Group #19136713 — subgroups

Subgroups — #19136713

Order 5504.

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

normal subgroups only

This group has 148 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	C₂×#13063266	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583316	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583169	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582728	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582712	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582711	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063350	—	2	1	no	—
9	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
10	#13063266	—	2	1	no	—
11	#13063266	—	2	1	no	—
12	#13063265	—	2	1	no	—
13	#13063265	C₂²	1	1	yes	characteristic
14	C₂×C₄₃⋊C₁₆	—	2	1	no	—
15	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
16	#13063261	C₂²	1	1	yes	characteristic
17	#13063241	—	2	1	no	—
18	AGL(1,ℤ/8)×C₄₃	—	2	1	no	—
19	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
20	#131×C₄₃	C₂²	1	1	yes	characteristic
21	#108×C₄₃	C₂²	1	1	yes	characteristic
22	#100×C₄₃	—	2	1	no	—
23	#41×C₄₃	D₄	1	1	yes	characteristic
24	C₂×D₄×C₄₃	—	2	1	no	—
25	C₂×D₁₇₂	—	2	1	no	—
26	SD₁₆×C₄₃	—	4	1	no	—
27	D₈×C₄₃	—	2	1	no	—
28	D₈×C₄₃	—	2	1	no	—
29	D₈×C₄₃	—	4	1	no	—
30	M₁₆×C₄₃	—	2	1	no	—
31	M₁₆×C₄₃	—	2	1	no	—
32	M₁₆×C₄₃	D₄	1	1	yes	characteristic
33	C₂×C₈×C₄₃	—	2	1	no	—
34	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
35	#10621884	—	4	1	no	—
36	#10621882	—	4	1	no	—
37	#10621877	—	2	1	no	—
38	D₃₄₄	—	2	1	no	—
39	D₃₄₄	—	2	1	no	—
40	C₄₃⋊C₁₆	—	2	1	no	—
41	C₄₃⋊C₁₆	D₄	1	1	yes	characteristic
42	C₄₃⋊C₁₆	D₄	1	1	yes	characteristic
43	C₂³×C₄₃	—	4	1	no	—
44	C₂²×D₄₃	—	4	1	no	—
45	Q₈×C₄₃	D₈	1	1	yes	characteristic
46	D₄×C₄₃	—	2	1	no	—
47	D₄×C₄₃	—	4	1	no	—
48	D₄×C₄₃	—	4	1	no	—
49	D₄×C₄₃	D₈	1	1	yes	characteristic
50	C₂×C₄×C₄₃	—	2	1	no	—
51	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
52	D₁₇₂	—	4	1	no	—
53	D₁₇₂	—	4	1	no	—
54	C₈×C₄₃	—	2	1	no	—
55	C₈×C₄₃	—	4	1	no	—
56	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
57	C₈×C₄₃	#41	1	1	yes	characteristic
58	C₄₃⋊C₈	—	4	1	no	—
59	C₂²×C₄₃	—	2	1	no	—
60	C₂²×C₄₃	—	8	1	no	—
61	C₂²×C₄₃	—	16	1	no	—
62	C₂²×C₄₃	#135	1	1	yes	characteristic
