Group #24999350 — subgroups

Subgroups — #24999350

Order 11008.

592 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 89 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	#19145976	C₂	1	3	yes	maximal, complemented
2	#19135422	C₂	1	3	yes	maximal, complemented
3	C₄₃×#1309	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583449	C₂²	1	3	yes	—
5	#14583190	—	2	6	no	—
6	#14583152	—	2	6	no	—
7	#14583095	—	2	6	no	—
8	C₂×#13063251	—	2	6	no	—
9	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
10	C₄₃×#423	C₂²	1	3	yes	—
11	C₂×#10621898	—	2	3	no	—
12	C₂×D₃₄₄	—	2	6	no	—
13	#13063325	D₄	1	3	yes	—
14	#13063322	D₄	1	3	yes	—
15	#13063313	—	2	3	no	—
16	#13063299	—	2	6	no	—
17	C₄×D₁₇₂	—	2	6	no	—
18	C₂×C₄×Dic₄₃	—	2	3	no	—
19	#13063257	—	2	6	no	—
20	#13063251	—	4	12	no	—
21	#13063247	—	2	12	no	—
22	C₂×M₁₆×C₄₃	D₄	1	6	yes	—
23	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
24	C₄⋊C₈×C₄₃	—	2	6	no	—
25	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
26	C₂×C₂²⋊D₄₃	—	4	3	no	—
27	C₂²×Dic₄₃	—	4	1	no	—
28	#10621898	—	4	6	no	—
29	#10621898	—	4	6	no	—
30	C₂×D₁₇₂	—	2	6	no	—
31	C₂×D₁₇₂	—	2	3	no	—
32	C₂×C₄×D₄₃	—	4	3	no	—
33	C₂×Dic₈₆	—	2	3	no	—
34	M₁₆×C₄₃	—	4	6	no	—
35	C₂×C₈×C₄₃	—	2	6	no	—
36	C₄²×C₄₃	C₂×D₄	1	3	yes	—
37	C₄²×C₄₃	#41	1	1	yes	characteristic
38	(C₂×D₄₃)⋊C₄	—	4	6	no	—
39	C₄⋊Dic₄₃	—	2	6	no	—
40	C₄×Dic₄₃	—	2	6	no	—
41	C₄×Dic₄₃	—	4	3	no	—
42	D₃₄₄	—	8	6	no	—
43	C₂³×C₄₃	#127	1	1	yes	characteristic
44	C₂²×D₄₃	—	4	3	no	—
45	C₂×C₄×C₄₃	—	2	3	no	—
46	C₂×C₄×C₄₃	—	2	3	no	—
47	C₂×C₄×C₄₃	#120	1	3	yes	—
48	C₂×C₄×C₄₃	#121	1	3	yes	—
49	C₂²⋊D₄₃	—	8	6	no	—
50	C₂×Dic₄₃	—	4	6	no	—
51	C₂×Dic₄₃	—	4	3	no	—
52	D₁₇₂	—	4	6	no	—
53	D₁₇₂	—	4	6	no	—
54	D₁₇₂	—	4	6	no	—
55	C₄×D₄₃	—	8	3	no	—
56	C₄×D₄₃	—	8	3	no	—
57	Dic₈₆	—	4	6	no	—
58	C₈×C₄₃	—	4	6	no	—
59	#10300	—	43	1	no	maximal, Sylow
60	C₂²×C₄₃	—	2	3	no	—
61	C₂²×C₄₃	#392	1	1	yes	characteristic
62	C₂×D₄₃	—	8	3	no	—
63	C₂×D₄₃	—	8	6	no	—
64	C₄×C₄₃	—	2	3	no	—
