Group #49094604 — subgroups

Subgroups — #49094604

Order 35968.

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

normal subgroups only

This group has 182 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	C₂₈₁⋊#564	C₂	1	1	yes	maximal, characteristic, complemented
2	#31823827	C₂	1	2	yes	maximal
3	#31823205	C₂	1	1	yes	maximal, characteristic, complemented
4	#31823204	C₂	1	2	yes	maximal, complemented
5	#490×C₂₈₁	C₂	1	1	yes	maximal, characteristic
6	#22582871	C₂²	1	2	yes	—
7	#22582870	—	2	2	no	—
8	#22582869	—	2	2	no	—
9	#22582869	—	2	2	no	—
10	#22582800	—	2	2	no	—
11	#22582800	—	2	2	no	—
12	#22582790	C₂²	1	2	yes	—
13	#127×C₂₈₁	C₂²	1	1	yes	characteristic
14	#125×C₂₈₁	C₂²	1	1	yes	characteristic
15	#102×C₂₈₁	—	2	2	no	—
16	#97×C₂₈₁	C₂²	1	1	yes	characteristic
17	C₂×#14555886	—	2	2	no	—
18	C₄⋊Dic₂₈₁	—	2	2	no	—
19	C₄⋊Dic₂₈₁	D₄	1	2	yes	—
20	C₄⋊Dic₂₈₁	D₄	1	2	yes	—
21	#17985117	—	2	2	no	—
22	#17985117	—	2	2	no	—
23	#17985117	—	2	2	no	—
24	#17985117	—	2	2	no	—
25	C₄×Dic₂₈₁	—	2	2	no	—
26	C₂×D₄×C₂₈₁	—	2	2	no	—
27	C₂×D₄×C₂₈₁	—	2	1	no	—
28	C₂×C₈×C₂₈₁	—	2	1	no	—
29	C₄⋊C₄×C₂₈₁	—	2	2	no	—
30	C₄⋊C₄×C₂₈₁	D₄	1	2	yes	—
31	C₄²×C₂₈₁	C₂³	1	1	yes	characteristic
32	C₂×Dic₂₈₁	—	2	2	no	—
33	C₂×Dic₂₈₁	—	2	2	no	—
34	#14555886	—	4	2	no	—
35	C₂³×C₂₈₁	—	4	1	no	—
36	D₄×C₂₈₁	—	4	2	no	—
37	D₄×C₂₈₁	—	4	4	no	—
38	C₂×C₄×C₂₈₁	—	2	2	no	—
39	C₂×C₄×C₂₈₁	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
41	C₈×C₂₈₁	—	4	1	no	—
42	C₂²×C₂₈₁	—	8	2	no	—
43	C₂²×C₂₈₁	—	8	1	no	—
44	C₂²×C₂₈₁	#120	1	1	yes	characteristic
45	C₄×C₂₈₁	—	2	1	no	—
46	C₄×C₂₈₁	—	2	2	no	—
47	C₄×C₂₈₁	—	4	2	no	—
48	Dic₂₈₁	—	4	2	no	—
49	Dic₂₈₁	—	4	2	no	—
50	C₂×C₂₈₁	—	16	1	no	—
51	C₂×C₂₈₁	#454	1	2	yes	—
52	C₂×C₂₈₁	#454	1	1	yes	characteristic
53	C₂₈₁	#1658	1	1	yes	characteristic, complemented, Sylow
54	#1658	—	281	1	no	maximal, Sylow
55	#564	—	281	1	no	—
56	#490	—	281	2	no	—
57	#490	D₂₈₁	1	1	yes	characteristic
58	#330	—	281	1	no	—
59	#330	—	281	2	no	—
60	#127	C₂×D₂₈₁	1	1	yes	characteristic
61	#125	—	281	2	no	—
62	#125	—	562	2	no	—
63	#125	—	562	2	no	—
64	#125	—	562	2	no	—
65	#125	C₂×D₂₈₁	1	1	yes	characteristic
66	#102	—	2	2	no	—
67	#102	—	562	2	no	—
68	#102	—	562	2	no	—
69	#97	—	281	2	no	—
70	#97	C₂×D₂₈₁	1	1	yes	characteristic
71	C₂×D₄	—	2	2	no	—
72	C₂×D₄	—	2	1	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	562	2	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	281	2	no	—
77	C₄⋊C₄	—	281	2	no	—
78	C₄⋊C₄	—	562	2	no	—
79	C₄⋊C₄	—	562	2	no	—
80	C₄⋊C₄	—	562	2	no	—
81	C₄⋊C₄	—	562	2	no	—
82	C₄⋊C₄	—	562	2	no	—
83	C₄⋊C₄	C₂²⋊D₂₈₁	1	2	yes	—
84	C₄²	—	562	2	no	—
85	C₄²	C₂²×D₂₈₁	1	1	yes	characteristic
86	C₂³	—	4	1	no	—
87	D₄	—	4	4	no	—
88	D₄	—	4	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	562	2	no	—
91	C₂×C₄	—	562	2	no	—
92	C₂×C₄	D₄×D₂₈₁	1	2	yes	—
93	C₂×C₄	C₂×C₂²⋊D₂₈₁	1	1	yes	characteristic
94	C₈	—	4	1	no	—
95	C₈	—	1124	2	no	—
96	C₂²	—	8	2	no	—
97	C₂²	—	8	1	no	—
98	C₂²	#22582847	1	1	yes	characteristic
99	C₄	—	2	2	no	—
100	C₄	—	2	1	no	—
101	C₄	—	4	2	no	—
102	C₄	—	1124	2	no	—
103	C₄	—	1124	2	no	—
104	C₂	—	16	1	no	—
105	C₂	#31823634	1	2	yes	—
106	C₂	#31823635	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₈₁⋊#564

