Group #24990396 — subgroups

Subgroups — #24990396

Order 11008.

354 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 171 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	#19134767	C₂	1	1	yes	maximal, characteristic
2	#19133350	C₂	1	4	yes	maximal
3	C₂×C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1848	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063261	—	2	2	no	—
6	#14582923	C₂²	1	2	yes	—
7	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
8	#14582649	—	2	8	no	—
9	C₈×C₄₃⋊C₈	C₄	1	1	yes	characteristic
10	C₈×C₄₃⋊C₈	C₄	1	2	yes	—
11	C₈×C₄₃⋊C₈	C₄	1	1	yes	characteristic
12	C₂×#108×C₄₃	—	2	2	no	—
13	C₄₃×#423	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#10621877	—	2	2	no	—
16	C₂²×C₄₃⋊C₈	Q₈	1	4	yes	—
17	#13063261	—	4	4	no	—
18	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
19	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
20	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
21	C₄×C₄₃⋊C₈	D₄	1	4	yes	—
22	C₂×M₁₆×C₄₃	—	2	2	no	—
23	C₂²×C₈×C₄₃	D₄	1	2	yes	—
24	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
25	#108×C₄₃	—	4	4	no	—
26	C₄⋊C₈×C₄₃	—	2	4	no	—
27	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈×C₄₃	Q₈	1	2	yes	—
30	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
32	M₁₆×C₄₃	—	4	4	no	—
33	C₂×C₈×C₄₃	—	4	2	no	—
34	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
35	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
36	C₂×C₈×C₄₃	SD₁₆	1	4	yes	—
37	C₂×C₈×C₄₃	SD₁₆	1	4	yes	—
38	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
39	C₄²×C₄₃	C₂×D₄	1	2	yes	—
40	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
41	#10621877	—	4	4	no	—
42	C₂×C₄₃⋊C₈	—	2	8	no	—
43	C₂×C₄₃⋊C₈	—	4	2	no	—
44	C₂×C₄₃⋊C₈	C₄⋊C₄	1	4	yes	—
45	C₂×C₄₃⋊C₈	C₄⋊C₄	1	4	yes	—
46	C₂³×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
47	C₂×C₄×C₄₃	—	2	4	no	—
48	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
49	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
51	C₂×C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
52	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
53	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
54	C₈×C₄₃	—	8	2	no	—
55	C₈×C₄₃	#106	1	4	yes	—
56	C₈×C₄₃	#106	1	4	yes	—
57	C₄₃⋊C₈	—	2	4	no	—
58	C₄₃⋊C₈	—	8	2	no	—
59	C₄₃⋊C₈	#108	1	8	yes	complemented
60	#8822	—	43	1	no	maximal, Sylow
61	C₂²×C₄₃	—	2	2	no	—
62	C₂²×C₄₃	#384	1	1	yes	characteristic
63	C₂²×C₄₃	#498	1	2	yes	—
64	C₄×C₄₃	—	2	2	no	—
65	C₄×C₄₃	C₂×#106	1	2	yes	—
66	C₄×C₄₃	C₂×#108	1	4	yes	—
67	C₄×C₄₃	#492	1	1	yes	characteristic
68	C₄×C₄₃	#492	1	1	yes	characteristic
69	#1848	—	43	1	no	—
70	#1848	D₄₃	1	1	yes	characteristic
71	#1566	—	43	4	no	—
72	C₂×C₈²	—	43	1	no	—
73	C₂×C₄₃	—	2	2	no	—
74	C₂×C₄₃	#1844	1	1	yes	characteristic
75	C₂×C₄₃	#1848	1	2	yes	—
76	C₂×#108	—	2	2	no	—
77	C₂×#108	—	86	2	no	—
78	#423	—	43	2	no	—
79	#423	C₂×D₄₃	1	2	yes	—
80	C₂×C₄×C₈	—	43	2	no	—
81	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
82	#334	—	86	8	no	—
83	C₈²	—	43	1	no	—
84	C₈²	—	43	2	no	—
85	C₈²	—	43	1	no	—
86	C₄₃	#8822	1	1	yes	characteristic, complemented, Sylow
87	C₂×M₁₆	—	2	2	no	—
88	C₂×M₁₆	—	86	2	no	—
89	C₂²×C₈	—	43	4	no	—
90	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
91	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
92	#108	—	4	4	no	—
93	#108	—	172	4	no	—
94	C₄⋊C₈	—	2	4	no	—
95	C₄⋊C₈	—	86	4	no	—
96	C₄×C₈	—	43	2	no	—
97	C₄×C₈	—	43	2	no	—
98	C₄×C₈	—	43	4	no	—
99	C₄×C₈	Dic₈₆	1	2	yes	—
100	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
101	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
102	C₂²×C₄	Q₈×D₄₃	1	2	yes	—
103	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
104	M₁₆	—	4	4	no	—
105	M₁₆	—	172	4	no	—
106	C₂×C₈	—	4	2	no	—
107	C₂×C₈	—	43	4	no	—
108	C₂×C₈	—	43	4	no	—
109	C₂×C₈	—	86	8	no	—
110	C₂×C₈	—	172	2	no	—
111	C₂×C₈	Dic₄₃⋊C₄	1	2	yes	—
112	C₂×C₈	Dic₄₃⋊C₄	1	2	yes	—
113	C₂×C₈	#10621883	1	4	yes	—
114	C₂×C₈	#10621884	1	4	yes	—
115	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
116	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
117	C₄²	D₄×D₄₃	1	2	yes	—
118	C₂³	#13063323	1	1	yes	characteristic
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
121	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
122	C₂×C₄	#13063321	1	1	yes	characteristic
123	C₂×C₄	#13063324	1	2	yes	—
124	C₂×C₄	C₂×#10621884	1	2	yes	—
125	C₂×C₄	C₂×#10621883	1	2	yes	—
126	C₈	—	8	2	no	—
127	C₈	—	43	8	no	—
128	C₈	—	86	4	no	—
129	C₈	—	344	2	no	—
130	C₈	#13063256	1	4	yes	—
131	C₈	#13063256	1	4	yes	—
132	C₂²	—	2	2	no	—
133	C₂²	#14582768	1	1	yes	characteristic
134	C₂²	#14583295	1	2	yes	—
135	C₄	—	2	2	no	—
136	C₄	C₂×#13063256	1	2	yes	—
137	C₄	#108×D₄₃	1	4	yes	—
138	C₄	#14583271	1	1	yes	characteristic
139	C₄	#14583273	1	1	yes	characteristic
140	C₂	—	2	2	no	—
141	C₂	#19134751	1	1	yes	characteristic
142	C₂	#19134765	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134767

