Group #46810511 — subgroups

Subgroups — #46810511

Order 34432.

220 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 65 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	#31771003	C₂	1	1	yes	maximal, characteristic, complemented
2	#31770977	C₂	1	2	yes	maximal, complemented
3	#31770951	C₂	1	2	yes	maximal, complemented
4	#31770326	C₂	1	1	yes	maximal, characteristic, complemented
5	#493×C₂₆₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#16864390	—	2	4	no	—
7	#22575453	C₂²	1	2	yes	—
8	#22575385	—	2	2	no	—
9	#22575374	—	2	4	no	—
10	C₄×#14524130	C₂²	1	2	yes	—
11	C₂×D₈×C₂₆₉	—	2	2	no	—
12	#127×C₂₆₉	C₂²	1	1	yes	characteristic
13	#127×C₂₆₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₅₃₈	—	2	2	no	—
16	#16864390	—	4	8	no	—
17	C₂×#14524130	D₄	1	4	yes	—
18	C₄⋊Dic₂₆₉	—	2	2	no	—
19	C₄⋊Dic₂₆₉	—	2	2	no	—
20	C₂×D₄×C₂₆₉	—	2	2	no	—
21	C₂×D₄×C₂₆₉	—	2	2	no	—
22	C₂×D₄×C₂₆₉	—	2	1	no	—
23	C₂×D₄×C₂₆₉	—	2	1	no	—
24	D₈×C₂₆₉	—	4	4	no	—
25	C₂×C₈×C₂₆₉	D₄	1	2	yes	—
26	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
27	Dic₅₃₈	—	4	4	no	—
28	C₂×Dic₂₆₉	—	4	2	no	—
29	#14524130	—	2	4	no	—
30	C₂³×C₂₆₉	—	4	1	no	—
31	C₂³×C₂₆₉	—	4	1	no	—
32	D₄×C₂₆₉	—	4	2	no	—
33	D₄×C₂₆₉	—	4	2	no	—
34	D₄×C₂₆₉	—	4	4	no	—
35	D₄×C₂₆₉	—	4	4	no	—
36	C₂×C₄×C₂₆₉	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₂₆₉	SD₁₆	1	4	yes	complemented
39	C₂²×C₂₆₉	—	8	1	no	—
40	C₂²×C₂₆₉	—	8	1	no	—
41	C₂²×C₂₆₉	—	8	2	no	—
42	C₂²×C₂₆₉	—	8	2	no	—
43	C₂²×C₂₆₉	#127	1	1	yes	characteristic
44	C₄×C₂₆₉	C₂×SD₁₆	1	2	yes	—
45	C₄×C₂₆₉	AGL(1,ℤ/8)	1	4	yes	—
46	Dic₂₆₉	—	8	2	no	—
47	C₂×C₂₆₉	—	16	1	no	—
48	C₂×C₂₆₉	—	16	1	no	—
49	C₂×C₂₆₉	#492	1	1	yes	characteristic
50	C₂×C₂₆₉	#496	1	2	yes	—
51	C₂₆₉	#1715	1	1	yes	characteristic, complemented, Sylow
52	#1715	—	269	1	no	maximal, Sylow
53	#498	—	269	1	no	—
54	#493	D₂₆₉	1	1	yes	characteristic
55	#492	—	269	2	no	—
56	#486	—	269	2	no	—
57	#322	—	269	1	no	—
58	C₂×SD₁₆	—	538	4	no	—
59	C₂×D₈	—	2	2	no	—
60	C₄⋊Q₈	—	269	2	no	—
61	#127	C₂×D₂₆₉	1	1	yes	characteristic
62	#127	C₂×D₂₆₉	1	1	yes	characteristic
63	#106	—	538	2	no	—
64	#102	—	538	4	no	—
65	C₄×C₈	—	269	2	no	—
66	C₄×C₈	C₂×D₂₆₉	1	1	yes	characteristic
67	C₂×Q₈	—	538	2	no	—
68	C₂×D₄	—	2	2	no	—
69	C₂×D₄	—	2	2	no	—
70	C₂×D₄	—	2	1	no	—
71	C₂×D₄	—	2	1	no	—
72	SD₁₆	—	1076	8	no	—
73	D₈	—	4	4	no	—
74	C₂×C₈	—	269	4	no	—
75	C₂×C₈	C₂²⋊D₂₆₉	1	2	yes	—
76	C₄⋊C₄	—	538	2	no	—
77	C₄⋊C₄	—	538	2	no	—
78	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
79	C₂³	—	4	1	no	—
80	C₂³	—	4	1	no	—
81	Q₈	—	1076	4	no	—
82	D₄	—	4	2	no	—
83	D₄	—	4	2	no	—
84	D₄	—	4	4	no	—
85	D₄	—	4	4	no	—
86	C₂×C₄	—	1076	2	no	—
87	C₂×C₄	D₄×D₂₆₉	1	2	yes	—
88	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
89	C₈	—	538	4	no	—
90	C₈	#16864390	1	4	yes	complemented
91	C₂²	—	8	1	no	—
92	C₂²	—	8	1	no	—
93	C₂²	—	8	2	no	—
94	C₂²	—	8	2	no	—
95	C₂²	#22575449	1	1	yes	characteristic
96	C₄	—	2152	2	no	—
97	C₄	C₂×#16864390	1	2	yes	—
98	C₄	#22575477	1	4	yes	—
99	C₂	—	16	1	no	—
100	C₂	—	16	1	no	—
101	C₂	#31770977	1	1	yes	characteristic
102	C₂	#31770993	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#31771003

