Group #19132544 — subgroups

Subgroups — #19132544

Order 5504.

158 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 37 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	#14582771	C₂	1	1	yes	maximal, characteristic
2	#14582623	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#323	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₄₃	C₄	1	1	yes	characteristic
5	C₂×Dic₄₃⋊C₄	—	2	1	no	—
6	C₂×C₂²⋊Dic₄₃	C₄	1	1	yes	characteristic
7	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
8	C₄₃⋊#95	—	2	1	no	—
9	C₂×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²⋊C₈×C₄₃	—	2	1	no	—
11	C₂⁴×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
13	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
14	C₂²×Dic₄₃	—	2	1	no	—
15	C₂²×Dic₄₃	—	2	1	no	—
16	C₂²×Dic₄₃	—	4	1	no	—
17	C₂²×Dic₄₃	—	4	2	no	—
18	C₂×C₈×C₄₃	—	4	1	no	—
19	C₂²⋊C₄×C₄₃	—	4	1	no	—
20	C₂²⋊Dic₄₃	—	2	1	no	—
21	C₂²⋊Dic₄₃	C₈	1	2	yes	complemented
22	Dic₄₃⋊C₄	—	4	2	no	—
23	C₂×C₄₃⋊C₈	—	4	1	no	—
24	C₂³×C₄₃	—	2	1	no	—
25	C₂³×C₄₃	—	2	1	no	—
26	C₂³×C₄₃	—	4	1	no	—
27	C₂³×C₄₃	—	4	1	no	—
28	C₂³×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂³×C₄₃	C₂×C₈	1	1	yes	characteristic
30	C₂³×C₄₃	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₄₃	—	2	1	no	—
32	C₂×C₄×C₄₃	—	2	1	no	—
33	C₂×C₄×C₄₃	—	4	1	no	—
34	C₂×C₄×C₄₃	—	4	1	no	—
35	C₂×Dic₄₃	—	2	2	no	—
36	C₂×Dic₄₃	—	2	2	no	—
37	C₂×Dic₄₃	—	4	1	no	—
38	C₂×Dic₄₃	—	4	1	no	—
39	C₂×Dic₄₃	—	4	1	no	—
40	C₂×Dic₄₃	—	4	2	no	—
41	C₂×Dic₄₃	—	4	1	no	—
42	C₂×Dic₄₃	—	4	2	no	—
43	C₈×C₄₃	—	8	1	no	—
44	C₄₃⋊C₈	—	8	1	no	—
45	C₂²×C₄₃	—	2	1	no	—
46	C₂²×C₄₃	—	2	1	no	—
47	C₂²×C₄₃	—	2	1	no	—
48	C₂²×C₄₃	—	2	1	no	—
49	C₂²×C₄₃	—	4	1	no	—
50	C₂²×C₄₃	—	4	1	no	—
51	C₂²×C₄₃	—	4	2	no	—
52	C₂²×C₄₃	—	4	1	no	—
53	C₂²×C₄₃	—	4	1	no	—
54	C₂²×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
55	C₂²×C₄₃	#99	1	1	yes	characteristic
56	C₂²×C₄₃	#101	1	1	yes	characteristic
57	C₄×C₄₃	—	4	1	no	—
58	C₄×C₄₃	—	4	1	no	—
59	Dic₄₃	—	4	2	no	—
60	Dic₄₃	—	4	2	no	—
61	#1326	—	43	1	no	maximal, Sylow
62	C₂×C₄₃	—	2	1	no	—
63	C₂×C₄₃	—	2	1	no	—
64	C₂×C₄₃	—	4	1	no	—
65	C₂×C₄₃	—	4	1	no	—
66	C₂×C₄₃	#324	1	1	yes	characteristic
67	C₂×C₄₃	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
68	C₂×C₄₃	#352	1	1	yes	characteristic
69	#385	—	43	1	no	—
70	#323	—	43	1	no	—
71	#323	D₄₃	1	1	yes	characteristic
72	C₄₃	#1326	1	1	yes	characteristic, complemented, Sylow
73	C₂³×C₄	—	43	1	no	—
74	C₂×C₄⋊C₄	—	86	1	no	—
75	C₂×C₂²⋊C₄	—	43	1	no	—
76	C₂×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
77	C₂²⋊C₈	—	2	1	no	—
78	C₂²⋊C₈	—	86	1	no	—
79	#95	—	86	1	no	—
80	C₂⁴	C₄×D₄₃	1	1	yes	characteristic
81	C₂²×C₄	—	86	1	no	—
82	C₂²×C₄	—	86	1	no	—
83	C₂²×C₄	—	172	2	no	—
84	C₂²×C₄	—	172	1	no	—
85	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
86	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
87	C₂×C₈	—	4	1	no	—
88	C₂×C₈	—	172	1	no	—
89	C₄⋊C₄	—	172	2	no	—
90	C₂²⋊C₄	—	4	1	no	—
91	C₂²⋊C₄	—	43	2	no	—
92	C₂²⋊C₄	—	86	1	no	—
93	C₂³	—	2	1	no	—
94	C₂³	—	2	1	no	—
95	C₂³	—	4	1	no	—
96	C₂³	—	4	1	no	—
97	C₂³	C₈×D₄₃	1	1	yes	characteristic
98	C₂³	#10621872	1	1	yes	characteristic
99	C₂³	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	4	1	no	—
103	C₂×C₄	—	4	1	no	—
104	C₂×C₄	—	86	2	no	—
105	C₂×C₄	—	86	2	no	—
106	C₂×C₄	—	172	1	no	—
107	C₂×C₄	—	172	1	no	—
108	C₂×C₄	—	172	1	no	—
109	C₂×C₄	—	172	2	no	—
110	C₂×C₄	—	172	1	no	—
111	C₂×C₄	—	172	2	no	—
112	C₈	—	8	1	no	—
113	C₈	—	344	1	no	—
114	C₂²	—	2	1	no	—
115	C₂²	—	2	1	no	—
116	C₂²	—	2	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	4	1	no	—
119	C₂²	—	4	1	no	—
120	C₂²	—	4	2	no	—
121	C₂²	—	4	1	no	—
122	C₂²	—	4	1	no	—
123	C₂²	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
124	C₂²	#13063239	1	1	yes	characteristic
125	C₂²	#13063243	1	1	yes	characteristic
126	C₄	—	4	1	no	—
127	C₄	—	4	1	no	—
128	C₄	—	172	2	no	—
129	C₄	—	172	2	no	—
130	C₂	—	2	1	no	—
131	C₂	—	2	1	no	—
132	C₂	—	4	1	no	—
133	C₂	—	4	1	no	—
134	C₂	#14582624	1	1	yes	characteristic
135	C₂	#14582687	1	1	yes	characteristic
136	C₂	#14582688	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582771

