Group #24984216 — subgroups

Subgroups — #24984216

Order 11008.

170 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 37 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	#19136148	C₂	1	1	yes	maximal, characteristic
2	#19132718	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1315	C₂	1	1	yes	maximal, characteristic
4	#14582948	C₄	1	1	yes	characteristic
5	#14582925	—	2	1	no	—
6	#14582916	—	2	1	no	—
7	#14582883	—	2	1	no	—
8	#14582656	C₄	1	1	yes	characteristic
9	C₄₃×#408	C₂²	1	1	yes	characteristic
10	C₄₃×C₂²⋊C₁₆	—	2	1	no	—
11	C₂×#10621877	—	2	1	no	—
12	C₂×#10621877	—	4	1	no	—
13	#13063284	—	2	1	no	—
14	#13063261	—	4	1	no	—
15	Dic₄₃⋊C₈	—	4	2	no	—
16	#13063252	—	4	2	no	—
17	#13063244	—	4	1	no	—
18	#13063242	—	2	2	no	—
19	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
20	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
22	C₂×C₁₆×C₄₃	—	4	1	no	—
23	C₂²⋊C₈×C₄₃	—	4	1	no	—
24	#41×C₄₃	—	4	1	no	—
25	#41×C₄₃	—	4	1	no	—
26	C₂×Q₈×C₄₃	SD₁₆	1	1	yes	characteristic
27	C₂×D₄×C₄₃	—	2	1	no	—
28	C₂×D₄×C₄₃	Q₁₆	1	1	yes	characteristic
29	C₂²×C₄×C₄₃	—	2	1	no	—
30	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
31	M₁₆×C₄₃	—	4	1	no	—
32	C₂×C₈×C₄₃	—	2	1	no	—
33	C₂×C₈×C₄₃	—	2	1	no	—
34	C₂×C₈×C₄₃	—	4	1	no	—
35	C₂²⋊Dic₄₃	—	4	1	no	—
36	C₄⋊Dic₄₃	—	4	1	no	—
37	C₄×Dic₄₃	—	2	2	no	—
38	#10621877	—	4	2	no	—
39	#10621877	—	4	1	no	—
40	#10621877	—	4	1	no	—
41	#10621877	—	8	1	no	—
42	C₂×C₄₃⋊C₈	—	4	1	no	—
43	C₂×C₄₃⋊C₈	—	8	1	no	—
44	C₁₆×C₄₃	—	8	1	no	—
45	C₂³×C₄₃	—	2	1	no	—
46	C₂³×C₄₃	#104	1	1	yes	characteristic
47	Q₈×C₄₃	—	4	1	no	—
48	D₄×C₄₃	—	4	1	no	—
49	D₄×C₄₃	—	8	1	no	—
50	C₂×C₄×C₄₃	—	2	1	no	—
51	C₂×C₄×C₄₃	—	2	1	no	—
52	C₂×C₄×C₄₃	—	2	1	no	—
53	C₂×C₄×C₄₃	—	4	1	no	—
54	C₂×C₄×C₄₃	—	4	1	no	—
55	C₂×C₄×C₄₃	#99	1	1	yes	characteristic
56	C₂×C₄×C₄₃	#103	1	1	yes	characteristic
57	C₂×Dic₄₃	—	4	2	no	—
58	C₈×C₄₃	—	4	1	no	—
59	C₈×C₄₃	—	4	1	no	—
60	C₄₃⋊C₈	—	8	2	no	—
61	C₄₃⋊C₈	—	8	1	no	—
62	#7439	—	43	1	no	maximal, Sylow
63	C₂²×C₄₃	—	2	1	no	—
64	C₂²×C₄₃	—	4	1	no	—
65	C₂²×C₄₃	—	4	1	no	—
66	C₂²×C₄₃	—	8	1	no	—
67	C₂²×C₄₃	#328	1	1	yes	characteristic
68	C₄×C₄₃	—	2	1	no	—
69	C₄×C₄₃	—	4	1	no	—
