Group #19133978 — subgroups

Subgroups — #19133978

Order 5504.

150 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14583297	C₂	1	1	yes	maximal, characteristic
2	#14583195	C₂	1	1	yes	maximal, characteristic
3	#14583110	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic
5	#14582647	C₂	1	1	yes	maximal, characteristic
6	#14582646	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#334	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₇₂	—	2	1	no	—
9	#13063325	C₂²	1	1	yes	characteristic
10	#13063325	C₂²	1	1	yes	characteristic
11	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
12	#13063259	—	2	1	no	—
13	#13063257	—	2	1	no	—
14	#13063257	—	2	1	no	—
15	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
16	Dic₄₃⋊C₈	—	2	1	no	—
17	#13063250	—	2	1	no	—
18	#13063250	—	2	1	no	—
19	C₈×Dic₄₃	—	2	1	no	—
20	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×Dic₈₆	—	2	1	no	—
24	C₂×Dic₈₆	—	2	1	no	—
25	C₂×Dic₈₆	D₄	1	1	yes	characteristic
26	C₂×C₈×C₄₃	—	2	1	no	—
27	C₂×C₈×C₄₃	—	2	1	no	—
28	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
29	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
30	C₄²×C₄₃	C₂³	1	1	yes	characteristic
31	C₄⋊Dic₄₃	—	2	1	no	—
32	C₄⋊Dic₄₃	—	2	1	no	—
33	C₄⋊Dic₄₃	—	2	1	no	—
34	C₄⋊Dic₄₃	—	2	1	no	—
35	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
36	Dic₄₃⋊C₄	—	2	1	no	—
37	C₄×Dic₄₃	—	2	1	no	—
38	C₂×C₄₃⋊C₈	—	2	1	no	—
39	Dic₁₇₂	—	4	2	no	—
40	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
43	C₂×Dic₄₃	—	2	1	no	—
44	C₂×Dic₄₃	—	2	1	no	—
45	C₂×Dic₄₃	—	4	1	no	—
46	C₂×Dic₄₃	—	4	1	no	—
47	Dic₈₆	—	2	1	no	—
48	Dic₈₆	—	4	1	no	—
49	Dic₈₆	—	4	1	no	—
50	Dic₈₆	—	8	1	no	—
51	Dic₈₆	SD₁₆	1	2	yes	—
52	C₈×C₄₃	—	2	1	no	—
53	C₈×C₄₃	—	4	1	no	—
54	C₈×C₄₃	—	4	1	no	—
55	C₈×C₄₃	Q₁₆	1	2	yes	complemented
56	C₄₃⋊C₈	—	4	1	no	—
57	C₂²×C₄₃	#121	1	1	yes	characteristic
58	C₄×C₄₃	—	2	1	no	—
59	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
60	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
61	C₄×C₄₃	#135	1	1	yes	characteristic
62	C₄×C₄₃	#137	1	1	yes	characteristic
63	Dic₄₃	—	2	2	no	—
64	Dic₄₃	—	4	1	no	—
65	Dic₄₃	—	8	1	no	—
66	Dic₄₃	—	8	1	no	—
67	#1672	—	43	1	no	maximal, Sylow
68	C₂×C₄₃	#462	1	1	yes	characteristic
69	C₂×C₄₃	#465	1	1	yes	characteristic
70	C₂×C₄₃	#471	1	1	yes	characteristic
71	#498	—	43	1	no	—
72	#477	—	43	1	no	—
73	#462	—	43	1	no	—
74	C₈×Q₈	—	43	1	no	—
75	#334	D₄₃	1	1	yes	characteristic
76	#333	—	43	1	no	—
77	#332	—	43	1	no	—
78	C₄₃	#1672	1	1	yes	characteristic, complemented, Sylow
79	C₂×Q₁₆	—	86	1	no	—
80	C₄⋊Q₈	—	43	1	no	—
81	C₄⋊Q₈	—	43	1	no	—
82	C₄×Q₈	—	43	1	no	—
83	#107	—	86	1	no	—
84	#106	—	86	1	no	—
85	#106	—	86	1	no	—
86	C₄⋊C₈	—	43	1	no	—
87	C₄⋊C₈	—	86	1	no	—
88	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
89	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
90	#103	—	86	1	no	—
91	#103	—	86	1	no	—
92	C₄×C₈	—	86	1	no	—
93	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
94	C₂×Q₈	—	43	1	no	—
95	C₂×Q₈	—	86	1	no	—
96	C₂×Q₈	—	86	1	no	—
97	Q₁₆	—	172	2	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	86	1	no	—
101	C₂×C₈	D₁₇₂	1	1	yes	characteristic
102	C₂×C₈	D₁₇₂	1	1	yes	characteristic
103	C₄⋊C₄	—	43	1	no	—
104	C₄⋊C₄	—	86	1	no	—
105	C₄⋊C₄	—	86	1	no	—
106	C₄⋊C₄	—	86	1	no	—
107	C₄⋊C₄	—	86	1	no	—
108	C₄⋊C₄	—	86	1	no	—
109	C₄²	—	86	1	no	—
110	C₄²	C₂²×D₄₃	1	1	yes	characteristic
111	Q₈	—	43	2	no	—
112	Q₈	—	86	1	no	—
113	Q₈	—	344	1	no	—
114	Q₈	—	172	1	no	—
115	Q₈	—	172	1	no	—
116	C₂×C₄	—	86	1	no	—
117	C₂×C₄	—	86	1	no	—
118	C₂×C₄	—	172	1	no	—
119	C₂×C₄	—	172	1	no	—
120	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
121	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
122	C₂×C₄	#10621902	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	4	1	no	—
125	C₈	—	4	1	no	—
126	C₈	—	172	1	no	—
127	C₈	Dic₁₇₂	1	2	yes	complemented
128	C₂²	#13063300	1	1	yes	characteristic
129	C₄	—	2	1	no	—
130	C₄	—	86	2	no	—
131	C₄	—	344	1	no	—
132	C₄	—	344	1	no	—
133	C₄	—	172	1	no	—
134	C₄	SD₁₆×D₄₃	1	1	yes	characteristic
135	C₄	C₂×Dic₁₇₂	1	1	yes	characteristic
136	C₄	#13063346	1	1	yes	characteristic
137	C₄	#13063358	1	1	yes	characteristic
138	C₂	#14583110	1	1	yes	characteristic
139	C₂	#14583129	1	1	yes	characteristic
140	C₂	#14583163	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583297

