Group #19136495 — subgroups

Subgroups — #19136495

Order 5504.

154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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	#14583337	C₂	1	1	yes	maximal, characteristic
2	#14583022	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583012	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582722	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582713	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582710	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#347	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063347	C₂²	1	1	yes	characteristic
9	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
10	#13063331	—	2	1	no	—
11	C₄×D₁₇₂	—	2	1	no	—
12	#13063270	C₄	1	2	yes	complemented
13	D₆₈₈	C₄	1	2	yes	complemented
14	#13063261	C₂²	1	1	yes	characteristic
15	#13063257	C₂²	1	1	yes	characteristic
16	#13063253	—	2	1	no	—
17	#13063247	—	2	1	no	—
18	M₃₂×C₄₃	C₂²	1	1	yes	characteristic
19	M₃₂×C₄₃	C₂²	1	1	yes	characteristic
20	#97×C₄₃	C₂²	1	1	yes	characteristic
21	#10621898	—	2	1	no	—
22	C₂×D₁₇₂	—	2	1	no	—
23	C₂×C₄×D₄₃	—	4	1	no	—
24	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
25	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
26	C₄²×C₄₃	D₄	1	1	yes	characteristic
27	(C₂×D₄₃)⋊C₄	—	4	1	no	—
28	C₄⋊Dic₄₃	—	2	1	no	—
29	#10621877	—	2	1	no	—
30	Dic₁₇₂	C₂×C₄	1	1	yes	characteristic, complemented
31	D₃₄₄	—	2	1	no	—
32	D₃₄₄	C₂×C₄	1	2	yes	—
33	D₃₄₄	C₂×C₄	1	1	yes	characteristic, complemented
34	#10621873	—	2	1	no	—
35	#10621872	—	4	1	no	—
36	C₈×D₄₃	—	4	1	no	—
37	C₁₆×C₄₃	—	2	1	no	—
38	C₁₆×C₄₃	C₂×C₄	1	2	yes	complemented
39	C₂²×D₄₃	—	4	1	no	—
40	C₂×C₄×C₄₃	—	2	1	no	—
41	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂²⋊D₄₃	—	4	1	no	—
43	C₂×Dic₄₃	—	4	1	no	—
44	D₁₇₂	—	2	1	no	—
45	D₁₇₂	—	2	2	no	—
46	D₁₇₂	—	4	1	no	—
47	C₄×D₄₃	—	4	1	no	—
48	C₄×D₄₃	—	8	2	no	—
49	Dic₈₆	—	2	1	no	—
50	C₈×C₄₃	—	2	1	no	—
51	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
52	C₈×C₄₃	#41	1	1	yes	characteristic
53	C₄₃⋊C₈	—	4	1	no	—
54	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
55	C₂×D₄₃	—	4	2	no	—
56	C₂×D₄₃	—	4	1	no	—
57	C₂×D₄₃	—	8	1	no	—
58	C₂×D₄₃	—	8	1	no	—
59	C₄×C₄₃	—	4	1	no	—
60	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
61	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
62	Dic₄₃	—	4	1	no	—
63	Dic₄₃	—	8	1	no	—
64	AGL(1,ℤ/16)	—	43	1	no	maximal, Sylow
65	C₂×C₄₃	—	2	1	no	—
66	C₂×C₄₃	#442	1	1	yes	characteristic
67	D₄₃	—	8	1	no	—
68	D₄₃	—	8	2	no	—
69	#509	—	43	1	no	—
70	#444	—	43	1	no	—
71	#442	—	43	1	no	—
72	#365	—	43	1	no	—
73	#361	—	43	1	no	—
74	#360	—	43	1	no	—
75	#347	D₄₃	1	1	yes	characteristic, complemented
76	C₄₃	AGL(1,ℤ/16)	1	1	yes	characteristic, complemented, Sylow
77	#135	—	43	1	no	—
78	C₂×D₈	—	43	1	no	—
79	#131	—	86	1	no	—
80	C₄×D₄	—	86	1	no	—
81	SD₃₂	—	43	2	no	—
82	D₁₆	—	43	2	no	—
83	M₃₂	C₂×D₄₃	1	1	yes	characteristic
84	M₃₂	C₂×D₄₃	1	1	yes	characteristic
85	#108	—	43	1	no	—
86	#106	—	43	1	no	—
87	#104	—	86	1	no	—
88	#102	—	86	1	no	—
89	#97	C₂×D₄₃	1	1	yes	characteristic
90	#41	—	86	1	no	—
91	C₂×D₄	—	86	1	no	—
92	C₂²×C₄	—	172	1	no	—
93	Q₁₆	—	43	1	no	—
94	SD₁₆	—	86	1	no	—
95	D₈	—	43	1	no	—
96	D₈	—	43	2	no	—
97	D₈	—	86	1	no	—
98	M₁₆	—	86	1	no	—
99	M₁₆	—	172	1	no	—
100	C₂×C₈	—	172	1	no	—
101	C₂×C₈	D₁₇₂	1	1	yes	characteristic
102	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
103	C₄⋊C₄	—	86	1	no	—
104	C₂²⋊C₄	—	172	1	no	—
105	C₄²	D₁₇₂	1	1	yes	characteristic
106	C₁₆	—	2	1	no	—
107	C₁₆	C₄×D₄₃	1	2	yes	complemented
108	C₂³	—	172	1	no	—
109	Q₈	—	86	1	no	—
110	D₄	—	86	2	no	—
111	D₄	—	86	1	no	—
112	D₄	—	172	1	no	—
113	D₄	—	172	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	344	2	no	—
116	C₂×C₄	—	172	1	no	—
117	C₂×C₄	—	172	1	no	—
118	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
119	C₈	—	2	1	no	—
120	C₈	—	172	1	no	—
121	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
122	C₈	#10621898	1	1	yes	characteristic
123	C₂²	—	344	1	no	—
124	C₂²	—	344	1	no	—
125	C₂²	—	172	1	no	—
126	C₂²	—	172	2	no	—
127	C₂²	#13063353	1	1	yes	characteristic
128	C₄	—	4	1	no	—
129	C₄	—	344	1	no	—
130	C₄	—	172	1	no	—
131	C₄	C₄×D₁₇₂	1	1	yes	characteristic
132	C₄	#13063353	1	1	yes	characteristic
133	C₂	—	2	1	no	—
134	C₂	—	344	2	no	—
135	C₂	—	344	1	no	—
136	C₂	#14583012	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583337

