Group #24984028 — subgroups

Subgroups — #24984028

Order 11008.

170 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 39 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	#19134814	C₂	1	1	yes	maximal, characteristic
2	#19132521	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1321	C₂	1	1	yes	maximal, characteristic
4	#14583666	C₄	1	1	yes	characteristic
5	#14582947	—	2	1	no	—
6	#14582883	C₄	1	1	yes	characteristic
7	C₂²⋊(C₄₃⋊C₁₆)	—	2	1	no	—
8	#14582664	—	2	1	no	—
9	C₄₃×#408	C₂²	1	1	yes	characteristic
10	C₄₃×#349	—	2	1	no	—
11	#13063332	—	4	2	no	—
12	C₂×#10621877	—	2	1	no	—
13	C₂×#10621877	—	2	1	no	—
14	C₂×#10621877	—	4	1	no	—
15	C₂×C₄₃⋊C₁₆	—	4	1	no	—
16	#13063260	—	4	2	no	—
17	#13063244	—	2	1	no	—
18	#13063242	C₈	1	2	yes	—
19	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
22	M₃₂×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	M₁₆	1	1	yes	characteristic
27	C₂×D₄×C₄₃	—	2	1	no	—
28	C₂×D₄×C₄₃	C₂×C₈	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	#10621877	—	2	2	no	—
36	#10621877	—	2	2	no	—
37	#10621877	—	4	1	no	—
38	#10621877	—	4	2	no	—
39	#10621877	—	4	1	no	—
40	C₂×C₄₃⋊C₈	—	4	1	no	—
41	C₂×C₄₃⋊C₈	—	4	1	no	—
42	C₂×C₄₃⋊C₈	—	4	2	no	—
43	C₁₆×C₄₃	—	8	1	no	—
44	C₄₃⋊C₁₆	—	8	1	no	—
45	C₂³×C₄₃	—	2	1	no	—
46	C₂³×C₄₃	#101	1	1	yes	characteristic
47	Q₈×C₄₃	—	4	1	no	—
48	D₄×C₄₃	—	4	1	no	—
49	D₄×C₄₃	—	4	2	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	C₂²⋊C₈	1	1	yes	characteristic
56	C₂×C₄×C₄₃	#99	1	1	yes	characteristic
57	C₈×C₄₃	—	4	1	no	—
58	C₈×C₄₃	—	4	1	no	—
59	C₄₃⋊C₈	—	4	2	no	—
60	C₄₃⋊C₈	—	4	2	no	—
61	#7377	—	43	1	no	maximal, Sylow
62	C₂²×C₄₃	—	2	1	no	—
63	C₂²×C₄₃	—	4	1	no	—
64	C₂²×C₄₃	—	4	1	no	—
65	C₂²×C₄₃	—	8	1	no	—
66	C₂²×C₄₃	#324	1	1	yes	characteristic
67	C₄×C₄₃	—	2	1	no	—
68	C₄×C₄₃	—	4	1	no	—
69	C₄×C₄₃	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
70	C₄×C₄₃	#352	1	1	yes	characteristic
71	#1858	—	43	1	no	—
72	#1321	D₄₃	1	1	yes	characteristic
73	#1315	—	43	1	no	—
74	C₂×C₄₃	—	2	1	no	—
75	C₂×C₄₃	—	4	1	no	—
76	C₂×C₄₃	—	8	1	no	—
77	C₂×C₄₃	#1326	1	1	yes	characteristic
78	#568	—	43	1	no	—
79	#430	—	86	1	no	—
80	#413	—	43	1	no	—
81	#408	C₂×D₄₃	1	1	yes	characteristic
82	#349	—	2	1	no	—
83	C₂²⋊C₁₆	—	86	1	no	—
84	#341	—	86	1	no	—
85	C₄₃	#7377	1	1	yes	characteristic, complemented, Sylow
86	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
87	#131	—	172	2	no	—
88	C₂×M₁₆	—	86	1	no	—
89	C₂×M₁₆	—	86	1	no	—
90	C₂×M₁₆	—	172	1	no	—
91	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
92	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
93	M₃₂	—	4	1	no	—
94	C₂×C₁₆	—	172	1	no	—
95	#108	—	172	2	no	—
96	#101	—	86	1	no	—
97	#100	—	43	2	no	—
98	C₂²⋊C₈	—	4	1	no	—
99	#41	—	4	1	no	—
100	#41	—	4	1	no	—
101	C₂×Q₈	#10621872	1	1	yes	characteristic
102	C₂×D₄	—	2	1	no	—
103	C₂×D₄	C₈×D₄₃	1	1	yes	characteristic
104	C₂²×C₄	—	2	1	no	—
105	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
106	M₁₆	—	4	1	no	—
107	M₁₆	—	86	2	no	—
108	M₁₆	—	86	2	no	—
109	M₁₆	—	172	1	no	—
110	M₁₆	—	172	2	no	—
111	M₁₆	—	172	1	no	—
112	C₂×C₈	—	2	1	no	—
113	C₂×C₈	—	2	1	no	—
114	C₂×C₈	—	4	1	no	—
115	C₂×C₈	—	172	1	no	—
116	C₂×C₈	—	172	1	no	—
117	C₂×C₈	—	172	2	no	—
118	C₁₆	—	8	1	no	—
119	C₁₆	—	344	1	no	—
120	C₂³	—	2	1	no	—
121	C₂³	#13063243	1	1	yes	characteristic
122	Q₈	—	4	1	no	—
123	D₄	—	4	1	no	—
124	D₄	—	4	2	no	—
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	—	4	1	no	—
130	C₂×C₄	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
131	C₂×C₄	#13063239	1	1	yes	characteristic
132	C₈	—	4	1	no	—
133	C₈	—	4	1	no	—
134	C₈	—	172	2	no	—
135	C₈	—	172	2	no	—
136	C₂²	—	2	1	no	—
137	C₂²	—	4	1	no	—
138	C₂²	—	4	1	no	—
139	C₂²	—	8	1	no	—
140	C₂²	#14582624	1	1	yes	characteristic
141	C₄	—	2	1	no	—
142	C₄	—	4	1	no	—
143	C₄	#14582685	1	1	yes	characteristic
144	C₄	#14582690	1	1	yes	characteristic
145	C₂	—	2	1	no	—
146	C₂	—	4	1	no	—
147	C₂	—	8	1	no	—
148	C₂	#19132542	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134814

