Group #49095456 — subgroups

Subgroups — #49095456

Order 35968.

256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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	C₂×C₄⋊#14555886	C₂	1	1	yes	maximal, characteristic
2	C₂×#22582808	C₂	1	4	yes	maximal
3	#31823309	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊C₈×C₂₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#14555886	C₂²	1	2	yes	—
6	C₂×C₄×Dic₂₈₁	C₂²	1	2	yes	—
7	C₄⋊#14555886	—	2	2	no	—
8	#22582808	—	2	8	no	—
9	#22582786	C₄	1	2	yes	—
10	#22582786	C₄	1	2	yes	—
11	C₂²×C₈×C₂₈₁	C₂²	1	2	yes	—
12	C₂×C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
13	C₄⋊C₈×C₂₈₁	—	2	2	no	—
14	C₂²×Dic₂₈₁	C₂×C₄	1	4	yes	—
15	C₂×#14555886	—	2	4	no	—
16	C₂×#14555886	—	2	2	no	—
17	C₄×Dic₂₈₁	D₄	1	4	yes	—
18	C₄×Dic₂₈₁	Q₈	1	4	yes	—
19	C₂²×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
22	C₂×C₈×C₂₈₁	—	2	4	no	—
23	C₂×C₈×C₂₈₁	—	2	2	no	—
24	C₄²×C₂₈₁	D₄	1	2	yes	—
25	C₄²×C₂₈₁	Q₈	1	2	yes	—
26	C₂×Dic₂₈₁	—	2	4	no	—
27	C₂×Dic₂₈₁	—	2	4	no	—
28	C₂×Dic₂₈₁	C₄⋊C₄	1	8	yes	—
29	#14555886	—	4	2	no	—
30	C₂³×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₂₈₁	—	2	2	no	—
32	C₂×C₄×C₂₈₁	—	2	2	no	—
33	C₂×C₄×C₂₈₁	C₄⋊C₄	1	2	yes	—
34	C₂×C₄×C₂₈₁	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₂₈₁	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₂₈₁	C₂×Q₈	1	2	yes	—
38	C₂×C₄×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
39	C₈×C₂₈₁	—	4	2	no	—
40	C₂²×C₂₈₁	C₂×C₄⋊C₄	1	2	yes	—
41	C₂²×C₂₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₂₈₁	#131	1	2	yes	—
43	C₂²×C₂₈₁	#131	1	2	yes	—
44	C₄×C₂₈₁	—	2	2	no	—
45	C₄×C₂₈₁	—	2	2	no	—
46	C₄×C₂₈₁	#127	1	1	yes	characteristic
47	C₄×C₂₈₁	C₄⋊Q₈	1	1	yes	characteristic
48	C₄×C₂₈₁	C₄⋊Q₈	1	2	yes	—
49	Dic₂₈₁	—	2	8	no	—