63	C₂×D₄₃	—	8	1	no	—
64	C₂×D₄₃	—	16	1	no	—
65	C₄×C₄₃	—	2	1	no	—
66	C₄×C₄₃	#121	1	1	yes	characteristic
67	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
68	#2221	—	43	1	no	maximal, Sylow
69	C₂×C₄₃	—	2	1	no	—
70	C₂×C₄₃	—	4	1	no	—
71	C₂×C₄₃	—	16	1	no	—
72	C₂×C₄₃	#466	1	1	yes	characteristic
73	D₄₃	—	16	1	no	—
74	C₂×D₁₆	—	43	1	no	—
75	#504	—	43	1	no	—
76	#472	—	43	1	no	—
77	#472	D₄₃	1	1	yes	characteristic, complemented
78	#368	—	43	1	no	—
79	#361	—	43	1	no	—
80	#361	—	43	1	no	—
81	C₄₃	#2221	1	1	yes	characteristic, complemented, Sylow
82	AGL(1,ℤ/8)	—	2	1	no	—
83	AGL(1,ℤ/8)	—	86	1	no	—
84	C₂×D₈	—	43	1	no	—
85	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
86	#131	C₂×D₄₃	1	1	yes	characteristic
87	D₁₆	—	86	1	no	—
88	D₁₆	—	86	1	no	—
89	M₃₂	—	43	1	no	—
90	M₃₂	—	86	1	no	—
91	C₂×C₁₆	—	43	1	no	—
92	C₂×C₁₆	—	86	1	no	—
93	#108	—	43	1	no	—
94	#108	C₂×D₄₃	1	1	yes	characteristic
95	#100	—	2	1	no	—
96	#100	—	86	1	no	—
97	#41	C₂²⋊D₄₃	1	1	yes	characteristic
98	C₂×D₄	—	2	1	no	—
99	C₂×D₄	—	86	1	no	—
100	SD₁₆	—	4	1	no	—
101	SD₁₆	—	172	1	no	—
102	D₈	—	2	1	no	—
103	D₈	—	2	1	no	—
104	D₈	—	4	1	no	—
105	D₈	—	86	1	no	—
106	D₈	—	86	1	no	—
107	D₈	—	172	1	no	—
108	M₁₆	—	2	1	no	—
109	M₁₆	—	2	1	no	—
110	M₁₆	—	86	1	no	—
111	M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
112	C₂×C₈	—	2	1	no	—
113	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
114	C₁₆	—	43	1	no	—
115	C₁₆	—	43	1	no	—
116	C₁₆	—	86	1	no	—
117	C₂³	—	4	1	no	—
118	C₂³	—	172	1	no	—
119	Q₈	#10621882	1	1	yes	characteristic
120	D₄	—	2	1	no	—
121	D₄	—	4	1	no	—
122	D₄	—	4	1	no	—
123	D₄	—	172	1	no	—
124	D₄	—	172	1	no	—
125	D₄	#10621882	1	1	yes	characteristic
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
128	C₈	—	2	1	no	—
129	C₈	—	4	1	no	—
130	C₈	—	172	1	no	—
131	C₈	D₄×D₄₃	1	1	yes	characteristic
132	C₈	#10621900	1	1	yes	characteristic
133	C₂²	—	2	1	no	—
134	C₂²	—	8	1	no	—
135	C₂²	—	16	1	no	—
136	C₂²	—	344	1	no	—
137	C₂²	—	688	1	no	—
138	C₂²	#13063345	1	1	yes	characteristic
139	C₄	—	2	1	no	—
140	C₄	#13063297	1	1	yes	characteristic
141	C₄	C₂×#10621882	1	1	yes	characteristic
142	C₂	—	2	1	no	—
143	C₂	—	4	1	no	—
144	C₂	—	16	1	no	—
145	C₂	—	688	1	no	—
146	C₂	#14583133	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063266