C₂

yes

maximal, characteristic

#19132521

C₂

yes

maximal, characteristic

C₄₃×#1321

C₂

yes

maximal, characteristic

#14583666

C₄

yes

characteristic

#14582947

—

#14582883

C₄

yes

characteristic

C₂²⋊(C₄₃⋊C₁₆)

—

#14582664

—

C₄₃×#408

C₂²

yes

characteristic

C₄₃×#349

—

—

—

—

—

C₂×C₄₃⋊C₁₆

—

#13063260

—

#13063244

—

#13063242

C₈

yes

—

C₂×#41×C₄₃

C₂×C₄

yes

characteristic

C₂×M₁₆×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

D₄

yes

characteristic

M₃₂×C₄₃

—

C₂²⋊C₈×C₄₃

—

#41×C₄₃

—

#41×C₄₃

—

C₂×Q₈×C₄₃

M₁₆

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

C₂×C₈

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

—

—

—

—

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

C₂³×C₄₃

#101

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

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₄₃

#99

yes

characteristic

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#7377

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#324

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

AΣL(1,𝔽₁₆)

yes

C₄×C₄₃

yes

—

D₄₃

yes

characteristic

#1315

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

—

—

C₂×D₄₃

yes

characteristic

#349

—

C₂²⋊C₁₆

—

#341

—

C₄₃

#7377

yes

characteristic, complemented, Sylow

C₂×#41

C₄×D₄₃

yes

characteristic

#131

—

172

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

172

—

C₂×M₁₆

C₂²⋊D₄₃

yes

characteristic

C₂²×C₈

D₁₇₂

yes

characteristic

M₃₂

—

C₂×C₁₆

—

172

—

#108

—

172

—

#101

—

#100

—

C₂²⋊C₈

—

#41

—

100

#41

—

101

C₂×Q₈

#10621872

yes

characteristic

102

C₂×D₄

—

103

C₂×D₄

C₈×D₄₃

yes

characteristic

104

C₂²×C₄

—

105

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

106

M₁₆

—

107

M₁₆

—

108

M₁₆

—

109

M₁₆

—

172

—

110

M₁₆

—

172

—

111

M₁₆

—

172

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

172

—

116

C₂×C₈

—

172

—

117

C₂×C₈

—

172

—

118

C₁₆

—

119

C₁₆

—

344

—

120

C₂³

—

121

C₂³

#13063243

yes

characteristic

122

Q₈

—

123

D₄

—

124

D₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

(C₂×D₄₃)⋊C₈

yes

characteristic

131

C₂×C₄

#13063239

yes

characteristic

132

C₈

—

133

C₈

—

134

C₈

—

172

—

135

C₈

—

172

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

#14582624

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

#14582685

yes

characteristic

144

C₄

#14582690

yes

characteristic

145

C₂

—

146

C₂

—

147

C₂

—

148

C₂

#19132542

yes

characteristic

	subgroup	G/H
center	C₄	#14582685
commutator	C₂×D₄×C₄₃	C₂×C₈
Frattini	#408	C₂×D₄₃
Fitting	C₄₃×#1321	C₂
socle	C₂×C₄₃	#1326
prime radical	C₂×#41×C₄₃	C₂×C₄
cosocle	C₄₃×#408	C₂²
hypercenter	#1321	D₄₃
hypocenter	C₄₃	#7377
LCS	G ▷ C₂×D₄×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #408 ◁ #1321

subgroup

G/H

center

C₄

#14582685

commutator

C₂×D₄×C₄₃

C₂×C₈

Frattini

#408

C₂×D₄₃

Fitting

C₄₃×#1321

C₂

socle

C₂×C₄₃

#1326

prime radical

C₂×#41×C₄₃

C₂×C₄

cosocle

C₄₃×#408

C₂²

D₄₃

C₄₃

G ▷ C₂×D₄×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #408 ◁ #1321

N	H ≅ G/N	type
85. C₄₃	#7377	semidirect

H ≅ G/N

type

85. C₄₃

#7377

semidirect

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

subgroup	index
#19134814	2
#19132521	2
C₄₃×#1321	2
#7377	43

subgroup

index

#19134814

#19132521

C₄₃×#1321

#7377

Subgroups — #24984028

Conjugacy classes of subgroups

Complements

Maximal subgroups