Group #19145106 — subgroups

Subgroups — #19145106

Order 5504.

356 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 145 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	#14583454	C₂	1	2	yes	maximal
2	#14583304	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583300	C₂	1	4	yes	maximal, complemented
4	#14583295	C₂	1	2	yes	maximal, complemented
5	#14582936	C₂	1	4	yes	maximal
6	C₄×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄₃	C₂²	1	2	yes	—
9	#13063325	C₂²	1	2	yes	—
10	#13063316	C₂²	1	4	yes	—
11	#13063305	—	2	2	no	—
12	#13063301	—	2	2	no	—
13	Q₈×Dic₄₃	—	2	2	no	—
14	#13063290	—	2	2	no	—
15	#13063283	C₂²	1	4	yes	—
16	C₄²×D₄₃	C₂²	1	1	yes	characteristic
17	#13063259	C₂²	1	4	yes	—
18	#13063256	C₂²	1	8	yes	—
19	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₈×Dic₄₃	C₂²	1	2	yes	—
21	C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
22	#107×C₄₃	C₂²	1	4	yes	—
23	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×Q₈×C₄₃	—	2	2	no	—
25	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
26	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
27	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
28	C₂×Dic₈₆	—	2	2	no	—
29	C₂×C₈×C₄₃	C₂³	1	2	yes	—
30	C₄⋊C₄×C₄₃	—	2	2	no	—
31	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
32	C₄²×C₄₃	C₂³	1	1	yes	characteristic
33	(C₂×D₄₃)⋊C₄	—	2	4	no	—
34	C₄⋊Dic₄₃	—	2	2	no	—
35	C₄⋊Dic₄₃	—	2	4	no	—
36	C₄⋊Dic₄₃	C₂³	1	4	yes	—
37	Dic₄₃⋊C₄	—	2	4	no	—
38	C₄×Dic₄₃	—	2	4	no	—
39	C₄×Dic₄₃	D₄	1	1	yes	characteristic
40	C₄×Dic₄₃	D₄	1	1	yes	characteristic
41	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
42	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
43	C₈×D₄₃	Q₈	1	8	yes	complemented
44	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
45	Q₈×C₄₃	—	4	4	no	—
46	C₂×C₄×C₄₃	—	2	4	no	—
47	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₄₃	—	2	4	no	—
51	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
52	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
53	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
54	C₄×D₄₃	—	2	2	no	—
55	C₄×D₄₃	—	2	2	no	—
56	C₄×D₄₃	C₂×Q₈	1	4	yes	—
57	Dic₈₆	—	4	4	no	—
58	C₈×C₄₃	C₂×Q₈	1	4	yes	—
59	C₄₃⋊C₈	C₂×Q₈	1	4	yes	—
60	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
61	C₂×D₄₃	—	2	1	no	—
62	C₂×D₄₃	—	2	1	no	—
63	C₂×D₄₃	C₄⋊Q₈	1	2	yes	—
64	C₄×C₄₃	—	4	4	no	—
65	C₄×C₄₃	#135	1	2	yes	—
66	C₄×C₄₃	#135	1	2	yes	—
67	C₄×C₄₃	C₂²×Q₈	1	2	yes	—
68	Dic₄₃	—	2	1	no	—
69	Dic₄₃	—	2	1	no	—
70	Dic₄₃	—	4	4	no	—
71	Dic₄₃	C₄⋊Q₈	1	2	yes	—
72	#3160	—	43	1	no	maximal, Sylow
73	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
74	C₂×C₄₃	C₂×#135	1	1	yes	characteristic
75	C₂×C₄₃	C₂×#135	1	1	yes	characteristic
76	D₄₃	—	2	2	no	—
77	#533	—	43	2	no	—
78	#500	—	43	1	no	—
79	#500	D₄₃	1	1	yes	characteristic, complemented
80	#499	—	43	4	no	—
81	#498	—	43	2	no	—
82	#427	—	43	4	no	—
83	C₂×C₄×C₈	—	43	1	no	—
84	C₄₃	#3160	1	1	yes	characteristic, complemented, Sylow
85	C₂²×C₈	—	43	2	no	—
86	C₄⋊Q₈	—	43	2	no	—
87	C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
88	#125	—	43	4	no	—
89	C₂²⋊Q₈	—	86	2	no	—
90	C₂²⋊Q₈	—	86	2	no	—
91	C₄×Q₈	—	86	2	no	—
92	C₄×Q₈	—	86	2	no	—
93	#117	—	43	4	no	—
94	C₂×C₄²	—	43	1	no	—
95	#107	—	43	4	no	—
96	#107	C₂×D₄₃	1	4	yes	—
97	#106	—	43	8	no	—
98	C₄×C₈	—	43	2	no	—
99	C₄×C₈	—	43	1	no	—
100	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
101	C₂×Q₈	—	2	2	no	—
102	C₂×Q₈	—	86	2	no	—
103	C₂²×C₄	—	43	1	no	—
104	C₂²×C₄	—	43	1	no	—
105	C₂²×C₄	—	43	1	no	—
106	C₂×C₈	—	43	2	no	—
107	C₂×C₈	—	43	8	no	—
108	C₂×C₈	C₂²×D₄₃	1	2	yes	—
109	C₄⋊C₄	—	2	2	no	—
110	C₄⋊C₄	—	43	4	no	—
111	C₄⋊C₄	—	86	4	no	—
112	C₄⋊C₄	—	86	4	no	—
113	C₄⋊C₄	—	86	2	no	—
114	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
115	C₂²⋊C₄	—	86	4	no	—
116	C₄²	—	43	1	no	—
117	C₄²	—	43	1	no	—
118	C₄²	—	43	1	no	—
119	C₄²	—	86	4	no	—
120	C₄²	C₂²×D₄₃	1	1	yes	characteristic
121	C₂³	—	43	1	no	—
122	Q₈	—	4	4	no	—
123	Q₈	—	172	4	no	—
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	43	1	no	—
126	C₂×C₄	—	43	4	no	—
127	C₂×C₄	—	43	1	no	—
128	C₂×C₄	—	43	1	no	—
129	C₂×C₄	—	86	2	no	—
130	C₂×C₄	—	86	2	no	—
131	C₂×C₄	—	86	4	no	—
132	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
133	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
134	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
135	C₈	—	43	4	no	—
136	C₈	Q₈×D₄₃	1	4	yes	—
137	C₂²	—	43	2	no	—
138	C₂²	—	86	1	no	—
139	C₂²	—	86	1	no	—
140	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
141	C₄	—	4	4	no	—
142	C₄	—	43	2	no	—
143	C₄	—	86	1	no	—
144	C₄	—	86	1	no	—
145	C₄	—	172	4	no	—
146	C₄	#13063344	1	2	yes	—
147	C₄	#13063348	1	2	yes	—
148	C₄	C₂×Q₈×D₄₃	1	2	yes	—
149	C₂	—	86	2	no	—
150	C₂	C₄⋊Q₈×D₄₃	1	1	yes	characteristic
151	C₂	C₂×#13063344	1	1	yes	characteristic
152	C₂	C₂×#13063348	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583454

