Group #25001106 — subgroups

Subgroups — #25001106

Order 11008.

350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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	#19134728	C₂	1	3	yes	maximal
2	#19132476	C₂	1	3	yes	maximal
3	C₄₃×#2845	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063236	C₂²	1	3	yes	—
5	#14582769	C₂²	1	1	yes	characteristic
6	#14582661	—	2	6	no	—
7	C₄₃×#398	—	2	6	no	—
8	C₄₃×#382	C₂²	1	3	yes	—
9	C₂²×C₄₃⋊C₈	—	2	3	no	—
10	C₂×C₄⋊Dic₄₃	—	2	3	no	—
11	#13063236	—	2	3	no	—
12	#13063236	Q₈	1	6	yes	—
13	C₂×C₄⋊C₄×C₄₃	—	2	6	no	—
14	C₂×C₄⋊C₄×C₄₃	D₄	1	6	yes	—
15	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
16	#95×C₄₃	—	2	2	no	—
17	#95×C₄₃	—	2	6	no	—
18	C₂²×C₄×C₄₃	—	2	6	no	—
19	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
20	C₂²×Dic₄₃	—	4	1	no	—
21	C₄⋊C₄×C₄₃	—	4	6	no	—
22	C₄⋊C₄×C₄₃	—	8	6	no	—
23	C₄²×C₄₃	C₂×Q₈	1	3	yes	—
24	C₄²×C₄₃	#41	1	1	yes	characteristic
25	C₄⋊Dic₄₃	—	4	6	no	—
26	C₂×C₄₃⋊C₈	—	2	6	no	—
27	C₂×C₄₃⋊C₈	—	4	3	no	—
28	C₂×C₄₃⋊C₈	—	4	3	no	—
29	C₂³×C₄₃	#120	1	1	yes	characteristic
30	C₂×C₄×C₄₃	—	2	3	no	—
31	C₂×C₄×C₄₃	—	2	3	no	—
32	C₂×C₄×C₄₃	—	4	6	no	—
33	C₂×C₄×C₄₃	—	4	6	no	—
34	C₂×C₄×C₄₃	—	4	6	no	—
35	C₂×C₄×C₄₃	C₂²⋊Q₈	1	3	yes	—
36	C₂×C₄×C₄₃	C₄⋊Q₈	1	3	yes	—
37	C₂×Dic₄₃	—	8	3	no	—
38	C₄₃⋊C₈	—	4	6	no	—
39	#10586	—	43	1	no	maximal, Sylow
40	C₂²×C₄₃	#395	1	1	yes	characteristic
41	C₂²×C₄₃	#454	1	3	yes	—
42	C₂²×C₄₃	#455	1	3	yes	—
43	C₄×C₄₃	—	2	3	no	—
44	C₄×C₄₃	—	2	3	no	—
45	C₄×C₄₃	—	8	6	no	—
46	Dic₄₃	—	16	1	no	—
47	#2845	D₄₃	1	1	yes	characteristic
48	#1836	—	43	3	no	—
49	#1295	—	43	3	no	—
50	C₂×C₄₃	#1658	1	1	yes	characteristic
51	C₂×C₄₃	#1662	1	3	yes	—
52	C₂×C₄₃	#2061	1	3	yes	—
53	C₂×#97	—	43	3	no	—
54	#398	—	2	6	no	—
55	#384	—	43	1	no	—
56	#382	C₂×D₄₃	1	3	yes	—
57	#340	—	86	6	no	—
58	C₄₃	#10586	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₈	—	86	3	no	—
60	C₂×C₄⋊C₄	—	2	6	no	—
61	C₂×C₄⋊C₄	—	86	3	no	—
62	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	6	yes	—
63	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
64	#97	—	43	6	no	—
65	#97	—	86	3	no	—
66	#95	—	2	2	no	—
67	#95	—	2	6	no	—
68	C₂²×C₄	—	2	6	no	—
69	C₂²×C₄	—	172	1	no	—
70	C₂²×C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
71	C₂×C₈	—	86	6	no	—
72	C₂×C₈	—	172	3	no	—
73	C₂×C₈	—	172	3	no	—
74	C₄⋊C₄	—	4	6	no	—
75	C₄⋊C₄	—	8	6	no	—
76	C₄⋊C₄	—	172	6	no	—
77	C₄²	Q₈×D₄₃	1	3	yes	—
78	C₄²	#10621902	1	1	yes	characteristic
79	C₂³	#13063294	1	1	yes	characteristic
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	4	6	no	—
83	C₂×C₄	—	4	6	no	—
84	C₂×C₄	—	4	6	no	—
85	C₂×C₄	—	344	3	no	—
86	C₂×C₄	#13063301	1	3	yes	—
87	C₂×C₄	#13063323	1	3	yes	—
88	C₈	—	172	6	no	—
89	C₂²	#14582818	1	1	yes	characteristic
90	C₂²	#14583072	1	3	yes	—
91	C₂²	#14583077	1	3	yes	—
92	C₄	—	2	3	no	—
93	C₄	—	2	3	no	—
94	C₄	—	8	6	no	—
95	C₄	—	688	1	no	—
96	C₂	#19133897	1	1	yes	characteristic
97	C₂	#19133918	1	3	yes	—
98	C₂	#19135942	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19134728

