Group #19136665 — subgroups

Subgroups — #19136665

Order 5504.

154 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14583342	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583337	C₂	1	1	yes	maximal, characteristic
3	#14583283	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583017	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582716	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582713	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#364	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063347	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
10	C₂×#10621873	—	2	1	no	—
11	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
12	#13063331	—	2	1	no	—
13	#13063313	—	2	1	no	—
14	Dic₃₄₄	—	2	1	no	—
15	#13063270	—	2	1	no	—
16	#13063270	—	2	1	no	—
17	D₆₈₈	—	2	1	no	—
18	#13063261	C₂²	1	1	yes	characteristic
19	#13063253	—	2	1	no	—
20	M₃₂×C₄₃	C₂²	1	1	yes	characteristic
21	M₃₂×C₄₃	C₂²	1	1	yes	characteristic
22	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
23	#10621898	—	2	1	no	—
24	C₂×D₁₇₂	—	2	1	no	—
25	C₂×Dic₈₆	—	2	1	no	—
26	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
27	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
28	C₄²×C₄₃	D₄	1	1	yes	characteristic
29	(C₂×D₄₃)⋊C₄	—	4	2	no	—
30	#10621877	—	2	1	no	—
31	Dic₁₇₂	—	2	1	no	—
32	Dic₁₇₂	—	2	1	no	—
33	Dic₁₇₂	D₄	1	1	yes	characteristic
34	D₃₄₄	—	2	1	no	—
35	D₃₄₄	—	2	1	no	—
36	D₃₄₄	D₄	1	1	yes	characteristic
37	#10621873	—	2	1	no	—
38	#10621873	—	4	1	no	—
39	#10621873	—	4	1	no	—
40	#10621872	—	4	1	no	—
41	C₈×D₄₃	—	4	1	no	—
42	C₁₆×C₄₃	—	2	1	no	—
43	C₁₆×C₄₃	—	2	1	no	—
44	C₂²×D₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	—	2	1	no	—
46	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂²⋊D₄₃	—	4	1	no	—
48	C₂×Dic₄₃	—	4	1	no	—
49	D₁₇₂	—	2	1	no	—
50	D₁₇₂	—	4	1	no	—
51	D₁₇₂	—	4	1	no	—
52	C₄×D₄₃	—	4	1	no	—
53	Dic₈₆	—	2	1	no	—
54	Dic₈₆	—	4	1	no	—
55	Dic₈₆	—	4	1	no	—
56	C₈×C₄₃	D₈	1	1	yes	characteristic
57	C₈×C₄₃	D₈	1	1	yes	characteristic
58	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
59	C₈×C₄₃	#41	1	1	yes	characteristic
60	C₄₃⋊C₈	—	4	1	no	—
61	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
62	C₂×D₄₃	—	4	1	no	—
63	C₂×D₄₃	—	8	2	no	—
64	C₂×D₄₃	—	8	1	no	—
65	C₄×C₄₃	—	4	1	no	—
66	C₄×C₄₃	#121	1	1	yes	characteristic
67	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
68	Dic₄₃	—	4	1	no	—
69	Dic₄₃	—	8	1	no	—
70	#2212	—	43	1	no	maximal, Sylow
71	C₂×C₄₃	—	2	1	no	—
72	C₂×C₄₃	#459	1	1	yes	characteristic
73	D₄₃	—	8	1	no	—
74	D₄₃	—	16	1	no	—
75	#510	—	43	1	no	—
76	#509	—	43	1	no	—
77	#495	—	43	1	no	—
78	#443	—	43	1	no	—
79	#364	D₄₃	1	1	yes	characteristic, complemented
80	#362	—	43	1	no	—
81	#361	—	43	1	no	—
82	C₄₃	#2212	1	1	yes	characteristic, complemented, Sylow
83	#135	—	43	1	no	—
84	C₂×Q₁₆	—	43	1	no	—
85	C₂×SD₁₆	—	86	1	no	—
86	C₂×D₈	—	43	1	no	—
87	#131	—	86	1	no	—
88	#124	—	86	1	no	—
89	Q₃₂	—	86	1	no	—
90	SD₃₂	—	86	1	no	—
91	SD₃₂	—	86	1	no	—
92	D₁₆	—	86	1	no	—
93	M₃₂	C₂×D₄₃	1	1	yes	characteristic
94	M₃₂	C₂×D₄₃	1	1	yes	characteristic
95	#108	—	43	1	no	—
96	#104	—	86	1	no	—
97	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
98	#41	—	86	1	no	—
99	C₂×Q₈	—	86	1	no	—
100	C₂×D₄	—	86	1	no	—
101	Q₁₆	—	43	1	no	—
102	Q₁₆	—	86	1	no	—
103	Q₁₆	—	86	1	no	—
104	SD₁₆	—	86	1	no	—
105	SD₁₆	—	172	1	no	—
106	SD₁₆	—	172	1	no	—
107	D₈	—	43	1	no	—
108	D₈	—	86	1	no	—
109	D₈	—	86	1	no	—
110	M₁₆	—	86	1	no	—
111	M₁₆	—	172	1	no	—
112	C₂×C₈	—	172	1	no	—
113	C₂×C₈	D₁₇₂	1	1	yes	characteristic
114	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
115	C₂²⋊C₄	—	172	2	no	—
116	C₄²	D₁₇₂	1	1	yes	characteristic
117	C₁₆	—	2	1	no	—
118	C₁₆	—	2	1	no	—
119	C₂³	—	172	1	no	—
120	Q₈	—	86	1	no	—
121	Q₈	—	172	1	no	—
122	Q₈	—	172	1	no	—
123	D₄	—	86	1	no	—
124	D₄	—	172	1	no	—
125	D₄	—	172	1	no	—
126	D₄	—	172	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	172	1	no	—
129	C₂×C₄	—	172	1	no	—
130	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
131	C₈	—	172	1	no	—
132	C₈	D₃₄₄	1	1	yes	characteristic
133	C₈	D₃₄₄	1	1	yes	characteristic
134	C₈	D₄×D₄₃	1	1	yes	characteristic
135	C₈	#10621902	1	1	yes	characteristic
136	C₂²	—	344	2	no	—
137	C₂²	—	344	1	no	—
138	C₂²	—	172	1	no	—
139	C₂²	#13063353	1	1	yes	characteristic
140	C₄	—	4	1	no	—
141	C₄	—	344	1	no	—
142	C₄	—	172	1	no	—
143	C₄	#13063300	1	1	yes	characteristic
144	C₄	C₂×D₃₄₄	1	1	yes	characteristic
145	C₂	—	2	1	no	—
146	C₂	—	344	1	no	—
147	C₂	—	688	1	no	—
148	C₂	#14583095	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583342