70	C₄×C₄₃	#352	1	1	yes	characteristic
71	C₄×C₄₃	#353	1	1	yes	characteristic
72	Dic₄₃	—	8	2	no	—
73	#2098	—	43	1	no	—
74	#1392	—	43	1	no	—
75	#1315	D₄₃	1	1	yes	characteristic
76	C₂×C₄₃	—	2	1	no	—
77	C₂×C₄₃	—	4	1	no	—
78	C₂×C₄₃	—	8	1	no	—
79	C₂×C₄₃	#1352	1	1	yes	characteristic
80	#430	—	43	1	no	—
81	#424	—	86	1	no	—
82	#421	—	86	1	no	—
83	#413	—	86	1	no	—
84	#408	C₂×D₄₃	1	1	yes	characteristic
85	C₂²⋊C₁₆	—	2	1	no	—
86	H(3,ℤ/4)	—	43	1	no	—
87	C₄₃	#7439	1	1	yes	characteristic, complemented, Sylow
88	C₂×#41	D₁₇₂	1	1	yes	characteristic
89	C₂×M₁₆	—	86	1	no	—
90	C₂×M₁₆	—	172	1	no	—
91	C₂×M₁₆	C₄×D₄₃	1	1	yes	characteristic
92	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
93	#117	—	86	1	no	—
94	C₂×C₁₆	—	4	1	no	—
95	#108	—	172	1	no	—
96	C₄⋊C₈	—	172	2	no	—
97	#104	—	172	2	no	—
98	#101	—	172	1	no	—
99	#100	—	86	2	no	—
100	C₂²⋊C₈	—	4	1	no	—
101	#41	—	4	1	no	—
102	#41	—	4	1	no	—
103	C₂×Q₈	#10621873	1	1	yes	characteristic
104	C₂×D₄	—	2	1	no	—
105	C₂×D₄	Dic₁₇₂	1	1	yes	characteristic
106	C₂²×C₄	—	2	1	no	—
107	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
108	M₁₆	—	4	1	no	—
109	M₁₆	—	344	1	no	—
110	M₁₆	—	172	2	no	—
111	M₁₆	—	172	1	no	—
112	M₁₆	—	172	1	no	—
113	C₂×C₈	—	2	1	no	—
114	C₂×C₈	—	2	1	no	—
115	C₂×C₈	—	4	1	no	—
116	C₂×C₈	—	344	1	no	—
117	C₂×C₈	—	172	1	no	—
118	C₄⋊C₄	—	172	1	no	—
119	C₂²⋊C₄	—	172	1	no	—
120	C₄²	—	86	2	no	—
121	C₁₆	—	8	1	no	—
122	C₂³	—	2	1	no	—
123	C₂³	#13063251	1	1	yes	characteristic
124	Q₈	—	4	1	no	—
125	D₄	—	4	1	no	—
126	D₄	—	8	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	4	1	no	—
131	C₂×C₄	—	4	1	no	—
132	C₂×C₄	—	172	2	no	—
133	C₂×C₄	#13063239	1	1	yes	characteristic
134	C₂×C₄	#13063250	1	1	yes	characteristic
135	C₈	—	4	1	no	—
136	C₈	—	4	1	no	—
137	C₈	—	344	2	no	—
138	C₈	—	344	1	no	—
139	C₂²	—	2	1	no	—
140	C₂²	—	4	1	no	—
141	C₂²	—	4	1	no	—
142	C₂²	—	8	1	no	—
143	C₂²	#14582637	1	1	yes	characteristic
144	C₄	—	2	1	no	—
145	C₄	—	4	1	no	—
146	C₄	—	344	2	no	—
147	C₄	#14582690	1	1	yes	characteristic
148	C₄	#14582691	1	1	yes	characteristic
149	C₂	—	2	1	no	—
150	C₂	—	4	1	no	—
151	C₂	—	8	1	no	—
152	C₂	#19132620	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136148

