Group #24985911 — subgroups

Subgroups — #24985911

Order 11008.

322 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 83 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	#19136158	C₂	1	3	yes	maximal
2	#19132418	C₂	1	3	yes	maximal
3	C₄₃×#2810	C₂	1	1	yes	maximal, characteristic
4	#14582769	C₂²	1	1	yes	characteristic
5	#14582661	—	2	3	no	—
6	#14582661	—	2	3	no	—
7	#14582654	C₂²	1	3	yes	—
8	C₄₃×#400	—	2	3	no	—
9	C₄₃×#389	C₂²	1	3	yes	—
10	C₄₃×#387	—	2	3	no	—
11	C₂²×C₄₃⋊C₈	—	2	3	no	—
12	C₂×C₄⋊Dic₄₃	—	2	3	no	—
13	C₂×C₄⋊C₄×C₄₃	—	2	3	no	—
14	C₂×C₄⋊C₄×C₄₃	D₄	1	3	yes	—
15	C₂×C₄⋊C₄×C₄₃	D₄	1	3	yes	—
16	C₂×C₄²×C₄₃	—	2	1	no	—
17	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
18	#95×C₄₃	—	2	3	no	—
19	#95×C₄₃	—	2	3	no	—
20	#95×C₄₃	—	2	1	no	—
21	#95×C₄₃	—	2	3	no	—
22	C₂²×C₄×C₄₃	—	2	3	no	—
23	C₂²×C₄×C₄₃	—	2	3	no	—
24	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
25	C₂²×Dic₄₃	—	4	1	no	—
26	C₄⋊C₄×C₄₃	—	2	3	no	—
27	C₄⋊C₄×C₄₃	—	2	3	no	—
28	C₄⋊C₄×C₄₃	—	4	3	no	—
29	C₄⋊C₄×C₄₃	—	4	3	no	—
30	C₄⋊C₄×C₄₃	—	4	3	no	—
31	C₄²×C₄₃	—	4	1	no	—
32	C₄²×C₄₃	—	8	1	no	—
33	C₄⋊Dic₄₃	—	4	6	no	—
34	C₂×C₄₃⋊C₈	—	4	3	no	—
35	C₂×C₄₃⋊C₈	—	4	3	no	—
36	C₂×C₄₃⋊C₈	—	4	3	no	—
37	C₂³×C₄₃	#120	1	1	yes	characteristic
38	C₂×C₄×C₄₃	—	2	3	no	—
39	C₂×C₄×C₄₃	—	2	3	no	—
40	C₂×C₄×C₄₃	—	4	3	no	—
41	C₂×C₄×C₄₃	—	4	3	no	—
42	C₂×C₄×C₄₃	—	4	3	no	—
43	C₂×C₄×C₄₃	—	4	3	no	—
44	C₂×C₄×C₄₃	—	4	3	no	—
45	C₂×C₄×C₄₃	—	4	3	no	—
46	C₂×C₄×C₄₃	#135	1	3	yes	—
47	C₂×C₄×C₄₃	#137	1	3	yes	—
48	C₂×Dic₄₃	—	8	3	no	—
49	C₄₃⋊C₈	—	8	3	no	—
50	#7832	—	43	1	no	maximal, Sylow
51	C₂²×C₄₃	#452	1	3	yes	—
52	C₂²×C₄₃	#454	1	3	yes	—
53	C₂²×C₄₃	#458	1	1	yes	characteristic
54	C₄×C₄₃	—	2	3	no	—
55	C₄×C₄₃	—	2	3	no	—
56	C₄×C₄₃	—	8	3	no	—
57	C₄×C₄₃	—	8	3	no	—
58	Dic₄₃	—	16	1	no	—
59	#2810	D₄₃	1	1	yes	characteristic
60	#2100	—	43	3	no	—
61	#1271	—	43	3	no	—
62	C₂×C₄₃	#1615	1	3	yes	—
63	C₂×C₄₃	#1638	1	3	yes	—
64	C₂×C₄₃	#1658	1	1	yes	characteristic
65	#400	—	2	3	no	—
66	#389	C₂×D₄₃	1	3	yes	—
67	#387	—	2	3	no	—
68	#384	—	43	1	no	—
69	#340	—	86	3	no	—
70	#340	—	86	3	no	—
71	#336	—	43	3	no	—
72	C₄₃	#7832	1	1	yes	characteristic, complemented, Sylow
73	C₂²×C₈	—	86	3	no	—
74	C₂×C₄⋊C₄	—	2	3	no	—
75	C₂×C₄⋊C₄	—	86	3	no	—
76	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	3	yes	—
77	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	3	yes	—
78	C₂×C₄²	—	2	1	no	—
79	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
80	#95	—	2	3	no	—
81	#95	—	2	3	no	—
82	#95	—	2	1	no	—
83	#95	—	2	3	no	—
84	C₂²×C₄	—	2	3	no	—
85	C₂²×C₄	—	2	3	no	—
86	C₂²×C₄	—	172	1	no	—
87	C₂²×C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
88	C₂×C₈	—	172	3	no	—
89	C₂×C₈	—	172	3	no	—
90	C₂×C₈	—	172	3	no	—
91	C₄⋊C₄	—	2	3	no	—
92	C₄⋊C₄	—	2	3	no	—
93	C₄⋊C₄	—	4	3	no	—
94	C₄⋊C₄	—	4	3	no	—
95	C₄⋊C₄	—	4	3	no	—
96	C₄⋊C₄	—	172	6	no	—
97	C₄²	—	4	1	no	—
98	C₄²	—	8	1	no	—
99	C₂³	#13063294	1	1	yes	characteristic
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	2	3	no	—
102	C₂×C₄	—	4	3	no	—
103	C₂×C₄	—	4	3	no	—
104	C₂×C₄	—	4	3	no	—
105	C₂×C₄	—	4	3	no	—
106	C₂×C₄	—	4	3	no	—
107	C₂×C₄	—	4	3	no	—
108	C₂×C₄	—	344	3	no	—
109	C₂×C₄	#13063345	1	3	yes	—
110	C₂×C₄	#13063355	1	3	yes	—
111	C₈	—	344	3	no	—
112	C₂²	#14583061	1	3	yes	—
113	C₂²	#14583072	1	3	yes	—
114	C₂²	#14583089	1	1	yes	characteristic
115	C₄	—	2	3	no	—
116	C₄	—	2	3	no	—
117	C₄	—	8	3	no	—
118	C₄	—	8	3	no	—
119	C₄	—	688	1	no	—
120	C₂	#19133626	1	3	yes	—
121	C₂	#19133767	1	3	yes	—
122	C₂	#19133897	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19136158

