Group #19136366 — subgroups

Subgroups — #19136366

Order 5504.

144 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 65 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	M₃₂×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#108×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582934	C₂	1	1	yes	maximal, characteristic
4	#14582723	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582722	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582721	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#365	C₂	1	1	yes	maximal, characteristic, complemented
8	M₁₆×D₄₃	—	2	1	no	—
9	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
10	#13063283	—	2	1	no	—
11	#13063265	C₂²	1	1	yes	characteristic
12	#13063264	C₄	1	2	yes	complemented
13	C₁₆×D₄₃	C₄	1	2	yes	complemented
14	#13063261	C₂²	1	1	yes	characteristic
15	#13063260	—	2	1	no	—
16	#13063258	—	2	1	no	—
17	#13063257	C₂²	1	1	yes	characteristic
18	M₃₂×C₄₃	C₂²	1	1	yes	characteristic
19	#108×C₄₃	C₂²	1	1	yes	characteristic
20	#106×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
22	M₁₆×C₄₃	—	2	1	no	—
23	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₄₃	—	2	1	no	—
25	(C₂×D₄₃)⋊C₄	—	4	1	no	—
26	C₄⋊Dic₄₃	—	2	1	no	—
27	C₄×Dic₄₃	—	4	1	no	—
28	#10621877	—	2	1	no	—
29	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
30	#10621872	—	4	1	no	—
31	C₈×D₄₃	—	4	1	no	—
32	C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
33	C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
34	C₈×D₄₃	Q₈	1	1	yes	characteristic
35	C₈×D₄₃	Q₈	1	1	yes	characteristic
36	C₁₆×C₄₃	C₂×C₄	1	2	yes	—
37	C₄₃⋊C₁₆	C₂×C₄	1	2	yes	—
38	C₂²×D₄₃	SD₁₆	1	1	yes	characteristic
39	C₂×C₄×C₄₃	—	4	1	no	—
40	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₄₃	—	4	1	no	—
42	C₂×Dic₄₃	SD₁₆	1	1	yes	characteristic
43	C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
44	C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
45	C₄×D₄₃	SD₁₆	1	1	yes	characteristic
46	C₄×D₄₃	SD₁₆	1	1	yes	characteristic
47	C₈×C₄₃	—	4	1	no	—
48	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
49	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
50	C₄₃⋊C₈	—	4	1	no	—
51	C₄₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
52	C₄₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
54	C₂×D₄₃	—	4	1	no	—
55	C₂×D₄₃	#106	1	1	yes	characteristic
56	C₂×D₄₃	#106	1	1	yes	characteristic
57	C₄×C₄₃	—	8	1	no	—
58	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
60	Dic₄₃	—	8	1	no	—
61	Dic₄₃	#106	1	1	yes	characteristic
62	Dic₄₃	#106	1	1	yes	characteristic
63	#2155	—	43	1	no	maximal, Sylow
64	C₂×C₄₃	—	2	1	no	—
65	C₂×C₄₃	C₂×#106	1	1	yes	characteristic
66	D₄₃	—	2	1	no	—
67	D₄₃	—	2	1	no	—
68	C₂×M₃₂	—	43	1	no	—
69	C₂×#108	—	43	1	no	—
70	#427	—	43	1	no	—
71	#365	—	43	1	no	—
72	#365	—	43	1	no	—
73	#365	—	43	1	no	—
74	#365	D₄₃	1	1	yes	characteristic, complemented
75	C₄₃	#2155	1	1	yes	characteristic, complemented, Sylow
76	C₂×M₁₆	—	86	1	no	—
77	C₂²×C₈	—	43	1	no	—
78	#117	—	86	1	no	—
79	M₃₂	—	43	1	no	—
80	M₃₂	—	43	2	no	—
81	M₃₂	C₂×D₄₃	1	1	yes	characteristic
82	C₂×C₁₆	—	43	2	no	—
83	#108	—	43	1	no	—
84	#108	—	86	1	no	—
85	#108	C₂×D₄₃	1	1	yes	characteristic
86	#107	—	86	1	no	—
87	#106	—	43	1	no	—
88	#106	C₂×D₄₃	1	1	yes	characteristic
89	C₂²×C₄	—	43	1	no	—
90	M₁₆	—	2	1	no	—
91	M₁₆	—	86	1	no	—
92	M₁₆	—	172	1	no	—
93	C₂×C₈	—	43	1	no	—
94	C₂×C₈	—	43	1	no	—
95	C₂×C₈	—	43	1	no	—
96	C₂×C₈	—	43	1	no	—
97	C₂×C₈	—	43	1	no	—
98	C₂×C₈	—	172	1	no	—
99	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
100	C₄⋊C₄	—	2	1	no	—
101	C₄⋊C₄	—	86	1	no	—
102	C₂²⋊C₄	—	172	1	no	—
103	C₄²	—	172	1	no	—
104	C₁₆	—	43	2	no	—
105	C₁₆	C₄×D₄₃	1	2	yes	—
106	C₂³	—	43	1	no	—
107	C₂×C₄	—	4	1	no	—
108	C₂×C₄	—	43	1	no	—
109	C₂×C₄	—	43	1	no	—
110	C₂×C₄	—	43	1	no	—
111	C₂×C₄	—	43	1	no	—
112	C₂×C₄	—	43	1	no	—
113	C₂×C₄	—	172	1	no	—
114	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
115	C₈	—	4	1	no	—
116	C₈	—	43	1	no	—
117	C₈	—	43	1	no	—
118	C₈	—	172	1	no	—
119	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
120	C₈	Q₈×D₄₃	1	1	yes	characteristic
121	C₂²	—	43	1	no	—
122	C₂²	—	43	1	no	—
123	C₂²	—	172	1	no	—
124	C₂²	SD₁₆×D₄₃	1	1	yes	characteristic
125	C₄	—	8	1	no	—
126	C₄	—	43	1	no	—
127	C₄	—	43	1	no	—
128	C₄	—	344	1	no	—
129	C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
130	C₄	SD₁₆×D₄₃	1	1	yes	characteristic
131	C₂	—	2	1	no	—
132	C₂	—	86	1	no	—
133	C₂	—	86	1	no	—
134	C₂	#106×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