C₂

yes

maximal, characteristic

#19133350

C₂

yes

maximal

C₂×C₈×C₄₃⋊C₈

C₂

yes

maximal, characteristic

C₄₃×#1848

C₂

yes

maximal, characteristic

C₂×#13063261

—

#14582923

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

#14582649

—

C₈×C₄₃⋊C₈

C₄

yes

characteristic

C₈×C₄₃⋊C₈

C₄

yes

—

C₈×C₄₃⋊C₈

C₄

yes

characteristic

C₂×#108×C₄₃

—

C₄₃×#423

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×#10621877

—

C₂²×C₄₃⋊C₈

Q₈

yes

—

#13063261

—

C₄⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₂×M₁₆×C₄₃

—

C₂²×C₈×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#108×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×Q₈

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₄⋊C₄

yes

—

C₂×C₈×C₄₃

C₄⋊C₄

yes

—

C₂×C₈×C₄₃

SD₁₆

yes

—

C₂×C₈×C₄₃

SD₁₆

yes

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

C₂×Q₈

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

—

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

—

C₂³×C₄₃

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

#127

yes

characteristic

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₈×C₄₃

—

C₈×C₄₃

#106

yes

—

C₈×C₄₃

#106

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

#384

yes

characteristic

C₂²×C₄₃

#498

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×#106

yes

—

C₄×C₄₃

C₂×#108

yes

—

C₄×C₄₃

yes

C₄×C₄₃

yes

—

D₄₃

yes

characteristic

#1566

—

C₂×C₈²

—

C₂×C₄₃

—

C₂×C₄₃

#1844

yes

characteristic

C₂×C₄₃

#1848

yes

—

—

—

—

C₂×D₄₃

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

#334

—

C₈²

—

C₈²

—

C₈²

—

C₄₃

#8822

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₄₃

yes

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

#108

—

#108

—

172

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₈₆

yes

—

100

C₄×C₈

C₄×D₄₃

yes

characteristic

101

C₄×C₈

C₄×D₄₃

yes

characteristic

102

C₂²×C₄

Q₈×D₄₃

yes

—

103

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

104

M₁₆

—

105

M₁₆

—

172

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

172

—

111

C₂×C₈

Dic₄₃⋊C₄

yes

—

112

C₂×C₈

Dic₄₃⋊C₄

yes

—

113

C₂×C₈

#10621883

yes

—

114

C₂×C₈

#10621884

yes

—

115

C₄²

C₂×Dic₈₆

yes

characteristic

116

C₄²

C₂×C₄×D₄₃

yes

characteristic

117

C₄²

D₄×D₄₃

yes

—

118

C₂³

#13063323

yes

characteristic

119

C₂×C₄

—

120

C₂×C₄

C₄⋊C₄×D₄₃

yes

—

121

C₂×C₄

C₂×Dic₄₃⋊C₄

yes

characteristic

122

C₂×C₄

#13063321

yes

characteristic

123

C₂×C₄

#13063324

yes

—

124

C₂×C₄

C₂×#10621884

yes

—

125

C₂×C₄

C₂×#10621883

yes

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

—

344

—

130

C₈

#13063256

yes

—

131

C₈

#13063256

yes

—

132

C₂²

—

133

C₂²

#14582768

yes

characteristic

134

C₂²

#14583295

yes

—

135

C₄

—

136

C₄

C₂×#13063256

yes

—

137

C₄

#108×D₄₃

yes

—

138

C₄

#14583271

yes

characteristic

139

C₄

#14583273

yes

characteristic

140

C₂

—

141

C₂

#19134751

yes

characteristic

142

C₂

#19134765

yes

—

	subgroup	G/H
center	C₂×C₄	#13063321
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1848	C₂
socle	C₂²×C₄₃	#384
prime radical	C₂³×C₄₃	C₄⋊Q₈
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1848	D₄₃
hypocenter	C₄₃	#8822
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

subgroup

G/H

center

C₂×C₄

#13063321

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1848

C₂

socle

C₂²×C₄₃

#384

prime radical

C₂³×C₄₃

C₄⋊Q₈

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

N	H ≅ G/N	type
59. C₄₃⋊C₈	#108	semidirect
86. C₄₃	#8822	semidirect

H ≅ G/N

type

59. C₄₃⋊C₈

#108

semidirect

86. C₄₃

#8822

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19134767	2
#19133350	2
C₂×C₈×C₄₃⋊C₈	2
C₄₃×#1848	2
#8822	43

subgroup

index

#19134767

#19133350

C₂×C₈×C₄₃⋊C₈

C₄₃×#1848

#8822

Subgroups — #24990396

Conjugacy classes of subgroups

Complements

Maximal subgroups