Group #19136730 — subgroups

Subgroups — #19136730

Order 5504.

142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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	#14583303	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582725	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582724	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582700	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#357	C₂	1	1	yes	maximal, characteristic
8	#13063324	—	2	1	no	—
9	D₄×Dic₄₃	—	2	1	no	—
10	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	#13063259	C₂²	1	1	yes	characteristic
12	#13063259	C₂²	1	1	yes	characteristic
13	#13063258	—	2	1	no	—
14	#13063246	—	2	1	no	—
15	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
16	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	#107×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×D₄×C₄₃	—	2	1	no	—
20	C₂²×Dic₄₃	—	4	1	no	—
21	C₂×Dic₈₆	—	4	1	no	—
22	D₈×C₄₃	—	2	1	no	—
23	D₈×C₄₃	Q₈	1	2	yes	complemented
24	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₄₃	—	2	1	no	—
26	C₂²⋊Dic₄₃	—	4	1	no	—
27	C₄⋊Dic₄₃	—	2	1	no	—
28	C₄⋊Dic₄₃	—	2	1	no	—
29	Dic₄₃⋊C₄	—	4	1	no	—
30	C₄×Dic₄₃	D₄	1	1	yes	characteristic
31	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
32	C₁₆×C₄₃	—	2	1	no	—
33	C₄₃⋊C₁₆	—	2	1	no	—
34	C₂³×C₄₃	—	4	1	no	—
35	D₄×C₄₃	—	2	2	no	—
36	D₄×C₄₃	—	4	1	no	—
37	C₂×C₄×C₄₃	—	4	1	no	—
38	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₄₃	—	4	1	no	—
40	C₂×Dic₄₃	—	4	1	no	—
41	C₂×Dic₄₃	—	8	2	no	—
42	C₂×Dic₄₃	D₈	1	1	yes	characteristic
43	C₂×Dic₄₃	D₈	1	1	yes	characteristic
44	Dic₈₆	—	8	2	no	—
45	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
46	C₈×C₄₃	#41	1	1	yes	characteristic
47	C₄₃⋊C₈	—	2	1	no	—
48	C₂²×C₄₃	—	4	2	no	—
49	C₂²×C₄₃	—	8	1	no	—
50	C₂²×C₄₃	—	8	1	no	—
51	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
52	C₄×C₄₃	—	8	1	no	—
53	C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
54	C₄×C₄₃	#137	1	1	yes	characteristic
55	Dic₄₃	—	2	1	no	—
56	Dic₄₃	—	8	1	no	—
57	Dic₄₃	—	8	1	no	—
58	Dic₄₃	D₁₆	1	2	yes	—
59	#2224	—	43	1	no	maximal, Sylow
60	C₂×C₄₃	—	8	2	no	—
61	C₂×C₄₃	#474	1	1	yes	characteristic
62	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
63	C₂×C₄₃	#510	1	1	yes	characteristic
64	#500	—	43	1	no	—
65	C₄×D₈	—	43	1	no	—
66	#366	—	43	1	no	—
67	#366	—	43	1	no	—
68	C₄⋊C₁₆	—	43	1	no	—
69	#357	—	43	1	no	—
70	#357	D₄₃	1	1	yes	characteristic
71	C₄₃	#2224	1	1	yes	characteristic, complemented, Sylow
72	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
73	C₄⋊Q₈	—	86	1	no	—
74	C₄×D₄	—	86	1	no	—
75	C₂×C₁₆	—	43	1	no	—
76	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
77	#107	—	43	1	no	—
78	#107	—	43	1	no	—
79	#107	—	86	1	no	—
80	#107	C₂×D₄₃	1	1	yes	characteristic
81	#102	—	86	1	no	—
82	C₄×C₈	—	43	1	no	—
83	C₂×Q₈	—	172	1	no	—
84	C₂×D₄	—	2	1	no	—
85	C₂²×C₄	—	172	1	no	—
86	D₈	—	2	1	no	—
87	D₈	Dic₈₆	1	2	yes	complemented
88	C₂×C₈	—	43	1	no	—
89	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
90	C₄⋊C₄	—	2	1	no	—
91	C₄⋊C₄	—	86	1	no	—
92	C₄⋊C₄	—	86	1	no	—
93	C₄⋊C₄	—	172	1	no	—
94	C₂²⋊C₄	—	172	1	no	—
95	C₄²	—	43	1	no	—
96	C₁₆	—	2	1	no	—
97	C₁₆	—	86	1	no	—
98	C₂³	—	4	1	no	—
99	Q₈	—	344	2	no	—
100	D₄	—	2	2	no	—
101	D₄	—	4	1	no	—
102	C₂×C₄	—	4	1	no	—
103	C₂×C₄	—	43	1	no	—
104	C₂×C₄	—	43	1	no	—
105	C₂×C₄	—	344	2	no	—
106	C₂×C₄	—	172	1	no	—
107	C₂×C₄	—	172	1	no	—
108	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
109	C₈	—	86	1	no	—
110	C₈	C₂×Dic₈₆	1	1	yes	characteristic
111	C₈	#10621900	1	1	yes	characteristic
112	C₂²	—	4	2	no	—
113	C₂²	—	8	1	no	—
114	C₂²	—	8	1	no	—
115	C₂²	D₈×D₄₃	1	1	yes	characteristic
116	C₄	—	8	1	no	—
117	C₄	—	43	2	no	—
118	C₄	—	86	1	no	—
119	C₄	—	344	1	no	—
120	C₄	—	344	1	no	—
121	C₄	#13063302	1	1	yes	characteristic
122	C₄	#13063354	1	1	yes	characteristic
123	C₂	—	8	2	no	—
124	C₂	#14583177	1	1	yes	characteristic
125	C₂	D₁₆×D₄₃	1	1	yes	characteristic
126	C₂	#14583338	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583303

