Group #19134328 — subgroups

Subgroups — #19134328

Order 5504.

420 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 189 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	2	yes	maximal
2	#14582666	C₂	1	4	yes	maximal
3	C₂×#117×C₄₃	C₂	1	1	yes	maximal, characteristic
4	#13063284	—	2	4	no	—
5	#13063284	C₄	1	8	yes	complemented
6	C₂×C₄⋊Dic₄₃	—	2	2	no	—
7	C₂×C₂²⋊Dic₄₃	C₂²	1	4	yes	—
8	C₂×C₄×Dic₄₃	—	2	2	no	—
9	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
10	#117×C₄₃	—	2	2	no	—
11	#117×C₄₃	—	2	2	no	—
12	C₂×C₄⋊C₄×C₄₃	C₄	1	2	yes	complemented
13	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₄₃	C₄	1	2	yes	complemented
15	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
17	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
18	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₄₃	D₄	1	2	yes	—
21	C₂²×C₄×C₄₃	D₄	1	2	yes	—
22	C₂²×C₄×C₄₃	D₄	1	2	yes	—
23	C₂²×C₄×C₄₃	Q₈	1	2	yes	—
24	C₂²×Dic₄₃	—	2	4	no	—
25	C₄⋊C₄×C₄₃	—	2	4	no	—
26	C₂²⋊C₄×C₄₃	—	2	4	no	—
27	C₄²×C₄₃	—	2	2	no	—
28	C₄²×C₄₃	—	2	2	no	—
29	C₂²⋊Dic₄₃	—	2	4	no	—
30	C₂²⋊Dic₄₃	C₂×C₄	1	8	yes	—
31	C₄⋊Dic₄₃	—	2	8	no	—
32	C₄×Dic₄₃	—	2	8	no	—
33	C₂³×C₄₃	—	4	2	no	—
34	C₂³×C₄₃	C₂²×C₄	1	2	yes	—
35	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
36	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
37	C₂³×C₄₃	C₂×D₄	1	2	yes	—
38	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₄₃	—	2	4	no	—
40	C₂×C₄×C₄₃	—	4	4	no	—
41	C₂×C₄×C₄₃	C₄²	1	2	yes	—
42	C₂×C₄×C₄₃	C₄²	1	2	yes	—
43	C₂×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
44	C₂×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
45	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
47	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
49	C₂×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
50	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
51	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
52	C₂×Dic₄₃	—	2	8	no	—
53	C₂×Dic₄₃	—	4	8	no	—
54	C₂²×C₄₃	—	2	2	no	—
55	C₂²×C₄₃	—	2	4	no	—
56	C₂²×C₄₃	—	4	2	no	—
57	C₂²×C₄₃	—	4	1	no	—
58	C₂²×C₄₃	—	4	1	no	—
59	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
60	C₂²×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
63	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₄×C₄₃	—	4	4	no	—
65	C₄×C₄₃	#95	1	4	yes	—
66	C₄×C₄₃	#95	1	2	yes	—
67	C₄×C₄₃	#95	1	2	yes	—
68	Dic₄₃	—	4	8	no	—
69	#1740	—	43	1	no	maximal, Sylow
70	C₂×C₄₃	—	2	2	no	—
71	C₂×C₄₃	—	2	1	no	—
72	C₂×C₄₃	—	2	2	no	—
73	C₂×C₄₃	—	2	1	no	—
74	C₂×C₄₃	C₂×#95	1	1	yes	characteristic
75	C₂×C₄₃	#410	1	2	yes	—
