Group #24983993 — subgroups

Subgroups — #24983993

Order 11008.

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

normal subgroups only

This group has 184 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	#19135571	C₂	1	1	yes	maximal, characteristic
2	#19132546	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1327	C₂	1	1	yes	maximal, characteristic
4	#14583456	C₄	1	1	yes	characteristic
5	C₄²×Dic₄₃	C₄	1	1	yes	characteristic
6	#14582681	—	2	1	no	—
7	#14582660	—	2	1	no	—
8	#14582660	—	2	1	no	—
9	C₄₃×#423	C₂²	1	1	yes	characteristic
10	C₄₃×#349	—	2	1	no	—
11	#13063325	—	2	1	no	—
12	#13063317	C₈	1	2	yes	—
13	#13063304	—	4	1	no	—
14	C₄×Dic₈₆	—	4	1	no	—
15	#13063284	—	2	1	no	—
16	C₂×C₄×Dic₄₃	—	2	1	no	—
17	C₂×C₄×Dic₄₃	—	4	1	no	—
18	#13063265	—	4	1	no	—
19	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
20	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
22	M₃₂×C₄₃	—	4	1	no	—
23	C₄⋊C₈×C₄₃	—	4	1	no	—
24	C₂²×C₄×C₄₃	—	2	1	no	—
25	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²×Dic₄₃	—	4	1	no	—
27	C₂×Dic₈₆	—	4	1	no	—
28	M₁₆×C₄₃	—	4	1	no	—
29	M₁₆×C₄₃	—	4	1	no	—
30	C₂×C₈×C₄₃	—	2	1	no	—
31	C₂×C₈×C₄₃	—	2	1	no	—
32	C₄²×C₄₃	—	2	1	no	—
33	C₄²×C₄₃	C₂×C₈	1	1	yes	characteristic
34	C₄²×C₄₃	M₁₆	1	1	yes	characteristic
35	C₂²⋊Dic₄₃	—	4	1	no	—
36	C₄⋊Dic₄₃	—	2	2	no	—
37	C₄⋊Dic₄₃	—	4	1	no	—
38	Dic₄₃⋊C₄	—	4	2	no	—
39	C₄×Dic₄₃	—	2	2	no	—
40	C₄×Dic₄₃	—	4	1	no	—
41	C₄×Dic₄₃	—	4	4	no	—
42	C₄×Dic₄₃	—	4	1	no	—
43	C₁₆×C₄₃	—	8	1	no	—
44	C₄₃⋊C₁₆	—	8	1	no	—
45	C₂³×C₄₃	#100	1	1	yes	characteristic
46	C₂×C₄×C₄₃	—	2	1	no	—
47	C₂×C₄×C₄₃	—	2	1	no	—
48	C₂×C₄×C₄₃	—	2	1	no	—
49	C₂×C₄×C₄₃	—	2	1	no	—
50	C₂×C₄×C₄₃	—	4	2	no	—
51	C₂×C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
52	C₂×C₄×C₄₃	#99	1	1	yes	characteristic
53	C₂×Dic₄₃	—	4	2	no	—
54	C₂×Dic₄₃	—	4	4	no	—
55	C₂×Dic₄₃	—	4	2	no	—
56	Dic₈₆	—	8	2	no	—
57	C₈×C₄₃	—	4	1	no	—
58	C₈×C₄₃	—	4	1	no	—
59	#7361	—	43	1	no	maximal, Sylow
60	C₂²×C₄₃	—	2	1	no	—
61	C₂²×C₄₃	—	4	1	no	—
62	C₂²×C₄₃	#323	1	1	yes	characteristic
63	C₄×C₄₃	—	2	2	no	—
64	C₄×C₄₃	—	2	1	no	—
65	C₄×C₄₃	—	4	1	no	—
66	C₄×C₄₃	#354	1	1	yes	characteristic
67	C₄×C₄₃	#356	1	1	yes	characteristic
68	Dic₄₃	—	4	4	no	—
69	Dic₄₃	—	8	2	no	—
70	#1994	—	43	1	no	—
71	#1327	—	43	1	no	—
72	#1327	D₄₃	1	1	yes	characteristic
73	C₂×C₄₃	—	2	1	no	—
74	C₂×C₄₃	—	4	1	no	—
75	C₂×C₄₃	#1319	1	1	yes	characteristic
76	#533	—	43	1	no	—
77	#423	C₂×D₄₃	1	1	yes	characteristic
78	C₄³	—	43	1	no	—
79	#349	—	2	1	no	—
80	#349	—	86	1	no	—
81	#339	—	86	1	no	—
82	#339	—	86	1	no	—
83	C₄₃	#7361	1	1	yes	characteristic, complemented, Sylow
84	C₂×M₁₆	D₁₇₂	1	1	yes	characteristic
85	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
86	C₄⋊Q₈	—	86	1	no	—
87	#125	—	43	2	no	—
88	C₂²⋊Q₈	—	172	1	no	—
89	C₄×Q₈	—	172	1	no	—
90	#117	—	86	1	no	—
91	C₂×C₄²	—	86	1	no	—
92	C₂×C₄²	—	172	1	no	—
93	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
94	M₃₂	—	4	1	no	—
95	M₃₂	—	172	1	no	—
96	C₄⋊C₈	—	4	1	no	—
97	C₂×Q₈	—	172	1	no	—
98	C₂²×C₄	—	2	1	no	—
99	C₂²×C₄	—	172	1	no	—
100	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
101	M₁₆	—	4	1	no	—
102	M₁₆	—	4	1	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	—	2	1	no	—
105	C₄⋊C₄	—	86	2	no	—
106	C₄⋊C₄	—	172	2	no	—
107	C₄⋊C₄	—	172	1	no	—
108	C₂²⋊C₄	—	172	1	no	—
109	C₄²	—	2	1	no	—
110	C₄²	—	86	2	no	—
111	C₄²	—	172	1	no	—
112	C₄²	—	172	4	no	—
113	C₄²	—	172	1	no	—
114	C₄²	C₈×D₄₃	1	1	yes	characteristic
115	C₄²	#10621872	1	1	yes	characteristic
116	C₁₆	—	8	1	no	—
117	C₁₆	—	344	1	no	—
118	C₂³	#13063241	1	1	yes	characteristic
119	Q₈	—	344	2	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	2	1	no	—
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	172	2	no	—
126	C₂×C₄	—	172	2	no	—
127	C₂×C₄	—	172	4	no	—
128	C₂×C₄	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
129	C₂×C₄	#13063239	1	1	yes	characteristic
130	C₈	—	4	1	no	—
131	C₈	—	4	1	no	—
132	C₂²	—	2	1	no	—
133	C₂²	—	4	1	no	—
134	C₂²	#14582622	1	1	yes	characteristic
135	C₄	—	2	2	no	—
136	C₄	—	2	1	no	—
137	C₄	—	4	1	no	—
138	C₄	—	344	2	no	—
139	C₄	—	172	4	no	—
140	C₄	#14582693	1	1	yes	characteristic
141	C₄	#14582697	1	1	yes	characteristic
142	C₂	—	2	1	no	—
143	C₂	—	4	1	no	—
144	C₂	#19132528	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19135571

