Group #19136808 — subgroups

Subgroups — #19136808

Order 5504.

134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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	#14583149	C₂	1	1	yes	maximal, characteristic
2	#14582946	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582723	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582722	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582712	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582680	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10621872	C₂²	1	1	yes	characteristic
9	M₁₆×D₄₃	—	2	1	no	—
10	#13063296	—	2	1	no	—
11	#13063265	C₂²	1	1	yes	characteristic
12	#13063261	C₂²	1	1	yes	characteristic
13	#13063260	—	2	1	no	—
14	#13063257	C₂²	1	1	yes	characteristic
15	#13063246	—	2	1	no	—
16	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
17	M₃₂×C₄₃	C₂²	1	1	yes	characteristic
18	#108×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×D₄×C₄₃	—	2	1	no	—
20	C₂×C₂²⋊D₄₃	—	4	1	no	—
21	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
22	D₈×C₄₃	—	2	1	no	—
23	D₈×C₄₃	—	2	1	no	—
24	M₁₆×C₄₃	—	2	1	no	—
25	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
26	C₂²⋊Dic₄₃	—	4	1	no	—
27	C₄⋊Dic₄₃	—	2	1	no	—
28	#10621877	—	2	1	no	—
29	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
30	#10621872	—	2	1	no	—
31	#10621872	—	2	1	no	—
32	#10621872	—	4	1	no	—
33	C₈×D₄₃	—	4	1	no	—
34	C₁₆×C₄₃	—	2	1	no	—
35	C₄₃⋊C₁₆	—	2	1	no	—
36	C₂³×C₄₃	—	4	1	no	—
37	C₂²×D₄₃	SD₁₆	1	1	yes	characteristic
38	D₄×C₄₃	—	4	1	no	—
39	D₄×C₄₃	—	4	1	no	—
40	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
41	C₂²⋊D₄₃	—	8	2	no	—
42	C₂×Dic₄₃	—	4	1	no	—
43	C₂×Dic₄₃	SD₁₆	1	1	yes	characteristic
44	C₄×D₄₃	—	2	1	no	—
45	C₄×D₄₃	—	2	1	no	—
46	C₈×C₄₃	—	4	1	no	—
47	C₈×C₄₃	#41	1	1	yes	characteristic
48	C₈×C₄₃	#41	1	1	yes	characteristic
49	C₄₃⋊C₈	—	2	1	no	—
50	C₄₃⋊C₈	—	4	1	no	—
51	C₂²×C₄₃	—	8	1	no	—
52	C₂²×C₄₃	—	8	1	no	—
53	C₂²×C₄₃	—	8	1	no	—
54	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
55	C₂×D₄₃	—	2	1	no	—
56	C₂×D₄₃	—	4	1	no	—
57	C₄×C₄₃	#123	1	1	yes	characteristic
58	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
59	Dic₄₃	—	2	1	no	—
60	Dic₄₃	—	8	1	no	—
61	#2238	—	43	1	no	maximal, Sylow
62	C₂×C₄₃	—	2	1	no	—
63	C₂×C₄₃	—	16	1	no	—
64	C₂×C₄₃	#481	1	1	yes	characteristic
65	D₄₃	—	4	1	no	—
66	#469	—	43	1	no	—
67	#430	—	43	1	no	—
68	#365	—	43	1	no	—
69	#365	—	43	1	no	—
70	#361	—	43	1	no	—
71	#361	D₄₃	1	1	yes	characteristic, complemented
72	#349	—	43	1	no	—
73	C₄₃	#2238	1	1	yes	characteristic, complemented, Sylow
74	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
75	C₂×M₁₆	—	43	1	no	—
76	C₂×M₁₆	—	86	1	no	—
77	#121	—	86	1	no	—
78	M₃₂	—	43	1	no	—
79	M₃₂	C₂×D₄₃	1	1	yes	characteristic
80	#108	—	43	1	no	—
81	#108	—	86	1	no	—
82	#108	C₂×D₄₃	1	1	yes	characteristic
83	#106	—	43	1	no	—
84	#102	—	86	1	no	—
85	C₂×D₄	—	2	1	no	—
86	C₂×D₄	—	172	1	no	—
87	C₂²×C₄	—	43	1	no	—
88	D₈	—	2	1	no	—
89	D₈	—	2	1	no	—
90	M₁₆	—	2	1	no	—
91	M₁₆	—	86	1	no	—
92	M₁₆	—	86	1	no	—
93	M₁₆	—	86	1	no	—
94	M₁₆	—	172	1	no	—
95	C₂×C₈	—	43	1	no	—
96	C₂×C₈	—	172	1	no	—
97	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
98	C₄⋊C₄	—	86	1	no	—
99	C₂²⋊C₄	—	172	1	no	—
100	C₁₆	—	2	1	no	—
101	C₁₆	—	86	1	no	—
102	C₂³	—	4	1	no	—
103	C₂³	—	43	1	no	—
104	D₄	—	4	1	no	—
105	D₄	—	4	1	no	—
106	D₄	—	344	2	no	—
107	C₂×C₄	—	43	1	no	—
108	C₂×C₄	—	86	1	no	—
109	C₂×C₄	—	86	1	no	—
110	C₂×C₄	—	172	1	no	—
111	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
112	C₈	—	4	1	no	—
113	C₈	—	86	1	no	—
114	C₈	—	172	1	no	—
115	C₈	#10621898	1	1	yes	characteristic
116	C₈	#10621900	1	1	yes	characteristic
117	C₂²	—	8	1	no	—
118	C₂²	—	8	1	no	—
119	C₂²	—	8	1	no	—
120	C₂²	—	86	1	no	—
121	C₂²	—	172	1	no	—
122	C₂²	SD₁₆×D₄₃	1	1	yes	characteristic
123	C₄	—	86	1	no	—
124	C₄	—	344	1	no	—
125	C₄	#13063307	1	1	yes	characteristic
126	C₄	#13063349	1	1	yes	characteristic
127	C₂	—	2	1	no	—
128	C₂	—	16	1	no	—
129	C₂	—	172	1	no	—
130	C₂	#14583216	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583149