C₂

yes

maximal, characteristic, complemented

#31823827

C₂

yes

maximal

#31823205

C₂

yes

maximal, characteristic, complemented

#31823204

C₂

yes

maximal, complemented

#490×C₂₈₁

C₂

yes

maximal, characteristic

#22582871

C₂²

yes

—

—

—

—

—

—

C₂²

yes

—

#127×C₂₈₁

C₂²

yes

characteristic

#125×C₂₈₁

C₂²

yes

characteristic

#102×C₂₈₁

—

#97×C₂₈₁

C₂²

yes

characteristic

C₂×#14555886

—

C₄⋊Dic₂₈₁

—

C₄⋊Dic₂₈₁

D₄

yes

—

C₄⋊Dic₂₈₁

D₄

yes

—

—

—

—

—

C₄×Dic₂₈₁

—

C₂×D₄×C₂₈₁

—

C₂×D₄×C₂₈₁

—

C₂×C₈×C₂₈₁

—

C₄⋊C₄×C₂₈₁

—

C₄⋊C₄×C₂₈₁

D₄

yes

—

C₄²×C₂₈₁

C₂³

yes

characteristic

C₂×Dic₂₈₁

—

C₂×Dic₂₈₁

—

#14555886

—

C₂³×C₂₈₁

—

D₄×C₂₈₁

—

D₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

C₂×D₄

yes

—

C₂×C₄×C₂₈₁

C₂×D₄

yes

characteristic

C₈×C₂₈₁

—

C₂²×C₂₈₁

—

C₂²×C₂₈₁

—

C₂²×C₂₈₁

#120

yes

characteristic

C₄×C₂₈₁

—

C₄×C₂₈₁

—

C₄×C₂₈₁

—

Dic₂₈₁

—

Dic₂₈₁

—

C₂×C₂₈₁

—

C₂×C₂₈₁

#454

yes

—

C₂×C₂₈₁

#454

yes

characteristic

C₂₈₁

#1658

yes

characteristic, complemented, Sylow

#1658

—

281

maximal, Sylow

#564

—

281

—

#490

—

281

—

#490

D₂₈₁

yes

characteristic

#330

—

281

—

#330

—

281

—

#127

C₂×D₂₈₁

yes

characteristic

#125

—

281

—

#125

—

562

—

#125

—

562

—

#125

—

562

—

#125

C₂×D₂₈₁

yes

characteristic

#102

—

#102

—

562

—

#102

—

562

—

#97

—

281

—

#97

C₂×D₂₈₁

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×C₈

—

C₂×C₈

—

562

—

C₄⋊C₄

—

C₄⋊C₄

—

281

—

C₄⋊C₄

—

281

—

C₄⋊C₄

—

562

—

C₄⋊C₄

—

562

—

C₄⋊C₄

—

562

—

C₄⋊C₄

—

562

—

C₄⋊C₄

—

562

—

C₄⋊C₄

C₂²⋊D₂₈₁

yes

—

C₄²

—

562

—

C₄²

C₂²×D₂₈₁

yes

characteristic

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

562

—

C₂×C₄

—

562

—

C₂×C₄

D₄×D₂₈₁

yes

—

C₂×C₄

C₂×C₂²⋊D₂₈₁

yes

characteristic

C₈

—

C₈

—

1124

—

C₂²

—

C₂²

—

C₂²

#22582847

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

1124

—

103

C₄

—

1124

—

104

C₂

—

105

C₂

#31823634

yes

—

106

C₂

#31823635

yes

characteristic

	subgroup	G/H
center	C₂²	#22582847
commutator, cosocle	C₄²×C₂₈₁	C₂³
Frattini	C₄²	C₂²×D₂₈₁
Fitting	#490×C₂₈₁	C₂
socle	C₂²×C₂₈₁	#120
prime radical	#127×C₂₈₁	C₂²
hypercenter	#490	D₂₈₁
hypocenter	C₂₈₁	#1658
LCS	G ▷ C₄²×C₂₈₁ ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #490

subgroup

G/H

center

C₂²

#22582847

commutator, cosocle

C₄²×C₂₈₁

C₂³

Frattini

C₄²

C₂²×D₂₈₁

Fitting

#490×C₂₈₁

C₂

socle

C₂²×C₂₈₁

#120

prime radical

#127×C₂₈₁

C₂²

D₂₈₁

C₂₈₁

G ▷ C₄²×C₂₈₁ ▷ C₂²×C₂₈₁ ▷ C₂₈₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #490

N	H ≅ G/N	type
1. C₂₈₁⋊#564	C₂	semidirect
3. #31823205	C₂	semidirect
4. #31823204	C₂	semidirect
53. C₂₈₁	#1658	semidirect

H ≅ G/N

type

1. C₂₈₁⋊#564

C₂

semidirect

3. #31823205

C₂

semidirect

4. #31823204

C₂

semidirect

53. C₂₈₁

#1658

semidirect

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

subgroup	index
C₂₈₁⋊#564	2
#31823827	2
#31823205	2
#31823204	2
#490×C₂₈₁	2
#1658	281

subgroup

index

C₂₈₁⋊#564

#490×C₂₈₁

281

Subgroups — #49094604

Conjugacy classes of subgroups

Complements

Maximal subgroups