Group #19133652 — subgroups

Subgroups — #19133652

Order 5504.

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

normal subgroups only

This group has 240 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	#14583635	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583096	C₂	1	2	yes	maximal, complemented
3	#14582643	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582631	C₂	1	2	yes	maximal, complemented
5	C₄₃×#493	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621883	—	2	2	no	—
7	#13063312	—	2	2	no	—
8	#13063306	—	2	2	no	—
9	C₄×Dic₈₆	C₂²	1	2	yes	—
10	D₄×Dic₄₃	—	2	2	no	—
11	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
12	#13063246	—	2	2	no	—
13	C₂×D₈×C₄₃	—	2	2	no	—
14	#127×C₄₃	C₂²	1	1	yes	characteristic
15	#127×C₄₃	C₂²	1	1	yes	characteristic
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×D₄×C₄₃	—	2	2	no	—
18	C₂×D₄×C₄₃	—	2	1	no	—
19	C₂×D₄×C₄₃	—	2	2	no	—
20	C₂×D₄×C₄₃	D₄	1	2	yes	—
21	C₂²×Dic₄₃	—	2	2	no	—
22	C₂×Dic₈₆	D₄	1	2	yes	—
23	D₈×C₄₃	—	4	4	no	—
24	C₂×C₈×C₄₃	—	2	1	no	—
25	C₄²×C₄₃	C₂³	1	1	yes	characteristic
26	C₂²⋊Dic₄₃	—	2	4	no	—
27	C₂²⋊Dic₄₃	—	2	2	no	—
28	#10621883	—	4	4	no	—
29	C₄⋊Dic₄₃	D₄	1	2	yes	—
30	Dic₄₃⋊C₄	—	2	2	no	—
31	C₄×Dic₄₃	—	2	2	no	—
32	C₂×C₄₃⋊C₈	—	2	2	no	—
33	C₂³×C₄₃	—	2	2	no	—
34	C₂³×C₄₃	—	4	1	no	—
35	D₄×C₄₃	—	4	2	no	—
36	D₄×C₄₃	—	4	2	no	—
37	D₄×C₄₃	—	4	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	2	yes	—
42	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂×Dic₄₃	—	2	2	no	—
44	C₂×Dic₄₃	—	2	2	no	—
45	C₂×Dic₄₃	—	8	2	no	—
46	Dic₈₆	—	2	2	no	—
47	Dic₈₆	—	2	2	no	—
48	C₈×C₄₃	—	2	2	no	—
49	C₄₃⋊C₈	—	4	2	no	—
50	C₂²×C₄₃	—	4	4	no	—
51	C₂²×C₄₃	—	4	2	no	—
52	C₂²×C₄₃	—	8	2	no	—
53	C₂²×C₄₃	—	8	1	no	—
54	C₂²×C₄₃	#120	1	1	yes	characteristic
55	C₄×C₄₃	—	2	1	no	—
56	C₄×C₄₃	#135	1	2	yes	—
57	C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
58	Dic₄₃	—	4	2	no	—
59	Dic₄₃	—	4	2	no	—
60	#1620	—	43	1	no	maximal, Sylow
61	C₂×C₄₃	—	8	2	no	—
62	C₂×C₄₃	—	16	1	no	—
63	C₂×C₄₃	#449	1	2	yes	—
64	C₂×C₄₃	#453	1	1	yes	characteristic
65	#559	—	43	1	no	—
66	#493	D₄₃	1	1	yes	characteristic
67	#460	—	43	2	no	—
68	#331	—	43	1	no	—
69	Q₈⋊C₈	—	43	2	no	—
70	C₄₃	#1620	1	1	yes	characteristic, complemented, Sylow
71	C₂×SD₁₆	—	86	2	no	—
72	C₂×D₈	—	2	2	no	—
73	#127	C₂×D₄₃	1	1	yes	characteristic
74	#127	C₂×D₄₃	1	1	yes	characteristic
75	#124	—	86	2	no	—
76	#123	—	86	2	no	—
77	C₄×Q₈	—	43	2	no	—
78	C₄×D₄	—	86	2	no	—
79	C₄⋊C₈	—	43	2	no	—
80	#102	—	86	2	no	—
81	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
82	C₂×Q₈	—	43	2	no	—
83	C₂×D₄	—	2	2	no	—
84	C₂×D₄	—	2	2	no	—
85	C₂×D₄	—	2	1	no	—
86	C₂×D₄	C₂²⋊D₄₃	1	2	yes	—
87	C₂²×C₄	—	86	2	no	—
88	SD₁₆	—	172	4	no	—
89	D₈	—	4	4	no	—
90	C₂×C₈	—	2	1	no	—
91	C₂×C₈	—	86	2	no	—
92	C₄⋊C₄	—	43	2	no	—
93	C₄⋊C₄	—	86	2	no	—
94	C₂²⋊C₄	—	86	4	no	—
95	C₂²⋊C₄	—	86	2	no	—
96	C₄²	—	86	2	no	—
97	C₄²	C₂²×D₄₃	1	1	yes	characteristic
98	C₂³	—	2	2	no	—
99	C₂³	—	4	1	no	—
100	Q₈	—	86	2	no	—
101	Q₈	—	86	2	no	—
102	D₄	—	4	2	no	—
103	D₄	—	4	2	no	—
104	D₄	—	4	2	no	—
105	D₄	—	4	2	no	—
106	D₄	—	4	2	no	—
107	D₄	—	4	2	no	—
108	C₂×C₄	—	86	2	no	—
109	C₂×C₄	—	86	2	no	—
110	C₂×C₄	—	344	2	no	—
111	C₂×C₄	D₄×D₄₃	1	2	yes	—
112	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
113	C₈	—	2	2	no	—
114	C₈	—	172	2	no	—
115	C₂²	—	4	4	no	—
116	C₂²	—	4	2	no	—
117	C₂²	—	8	2	no	—
118	C₂²	—	8	1	no	—
119	C₂²	#13063293	1	1	yes	characteristic
120	C₄	—	2	1	no	—
121	C₄	—	172	2	no	—
122	C₄	—	172	2	no	—
123	C₄	#13063344	1	2	yes	—
124	C₄	#13063349	1	2	yes	—
125	C₂	—	8	2	no	—
126	C₂	—	16	1	no	—
127	C₂	#14583041	1	2	yes	—
128	C₂	#14583066	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583635

