Group #24987032 — subgroups

Subgroups — #24987032

Order 11008.

382 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 179 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	#19134341	C₂	1	1	yes	maximal, characteristic
2	#19134341	C₂	1	1	yes	maximal, characteristic
3	C₄₃⋊#1273	C₂	1	4	yes	maximal
4	C₄₃×#1744	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
7	#14582654	C₄	1	4	yes	—
8	#14582654	C₄	1	4	yes	—
9	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
10	C₄³×C₄₃	C₂²	1	1	yes	characteristic
11	C₄₃×#336	C₄	1	4	yes	—
12	C₂²×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
13	C₂²×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
14	C₄×C₄₃⋊C₈	—	2	4	no	—
15	C₄×C₄₃⋊C₈	—	2	4	no	—
16	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
17	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
21	C₄×C₈×C₄₃	—	2	4	no	—
22	C₂²×C₄×C₄₃	C₄²	1	4	yes	—
23	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₈×C₄₃	—	2	4	no	—
27	C₂×C₈×C₄₃	—	2	8	no	—
28	C₄²×C₄₃	—	2	4	no	—
29	C₄²×C₄₃	—	2	4	no	—
30	C₄²×C₄₃	—	2	4	no	—
31	C₄²×C₄₃	#41	1	4	yes	—
32	C₂×C₄₃⋊C₈	—	2	4	no	—
33	C₂×C₄₃⋊C₈	—	2	4	no	—
34	C₂×C₄₃⋊C₈	—	2	8	no	—
35	C₂×C₄₃⋊C₈	—	2	8	no	—
36	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
37	C₂×C₄×C₄₃	—	2	4	no	—
38	C₂×C₄×C₄₃	—	2	4	no	—
39	C₂×C₄×C₄₃	—	2	4	no	—
40	C₂×C₄×C₄₃	#117	1	2	yes	—
41	C₂×C₄×C₄₃	#117	1	2	yes	—
42	C₂×C₄×C₄₃	#117	1	2	yes	—
43	C₂×C₄×C₄₃	#131	1	4	yes	—
44	C₂×C₄×C₄₃	#131	1	4	yes	—
45	C₂×C₄×C₄₃	#131	1	4	yes	—
46	C₈×C₄₃	—	4	4	no	—
47	C₄₃⋊C₈	—	4	4	no	—
48	C₄₃⋊C₈	—	4	4	no	—
49	#8135	—	43	1	no	maximal, Sylow
50	C₂²×C₄₃	#376	1	1	yes	characteristic
51	C₂²×C₄₃	#405	1	2	yes	—
52	C₂²×C₄₃	#405	1	2	yes	—
53	C₂²×C₄₃	#405	1	2	yes	—
54	C₄×C₄₃	—	4	4	no	—
55	C₄×C₄₃	#433	1	4	yes	—
56	C₄×C₄₃	#433	1	4	yes	—
57	C₄×C₄₃	#433	1	4	yes	—
58	#1744	—	43	1	no	—
59	#1744	—	43	1	no	—
60	#1744	D₄₃	1	1	yes	characteristic
61	#1273	—	43	4	no	—
62	C₂×C₄₃	#1454	1	4	yes	—
63	C₂×C₄₃	#1746	1	1	yes	characteristic
64	C₂×C₄₃	#1746	1	1	yes	characteristic
65	C₂×C₄₃	#1746	1	1	yes	characteristic
66	C₂×C₄×C₈	—	43	2	no	—
67	C₂×C₄×C₈	—	43	2	no	—
68	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
69	C₄³	C₂×D₄₃	1	1	yes	characteristic
70	#336	—	43	4	no	—
71	#336	—	43	4	no	—
72	#336	Dic₄₃	1	4	yes	—
73	C₄₃	#8135	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₈	—	43	4	no	—
75	C₂²×C₈	—	43	4	no	—
76	C₂²×C₈	C₂×Dic₄₃	1	4	yes	—
77	C₂×C₄²	C₄×D₄₃	1	2	yes	—
78	C₂×C₄²	C₄×D₄₃	1	2	yes	—
79	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
80	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
81	C₄×C₈	—	2	4	no	—
82	C₄×C₈	—	86	4	no	—
83	C₄×C₈	—	86	4	no	—
84	C₂²×C₄	C₄×Dic₄₃	1	4	yes	—
85	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
86	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
87	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
88	C₂×C₈	—	2	4	no	—
89	C₂×C₈	—	2	8	no	—
90	C₂×C₈	—	86	4	no	—
91	C₂×C₈	—	86	4	no	—
92	C₂×C₈	—	86	8	no	—
93	C₂×C₈	—	86	8	no	—
94	C₄²	—	2	4	no	—
95	C₄²	—	2	4	no	—
96	C₄²	—	2	4	no	—
97	C₄²	#10621898	1	4	yes	—
98	C₂³	C₂×C₄×Dic₄₃	1	1	yes	characteristic
99	C₂×C₄	—	2	4	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	#13063282	1	2	yes	—
103	C₂×C₄	#13063282	1	2	yes	—
104	C₂×C₄	#13063284	1	2	yes	—
105	C₂×C₄	#13063331	1	4	yes	—
106	C₂×C₄	#13063332	1	4	yes	—
107	C₂×C₄	#13063333	1	4	yes	—
108	C₈	—	4	4	no	—
109	C₈	—	172	4	no	—
110	C₈	—	172	4	no	—
111	C₂²	#14582745	1	1	yes	characteristic
112	C₂²	#14582854	1	2	yes	—
113	C₂²	#14582855	1	2	yes	—
114	C₂²	#14582857	1	2	yes	—
115	C₄	—	4	4	no	—
116	C₄	#14582958	1	4	yes	—
117	C₄	#14582960	1	4	yes	—
118	C₄	#14582961	1	4	yes	—
119	C₂	#19132895	1	4	yes	—
120	C₂	#19134346	1	1	yes	characteristic
121	C₂	#19134347	1	1	yes	characteristic
122	C₂	#19134348	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19134341