C₂

yes

maximal

#19132476

C₂

yes

maximal

C₄₃×#2845

C₂

yes

maximal, characteristic

C₂×#13063236

C₂²

yes

—

#14582769

C₂²

yes

characteristic

#14582661

—

C₄₃×#398

—

C₄₃×#382

C₂²

yes

—

C₂²×C₄₃⋊C₈

—

C₂×C₄⋊Dic₄₃

—

#13063236

—

#13063236

Q₈

yes

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#95×C₄₃

—

#95×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×Q₈

yes

—

C₄²×C₄₃

#41

yes

characteristic

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

C₂²⋊Q₈

yes

—

C₂×C₄×C₄₃

C₄⋊Q₈

yes

—

C₂×Dic₄₃

—

C₄₃⋊C₈

—

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

#455

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

#2845

D₄₃

yes

characteristic

#1836

—

#1295

—

C₂×C₄₃

#1658

yes

characteristic

C₂×C₄₃

#1662

yes

—

C₂×C₄₃

#2061

yes

—

C₂×#97

—

#398

—

#384

—

#382

C₂×D₄₃

yes

—

#340

—

C₄₃

#10586

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₄₃

yes

—

C₂×C₄²

C₂²×D₄₃

yes

—

—

—

—

C₂²×C₄

—

C₂²×C₄

—

172

—

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

—

172

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄²

Q₈×D₄₃

yes

—

C₄²

yes

C₂³

yes

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

344

—

C₂×C₄

#13063301

yes

—

C₂×C₄

#13063323

yes

—

C₈

—

172

—

C₂²

#14582818

yes

characteristic

C₂²

#14583072

yes

—

C₂²

#14583077

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

688

—

C₂

#19133897

yes

characteristic

C₂

#19133918

yes

—

C₂

#19135942

yes

—

	subgroup	G/H
center	C₂³	#13063294
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#2845	C₂
socle, prime radical	C₂³×C₄₃	#120
hypercenter	#2845	D₄₃
hypocenter	C₄₃	#10586
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

subgroup

G/H

center

C₂³

#13063294

commutator, cosocle

C₂×C₄²×C₄₃

C₂³

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄₃×#2845

C₂

C₂³×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

N	H ≅ G/N	type
58. C₄₃	#10586	semidirect

H ≅ G/N

type

58. C₄₃

#10586

semidirect

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

subgroup	index
#19134728	2
#19132476	2
C₄₃×#2845	2
#10586	43

subgroup

index

#19134728

#19132476

C₄₃×#2845

#10586

Subgroups — #25001106

Conjugacy classes of subgroups

Complements

Maximal subgroups