Group #44506774 — subgroups

Subgroups — #44506774

Order 30848.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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	C₂₄₁⋊#564	C₂	1	1	yes	maximal, characteristic
2	#29508126	C₂	1	2	yes	maximal
3	#29508087	C₂	1	1	yes	maximal, characteristic
4	#29507458	C₂	1	2	yes	maximal
5	#330×C₂₄₁	C₂	1	1	yes	maximal, characteristic
6	#21440642	C₂²	1	1	yes	characteristic
7	#21440634	C₂²	1	2	yes	—
8	#21440633	—	2	2	no	—
9	#21440632	—	2	2	no	—
10	#21440632	—	2	2	no	—
11	#21440576	—	2	2	no	—
12	#21440574	—	2	2	no	—
13	#21440565	—	2	2	no	—
14	#21440553	C₂²	1	1	yes	characteristic
15	#125×C₂₄₁	C₂²	1	1	yes	characteristic
16	#97×C₂₄₁	C₂²	1	2	yes	—
17	C₂×Dic₄₈₂	—	2	1	no	—
18	C₂×#14515349	—	2	1	no	—
19	C₄⋊Dic₂₄₁	—	2	2	no	—
20	C₄⋊Dic₂₄₁	—	2	2	no	—
21	C₄⋊Dic₂₄₁	D₄	1	2	yes	—
22	C₄⋊Dic₂₄₁	D₄	1	2	yes	—
23	#16838749	—	2	2	no	—
24	#16838749	—	2	2	no	—
25	#16838749	—	2	2	no	—
26	#16838749	—	2	2	no	—
27	C₄×Dic₂₄₁	—	2	2	no	—
28	C₂×C₈×C₂₄₁	—	2	2	no	—
29	C₄⋊C₄×C₂₄₁	—	2	2	no	—
30	C₄⋊C₄×C₂₄₁	D₄	1	2	yes	—
31	C₄²×C₂₄₁	C₂³	1	1	yes	characteristic
32	Dic₄₈₂	—	4	2	no	—
33	C₂×Dic₂₄₁	—	2	2	no	—
34	C₂×Dic₂₄₁	—	2	2	no	—
35	C₂×Dic₂₄₁	—	4	1	no	—
36	#14515349	—	4	1	no	—
37	C₂×C₄×C₂₄₁	—	2	2	no	—
38	C₂×C₄×C₂₄₁	C₂×D₄	1	2	yes	—
39	C₂×C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
40	C₈×C₂₄₁	—	2	4	no	—
41	C₂²×C₂₄₁	#120	1	1	yes	characteristic
42	C₄×C₂₄₁	—	2	1	no	—
43	C₄×C₂₄₁	—	2	2	no	—
44	C₄×C₂₄₁	—	4	2	no	—
45	Dic₂₄₁	—	4	2	no	—
46	Dic₂₄₁	—	4	2	no	—
47	Dic₂₄₁	—	8	1	no	—
48	C₂×C₂₄₁	#454	1	1	yes	characteristic
49	C₂×C₂₄₁	#456	1	2	yes	—
50	C₂₄₁	#1663	1	1	yes	characteristic, complemented, Sylow
51	#1663	—	241	1	no	maximal, Sylow
52	#564	—	241	1	no	—
53	#501	—	241	2	no	—
54	#491	—	241	1	no	—
55	#330	—	241	2	no	—
56	#330	D₂₄₁	1	1	yes	characteristic
57	C₄⋊Q₈	—	241	1	no	—
58	#125	—	482	2	no	—
59	#125	—	482	2	no	—
60	#125	—	482	2	no	—
61	#125	—	241	2	no	—
62	#125	C₂×D₂₄₁	1	1	yes	characteristic
63	#107	—	482	2	no	—
64	#106	—	482	2	no	—
65	#103	—	482	2	no	—
66	#97	—	241	1	no	—
67	#97	C₂×D₂₄₁	1	2	yes	—
68	C₂×Q₈	—	482	1	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	482	1	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	482	2	no	—
73	C₄⋊C₄	—	482	2	no	—
74	C₄⋊C₄	—	482	2	no	—
75	C₄⋊C₄	—	482	2	no	—
76	C₄⋊C₄	—	482	2	no	—
77	C₄⋊C₄	—	482	2	no	—
78	C₄⋊C₄	—	241	2	no	—
79	C₄⋊C₄	—	241	2	no	—
80	C₄⋊C₄	D₉₆₄	1	2	yes	—
81	C₄²	—	482	2	no	—
82	C₄²	C₂²×D₂₄₁	1	1	yes	characteristic
83	Q₈	—	964	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	964	1	no	—
86	C₂×C₄	—	482	2	no	—
87	C₂×C₄	—	482	2	no	—
88	C₂×C₄	D₄×D₂₄₁	1	2	yes	—
89	C₂×C₄	C₂×D₉₆₄	1	1	yes	characteristic
90	C₈	—	2	4	no	—
91	C₈	—	964	1	no	—
92	C₂²	#21440612	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	4	2	no	—
96	C₄	—	1928	1	no	—
97	C₄	—	964	2	no	—
98	C₄	—	964	2	no	—
99	C₂	#29507892	1	1	yes	characteristic
100	C₂	#29507901	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₄₁⋊#564

