Group #25008486 — subgroups

Subgroups — #25008486

Order 11008.

204 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 73 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	#19136482	C₂	1	1	yes	maximal, characteristic
2	#19136436	C₂	1	2	yes	maximal, complemented
3	#19132570	C₂	1	2	yes	maximal, complemented
4	#19132515	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1369	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583331	C₄	1	1	yes	characteristic
7	#14583317	—	2	2	no	—
8	#14583017	C₂²	1	2	yes	—
9	#14582729	C₄	1	1	yes	characteristic
10	#14582707	C₄	1	2	yes	—
11	#14582684	—	2	2	no	—
12	#14582675	C₂²	1	1	yes	characteristic
13	#14582620	C₂²	1	1	yes	characteristic
14	C₄₃×#364	C₂²	1	2	yes	—
15	C₄₃×#346	C₂²	1	1	yes	characteristic
16	#13063347	C₂×C₄	1	2	yes	—
17	#13063331	—	2	2	no	—
18	Dic₃₄₄	C₈	1	1	yes	characteristic, complemented
19	#13063270	C₈	1	2	yes	complemented
20	D₆₈₈	C₈	1	1	yes	characteristic, complemented
21	#13063264	—	4	2	no	—
22	C₂×C₄₃⋊C₁₆	D₄	1	2	yes	—
23	C₁₆×D₄₃	—	4	2	no	—
24	#13063261	C₂×C₄	1	2	yes	—
25	#13063253	—	2	2	no	—
26	C₄×C₄₃⋊C₈	—	2	1	no	—
27	M₃₂×C₄₃	—	2	2	no	—
28	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
30	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
31	#10621898	—	2	2	no	—
32	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
34	C₄²×C₄₃	#41	1	1	yes	characteristic
35	#10621877	—	2	2	no	—
36	C₂×C₄₃⋊C₈	—	4	1	no	—
37	Dic₁₇₂	C₂×C₈	1	2	yes	—
38	D₃₄₄	C₂×C₈	1	2	yes	—
39	#10621873	—	2	2	no	—
40	#10621872	—	4	2	no	—
41	C₈×D₄₃	—	4	2	no	—
42	C₁₆×C₄₃	—	2	1	no	—
43	C₁₆×C₄₃	—	4	2	no	—
44	C₁₆×C₄₃	C₂×C₈	1	1	yes	characteristic
45	C₁₆×C₄₃	C₂×C₈	1	1	yes	characteristic
46	C₄₃⋊C₁₆	—	2	2	no	—
47	C₂×C₄×C₄₃	—	2	1	no	—
48	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
49	C₂²⋊D₄₃	—	4	2	no	—
50	D₁₇₂	—	2	2	no	—
51	C₄×D₄₃	—	4	2	no	—
52	Dic₈₆	—	2	2	no	—
53	C₈×C₄₃	C₂²×C₈	1	1	yes	characteristic
54	C₈×C₄₃	#131	1	1	yes	characteristic
55	C₈×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
56	C₄₃⋊C₈	—	4	2	no	—
57	C₄₃⋊C₈	—	8	1	no	—
58	#12068	—	43	1	no	maximal, Sylow
59	C₂²×C₄₃	#444	1	1	yes	characteristic
