Group #46835992 — subgroups

Subgroups — #46835992

Order 34688.

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

normal subgroups only

This group has 220 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	#31774295	C₂	1	1	yes	maximal, characteristic, complemented
2	#31774274	C₂	1	1	yes	maximal, characteristic
3	#31774270	C₂	1	2	yes	maximal, complemented
4	#31774244	C₂	1	2	yes	maximal, complemented
5	#322×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864643	—	2	4	no	—
7	C₂×D₂₁₆₈	—	2	2	no	—
8	#22576160	C₂²	1	2	yes	—
9	#22576157	C₂²	1	1	yes	characteristic
10	#22576157	C₂²	1	1	yes	characteristic
11	#22576092	—	2	2	no	—
12	#22576082	—	2	4	no	—
13	C₄×C₈×C₂₇₁	C₂²	1	2	yes	—
14	C₄×C₈×C₂₇₁	C₂²	1	1	yes	characteristic
15	C₂×Dic₅₄₂	—	2	2	no	—
16	C₂×D₁₀₈₄	—	2	1	no	—
17	C₂×D₁₀₈₄	—	2	1	no	—
18	C₂×D₁₀₈₄	—	2	2	no	—
19	C₂×D₁₀₈₄	—	2	2	no	—
20	#16864643	—	4	8	no	—
21	D₂₁₆₈	—	4	4	no	—
22	C₄⋊Dic₂₇₁	—	2	2	no	—
23	C₄⋊Dic₂₇₁	—	2	2	no	—
24	C₂×C₈×C₂₇₁	D₄	1	4	yes	—
25	C₂×C₈×C₂₇₁	D₄	1	2	yes	—
26	C₄²×C₂₇₁	C₂³	1	1	yes	characteristic
27	C₂²×D₂₇₁	—	4	1	no	—
28	C₂²×D₂₇₁	—	4	1	no	—
29	Dic₅₄₂	—	4	4	no	—
30	D₁₀₈₄	—	4	2	no	—
31	D₁₀₈₄	—	4	2	no	—
32	D₁₀₈₄	—	4	4	no	—
33	D₁₀₈₄	—	4	4	no	—
34	C₂×Dic₂₇₁	—	4	2	no	—
35	C₂×C₄×C₂₇₁	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₂₇₁	C₂×D₄	1	2	yes	—
37	C₈×C₂₇₁	—	2	4	no	—
38	C₈×C₂₇₁	SD₁₆	1	4	yes	complemented
39	C₂²×C₂₇₁	#127	1	1	yes	characteristic
40	C₂×D₂₇₁	—	8	1	no	—
41	C₂×D₂₇₁	—	8	1	no	—
42	C₂×D₂₇₁	—	8	2	no	—
43	C₂×D₂₇₁	—	8	2	no	—
44	C₄×C₂₇₁	C₂×SD₁₆	1	2	yes	—
45	C₄×C₂₇₁	AGL(1,ℤ/8)	1	4	yes	—
46	Dic₂₇₁	—	8	2	no	—
47	C₂×C₂₇₁	#492	1	1	yes	characteristic
48	C₂×C₂₇₁	#496	1	2	yes	—
49	D₂₇₁	—	16	1	no	—
50	D₂₇₁	—	16	1	no	—
51	C₂₇₁	#1715	1	1	yes	characteristic, complemented, Sylow
52	#1715	—	271	1	no	maximal, Sylow
53	#498	—	271	1	no	—
54	#493	—	271	1	no	—
55	#492	—	271	2	no	—
56	#486	—	271	2	no	—
57	#322	D₂₇₁	1	1	yes	characteristic, complemented
58	C₂×SD₁₆	—	542	4	no	—
59	C₂×D₈	—	542	2	no	—
60	C₄⋊Q₈	—	271	2	no	—
61	#127	—	271	1	no	—
62	#127	—	271	1	no	—
63	#106	—	542	2	no	—
64	#102	—	542	4	no	—
65	C₄×C₈	C₂×D₂₇₁	1	2	yes	—
66	C₄×C₈	C₂×D₂₇₁	1	1	yes	characteristic
67	C₂×Q₈	—	542	2	no	—
68	C₂×D₄	—	542	2	no	—
69	C₂×D₄	—	542	1	no	—
70	C₂×D₄	—	542	1	no	—
71	C₂×D₄	—	542	2	no	—
72	SD₁₆	—	1084	8	no	—
73	D₈	—	1084	4	no	—
74	C₂×C₈	D₁₀₈₄	1	4	yes	—
75	C₂×C₈	D₁₀₈₄	1	2	yes	—
76	C₄⋊C₄	—	542	2	no	—
77	C₄⋊C₄	—	542	2	no	—
78	C₄²	C₂²×D₂₇₁	1	1	yes	characteristic
79	C₂³	—	1084	1	no	—
80	C₂³	—	1084	1	no	—
81	Q₈	—	1084	4	no	—
82	D₄	—	1084	2	no	—
83	D₄	—	1084	2	no	—
84	D₄	—	1084	4	no	—
85	D₄	—	1084	4	no	—
86	C₂×C₄	—	1084	2	no	—
87	C₂×C₄	C₂×D₁₀₈₄	1	1	yes	characteristic
88	C₂×C₄	C₂×D₁₀₈₄	1	2	yes	—
89	C₈	—	2	4	no	—
90	C₈	#16864643	1	4	yes	complemented
91	C₂²	—	2168	1	no	—
92	C₂²	—	2168	1	no	—
93	C₂²	—	2168	2	no	—
94	C₂²	—	2168	2	no	—
95	C₂²	#22576157	1	1	yes	characteristic
96	C₄	—	2168	2	no	—
97	C₄	C₂×#16864643	1	2	yes	—
98	C₄	#22576188	1	4	yes	—
99	C₂	—	4336	1	no	—
100	C₂	—	4336	1	no	—
101	C₂	#31774270	1	1	yes	characteristic
102	C₂	#31774286	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#31774295

