Group #24990406 — subgroups

Subgroups — #24990406

Order 11008.

338 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 163 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	#19134767	C₂	1	1	yes	maximal, characteristic
2	#19133350	C₂	1	4	yes	maximal
3	C₂×#14582620	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1848	C₂	1	1	yes	maximal, characteristic
5	C₂×#13063261	—	2	2	no	—
6	#14582923	C₂²	1	2	yes	—
7	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
8	#14582649	—	2	8	no	—
9	#14582620	C₄	1	4	yes	—
10	C₂×#108×C₄₃	—	2	2	no	—
11	C₄₃×#423	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#10621877	—	2	2	no	—
14	C₂²×C₄₃⋊C₈	Q₈	1	4	yes	—
15	#13063261	—	4	4	no	—
16	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
17	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
18	C₄×C₄₃⋊C₈	D₄	1	4	yes	—
19	C₂×M₁₆×C₄₃	—	2	2	no	—
20	C₂²×C₈×C₄₃	D₄	1	2	yes	—
21	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
22	#108×C₄₃	—	4	4	no	—
23	C₄⋊C₈×C₄₃	—	2	4	no	—
24	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₄₃	Q₈	1	2	yes	—
26	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
28	M₁₆×C₄₃	—	4	4	no	—
29	C₂×C₈×C₄₃	—	4	2	no	—
30	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	—
31	C₂×C₈×C₄₃	SD₁₆	1	4	yes	—
32	C₂×C₈×C₄₃	SD₁₆	1	4	yes	—
33	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
34	C₄²×C₄₃	C₂×D₄	1	2	yes	—
35	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
36	#10621877	—	4	4	no	—
37	C₂×C₄₃⋊C₈	—	4	4	no	—
38	C₂×C₄₃⋊C₈	—	4	2	no	—
39	C₂×C₄₃⋊C₈	C₄⋊C₄	1	8	yes	—
40	C₂³×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
41	C₂×C₄×C₄₃	—	2	4	no	—
42	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
43	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
45	C₂×C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
46	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
47	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
48	C₈×C₄₃	—	8	2	no	—
49	C₈×C₄₃	#106	1	8	yes	—
50	C₄₃⋊C₈	—	2	8	no	—
51	C₄₃⋊C₈	—	8	2	no	—
52	#8825	—	43	1	no	maximal, Sylow
53	C₂²×C₄₃	—	2	2	no	—
54	C₂²×C₄₃	#384	1	1	yes	characteristic
55	C₂²×C₄₃	#498	1	2	yes	—
56	C₄×C₄₃	—	2	2	no	—
57	C₄×C₄₃	C₂×#106	1	2	yes	—
58	C₄×C₄₃	#430	1	4	yes	—
59	C₄×C₄₃	#492	1	1	yes	characteristic
60	C₄×C₄₃	#492	1	1	yes	characteristic
61	#1848	—	43	1	no	—
62	#1848	D₄₃	1	1	yes	characteristic
63	#1566	—	43	4	no	—
64	C₂×#322	—	43	1	no	—
65	C₂×C₄₃	—	2	2	no	—
66	C₂×C₄₃	#1844	1	1	yes	characteristic
67	C₂×C₄₃	#1849	1	2	yes	—
68	C₂×#108	—	2	2	no	—
69	C₂×#108	—	86	2	no	—
70	#423	—	43	2	no	—
71	#423	C₂×D₄₃	1	2	yes	—
72	C₂×C₄×C₈	—	43	2	no	—
73	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
74	#334	—	86	8	no	—
75	#322	—	43	4	no	—
76	C₄₃	#8825	1	1	yes	characteristic, complemented, Sylow
77	C₂×M₁₆	—	2	2	no	—
78	C₂×M₁₆	—	86	2	no	—
79	C₂²×C₈	—	43	4	no	—
80	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
81	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
82	#108	—	4	4	no	—
83	#108	—	172	4	no	—
84	C₄⋊C₈	—	2	4	no	—
85	C₄⋊C₈	—	86	4	no	—
86	C₄×C₈	—	43	4	no	—
87	C₄×C₈	—	43	4	no	—
88	C₄×C₈	Dic₈₆	1	2	yes	—
89	C₄×C₈	C₄×D₄₃	1	2	yes	—
90	C₂²×C₄	Q₈×D₄₃	1	2	yes	—
91	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
92	M₁₆	—	4	4	no	—
93	M₁₆	—	172	4	no	—
94	C₂×C₈	—	4	2	no	—
95	C₂×C₈	—	43	8	no	—
96	C₂×C₈	—	172	4	no	—
97	C₂×C₈	—	172	2	no	—
98	C₂×C₈	Dic₄₃⋊C₄	1	4	yes	—
99	C₂×C₈	#10621883	1	4	yes	—
100	C₂×C₈	#10621884	1	4	yes	—
101	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
102	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
103	C₄²	D₄×D₄₃	1	2	yes	—
104	C₂³	#13063323	1	1	yes	characteristic
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
107	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
108	C₂×C₄	#13063321	1	1	yes	characteristic
109	C₂×C₄	#13063324	1	2	yes	—
110	C₂×C₄	C₂×#10621884	1	2	yes	—
111	C₂×C₄	C₂×#10621883	1	2	yes	—
112	C₈	—	8	2	no	—
113	C₈	—	86	8	no	—
114	C₈	—	344	2	no	—
115	C₈	#13063256	1	8	yes	—
116	C₂²	—	2	2	no	—
117	C₂²	#14582768	1	1	yes	characteristic
118	C₂²	#14583295	1	2	yes	—
119	C₄	—	2	2	no	—
120	C₄	C₂×#13063256	1	2	yes	—
121	C₄	#14582946	1	4	yes	—
122	C₄	#14583271	1	1	yes	characteristic
123	C₄	#14583273	1	1	yes	characteristic
124	C₂	—	2	2	no	—
125	C₂	#19134751	1	1	yes	characteristic
126	C₂	#19134768	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134767

