Group #19143230 — subgroups

Subgroups — #19143230

Order 5504.

392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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	C₂×#13063284	C₂	1	1	yes	maximal, characteristic
2	#14582957	C₂	1	8	yes	maximal, complemented
3	#14582922	C₂	1	2	yes	maximal, complemented
4	#14582863	C₂	1	1	yes	maximal, characteristic
5	M₁₆×Dic₄₃	C₂	1	2	yes	maximal, complemented
6	C₄₃×#407	C₂	1	1	yes	maximal, characteristic
7	C₂×#10621877	C₂²	1	2	yes	—
8	#13063284	C₄	1	4	yes	—
9	#13063284	C₂²	1	4	yes	—
10	C₂×C₄⋊Dic₄₃	C₄	1	2	yes	—
11	C₂×C₂²⋊Dic₄₃	C₄	1	2	yes	—
12	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
14	Dic₄₃⋊C₈	C₂²	1	8	yes	complemented
15	C₂²⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
16	#13063235	C₂²	1	4	yes	complemented
17	C₈×Dic₄₃	C₂²	1	4	yes	complemented
18	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
20	C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
21	C₂⁴×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	—	2	4	no	—
23	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
26	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
28	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
29	M₁₆×C₄₃	—	2	4	no	—
30	C₂×C₈×C₄₃	C₂³	1	4	yes	—
31	C₂²⋊Dic₄₃	C₂×C₄	1	8	yes	—
32	C₄⋊Dic₄₃	C₂×C₄	1	8	yes	—
33	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
34	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
35	C₄×Dic₄₃	C₂³	1	2	yes	—
36	C₄×Dic₄₃	C₂³	1	2	yes	—
37	#10621877	—	2	4	no	—
38	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
39	C₂³×C₄₃	—	2	2	no	—
40	C₂³×C₄₃	—	4	2	no	—
41	C₂³×C₄₃	C₂²×C₄	1	2	yes	—
42	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₄×C₄₃	—	2	2	no	—
44	C₂×C₄×C₄₃	—	2	4	no	—
45	C₂×C₄×C₄₃	—	2	4	no	—
46	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₄₃	#41	1	4	yes	—
49	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₄₃	—	4	2	no	—
51	C₂×Dic₄₃	—	4	2	no	—
52	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
53	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
54	C₈×C₄₃	—	2	4	no	—
55	C₄₃⋊C₈	—	2	4	no	—
56	C₂²×C₄₃	—	2	2	no	—
57	C₂²×C₄₃	—	2	2	no	—
58	C₂²×C₄₃	—	2	4	no	—
59	C₂²×C₄₃	—	4	4	no	—
60	C₂²×C₄₃	#117	1	2	yes	—
61	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
62	C₄×C₄₃	—	2	2	no	—
63	C₄×C₄₃	#117	1	2	yes	—
64	C₄×C₄₃	C₂×#41	1	2	yes	—
65	Dic₄₃	—	2	4	no	—
66	Dic₄₃	—	2	4	no	—
67	#2921	—	43	1	no	maximal, Sylow
68	C₂×C₄₃	—	2	2	no	—
69	C₂×C₄₃	—	4	2	no	—
70	C₂×C₄₃	C₂×#117	1	1	yes	characteristic
71	C₂×C₄₃	#568	1	2	yes	—
72	C₂×#117	—	43	1	no	—
73	#433	—	43	8	no	—
74	#423	—	43	2	no	—
75	#407	—	43	1	no	—
76	#407	D₄₃	1	1	yes	characteristic
77	C₄×M₁₆	—	43	2	no	—
78	C₄₃	#2921	1	1	yes	characteristic, complemented, Sylow
79	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
80	C₂×M₁₆	—	43	2	no	—
81	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
82	#117	—	43	4	no	—
83	#117	—	43	4	no	—
84	C₂×C₄⋊C₄	—	43	2	no	—
85	C₂×C₂²⋊C₄	—	43	2	no	—
86	C₂×C₄²	—	43	1	no	—
87	C₂×C₄²	—	43	1	no	—
88	C₄⋊C₈	—	43	8	no	—
89	C₂²⋊C₈	—	43	4	no	—
90	C₂²⋊C₈	C₂×D₄₃	1	4	yes	—
91	#97	—	43	4	no	—
92	C₄×C₈	—	43	4	no	—
93	C₂⁴	C₄×D₄₃	1	1	yes	characteristic
94	C₂²×C₄	—	2	4	no	—
95	C₂²×C₄	—	43	2	no	—
96	C₂²×C₄	—	43	2	no	—
97	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
98	C₂²×C₄	C₄×D₄₃	1	2	yes	—
99	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
100	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
101	M₁₆	—	2	4	no	—
102	M₁₆	—	86	4	no	—
103	C₂×C₈	—	43	4	no	—
104	C₂×C₈	C₂²×D₄₃	1	4	yes	—
105	C₄⋊C₄	—	43	8	no	—
106	C₂²⋊C₄	—	43	8	no	—
107	C₄²	—	43	2	no	—
108	C₄²	—	43	2	no	—
109	C₄²	—	43	2	no	—
110	C₄²	—	43	2	no	—
111	C₂³	—	2	2	no	—
112	C₂³	—	4	2	no	—
113	C₂³	C₂×C₄×D₄₃	1	2	yes	—
114	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	43	4	no	—
119	C₂×C₄	—	43	4	no	—
120	C₂×C₄	—	172	2	no	—
121	C₂×C₄	—	172	2	no	—
122	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
123	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
124	C₂×C₄	#10621900	1	4	yes	—
125	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
126	C₈	—	2	4	no	—
127	C₈	—	86	4	no	—
128	C₂²	—	2	2	no	—
129	C₂²	—	2	2	no	—
130	C₂²	—	2	4	no	—
131	C₂²	—	4	4	no	—
132	C₂²	#13063281	1	2	yes	—
133	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
134	C₄	—	2	2	no	—
135	C₄	—	86	4	no	—
136	C₄	—	86	4	no	—
137	C₄	#13063281	1	2	yes	—
138	C₄	C₂×#10621900	1	2	yes	—
139	C₂	—	2	2	no	—
140	C₂	—	4	2	no	—
141	C₂	C₂×#13063281	1	1	yes	characteristic
142	C₂	#14583665	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063284