C₂

yes

maximal, characteristic, complemented

#14583096

C₂

yes

maximal, complemented

#14582643

C₂

yes

maximal, characteristic, complemented

#14582631

C₂

yes

maximal, complemented

C₄₃×#493

C₂

yes

maximal, characteristic

C₂×#10621883

—

#13063312

—

#13063306

—

C₄×Dic₈₆

C₂²

yes

—

D₄×Dic₄₃

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

#13063246

—

C₂×D₈×C₄₃

—

#127×C₄₃

C₂²

yes

characteristic

#127×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

D₄

yes

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

D₄

yes

—

D₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

#10621883

—

C₄⋊Dic₄₃

D₄

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#120

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

#135

yes

—

C₄×C₄₃

AGL(1,ℤ/8)

yes

—

Dic₄₃

—

Dic₄₃

—

#1620

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#449

yes

—

C₂×C₄₃

yes

—

D₄₃

yes

characteristic

#460

—

#331

—

Q₈⋊C₈

—

C₄₃

#1620

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×D₈

—

#127

C₂×D₄₃

yes

characteristic

#127

C₂×D₄₃

yes

characteristic

#124

—

#123

—

C₄×Q₈

—

C₄×D₄

—

C₄⋊C₈

—

#102

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

—

SD₁₆

—

172

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

—

C₂³

—

100

Q₈

—

101

Q₈

—

102

D₄

—

103

D₄

—

104

D₄

—

105

D₄

—

106

D₄

—

107

D₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

344

—

111

C₂×C₄

D₄×D₄₃

yes

—

112

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

113

C₈

—

114

C₈

—

172

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

#13063293

yes

characteristic

120

C₄

—

121

C₄

—

172

—

122

C₄

—

172

—

123

C₄

#13063344

yes

—

124

C₄

#13063349

yes

—

125

C₂

—

126

C₂

—

127

C₂

#14583041

yes

—

128

C₂

#14583066

yes

characteristic

	subgroup	G/H
center	C₂²	#13063293
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#493	C₂
socle	C₂²×C₄₃	#120
hypercenter	#493	D₄₃
hypocenter	C₄₃	#1620
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#13063293

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#493

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. #14583635	C₂	semidirect
2. #14583096	C₂	semidirect
3. #14582643	C₂	semidirect
4. #14582631	C₂	semidirect
70. C₄₃	#1620	semidirect

H ≅ G/N

type

1. #14583635

C₂

semidirect

2. #14583096

C₂

semidirect

3. #14582643

C₂

semidirect

4. #14582631

C₂

semidirect

70. C₄₃

#1620

semidirect

Subgroups — #19133652

Conjugacy classes of subgroups

Complements