C₂

yes

maximal, characteristic

#19132718

C₂

yes

maximal, characteristic

C₄₃×#1315

C₂

yes

maximal, characteristic

#14582948

C₄

yes

—

—

—

C₄

yes

characteristic

C₄₃×#408

C₂²

yes

characteristic

C₄₃×C₂²⋊C₁₆

—

—

—

—

—

Dic₄₃⋊C₈

—

#13063252

—

#13063244

—

#13063242

—

C₂×#41×C₄₃

D₄

yes

characteristic

C₂×M₁₆×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂²⋊C₈×C₄₃

—

#41×C₄₃

—

#41×C₄₃

—

C₂×Q₈×C₄₃

SD₁₆

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

Q₁₆

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

—

—

—

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

#104

yes

characteristic

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#7439

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#328

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#2098

—

#1392

—

#1315

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

—

—

—

C₂×D₄₃

yes

characteristic

C₂²⋊C₁₆

—

H(3,ℤ/4)

—

C₄₃

#7439

yes

characteristic, complemented, Sylow

C₂×#41

D₁₇₂

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

172

—

C₂×M₁₆

C₄×D₄₃

yes

characteristic

C₂²×C₈

C₂²⋊D₄₃

yes

characteristic

#117

—

C₂×C₁₆

—

#108

—

172

—

C₄⋊C₈

—

172

—

#104

—

172

—

#101

—

172

—

#100

—

100

C₂²⋊C₈

—

101

#41

—

102

#41

—

103

C₂×Q₈

#10621873

yes

characteristic

104

C₂×D₄

—

105

C₂×D₄

Dic₁₇₂

yes

characteristic

106

C₂²×C₄

—

107

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

108

M₁₆

—

109

M₁₆

—

344

—

110

M₁₆

—

172

—

111

M₁₆

—

172

—

112

M₁₆

—

172

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

344

—

117

C₂×C₈

—

172

—

118

C₄⋊C₄

—

172

—

119

C₂²⋊C₄

—

172

—

120

C₄²

—

121

C₁₆

—

122

C₂³

—

123

C₂³

#13063251

yes

characteristic

124

Q₈

—

125

D₄

—

126

D₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

172

—

133

C₂×C₄

#13063239

yes

characteristic

134

C₂×C₄

#13063250

yes

characteristic

135

C₈

—

136

C₈

—

137

C₈

—

344

—

138

C₈

—

344

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

#14582637

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

344

—

147

C₄

#14582690

yes

characteristic

148

C₄

#14582691

yes

characteristic

149

C₂

—

150

C₂

—

151

C₂

—

152

C₂

#19132620

yes

characteristic

	subgroup	G/H
center	C₄	#14582691
commutator	C₂×M₁₆×C₄₃	C₂×C₄
Frattini	#408	C₂×D₄₃
Fitting	C₄₃×#1315	C₂
socle	C₂×C₄₃	#1352
prime radical	C₂×#41×C₄₃	D₄
cosocle	C₄₃×#408	C₂²
hypercenter	#1315	D₄₃
hypocenter	C₄₃	#7439
LCS	G ▷ C₂×M₁₆×C₄₃ ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #408 ◁ #1315

subgroup

G/H

center

C₄

#14582691

commutator

C₂×M₁₆×C₄₃

C₂×C₄

Frattini

#408

C₂×D₄₃

Fitting

C₄₃×#1315

C₂

socle

C₂×C₄₃

#1352

prime radical

C₂×#41×C₄₃

D₄

cosocle

C₄₃×#408

C₂²

D₄₃

C₄₃

G ▷ C₂×M₁₆×C₄₃ ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #408 ◁ #1315

N	H ≅ G/N	type
87. C₄₃	#7439	semidirect

H ≅ G/N

type

87. C₄₃

#7439

semidirect

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

subgroup	index
#19136148	2
#19132718	2
C₄₃×#1315	2
#7439	43

subgroup

index

#19136148

#19132718

C₄₃×#1315

#7439

Subgroups — #24984216

Conjugacy classes of subgroups

Complements

Maximal subgroups