Group #49095438 — subgroups

Subgroups — #49095438

Order 35968.

224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22582790	C₂	1	1	yes	maximal, characteristic
2	#31823329	C₂	1	1	yes	maximal, characteristic
3	#31823225	C₂	1	4	yes	maximal
4	#384×C₂₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#14555886	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₂₈₁	C₂²	1	2	yes	—
7	#22582790	C₄	1	4	yes	complemented
8	#22582786	—	2	2	no	—
9	C₂×C₄⋊C₄×C₂₈₁	—	2	2	no	—
10	C₂×C₄⋊C₄×C₂₈₁	C₂²	1	2	yes	—
11	C₂×C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
12	C₂²×Dic₂₈₁	—	2	2	no	—
13	C₂×#14555886	—	2	2	no	—
14	C₂×#14555886	—	2	2	no	—
15	C₂×#14555886	C₂×C₄	1	4	yes	—
16	C₄⋊Dic₂₈₁	—	2	4	no	—
17	C₂²×C₄×C₂₈₁	—	2	2	no	—
18	C₂²×C₄×C₂₈₁	D₄	1	2	yes	—
19	C₂²×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₂₈₁	—	2	4	no	—
21	C₄⋊C₄×C₂₈₁	—	4	4	no	—
22	C₄²×C₂₈₁	C₂×C₄	1	2	yes	—
23	C₄²×C₂₈₁	Q₈	1	2	yes	—
24	C₂×Dic₂₈₁	—	4	2	no	—
25	C₂×Dic₂₈₁	—	4	2	no	—
26	C₂×Dic₂₈₁	—	4	2	no	—
27	#14555886	—	2	4	no	—
28	C₂³×C₂₈₁	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₂₈₁	—	2	2	no	—
30	C₂×C₄×C₂₈₁	—	2	2	no	—
31	C₂×C₄×C₂₈₁	—	4	2	no	—
32	C₂×C₄×C₂₈₁	—	4	4	no	—
33	C₂×C₄×C₂₈₁	C₄⋊C₄	1	4	yes	—
34	C₂×C₄×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₄×C₂₈₁	#41	1	2	yes	—
37	C₂×C₄×C₂₈₁	#41	1	2	yes	—
38	C₂²×C₂₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₂₈₁	#124	1	1	yes	characteristic
40	C₂²×C₂₈₁	#124	1	1	yes	characteristic
41	C₂²×C₂₈₁	AGL(1,ℤ/8)	1	2	yes	—
42	C₂²×C₂₈₁	#137	1	2	yes	—
43	C₄×C₂₈₁	—	2	4	no	—
44	C₄×C₂₈₁	—	8	2	no	—
45	C₄×C₂₈₁	#117	1	2	yes	—
46	C₄×C₂₈₁	#125	1	2	yes	—
47	Dic₂₈₁	—	8	2	no	—
48	C₂×C₂₈₁	#382	1	1	yes	characteristic
49	C₂×C₂₈₁	#428	1	2	yes	—
50	C₂×C₂₈₁	#489	1	2	yes	—
51	C₂×C₂₈₁	#490	1	1	yes	characteristic
52	C₂×C₂₈₁	#491	1	1	yes	characteristic
53	C₂₈₁	#1836	1	1	yes	characteristic, complemented, Sylow
54	#1836	—	281	1	no	maximal, Sylow
55	C₂×#97	—	281	1	no	—
56	#384	D₂₈₁	1	1	yes	characteristic
57	#382	—	281	1	no	—
58	#340	—	281	4	no	—
59	C₂²×C₈	—	281	2	no	—
60	C₂×C₄⋊C₄	—	2	2	no	—
61	C₂×C₄⋊C₄	—	281	2	no	—
62	C₂×C₄⋊C₄	C₂×D₂₈₁	1	2	yes	—
63	C₂×C₄²	C₂×D₂₈₁	1	1	yes	characteristic
64	#97	—	281	4	no	—
65	#95	—	562	2	no	—
66	C₂²×C₄	—	2	2	no	—
67	C₂²×C₄	—	562	2	no	—
68	C₂²×C₄	C₂²⋊D₂₈₁	1	2	yes	—
69	C₂²×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
70	C₂×C₈	—	281	4	no	—
71	C₂×C₈	—	562	2	no	—
72	C₂×C₈	—	562	2	no	—
73	C₄⋊C₄	—	2	4	no	—
74	C₄⋊C₄	—	4	4	no	—
75	C₄⋊C₄	—	562	4	no	—
76	C₄²	C₄×D₂₈₁	1	2	yes	—
77	C₄²	Dic₅₆₂	1	2	yes	—
78	C₂³	C₂×C₂²⋊D₂₈₁	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	4	4	no	—
83	C₂×C₄	—	1124	2	no	—
84	C₂×C₄	—	1124	2	no	—
85	C₂×C₄	—	1124	2	no	—
86	C₂×C₄	#17985117	1	4	yes	—
87	C₂×C₄	C₂×C₄×D₂₈₁	1	1	yes	characteristic
88	C₂×C₄	C₂×Dic₅₆₂	1	1	yes	characteristic
89	C₂×C₄	#17985137	1	2	yes	—
90	C₂×C₄	#17985139	1	2	yes	—
91	C₈	—	562	4	no	—
92	C₂²	C₂×#17985117	1	1	yes	characteristic
93	C₂²	#22582866	1	1	yes	characteristic
94	C₂²	#22582868	1	1	yes	characteristic
95	C₂²	#22582905	1	2	yes	—
96	C₂²	#22582910	1	2	yes	—
97	C₄	—	2	4	no	—
98	C₄	—	8	2	no	—
99	C₄	—	2248	2	no	—
100	C₄	#22582837	1	2	yes	—
101	C₄	#22582870	1	2	yes	—
102	C₂	#31823328	1	1	yes	characteristic
103	C₂	#31823503	1	2	yes	—
104	C₂	#31823825	1	2	yes	—
105	C₂	#31823827	1	1	yes	characteristic
106	C₂	#31823831	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#22582790