C₂

yes

maximal, characteristic

#14582623

C₂

yes

maximal, characteristic

C₄₃×#323

C₂

yes

maximal, characteristic

C₂³×Dic₄₃

C₄

yes

characteristic

C₂×Dic₄₃⋊C₄

—

C₂×C₂²⋊Dic₄₃

C₄

yes

characteristic

C₂²⋊(C₄₃⋊C₈)

—

C₄₃⋊#95

—

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

characteristic

C₂²⋊C₈×C₄₃

—

C₂⁴×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

C₈

yes

complemented

Dic₄₃⋊C₄

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²⋊C₄

yes

characteristic

C₂³×C₄₃

C₂×C₈

yes

characteristic

C₂³×C₄₃

M₁₆

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊C₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#1326

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#324

yes

characteristic

C₂×C₄₃

AΣL(1,𝔽₁₆)

yes

C₂×C₄₃

yes

—

—

D₄₃

yes

characteristic

C₄₃

#1326

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₃

yes

characteristic

C₂²⋊C₈

—

C₂²⋊C₈

—

#95

—

C₂⁴

C₄×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

172

—

C₂²×C₄

—

172

—

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

172

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₈×D₄₃

yes

characteristic

C₂³

#10621872

yes

characteristic

C₂³

(C₂×D₄₃)⋊C₄

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

172

—

107

C₂×C₄

—

172

—

108

C₂×C₄

—

172

—

109

C₂×C₄

—

172

—

110

C₂×C₄

—

172

—

111

C₂×C₄

—

172

—

112

C₈

—

113

C₈

—

344

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

(C₂×D₄₃)⋊C₈

yes

characteristic

124

C₂²

#13063239

yes

characteristic

125

C₂²

#13063243

yes

characteristic

126

C₄

—

127

C₄

—

128

C₄

—

172

—

129

C₄

—

172

—

130

C₂

—

131

C₂

—

132

C₂

—

133

C₂

—

134

C₂

#14582624

yes

characteristic

135

C₂

#14582687

yes

characteristic

136

C₂

#14582688

yes

characteristic

	subgroup	G/H
center	C₂²	#13063239
commutator	C₂³×C₄₃	C₂×C₈
Frattini	C₂×C₂²⋊C₄	C₂×D₄₃
Fitting	C₄₃×#323	C₂
socle	C₂²×C₄₃	#99
hypercenter	#323	D₄₃
hypocenter	C₄₃	#1326
LCS	G ▷ C₂³×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₂²⋊C₄ ◁ #323

subgroup

G/H

center

C₂²

#13063239

commutator

C₂³×C₄₃

C₂×C₈

Frattini

C₂×C₂²⋊C₄

C₂×D₄₃

Fitting

C₄₃×#323

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₂²⋊C₄ ◁ #323

N	H ≅ G/N	type
21. C₂²⋊Dic₄₃	C₈	semidirect
72. C₄₃	#1326	semidirect

H ≅ G/N

type

21. C₂²⋊Dic₄₃

C₈

semidirect

72. C₄₃

#1326

semidirect

Subgroups — #19132544

Conjugacy classes of subgroups

Complements