76	C₂×#117	—	43	2	no	—
77	C₂×#117	D₄₃	1	1	yes	characteristic
78	#342	—	43	4	no	—
79	C₄₃	#1740	1	1	yes	characteristic, complemented, Sylow
80	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
81	#117	—	2	2	no	—
82	#117	—	2	2	no	—
83	#117	—	43	8	no	—
84	#117	—	86	4	no	—
85	C₂×C₄⋊C₄	—	86	2	no	—
86	C₂×C₄⋊C₄	Dic₄₃	1	2	yes	complemented
87	C₂×C₂²⋊C₄	—	43	4	no	—
88	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
89	C₂×C₄²	—	86	2	no	—
90	C₂×C₄²	Dic₄₃	1	2	yes	complemented
91	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
92	C₂²×C₄	—	86	4	no	—
93	C₂²×C₄	Dic₈₆	1	2	yes	—
94	C₂²×C₄	C₄×D₄₃	1	4	yes	—
95	C₂²×C₄	D₁₇₂	1	2	yes	—
96	C₂²×C₄	C₂×Dic₄₃	1	4	yes	—
97	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
98	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
99	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
100	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
101	C₄⋊C₄	—	2	4	no	—
102	C₄⋊C₄	—	86	8	no	—
103	C₂²⋊C₄	—	2	4	no	—
104	C₂²⋊C₄	—	43	8	no	—
105	C₂²⋊C₄	—	86	4	no	—
106	C₄²	—	2	2	no	—
107	C₄²	—	2	2	no	—
108	C₄²	—	86	8	no	—
109	C₂³	—	4	2	no	—
110	C₂³	C₂×Dic₈₆	1	1	yes	characteristic
111	C₂³	C₂×C₄×D₄₃	1	2	yes	—
112	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
113	C₂³	C₂²×Dic₄₃	1	1	yes	characteristic
114	C₂³	C₂×C₂²⋊D₄₃	1	2	yes	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	4	4	no	—
117	C₂×C₄	—	86	8	no	—
118	C₂×C₄	—	172	8	no	—
119	C₂×C₄	C₄×Dic₄₃	1	2	yes	—
120	C₂×C₄	C₄×Dic₄₃	1	2	yes	—
121	C₂×C₄	Dic₄₃⋊C₄	1	4	yes	—
122	C₂×C₄	Dic₄₃⋊C₄	1	4	yes	—
123	C₂×C₄	C₄⋊Dic₄₃	1	2	yes	—
124	C₂×C₄	C₄⋊Dic₄₃	1	2	yes	—
125	C₂×C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
126	C₂×C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
127	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
128	C₂×C₄	C₂²⋊Dic₄₃	1	2	yes	—
129	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
130	C₂²	—	2	2	no	—
131	C₂²	—	2	4	no	—
132	C₂²	—	4	1	no	—
133	C₂²	—	4	2	no	—
134	C₂²	—	4	1	no	—
135	C₂²	C₂×C₄×Dic₄₃	1	1	yes	characteristic
136	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
137	C₂²	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
138	C₂²	C₂×Dic₄₃⋊C₄	1	2	yes	—
139	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
140	C₄	—	4	4	no	—
141	C₄	—	172	8	no	—
142	C₄	C₄₃⋊#95	1	4	yes	—
143	C₄	C₄₃⋊#95	1	2	yes	—
144	C₄	C₄₃⋊#95	1	2	yes	—
145	C₂	—	2	2	no	—
146	C₂	—	2	1	no	—
147	C₂	—	2	2	no	—
148	C₂	—	2	1	no	—
149	C₂	C₂×C₄₃⋊#95	1	1	yes	characteristic
150	C₂	#14582873	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063284