60	C₂×D₄₃	—	4	2	no	—
61	C₄×C₄₃	—	4	1	no	—
62	C₄×C₄₃	C₈×D₄	1	1	yes	characteristic
63	C₄×C₄₃	#442	1	1	yes	characteristic
64	Dic₄₃	—	4	2	no	—
65	#2179	—	43	1	no	—
66	#2171	—	43	2	no	—
67	#1369	D₄₃	1	1	yes	characteristic, complemented
68	#1336	—	43	2	no	—
69	#1313	—	43	1	no	—
70	C₂×C₄₃	—	2	1	no	—
71	C₂×C₄₃	#1580	1	1	yes	characteristic
72	D₄₃	—	8	2	no	—
73	#508	—	43	1	no	—
74	#504	—	86	2	no	—
75	#443	—	43	2	no	—
76	#368	—	43	1	no	—
77	#364	C₂×D₄₃	1	2	yes	—
78	#359	—	43	2	no	—
79	#350	—	86	2	no	—
80	#346	—	43	1	no	—
81	#346	C₂×D₄₃	1	1	yes	characteristic
82	#322	—	43	1	no	—
83	C₄₃	#12068	1	1	yes	characteristic, complemented, Sylow
84	#135	—	43	2	no	—
85	#131	—	86	2	no	—
86	Q₃₂	—	43	1	no	—
87	SD₃₂	—	43	2	no	—
88	D₁₆	—	43	1	no	—
89	M₃₂	—	2	2	no	—
90	M₃₂	—	172	2	no	—
91	C₂×C₁₆	—	43	2	no	—
92	C₂×C₁₆	—	172	2	no	—
93	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
94	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
95	#108	—	43	2	no	—
96	#104	—	86	2	no	—
97	C₄×C₈	—	86	1	no	—
98	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
99	#41	—	86	2	no	—
100	Q₁₆	—	43	2	no	—
101	SD₁₆	—	86	2	no	—
102	D₈	—	43	2	no	—
103	M₁₆	—	86	2	no	—
104	M₁₆	—	172	2	no	—
105	C₂×C₈	—	172	1	no	—
106	C₂×C₈	—	172	2	no	—
107	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
108	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
109	C₄²	#10621902	1	1	yes	characteristic
110	C₁₆	—	2	1	no	—
111	C₁₆	—	4	2	no	—
112	C₁₆	—	86	2	no	—
113	C₁₆	C₈×D₄₃	1	1	yes	characteristic
114	C₁₆	C₈×D₄₃	1	1	yes	characteristic
115	Q₈	—	86	2	no	—
116	D₄	—	86	2	no	—
117	D₄	—	172	2	no	—
118	C₂×C₄	—	2	1	no	—
119	C₂×C₄	—	172	2	no	—
120	C₂×C₄	#13063287	1	1	yes	characteristic
121	C₈	—	344	1	no	—
122	C₈	—	172	2	no	—
123	C₈	C₂×C₈×D₄₃	1	1	yes	characteristic
124	C₈	#13063333	1	1	yes	characteristic
125	C₈	#13063352	1	2	yes	—
126	C₂²	—	172	2	no	—
127	C₂²	#14583020	1	1	yes	characteristic
128	C₄	—	4	1	no	—
129	C₄	—	172	2	no	—
130	C₄	#14582964	1	1	yes	characteristic
131	C₄	#14583010	1	1	yes	characteristic
132	C₂	—	2	1	no	—
133	C₂	—	344	2	no	—
134	C₂	#19133418	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136482

