Group #19136488 — subgroups

Subgroups — #19136488

Order 5504.

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

normal subgroups only

This group has 142 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	#14583342	C₂	1	1	yes	maximal, characteristic
2	#14583022	C₂	1	1	yes	maximal, characteristic
3	#14583007	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582722	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582716	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582710	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#347	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063347	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
10	#13063331	—	2	1	no	—
11	C₄×Dic₈₆	—	2	1	no	—
12	Dic₃₄₄	C₄	1	2	yes	complemented
13	#13063270	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	#13063250	—	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×Dic₈₆	—	2	1	no	—
23	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
25	C₄²×C₄₃	D₄	1	1	yes	characteristic
26	C₄⋊Dic₄₃	—	2	1	no	—
27	Dic₄₃⋊C₄	—	4	1	no	—
28	C₄×Dic₄₃	—	4	1	no	—
29	#10621877	—	2	1	no	—
30	Dic₁₇₂	—	2	1	no	—
31	Dic₁₇₂	C₂×C₄	1	2	yes	—
32	Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
33	D₃₄₄	C₂×C₄	1	1	yes	characteristic
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	—
39	C₂×C₄×C₄₃	—	2	1	no	—
40	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
41	C₂²⋊D₄₃	—	4	1	no	—
42	C₂×Dic₄₃	—	4	1	no	—
43	C₂×Dic₄₃	—	4	1	no	—
44	D₁₇₂	—	2	1	no	—
45	C₄×D₄₃	—	4	1	no	—
46	Dic₈₆	—	2	1	no	—
47	Dic₈₆	—	2	2	no	—
48	Dic₈₆	—	4	1	no	—
49	C₈×C₄₃	—	2	1	no	—
50	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
51	C₈×C₄₃	#41	1	1	yes	characteristic
52	C₄₃⋊C₈	—	4	1	no	—
53	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
54	C₂×D₄₃	—	4	1	no	—
55	C₄×C₄₃	—	4	1	no	—
56	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
57	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
58	Dic₄₃	—	4	2	no	—
59	Dic₄₃	—	4	1	no	—
60	Dic₄₃	—	8	1	no	—
61	#2180	—	43	1	no	maximal, Sylow
62	C₂×C₄₃	—	2	1	no	—
63	C₂×C₄₃	#442	1	1	yes	characteristic
64	D₄₃	—	8	1	no	—
65	#510	—	43	1	no	—
66	#444	—	43	1	no	—
67	#441	—	43	1	no	—
68	#365	—	43	1	no	—
69	#362	—	43	1	no	—
70	#360	—	43	1	no	—
71	#347	D₄₃	1	1	yes	characteristic, complemented
72	C₄₃	#2180	1	1	yes	characteristic, complemented, Sylow
73	#135	—	43	1	no	—
74	C₂×Q₁₆	—	43	1	no	—
75	#131	—	86	1	no	—
76	C₄×Q₈	—	86	1	no	—
77	Q₃₂	—	43	2	no	—
78	SD₃₂	—	43	2	no	—
79	M₃₂	C₂×D₄₃	1	1	yes	characteristic
80	M₃₂	C₂×D₄₃	1	1	yes	characteristic
81	#108	—	43	1	no	—
82	#106	—	43	1	no	—
83	#104	—	86	1	no	—
84	#103	—	86	1	no	—
85	#97	C₂×D₄₃	1	1	yes	characteristic
86	#41	—	86	1	no	—
87	C₂×Q₈	—	86	1	no	—
88	Q₁₆	—	43	2	no	—
89	Q₁₆	—	43	1	no	—
90	Q₁₆	—	86	1	no	—
91	SD₁₆	—	86	1	no	—
92	D₈	—	43	1	no	—
93	M₁₆	—	86	1	no	—
94	M₁₆	—	172	1	no	—
95	C₂×C₈	—	172	1	no	—
96	C₂×C₈	D₁₇₂	1	1	yes	characteristic
97	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
98	C₄⋊C₄	—	86	1	no	—
99	C₄⋊C₄	—	172	1	no	—
100	C₄²	—	172	1	no	—
101	C₄²	D₁₇₂	1	1	yes	characteristic
102	C₁₆	—	2	1	no	—
103	C₁₆	C₄×D₄₃	1	2	yes	—
104	Q₈	—	86	1	no	—
105	Q₈	—	86	2	no	—
106	Q₈	—	172	1	no	—
107	D₄	—	86	1	no	—
108	D₄	—	172	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	172	1	no	—
111	C₂×C₄	—	172	1	no	—
112	C₂×C₄	—	172	1	no	—
113	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
114	C₈	—	2	1	no	—
115	C₈	—	172	1	no	—
116	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
117	C₈	#10621898	1	1	yes	characteristic
118	C₂²	—	172	1	no	—
119	C₂²	#13063353	1	1	yes	characteristic
120	C₄	—	4	1	no	—
121	C₄	—	344	1	no	—
122	C₄	—	172	1	no	—
123	C₄	—	172	2	no	—
124	C₄	C₄×D₁₇₂	1	1	yes	characteristic
125	C₄	#13063353	1	1	yes	characteristic
126	C₂	—	2	1	no	—
127	C₂	—	344	1	no	—
128	C₂	#14583012	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583342