C₂

yes

maximal, characteristic

#31823329

C₂

yes

maximal, characteristic

#31823225

C₂

yes

maximal

#384×C₂₈₁

C₂

yes

maximal, characteristic

C₂²×#14555886

C₂²

yes

—

C₂×C₄⋊Dic₂₈₁

C₂²

yes

—

#22582790

C₄

yes

complemented

#22582786

—

C₂×C₄⋊C₄×C₂₈₁

—

C₂×C₄⋊C₄×C₂₈₁

C₂²

yes

—

C₂×C₄²×C₂₈₁

C₂²

yes

characteristic

C₂²×Dic₂₈₁

—

C₂×#14555886

—

C₂×#14555886

—

C₂×#14555886

C₂×C₄

yes

—

C₄⋊Dic₂₈₁

—

C₂²×C₄×C₂₈₁

—

C₂²×C₄×C₂₈₁

D₄

yes

—

C₂²×C₄×C₂₈₁

C₂³

yes

characteristic

C₄⋊C₄×C₂₈₁

—

C₄⋊C₄×C₂₈₁

—

C₄²×C₂₈₁

C₂×C₄

yes

—

C₄²×C₂₈₁

Q₈

yes

—

C₂×Dic₂₈₁

—

C₂×Dic₂₈₁

—

C₂×Dic₂₈₁

—

#14555886

—

C₂³×C₂₈₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

C₄⋊C₄

yes

—

C₂×C₄×C₂₈₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₈₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₈₁

#41

yes

—

C₂×C₄×C₂₈₁

#41

yes

—

C₂²×C₂₈₁

C₂×C₄⋊C₄

yes

C₂²×C₂₈₁

yes

C₂²×C₂₈₁

yes

C₂²×C₂₈₁

yes

—

C₂²×C₂₈₁

#137

yes

—

C₄×C₂₈₁

—

C₄×C₂₈₁

—

C₄×C₂₈₁

#117

yes

—

C₄×C₂₈₁

#125

yes

—

Dic₂₈₁

—

C₂×C₂₈₁

#382

yes

characteristic

C₂×C₂₈₁

#428

yes

—

C₂×C₂₈₁

#489

yes

—

C₂×C₂₈₁

yes

C₂×C₂₈₁

yes

C₂₈₁

yes

characteristic, complemented, Sylow

#1836

—

281

maximal, Sylow

C₂×#97

—

281

—

#384

D₂₈₁

yes

characteristic

#382

—

281

—

#340

—

281

—

C₂²×C₈

—

281

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

281

—

C₂×C₄⋊C₄

C₂×D₂₈₁

yes

—

C₂×C₄²

C₂×D₂₈₁

yes

characteristic

#97

—

281

—

#95

—

562

—

C₂²×C₄

—

C₂²×C₄

—

562

—

C₂²×C₄

C₂²⋊D₂₈₁

yes

—

C₂²×C₄

C₂²×D₂₈₁

yes

characteristic

C₂×C₈

—

281

—

C₂×C₈

—

562

—

C₂×C₈

—

562

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

562

—

C₄²

C₄×D₂₈₁

yes

—

C₄²

Dic₅₆₂

yes

—

C₂³

C₂×C₂²⋊D₂₈₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

1124

—

C₂×C₄

—

1124

—

C₂×C₄

—

1124

—

C₂×C₄

#17985117

yes

—

C₂×C₄

C₂×C₄×D₂₈₁

yes

characteristic

C₂×C₄

C₂×Dic₅₆₂

yes

characteristic

C₂×C₄

#17985137

yes

—

C₂×C₄

#17985139

yes

—

C₈

—

562

—

C₂²

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₂²

#22582910

yes

—

C₄

—

C₄

—

C₄

—

2248

—

100

C₄

#22582837

yes

—

101

C₄

#22582870

yes

—

102

C₂

#31823328

yes

characteristic

103

C₂

#31823503

yes

—

104

C₂

#31823825

yes

—

105

C₂

#31823827

yes

characteristic

106

C₂

#31823831

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₈₁
commutator	C₂×C₄×C₂₈₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₈₁
Fitting	#384×C₂₈₁	C₂
socle, prime radical	C₂³×C₂₈₁	C₂×D₄
cosocle	C₂²×C₄×C₂₈₁	C₂³
hypercenter	#384	D₂₈₁
hypocenter	C₂₈₁	#1836
LCS	G ▷ C₂×C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₈₁

commutator

C₂×C₄×C₂₈₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₈₁

Fitting

#384×C₂₈₁

C₂

socle, prime radical

C₂³×C₂₈₁

C₂×D₄

cosocle

C₂²×C₄×C₂₈₁

C₂³

D₂₈₁

C₂₈₁

G ▷ C₂×C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
7. #22582790	C₄	semidirect
53. C₂₈₁	#1836	semidirect

H ≅ G/N

type

7. #22582790

C₄

semidirect

53. C₂₈₁

#1836

semidirect

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

subgroup	index
C₂×#22582790	2
#31823329	2
#31823225	2
#384×C₂₈₁	2
#1836	281

subgroup

index

#384×C₂₈₁

281

Subgroups — #49095438

Conjugacy classes of subgroups

Complements

Maximal subgroups