Group #24990325 — subgroups

Subgroups — #24990325

Order 11008.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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	#19132440	C₂	1	2	yes	maximal
2	#19132428	C₂	1	2	yes	maximal
3	#19132426	C₂	1	2	yes	maximal
4	C₄₃×#1745	C₂	1	1	yes	maximal, characteristic
5	#14582952	C₂²	1	4	yes	—
6	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
8	C₄³×C₄₃	C₂²	1	1	yes	characteristic
9	C₄₃×#336	C₄	1	4	yes	—
10	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
11	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
12	C₄×C₄₃⋊C₈	—	2	4	no	—
13	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
14	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₄₃	—	2	2	no	—
16	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
18	#97×C₄₃	—	2	2	no	—
19	#97×C₄₃	—	2	2	no	—
20	C₂²×C₄×C₄₃	—	2	2	no	—
21	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	#41	1	2	yes	—
23	C₂×C₈×C₄₃	—	2	2	no	—
24	C₂×C₈×C₄₃	—	2	2	no	—
25	C₂×C₈×C₄₃	—	2	4	no	—
26	C₂×C₈×C₄₃	—	2	4	no	—
27	C₄²×C₄₃	—	2	4	no	—
28	C₄²×C₄₃	—	4	4	no	—
29	C₄²×C₄₃	#41	1	2	yes	—
30	C₄²×C₄₃	#41	1	2	yes	—
31	C₂×C₄₃⋊C₈	—	4	4	no	—
32	C₂³×C₄₃	#117	1	1	yes	characteristic
33	C₂×C₄×C₄₃	—	2	4	no	—
34	C₂×C₄×C₄₃	—	4	2	no	—
35	C₂×C₄×C₄₃	—	4	2	no	—
36	C₂×C₄×C₄₃	—	4	2	no	—
37	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
38	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
39	C₂×C₄×C₄₃	#126	1	4	yes	—
40	C₂×C₄×C₄₃	#131	1	4	yes	—
41	C₈×C₄₃	—	4	2	no	—
42	C₈×C₄₃	—	4	2	no	—
43	C₄₃⋊C₈	—	8	4	no	—
44	#8802	—	43	1	no	maximal, Sylow
45	C₂²×C₄₃	—	2	2	no	—
46	C₂²×C₄₃	#383	1	1	yes	characteristic
47	C₂²×C₄₃	#433	1	2	yes	—
48	C₄×C₄₃	—	2	4	no	—
49	C₄×C₄₃	—	4	4	no	—
50	C₄×C₄₃	#433	1	2	yes	—
51	C₄×C₄₃	#433	1	2	yes	—
52	#1745	D₄₃	1	1	yes	characteristic
53	#1281	—	43	2	no	—
54	#1276	—	43	2	no	—
55	#1275	—	43	2	no	—
56	C₂×C₄₃	—	2	2	no	—
57	C₂×C₄₃	#1840	1	1	yes	characteristic
58	C₂×C₄₃	#1841	1	2	yes	—
59	#431	—	43	4	no	—
60	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
61	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
62	C₄³	C₂×D₄₃	1	1	yes	characteristic
63	#336	Dic₄₃	1	4	yes	—
64	C₄₃	#8802	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₈	C₂×Dic₄₃	1	2	yes	—
66	C₂²×C₈	C₂×Dic₄₃	1	2	yes	—
67	C₂×C₄²	—	2	2	no	—
68	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
69	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
70	C₄⋊C₈	—	86	4	no	—
71	C₂²⋊C₈	—	86	4	no	—
72	#97	—	2	2	no	—
73	#97	—	2	2	no	—
74	C₄×C₈	—	86	4	no	—
75	C₂²×C₄	—	2	2	no	—
76	C₂²×C₄	#10621898	1	2	yes	—
77	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	2	4	no	—
81	C₂×C₈	—	2	4	no	—
82	C₂×C₈	—	172	4	no	—
83	C₄²	—	2	4	no	—
84	C₄²	—	4	4	no	—
85	C₄²	#10621898	1	2	yes	—
86	C₄²	#10621898	1	2	yes	—
87	C₂³	#13063284	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	4	2	no	—
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	#13063284	1	1	yes	characteristic
93	C₂×C₄	#13063284	1	1	yes	characteristic
94	C₂×C₄	#13063319	1	4	yes	—
95	C₂×C₄	#13063332	1	4	yes	—
96	C₈	—	4	2	no	—
97	C₈	—	4	2	no	—
98	C₈	—	344	4	no	—
99	C₂²	—	2	2	no	—
100	C₂²	#14582767	1	1	yes	characteristic
101	C₂²	#14582960	1	2	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	4	4	no	—
104	C₄	#14582960	1	2	yes	—
105	C₄	#14582960	1	2	yes	—
106	C₂	—	2	2	no	—
107	C₂	#19134740	1	1	yes	characteristic
108	C₂	#19134744	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19132440

C₂

yes

maximal

#19132428

C₂

yes

maximal

#19132426

C₂

yes

maximal

C₄₃×#1745

C₂

yes

maximal, characteristic

#14582952

C₂²

yes

—

C₂×#97×C₄₃

C₂²

yes

characteristic

C₂×#97×C₄₃

C₂²

yes

characteristic

C₄³×C₄₃

C₂²

yes

characteristic

C₄₃×#336

C₄

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#97×C₄₃

—

#97×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

#41

yes

—

C₄²×C₄₃

#41

yes

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#117

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

—

C₂×C₄×C₄₃

#131

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

#8802

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

#383

yes

characteristic

C₂²×C₄₃

#433

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#433

yes

—

C₄×C₄₃

#433

yes

—

#1745

D₄₃

yes

—

—

—

C₂×C₄₃

—

C₂×C₄₃

#1840

yes

characteristic

C₂×C₄₃

#1841

yes

—

#431

—

C₂×#97

C₂×D₄₃

yes

characteristic

C₂×#97

C₂×D₄₃

yes

characteristic

C₄³

C₂×D₄₃

yes

characteristic

#336

Dic₄₃

yes

—

C₄₃

#8802

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×Dic₄₃

yes

—

C₂²×C₈

C₂×Dic₄₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×Dic₄₃

yes

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

#10621898

yes

—

C₂²×C₄

C₂²×Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

172

—

C₄²

—

C₄²

—

C₄²

#10621898

yes

—

C₄²

#10621898

yes

—

C₂³

#13063284

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

—

C₂×C₄

#13063332

yes

—

C₈

—

C₈

—

C₈

—

344

—

C₂²

—

100

C₂²

#14582767

yes

characteristic

101

C₂²

#14582960

yes

—

102

C₄

—

103

C₄

—

104

C₄

#14582960

yes

—

105

C₄

#14582960

yes

—

106

C₂

—

107

C₂

#19134740

yes

characteristic

108

C₂

#19134744

yes

—

	subgroup	G/H
center	C₂×C₄	#13063284
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1745	C₂
socle	C₂²×C₄₃	#383
prime radical	C₂³×C₄₃	#117
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1745	D₄₃
hypocenter	C₄₃	#8802
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1745

subgroup

G/H

center

C₂×C₄

#13063284

commutator

C₂²×C₄×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1745

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1745

N	H ≅ G/N	type
64. C₄₃	#8802	semidirect

H ≅ G/N

type

64. C₄₃

#8802

semidirect

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

subgroup	index
#19132440	2
#19132428	2
#19132426	2
C₄₃×#1745	2
#8802	43

subgroup

index

C₄₃×#1745

Subgroups — #24990325

Conjugacy classes of subgroups

Complements

Maximal subgroups