Group #24990310 — subgroups

Subgroups — #24990310

Order 11008.

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

normal subgroups only

This group has 220 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	#19133358	C₂	1	2	yes	maximal
2	#19132457	C₂	1	4	yes	maximal
3	C₄₃×#1452	C₂	1	1	yes	maximal, characteristic
4	#14582956	C₂²	1	4	yes	—
5	#14582652	—	2	2	no	—
6	#14582650	—	2	2	no	—
7	C₄₃×#431	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₄₃×#322	C₄	1	4	yes	—
10	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
11	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
12	#13063236	—	2	4	no	—
13	C₂²×C₈×C₄₃	Q₈	1	2	yes	—
14	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
15	C₄⋊C₈×C₄₃	—	2	2	no	—
16	C₂²⋊C₈×C₄₃	—	2	2	no	—
17	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
18	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
20	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	#41	1	2	yes	—
23	C₂×C₈×C₄₃	—	2	4	no	—
24	C₂×C₈×C₄₃	—	4	2	no	—
25	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
26	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
27	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
28	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
29	C₄²×C₄₃	#41	1	2	yes	—
30	C₂×C₄₃⋊C₈	—	4	4	no	—
31	C₂³×C₄₃	#125	1	1	yes	characteristic
32	C₂×C₄×C₄₃	—	2	2	no	—
33	C₂×C₄×C₄₃	—	4	2	no	—
34	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	#117	1	2	yes	—
36	C₂×C₄×C₄₃	#124	1	2	yes	—
37	C₂×C₄×C₄₃	#125	1	1	yes	characteristic
38	C₈×C₄₃	—	2	2	no	—
39	C₈×C₄₃	—	2	2	no	—
40	C₈×C₄₃	—	4	4	no	—
41	C₄₃⋊C₈	—	8	4	no	—
42	#8798	—	43	1	no	maximal, Sylow
43	C₂²×C₄₃	—	2	2	no	—
44	C₂²×C₄₃	—	2	1	no	—
45	C₂²×C₄₃	#382	1	1	yes	characteristic
46	C₄×C₄₃	—	2	2	no	—
47	C₄×C₄₃	—	2	2	no	—
48	C₄×C₄₃	—	2	1	no	—
49	C₄×C₄₃	#430	1	2	yes	—
50	#1568	—	43	2	no	—
51	#1452	D₄₃	1	1	yes	characteristic
52	#1287	—	43	4	no	—
53	C₂×C₄₃	—	4	1	no	—
54	C₂×C₄₃	#1833	1	2	yes	—
55	C₂×C₄₃	#1838	1	1	yes	characteristic
56	#432	—	43	4	no	—
57	#431	C₂×D₄₃	1	2	yes	—
58	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
59	#335	—	86	2	no	—
60	#334	—	86	2	no	—
61	#322	Dic₄₃	1	4	yes	—
62	C₄₃	#8798	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₈	Dic₈₆	1	2	yes	—
64	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
65	C₄⋊C₈	—	2	2	no	—
66	C₄⋊C₈	—	86	4	no	—
67	C₂²⋊C₈	—	2	2	no	—
68	C₂²⋊C₈	—	86	4	no	—
69	#97	—	86	4	no	—
70	C₄×C₈	D₁₇₂	1	1	yes	characteristic
71	C₄×C₈	D₁₇₂	1	1	yes	characteristic
72	C₄×C₈	C₂×Dic₄₃	1	4	yes	—
73	C₄×C₈	C₂×Dic₄₃	1	2	yes	—
74	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
75	C₂²×C₄	#10621898	1	2	yes	—
76	C₂×C₈	—	2	4	no	—
77	C₂×C₈	—	4	2	no	—
78	C₂×C₈	—	172	4	no	—
79	C₂×C₈	C₄⋊Dic₄₃	1	2	yes	—
80	C₂×C₈	C₄⋊Dic₄₃	1	2	yes	—
81	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
82	C₄²	#10621898	1	2	yes	—
83	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
84	C₂³	#13063317	1	1	yes	characteristic
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	4	2	no	—
87	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
88	C₂×C₄	#13063284	1	2	yes	—
89	C₂×C₄	#13063313	1	2	yes	—
90	C₂×C₄	#13063317	1	1	yes	characteristic
91	C₈	—	2	2	no	—
92	C₈	—	2	2	no	—
93	C₈	—	4	4	no	—
94	C₈	—	344	4	no	—
95	C₂²	—	2	1	no	—
96	C₂²	—	2	2	no	—
97	C₂²	#14582765	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	2	2	no	—
100	C₄	—	2	2	no	—
101	C₄	#14582948	1	2	yes	—
102	C₂	—	4	1	no	—
103	C₂	#19134719	1	2	yes	—
104	C₂	#19134736	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19133358

