Group #24984161 — subgroups

Subgroups — #24984161

Order 11008.

140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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	C₂²⋊(C₄₃⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
2	#19132689	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2216	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063261	—	2	1	no	—
5	C₂×C₄₃⋊C₃₂	—	2	1	no	—
6	C₂×Q₃₂×C₄₃	C₄	1	1	yes	characteristic
7	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
8	C₄₃×#467	—	2	1	no	—
9	C₄₃×#366	C₄	1	1	yes	characteristic
10	C₄₃×#358	—	2	1	no	—
11	C₂×#10621877	—	4	1	no	—
12	#13063261	—	2	2	no	—
13	#13063261	—	4	1	no	—
14	C₄₃⋊C₃₂	—	4	1	no	—
15	C₂×Q₁₆×C₄₃	—	2	1	no	—
16	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
17	C₂²⋊Q₈×C₄₃	—	4	1	no	—
18	Q₃₂×C₄₃	—	4	1	no	—
19	C₂×C₁₆×C₄₃	—	4	1	no	—
20	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
22	#107×C₄₃	—	2	1	no	—
23	#103×C₄₃	—	4	1	no	—
24	C₂×Q₈×C₄₃	—	4	1	no	—
25	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
26	Q₁₆×C₄₃	—	4	1	no	—
27	Q₁₆×C₄₃	—	4	1	no	—
28	C₂×C₈×C₄₃	—	2	1	no	—
29	C₂×C₈×C₄₃	—	2	1	no	—
30	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
32	C₄⋊C₄×C₄₃	—	4	1	no	—
33	C₄⋊C₄×C₄₃	—	8	1	no	—
34	C₂²⋊C₄×C₄₃	—	8	1	no	—
35	#10621877	—	4	2	no	—
36	#10621877	—	8	1	no	—
37	C₂×C₄₃⋊C₈	—	8	1	no	—
38	C₁₆×C₄₃	—	2	1	no	—
39	C₁₆×C₄₃	—	2	1	no	—
40	C₂³×C₄₃	SD₃₂	1	1	yes	characteristic
41	Q₈×C₄₃	—	8	1	no	—
42	Q₈×C₄₃	—	8	1	no	—
43	C₂×C₄×C₄₃	—	2	1	no	—
44	C₂×C₄×C₄₃	—	2	1	no	—
45	C₂×C₄×C₄₃	—	8	1	no	—
46	C₂×C₄×C₄₃	—	8	1	no	—
47	C₂×C₄×C₄₃	#102	1	1	yes	characteristic
48	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
49	C₈×C₄₃	—	2	1	no	—
50	C₈×C₄₃	#99	1	1	yes	characteristic
51	C₈×C₄₃	#104	1	1	yes	characteristic
52	C₄₃⋊C₈	—	8	2	no	—
53	#7421	—	43	1	no	maximal, Sylow
54	C₂²×C₄₃	—	2	1	no	—
55	C₂²×C₄₃	—	2	1	no	—
56	C₂²×C₄₃	—	2	1	no	—
57	C₂²×C₄₃	#357	1	1	yes	characteristic
58	C₄×C₄₃	—	2	1	no	—
59	C₄×C₄₃	—	16	1	no	—
60	C₄×C₄₃	—	16	1	no	—
61	C₄×C₄₃	#327	1	1	yes	characteristic
62	C₄×C₄₃	#360	1	1	yes	characteristic
63	#2216	D₄₃	1	1	yes	characteristic
64	C₂²⋊C₃₂	—	43	1	no	—
65	#1381	—	43	1	no	—
66	C₂×C₄₃	—	4	1	no	—
67	C₂×C₄₃	#1347	1	1	yes	characteristic
68	C₂×C₄₃	#1417	1	1	yes	characteristic
69	C₂×C₄₃	#1420	1	1	yes	characteristic
70	C₂×Q₃₂	Dic₄₃	1	1	yes	characteristic
71	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
72	#467	—	2	1	no	—
73	C₂×#108	—	86	1	no	—
74	C₂×C₃₂	—	86	1	no	—
75	#366	Dic₄₃	1	1	yes	characteristic
76	#358	—	2	1	no	—
77	C₄₃	#7421	1	1	yes	characteristic, complemented, Sylow
78	C₂×Q₁₆	—	2	1	no	—
79	C₂×M₁₆	—	172	1	no	—
80	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
81	C₂²⋊Q₈	—	4	1	no	—
82	Q₃₂	—	4	1	no	—
83	C₂×C₁₆	—	4	1	no	—
84	C₂×C₁₆	C₂×Dic₄₃	1	1	yes	characteristic
85	C₂×C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
86	#108	—	86	2	no	—
87	#108	—	172	1	no	—
88	#107	—	2	1	no	—
89	#103	—	4	1	no	—
90	C₃₂	—	172	1	no	—
91	C₂×Q₈	—	4	1	no	—
92	C₂²×C₄	#10621882	1	1	yes	characteristic
93	Q₁₆	—	4	1	no	—
94	Q₁₆	—	4	1	no	—
95	M₁₆	—	344	1	no	—
96	M₁₆	—	172	2	no	—
97	C₂×C₈	—	2	1	no	—
98	C₂×C₈	—	2	1	no	—
99	C₂×C₈	—	344	1	no	—
100	C₂×C₈	#10621883	1	1	yes	characteristic
101	C₂×C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
102	C₄⋊C₄	—	4	1	no	—
103	C₄⋊C₄	—	8	1	no	—
104	C₂²⋊C₄	—	8	1	no	—
105	C₁₆	—	2	1	no	—
106	C₁₆	—	2	1	no	—
107	C₂³	#13063269	1	1	yes	characteristic
108	Q₈	—	8	1	no	—
109	Q₈	—	8	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	8	1	no	—
113	C₂×C₄	—	8	1	no	—
114	C₂×C₄	#13063246	1	1	yes	characteristic
115	C₂×C₄	#13063266	1	1	yes	characteristic
116	C₈	—	2	1	no	—
117	C₈	—	344	2	no	—
118	C₈	#13063240	1	1	yes	characteristic
119	C₈	#13063252	1	1	yes	characteristic
120	C₂²	—	2	1	no	—
121	C₂²	—	2	1	no	—
122	C₂²	—	2	1	no	—
123	C₂²	#14582700	1	1	yes	characteristic
124	C₄	—	2	1	no	—
125	C₄	—	16	1	no	—
126	C₄	—	16	1	no	—
127	C₄	#14582633	1	1	yes	characteristic
128	C₄	#14582709	1	1	yes	characteristic
129	C₂	—	4	1	no	—
130	C₂	#19132604	1	1	yes	characteristic
131	C₂	#19132779	1	1	yes	characteristic
132	C₂	#19132788	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²⋊(C₄₃⋊C₃₂)