C₂

yes

maximal, characteristic

#14583195

C₂

yes

maximal, characteristic

#14583110

C₂

yes

maximal, characteristic

C₈×Dic₈₆

C₂

yes

maximal, characteristic

#14582647

C₂

yes

maximal, characteristic

#14582646

C₂

yes

maximal, characteristic

C₄₃×#334

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

—

#13063325

C₂²

yes

characteristic

#13063325

C₂²

yes

characteristic

C₄×Dic₈₆

C₂²

yes

—

—

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

#13063250

—

#13063250

—

C₈×Dic₄₃

—

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

D₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

SD₁₆

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

Q₁₆

yes

complemented

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₄×C₄₃

C₂×Q₁₆

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

C₈×Q₈

—

#334

D₄₃

yes

characteristic

#333

—

#332

—

C₄₃

#1672

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄×Q₈

—

#107

—

#106

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

characteristic

C₄⋊C₈

C₂×D₄₃

yes

characteristic

#103

—

#103

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

D₁₇₂

yes

characteristic

102

C₂×C₈

D₁₇₂

yes

characteristic

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄²

—

110

C₄²

C₂²×D₄₃

yes

characteristic

111

Q₈

—

112

Q₈

—

113

Q₈

—

344

—

114

Q₈

—

172

—

115

Q₈

—

172

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

172

—

119

C₂×C₄

—

172

—

120

C₂×C₄

C₂×D₁₇₂

yes

characteristic

121

C₂×C₄

D₄×D₄₃

yes

characteristic

122

C₂×C₄

#10621902

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

172

—

127

C₈

Dic₁₇₂

yes

complemented

128

C₂²

#13063300

yes

characteristic

129

C₄

—

130

C₄

—

131

C₄

—

344

—

132

C₄

—

344

—

133

C₄

—

172

—

134

C₄

SD₁₆×D₄₃

yes

characteristic

135

C₄

C₂×Dic₁₇₂

yes

characteristic

136

C₄

#13063346

yes

characteristic

137

C₄

#13063358

yes

characteristic

138

C₂

#14583110

yes

characteristic

139

C₂

#14583129

yes

characteristic

140

C₂

#14583163

yes

characteristic

	subgroup	G/H
center	C₂²	#13063300
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#334	C₂
socle	C₂²×C₄₃	#121
hypercenter	#334	D₄₃
hypocenter	C₄₃	#1672
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#13063300

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#334

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
55. C₈×C₄₃	Q₁₆	semidirect
78. C₄₃	#1672	semidirect
127. C₈	Dic₁₇₂	semidirect

H ≅ G/N

type

55. C₈×C₄₃

Q₁₆

semidirect

78. C₄₃

#1672

semidirect

127. C₈

Dic₁₇₂

semidirect

Subgroups — #19133978

Conjugacy classes of subgroups

Complements