C₂

yes

maximal

#14582666

C₂

yes

maximal

C₂×#117×C₄₃

C₂

yes

maximal, characteristic

#13063284

—

#13063284

C₄

yes

complemented

C₂×C₄⋊Dic₄₃

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

#117×C₄₃

—

#117×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₄

yes

complemented

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₄

yes

complemented

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

Q₈

yes

—

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

C₂×C₄

yes

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂²×C₄

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄²

yes

—

C₂×C₄×C₄₃

C₄²

yes

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄²

yes

characteristic

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

C₂×C₄⋊C₄

yes

—

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

#95

yes

—

C₄×C₄₃

#95

yes

—

C₄×C₄₃

#95

yes

—

Dic₄₃

—

#1740

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

C₂×#95

yes

characteristic

C₂×C₄₃

#410

yes

—

C₂×#117

—

C₂×#117

D₄₃

yes

characteristic

#342

—

C₄₃

#1740

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₃

yes

—

—

—

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

Dic₄₃

yes

complemented

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

Dic₄₃

yes

complemented

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

Dic₈₆

yes

—

C₂²×C₄

C₄×D₄₃

yes

—

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

—

100

C₂²×C₄

C₂²⋊D₄₃

yes

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

—

105

C₂²⋊C₄

—

106

C₄²

—

107

C₄²

—

108

C₄²

—

109

C₂³

—

110

C₂³

C₂×Dic₈₆

yes

characteristic

111

C₂³

C₂×C₄×D₄₃

yes

—

112

C₂³

C₂×D₁₇₂

yes

characteristic

113

C₂³

C₂²×Dic₄₃

yes

characteristic

114

C₂³

C₂×C₂²⋊D₄₃

yes

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

172

—

119

C₂×C₄

C₄×Dic₄₃

yes

—

120

C₂×C₄

C₄×Dic₄₃

yes

—

121

C₂×C₄

Dic₄₃⋊C₄

yes

—

122

C₂×C₄

Dic₄₃⋊C₄

yes

—

123

C₂×C₄

C₄⋊Dic₄₃

yes

—

124

C₂×C₄

C₄⋊Dic₄₃

yes

—

125

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

126

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

127

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

128

C₂×C₄

C₂²⋊Dic₄₃

yes

—

129

C₂×C₄

C₂²⋊Dic₄₃

yes

characteristic

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

C₂×C₄×Dic₄₃

yes

characteristic

136

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

—

137

C₂²

C₂×C₂²⋊Dic₄₃

yes

characteristic

138

C₂²

C₂×Dic₄₃⋊C₄

yes

—

139

C₂²

C₂×C₄⋊Dic₄₃

yes

characteristic

140

C₄

—

141

C₄

—

172

—

142

C₄

C₄₃⋊#95

yes

—

143

C₄

C₄₃⋊#95

yes

—

144

C₄

C₄₃⋊#95

yes

—

145

C₂

—

146

C₂

—

147

C₂

—

148

C₂

—

149

C₂

C₂×C₄₃⋊#95

yes

characteristic

150

C₂

#14582873

yes

—

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₄₃
commutator	C₂²×C₄₃	C₂×C₄²
Frattini	C₂⁴	C₂²×D₄₃
Fitting	C₂×#117×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₄
hypercenter	C₂×#117	D₄₃
hypocenter	C₄₃	#1740
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#117

subgroup

G/H

center

C₂×C₄

C₂²⋊Dic₄₃

commutator

C₂²×C₄₃

C₂×C₄²

Frattini

C₂⁴

C₂²×D₄₃

Fitting

C₂×#117×C₄₃

C₂

socle

C₂²×C₄₃

C₂×C₂²⋊C₄

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#117

N	H ≅ G/N	type
5. #13063284	C₄	semidirect
12. C₂×C₄⋊C₄×C₄₃	C₄	semidirect
14. C₂×C₄²×C₄₃	C₄	semidirect
79. C₄₃	#1740	semidirect
86. C₂×C₄⋊C₄	Dic₄₃	semidirect
90. C₂×C₄²	Dic₄₃	semidirect

H ≅ G/N

type

5. #13063284

C₄

semidirect

12. C₂×C₄⋊C₄×C₄₃

C₄

semidirect

14. C₂×C₄²×C₄₃

C₄

semidirect

79. C₄₃

#1740

semidirect

86. C₂×C₄⋊C₄

Dic₄₃

semidirect

90. C₂×C₄²

Dic₄₃

semidirect

Subgroups — #19134328

Conjugacy classes of subgroups

Complements