Group #25096848 — subgroups

Subgroups — #25096848

Order 11008.

830 conjugacy classes of subgroups; only the 243 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 243 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	#376×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#19134740	C₂	1	1	yes	maximal, characteristic, complemented
3	#19134739	C₂	1	6	yes	maximal, complemented
4	#19134287	C₂	1	6	yes	maximal
5	C₄₃×#1840	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#10621872	C₂²	1	4	yes	—
7	C₂×C₄²×D₄₃	C₂²	1	3	yes	—
8	#14582745	C₂²	1	3	yes	—
9	#14582744	C₄	1	4	yes	—
10	#95×D₄₃	C₄	1	4	yes	—
11	#14582654	C₂²	1	6	yes	—
12	#14582653	C₂²	1	12	yes	—
13	C₄₃×#376	C₂²	1	1	yes	characteristic
14	C₄₃×#336	C₂²	1	6	yes	—
15	C₂²×C₄×D₄₃	C₂×C₄	1	6	yes	—
16	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
17	C₂×#10621872	—	2	24	no	—
18	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
19	C₂×C₄×Dic₄₃	C₂×C₄	1	6	yes	—
20	C₂×C₄×Dic₄₃	C₂³	1	3	yes	—
21	C₄²×D₄₃	—	2	12	no	—
22	C₄₃⋊#95	C₂×C₄	1	12	yes	—
23	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
24	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
25	#95×C₄₃	C₂×C₄	1	4	yes	—
26	C₂³×D₄₃	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₄₃	C₂²×C₄	1	6	yes	—
28	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
29	C₂²×Dic₄₃	C₂²×C₄	1	6	yes	—
30	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×D₄₃	—	2	12	no	—
32	C₂×C₄×D₄₃	—	4	12	no	—
33	C₂×C₄×D₄₃	#41	1	12	yes	—
34	C₂×C₈×C₄₃	—	2	12	no	—
35	C₄²×C₄₃	—	2	6	no	—
36	C₄×Dic₄₃	—	2	6	no	—
37	C₄×Dic₄₃	—	2	12	no	—
38	C₂×C₄₃⋊C₈	—	2	12	no	—
39	#10621872	—	4	16	no	—
40	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
41	C₂²×D₄₃	—	2	4	no	—
42	C₂²×D₄₃	#117	1	6	yes	—
43	C₂×C₄×C₄₃	—	2	6	no	—
44	C₂×C₄×C₄₃	—	2	12	no	—
45	C₂×C₄×C₄₃	C₂×#41	1	6	yes	—
46	C₂×Dic₄₃	—	2	6	no	—
47	C₂×Dic₄₃	—	2	12	no	—
48	C₂×Dic₄₃	#117	1	6	yes	—
49	C₄×D₄₃	—	4	24	no	—
50	C₄×D₄₃	#126	1	16	yes	—
51	C₈×C₄₃	—	4	4	no	—
52	C₄₃⋊C₈	—	4	4	no	—
53	#20773	—	43	1	no	maximal, Sylow
54	C₂²×C₄₃	C₂×#117	1	3	yes	—
55	C₂²×C₄₃	#568	1	4	yes	—
56	C₂×D₄₃	—	2	12	no	—
57	C₂×D₄₃	#383	1	4	yes	—
58	C₄×C₄₃	—	4	6	no	—
59	C₄×C₄₃	C₂×#126	1	4	yes	—
60	Dic₄₃	—	4	6	no	—
61	Dic₄₃	#383	1	4	yes	—
62	C₂×#376	—	43	1	no	—
63	#1840	—	43	1	no	—
64	#1840	—	43	6	no	—
65	#1840	D₄₃	1	1	yes	characteristic, complemented
66	#1728	—	43	6	no	—
67	C₂×C₄₃	C₂×#383	1	1	yes	characteristic
68	C₂×C₄₃	#2921	1	6	yes	—
69	D₄₃	—	2	4	no	—
70	C₂²×M₁₆	—	43	4	no	—
71	C₂²×C₄²	—	43	3	no	—
72	#376	—	43	3	no	—
73	#376	—	43	4	no	—
74	#376	C₂×D₄₃	1	1	yes	characteristic
75	C₂×#95	—	43	4	no	—
76	#336	—	43	12	no	—
77	#336	—	43	6	no	—
78	#336	C₂×D₄₃	1	6	yes	—
79	C₄₃	#20773	1	1	yes	characteristic, complemented, Sylow
80	C₂³×C₄	—	43	1	no	—
81	C₂³×C₄	—	43	6	no	—
82	C₂×M₁₆	—	86	24	no	—
83	C₂²×C₈	—	43	4	no	—
84	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
85	C₂×C₄²	—	43	6	no	—
86	C₂×C₄²	—	43	3	no	—
87	C₂×C₄²	—	86	12	no	—
88	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
89	#95	—	43	12	no	—
90	#95	C₄×D₄₃	1	4	yes	—
91	C₂⁴	—	43	1	no	—
92	C₂²×C₄	—	43	1	no	—
93	C₂²×C₄	—	43	12	no	—
94	C₂²×C₄	—	43	6	no	—
95	C₂²×C₄	—	86	12	no	—
96	C₂²×C₄	—	172	12	no	—
97	C₂²×C₄	C₂×C₄×D₄₃	1	6	yes	—
98	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
99	M₁₆	—	172	16	no	—
100	C₂×C₈	—	2	12	no	—
101	C₂×C₈	—	86	12	no	—
102	C₄²	—	2	6	no	—
103	C₄²	—	86	12	no	—
104	C₄²	—	86	6	no	—
105	C₂³	—	43	6	no	—
106	C₂³	—	86	4	no	—
107	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
108	C₂×C₄	—	2	6	no	—
109	C₂×C₄	—	2	12	no	—
110	C₂×C₄	—	43	6	no	—
111	C₂×C₄	—	43	16	no	—
112	C₂×C₄	—	86	6	no	—
113	C₂×C₄	—	86	12	no	—
114	C₂×C₄	—	172	24	no	—
115	C₂×C₄	#41×D₄₃	1	6	yes	—
116	C₈	—	4	4	no	—
117	C₈	—	172	4	no	—
118	C₂²	—	43	4	no	—
119	C₂²	—	86	12	no	—
120	C₂²	#117×D₄₃	1	3	yes	—
121	C₂²	#14583664	1	4	yes	—
122	C₄	—	4	6	no	—
123	C₄	—	43	4	no	—
124	C₄	—	172	6	no	—
125	C₄	#126×D₄₃	1	4	yes	—
126	C₂	—	86	4	no	—
127	C₂	#383×D₄₃	1	1	yes	characteristic
128	C₂	#19143229	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#376×D₄₃