C₂

yes

maximal, characteristic, complemented

#14583316

C₂

yes

maximal, characteristic, complemented

#14583169

C₂

yes

maximal, characteristic, complemented

#14582728

C₂

yes

maximal, characteristic, complemented

#14582712

C₂

yes

maximal, characteristic, complemented

#14582711

C₂

yes

maximal, characteristic, complemented

C₄₃×#472

C₂

yes

maximal, characteristic, complemented

#13063350

—

C₂×D₃₄₄

C₂²

yes

—

—

—

C₂²

yes

characteristic

C₂×C₄₃⋊C₁₆

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063261

C₂²

yes

characteristic

#13063241

—

AGL(1,ℤ/8)×C₄₃

—

C₂×D₈×C₄₃

C₂²

yes

characteristic

#131×C₄₃

C₂²

yes

characteristic

#108×C₄₃

C₂²

yes

characteristic

#100×C₄₃

—

#41×C₄₃

D₄

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₁₇₂

—

SD₁₆×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

—

D₈×C₄₃

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

M₁₆×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

—

—

D₃₄₄

—

D₃₄₄

—

C₄₃⋊C₁₆

—

C₄₃⋊C₁₆

D₄

yes

characteristic

C₄₃⋊C₁₆

D₄

yes

characteristic

C₂³×C₄₃

—

C₂²×D₄₃

—

Q₈×C₄₃

D₈

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#135

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#121

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

#2221

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#466

yes

characteristic

D₄₃

—

C₂×D₁₆

—

#504

—

#472

—

#472

D₄₃

yes

characteristic, complemented

#368

—

#361

—

#361

—

C₄₃

#2221

yes

characteristic, complemented, Sylow

AGL(1,ℤ/8)

—

AGL(1,ℤ/8)

—

C₂×D₈

—

C₂×D₈

C₂×D₄₃

yes

characteristic

#131

C₂×D₄₃

yes

characteristic

D₁₆

—

D₁₆

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

#108

—

#108

C₂×D₄₃

yes

—

—

C₂²⋊D₄₃

yes

characteristic

C₂×D₄

—

C₂×D₄

—

100

SD₁₆

—

101

SD₁₆

—

172

—

102

D₈

—

103

D₈

—

104

D₈

—

105

D₈

—

106

D₈

—

107

D₈

—

172

—

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

M₁₆

C₂²⋊D₄₃

yes

characteristic

112

C₂×C₈

—

113

C₂×C₈

C₂²×D₄₃

yes

characteristic

114

C₁₆

—

115

C₁₆

—

116

C₁₆

—

117

C₂³

—

118

C₂³

—

172

—

119

Q₈

#10621882

yes

characteristic

120

D₄

—

121

D₄

—

122

D₄

—

123

D₄

—

172

—

124

D₄

—

172

—

125

D₄

#10621882

yes

characteristic

126

C₂×C₄

—

127

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

128

C₈

—

129

C₈

—

130

C₈

—

172

—

131

C₈

D₄×D₄₃

yes

characteristic

132

C₈

#10621900

yes

characteristic

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

344

—

137

C₂²

—

688

—

138

C₂²

#13063345

yes

characteristic

139

C₄

—

140

C₄

#13063297

yes

characteristic

141

C₄

C₂×#10621882

yes

characteristic

142

C₂

—

143

C₂

—

144

C₂

—

145

C₂

—

688

—

146

C₂

#14583133

yes

characteristic

	subgroup	G/H
center	C₂	#14583133
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#472	C₂
socle	C₂×C₄₃	#466
hypercenter	#472	D₄₃
hypocenter	C₄₃	#2221
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #472

subgroup

G/H

center

C₂

#14583133

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#472

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #472

N	H ≅ G/N	type
1. C₂×#13063266	C₂	semidirect
2. #14583316	C₂	semidirect
3. #14583169	C₂	semidirect
4. #14582728	C₂	semidirect
5. #14582712	C₂	semidirect
6. #14582711	C₂	semidirect
7. C₄₃×#472	C₂	semidirect
77. #472	D₄₃	semidirect
81. C₄₃	#2221	semidirect

H ≅ G/N

type

1. C₂×#13063266

C₂

semidirect

2. #14583316

C₂

semidirect

3. #14583169

C₂

semidirect

4. #14582728

C₂

semidirect

5. #14582712

C₂

semidirect

6. #14582711

C₂

semidirect

7. C₄₃×#472

C₂

semidirect

77. #472

D₄₃

semidirect

81. C₄₃

#2221

semidirect

Subgroups — #19136713

Conjugacy classes of subgroups

Complements