50	C₂×C₂₈₁	#384	1	1	yes	characteristic
51	C₂×C₂₈₁	#424	1	4	yes	—
52	C₂×C₂₈₁	#424	1	1	yes	characteristic
53	C₂×C₂₈₁	#424	1	1	yes	characteristic
54	C₂₈₁	#1843	1	1	yes	characteristic, complemented, Sylow
55	#1843	—	281	1	no	maximal, Sylow
56	C₂×C₄⋊C₈	—	281	4	no	—
57	C₂×C₄⋊C₈	—	281	1	no	—
58	C₂×C₄⋊C₈	D₂₈₁	1	1	yes	characteristic
59	#376	—	281	1	no	—
60	C₂²×C₈	—	281	2	no	—
61	C₂²×C₈	C₂×D₂₈₁	1	2	yes	—
62	C₂×C₄²	—	281	2	no	—
63	C₂×C₄²	C₂×D₂₈₁	1	1	yes	characteristic
64	C₄⋊C₈	—	2	2	no	—
65	C₄⋊C₈	—	562	8	no	—
66	C₄⋊C₈	—	562	2	no	—
67	#95	—	281	2	no	—
68	#95	—	281	2	no	—
69	C₂²×C₄	—	281	4	no	—
70	C₂²×C₄	C₄×D₂₈₁	1	1	yes	characteristic
71	C₂²×C₄	C₄×D₂₈₁	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
73	C₂×C₈	—	2	4	no	—
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	562	4	no	—
76	C₂×C₈	—	562	2	no	—
77	C₄²	—	281	4	no	—
78	C₄²	—	281	4	no	—
79	C₄²	C₂²⋊D₂₈₁	1	2	yes	—
80	C₄²	Dic₅₆₂	1	2	yes	—
81	C₂³	C₂×C₄×D₂₈₁	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	281	8	no	—
85	C₂×C₄	—	562	4	no	—
86	C₂×C₄	—	562	4	no	—
87	C₂×C₄	#17985117	1	2	yes	—
88	C₂×C₄	#17985117	1	2	yes	—
89	C₂×C₄	D₄×D₂₈₁	1	2	yes	—
90	C₂×C₄	C₂×C₂²⋊D₂₈₁	1	1	yes	characteristic
91	C₂×C₄	Q₈×D₂₈₁	1	2	yes	—
92	C₂×C₄	C₂×Dic₅₆₂	1	1	yes	characteristic
93	C₈	—	4	2	no	—
94	C₈	—	1124	2	no	—
95	C₂²	C₄⋊C₄×D₂₈₁	1	2	yes	—
96	C₂²	C₂×#17985117	1	1	yes	characteristic
97	C₂²	#22582885	1	2	yes	—
98	C₂²	#22582887	1	2	yes	—
99	C₄	—	2	2	no	—
100	C₄	—	2	2	no	—
101	C₄	—	562	8	no	—
102	C₄	#22582875	1	1	yes	characteristic
103	C₄	#22582877	1	1	yes	characteristic
104	C₄	#22582878	1	2	yes	—
105	C₂	#31823332	1	1	yes	characteristic
106	C₂	#31823488	1	4	yes	—
107	C₂	#31823489	1	1	yes	characteristic
108	C₂	#31823491	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#14555886

