Group #19145108 — subgroups

Subgroups — #19145108

Order 5504.

356 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 141 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	#14583455	C₂	1	2	yes	maximal
2	#14583303	C₂	1	2	yes	maximal, complemented
3	#14583301	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583298	C₂	1	2	yes	maximal, complemented
5	#14583296	C₂	1	2	yes	maximal, complemented
6	#14582936	C₂	1	2	yes	maximal
7	#14582934	C₂	1	2	yes	maximal
8	C₄×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
9	C₄₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
12	#13063324	C₂²	1	4	yes	—
13	#13063317	C₂²	1	2	yes	—
14	#13063303	—	2	4	no	—
15	#13063290	—	2	4	no	—
16	#13063283	C₂²	1	4	yes	—
17	C₄²×D₄₃	C₂²	1	1	yes	characteristic
18	#13063259	C₂²	1	2	yes	—
19	#13063258	C₂²	1	4	yes	—
20	#13063257	C₂²	1	2	yes	—
21	#13063256	C₂²	1	4	yes	—
22	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
24	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
25	#125×C₄₃	C₂²	1	2	yes	—
26	#107×C₄₃	C₂²	1	2	yes	—
27	#106×C₄₃	C₂²	1	2	yes	—
28	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄₃	D₄	1	2	yes	—
30	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
31	C₂×Dic₈₆	—	2	4	no	—
32	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
33	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
34	C₄⋊C₄×C₄₃	—	2	4	no	—
35	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
36	C₄²×C₄₃	C₂³	1	1	yes	characteristic
37	(C₂×D₄₃)⋊C₄	—	2	4	no	—
38	C₄⋊Dic₄₃	C₂³	1	4	yes	—
39	Dic₄₃⋊C₄	—	2	4	no	—
40	Dic₄₃⋊C₄	—	2	4	no	—
41	C₄×Dic₄₃	—	2	4	no	—
42	C₄×Dic₄₃	D₄	1	2	yes	—
43	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
44	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
45	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
46	C₈×D₄₃	Q₈	1	4	yes	complemented
47	C₈×D₄₃	Q₈	1	4	yes	complemented
48	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₃	—	2	4	no	—
50	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
52	C₂×Dic₄₃	—	2	4	no	—
53	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
54	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
55	C₄×D₄₃	—	2	4	no	—
56	C₄×D₄₃	C₂×Q₈	1	2	yes	—
57	C₄×D₄₃	C₂×Q₈	1	2	yes	—
58	Dic₈₆	—	4	8	no	—
59	C₈×C₄₃	C₂×Q₈	1	2	yes	—
60	C₈×C₄₃	C₂×Q₈	1	2	yes	—
61	C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
62	C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
63	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
64	C₂×D₄₃	—	2	2	no	—
65	C₂×D₄₃	C₄⋊Q₈	1	2	yes	—
