Group #19134237 — subgroups

Subgroups — #19134237

Order 5504.

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

normal subgroups only

This group has 208 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	#14583276	C₂	1	1	yes	maximal, characteristic
2	#14583273	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583247	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583247	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583247	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582621	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621884	—	2	2	no	—
9	C₂×D₃₄₄	—	2	2	no	—
10	#13063322	C₂²	1	1	yes	characteristic
11	#13063322	C₂²	1	1	yes	characteristic
12	#13063245	—	2	2	no	—
13	#13063245	—	2	2	no	—
14	#13063245	—	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	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	#103×C₄₃	—	2	2	no	—
20	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₄₃	—	2	1	no	—
22	C₂×Q₈×C₄₃	—	2	1	no	—
23	C₂×D₁₇₂	—	2	1	no	—
24	C₂×D₁₇₂	—	2	1	no	—
25	C₂×D₁₇₂	—	2	1	no	—
26	C₂×D₁₇₂	—	2	1	no	—
27	C₂×D₁₇₂	—	2	1	no	—
28	C₂×D₁₇₂	—	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	C₄⋊C₄×C₄₃	—	2	1	no	—
33	C₄⋊C₄×C₄₃	—	2	1	no	—
34	C₄²×C₄₃	C₂³	1	1	yes	characteristic
35	#10621884	—	4	4	no	—
36	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
37	C₂×C₄₃⋊C₈	D₄	1	2	yes	—
38	D₃₄₄	—	4	4	no	—
39	C₂²×D₄₃	—	4	1	no	—
40	C₂²×D₄₃	—	4	1	no	—
41	Q₈×C₄₃	—	4	2	no	—
42	Q₈×C₄₃	—	4	2	no	—
43	C₂×C₄×C₄₃	—	4	1	no	—
44	C₂×C₄×C₄₃	—	4	1	no	—
45	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	D₁₇₂	—	4	2	no	—
49	D₁₇₂	—	4	2	no	—
50	D₁₇₂	—	4	2	no	—
51	D₁₇₂	—	4	2	no	—
52	D₁₇₂	—	4	2	no	—
53	D₁₇₂	—	4	2	no	—
54	C₈×C₄₃	—	2	2	no	—
55	C₄₃⋊C₈	—	2	2	no	—
56	C₄₃⋊C₈	—	2	2	no	—
57	C₂²×C₄₃	#127	1	1	yes	characteristic
58	C₂×D₄₃	—	8	1	no	—
59	C₂×D₄₃	—	8	1	no	—
60	C₂×D₄₃	—	8	1	no	—
61	C₂×D₄₃	—	8	1	no	—
62	C₂×D₄₃	—	8	1	no	—
63	C₂×D₄₃	—	8	1	no	—
64	C₄×C₄₃	—	8	1	no	—
65	C₄×C₄₃	—	8	1	no	—
66	C₄×C₄₃	#135	1	2	yes	—
67	C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
68	C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
69	#1717	—	43	1	no	maximal, Sylow
70	C₂×C₄₃	#495	1	1	yes	characteristic
71	C₂×C₄₃	#496	1	1	yes	characteristic
72	C₂×C₄₃	#496	1	1	yes	characteristic
73	D₄₃	—	16	1	no	—
74	D₄₃	—	16	1	no	—
75	#493	—	43	1	no	—
76	#492	—	43	1	no	—
77	#487	D₄₃	1	1	yes	characteristic, complemented
78	#486	—	43	1	no	—
79	#486	—	43	1	no	—
80	#486	—	43	1	no	—
81	#322	—	43	1	no	—
82	C₄₃	#1717	1	1	yes	characteristic, complemented, Sylow
83	C₂×SD₁₆	—	86	2	no	—
84	C₂×D₈	—	86	2	no	—
85	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
86	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
87	#127	—	43	1	no	—
88	#127	—	43	1	no	—
89	#103	—	2	2	no	—
90	#102	—	86	2	no	—
91	#102	—	86	2	no	—
92	#102	—	86	2	no	—
93	C₄×C₈	—	43	1	no	—
94	C₄×C₈	—	43	1	no	—
95	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
96	C₂×Q₈	—	2	1	no	—
97	C₂×Q₈	—	2	1	no	—
98	C₂×D₄	—	86	1	no	—
99	C₂×D₄	—	86	1	no	—
100	C₂×D₄	—	86	1	no	—
101	C₂×D₄	—	86	1	no	—
102	C₂×D₄	—	86	1	no	—
103	C₂×D₄	—	86	1	no	—
104	SD₁₆	—	172	4	no	—
105	D₈	—	172	4	no	—
106	C₂×C₈	—	43	2	no	—
107	C₂×C₈	—	43	2	no	—
108	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
109	C₄⋊C₄	—	2	1	no	—
110	C₄⋊C₄	—	2	1	no	—
111	C₄⋊C₄	—	2	1	no	—
112	C₄⋊C₄	—	2	1	no	—
113	C₄²	C₂²×D₄₃	1	1	yes	characteristic
114	C₂³	—	172	1	no	—
115	C₂³	—	172	1	no	—
116	Q₈	—	4	2	no	—
117	Q₈	—	4	2	no	—
118	D₄	—	172	2	no	—
119	D₄	—	172	2	no	—
120	D₄	—	172	2	no	—
121	D₄	—	172	2	no	—
122	D₄	—	172	2	no	—
123	D₄	—	172	2	no	—
124	C₂×C₄	—	4	1	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
127	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
128	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
129	C₈	—	2	2	no	—
130	C₈	—	86	2	no	—
131	C₈	—	86	2	no	—
132	C₂²	—	344	1	no	—
133	C₂²	—	344	1	no	—
134	C₂²	—	344	1	no	—
135	C₂²	—	344	1	no	—
136	C₂²	—	344	1	no	—
137	C₂²	—	344	1	no	—
138	C₂²	#13063321	1	1	yes	characteristic
139	C₄	—	8	1	no	—
140	C₄	—	8	1	no	—
141	C₄	#13063348	1	2	yes	—
142	C₄	#13063350	1	2	yes	—
143	C₄	#13063352	1	2	yes	—
144	C₂	—	688	1	no	—
145	C₂	—	688	1	no	—
146	C₂	#14583284	1	1	yes	characteristic
147	C₂	#14583285	1	1	yes	characteristic
148	C₂	#14583289	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583276