C₂

yes

maximal, characteristic

#29508126

C₂

yes

maximal

#29508087

C₂

yes

maximal, characteristic

#29507458

C₂

yes

maximal

#330×C₂₄₁

C₂

yes

maximal, characteristic

#21440642

C₂²

yes

characteristic

#21440634

C₂²

yes

—

—

—

—

—

—

—

C₂²

yes

characteristic

#125×C₂₄₁

C₂²

yes

characteristic

#97×C₂₄₁

C₂²

yes

—

C₂×Dic₄₈₂

—

C₂×#14515349

—

C₄⋊Dic₂₄₁

—

C₄⋊Dic₂₄₁

—

C₄⋊Dic₂₄₁

D₄

yes

—

C₄⋊Dic₂₄₁

D₄

yes

—

—

—

—

—

C₄×Dic₂₄₁

—

C₂×C₈×C₂₄₁

—

C₄⋊C₄×C₂₄₁

—

C₄⋊C₄×C₂₄₁

D₄

yes

—

C₄²×C₂₄₁

C₂³

yes

characteristic

Dic₄₈₂

—

C₂×Dic₂₄₁

—

C₂×Dic₂₄₁

—

C₂×Dic₂₄₁

—

#14515349

—

C₂×C₄×C₂₄₁

—

C₂×C₄×C₂₄₁

C₂×D₄

yes

—

C₂×C₄×C₂₄₁

C₂×D₄

yes

characteristic

C₈×C₂₄₁

—

C₂²×C₂₄₁

#120

yes

characteristic

C₄×C₂₄₁

—

C₄×C₂₄₁

—

C₄×C₂₄₁

—

Dic₂₄₁

—

Dic₂₄₁

—

Dic₂₄₁

—

C₂×C₂₄₁

#454

yes

characteristic

C₂×C₂₄₁

#456

yes

—

C₂₄₁

#1663

yes

characteristic, complemented, Sylow

#1663

—

241

maximal, Sylow

#564

—

241

—

#501

—

241

—

#491

—

241

—

#330

—

241

—

#330

D₂₄₁

yes

characteristic

C₄⋊Q₈

—

241

—

#125

—

482

—

#125

—

482

—

#125

—

482

—

#125

—

241

—

#125

C₂×D₂₄₁

yes

characteristic

#107

—

482

—

#106

—

482

—

#103

—

482

—

#97

—

241

—

#97

C₂×D₂₄₁

yes

—

C₂×Q₈

—

482

—

C₂×C₈

—

C₂×C₈

—

482

—

C₄⋊C₄

—

C₄⋊C₄

—

482

—

C₄⋊C₄

—

482

—

C₄⋊C₄

—

482

—

C₄⋊C₄

—

482

—

C₄⋊C₄

—

482

—

C₄⋊C₄

—

482

—

C₄⋊C₄

—

241

—

C₄⋊C₄

—

241

—

C₄⋊C₄

D₉₆₄

yes

—

C₄²

—

482

—

C₄²

C₂²×D₂₄₁

yes

characteristic

Q₈

—

964

—

C₂×C₄

—

C₂×C₄

—

964

—

C₂×C₄

—

482

—

C₂×C₄

—

482

—

C₂×C₄

D₄×D₂₄₁

yes

—

C₂×C₄

C₂×D₉₆₄

yes

characteristic

C₈

—

C₈

—

964

—

C₂²

#21440612

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

1928

—

C₄

—

964

—

C₄

—

964

—

C₂

#29507892

yes

characteristic

100

C₂

#29507901

yes

—

	subgroup	G/H
center	C₂²	#21440612
commutator, cosocle	C₄²×C₂₄₁	C₂³
Frattini	C₄²	C₂²×D₂₄₁
Fitting	#330×C₂₄₁	C₂
socle, prime radical	C₂²×C₂₄₁	#120
hypercenter	#330	D₂₄₁
hypocenter	C₂₄₁	#1663
LCS	G ▷ C₄²×C₂₄₁ ▷ C₂²×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

#21440612

commutator, cosocle

C₄²×C₂₄₁

C₂³

Frattini

C₄²

C₂²×D₂₄₁

Fitting

#330×C₂₄₁

C₂

C₂²×C₂₄₁

D₂₄₁

C₂₄₁

G ▷ C₄²×C₂₄₁ ▷ C₂²×C₂₄₁ ▷ C₂₄₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
50. C₂₄₁	#1663	semidirect

H ≅ G/N

type

50. C₂₄₁

#1663

semidirect

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

subgroup	index
C₂₄₁⋊#564	2
#29508126	2
#29508087	2
#29507458	2
#330×C₂₄₁	2
#1663	241

subgroup

index

C₂₄₁⋊#564

#330×C₂₄₁

241

Subgroups — #44506774

Conjugacy classes of subgroups

Complements

Maximal subgroups