66	C₄×C₄₃	—	2	2	no	—
67	C₄×C₄₃	—	4	4	no	—
68	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
69	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
70	Dic₄₃	—	4	4	no	—
71	Dic₄₃	C₄⋊Q₈	1	2	yes	—
72	Dic₄₃	#135	1	4	yes	—
73	#3160	—	43	1	no	maximal, Sylow
74	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
75	C₂×C₄₃	C₂×#135	1	2	yes	—
76	D₄₃	—	2	2	no	—
77	#533	—	43	2	no	—
78	#500	—	43	2	no	—
79	#499	—	43	2	no	—
80	#499	—	43	1	no	—
81	#499	D₄₃	1	1	yes	characteristic, complemented
82	#498	—	43	2	no	—
83	#427	—	43	2	no	—
84	#427	—	43	2	no	—
85	C₂×C₄×C₈	—	43	1	no	—
86	C₄₃	#3160	1	1	yes	characteristic, complemented, Sylow
87	C₂²×C₈	—	43	1	no	—
88	C₂²×C₈	—	43	1	no	—
89	C₄⋊Q₈	—	43	4	no	—
90	#125	—	43	2	no	—
91	#125	C₂×D₄₃	1	2	yes	—
92	C₂²⋊Q₈	—	86	4	no	—
93	C₄×Q₈	—	86	4	no	—
94	#117	—	43	4	no	—
95	C₂×C₄²	—	43	1	no	—
96	#107	—	43	2	no	—
97	#107	—	43	4	no	—
98	#107	C₂×D₄₃	1	2	yes	—
99	#106	—	43	2	no	—
100	#106	—	43	4	no	—
101	#106	C₂×D₄₃	1	2	yes	—
102	C₄×C₈	—	43	1	no	—
103	C₄×C₈	—	43	1	no	—
104	C₄×C₈	—	43	1	no	—
105	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
106	C₂×Q₈	—	86	4	no	—
107	C₂²×C₄	—	43	1	no	—
108	C₂²×C₄	—	43	2	no	—
109	C₂×C₈	—	43	1	no	—
110	C₂×C₈	—	43	1	no	—
111	C₂×C₈	—	43	4	no	—
112	C₂×C₈	—	43	4	no	—
113	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
114	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
115	C₄⋊C₄	—	2	4	no	—
116	C₄⋊C₄	—	43	4	no	—
117	C₄⋊C₄	—	86	4	no	—
118	C₄⋊C₄	—	86	4	no	—
119	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
120	C₂²⋊C₄	—	86	4	no	—
121	C₄²	—	43	2	no	—
122	C₄²	—	43	1	no	—
123	C₄²	—	86	4	no	—
124	C₄²	C₂²×D₄₃	1	1	yes	characteristic
125	C₂³	—	43	1	no	—
126	Q₈	—	172	8	no	—
127	C₂×C₄	—	2	4	no	—
128	C₂×C₄	—	43	1	no	—
129	C₂×C₄	—	43	2	no	—
130	C₂×C₄	—	43	2	no	—
131	C₂×C₄	—	43	2	no	—
132	C₂×C₄	—	86	4	no	—
133	C₂×C₄	—	86	4	no	—
134	C₂×C₄	D₄×D₄₃	1	2	yes	—
135	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
136	C₈	—	43	2	no	—
137	C₈	—	43	2	no	—
138	C₈	Q₈×D₄₃	1	2	yes	—
139	C₈	Q₈×D₄₃	1	2	yes	—
140	C₂²	—	43	2	no	—
141	C₂²	—	86	2	no	—
142	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
143	C₄	—	2	2	no	—
144	C₄	—	4	4	no	—
145	C₄	—	43	4	no	—
146	C₄	—	43	2	no	—
147	C₄	—	172	4	no	—
148	C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
149	C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
150	C₂	—	86	2	no	—
151	C₂	C₄⋊Q₈×D₄₃	1	1	yes	characteristic
152	C₂	#135×D₄₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583455