C₂

yes

maximal, characteristic

#19134341

C₂

yes

maximal, characteristic

C₄₃⋊#1273

C₂

yes

maximal

C₄₃×#1744

C₂

yes

maximal, characteristic

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

#14582654

C₄

yes

—

#14582654

C₄

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

—

C₄³×C₄₃

C₂²

yes

characteristic

C₄₃×#336

C₄

yes

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

—

C₂²×C₄₃⋊C₈

C₂×C₄

yes

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄×C₈×C₄₃

—

C₂²×C₄×C₄₃

C₄²

yes

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

#41

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#405

yes

—

C₂²×C₄₃

#405

yes

—

C₄×C₄₃

—

C₄×C₄₃

#433

yes

—

C₄×C₄₃

#433

yes

—

C₄×C₄₃

#433

yes

—

#1744

—

#1744

—

#1744

D₄₃

yes

characteristic

#1273

—

C₂×C₄₃

#1454

yes

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₄₃

yes

—

C₄³

C₂×D₄₃

yes

—

—

Dic₄₃

yes

—

C₄₃

#8135

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×Dic₄₃

yes

—

C₂×C₄²

C₄×D₄₃

yes

—

C₂×C₄²

C₄×D₄₃

yes

—

C₂×C₄²

C₂×Dic₄₃

yes

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

C₄×Dic₄₃

yes

—

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂²×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂²×C₄

C₂²×Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

#10621898

yes

—

C₂³

C₂×C₄×Dic₄₃

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

#13063282

yes

—

103

C₂×C₄

#13063282

yes

—

104

C₂×C₄

#13063284

yes

—

105

C₂×C₄

#13063331

yes

—

106

C₂×C₄

#13063332

yes

—

107

C₂×C₄

#13063333

yes

—

108

C₈

—

109

C₈

—

172

—

110

C₈

—

172

—

111

C₂²

#14582745

yes

characteristic

112

C₂²

#14582854

yes

—

113

C₂²

#14582855

yes

—

114

C₂²

#14582857

yes

—

115

C₄

—

116

C₄

#14582958

yes

—

117

C₄

#14582960

yes

—

118

C₄

#14582961

yes

—

119

C₂

#19132895

yes

—

120

C₂

#19134346

yes

characteristic

121

C₂

#19134347

yes

characteristic

122

C₂

#19134348

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₄₃
commutator, socle, prime radical	C₂³×C₄₃	C₂×C₄²
Fitting	C₄₃×#1744	C₂
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1744	D₄₃
hypocenter	C₄₃	#8135
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄² ◁ #1744

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₄₃

commutator, socle, prime radical

C₂³×C₄₃

C₂×C₄²

Fitting

C₄₃×#1744

C₂

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄² ◁ #1744

N	H ≅ G/N	type
73. C₄₃	#8135	semidirect

H ≅ G/N

type

73. C₄₃

#8135

semidirect

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

subgroup	index
#19134341	2
C₄₃⋊#1273	2
C₄₃×#1744	2
#8135	43

subgroup

index

#19134341

C₄₃⋊#1273

C₄₃×#1744

#8135

Subgroups — #24987032

Conjugacy classes of subgroups

Complements

Maximal subgroups