Group #19134186 — subgroups

Subgroups — #19134186

Order 5504.

224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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	#14583302	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583275	C₂	1	1	yes	maximal, characteristic
3	#14583273	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583271	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583246	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621883	—	2	2	no	—
9	C₂×#10621884	—	2	2	no	—
10	C₂×#10621882	—	2	2	no	—
11	#13063325	C₂²	1	1	yes	characteristic
12	#13063322	C₂²	1	1	yes	characteristic
13	#13063258	—	2	2	no	—
14	#13063247	—	2	2	no	—
15	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	#127×C₄₃	C₂²	1	1	yes	characteristic
19	#102×C₄₃	—	2	2	no	—
20	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₄₃	—	2	1	no	—
22	C₂×D₄×C₄₃	—	2	1	no	—
23	C₂×D₄×C₄₃	—	2	1	no	—
24	C₂×D₄×C₄₃	—	2	1	no	—
25	C₂×D₁₇₂	—	2	1	no	—
26	C₂×D₁₇₂	—	2	1	no	—
27	C₂×D₁₇₂	—	2	1	no	—
28	C₂×Dic₈₆	—	2	1	no	—
29	C₂×C₈×C₄₃	D₄	1	2	yes	—
30	C₄⋊C₄×C₄₃	—	2	1	no	—
31	C₄⋊C₄×C₄₃	—	2	1	no	—
32	C₄²×C₄₃	C₂³	1	1	yes	characteristic
33	#10621884	—	4	4	no	—
34	#10621883	—	4	4	no	—
35	#10621882	—	4	4	no	—
36	C₄⋊Dic₄₃	—	2	1	no	—
37	C₄⋊Dic₄₃	—	2	1	no	—
38	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
39	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
40	C₂³×C₄₃	—	4	1	no	—
41	C₂²×D₄₃	—	4	1	no	—
42	Q₈×C₄₃	—	4	2	no	—
43	D₄×C₄₃	—	4	2	no	—
44	D₄×C₄₃	—	4	2	no	—
45	D₄×C₄₃	—	4	2	no	—
46	C₂×C₄×C₄₃	—	4	1	no	—
47	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
50	C₂×Dic₄₃	—	4	1	no	—
51	D₁₇₂	—	4	2	no	—
52	D₁₇₂	—	4	2	no	—
53	D₁₇₂	—	4	2	no	—
54	Dic₈₆	—	4	2	no	—
55	C₈×C₄₃	—	2	2	no	—
56	C₄₃⋊C₈	D₈	1	4	yes	complemented
57	C₄₃⋊C₈	SD₁₆	1	4	yes	complemented
58	C₂²×C₄₃	—	8	1	no	—
59	C₂²×C₄₃	—	8	1	no	—
60	C₂²×C₄₃	—	8	1	no	—
61	C₂²×C₄₃	#127	1	1	yes	characteristic
62	C₂×D₄₃	—	8	1	no	—
63	C₂×D₄₃	—	8	1	no	—
64	C₂×D₄₃	—	8	1	no	—
65	C₄×C₄₃	—	8	1	no	—
66	C₄×C₄₃	C₂×D₈	1	2	yes	—
67	C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
68	C₄×C₄₃	#135	1	2	yes	—
69	Dic₄₃	—	8	1	no	—
70	#1706	—	43	1	no	maximal, Sylow
71	C₂×C₄₃	—	16	1	no	—
72	C₂×C₄₃	#492	1	1	yes	characteristic
73	C₂×C₄₃	#493	1	1	yes	characteristic
74	C₂×C₄₃	#495	1	1	yes	characteristic
75	D₄₃	—	16	1	no	—
76	#500	—	43	1	no	—
77	#493	—	43	1	no	—
78	#492	—	43	1	no	—
79	#492	—	43	1	no	—
80	#486	—	43	1	no	—
81	#486	D₄₃	1	1	yes	characteristic, complemented
82	C₈²	—	43	1	no	—
83	C₄₃	#1706	1	1	yes	characteristic, complemented, Sylow
84	C₂×SD₁₆	—	86	2	no	—
85	C₂×SD₁₆	—	86	2	no	—
86	C₂×D₈	—	86	2	no	—
87	C₄⋊Q₈	—	43	1	no	—
88	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
89	#127	—	43	1	no	—
90	#127	C₂×D₄₃	1	1	yes	characteristic
91	#107	—	86	2	no	—
92	#102	—	2	2	no	—
93	#102	—	86	2	no	—
94	C₄×C₈	—	43	1	no	—
95	C₄×C₈	—	43	1	no	—
96	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
97	C₂×Q₈	—	2	1	no	—
98	C₂×Q₈	—	86	1	no	—
99	C₂×D₄	—	2	1	no	—
100	C₂×D₄	—	2	1	no	—
101	C₂×D₄	—	2	1	no	—
102	C₂×D₄	—	86	1	no	—
103	C₂×D₄	—	86	1	no	—
104	C₂×D₄	—	86	1	no	—
105	SD₁₆	—	172	4	no	—
106	SD₁₆	—	172	4	no	—
107	D₈	—	172	4	no	—
108	C₂×C₈	—	43	2	no	—
109	C₂×C₈	—	43	2	no	—
110	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
111	C₄⋊C₄	—	2	1	no	—
112	C₄⋊C₄	—	2	1	no	—
113	C₄⋊C₄	—	86	1	no	—
114	C₄⋊C₄	—	86	1	no	—
115	C₄²	C₂²×D₄₃	1	1	yes	characteristic
116	C₂³	—	4	1	no	—
117	C₂³	—	172	1	no	—
118	Q₈	—	4	2	no	—
119	Q₈	—	172	2	no	—
120	D₄	—	4	2	no	—
121	D₄	—	4	2	no	—
122	D₄	—	4	2	no	—
123	D₄	—	172	2	no	—
124	D₄	—	172	2	no	—
125	D₄	—	172	2	no	—
126	C₂×C₄	—	4	1	no	—
127	C₂×C₄	—	172	1	no	—
128	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
129	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
130	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
131	C₈	—	2	2	no	—
132	C₈	—	43	4	no	—
133	C₈	—	43	4	no	—
134	C₂²	—	8	1	no	—
135	C₂²	—	8	1	no	—
136	C₂²	—	8	1	no	—
137	C₂²	—	344	1	no	—
138	C₂²	—	344	1	no	—
139	C₂²	—	344	1	no	—
140	C₂²	#13063321	1	1	yes	characteristic
141	C₄	—	8	1	no	—
142	C₄	—	344	1	no	—
143	C₄	D₈×D₄₃	1	2	yes	—
144	C₄	SD₁₆×D₄₃	1	2	yes	—
145	C₄	#13063345	1	2	yes	—
146	C₂	—	16	1	no	—
147	C₂	—	688	1	no	—
148	C₂	#14583270	1	1	yes	characteristic
149	C₂	#14583274	1	1	yes	characteristic
150	C₂	#14583281	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583302

