Group #19137784 — subgroups

Subgroups — #19137784

Order 5504.

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

normal subgroups only

This group has 456 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×#13063319	C₂	1	1	yes	maximal, characteristic
2	#14582796	C₂	1	3	yes	maximal, complemented
3	#14582791	C₂	1	3	yes	maximal
4	#14582786	C₂	1	3	yes	maximal, complemented
5	#14582773	C₂	1	3	yes	maximal
6	#14582769	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#383	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
9	#13063319	C₄	1	8	yes	complemented
10	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
11	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
12	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
13	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
14	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
15	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
16	C₂×C₄×Dic₄₃	C₂²	1	3	yes	—
17	C₄₃⋊#95	C₂²	1	3	yes	—
18	C₄₃⋊#95	C₂²	1	3	yes	—
19	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	#95×C₄₃	C₂²	1	3	yes	—
21	#95×C₄₃	C₂²	1	3	yes	—
22	C₂³×D₄₃	C₂³	1	1	yes	characteristic
23	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
26	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₄₃	C₂³	1	3	yes	—
28	C₂²×Dic₄₃	C₂³	1	3	yes	—
29	C₂×C₄×D₄₃	—	4	3	no	—
30	C₄²×C₄₃	C₂×C₄	1	4	yes	complemented
31	(C₂×D₄₃)⋊C₄	—	4	3	no	—
32	(C₂×D₄₃)⋊C₄	C₂×C₄	1	12	yes	—
33	C₄⋊Dic₄₃	—	4	3	no	—
34	C₄⋊Dic₄₃	—	4	3	no	—
35	Dic₄₃⋊C₄	—	4	3	no	—
36	Dic₄₃⋊C₄	C₂×C₄	1	12	yes	complemented
37	C₄×Dic₄₃	—	4	3	no	—
38	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
39	C₂²×D₄₃	—	2	3	no	—
40	C₂²×D₄₃	—	2	3	no	—
41	C₂²×D₄₃	C₂²×C₄	1	2	yes	—
42	C₂×C₄×C₄₃	—	2	3	no	—
43	C₂×C₄×C₄₃	—	2	3	no	—
44	C₂×C₄×C₄₃	—	2	3	no	—
45	C₂×C₄×C₄₃	—	2	3	no	—
46	C₂×C₄×C₄₃	—	2	6	no	—
47	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
48	C₂×Dic₄₃	—	2	3	no	—
49	C₂×Dic₄₃	—	2	3	no	—
50	C₂×Dic₄₃	—	2	3	no	—
51	C₂×Dic₄₃	—	2	3	no	—
52	C₂×Dic₄₃	—	2	3	no	—
53	C₂×Dic₄₃	—	2	3	no	—
54	C₂×Dic₄₃	C₂²×C₄	1	6	yes	—
55	C₄×D₄₃	—	4	4	no	—
56	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
57	C₂²×C₄₃	H(5,𝔽₂)	1	3	yes	—
58	C₂²×C₄₃	2₋¹⁺⁴	1	3	yes	—
59	C₂×D₄₃	—	2	6	no	—
60	C₂×D₄₃	—	4	1	no	—
61	C₂×D₄₃	—	4	3	no	—
62	C₄×C₄₃	—	2	6	no	—
63	C₄×C₄₃	—	4	1	no	—
64	C₄×C₄₃	—	4	3	no	—
65	Dic₄₃	—	2	6	no	—
66	Dic₄₃	—	4	1	no	—
67	Dic₄₃	—	4	3	no	—
68	#2383	—	43	1	no	maximal, Sylow
69	C₂×C₄₃	#520	1	3	yes	—
70	C₂×C₄₃	#560	1	1	yes	characteristic
71	C₂×C₄₃	#563	1	3	yes	—
72	D₄₃	—	4	2	no	—
73	C₂×#126	—	43	1	no	—
74	#389	—	43	3	no	—
75	#388	—	43	3	no	—
76	#387	—	43	3	no	—
77	#385	—	43	3	no	—
78	#384	—	43	1	no	—
79	#383	D₄₃	1	1	yes	characteristic, complemented
80	C₄₃	#2383	1	1	yes	characteristic, complemented, Sylow
81	C₂³×C₄	—	43	1	no	—
82	#126	—	43	8	no	—
83	C₂×C₄⋊C₄	—	43	3	no	—
84	C₂×C₄⋊C₄	—	43	3	no	—
85	C₂×C₄⋊C₄	—	43	3	no	—
86	C₂×C₄⋊C₄	—	43	3	no	—
87	C₂×C₂²⋊C₄	—	43	3	no	—
88	C₂×C₂²⋊C₄	—	43	3	no	—
89	C₂×C₄²	—	43	3	no	—
90	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
91	#95	—	43	3	no	—
92	#95	—	43	3	no	—
93	#95	C₂×D₄₃	1	3	yes	—
94	#95	C₂×D₄₃	1	3	yes	—
95	C₂⁴	—	43	1	no	—
96	C₂²×C₄	—	43	3	no	—
97	C₂²×C₄	—	43	1	no	—
98	C₂²×C₄	—	43	3	no	—
99	C₂²×C₄	—	172	3	no	—
100	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
101	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
102	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
103	C₄⋊C₄	—	43	12	no	—
104	C₄⋊C₄	—	172	3	no	—
105	C₄⋊C₄	—	172	3	no	—
106	C₄⋊C₄	—	172	3	no	—
107	C₂²⋊C₄	—	43	12	no	—
108	C₂²⋊C₄	—	172	3	no	—
109	C₄²	—	172	3	no	—
110	C₄²	C₄×D₄₃	1	4	yes	complemented
111	C₂³	—	43	2	no	—
112	C₂³	—	86	3	no	—
113	C₂³	—	86	3	no	—
114	C₂³	C₂³×D₄₃	1	1	yes	characteristic
115	C₂×C₄	—	2	3	no	—
116	C₂×C₄	—	2	3	no	—
117	C₂×C₄	—	2	3	no	—
118	C₂×C₄	—	2	3	no	—
119	C₂×C₄	—	2	6	no	—
120	C₂×C₄	—	43	6	no	—
121	C₂×C₄	—	86	3	no	—
122	C₂×C₄	—	86	3	no	—
123	C₂×C₄	—	86	3	no	—
124	C₂×C₄	—	86	3	no	—
125	C₂×C₄	—	86	3	no	—
126	C₂×C₄	—	86	3	no	—
127	C₂×C₄	—	172	4	no	—
128	C₂×C₄	C₂×C₄×D₄₃	1	6	yes	—
129	C₂²	—	86	6	no	—
130	C₂²	—	172	1	no	—
131	C₂²	—	172	3	no	—
132	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
133	C₂²	#13063371	1	3	yes	—
134	C₂²	#13063372	1	3	yes	—
135	C₄	—	2	6	no	—
136	C₄	—	4	1	no	—
137	C₄	—	4	3	no	—
138	C₄	—	86	6	no	—
139	C₄	—	172	1	no	—
140	C₄	—	172	3	no	—
141	C₂	—	172	2	no	—
142	C₂	#14583379	1	3	yes	—
143	C₂	#14583640	1	1	yes	characteristic
144	C₂	#14583651	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063319