C₂

yes

maximal, characteristic, complemented

#14583337

C₂

yes

maximal, characteristic

#14583283

C₂

yes

maximal, characteristic, complemented

#14583017

C₂

yes

maximal, characteristic, complemented

#14582716

C₂

yes

maximal, characteristic, complemented

#14582713

C₂

yes

maximal, characteristic, complemented

C₄₃×#364

C₂

yes

maximal, characteristic, complemented

#13063347

C₂²

yes

characteristic

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₂×#10621873

—

C₂×D₃₄₄

C₂²

yes

characteristic

#13063331

—

#13063313

—

Dic₃₄₄

—

#13063270

—

#13063270

—

D₆₈₈

—

#13063261

C₂²

yes

characteristic

#13063253

—

M₃₂×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

#10621898

—

C₂×D₁₇₂

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

(C₂×D₄₃)⋊C₄

—

#10621877

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

D₄

yes

characteristic

D₃₄₄

—

D₃₄₄

—

D₃₄₄

D₄

yes

—

—

—

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₁₆×C₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

D₈

yes

characteristic

C₈×C₄₃

D₈

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

AGL(1,ℤ/8)

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#121

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#2212

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#459

yes

characteristic

D₄₃

—

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

#362

—

#361

—

C₄₃

#2212

yes

characteristic, complemented, Sylow

#135

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

#131

—

#124

—

Q₃₂

—

SD₃₂

—

SD₃₂

—

D₁₆

—

M₃₂

C₂×D₄₃

yes

characteristic

M₃₂

C₂×D₄₃

yes

characteristic

#108

—

#104

—

C₄×C₈

C₂×D₄₃

yes

characteristic

#41

—

C₂×Q₈

—

100

C₂×D₄

—

101

Q₁₆

—

102

Q₁₆

—

103

Q₁₆

—

104

SD₁₆

—

105

SD₁₆

—

172

—

106

SD₁₆

—

172

—

107

D₈

—

108

D₈

—

109

D₈

—

110

M₁₆

—

111

M₁₆

—

172

—

112

C₂×C₈

—

172

—

113

C₂×C₈

D₁₇₂

yes

characteristic

114

C₂×C₈

C₂²×D₄₃

yes

characteristic

115

C₂²⋊C₄

—

172

—

116

C₄²

D₁₇₂

yes

characteristic

117

C₁₆

—

118

C₁₆

—

119

C₂³

—

172

—

120

Q₈

—

121

Q₈

—

172

—

122

Q₈

—

172

—

123

D₄

—

124

D₄

—

172

—

125

D₄

—

172

—

126

D₄

—

172

—

127

C₂×C₄

—

128

C₂×C₄

—

172

—

129

C₂×C₄

—

172

—

130

C₂×C₄

C₂×D₁₇₂

yes

characteristic

131

C₈

—

172

—

132

C₈

D₃₄₄

yes

characteristic

133

C₈

D₃₄₄

yes

characteristic

134

C₈

D₄×D₄₃

yes

characteristic

135

C₈

#10621902

yes

characteristic

136

C₂²

—

344

—

137

C₂²

—

344

—

138

C₂²

—

172

—

139

C₂²

#13063353

yes

characteristic

140

C₄

—

141

C₄

—

344

—

142

C₄

—

172

—

143

C₄

#13063300

yes

characteristic

144

C₄

C₂×D₃₄₄

yes

characteristic

145

C₂

—

146

C₂

—

344

—

147

C₂

—

688

—

148

C₂

#14583095

yes

characteristic

	subgroup	G/H
center	C₂	#14583095
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#364	C₂
socle	C₂×C₄₃	#459
hypercenter	#364	D₄₃
hypocenter	C₄₃	#2212
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

subgroup

G/H

center

C₂

#14583095

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#364

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

N	H ≅ G/N	type
1. #14583342	C₂	semidirect
3. #14583283	C₂	semidirect
4. #14583017	C₂	semidirect
5. #14582716	C₂	semidirect
6. #14582713	C₂	semidirect
7. C₄₃×#364	C₂	semidirect
79. #364	D₄₃	semidirect
82. C₄₃	#2212	semidirect

H ≅ G/N

type

1. #14583342

C₂

semidirect

3. #14583283

C₂

semidirect

4. #14583017

C₂

semidirect

5. #14582716

C₂

semidirect

6. #14582713

C₂

semidirect

7. C₄₃×#364

C₂

semidirect

79. #364

D₄₃

semidirect

82. C₄₃

#2212

semidirect

Subgroups — #19136665

Conjugacy classes of subgroups

Complements