Group #19134696 — subgroups

Subgroups — #19134696

Order 5504.

262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 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	#41×Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	#14582883	C₂	1	1	yes	maximal, characteristic
3	#14582658	C₂	1	2	yes	maximal, complemented
4	#14582655	C₂	1	2	yes	maximal, complemented
5	C₄₃×#410	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621877	C₂²	1	2	yes	—
7	Q₈×Dic₄₃	—	2	1	no	—
8	D₄×Dic₄₃	—	2	1	no	—
9	D₄×Dic₄₃	—	2	2	no	—
10	#13063284	C₄	1	2	yes	complemented
11	#13063284	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₄₃	C₄	1	2	yes	complemented
13	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
14	#13063244	—	2	1	no	—
15	#13063242	—	2	1	no	—
16	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
17	#117×C₄₃	C₂²	1	2	yes	—
18	#99×C₄₃	—	2	2	no	—
19	#41×C₄₃	—	2	2	no	—
20	#41×C₄₃	—	2	2	no	—
21	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
22	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
23	C₂×D₄×C₄₃	D₄	1	2	yes	—
24	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₃	—	2	2	no	—
27	C₂²×Dic₄₃	—	2	1	no	—
28	C₄⋊C₄×C₄₃	—	2	2	no	—
29	C₂²⋊C₄×C₄₃	—	2	2	no	—
30	C₄²×C₄₃	—	2	2	no	—
31	C₂²⋊Dic₄₃	—	2	2	no	—
32	C₂²⋊Dic₄₃	—	2	1	no	—
33	C₄⋊Dic₄₃	—	2	2	no	—
34	C₄⋊Dic₄₃	—	2	1	no	—
35	C₄×Dic₄₃	—	2	2	no	—
36	C₄×Dic₄₃	—	2	1	no	—
37	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
38	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
39	C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
40	#10621877	—	2	2	no	—
41	#10621877	—	2	2	no	—
42	C₂×C₄₃⋊C₈	—	2	2	no	—
43	C₂³×C₄₃	C₂²⋊C₄	1	2	yes	—
44	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
45	Q₈×C₄₃	—	2	2	no	—
46	D₄×C₄₃	—	2	4	no	—
47	D₄×C₄₃	—	2	2	no	—
48	C₂×C₄×C₄₃	—	2	2	no	—
49	C₂×C₄×C₄₃	—	2	2	no	—
50	C₂×C₄×C₄₃	—	4	2	no	—
51	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
52	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₄₃	#41	1	2	yes	—
55	C₂×C₄×C₄₃	#41	1	2	yes	—
56	C₂×Dic₄₃	—	2	1	no	—
57	C₂×Dic₄₃	—	2	2	no	—
58	C₂×Dic₄₃	—	2	1	no	—
59	C₂×Dic₄₃	—	4	2	no	—
60	C₂×Dic₄₃	—	4	4	no	—
61	C₄₃⋊C₈	—	4	2	no	—
62	C₂²×C₄₃	—	2	2	no	—
63	C₂²×C₄₃	—	4	1	no	—
64	C₂²×C₄₃	—	4	2	no	—
65	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄₃	#123	1	2	yes	—
67	C₄×C₄₃	—	2	2	no	—
68	C₄×C₄₃	—	8	2	no	—
69	C₄×C₄₃	#117	1	1	yes	characteristic
70	C₄×C₄₃	#117	1	1	yes	characteristic
71	C₄×C₄₃	#123	1	2	yes	—
72	Dic₄₃	—	2	2	no	—
73	Dic₄₃	—	4	2	no	—
74	Dic₄₃	—	4	1	no	—
75	#1827	—	43	1	no	maximal, Sylow
76	C₂×C₄₃	—	2	1	no	—
77	C₂×C₄₃	—	2	2	no	—
78	C₂×C₄₃	—	4	2	no	—
79	C₂×C₄₃	#381	1	1	yes	characteristic
80	C₄×#41	—	43	1	no	—
81	#413	—	43	1	no	—
82	#410	D₄₃	1	1	yes	characteristic
83	#339	—	43	2	no	—
84	H(3,ℤ/4)	—	43	2	no	—
85	C₄₃	#1827	1	1	yes	characteristic, complemented, Sylow
86	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
87	C₂×M₁₆	—	43	2	no	—
88	C₄×Q₈	—	86	1	no	—
89	C₄×D₄	—	86	1	no	—
90	C₄×D₄	—	86	2	no	—
91	#117	—	43	1	no	—
92	#117	—	43	2	no	—
93	#117	C₂×D₄₃	1	2	yes	—
94	C₂×C₄²	—	43	1	no	—
95	C₂×C₄²	—	43	2	no	—
96	#101	—	86	1	no	—
97	#100	—	86	1	no	—
98	#99	—	2	2	no	—
99	#41	—	2	2	no	—
100	#41	—	2	2	no	—
101	C₂×Q₈	D₁₇₂	1	1	yes	characteristic
102	C₂×D₄	D₁₇₂	1	1	yes	characteristic
103	C₂×D₄	C₂²⋊D₄₃	1	2	yes	—
104	C₂²×C₄	—	86	2	no	—
105	C₂²×C₄	—	86	1	no	—
106	C₂²×C₄	C₄×D₄₃	1	2	yes	—
107	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
108	M₁₆	—	86	2	no	—
109	M₁₆	—	86	2	no	—
110	C₂×C₈	—	86	2	no	—
111	C₄⋊C₄	—	2	2	no	—
112	C₄⋊C₄	—	86	2	no	—
113	C₄⋊C₄	—	86	1	no	—
114	C₂²⋊C₄	—	2	2	no	—
115	C₂²⋊C₄	—	86	2	no	—
116	C₂²⋊C₄	—	86	1	no	—
117	C₄²	—	2	2	no	—
118	C₄²	—	43	1	no	—
119	C₄²	—	43	1	no	—
120	C₄²	—	43	2	no	—
121	C₄²	—	86	2	no	—
122	C₄²	—	86	1	no	—
123	C₂³	(C₂×D₄₃)⋊C₄	1	2	yes	—
124	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
125	Q₈	—	2	2	no	—
126	D₄	—	2	4	no	—
127	D₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	4	2	no	—
131	C₂×C₄	—	86	1	no	—
132	C₂×C₄	—	86	2	no	—
133	C₂×C₄	—	86	1	no	—
134	C₂×C₄	—	172	2	no	—
135	C₂×C₄	—	172	4	no	—
136	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
137	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
138	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
139	C₂×C₄	#10621900	1	2	yes	—
140	C₂×C₄	#10621900	1	2	yes	—
141	C₈	—	172	2	no	—
142	C₂²	—	2	2	no	—
143	C₂²	—	4	1	no	—
144	C₂²	—	4	2	no	—
145	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
146	C₂²	#13063306	1	2	yes	—
147	C₄	—	2	2	no	—
148	C₄	—	8	2	no	—
149	C₄	—	86	2	no	—
150	C₄	—	172	2	no	—
151	C₄	—	172	1	no	—
152	C₄	#13063281	1	1	yes	characteristic
153	C₄	#13063281	1	1	yes	characteristic
154	C₄	#13063309	1	2	yes	—
155	C₂	—	2	2	no	—
156	C₂	—	2	1	no	—
157	C₂	—	4	2	no	—
158	C₂	#14582760	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#41×Dic₄₃

