Group #46837874 — subgroups

Subgroups — #46837874

Order 34688.

176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 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	#31773940	C₂	1	2	yes	maximal
2	C₂×#22576092	C₂	1	1	yes	maximal, characteristic
3	#31773665	C₂	1	2	yes	maximal
4	#31773662	C₂	1	1	yes	maximal, characteristic
5	#424×C₂₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#16864638	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₂₇₁	C₂²	1	2	yes	—
8	#22576093	—	2	2	no	—
9	#22576092	—	2	2	no	—
10	#22576091	—	2	2	no	—
11	C₂×M₁₆×C₂₇₁	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₂₇₁	C₂²	1	1	yes	characteristic
13	#117×C₂₇₁	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₂₇₁	—	2	2	no	—
15	C₂²×Dic₂₇₁	—	2	2	no	—
16	#16864638	—	2	2	no	—
17	#16864638	Q₈	1	4	yes	—
18	C₂×C₂₇₁⋊C₈	—	2	2	no	—
19	C₄⋊Dic₂₇₁	—	2	2	no	—
20	C₄⋊Dic₂₇₁	—	2	2	no	—
21	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
22	M₁₆×C₂₇₁	—	2	2	no	—
23	C₂×C₈×C₂₇₁	—	2	2	no	—
24	C₂×C₈×C₂₇₁	—	2	1	no	—
25	C₂×C₈×C₂₇₁	D₄	1	2	yes	—
26	C₄⋊C₄×C₂₇₁	D₄	1	2	yes	—
27	C₂²⋊C₄×C₂₇₁	—	2	1	no	—
28	C₄²×C₂₇₁	—	2	1	no	—
29	C₂×Dic₂₇₁	—	4	2	no	—
30	C₂×Dic₂₇₁	—	8	2	no	—
31	C₂₇₁⋊C₈	—	2	4	no	—
32	C₂³×C₂₇₁	#41	1	1	yes	characteristic
33	C₂×C₄×C₂₇₁	—	2	2	no	—
34	C₂×C₄×C₂₇₁	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₂₇₁	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₂₇₁	C₂×Q₈	1	2	yes	—
37	C₂×C₄×C₂₇₁	#41	1	2	yes	—
38	C₈×C₂₇₁	—	2	2	no	—
39	C₈×C₂₇₁	—	4	1	no	—
40	C₂²×C₂₇₁	—	2	2	no	—
41	C₂²×C₂₇₁	#121	1	1	yes	characteristic
42	C₂²×C₂₇₁	#125	1	2	yes	—
43	C₄×C₂₇₁	—	4	2	no	—
44	C₄×C₂₇₁	C₂²⋊Q₈	1	2	yes	—
45	C₄×C₂₇₁	#123	1	1	yes	characteristic
46	C₄×C₂₇₁	C₄⋊Q₈	1	1	yes	characteristic
47	Dic₂₇₁	—	8	2	no	—
48	C₂×C₂₇₁	—	2	2	no	—
49	C₂×C₂₇₁	#398	1	1	yes	characteristic
50	C₂×C₂₇₁	#471	1	2	yes	—
51	C₂₇₁	#2090	1	1	yes	characteristic, complemented, Sylow
52	#2090	—	271	1	no	maximal, Sylow
53	#428	—	271	2	no	—
54	C₂×#106	—	271	1	no	—
55	#424	D₂₇₁	1	1	yes	characteristic
56	#343	—	271	2	no	—
57	#341	—	271	1	no	—
58	C₂×M₁₆	—	271	2	no	—
59	C₂×M₁₆	C₂×D₂₇₁	1	1	yes	characteristic
60	C₂²×C₈	C₂×D₂₇₁	1	1	yes	characteristic
61	#117	C₂×D₂₇₁	1	1	yes	characteristic
62	C₂×C₄⋊C₄	—	271	2	no	—
63	#107	—	542	2	no	—
64	#106	—	542	2	no	—
65	#106	—	542	2	no	—
66	C₄⋊C₈	—	2	2	no	—
67	C₂²×C₄	—	542	2	no	—
68	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
69	M₁₆	—	2	2	no	—
70	M₁₆	—	271	4	no	—
71	M₁₆	—	542	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	542	2	no	—
75	C₂×C₈	C₂²⋊D₂₇₁	1	2	yes	—
76	C₄⋊C₄	—	542	2	no	—
77	C₄⋊C₄	—	542	2	no	—
78	C₄⋊C₄	D₁₀₈₄	1	2	yes	—
79	C₂²⋊C₄	—	2	1	no	—
80	C₄²	—	2	1	no	—
81	C₂³	#16864654	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	1084	2	no	—
84	C₂×C₄	—	2168	2	no	—
85	C₂×C₄	C₂×C₂²⋊D₂₇₁	1	1	yes	characteristic
86	C₂×C₄	C₂×D₁₀₈₄	1	1	yes	characteristic
87	C₂×C₄	Q₈×D₂₇₁	1	2	yes	—
88	C₂×C₄	#16864653	1	2	yes	—
89	C₈	—	2	2	no	—
90	C₈	—	4	1	no	—
91	C₈	—	542	4	no	—
92	C₂²	—	2	2	no	—
93	C₂²	#22576134	1	1	yes	characteristic
94	C₂²	#22576150	1	2	yes	—
95	C₄	—	4	2	no	—
96	C₄	—	2168	2	no	—
97	C₄	#22576140	1	2	yes	—
98	C₄	#22576141	1	1	yes	characteristic
99	C₄	#22576158	1	1	yes	characteristic
100	C₂	—	2	2	no	—
101	C₂	#31773827	1	1	yes	characteristic
102	C₂	#31774160	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#31773940