C₂

yes

maximal, characteristic

#19134740

C₂

yes

maximal, characteristic, complemented

#19134739

C₂

yes

maximal, complemented

#19134287

C₂

yes

maximal

C₄₃×#1840

C₂

yes

maximal, characteristic, complemented

C₂²×#10621872

C₂²

yes

—

C₂×C₄²×D₄₃

C₂²

yes

—

#14582745

C₂²

yes

—

#14582744

C₄

yes

—

#95×D₄₃

C₄

yes

—

#14582654

C₂²

yes

—

#14582653

C₂²

yes

—

C₄₃×#376

C₂²

yes

characteristic

C₄₃×#336

C₂²

yes

—

C₂²×C₄×D₄₃

C₂×C₄

yes

—

C₂²×C₄×D₄₃

C₂³

yes

characteristic

C₂×#10621872

—

C₂²×C₄₃⋊C₈

C₂³

yes

—

C₂×C₄×Dic₄₃

C₂×C₄

yes

—

C₂×C₄×Dic₄₃

C₂³

yes

—

C₄²×D₄₃

—

C₄₃⋊#95

C₂×C₄

yes

—

C₂²×C₈×C₄₃

C₂³

yes

—

C₂×C₄²×C₄₃

C₂³

yes

—

#95×C₄₃

C₂×C₄

yes

—

C₂³×D₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

—

C₂²×C₄×C₄₃

C₂⁴

yes

characteristic

C₂²×Dic₄₃

C₂²×C₄

yes

—

C₂²×Dic₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

#41

yes

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

#10621872

—

C₂³×C₄₃

C₂³×C₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

#117

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

#117

yes

—

C₄×D₄₃

—

C₄×D₄₃

#126

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

#20773

—

maximal, Sylow

C₂²×C₄₃

C₂×#117

yes

—

C₂²×C₄₃

#568

yes

—

C₂×D₄₃

—

C₂×D₄₃

#383

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×#126

yes

—

Dic₄₃

—

Dic₄₃

#383

yes

—

—

—

—

D₄₃

yes

characteristic, complemented

#1728

—

C₂×C₄₃

C₂×#383

yes

characteristic

C₂×C₄₃

#2921

yes

—

D₄₃

—

C₂²×M₁₆

—

C₂²×C₄²

—

#376

—

#376

—

#376

C₂×D₄₃

yes

characteristic

C₂×#95

—

#336

—

#336

—

#336

C₂×D₄₃

yes

—

C₄₃

#20773

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²×D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₄₃

yes

—

#95

—

#95

C₄×D₄₃

yes

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

172

—

C₂²×C₄

C₂×C₄×D₄₃

yes

—

C₂²×C₄

C₂³×D₄₃

yes

characteristic

M₁₆

—

172

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₄²

—

103

C₄²

—

104

C₄²

—

105

C₂³

—

106

C₂³

—

107

C₂³

C₂²×C₄×D₄₃

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

172

—

115

C₂×C₄

#41×D₄₃

yes

—

116

C₈

—

117

C₈

—

172

—

118

C₂²

—

119

C₂²

—

120

C₂²

#117×D₄₃

yes

—

121

C₂²

#14583664

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

172

—

125

C₄

#126×D₄₃

yes

—

126

C₂

—

127

C₂

#383×D₄₃

yes

characteristic

128

C₂

#19143229

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#1840	C₂
prime radical	C₂³×D₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1840	D₄₃
hypocenter	C₄₃	#20773
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1840

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂³×C₄

Fitting

C₄₃×#1840

C₂

prime radical

C₂³×D₄₃

C₂²×C₄

cosocle

C₂²×C₄×C₄₃

C₂⁴

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂²×C₄ ◁ #1840

N	H ≅ G/N	type
2. #19134740	C₂	semidirect
3. #19134739	C₂	semidirect
5. C₄₃×#1840	C₂	semidirect
65. #1840	D₄₃	semidirect
79. C₄₃	#20773	semidirect

H ≅ G/N

type

2. #19134740

C₂

semidirect

3. #19134739

C₂

semidirect

5. C₄₃×#1840

C₂

semidirect

65. #1840

D₄₃

semidirect

79. C₄₃

#20773

semidirect

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

subgroup	index
#376×D₄₃	2
#19134740	2
#19134739	2
#19134287	2
C₄₃×#1840	2
#20773	43

subgroup

index

#376×D₄₃

C₄₃×#1840

Subgroups — #25096848

Conjugacy classes of subgroups

Complements

Maximal subgroups