C₂

yes

maximal, characteristic

#14582957

C₂

yes

maximal, complemented

#14582922

C₂

yes

maximal, complemented

#14582863

C₂

yes

maximal, characteristic

M₁₆×Dic₄₃

C₂

yes

maximal, complemented

C₄₃×#407

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

#13063284

C₄

yes

—

#13063284

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₄

yes

—

C₂×C₂²⋊Dic₄₃

C₄

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

Dic₄₃⋊C₈

C₂²

yes

complemented

C₂²⋊(C₄₃⋊C₈)

C₂²

yes

—

#13063235

C₂²

yes

complemented

C₈×Dic₄₃

C₂²

yes

complemented

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₂²

yes

—

C₂²⋊C₈×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂²×Dic₄₃

C₂×C₄

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

C₂²⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₄×Dic₄₃

C₂³

yes

—

#10621877

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²×C₄

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#117

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

#117

yes

—

C₄×C₄₃

C₂×#41

yes

—

Dic₄₃

—

Dic₄₃

—

#2921

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

C₂×#117

yes

characteristic

C₂×C₄₃

#568

yes

—

—

—

—

—

D₄₃

yes

characteristic

C₄×M₁₆

—

C₄₃

#2921

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

C₂×D₄₃

yes

—

#97

—

C₄×C₈

—

C₂⁴

C₄×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

C₄×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

100

C₂²×C₄

C₂²×D₄₃

yes

characteristic

101

M₁₆

—

102

M₁₆

—

103

C₂×C₈

—

104

C₂×C₈

C₂²×D₄₃

yes

—

105

C₄⋊C₄

—

106

C₂²⋊C₄

—

107

C₄²

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₂³

—

112

C₂³

—

113

C₂³

C₂×C₄×D₄₃

yes

—

114

C₂³

C₂×C₄×D₄₃

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

172

—

121

C₂×C₄

—

172

—

122

C₂×C₄

C₂×C₄×D₄₃

yes

—

123

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

124

C₂×C₄

#10621900

yes

—

125

C₂×C₄

C₂³×D₄₃

yes

characteristic

126

C₈

—

127

C₈

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

#13063281

yes

—

133

C₂²

C₂²×C₄×D₄₃

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

#13063281

yes

—

138

C₄

C₂×#10621900

yes

—

139

C₂

—

140

C₂

—

141

C₂

C₂×#13063281

yes

characteristic

142

C₂

#14583665

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₄
Fitting	C₄₃×#407	C₂
hypercenter	#407	D₄₃
hypocenter	C₄₃	#2921
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #407

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₄₃

commutator, socle

C₂²×C₄₃

C₂³×C₄

Fitting

C₄₃×#407

C₂

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄ ◁ #407

N	H ≅ G/N	type
2. #14582957	C₂	semidirect
3. #14582922	C₂	semidirect
5. M₁₆×Dic₄₃	C₂	semidirect
14. Dic₄₃⋊C₈	C₂²	semidirect
16. #13063235	C₂²	semidirect
17. C₈×Dic₄₃	C₂²	semidirect
78. C₄₃	#2921	semidirect

H ≅ G/N

type

2. #14582957

C₂

semidirect

3. #14582922

C₂

semidirect

5. M₁₆×Dic₄₃

C₂

semidirect

14. Dic₄₃⋊C₈

C₂²

semidirect

16. #13063235

C₂²

semidirect

17. C₈×Dic₄₃

C₂²

semidirect

78. C₄₃

#2921

semidirect

Subgroups — #19143230

Conjugacy classes of subgroups

Complements