C₂

yes

maximal, characteristic

#19136436

C₂

yes

maximal, complemented

#19132570

C₂

yes

maximal, complemented

#19132515

C₂

yes

maximal, characteristic, complemented

C₄₃×#1369

C₂

yes

maximal, characteristic, complemented

#14583331

C₄

yes

characteristic

#14583317

—

#14583017

C₂²

yes

—

#14582729

C₄

yes

characteristic

#14582707

C₄

yes

—

#14582684

—

#14582675

C₂²

yes

characteristic

#14582620

C₂²

yes

characteristic

C₄₃×#364

C₂²

yes

—

C₄₃×#346

C₂²

yes

characteristic

#13063347

C₂×C₄

yes

—

#13063331

—

Dic₃₄₄

C₈

yes

characteristic, complemented

#13063270

C₈

yes

complemented

D₆₈₈

C₈

yes

characteristic, complemented

#13063264

—

C₂×C₄₃⋊C₁₆

D₄

yes

—

C₁₆×D₄₃

—

#13063261

C₂×C₄

yes

—

#13063253

—

C₄×C₄₃⋊C₈

—

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

characteristic

C₂×C₁₆×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂³

yes

characteristic

#10621898

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

C₄²×C₄₃

yes

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

C₂×C₈

yes

—

D₃₄₄

C₂×C₈

yes

—

#10621873

—

#10621872

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₁₆×C₄₃

—

C₁₆×C₄₃

C₂×C₈

yes

characteristic

C₁₆×C₄₃

C₂×C₈

yes

characteristic

C₄₃⋊C₁₆

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄×D₄

yes

characteristic

C₂²⋊D₄₃

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

C₂²×C₈

yes

C₈×C₄₃

yes

C₈×C₄₃

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₈×D₄

yes

characteristic

C₄×C₄₃

#442

yes

characteristic

Dic₄₃

—

#2179

—

#2171

—

#1369

D₄₃

yes

characteristic, complemented

#1336

—

#1313

—

C₂×C₄₃

—

C₂×C₄₃

#1580

yes

characteristic

D₄₃

—

—

—

—

—

C₂×D₄₃

yes

—

—

—

—

C₂×D₄₃

yes

characteristic

#322

—

C₄₃

#12068

yes

characteristic, complemented, Sylow

#135

—

#131

—

Q₃₂

—

SD₃₂

—

D₁₆

—

M₃₂

—

M₃₂

—

172

—

C₂×C₁₆

—

C₂×C₁₆

—

172

—

C₂×C₁₆

C₄×D₄₃

yes

characteristic

C₂×C₁₆

C₄×D₄₃

yes

characteristic

#108

—

#104

—

C₄×C₈

—

C₄×C₈

C₂²×D₄₃

yes

characteristic

#41

—

100

Q₁₆

—

101

SD₁₆

—

102

D₈

—

103

M₁₆

—

104

M₁₆

—

172

—

105

C₂×C₈

—

172

—

106

C₂×C₈

—

172

—

107

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

108

C₂×C₈

D₄×D₄₃

yes

characteristic

109

C₄²

#10621902

yes

characteristic

110

C₁₆

—

111

C₁₆

—

112

C₁₆

—

113

C₁₆

C₈×D₄₃

yes

characteristic

114

C₁₆

C₈×D₄₃

yes

characteristic

115

Q₈

—

116

D₄

—

117

D₄

—

172

—

118

C₂×C₄

—

119

C₂×C₄

—

172

—

120

C₂×C₄

#13063287

yes

characteristic

121

C₈

—

344

—

122

C₈

—

172

—

123

C₈

C₂×C₈×D₄₃

yes

characteristic

124

C₈

#13063333

yes

characteristic

125

C₈

#13063352

yes

—

126

C₂²

—

172

—

127

C₂²

#14583020

yes

characteristic

128

C₄

—

129

C₄

—

172

—

130

C₄

#14582964

yes

characteristic

131

C₄

#14583010

yes

characteristic

132

C₂

—

133

C₂

—

344

—

134

C₂

#19133418

yes

characteristic

	subgroup	G/H
center	C₄	#14583010
commutator	C₈×C₄₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₄₃×#1369	C₂
socle	C₂×C₄₃	#1580
prime radical	#14583331	C₄
cosocle	C₄×C₈×C₄₃	C₂³
hypercenter	#1369	D₄₃
hypocenter	C₄₃	#12068
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1369

subgroup

G/H

center

C₄

#14583010

commutator

C₈×C₄₃

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₄₃

Fitting

C₄₃×#1369

C₂

C₂×C₄₃

C₄

C₄×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1369

N	H ≅ G/N	type
2. #19136436	C₂	semidirect
3. #19132570	C₂	semidirect
4. #19132515	C₂	semidirect
5. C₄₃×#1369	C₂	semidirect
18. Dic₃₄₄	C₈	semidirect
19. #13063270	C₈	semidirect
20. D₆₈₈	C₈	semidirect
67. #1369	D₄₃	semidirect
83. C₄₃	#12068	semidirect

H ≅ G/N

type

2. #19136436

C₂

semidirect

3. #19132570

C₂

semidirect

4. #19132515

C₂

semidirect

5. C₄₃×#1369

C₂

semidirect

18. Dic₃₄₄

C₈

semidirect

19. #13063270

C₈

semidirect

20. D₆₈₈

C₈

semidirect

67. #1369

D₄₃

semidirect

83. C₄₃

#12068

semidirect

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

subgroup	index
#19136482	2
#19136436	2
#19132570	2
#19132515	2
C₄₃×#1369	2
#12068	43

subgroup

index

C₄₃×#1369

Subgroups — #25008486

Conjugacy classes of subgroups

Complements

Maximal subgroups