C₂

yes

maximal, characteristic

#19132689

C₂

yes

maximal, characteristic

C₄₃×#2216

C₂

yes

maximal, characteristic

C₂×#13063261

—

C₂×C₄₃⋊C₃₂

—

C₂×Q₃₂×C₄₃

C₄

yes

characteristic

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₄₃×#467

—

C₄₃×#366

C₄

yes

characteristic

C₄₃×#358

—

C₂×#10621877

—

#13063261

—

#13063261

—

C₄₃⋊C₃₂

—

C₂×Q₁₆×C₄₃

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²⋊Q₈×C₄₃

—

Q₃₂×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₄₃

D₄

yes

characteristic

#107×C₄₃

—

#103×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

D₈

yes

characteristic

Q₁₆×C₄₃

—

Q₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

SD₁₆

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₁₆×C₄₃

—

C₂³×C₄₃

SD₃₂

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#102

yes

characteristic

C₂×C₄×C₄₃

D₁₆

yes

characteristic

C₈×C₄₃

—

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

—

#7421

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#357

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

D₄₃

yes

characteristic

C₂²⋊C₃₂

—

#1381

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×Q₃₂

Dic₄₃

yes

characteristic

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

#467

—

C₂×#108

—

C₂×C₃₂

—

#366

Dic₄₃

yes

characteristic

#358

—

C₄₃

#7421

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×M₁₆

—

172

—

C₂²×C₈

C₂²⋊D₄₃

yes

characteristic

C₂²⋊Q₈

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₄₃

yes

characteristic

C₂×C₁₆

C₂²⋊D₄₃

yes

characteristic

#108

—

#108

—

172

—

#107

—

#103

—

C₃₂

—

172

—

C₂×Q₈

—

C₂²×C₄

#10621882

yes

characteristic

Q₁₆

—

Q₁₆

—

M₁₆

—

344

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

344

—

100

C₂×C₈

#10621883

yes

characteristic

101

C₂×C₈

C₂²⋊Dic₄₃

yes

characteristic

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₂²⋊C₄

—

105

C₁₆

—

106

C₁₆

—

107

C₂³

#13063269

yes

characteristic

108

Q₈

—

109

Q₈

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

#13063246

yes

characteristic

115

C₂×C₄

#13063266

yes

characteristic

116

C₈

—

117

C₈

—

344

—

118

C₈

#13063240

yes

characteristic

119

C₈

#13063252

yes

characteristic

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

#14582700

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

#14582633

yes

characteristic

128

C₄

#14582709

yes

characteristic

129

C₂

—

130

C₂

#19132604

yes

characteristic

131

C₂

#19132779

yes

characteristic

132

C₂

#19132788

yes

characteristic

	subgroup	G/H
center	C₂²	#14582700
commutator	C₂×C₁₆×C₄₃	C₂×C₄
Frattini	C₂²×C₁₆	C₂×D₄₃
Fitting	C₄₃×#2216	C₂
socle	C₂²×C₄₃	#357
prime radical	C₂³×C₄₃	SD₃₂
cosocle	C₂²×C₁₆×C₄₃	C₂²
hypercenter	#2216	D₄₃
hypocenter	C₄₃	#7421
LCS	G ▷ C₂×C₁₆×C₄₃ ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ #2216

subgroup

G/H

center

C₂²

#14582700

commutator

C₂×C₁₆×C₄₃

C₂×C₄

Frattini

C₂²×C₁₆

C₂×D₄₃

Fitting

C₄₃×#2216

C₂

socle

C₂²×C₄₃

#357

prime radical

C₂³×C₄₃

SD₃₂

cosocle

C₂²×C₁₆×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₂×C₁₆×C₄₃ ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ #2216

N	H ≅ G/N	type
77. C₄₃	#7421	semidirect

H ≅ G/N

type

77. C₄₃

#7421

semidirect

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

subgroup	index
C₂²⋊(C₄₃⋊C₃₂)	2
#19132689	2
C₄₃×#2216	2
#7421	43

subgroup

index

C₂²⋊(C₄₃⋊C₃₂)

#19132689

C₄₃×#2216

#7421

Subgroups — #24984161

Conjugacy classes of subgroups

Complements

Maximal subgroups