C₂

yes

maximal, characteristic

#19132546

C₂

yes

maximal, characteristic

C₄₃×#1327

C₂

yes

maximal, characteristic

#14583456

C₄

yes

characteristic

C₄²×Dic₄₃

C₄

yes

—

—

—

C₄₃×#423

C₂²

yes

characteristic

C₄₃×#349

—

#13063325

—

#13063317

C₈

yes

—

#13063304

—

C₄×Dic₈₆

—

#13063284

—

C₂×C₄×Dic₄₃

—

C₂×C₄×Dic₄₃

—

#13063265

—

C₂×M₁₆×C₄₃

D₄

yes

characteristic

C₂×M₁₆×C₄₃

D₄

yes

characteristic

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

M₃₂×C₄₃

—

C₄⋊C₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₈

yes

characteristic

C₄²×C₄₃

M₁₆

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₁₆×C₄₃

—

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

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₄₃

#99

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

#7361

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#323

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#1994

—

#1327

—

#1327

D₄₃

yes

characteristic

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

C₂×D₄₃

yes

characteristic

C₄³

—

—

—

—

—

C₄₃

#7361

yes

characteristic, complemented, Sylow

C₂×M₁₆

D₁₇₂

yes

characteristic

C₂×M₁₆

C₂²⋊D₄₃

yes

characteristic

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

172

—

C₄×Q₈

—

172

—

#117

—

C₂×C₄²

—

C₂×C₄²

—

172

—

C₂×C₄²

C₄×D₄₃

yes

characteristic

M₃₂

—

M₃₂

—

172

—

C₄⋊C₈

—

C₂×Q₈

—

172

—

C₂²×C₄

—

C₂²×C₄

—

172

—

100

C₂²×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

101

M₁₆

—

102

M₁₆

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

172

—

107

C₄⋊C₄

—

172

—

108

C₂²⋊C₄

—

172

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

172

—

112

C₄²

—

172

—

113

C₄²

—

172

—

114

C₄²

C₈×D₄₃

yes

characteristic

115

C₄²

#10621872

yes

characteristic

116

C₁₆

—

117

C₁₆

—

344

—

118

C₂³

#13063241

yes

characteristic

119

Q₈

—

344

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

172

—

126

C₂×C₄

—

172

—

127

C₂×C₄

—

172

—

128

C₂×C₄

(C₂×D₄₃)⋊C₈

yes

characteristic

129

C₂×C₄

#13063239

yes

characteristic

130

C₈

—

131

C₈

—

132

C₂²

—

133

C₂²

—

134

C₂²

#14582622

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

344

—

139

C₄

—

172

—

140

C₄

#14582693

yes

characteristic

141

C₄

#14582697

yes

characteristic

142

C₂

—

143

C₂

—

144

C₂

#19132528

yes

characteristic

	subgroup	G/H
center	C₄	#14582693
commutator	C₄²×C₄₃	C₂×C₈
Frattini	#423	C₂×D₄₃
Fitting	C₄₃×#1327	C₂
socle	C₂×C₄₃	#1319
prime radical	C₂³×C₄₃	#100
cosocle	C₄₃×#423	C₂²
hypercenter	#1327	D₄₃
hypocenter	C₄₃	#7361
LCS	G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1327

subgroup

G/H

center

C₄

#14582693

commutator

C₄²×C₄₃

C₂×C₈

Frattini

#423

C₂×D₄₃

Fitting

C₄₃×#1327

C₂

C₂×C₄₃

C₂³×C₄₃

C₄₃×#423

C₂²

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1327

N	H ≅ G/N	type
83. C₄₃	#7361	semidirect

H ≅ G/N

type

83. C₄₃

#7361

semidirect

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

subgroup	index
#19135571	2
#19132546	2
C₄₃×#1327	2
#7361	43

subgroup

index

#19135571

#19132546

C₄₃×#1327

#7361

Subgroups — #24983993

Conjugacy classes of subgroups

Complements

Maximal subgroups