Group #24983413 — subgroups

Subgroups — #24983413

Order 11008.

206 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 71 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	#19132675	C₂	1	2	yes	maximal
2	C₄₃×#1992	C₂	1	1	yes	maximal, characteristic
3	C₂×#13063265	—	2	2	no	—
4	C₂×#125×C₄₃	C₄	1	1	yes	characteristic
5	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
6	C₄₃×#384	C₄	1	1	yes	characteristic
7	C₄₃×#340	—	2	2	no	—
8	#13063265	—	4	2	no	—
9	#13063265	—	4	2	no	—
10	C₂×C₄₃⋊C₁₆	—	2	4	no	—
11	C₂²×C₈×C₄₃	D₄	1	2	yes	—
12	#125×C₄₃	—	2	1	no	—
13	#125×C₄₃	—	4	1	no	—
14	#125×C₄₃	C₈	1	2	yes	—
15	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
16	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
17	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
18	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
19	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
20	#97×C₄₃	—	4	1	no	—
21	C₂²×C₄×C₄₃	—	2	1	no	—
22	C₂²×C₄×C₄₃	—	4	1	no	—
23	C₂²×C₄×C₄₃	—	4	1	no	—
24	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₈×C₄₃	—	2	2	no	—
26	C₂×C₈×C₄₃	—	2	2	no	—
27	C₂×C₈×C₄₃	SD₁₆	1	2	yes	—
28	C₂×C₈×C₄₃	Q₁₆	1	2	yes	—
29	C₄⋊C₄×C₄₃	—	2	2	no	—
30	C₄⋊C₄×C₄₃	—	4	2	no	—
31	C₄⋊C₄×C₄₃	—	4	2	no	—
32	C₄⋊C₄×C₄₃	—	4	1	no	—
33	C₄⋊C₄×C₄₃	—	4	2	no	—
34	C₄⋊C₄×C₄₃	—	8	2	no	—
35	C₄²×C₄₃	—	2	1	no	—
36	C₄²×C₄₃	C₂×C₈	1	1	yes	characteristic
37	C₄²×C₄₃	M₁₆	1	1	yes	characteristic
38	C₄₃⋊C₁₆	—	4	4	no	—
39	C₂³×C₄₃	#100	1	1	yes	characteristic
40	C₂×C₄×C₄₃	—	2	1	no	—
41	C₂×C₄×C₄₃	—	2	1	no	—
42	C₂×C₄×C₄₃	—	4	1	no	—
43	C₂×C₄×C₄₃	—	4	1	no	—
44	C₂×C₄×C₄₃	—	4	2	no	—
45	C₂×C₄×C₄₃	—	8	1	no	—
46	C₂×C₄×C₄₃	—	8	1	no	—
47	C₂×C₄×C₄₃	—	8	2	no	—
48	C₂×C₄×C₄₃	—	8	1	no	—
49	C₂×C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
50	C₂×C₄×C₄₃	#99	1	1	yes	characteristic
51	C₂×C₄×C₄₃	#103	1	2	yes	—
52	C₂×C₄×C₄₃	#104	1	2	yes	—
53	C₈×C₄₃	—	2	2	no	—
54	C₈×C₄₃	—	2	2	no	—
55	#7130	—	43	1	no	maximal, Sylow
56	C₂²×C₄₃	—	2	1	no	—
57	C₂²×C₄₃	—	2	1	no	—
58	C₂²×C₄₃	#323	1	1	yes	characteristic
59	C₂²×C₄₃	#329	1	1	yes	characteristic
60	C₂²×C₄₃	#333	1	1	yes	characteristic
61	C₄×C₄₃	—	4	1	no	—
62	C₄×C₄₃	—	4	1	no	—
63	C₄×C₄₃	—	8	2	no	—
64	C₄×C₄₃	—	16	1	no	—
65	C₄×C₄₃	Q₈⋊C₈	1	2	yes	—
66	C₄×C₄₃	#328	1	2	yes	—
67	#1992	D₄₃	1	1	yes	characteristic
68	#1375	—	43	2	no	—
69	C₂×C₄₃	—	2	1	no	—
70	C₂×C₄₃	—	2	1	no	—
71	C₂×C₄₃	#1272	1	1	yes	characteristic
72	C₂×C₄₃	#1355	1	1	yes	characteristic
73	C₂×C₄₃	#1356	1	1	yes	characteristic
74	C₂×#125	Dic₄₃	1	1	yes	characteristic
75	C₂×M₃₂	—	86	2	no	—
76	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
77	#384	Dic₄₃	1	1	yes	characteristic
78	#340	—	2	2	no	—
79	C₄₃	#7130	1	1	yes	characteristic, complemented, Sylow
80	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
81	#125	—	2	1	no	—
82	#125	—	4	1	no	—
83	#125	C₄₃⋊C₈	1	2	yes	—
84	C₂×C₄⋊C₄	—	2	1	no	—
85	C₂×C₄⋊C₄	—	2	1	no	—
86	C₂×C₄⋊C₄	—	4	1	no	—
87	C₂×C₄⋊C₄	—	4	1	no	—
88	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
89	M₃₂	—	172	2	no	—
90	M₃₂	—	172	2	no	—
91	C₂×C₁₆	—	86	4	no	—
92	#97	—	4	1	no	—
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	—	4	1	no	—
95	C₂²×C₄	—	4	1	no	—
96	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	#10621884	1	2	yes	—
100	C₂×C₈	#10621885	1	2	yes	—
101	C₄⋊C₄	—	2	2	no	—
102	C₄⋊C₄	—	4	2	no	—
103	C₄⋊C₄	—	4	2	no	—
104	C₄⋊C₄	—	4	1	no	—
105	C₄⋊C₄	—	4	2	no	—
106	C₄⋊C₄	—	8	2	no	—
107	C₄²	—	2	1	no	—
108	C₄²	C₂×C₄₃⋊C₈	1	1	yes	characteristic
109	C₄²	#10621877	1	1	yes	characteristic
110	C₁₆	—	172	4	no	—
111	C₂³	#13063242	1	1	yes	characteristic
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	4	1	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	8	1	no	—
118	C₂×C₄	—	8	1	no	—
119	C₂×C₄	—	8	2	no	—
120	C₂×C₄	—	8	1	no	—
121	C₂×C₄	C₂²⋊(C₄₃⋊C₈)	1	1	yes	characteristic
122	C₂×C₄	#13063240	1	1	yes	characteristic
123	C₂×C₄	#13063249	1	2	yes	—
124	C₂×C₄	#13063252	1	2	yes	—
125	C₈	—	2	2	no	—
126	C₈	—	2	2	no	—
127	C₂²	—	2	1	no	—
128	C₂²	—	2	1	no	—
129	C₂²	#14582623	1	1	yes	characteristic
130	C₂²	#14582639	1	1	yes	characteristic
131	C₂²	#14582648	1	1	yes	characteristic
132	C₄	—	4	1	no	—
133	C₄	—	4	1	no	—
134	C₄	—	8	2	no	—
135	C₄	—	16	1	no	—
136	C₄	Q₈⋊(C₄₃⋊C₈)	1	2	yes	—
137	C₄	#14582636	1	2	yes	—
138	C₂	—	2	1	no	—
139	C₂	—	2	1	no	—
140	C₂	#19132421	1	1	yes	characteristic
141	C₂	#19132628	1	1	yes	characteristic
142	C₂	#19132630	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19132675