C₂

yes

maximal

#14583304

C₂

yes

maximal, characteristic, complemented

#14583300

C₂

yes

maximal, complemented

#14583295

C₂

yes

maximal, complemented

#14582936

C₂

yes

maximal

C₄×C₈×D₄₃

C₂

yes

maximal, characteristic

C₄₃×#500

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₃

C₂²

yes

—

#13063325

C₂²

yes

—

#13063316

C₂²

yes

—

#13063305

—

#13063301

—

Q₈×Dic₄₃

—

#13063290

—

#13063283

C₂²

yes

—

C₄²×D₄₃

C₂²

yes

characteristic

#13063259

C₂²

yes

—

#13063256

C₂²

yes

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₈×Dic₄₃

C₂²

yes

—

C₄⋊Q₈×C₄₃

C₂²

yes

—

#107×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

characteristic

C₂×C₄×D₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂³

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

D₄

yes

characteristic

C₄×Dic₄₃

D₄

yes

characteristic

C₄×Dic₄₃

C₂³

yes

characteristic

C₂×C₄₃⋊C₈

C₂³

yes

—

C₈×D₄₃

Q₈

yes

complemented

C₂²×D₄₃

C₂×D₄

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

C₂×D₄

yes

characteristic

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

C₂×Q₈

yes

—

Dic₈₆

—

C₈×C₄₃

C₂×Q₈

yes

—

C₄₃⋊C₈

C₂×Q₈

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

C₄⋊Q₈

yes

—

C₄×C₄₃

—

C₄×C₄₃

#135

yes

—

C₄×C₄₃

#135

yes

—

C₄×C₄₃

C₂²×Q₈

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

C₄⋊Q₈

yes

—

#3160

—

maximal, Sylow

C₂×C₄₃

C₂×C₄⋊Q₈

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

#533

—

#500

—

#500

D₄₃

yes

characteristic, complemented

#499

—

#498

—

#427

—

C₂×C₄×C₈

—

C₄₃

#3160

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

#107

—

#107

C₂×D₄₃

yes

—

#106

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

C₂×D₄₃

yes

characteristic

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

C₂²×D₄₃

yes

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

C₂²×D₄₃

yes

—

115

C₂²⋊C₄

—

116

C₄²

—

117

C₄²

—

118

C₄²

—

119

C₄²

—

120

C₄²

C₂²×D₄₃

yes

characteristic

121

C₂³

—

122

Q₈

—

123

Q₈

—

172

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

D₄×D₄₃

yes

characteristic

133

C₂×C₄

D₄×D₄₃

yes

characteristic

134

C₂×C₄

C₂³×D₄₃

yes

characteristic

135

C₈

—

136

C₈

Q₈×D₄₃

yes

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

C₂×D₄×D₄₃

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

—

172

—

146

C₄

#13063344

yes

—

147

C₄

#13063348

yes

—

148

C₄

C₂×Q₈×D₄₃

yes

—

149

C₂

—

150

C₂

C₄⋊Q₈×D₄₃

yes

characteristic

151

C₂

C₂×#13063344

yes

characteristic

152

C₂

C₂×#13063348

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#500	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#500	D₄₃
hypocenter	C₄₃	#3160
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

C₂×D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#500

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
2. #14583304	C₂	semidirect
3. #14583300	C₂	semidirect
4. #14583295	C₂	semidirect
7. C₄₃×#500	C₂	semidirect
43. C₈×D₄₃	Q₈	semidirect
79. #500	D₄₃	semidirect
84. C₄₃	#3160	semidirect

H ≅ G/N

type

2. #14583304

C₂

semidirect

3. #14583300

C₂

semidirect

4. #14583295

C₂

semidirect

7. C₄₃×#500

C₂

semidirect

43. C₈×D₄₃

Q₈

semidirect

79. #500

D₄₃

semidirect

84. C₄₃

#3160

semidirect

Subgroups — #19145106

Conjugacy classes of subgroups

Complements