C₂

yes

maximal, characteristic

#14582796

C₂

yes

maximal, complemented

#14582791

C₂

yes

maximal

#14582786

C₂

yes

maximal, complemented

#14582773

C₂

yes

maximal

#14582769

C₂

yes

maximal, characteristic, complemented

C₄₃×#383

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₃

C₂²

yes

characteristic

#13063319

C₄

yes

complemented

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

—

C₂³×D₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×C₄×D₄₃

—

C₄²×C₄₃

C₂×C₄

yes

complemented

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

C₂×C₄

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

C₂×C₄

yes

complemented

C₄×Dic₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₄×D₄₃

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2383

—

maximal, Sylow

C₂×C₄₃

#520

yes

—

C₂×C₄₃

#560

yes

characteristic

C₂×C₄₃

#563

yes

—

D₄₃

—

—

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2383

yes

characteristic, complemented, Sylow

C₂³×C₄

—

#126

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

—

#95

C₂×D₄₃

yes

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

172

—

100

C₂²×C₄

C₂²×D₄₃

yes

—

101

C₂²×C₄

C₂²×D₄₃

yes

characteristic

102

C₂²×C₄

C₂²×D₄₃

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

172

—

105

C₄⋊C₄

—

172

—

106

C₄⋊C₄

—

172

—

107

C₂²⋊C₄

—

108

C₂²⋊C₄

—

172

—

109

C₄²

—

172

—

110

C₄²

C₄×D₄₃

yes

complemented

111

C₂³

—

112

C₂³

—

113

C₂³

—

114

C₂³

C₂³×D₄₃

yes

characteristic

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

172

—

128

C₂×C₄

C₂×C₄×D₄₃

yes

—

129

C₂²

—

130

C₂²

—

172

—

131

C₂²

—

172

—

132

C₂²

C₂²×C₄×D₄₃

yes

characteristic

133

C₂²

#13063371

yes

—

134

C₂²

#13063372

yes

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

172

—

140

C₄

—

172

—

141

C₂

—

172

—

142

C₂

#14583379

yes

—

143

C₂

#14583640

yes

characteristic

144

C₂

#14583651

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Fitting	C₄₃×#383	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	#383	D₄₃
hypocenter	C₄₃	#2383
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #383

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator

C₂²×C₄₃

C₂³×C₄

Fitting

C₄₃×#383

C₂

socle

C₂³×C₄₃

C₂⁴

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #383

N	H ≅ G/N	type
2. #14582796	C₂	semidirect
4. #14582786	C₂	semidirect
6. #14582769	C₂	semidirect
7. C₄₃×#383	C₂	semidirect
9. #13063319	C₄	semidirect
30. C₄²×C₄₃	C₂×C₄	semidirect
36. Dic₄₃⋊C₄	C₂×C₄	semidirect
79. #383	D₄₃	semidirect
80. C₄₃	#2383	semidirect
110. C₄²	C₄×D₄₃	semidirect

H ≅ G/N

type

2. #14582796

C₂

semidirect

4. #14582786

C₂

semidirect

6. #14582769

C₂

semidirect

7. C₄₃×#383

C₂

semidirect

9. #13063319

C₄

semidirect

30. C₄²×C₄₃

C₂×C₄

semidirect

36. Dic₄₃⋊C₄

C₂×C₄

semidirect

79. #383

D₄₃

semidirect

80. C₄₃

#2383

semidirect

110. C₄²

C₄×D₄₃

semidirect

Subgroups — #19137784

Conjugacy classes of subgroups

Complements