C₂

yes

maximal

#14583303

C₂

yes

maximal, complemented

#14583301

C₂

yes

maximal, characteristic, complemented

#14583298

C₂

yes

maximal, complemented

#14583296

C₂

yes

maximal, complemented

#14582936

C₂

yes

maximal

#14582934

C₂

yes

maximal

C₄×C₈×D₄₃

C₂

yes

maximal, characteristic

C₄₃×#499

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₃

C₂²

yes

characteristic

C₂×C₈×D₄₃

C₂²

yes

characteristic

#13063324

C₂²

yes

—

#13063317

C₂²

yes

—

#13063303

—

#13063290

—

#13063283

C₂²

yes

—

C₄²×D₄₃

C₂²

yes

characteristic

#13063259

C₂²

yes

—

#13063258

C₂²

yes

—

#13063257

C₂²

yes

—

#13063256

C₂²

yes

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₈×Dic₄₃

C₂²

yes

characteristic

C₈×Dic₄₃

C₂²

yes

characteristic

#125×C₄₃

C₂²

yes

—

#107×C₄₃

C₂²

yes

—

#106×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄×D₄₃

D₄

yes

—

C₂×C₄×D₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂³

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

D₄

yes

—

C₄×Dic₄₃

C₂³

yes

characteristic

C₂×C₄₃⋊C₈

C₂³

yes

characteristic

C₂×C₄₃⋊C₈

C₂³

yes

characteristic

C₈×D₄₃

Q₈

yes

complemented

C₈×D₄₃

Q₈

yes

complemented

C₂²×D₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

C₂×D₄

yes

—

C₄×D₄₃

—

C₄×D₄₃

C₂×Q₈

yes

—

C₄×D₄₃

C₂×Q₈

yes

—

Dic₈₆

—

C₈×C₄₃

C₂×Q₈

yes

—

C₈×C₄₃

C₂×Q₈

yes

—

C₄₃⋊C₈

C₂×Q₈

yes

—

C₄₃⋊C₈

C₂×Q₈

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

C₄⋊Q₈

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²×Q₈

yes

characteristic

C₄×C₄₃

C₂²×Q₈

yes

characteristic

Dic₄₃

—

Dic₄₃

C₄⋊Q₈

yes

—

Dic₄₃

#135

yes

—

#3160

—

maximal, Sylow

C₂×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₃

C₂×#135

yes

—

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

#498

—

#427

—

#427

—

C₂×C₄×C₈

—

C₄₃

#3160

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₄⋊Q₈

—

#125

—

#125

C₂×D₄₃

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

#107

—

#107

—

#107

C₂×D₄₃

yes

—

#106

—

100

#106

—

101

#106

C₂×D₄₃

yes

—

102

C₄×C₈

—

103

C₄×C₈

—

104

C₄×C₈

—

105

C₄×C₈

C₂×D₄₃

yes

characteristic

106

C₂×Q₈

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

C₂²×D₄₃

yes

characteristic

114

C₂×C₈

C₂²×D₄₃

yes

characteristic

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

C₂²×D₄₃

yes

—

120

C₂²⋊C₄

—

121

C₄²

—

122

C₄²

—

123

C₄²

—

124

C₄²

C₂²×D₄₃

yes

characteristic

125

C₂³

—

126

Q₈

—

172

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

D₄×D₄₃

yes

—

135

C₂×C₄

C₂³×D₄₃

yes

characteristic

136

C₈

—

137

C₈

—

138

C₈

Q₈×D₄₃

yes

—

139

C₈

Q₈×D₄₃

yes

—

140

C₂²

—

141

C₂²

—

142

C₂²

C₂×D₄×D₄₃

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

172

—

148

C₄

C₂×Q₈×D₄₃

yes

characteristic

149

C₄

C₂×Q₈×D₄₃

yes

characteristic

150

C₂

—

151

C₂

C₄⋊Q₈×D₄₃

yes

characteristic

152

C₂

#135×D₄₃

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#499	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#499	D₄₃
hypocenter	C₄₃	#3160
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #499

subgroup

G/H

center

C₂²

C₂×D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#499

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #499

N	H ≅ G/N	type
2. #14583303	C₂	semidirect
3. #14583301	C₂	semidirect
4. #14583298	C₂	semidirect
5. #14583296	C₂	semidirect
9. C₄₃×#499	C₂	semidirect
46. C₈×D₄₃	Q₈	semidirect
47. C₈×D₄₃	Q₈	semidirect
81. #499	D₄₃	semidirect
86. C₄₃	#3160	semidirect

H ≅ G/N

type

2. #14583303

C₂

semidirect

3. #14583301

C₂

semidirect

4. #14583298

C₂

semidirect

5. #14583296

C₂

semidirect

9. C₄₃×#499

C₂

semidirect

46. C₈×D₄₃

Q₈

semidirect

47. C₈×D₄₃

Q₈

semidirect

81. #499

D₄₃

semidirect

86. C₄₃

#3160

semidirect

Subgroups — #19145108

Conjugacy classes of subgroups

Complements