65	C₄×C₄₃	#453	1	3	yes	—
66	C₄×C₄₃	#454	1	3	yes	—
67	Dic₄₃	—	4	4	no	—
68	Dic₄₃	—	8	3	no	—
69	#3253	—	43	3	no	—
70	#1962	—	43	3	no	—
71	#1309	D₄₃	1	1	yes	characteristic, complemented
72	C₂×C₄₃	—	4	1	no	—
73	C₂×C₄₃	#2006	1	3	yes	—
74	D₄₃	—	16	3	no	—
75	#532	—	43	3	no	—
76	#476	—	86	6	no	—
77	#469	—	86	6	no	—
78	#459	—	86	6	no	—
79	#423	C₂×D₄₃	1	3	yes	—
80	C₂×#104	—	86	6	no	—
81	C₄³	—	43	1	no	—
82	C₄₃	#10300	1	1	yes	characteristic, complemented, Sylow
83	C₂×#41	—	86	3	no	—
84	C₂×D₈	—	86	6	no	—
85	C₂×M₁₆	D₁₇₂	1	6	yes	—
86	C₄⋊Q₈	—	43	3	no	—
87	#127	—	43	3	no	—
88	#124	—	86	3	no	—
89	#121	—	86	6	no	—
90	C₄×D₄	—	86	6	no	—
91	C₂×C₄²	—	86	3	no	—
92	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
93	#106	—	86	6	no	—
94	C₄⋊C₈	—	2	6	no	—
95	#104	—	172	12	no	—
96	#102	—	86	12	no	—
97	#41	—	172	6	no	—
98	#41	—	172	6	no	—
99	C₂×Q₈	—	86	3	no	—
100	C₂×D₄	—	86	6	no	—
101	C₂×D₄	—	86	3	no	—
102	C₂×D₄	—	172	3	no	—
103	C₂²×C₄	—	172	3	no	—
104	C₂²×C₄	—	172	1	no	—
105	C₂²×C₄	C₂×D₁₇₂	1	3	yes	—
106	D₈	—	344	6	no	—
107	M₁₆	—	4	6	no	—
108	C₂×C₈	—	2	6	no	—
109	C₄⋊C₄	—	86	6	no	—
110	C₂²⋊C₄	—	172	6	no	—
111	C₄²	—	86	6	no	—
112	C₄²	—	172	3	no	—
113	C₄²	D₄×D₄₃	1	3	yes	—
114	C₄²	#10621902	1	1	yes	characteristic
115	C₂³	—	172	3	no	—
116	C₂³	#13063322	1	1	yes	characteristic
117	Q₈	—	172	6	no	—
118	D₄	—	344	6	no	—
119	D₄	—	172	6	no	—
120	D₄	—	172	6	no	—
121	D₄	—	172	6	no	—
122	C₂×C₄	—	2	3	no	—
123	C₂×C₄	—	2	3	no	—
124	C₂×C₄	—	344	3	no	—
125	C₂×C₄	—	344	3	no	—
126	C₂×C₄	—	172	3	no	—
127	C₂×C₄	—	172	6	no	—
128	C₂×C₄	#13063295	1	3	yes	—
129	C₂×C₄	#13063300	1	3	yes	—
130	C₈	—	4	6	no	—
131	C₂²	—	2	3	no	—
132	C₂²	—	344	3	no	—
133	C₂²	—	344	6	no	—
134	C₂²	#14582809	1	1	yes	characteristic
135	C₄	—	2	3	no	—
136	C₄	—	344	3	no	—
137	C₄	—	172	4	no	—
138	C₄	#14583069	1	3	yes	—
139	C₄	#14583074	1	3	yes	—
140	C₂	—	4	1	no	—
141	C₂	—	688	3	no	—
142	C₂	#19135639	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19145976