C₂

yes

maximal

C₂×#22576092

C₂

yes

maximal, characteristic

#31773665

C₂

yes

maximal

#31773662

C₂

yes

maximal, characteristic

#424×C₂₇₁

C₂

yes

maximal, characteristic

C₂×#16864638

C₂²

yes

—

C₂×C₄⋊Dic₂₇₁

C₂²

yes

—

#22576093

—

#22576092

—

#22576091

—

C₂×M₁₆×C₂₇₁

C₂²

yes

characteristic

C₂²×C₈×C₂₇₁

C₂²

yes

characteristic

#117×C₂₇₁

C₂²

yes

characteristic

C₄⋊C₈×C₂₇₁

—

C₂²×Dic₂₇₁

—

#16864638

—

#16864638

Q₈

yes

—

C₂×C₂₇₁⋊C₈

—

C₄⋊Dic₂₇₁

—

C₄⋊Dic₂₇₁

—

C₂²×C₄×C₂₇₁

C₂³

yes

characteristic

M₁₆×C₂₇₁

—

C₂×C₈×C₂₇₁

—

C₂×C₈×C₂₇₁

—

C₂×C₈×C₂₇₁

D₄

yes

—

C₄⋊C₄×C₂₇₁

D₄

yes

—

C₂²⋊C₄×C₂₇₁

—

C₄²×C₂₇₁

—

C₂×Dic₂₇₁

—

C₂×Dic₂₇₁

—

C₂₇₁⋊C₈

—

C₂³×C₂₇₁

#41

yes

characteristic

C₂×C₄×C₂₇₁

—

C₂×C₄×C₂₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₇₁

C₂×Q₈

yes

—

C₂×C₄×C₂₇₁

#41

yes

—

C₈×C₂₇₁

—

C₈×C₂₇₁

—

C₂²×C₂₇₁

—

C₂²×C₂₇₁

#121

yes

characteristic

C₂²×C₂₇₁

#125

yes

—

C₄×C₂₇₁

—

C₄×C₂₇₁

C₂²⋊Q₈

yes

—

C₄×C₂₇₁

#123

yes

characteristic

C₄×C₂₇₁

C₄⋊Q₈

yes

characteristic

Dic₂₇₁

—

C₂×C₂₇₁

—

C₂×C₂₇₁

#398

yes

characteristic

C₂×C₂₇₁

#471

yes

—

C₂₇₁

#2090

yes

characteristic, complemented, Sylow

#2090

—

271

maximal, Sylow

#428

—

271

—

C₂×#106

—

271

—

#424

D₂₇₁

yes

characteristic

#343

—

271

—

#341

—

271

—

C₂×M₁₆

—

271

—

C₂×M₁₆

C₂×D₂₇₁

yes

characteristic

C₂²×C₈

C₂×D₂₇₁

yes

characteristic

#117

C₂×D₂₇₁

yes

characteristic

C₂×C₄⋊C₄

—

271

—

#107

—

542

—

#106

—

542

—

#106

—

542

—

C₄⋊C₈

—

C₂²×C₄

—

542

—

C₂²×C₄

C₂²×D₂₇₁

yes

characteristic

M₁₆

—

M₁₆

—

271

—

M₁₆

—

542

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

542

—

C₂×C₈

C₂²⋊D₂₇₁

yes

—

C₄⋊C₄

—

542

—

C₄⋊C₄

—

542

—

C₄⋊C₄

D₁₀₈₄

yes

—

C₂²⋊C₄

—

C₄²

—

C₂³

#16864654

yes

characteristic

C₂×C₄

—

C₂×C₄

—

1084

—

C₂×C₄

—

2168

—

C₂×C₄

C₂×C₂²⋊D₂₇₁

yes

characteristic

C₂×C₄

C₂×D₁₀₈₄

yes

characteristic

C₂×C₄

Q₈×D₂₇₁

yes

—

C₂×C₄

#16864653

yes

—

C₈

—

C₈

—

C₈

—

542

—

C₂²

—

C₂²

#22576134

yes

characteristic

C₂²

#22576150

yes

—

C₄

—

C₄

—

2168

—

C₄

#22576140

yes

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

#31773827

yes

characteristic

102

C₂

#31774160

yes

—

	subgroup	G/H
center	C₂²	#22576134
commutator, cosocle	C₂²×C₄×C₂₇₁	C₂³
Frattini	C₂²×C₄	C₂²×D₂₇₁
Fitting	#424×C₂₇₁	C₂
socle	C₂²×C₂₇₁	#121
prime radical	C₂³×C₂₇₁	#41
hypercenter	#424	D₂₇₁
hypocenter	C₂₇₁	#2090
LCS	G ▷ C₂²×C₄×C₂₇₁ ▷ C₂×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

subgroup

G/H

center

C₂²

#22576134

commutator, cosocle

C₂²×C₄×C₂₇₁

C₂³

Frattini

C₂²×C₄

C₂²×D₂₇₁

Fitting

#424×C₂₇₁

C₂

C₂²×C₂₇₁

C₂³×C₂₇₁

D₂₇₁

C₂₇₁

G ▷ C₂²×C₄×C₂₇₁ ▷ C₂×C₂₇₁ ▷ C₂₇₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

N	H ≅ G/N	type
51. C₂₇₁	#2090	semidirect

H ≅ G/N

type

51. C₂₇₁

#2090

semidirect

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

subgroup	index
#31773940	2
C₂×#22576092	2
#31773665	2
#31773662	2
#424×C₂₇₁	2
#2090	271

subgroup

index

#424×C₂₇₁

271

Subgroups — #46837874

Conjugacy classes of subgroups

Complements

Maximal subgroups