C₂

yes

maximal, characteristic

#14583273

C₂

yes

maximal, characteristic, complemented

#14583247

C₂

yes

maximal, characteristic, complemented

#14583247

C₂

yes

maximal, characteristic, complemented

#14583247

C₂

yes

maximal, characteristic, complemented

#14582621

C₂

yes

maximal, characteristic, complemented

C₄₃×#487

C₂

yes

maximal, characteristic, complemented

C₂×#10621884

—

C₂×D₃₄₄

—

#13063322

C₂²

yes

characteristic

#13063322

C₂²

yes

—

—

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

#103×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₈×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

#10621884

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂×C₄₃⋊C₈

D₄

yes

—

D₃₄₄

—

C₂²×D₄₃

—

C₂²×D₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×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

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

#127

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#135

yes

—

C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₄×C₄₃

AGL(1,ℤ/8)

yes

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

D₄₃

—

#493

—

#492

—

#487

D₄₃

yes

characteristic, complemented

—

—

—

—

C₄₃

#1717

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

C₂×D₄₃

yes

—

—

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂×D₄

—

104

SD₁₆

—

172

—

105

D₈

—

172

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

C₂²⋊D₄₃

yes

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄²

C₂²×D₄₃

yes

characteristic

114

C₂³

—

172

—

115

C₂³

—

172

—

116

Q₈

—

117

Q₈

—

118

D₄

—

172

—

119

D₄

—

172

—

120

D₄

—

172

—

121

D₄

—

172

—

122

D₄

—

172

—

123

D₄

—

172

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

D₄×D₄₃

yes

characteristic

127

C₂×C₄

D₄×D₄₃

yes

characteristic

128

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

129

C₈

—

130

C₈

—

131

C₈

—

132

C₂²

—

344

—

133

C₂²

—

344

—

134

C₂²

—

344

—

135

C₂²

—

344

—

136

C₂²

—

344

—

137

C₂²

—

344

—

138

C₂²

#13063321

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

#13063348

yes

—

142

C₄

#13063350

yes

—

143

C₄

#13063352

yes

—

144

C₂

—

688

—

145

C₂

—

688

—

146

C₂

#14583284

yes

characteristic

147

C₂

#14583285

yes

characteristic

148

C₂

#14583289

yes

characteristic

	subgroup	G/H
center	C₂²	#13063321
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#487	C₂
socle	C₂²×C₄₃	#127
hypercenter	#487	D₄₃
hypocenter	C₄₃	#1717
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #487

subgroup

G/H

center

C₂²

#13063321

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#487

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #487

N	H ≅ G/N	type
2. #14583273	C₂	semidirect
3. #14583247	C₂	semidirect
4. #14583247	C₂	semidirect
5. #14583247	C₂	semidirect
6. #14582621	C₂	semidirect
7. C₄₃×#487	C₂	semidirect
77. #487	D₄₃	semidirect
82. C₄₃	#1717	semidirect

H ≅ G/N

type

2. #14583273

C₂

semidirect

3. #14583247

C₂

semidirect

4. #14583247

C₂

semidirect

5. #14583247

C₂

semidirect

6. #14582621

C₂

semidirect

7. C₄₃×#487

C₂

semidirect

77. #487

D₄₃

semidirect

82. C₄₃

#1717

semidirect

Subgroups — #19134237

Conjugacy classes of subgroups

Complements