C₂

yes

maximal, complemented

#19135422

C₂

yes

maximal, complemented

C₄₃×#1309

C₂

yes

maximal, characteristic, complemented

#14583449

C₂²

yes

—

—

—

—

—

C₄²×Dic₄₃

C₂²

yes

characteristic

C₄₃×#423

C₂²

yes

—

C₂×#10621898

—

C₂×D₃₄₄

—

#13063325

D₄

yes

—

#13063322

D₄

yes

—

#13063313

—

#13063299

—

C₄×D₁₇₂

—

C₂×C₄×Dic₄₃

—

#13063257

—

#13063251

—

#13063247

—

C₂×M₁₆×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₂²⋊D₄₃

—

C₂²×Dic₄₃

—

#10621898

—

#10621898

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

—

C₂×Dic₈₆

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

#41

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

D₃₄₄

—

C₂³×C₄₃

#127

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#120

yes

—

C₂×C₄×C₄₃

#121

yes

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

#10300

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#392

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#453

yes

—

C₄×C₄₃

#454

yes

—

Dic₄₃

—

Dic₄₃

—

#3253

—

#1962

—

#1309

D₄₃

yes

characteristic, complemented

C₂×C₄₃

—

C₂×C₄₃

#2006

yes

—

D₄₃

—

—

—

—

—

C₂×D₄₃

yes

—

C₂×#104

—

C₄³

—

C₄₃

#10300

yes

characteristic, complemented, Sylow

C₂×#41

—

C₂×D₈

—

C₂×M₁₆

D₁₇₂

yes

—

C₄⋊Q₈

—

#127

—

#124

—

#121

—

C₄×D₄

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

#106

—

C₄⋊C₈

—

#104

—

172

—

#102

—

#41

—

172

—

#41

—

172

—

C₂×Q₈

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

172

—

103

C₂²×C₄

—

172

—

104

C₂²×C₄

—

172

—

105

C₂²×C₄

C₂×D₁₇₂

yes

—

106

D₈

—

344

—

107

M₁₆

—

108

C₂×C₈

—

109

C₄⋊C₄

—

110

C₂²⋊C₄

—

172

—

111

C₄²

—

112

C₄²

—

172

—

113

C₄²

D₄×D₄₃

yes

—

114

C₄²

#10621902

yes

characteristic

115

C₂³

—

172

—

116

C₂³

#13063322

yes

characteristic

117

Q₈

—

172

—

118

D₄

—

344

—

119

D₄

—

172

—

120

D₄

—

172

—

121

D₄

—

172

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

344

—

125

C₂×C₄

—

344

—

126

C₂×C₄

—

172

—

127

C₂×C₄

—

172

—

128

C₂×C₄

#13063295

yes

—

129

C₂×C₄

#13063300

yes

—

130

C₈

—

131

C₂²

—

132

C₂²

—

344

—

133

C₂²

—

344

—

134

C₂²

#14582809

yes

characteristic

135

C₄

—

136

C₄

—

344

—

137

C₄

—

172

—

138

C₄

#14583069

yes

—

139

C₄

#14583074

yes

—

140

C₂

—

141

C₂

—

688

—

142

C₂

#19135639

yes

—

	subgroup	G/H
center	C₂²	#14582809
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1309	C₂
socle	C₂²×C₄₃	#392
hypercenter	#1309	D₄₃
hypocenter	C₄₃	#10300
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

subgroup

G/H

center

C₂²

#14582809

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1309

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

N	H ≅ G/N	type
1. #19145976	C₂	semidirect
2. #19135422	C₂	semidirect
3. C₄₃×#1309	C₂	semidirect
71. #1309	D₄₃	semidirect
82. C₄₃	#10300	semidirect

H ≅ G/N

type

1. #19145976

C₂

semidirect

2. #19135422

C₂

semidirect

3. C₄₃×#1309

C₂

semidirect

71. #1309

D₄₃

semidirect

82. C₄₃

#10300

semidirect

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

subgroup	index
#19145976	2
#19135422	2
C₄₃×#1309	2
#10300	43

subgroup

index

#19145976

#19135422

C₄₃×#1309

#10300

Subgroups — #24999350

Conjugacy classes of subgroups

Complements

Maximal subgroups