C₂

yes

maximal, characteristic

#14583022

C₂

yes

maximal, characteristic, complemented

#14583012

C₂

yes

maximal, characteristic, complemented

#14582722

C₂

yes

maximal, characteristic, complemented

#14582713

C₂

yes

maximal, characteristic, complemented

#14582710

C₂

yes

maximal, characteristic, complemented

C₄₃×#347

C₂

yes

maximal, characteristic, complemented

#13063347

C₂²

yes

characteristic

C₂×D₃₄₄

C₂²

yes

characteristic

#13063331

—

C₄×D₁₇₂

—

#13063270

C₄

yes

complemented

D₆₈₈

C₄

yes

complemented

#13063261

C₂²

yes

characteristic

#13063257

C₂²

yes

characteristic

#13063253

—

#13063247

—

M₃₂×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₂²

yes

characteristic

#10621898

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

#10621877

—

Dic₁₇₂

C₂×C₄

yes

characteristic, complemented

D₃₄₄

—

D₃₄₄

C₂×C₄

yes

—

D₃₄₄

C₂×C₄

yes

characteristic, complemented

#10621873

—

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₁₆×C₄₃

C₂×C₄

yes

complemented

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

AGL(1,ℤ/8)

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

Dic₄₃

—

Dic₄₃

—

AGL(1,ℤ/16)

