes	—
116	C₂×C₄	#10621902	1	1	yes	characteristic
117	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
118	C₈	—	172	2	no	—
119	C₂²	#13063294	1	1	yes	characteristic
120	C₂²	#13063301	1	1	yes	characteristic
121	C₂²	#13063314	1	1	yes	characteristic
122	C₂²	#13063345	1	2	yes	—
123	C₂²	#13063355	1	2	yes	—
124	C₄	—	4	2	no	—
125	C₄	—	4	4	no	—
126	C₄	—	344	1	no	—
127	C₄	—	172	2	no	—
128	C₄	#13063301	1	2	yes	—
129	C₄	#13063314	1	2	yes	—
130	C₂	#14582810	1	1	yes	characteristic
131	C₂	#14583061	1	2	yes	—
132	C₂	#14583203	1	2	yes	—
133	C₂	#14583256	1	1	yes	characteristic
134	C₂	#14583269	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063248

C₂

yes

maximal

#14582805

C₂

yes

maximal, characteristic

#14582661

C₂

yes

maximal

#14582654

C₂

yes

maximal, characteristic

C₂×#125×C₄₃

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

#13063248

—

C₄₃⋊#95

—

#125×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

Q₈

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₄₃⋊C₈

—

C₂²×C₄₃

#120

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#137

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

—

C₄×C₄₃

#124

yes

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#479

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

—

—

—

—

C₄₃

#2026

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#103

—

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²⋊D₄₃

yes

—

C₄²

—

100

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

101

Q₈

—

102

Q₈

—

172

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

172

—

111

C₂×C₄

—

172

—

112

C₂×C₄

—

172

—

113

C₂×C₄

—

172

—

114

C₂×C₄

Q₈×D₄₃

yes

characteristic

115

C₂×C₄

#10621902

yes

—

116

C₂×C₄

#10621902

yes

characteristic

117

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

118

C₈

—

172

—

119

C₂²

#13063294

yes

characteristic

120

C₂²

#13063301

yes

characteristic

121

C₂²

#13063314

yes

characteristic

122

C₂²

#13063345

yes

—

123

C₂²

#13063355

yes

—

124

C₄

—

125

C₄

—

126

C₄

—

344

—

127

C₄

—

172

—

128

C₄

#13063301

yes

—

129

C₄

#13063314

yes

—

130

C₂

#14582810

yes

characteristic

131

C₂

#14583061

yes

—

132

C₂

#14583203

yes

—

133

C₂

#14583256

yes

characteristic

134

C₂

#14583269

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₂×#125×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×#125	D₄₃
hypocenter	C₄₃	#2026
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₂×#125×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
73. C₄₃	#2026	semidirect

H ≅ G/N

type

73. C₄₃

#2026

semidirect

Subgroups — #19135743

Conjugacy classes of subgroups

Complements