C₂

yes

maximal

C₄₃×#1992

C₂

yes

maximal, characteristic

C₂×#13063265

—

C₂×#125×C₄₃

C₄

yes

characteristic

C₂×#97×C₄₃

C₂²

yes

characteristic

C₄₃×#384

C₄

yes

characteristic

C₄₃×#340

—

#13063265

—

#13063265

—

C₂×C₄₃⋊C₁₆

—

C₂²×C₈×C₄₃

D₄

yes

—

#125×C₄₃

—

#125×C₄₃

—

#125×C₄₃

C₈

yes

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

#97×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

SD₁₆

yes

—

C₂×C₈×C₄₃

Q₁₆

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₈

yes

characteristic

C₄²×C₄₃

M₁₆

yes

characteristic

C₄₃⋊C₁₆

—

C₂³×C₄₃

#100

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×C₄×C₄₃

#104

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

#7130

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

Q₈⋊C₈

yes

—

C₄×C₄₃

#328

yes

—

#1992

D₄₃

yes

characteristic

#1375

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

Dic₄₃

yes

characteristic

C₂×M₃₂

—

C₂×#97

C₂×D₄₃

yes

characteristic

#384

Dic₄₃

yes

characteristic

#340

—

C₄₃

#7130

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂²⋊D₄₃

yes

—

#125

—

#125

—

#125

C₄₃⋊C₈

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×Dic₄₃

yes

characteristic

M₃₂

—

172

—

M₃₂

—

172

—

C₂×C₁₆

—

#97

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#10621884

yes

—

100

C₂×C₈

#10621885

yes

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄²

—

108

C₄²

C₂×C₄₃⋊C₈

yes

characteristic

109

C₄²

#10621877

yes

characteristic

110

C₁₆

—

172

—

111

C₂³

#13063242

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

C₂²⋊(C₄₃⋊C₈)

yes

characteristic

122

C₂×C₄

#13063240

yes

characteristic

123

C₂×C₄

#13063249

yes

—

124

C₂×C₄

#13063252

yes

—

125

C₈

—

126

C₈

—

127

C₂²

—

128

C₂²

—

129

C₂²

#14582623

yes

characteristic

130

C₂²

#14582639

yes

characteristic

131

C₂²

#14582648

yes

characteristic

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

Q₈⋊(C₄₃⋊C₈)

yes

—

137

C₄

#14582636

yes

—

138

C₂

—

139

C₂

—

140

C₂

#19132421

yes

characteristic

141

C₂

#19132628

yes

characteristic

142

C₂

#19132630

yes

characteristic

	subgroup	G/H
center	C₂²	#14582639
commutator	C₄²×C₄₃	C₂×C₈
Frattini	C₂×#97	C₂×D₄₃
Fitting	C₄₃×#1992	C₂
socle	C₂²×C₄₃	#329
prime radical	C₂³×C₄₃	#100
cosocle	C₂×#97×C₄₃	C₂²
hypercenter	#1992	D₄₃
hypocenter	C₄₃	#7130
LCS	G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1992

subgroup

G/H

center

C₂²

#14582639

commutator

C₄²×C₄₃

C₂×C₈

Frattini

C₂×#97

C₂×D₄₃

Fitting

C₄₃×#1992

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×#97×C₄₃

C₂²

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ #1992

N	H ≅ G/N	type
79. C₄₃	#7130	semidirect

H ≅ G/N

type

79. C₄₃

#7130

semidirect

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

subgroup	index
#19132675	2
C₄₃×#1992	2
#7130	43

subgroup

index

#19132675

C₄₃×#1992

#7130

Subgroups — #24983413

Conjugacy classes of subgroups

Complements

Maximal subgroups