C₂

yes

maximal, characteristic

#14582883

C₂

yes

maximal, characteristic

#14582658

C₂

yes

maximal, complemented

#14582655

C₂

yes

maximal, complemented

C₄₃×#410

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

Q₈×Dic₄₃

—

D₄×Dic₄₃

—

D₄×Dic₄₃

—

#13063284

C₄

yes

complemented

#13063284

C₂²

yes

characteristic

C₂×C₄×Dic₄₃

C₄

yes

complemented

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

#13063244

—

#13063242

—

C₂×#41×C₄₃

C₂²

yes

characteristic

#117×C₄₃

C₂²

yes

—

#99×C₄₃

—

#41×C₄₃

—

#41×C₄₃

—

C₂×Q₈×C₄₃

D₄

yes

characteristic

C₂×D₄×C₄₃

D₄

yes

characteristic

C₂×D₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂×C₄

yes

characteristic

C₄×Dic₄₃

C₂×C₄

yes

—

C₄×Dic₄₃

C₂×C₄

yes

characteristic

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²⋊C₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

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

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₃

#123

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#1827

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#381

yes

characteristic

C₄×#41

—

#413

—

#410

D₄₃

yes

characteristic

#339

—

H(3,ℤ/4)

—

C₄₃

#1827

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₄₃

yes

characteristic

C₂×M₁₆

—

C₄×Q₈

—

C₄×D₄

—

C₄×D₄

—

#117

—

#117

—

#117

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

—

—

—

—

100

#41

—

101

C₂×Q₈

D₁₇₂

yes

characteristic

102

C₂×D₄

D₁₇₂

yes

characteristic

103

C₂×D₄

C₂²⋊D₄₃

yes

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

C₄×D₄₃

yes

—

107

C₂²×C₄

C₂²×D₄₃

yes

characteristic

108

M₁₆

—

109

M₁₆

—

110

C₂×C₈

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₂²⋊C₄

—

115

C₂²⋊C₄

—

116

C₂²⋊C₄

—

117

C₄²

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₄²

—

122

C₄²

—

123

C₂³

(C₂×D₄₃)⋊C₄

yes

—

124

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

125

Q₈

—

126

D₄

—

127

D₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

172

—

135

C₂×C₄

—

172

—

136

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

137

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

138

C₂×C₄

C₂×D₁₇₂

yes

characteristic

139

C₂×C₄

#10621900

yes

—

140

C₂×C₄

#10621900

yes

—

141

C₈

—

172

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

146

C₂²

#13063306

yes

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

172

—

151

C₄

—

172

—

152

C₄

#13063281

yes

characteristic

153

C₄

#13063281

yes

characteristic

154

C₄

#13063309

yes

—

155

C₂

—

156

C₂

—

157

C₂

—

158

C₂

#14582760

yes

characteristic

	subgroup	G/H
center	C₄	#13063281
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#410	C₂
socle	C₂×C₄₃	#381
hypercenter	#410	D₄₃
hypocenter	C₄₃	#1827
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #410

subgroup

G/H

center

C₄

#13063281

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#410

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #410

N	H ≅ G/N	type
3. #14582658	C₂	semidirect
4. #14582655	C₂	semidirect
10. #13063284	C₄	semidirect
12. C₂×C₄×Dic₄₃	C₄	semidirect
85. C₄₃	#1827	semidirect

H ≅ G/N

type

3. #14582658

C₂

semidirect

4. #14582655

C₂

semidirect

10. #13063284

C₄

semidirect

12. C₂×C₄×Dic₄₃

C₄

semidirect

85. C₄₃

#1827

semidirect

Subgroups — #19134696

Conjugacy classes of subgroups

Complements