Group #19133712 — subgroups

Subgroups — #19133712

Order 5504.

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

normal subgroups only

This group has 314 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	#14583534	C₂	1	1	yes	maximal, characteristic
2	#14583271	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583190	C₂	1	2	yes	maximal, complemented
4	#14582626	C₂	1	2	yes	maximal, complemented
5	C₄₃×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×D₄₃	—	2	2	no	—
7	C₂×#10621883	—	2	2	no	—
8	#13063325	C₂²	1	1	yes	characteristic, complemented
9	#13063296	—	2	2	no	—
10	#13063293	—	2	2	no	—
11	C₄×D₁₇₂	C₂²	1	2	yes	—
12	#13063257	—	2	2	no	—
13	#13063247	—	2	2	no	—
14	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
15	#127×C₄₃	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
17	C₂³×D₄₃	—	2	2	no	—
18	C₂×D₄×C₄₃	—	2	2	no	—
19	C₂×D₄×C₄₃	D₄	1	2	yes	—
20	C₂×C₂²⋊D₄₃	—	2	4	no	—
21	D₄×D₄₃	—	4	4	no	—
22	D₄×D₄₃	—	4	4	no	—
23	C₂×D₁₇₂	D₄	1	2	yes	—
24	C₂×C₄×D₄₃	—	2	2	no	—
25	C₂×Dic₈₆	—	2	1	no	—
26	C₂×C₈×C₄₃	—	2	2	no	—
27	C₄²×C₄₃	C₂³	1	1	yes	characteristic
28	C₂²⋊Dic₄₃	—	2	2	no	—
29	#10621883	—	4	4	no	—
30	(C₂×D₄₃)⋊C₄	—	2	2	no	—
31	C₄⋊Dic₄₃	—	2	2	no	—
32	C₄⋊Dic₄₃	D₄	1	2	yes	—
33	C₂×C₄₃⋊C₈	—	2	1	no	—
34	C₂³×C₄₃	—	2	2	no	—
35	C₂²×D₄₃	—	2	2	no	—
36	C₂²×D₄₃	—	4	8	no	—
37	C₂²×D₄₃	—	8	2	no	—
38	D₄×C₄₃	—	4	2	no	—
39	D₄×C₄₃	—	4	2	no	—
40	D₄×C₄₃	—	4	2	no	—
41	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
43	C₂²⋊D₄₃	—	4	8	no	—
44	C₂×Dic₄₃	—	2	2	no	—
45	C₂×Dic₄₃	—	4	1	no	—
46	D₁₇₂	—	2	2	no	—
47	D₁₇₂	SD₁₆	1	4	yes	complemented
48	C₄×D₄₃	—	4	2	no	—
49	C₄×D₄₃	—	4	2	no	—
50	Dic₈₆	—	4	2	no	—
51	C₈×C₄₃	—	4	2	no	—
52	C₄₃⋊C₈	—	2	2	no	—
53	C₂²×C₄₃	—	4	4	no	—
54	C₂²×C₄₃	—	4	2	no	—
55	C₂²×C₄₃	#120	1	1	yes	characteristic
56	C₂×D₄₃	—	2	4	no	—
57	C₂×D₄₃	—	4	2	no	—
58	C₂×D₄₃	—	4	2	no	—
59	C₂×D₄₃	—	8	8	no	—
60	C₄×C₄₃	—	2	1	no	—
61	C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
62	C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
63	Dic₄₃	—	4	2	no	—
64	Dic₄₃	—	8	1	no	—
65	#1629	—	43	1	no	maximal, Sylow
66	C₂×C₄₃	—	8	2	no	—
67	C₂×C₄₃	#450	1	2	yes	—
68	C₂×C₄₃	#453	1	1	yes	characteristic
69	D₄₃	—	4	4	no	—
70	D₄²	—	43	1	no	—
71	#492	—	43	1	no	—
72	#476	—	43	2	no	—
73	#331	D₄₃	1	1	yes	characteristic, complemented
74	D₄⋊C₈	—	43	2	no	—
75	C₄₃	#1629	1	1	yes	characteristic, complemented, Sylow
76	C₂²×D₄	—	86	2	no	—
77	C₂×SD₁₆	—	86	2	no	—
78	C₄⋊Q₈	—	43	1	no	—
79	#127	C₂×D₄₃	1	1	yes	characteristic
80	#121	—	86	2	no	—
81	#120	—	86	2	no	—
82	C₄×D₄	—	43	2	no	—
83	#106	—	86	2	no	—
84	C₄⋊C₈	C₂×D₄₃	1	2	yes	complemented
85	#102	—	86	2	no	—
86	C₄×C₈	—	43	1	no	—
87	C₂⁴	—	86	2	no	—
88	C₂×Q₈	—	86	1	no	—
89	C₂×D₄	—	2	2	no	—
90	C₂×D₄	—	43	2	no	—
91	C₂×D₄	—	86	4	no	—
92	C₂×D₄	—	172	4	no	—
93	C₂×D₄	—	172	4	no	—
94	C₂×D₄	D₁₇₂	1	2	yes	—
95	C₂²×C₄	—	86	2	no	—
96	SD₁₆	—	172	4	no	—
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	86	1	no	—
99	C₄⋊C₄	—	43	2	no	—
100	C₄⋊C₄	—	86	2	no	—
101	C₂²⋊C₄	—	86	2	no	—
102	C₂²⋊C₄	—	86	2	no	—
103	C₄²	C₂²×D₄₃	1	1	yes	characteristic
104	C₂³	—	2	2	no	—
105	C₂³	—	86	2	no	—
106	C₂³	—	344	2	no	—
107	C₂³	—	172	8	no	—
108	Q₈	—	172	2	no	—
109	D₄	—	4	2	no	—
110	D₄	—	4	2	no	—
111	D₄	—	4	2	no	—
112	D₄	—	43	4	no	—
113	D₄	—	86	2	no	—
114	D₄	—	172	8	no	—
115	C₂×C₄	—	86	2	no	—
116	C₂×C₄	—	172	1	no	—
117	C₂×C₄	—	172	2	no	—
118	C₂×C₄	—	172	2	no	—
119	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
120	C₂×C₄	D₄×D₄₃	1	2	yes	—
121	C₈	—	4	2	no	—
122	C₈	—	86	2	no	—
123	C₂²	—	4	4	no	—
124	C₂²	—	4	2	no	—
125	C₂²	—	86	4	no	—
126	C₂²	—	344	8	no	—
127	C₂²	—	172	2	no	—
128	C₂²	—	172	2	no	—
129	C₂²	#13063295	1	1	yes	characteristic
130	C₄	—	2	1	no	—
131	C₄	—	344	1	no	—
132	C₄	—	172	2	no	—
133	C₄	SD₁₆×D₄₃	1	2	yes	—
134	C₄	#13063349	1	2	yes	—
135	C₂	—	8	2	no	—
136	C₂	—	172	4	no	—
137	C₂	#14583051	1	2	yes	—
138	C₂	#14583069	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583534