C₂

yes

maximal, characteristic

C₂×#22582808

C₂

yes

maximal

#31823309

C₂

yes

maximal, characteristic

C₂×C₄⋊C₈×C₂₈₁

C₂

yes

maximal, characteristic

C₂²×#14555886

C₂²

yes

—

C₂×C₄×Dic₂₈₁

C₂²

yes

—

C₄⋊#14555886

—

#22582808

—

#22582786

C₄

yes

—

#22582786

C₄

yes

—

C₂²×C₈×C₂₈₁

C₂²

yes

—

C₂×C₄²×C₂₈₁

C₂²

yes

characteristic

C₄⋊C₈×C₂₈₁

—

C₂²×Dic₂₈₁

C₂×C₄

yes

—

C₂×#14555886

—

C₂×#14555886

—

C₄×Dic₂₈₁

D₄

yes

—

C₄×Dic₂₈₁

Q₈

yes

—

C₂²×C₄×C₂₈₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₈₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₈₁

C₂³

yes

characteristic

C₂×C₈×C₂₈₁

—

C₂×C₈×C₂₈₁

—

C₄²×C₂₈₁

D₄

yes

—

C₄²×C₂₈₁

Q₈

yes

—

C₂×Dic₂₈₁

—

C₂×Dic₂₈₁

—

C₂×Dic₂₈₁

C₄⋊C₄

yes

—

#14555886

—

C₂³×C₂₈₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

C₄⋊C₄

yes

—

C₂×C₄×C₂₈₁

C₄⋊C₄

yes

—

C₂×C₄×C₂₈₁

C₂×D₄

yes

—

C₂×C₄×C₂₈₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₈₁

C₂×Q₈

yes

—

C₂×C₄×C₂₈₁

C₂×Q₈

yes

characteristic

C₈×C₂₈₁

—

C₂²×C₂₈₁

C₂×C₄⋊C₄

yes

—

C₂²×C₂₈₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₈₁

#131

yes

—

C₂²×C₂₈₁

#131

yes

—

C₄×C₂₈₁

—

C₄×C₂₈₁

—

C₄×C₂₈₁

#127

yes

characteristic

C₄×C₂₈₁

C₄⋊Q₈

yes

characteristic

C₄×C₂₈₁

C₄⋊Q₈

yes

—

Dic₂₈₁

—

C₂×C₂₈₁

#384

yes

characteristic

C₂×C₂₈₁

#424

yes

—

C₂×C₂₈₁

yes

C₂×C₂₈₁

yes

C₂₈₁

yes

characteristic, complemented, Sylow

#1843

—

281

maximal, Sylow

C₂×C₄⋊C₈

—

281

—

C₂×C₄⋊C₈

—

281

—

C₂×C₄⋊C₈

D₂₈₁

yes

characteristic

#376

—

281

—

C₂²×C₈

—

281

—

C₂²×C₈

C₂×D₂₈₁

yes

—

C₂×C₄²

—

281

—

C₂×C₄²

C₂×D₂₈₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

562

—

C₄⋊C₈

—

562

—

#95

—

281

—

#95

—

281

—

C₂²×C₄

—

281

—

C₂²×C₄

C₄×D₂₈₁

yes

characteristic

C₂²×C₄

C₄×D₂₈₁

yes

characteristic

C₂²×C₄

C₂²×D₂₈₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

562

—

C₂×C₈

—

562

—

C₄²

—

281

—

C₄²

—

281

—

C₄²

C₂²⋊D₂₈₁

yes

—

C₄²

Dic₅₆₂

yes

—

C₂³

C₂×C₄×D₂₈₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

281

—

C₂×C₄

—

562

—

C₂×C₄

—

562

—

C₂×C₄

#17985117

yes

—

C₂×C₄

#17985117

yes

—

C₂×C₄

D₄×D₂₈₁

yes

—

C₂×C₄

C₂×C₂²⋊D₂₈₁

yes

characteristic

C₂×C₄

Q₈×D₂₈₁

yes

—

C₂×C₄

C₂×Dic₅₆₂

yes

characteristic

C₈

—

C₈

—

1124

—

C₂²

C₄⋊C₄×D₂₈₁

yes

—

C₂²

C₂×#17985117

yes

characteristic

C₂²

#22582885

yes

—

C₂²

#22582887

yes

—

C₄

—

100

C₄

—

101

C₄

—

562

—

102

C₄

#22582875

yes

characteristic

103

C₄

#22582877

yes

characteristic

104

C₄

#22582878

yes

—

105

C₂

#31823332

yes

characteristic

106

C₂

#31823488

yes

—

107

C₂

#31823489

yes

characteristic

108

C₂

#31823491

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₈₁
commutator, socle, prime radical	C₂³×C₂₈₁	C₂²×C₄
Fitting	C₂×C₄⋊C₈×C₂₈₁	C₂
cosocle	C₂²×C₄×C₂₈₁	C₂³
hypercenter	C₂×C₄⋊C₈	D₂₈₁
hypocenter	C₂₈₁	#1843
LCS	G ▷ C₂³×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₂₈₁

commutator, socle, prime radical

C₂³×C₂₈₁

C₂²×C₄

Fitting

C₂×C₄⋊C₈×C₂₈₁

C₂

cosocle

C₂²×C₄×C₂₈₁

C₂³

hypercenter

C₂×C₄⋊C₈

D₂₈₁

C₂₈₁

G ▷ C₂³×C₂₈₁ ▷ C₂₈₁

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
54. C₂₈₁	#1843	semidirect

H ≅ G/N

type

54. C₂₈₁

#1843

semidirect

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

subgroup	index
C₂×C₄⋊#14555886	2
C₂×#22582808	2
#31823309	2
C₂×C₄⋊C₈×C₂₈₁	2
#1843	281

subgroup

index

C₂×C₄⋊C₈×C₂₈₁

281

Subgroups — #49095456

Conjugacy classes of subgroups

Complements

Maximal subgroups