C₂

yes

maximal, characteristic, complemented

#14583275

C₂

yes

maximal, characteristic

#14583273

C₂

yes

maximal, characteristic, complemented

#14583271

C₂

yes

maximal, characteristic, complemented

#14583246

C₂

yes

maximal, characteristic, complemented

C₈×C₄₃⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄₃×#486

C₂

yes

maximal, characteristic, complemented

—

—

—

C₂²

yes

characteristic

#13063322

C₂²

yes

characteristic

#13063258

—

#13063247

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

#127×C₄₃

C₂²

yes

characteristic

#102×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

—

—

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂³×C₄₃

—

C₂²×D₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

D₈

yes

complemented

C₄₃⋊C₈

SD₁₆

yes

complemented

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#127

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×D₈

yes

—

C₄×C₄₃

C₂×SD₁₆

yes

—

C₄×C₄₃

#135

yes

—

Dic₄₃

—

#1706

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₈²

—

C₄₃

#1706

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

#127

—

#127

C₂×D₄₃

yes

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

105

SD₁₆

—

172

—

106

SD₁₆

—

172

—

107

D₈

—

172

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

C₂²⋊D₄₃

yes

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄²

C₂²×D₄₃

yes

characteristic

116

C₂³

—

117

C₂³

—

172

—

118

Q₈

—

119

Q₈

—

172

—

120

D₄

—

121

D₄

—

122

D₄

—

123

D₄

—

172

—

124

D₄

—

172

—

125

D₄

—

172

—

126

C₂×C₄

—

127

C₂×C₄

—

172

—

128

C₂×C₄

D₄×D₄₃

yes

characteristic

129

C₂×C₄

D₄×D₄₃

yes

characteristic

130

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

131

C₈

—

132

C₈

—

133

C₈

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

344

—

138

C₂²

—

344

—

139

C₂²

—

344

—

140

C₂²

#13063321

yes

characteristic

141

C₄

—

142

C₄

—

344

—

143

C₄

D₈×D₄₃

yes

—

144

C₄

SD₁₆×D₄₃

yes

—

145

C₄

#13063345

yes

—

146

C₂

—

147

C₂

—

688

—

148

C₂

#14583270

yes

characteristic

149

C₂

#14583274

yes

characteristic

150

C₂

#14583281

yes

characteristic

	subgroup	G/H
center	C₂²	#13063321
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#486	C₂
socle	C₂²×C₄₃	#127
hypercenter	#486	D₄₃
hypocenter	C₄₃	#1706
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #486

subgroup

G/H

center

C₂²

#13063321

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#486

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #486

N	H ≅ G/N	type
1. #14583302	C₂	semidirect
3. #14583273	C₂	semidirect
4. #14583271	C₂	semidirect
5. #14583246	C₂	semidirect
6. C₈×C₄₃⋊C₈	C₂	semidirect
7. C₄₃×#486	C₂	semidirect
56. C₄₃⋊C₈	D₈	semidirect
57. C₄₃⋊C₈	SD₁₆	semidirect
81. #486	D₄₃	semidirect
83. C₄₃	#1706	semidirect

H ≅ G/N

type

1. #14583302

C₂

semidirect

3. #14583273

C₂

semidirect

4. #14583271

C₂

semidirect

5. #14583246

C₂

semidirect

6. C₈×C₄₃⋊C₈

C₂

semidirect

7. C₄₃×#486

C₂

semidirect

56. C₄₃⋊C₈

D₈

semidirect

57. C₄₃⋊C₈

SD₁₆

semidirect

81. #486

D₄₃

semidirect

83. C₄₃

#1706

semidirect

Subgroups — #19134186

Conjugacy classes of subgroups

Complements