C₂

yes

maximal, characteristic

#14582946

C₂

yes

maximal, characteristic, complemented

#14582723

C₂

yes

maximal, characteristic, complemented

#14582722

C₂

yes

maximal, characteristic, complemented

#14582712

C₂

yes

maximal, characteristic, complemented

#14582680

C₂

yes

maximal, characteristic, complemented

C₄₃×#361

C₂

yes

maximal, characteristic, complemented

C₂×#10621872

C₂²

yes

characteristic

M₁₆×D₄₃

—

#13063296

—

#13063265

C₂²

yes

characteristic

#13063261

C₂²

yes

characteristic

#13063260

—

#13063257

C₂²

yes

characteristic

#13063246

—

C₂×D₈×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

characteristic

#108×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂×C₂²⋊D₄₃

—

C₂×C₄×D₄₃

D₄

yes

characteristic

D₈×C₄₃

—

D₈×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

D₄

yes

—

—

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

C₂²×D₄₃

SD₁₆

yes

characteristic

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

SD₁₆

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#2238

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#481

yes

characteristic

D₄₃

—

—

—

—

—

—

D₄₃

yes

characteristic, complemented

#349

—

C₄₃

#2238

yes

characteristic, complemented, Sylow

C₂×D₈

C₂×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

#121

—

M₃₂

—

M₃₂

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

characteristic

#106

—

#102

—

C₂×D₄

—

C₂×D₄

—

172

—

C₂²×C₄

—

D₈

—

D₈

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

172

—

100

C₁₆

—

101

C₁₆

—

102

C₂³

—

103

C₂³

—

104

D₄

—

105

D₄

—

106

D₄

—

344

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

172

—

111

C₂×C₄

D₄×D₄₃

yes

characteristic

112

C₈

—

113

C₈

—

114

C₈

—

172

—

115

C₈

#10621898

yes

characteristic

116

C₈

#10621900

yes

characteristic

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

172

—

122

C₂²

SD₁₆×D₄₃

yes

characteristic

123

C₄

—

124

C₄

—

344

—

125

C₄

#13063307

yes

characteristic

126

C₄

#13063349

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

172

—

130

C₂

#14583216

yes

characteristic

	subgroup	G/H
center	C₂	#14583216
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#361	C₂
socle	C₂×C₄₃	#481
hypercenter	#361	D₄₃
hypocenter	C₄₃	#2238
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #361

subgroup

G/H

center

C₂

#14583216

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#361

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #361

N	H ≅ G/N	type
2. #14582946	C₂	semidirect
3. #14582723	C₂	semidirect
4. #14582722	C₂	semidirect
5. #14582712	C₂	semidirect
6. #14582680	C₂	semidirect
7. C₄₃×#361	C₂	semidirect
71. #361	D₄₃	semidirect
73. C₄₃	#2238	semidirect

H ≅ G/N

type

2. #14582946

C₂

semidirect

3. #14582723

C₂

semidirect

4. #14582722

C₂

semidirect

5. #14582712

C₂

semidirect

6. #14582680

C₂

semidirect

7. C₄₃×#361

C₂

semidirect

71. #361

D₄₃

semidirect

73. C₄₃

#2238

semidirect

Subgroups — #19136808

Conjugacy classes of subgroups

Complements