C₂

yes

maximal, characteristic

#14583271

C₂

yes

maximal, characteristic, complemented

#14583190

C₂

yes

maximal, complemented

#14582626

C₂

yes

maximal, complemented

C₄₃×#331

C₂

yes

maximal, characteristic, complemented

C₂×D₄×D₄₃

—

C₂×#10621883

—

#13063325

C₂²

yes

characteristic, complemented

#13063296

—

#13063293

—

C₄×D₁₇₂

C₂²

yes

—

#13063257

—

#13063247

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic, complemented

#127×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

complemented

C₂³×D₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

D₄

yes

—

C₂×C₂²⋊D₄₃

—

D₄×D₄₃

—

D₄×D₄₃

—

C₂×D₁₇₂

D₄

yes

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

#10621883

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

SD₁₆

yes

complemented

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#120

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×SD₁₆

yes

—

C₄×C₄₃

AGL(1,ℤ/8)

yes

—

Dic₄₃

—

Dic₄₃

—

#1629

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#450

yes

—

C₂×C₄₃

#453

yes

characteristic

D₄₃

—

D₄²

—

#492

—

#476

—

#331

D₄₃

yes

characteristic, complemented

D₄⋊C₈

—

C₄₃

#1629

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂×SD₁₆

—

C₄⋊Q₈

—

#127

C₂×D₄₃

yes

characteristic

#121

—

#120

—

C₄×D₄

—

#106

—

C₄⋊C₈

C₂×D₄₃

yes

complemented

#102

—

C₄×C₈

—

C₂⁴

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

172

—

C₂×D₄

—

172

—

C₂×D₄

D₁₇₂

yes

—

C₂²×C₄

—

SD₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₂²⋊C₄

—

102

C₂²⋊C₄

—

103

C₄²

C₂²×D₄₃

yes

characteristic

104

C₂³

—

105

C₂³

—

106

C₂³

—

344

—

107

C₂³

—

172

—

108

Q₈

—

172

—

109

D₄

—

110

D₄

—

111

D₄

—

112

D₄

—

113

D₄

—

114

D₄

—

172

—

115

C₂×C₄

—

116

C₂×C₄

—

172

—

117

C₂×C₄

—

172

—

118

C₂×C₄

—

172

—

119

C₂×C₄

C₂×D₁₇₂

yes

characteristic

120

C₂×C₄

D₄×D₄₃

yes

—

121

C₈

—

122

C₈

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

—

344

—

127

C₂²

—

172

—

128

C₂²

—

172

—

129

C₂²

#13063295

yes

characteristic

130

C₄

—

131

C₄

—

344

—

132

C₄

—

172

—

133

C₄

SD₁₆×D₄₃

yes

—

134

C₄

#13063349

yes

—

135

C₂

—

136

C₂

—

172

—

137

C₂

#14583051

yes

—

138

C₂

#14583069

yes

characteristic

	subgroup	G/H
center	C₂²	#13063295
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#331	C₂
socle	C₂²×C₄₃	#120
hypercenter	#331	D₄₃
hypocenter	C₄₃	#1629
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #331

subgroup

G/H

center

C₂²

#13063295

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#331

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #331

N	H ≅ G/N	type
2. #14583271	C₂	semidirect
3. #14583190	C₂	semidirect
4. #14582626	C₂	semidirect
5. C₄₃×#331	C₂	semidirect
8. #13063325	C₂²	semidirect
14. C₄×C₄₃⋊C₈	C₂²	semidirect
16. C₄⋊C₈×C₄₃	C₂²	semidirect
47. D₁₇₂	SD₁₆	semidirect
73. #331	D₄₃	semidirect
75. C₄₃	#1629	semidirect
84. C₄⋊C₈	C₂×D₄₃	semidirect

H ≅ G/N

type

2. #14583271

C₂

semidirect

3. #14583190

C₂

semidirect

4. #14582626

C₂

semidirect

5. C₄₃×#331

C₂

semidirect

8. #13063325

C₂²

semidirect

14. C₄×C₄₃⋊C₈

C₂²

semidirect

16. C₄⋊C₈×C₄₃

C₂²

semidirect

47. D₁₇₂

SD₁₆

semidirect

73. #331

D₄₃

semidirect

75. C₄₃

#1629

semidirect

84. C₄⋊C₈

C₂×D₄₃

semidirect

Subgroups — #19133712

Conjugacy classes of subgroups

Complements