C₂

yes

maximal, characteristic

#14583022

C₂

yes

maximal, characteristic

#14583007

C₂

yes

maximal, characteristic, complemented

#14582722

C₂

yes

maximal, characteristic, complemented

#14582716

C₂

yes

maximal, characteristic, complemented

#14582710

C₂

yes

maximal, characteristic

C₄₃×#347

C₂

yes

maximal, characteristic, complemented

#13063347

C₂²

yes

characteristic

C₂×Dic₁₇₂

C₂²

yes

characteristic

#13063331

—

C₄×Dic₈₆

—

Dic₃₄₄

C₄

yes

complemented

#13063270

C₄

yes

complemented

#13063261

C₂²

yes

characteristic

#13063257

C₂²

yes

characteristic

#13063253

—

#13063250

—

M₃₂×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₂²

yes

characteristic

#10621898

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

#10621877

—

Dic₁₇₂

—

Dic₁₇₂

C₂×C₄

yes

—

Dic₁₇₂

C₂×C₄

yes

characteristic

D₃₄₄

C₂×C₄

yes

characteristic

#10621873

—

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₁₆×C₄₃

C₂×C₄

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

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

—

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

AGL(1,ℤ/8)

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2180

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#442

yes

characteristic

D₄₃

—

—

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2180

yes

characteristic, complemented, Sylow

#135

—

C₂×Q₁₆

—

#131

—

C₄×Q₈

—

Q₃₂

—

SD₃₂

—

M₃₂

C₂×D₄₃

yes

characteristic

M₃₂

C₂×D₄₃

yes

—

—

—

—

C₂×D₄₃

yes

characteristic

#41

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

172

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

172

—

100

C₄²

—

172

—

101

C₄²

D₁₇₂

yes

characteristic

102

C₁₆

—

103

C₁₆

C₄×D₄₃

yes

—

104

Q₈

—

105

Q₈

—

106

Q₈

—

172

—

107

D₄

—

108

D₄

—

172

—

109

C₂×C₄

—

110

C₂×C₄

—

172

—

111

C₂×C₄

—

172

—

112

C₂×C₄

—

172

—

113

C₂×C₄

C₂×D₁₇₂

yes

characteristic

114

C₈

—

115

C₈

—

172

—

116

C₈

C₂×C₄×D₄₃

yes

characteristic

117

C₈

#10621898

yes

characteristic

118

C₂²

—

172

—

119

C₂²

#13063353

yes

characteristic

120

C₄

—

121

C₄

—

344

—

122

C₄

—

172

—

123

C₄

—

172

—

124

C₄

C₄×D₁₇₂

yes

characteristic

125

C₄

#13063353

yes

characteristic

126

C₂

—

127

C₂

—

344

—

128

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	#2180
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
3. #14583007	C₂	semidirect
4. #14582722	C₂	semidirect
5. #14582716	C₂	semidirect
7. C₄₃×#347	C₂	semidirect
12. Dic₃₄₄	C₄	semidirect
13. #13063270	C₄	semidirect
71. #347	D₄₃	semidirect
72. C₄₃	#2180	semidirect

H ≅ G/N

type

3. #14583007

C₂

semidirect

4. #14582722

C₂

semidirect

5. #14582716

C₂

semidirect

7. C₄₃×#347

C₂

semidirect

12. Dic₃₄₄

C₄

semidirect

13. #13063270

C₄

semidirect

71. #347

D₄₃

semidirect

72. C₄₃

#2180

semidirect

Subgroups — #19136488

Conjugacy classes of subgroups

Complements