C₂

yes

maximal, characteristic, complemented

#31774274

C₂

yes

maximal, characteristic

#31774270

C₂

yes

maximal, complemented

#31774244

C₂

yes

maximal, complemented

#322×C₂₇₁

C₂

yes

maximal, characteristic, complemented

C₂×#16864643

—

C₂×D₂₁₆₈

—

#22576160

C₂²

yes

—

#22576157

C₂²

yes

characteristic

#22576157

C₂²

yes

characteristic

#22576092

—

#22576082

—

C₄×C₈×C₂₇₁

C₂²

yes

—

C₄×C₈×C₂₇₁

C₂²

yes

characteristic

C₂×Dic₅₄₂

—

C₂×D₁₀₈₄

—

C₂×D₁₀₈₄

—

C₂×D₁₀₈₄

—

C₂×D₁₀₈₄

—

#16864643

—

D₂₁₆₈

—

C₄⋊Dic₂₇₁

—

C₄⋊Dic₂₇₁

—

C₂×C₈×C₂₇₁

D₄

yes

—

C₂×C₈×C₂₇₁

D₄

yes

—

C₄²×C₂₇₁

C₂³

yes

characteristic

C₂²×D₂₇₁

—

C₂²×D₂₇₁

—

Dic₅₄₂

—

D₁₀₈₄

—

D₁₀₈₄

—

D₁₀₈₄

—

D₁₀₈₄

—

C₂×Dic₂₇₁

—

C₂×C₄×C₂₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₇₁

C₂×D₄

yes

—

C₈×C₂₇₁

—

C₈×C₂₇₁

SD₁₆

yes

complemented

C₂²×C₂₇₁

#127

yes

characteristic

C₂×D₂₇₁

—

C₂×D₂₇₁

—

C₂×D₂₇₁

—

C₂×D₂₇₁

—

C₄×C₂₇₁

C₂×SD₁₆

yes

—

C₄×C₂₇₁

AGL(1,ℤ/8)