M₃₂×D₄₃

C₂

yes

maximal, characteristic

#108×D₄₃

C₂

yes

maximal, characteristic

#14582934

C₂

yes

maximal, characteristic

#14582723

C₂

yes

maximal, characteristic, complemented

#14582722

C₂

yes

maximal, characteristic, complemented

#14582721

C₂

yes

maximal, characteristic, complemented

C₄₃×#365

C₂

yes

maximal, characteristic, complemented

M₁₆×D₄₃

—

C₂×C₈×D₄₃

C₂²

yes

characteristic

#13063283

—

#13063265

C₂²

yes

characteristic

#13063264

C₄

yes

complemented

C₁₆×D₄₃

C₄

yes

complemented

#13063261

C₂²

yes

—

—

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

characteristic

#108×C₄₃

C₂²

yes

characteristic

#106×C₄₃

C₂²

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

#10621872

—

C₈×D₄₃

—

C₈×D₄₃

C₂×C₄

yes

characteristic

C₈×D₄₃

C₂×C₄

yes

characteristic

C₈×D₄₃

Q₈

yes

characteristic

C₈×D₄₃

Q₈

yes

characteristic

C₁₆×C₄₃

C₂×C₄

yes

—

C₄₃⋊C₁₆

C₂×C₄

yes

—

C₂²×D₄₃

SD₁₆

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

SD₁₆

yes

characteristic

C₄×D₄₃

C₄⋊C₄

yes

characteristic

C₄×D₄₃

C₄⋊C₄

yes

characteristic

C₄×D₄₃

SD₁₆

yes

characteristic

C₄×D₄₃

SD₁₆

yes

characteristic

C₈×C₄₃

—

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

C₂×Q₈

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

C₄⋊C₄

yes

characteristic

C₄₃⋊C₈

C₄⋊C₄

yes

characteristic

C₂²×C₄₃

C₂×SD₁₆

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

yes

C₂×D₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

Dic₄₃

—

Dic₄₃

yes

Dic₄₃

yes

—

C₂×C₄₃

—

C₂×C₄₃

C₂×#106

yes

characteristic

D₄₃

—

D₄₃

—

C₂×M₃₂

—

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2155

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

M₃₂

C₂×D₄₃

yes

characteristic

C₂×C₁₆

—

#108

—

#108

—

#108

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

characteristic

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

C₂²×D₄₃

yes

characteristic

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

172

—

103

C₄²

—

172

—

104

C₁₆

—

105

C₁₆

C₄×D₄₃

yes

—

106

C₂³

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

172

—

114

C₂×C₄

D₄×D₄₃

yes

characteristic

115

C₈

—

116

C₈

—

117

C₈

—

118

C₈

—

172

—

119

C₈

C₂×C₄×D₄₃

yes

characteristic

120

C₈

Q₈×D₄₃

yes

characteristic

121

C₂²

—

122

C₂²

—

123

C₂²

—

172

—

124

C₂²

SD₁₆×D₄₃

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

344

—

129

C₄

C₄⋊C₄×D₄₃

yes

characteristic

130

C₄

SD₁₆×D₄₃

yes

characteristic

131

C₂

—

132

C₂

—

133

C₂

—

134

C₂

#106×D₄₃

yes

characteristic

	subgroup	G/H
center	C₂	#106×D₄₃
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#365	C₂
socle	C₂×C₄₃	C₂×#106
hypercenter	#365	D₄₃
hypocenter	C₄₃	#2155
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #365

subgroup

G/H

center

C₂

#106×D₄₃

commutator

C₈×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#365

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #365

N	H ≅ G/N	type
4. #14582723	C₂	semidirect
5. #14582722	C₂	semidirect
6. #14582721	C₂	semidirect
7. C₄₃×#365	C₂	semidirect
12. #13063264	C₄	semidirect
13. C₁₆×D₄₃	C₄	semidirect
74. #365	D₄₃	semidirect
75. C₄₃	#2155	semidirect

H ≅ G/N

type

4. #14582723

C₂

semidirect

5. #14582722

C₂

semidirect

6. #14582721

C₂

semidirect

7. C₄₃×#365

C₂

semidirect

12. #13063264

C₄

semidirect

13. C₁₆×D₄₃

C₄

semidirect

74. #365

D₄₃

semidirect

75. C₄₃

#2155

semidirect

Subgroups — #19136366

Conjugacy classes of subgroups

Complements