C₂

yes

maximal, characteristic

#19133350

C₂

yes

maximal

C₂×#14582620

C₂

yes

maximal, characteristic

C₄₃×#1848

C₂

yes

maximal, characteristic

C₂×#13063261

—

#14582923

C₂²

yes

—

C₂×C₄×C₄₃⋊C₈

C₂²

yes

—

#14582649

—

#14582620

C₄

yes

—

C₂×#108×C₄₃

—

C₄₃×#423

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×#10621877

—

C₂²×C₄₃⋊C₈

Q₈

yes

—

#13063261

—

C₄⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

C₂×C₄

yes

—

C₄×C₄₃⋊C₈

D₄

yes

—

C₂×M₁₆×C₄₃

—

C₂²×C₈×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#108×C₄₃

—

C₄⋊C₈×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×Q₈

yes

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₄⋊C₄

yes

—

C₂×C₈×C₄₃

SD₁₆

yes

—

C₂×C₈×C₄₃

SD₁₆

yes

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

—

C₄²×C₄₃

C₂×Q₈

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₄⋊C₄

yes

—

C₂³×C₄₃

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

#127

yes

characteristic

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₈×C₄₃

—

C₈×C₄₃

#106

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#8825

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#384

yes

characteristic

C₂²×C₄₃

#498

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×#106

yes

—

C₄×C₄₃

#430

yes

—

C₄×C₄₃

yes

C₄×C₄₃

yes

—

D₄₃

yes

characteristic

#1566

—

C₂×#322

—

C₂×C₄₃

—

C₂×C₄₃

#1844

yes

characteristic

C₂×C₄₃

#1849

yes

—

—

—

—

C₂×D₄₃

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

#334

—

#322

—

C₄₃

#8825

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₄₃

yes

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

#108

—

#108

—

172

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₈₆

yes

—

C₄×C₈

C₄×D₄₃

yes

—

C₂²×C₄

Q₈×D₄₃

yes

—

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

—

172

—

C₂×C₈

Dic₄₃⋊C₄

yes

—

C₂×C₈

#10621883

yes

—

100

C₂×C₈

#10621884

yes

—

101

C₄²

C₂×Dic₈₆

yes

characteristic

102

C₄²

C₂×C₄×D₄₃

yes

characteristic

103

C₄²

D₄×D₄₃

yes

—

104

C₂³

#13063323

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

C₄⋊C₄×D₄₃

yes

—

107

C₂×C₄

C₂×Dic₄₃⋊C₄

yes

characteristic

108

C₂×C₄

#13063321

yes

characteristic

109

C₂×C₄

#13063324

yes

—

110

C₂×C₄

C₂×#10621884

yes

—

111

C₂×C₄

C₂×#10621883

yes

—

112

C₈

—

113

C₈

—

114

C₈

—

344

—

115

C₈

#13063256

yes

—

116

C₂²

—

117

C₂²

#14582768

yes

characteristic

118

C₂²

#14583295

yes

—

119

C₄

—

120

C₄

C₂×#13063256

yes

—

121

C₄

#14582946

yes

—

122

C₄

#14583271

yes

characteristic

123

C₄

#14583273

yes

characteristic

124

C₂

—

125

C₂

#19134751

yes

characteristic

126

C₂

#19134768

yes

—

	subgroup	G/H
center	C₂×C₄	#13063321
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1848	C₂
socle	C₂²×C₄₃	#384
prime radical	C₂³×C₄₃	C₄⋊Q₈
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1848	D₄₃
hypocenter	C₄₃	#8825
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

subgroup

G/H

center

C₂×C₄

#13063321

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1848

C₂

socle

C₂²×C₄₃

#384

prime radical

C₂³×C₄₃

C₄⋊Q₈

cosocle

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

N	H ≅ G/N	type
76. C₄₃	#8825	semidirect

H ≅ G/N

type

76. C₄₃

#8825

semidirect

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

subgroup	index
#19134767	2
#19133350	2
C₂×#14582620	2
C₄₃×#1848	2
#8825	43

subgroup

index

C₄₃×#1848

Subgroups — #24990406

Conjugacy classes of subgroups

Complements

Maximal subgroups