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#442

yes

characteristic

D₄₃

—

D₄₃

—

—

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

AGL(1,ℤ/16)

yes

characteristic, complemented, Sylow

#135

—

C₂×D₈

—

#131

—

C₄×D₄

—

SD₃₂

—

D₁₆

—

M₃₂

C₂×D₄₃

yes

characteristic

M₃₂

C₂×D₄₃

yes

—

—

—

—

C₂×D₄₃

yes

characteristic

#41

—

C₂×D₄

—

C₂²×C₄

—

172

—

Q₁₆

—

SD₁₆

—

D₈

—

D₈

—

D₈

—

M₁₆

—

M₁₆

—

172

—

100

C₂×C₈

—

172

—

101

C₂×C₈

D₁₇₂

yes

characteristic

102

C₂×C₈

C₂²×D₄₃

yes

characteristic

103

C₄⋊C₄

—

104

C₂²⋊C₄

—

172

—

105

C₄²

D₁₇₂

yes

characteristic

106

C₁₆

—

107

C₁₆

C₄×D₄₃

yes

complemented

108

C₂³

—

172

—

109

Q₈

—

110

D₄

—

111

D₄

—

112

D₄

—

172

—

113

D₄

—

172

—

114

C₂×C₄

—

115

C₂×C₄

—

344

—

116

C₂×C₄

—

172

—

117

C₂×C₄

—

172

—

118

C₂×C₄

C₂×D₁₇₂

yes

characteristic

119

C₈

—

120

C₈

—

172

—

121

C₈

C₂×C₄×D₄₃

yes

characteristic

122

C₈

#10621898

yes

characteristic

123

C₂²

—

344

—

124

C₂²

—

344

—

125

C₂²

—

172

—

126

C₂²

—

172

—

127

C₂²

#13063353

yes

characteristic

128

C₄

—

129

C₄

—

344

—

130

C₄

—

172

—

131

C₄

C₄×D₁₇₂

yes

characteristic

132

C₄

#13063353

yes

characteristic

133

C₂

—

134

C₂

—

344

—

135

C₂

—

344

—

136

C₂

#14583012

yes

characteristic

	subgroup	G/H
center	C₂	#14583012
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#347	C₂
socle	C₂×C₄₃	#442
hypercenter	#347	D₄₃
hypocenter	C₄₃	AGL(1,ℤ/16)
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #347

subgroup

G/H

center

C₂

#14583012

commutator

C₈×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#347

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #347

N	H ≅ G/N	type
2. #14583022	C₂	semidirect
3. #14583012	C₂	semidirect
4. #14582722	C₂	semidirect
5. #14582713	C₂	semidirect
6. #14582710	C₂	semidirect
7. C₄₃×#347	C₂	semidirect
12. #13063270	C₄	semidirect
13. D₆₈₈	C₄	semidirect
30. Dic₁₇₂	C₂×C₄	semidirect
33. D₃₄₄	C₂×C₄	semidirect
38. C₁₆×C₄₃	C₂×C₄	semidirect
75. #347	D₄₃	semidirect
76. C₄₃	AGL(1,ℤ/16)	semidirect
107. C₁₆	C₄×D₄₃	semidirect

H ≅ G/N

type

2. #14583022

C₂

semidirect

3. #14583012

C₂

semidirect

4. #14582722

C₂

semidirect

5. #14582713

C₂

semidirect

6. #14582710

C₂

semidirect

7. C₄₃×#347

C₂

semidirect

12. #13063270

C₄

semidirect

13. D₆₈₈

C₄

semidirect

30. Dic₁₇₂

C₂×C₄

semidirect

33. D₃₄₄

C₂×C₄

semidirect

38. C₁₆×C₄₃

C₂×C₄

semidirect

75. #347

D₄₃

semidirect

76. C₄₃

AGL(1,ℤ/16)

semidirect

107. C₁₆

C₄×D₄₃

semidirect

Subgroups — #19136495

Conjugacy classes of subgroups

Complements