C₂

yes

maximal

#19132457

C₂

yes

maximal

C₄₃×#1452

C₂

yes

maximal, characteristic

#14582956

C₂²

yes

—

#14582652

—

#14582650

—

C₄₃×#431

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#322

C₄

yes

—

C₄⋊(C₄₃⋊C₈)

—

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

C₂²×C₈×C₄₃

Q₈

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊C₈×C₄₃

—

C₂²⋊C₈×C₄₃

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

D₄

yes

characteristic

C₄×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂²×C₄×C₄₃

#41

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₄⋊C₄

yes

—

C₂×C₈×C₄₃

C₄⋊C₄

yes

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄²×C₄₃

C₂×D₄

yes

characteristic

C₄²×C₄₃

#41

yes

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#125

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

#117

yes

—

C₂×C₄×C₄₃

#124

yes

—

C₂×C₄×C₄₃

#125

yes

characteristic

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

#8798

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#382

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#430

yes

—

#1568

—

#1452

D₄₃

yes

characteristic

#1287

—

C₂×C₄₃

—

C₂×C₄₃

#1833

yes

—

C₂×C₄₃

yes

—

C₂×D₄₃

yes

—

C₂×C₄×C₈

C₂×D₄₃

yes

—

—

Dic₄₃

yes

—

C₄₃

#8798

yes

characteristic, complemented, Sylow

C₂²×C₈

Dic₈₆

yes

—

C₂×C₄²

C₂²×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

D₁₇₂

yes

characteristic

C₄×C₈

D₁₇₂

yes

characteristic

C₄×C₈

C₂×Dic₄₃

yes

—

C₄×C₈

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₈₆

yes

characteristic

C₂²×C₄

#10621898

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

C₄⋊Dic₄₃

yes

—

C₂×C₈

C₄⋊Dic₄₃

yes

—

C₄²

C₂×D₁₇₂

yes

characteristic

C₄²

#10621898

yes

—

C₄²

C₂²×Dic₄₃

yes

characteristic

C₂³

#13063317

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

#13063284

yes

—

C₂×C₄

#13063313

yes

—

C₂×C₄

#13063317

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

344

—

C₂²

—

C₂²

—

C₂²

#14582765

yes

characteristic

C₄

—

C₄

—

100

C₄

—

101

C₄

#14582948

yes

—

102

C₂

—

103

C₂

#19134719

yes

—

104

C₂

#19134736

yes

characteristic

	subgroup	G/H
center	C₂²	#14582765
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1452	C₂
socle	C₂²×C₄₃	#382
prime radical	C₂³×C₄₃	#125
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1452	D₄₃
hypocenter	C₄₃	#8798
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

subgroup

G/H

center

C₂²

#14582765

commutator

C₄²×C₄₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#1452

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂×C₄²×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

N	H ≅ G/N	type
62. C₄₃	#8798	semidirect

H ≅ G/N

type

62. C₄₃

#8798

semidirect

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

subgroup	index
#19133358	2
#19132457	2
C₄₃×#1452	2
#8798	43

subgroup

index

#19133358

#19132457

C₄₃×#1452

#8798

Subgroups — #24990310

Conjugacy classes of subgroups

Complements

Maximal subgroups