yes

—

Dic₂₇₁

—

C₂×C₂₇₁

#492

yes

characteristic

C₂×C₂₇₁

#496

yes

—

D₂₇₁

—

D₂₇₁

—

C₂₇₁

#1715

yes

characteristic, complemented, Sylow

#1715

—

271

maximal, Sylow

#498

—

271

—

#493

—

271

—

#492

—

271

—

#486

—

271

—

#322

D₂₇₁

yes

characteristic, complemented

C₂×SD₁₆

—

542

—

C₂×D₈

—

542

—

C₄⋊Q₈

—

271

—

#127

—

271

—

#127

—

271

—

#106

—

542

—

#102

—

542

—

C₄×C₈

C₂×D₂₇₁

yes

—

C₄×C₈

C₂×D₂₇₁

yes

characteristic

C₂×Q₈

—

542

—

C₂×D₄

—

542

—

C₂×D₄

—

542

—

C₂×D₄

—

542

—

C₂×D₄

—

542

—

SD₁₆

—

1084

—

D₈

—

1084

—

C₂×C₈

D₁₀₈₄

yes

—

C₂×C₈

D₁₀₈₄

yes

—

C₄⋊C₄

—

542

—

C₄⋊C₄

—

542

—

C₄²

C₂²×D₂₇₁

yes

characteristic

C₂³

—

1084

—

C₂³

—

1084

—

Q₈

—

1084

—

D₄

—

1084

—

D₄

—

1084

—

D₄

—

1084

—

D₄

—

1084

—

C₂×C₄

—

1084

—

C₂×C₄

C₂×D₁₀₈₄

yes

characteristic

C₂×C₄

C₂×D₁₀₈₄

yes

—

C₈

—

C₈

#16864643

yes

complemented

C₂²

—

2168

—

C₂²

—

2168

—

C₂²

—

2168

—

C₂²

—

2168

—

C₂²

#22576157

yes

characteristic

C₄

—

2168

—

C₄

C₂×#16864643

yes

—

C₄

#22576188

yes

—

C₂

—

4336

—

100

C₂

—

4336

—

101

C₂

#31774270

yes

characteristic

102

C₂

#31774286

yes

—

	subgroup	G/H
center	C₂²	#22576157
commutator, cosocle	C₄²×C₂₇₁	C₂³
Frattini	C₄²	C₂²×D₂₇₁
Fitting	#322×C₂₇₁	C₂
socle	C₂²×C₂₇₁	#127
prime radical	#31774274	C₂
hypercenter	#322	D₂₇₁
hypocenter	C₂₇₁	#1715
LCS	G ▷ C₄²×C₂₇₁ ▷ C₂²×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

subgroup

G/H

center

C₂²

#22576157

commutator, cosocle

C₄²×C₂₇₁

C₂³

Frattini

C₄²

C₂²×D₂₇₁

Fitting

#322×C₂₇₁

C₂

C₂²×C₂₇₁

C₂

D₂₇₁

C₂₇₁

G ▷ C₄²×C₂₇₁ ▷ C₂²×C₂₇₁ ▷ C₂₇₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #322

N	H ≅ G/N	type
1. #31774295	C₂	semidirect
3. #31774270	C₂	semidirect
4. #31774244	C₂	semidirect
5. #322×C₂₇₁	C₂	semidirect
38. C₈×C₂₇₁	SD₁₆	semidirect
51. C₂₇₁	#1715	semidirect
57. #322	D₂₇₁	semidirect
90. C₈	#16864643	semidirect

H ≅ G/N

type

1. #31774295

C₂

semidirect

3. #31774270

C₂

semidirect

4. #31774244

C₂

semidirect

5. #322×C₂₇₁

C₂

semidirect

38. C₈×C₂₇₁

SD₁₆

semidirect

51. C₂₇₁

#1715

semidirect

57. #322

D₂₇₁

semidirect

90. C₈

#16864643

semidirect

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

subgroup	index
#31774295	2
#31774274	2
#31774270	2
#31774244	2
#322×C₂₇₁	2
#1715	271

subgroup

index

#322×C₂₇₁

271

Subgroups — #46835992

Conjugacy classes of subgroups

Complements

Maximal subgroups