C₂

yes

maximal, characteristic, complemented

D₈×Dic₄₃

C₂

yes

maximal, characteristic

#14582725

C₂

yes

maximal, characteristic, complemented

#14582724

C₂

yes

maximal, characteristic, complemented

Dic₄₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#14582700

C₂

yes

maximal, characteristic

C₄₃×#357

C₂

yes

maximal, characteristic

#13063324

—

D₄×Dic₄₃

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063258

—

#13063246

—

C₈×Dic₄₃

C₂²

yes

characteristic

C₂×D₈×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#107×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

D₈×C₄₃

—

D₈×C₄₃

Q₈

yes

complemented

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

D₈

yes

characteristic

C₂×Dic₄₃

D₈

yes

characteristic

Dic₈₆

—

C₈×C₄₃

C₂×Q₈

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄×C₄₃

#137

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

D₁₆

yes

—

#2224

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#474

yes

characteristic

C₂×C₄₃

C₂×D₁₆

yes

C₂×C₄₃

yes

—

C₄×D₈

—

#366

—

#366

—

C₄⋊C₁₆

—

#357

—

#357

D₄₃

yes

characteristic

C₄₃

#2224

yes

characteristic, complemented, Sylow

C₂×D₈

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

—

C₄×D₄

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

—

—

C₂×D₄₃

yes

characteristic

#102

—

C₄×C₈

—

C₂×Q₈

—

172

—

C₂×D₄

—

C₂²×C₄

—

172

—

D₈

—

D₈

Dic₈₆

yes

complemented

C₂×C₈

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

172

—

C₄²

—

C₁₆

—

C₁₆

—

C₂³

—

Q₈

—

344

—

100

D₄

—

101

D₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

344

—

106

C₂×C₄

—

172

—

107

C₂×C₄

—

172

—

108

C₂×C₄

D₄×D₄₃

yes

characteristic

109

C₈

—

110

C₈

C₂×Dic₈₆

yes

characteristic

111

C₈

#10621900

yes

characteristic

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

D₈×D₄₃

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

344

—

120

C₄

—

344

—

121

C₄

#13063302

yes

characteristic

122

C₄

#13063354

yes

characteristic

123

C₂

—

124

C₂

#14583177

yes

characteristic

125

C₂

D₁₆×D₄₃

yes

characteristic

126

C₂

#14583338

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#357	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#357	D₄₃
hypocenter	C₄₃	#2224
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#357

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. #14583303	C₂	semidirect
3. #14582725	C₂	semidirect
4. #14582724	C₂	semidirect
5. Dic₄₃⋊C₁₆	C₂	semidirect
23. D₈×C₄₃	Q₈	semidirect
71. C₄₃	#2224	semidirect
87. D₈	Dic₈₆	semidirect

H ≅ G/N

type

1. #14583303

C₂

semidirect

3. #14582725

C₂

semidirect

4. #14582724

C₂

semidirect

5. Dic₄₃⋊C₁₆

C₂

semidirect

23. D₈×C₄₃

Q₈

semidirect

71. C₄₃

#2224

semidirect

87. D₈

Dic₈₆

semidirect

Subgroups — #19136730

Conjugacy classes of subgroups

Complements