C₂

yes

maximal

#19132418

C₂

yes

maximal

C₄₃×#2810

C₂

yes

maximal, characteristic

#14582769

C₂²

yes

—

—

C₂²

yes

—

C₄₃×#400

—

C₄₃×#389

C₂²

yes

—

C₄₃×#387

—

C₂²×C₄₃⋊C₈

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#95×C₄₃

—

#95×C₄₃

—

#95×C₄₃

—

#95×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#120

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

#135

yes

—

C₂×C₄×C₄₃

#137

yes

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

#7832

—

maximal, Sylow

C₂²×C₄₃

#452

yes

—

C₂²×C₄₃

#454

yes

—

C₂²×C₄₃

#458

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

#2810

D₄₃

yes

characteristic

#2100

—

#1271

—

C₂×C₄₃

#1615

yes

—

C₂×C₄₃

#1638

yes

—

C₂×C₄₃

yes

—

C₂×D₄₃

yes

—

—

—

—

—

—

C₄₃

#7832

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₄₃

yes

—

—

—

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

172

—

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

C₂×C₈

—

172

—

C₂×C₈

—

172

—

C₂×C₈

—

172

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄²

—

C₄²

—

C₂³

#13063294

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

344

—

109

C₂×C₄

#13063345

yes

—

110

C₂×C₄

#13063355

yes

—

111

C₈

—

344

—

112

C₂²

#14583061

yes

—

113

C₂²

#14583072

yes

—

114

C₂²

#14583089

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

688

—

120

C₂

#19133626

yes

—

121

C₂

#19133767

yes

—

122

C₂

#19133897

yes

characteristic

	subgroup	G/H
center	C₂³	#13063294
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#2810	C₂
socle, prime radical	C₂³×C₄₃	#120
hypercenter	#2810	D₄₃
hypocenter	C₄₃	#7832
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2810

subgroup

G/H

center

C₂³

#13063294

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#2810

C₂

C₂³×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂³×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2810

N	H ≅ G/N	type
72. C₄₃	#7832	semidirect

H ≅ G/N

type

72. C₄₃

#7832

semidirect

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

subgroup	index
#19136158	2
#19132418	2
C₄₃×#2810	2
#7832	43

subgroup

index

#19136158

#19132418

C₄₃×#2810

#7832

Subgroups — #24985911

Conjugacy classes of subgroups

Complements

Maximal subgroups