C₂

yes

maximal, characteristic, complemented

#31770977

C₂

yes

maximal, complemented

#31770951

C₂

yes

maximal, complemented

#31770326

C₂

yes

maximal, characteristic, complemented

#493×C₂₆₉

C₂

yes

maximal, characteristic

C₂×#16864390

—

#22575453

C₂²

yes

—

#22575385

—

#22575374

—

C₄×#14524130

C₂²

yes

—

C₂×D₈×C₂₆₉

—

#127×C₂₆₉

C₂²

yes

characteristic

#127×C₂₆₉

C₂²

yes

characteristic

C₄×C₈×C₂₆₉

C₂²

yes

characteristic

C₂×Dic₅₃₈

—

#16864390

—

C₂×#14524130

D₄

yes

—

C₄⋊Dic₂₆₉

—

C₄⋊Dic₂₆₉

—

C₂×D₄×C₂₆₉

—

C₂×D₄×C₂₆₉

—

C₂×D₄×C₂₆₉

—

C₂×D₄×C₂₆₉

—

D₈×C₂₆₉

—

C₂×C₈×C₂₆₉

D₄

yes

—

C₄²×C₂₆₉

C₂³

yes

characteristic

Dic₅₃₈

—

C₂×Dic₂₆₉

—

#14524130

—

C₂³×C₂₆₉

—

C₂³×C₂₆₉

—

D₄×C₂₆₉

—

D₄×C₂₆₉

—

D₄×C₂₆₉

—

D₄×C₂₆₉

—

C₂×C₄×C₂₆₉

C₂×D₄

yes

—

C₂×C₄×C₂₆₉

C₂×D₄

yes

characteristic

C₈×C₂₆₉

SD₁₆

yes

complemented

C₂²×C₂₆₉

—

C₂²×C₂₆₉

—

C₂²×C₂₆₉

—

C₂²×C₂₆₉

—

C₂²×C₂₆₉

#127

yes

characteristic

C₄×C₂₆₉

C₂×SD₁₆

yes

—

C₄×C₂₆₉

AGL(1,ℤ/8)

yes

—

Dic₂₆₉

—

C₂×C₂₆₉

—

C₂×C₂₆₉

—

C₂×C₂₆₉

#492

yes

characteristic

C₂×C₂₆₉

#496

yes

—

C₂₆₉

#1715

yes

characteristic, complemented, Sylow

#1715

—

269

maximal, Sylow

#498

—

269

—

#493

D₂₆₉

yes

characteristic

#492

—

269

—

#486

—

269

—

#322

—

269

—

C₂×SD₁₆

—

538

—

C₂×D₈

—

C₄⋊Q₈

—

269

—

#127

C₂×D₂₆₉

yes

characteristic

#127

C₂×D₂₆₉

yes

characteristic

#106

—

538

—

#102

—

538

—

C₄×C₈

—

269

—

C₄×C₈

C₂×D₂₆₉

yes

characteristic

C₂×Q₈

—

538

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

1076

—

D₈

—

C₂×C₈

—

269

—

C₂×C₈

C₂²⋊D₂₆₉

yes

—

C₄⋊C₄

—

538

—

C₄⋊C₄

—

538

—

C₄²

C₂²×D₂₆₉

yes

characteristic

C₂³

—

C₂³

—

Q₈

—

1076

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

1076

—

C₂×C₄

D₄×D₂₆₉

yes

—

C₂×C₄

C₂×C₂²⋊D₂₆₉

yes

characteristic

C₈

—

538

—

C₈

#16864390

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#22575449

yes

characteristic

C₄

—

2152

—

C₄

C₂×#16864390

yes

—

C₄

#22575477

yes

—

C₂

—

100

C₂

—

101

C₂

#31770977

yes

characteristic

102

C₂

#31770993

yes

—

	subgroup	G/H
center	C₂²	#22575449
commutator, cosocle	C₄²×C₂₆₉	C₂³
Frattini	C₄²	C₂²×D₂₆₉
Fitting, prime radical	#493×C₂₆₉	C₂
socle	C₂²×C₂₆₉	#127
hypercenter	#493	D₂₆₉
hypocenter	C₂₆₉	#1715
LCS	G ▷ C₄²×C₂₆₉ ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#22575449

commutator, cosocle

C₄²×C₂₆₉

C₂³

Frattini

C₄²

C₂²×D₂₆₉

Fitting, prime radical

#493×C₂₆₉

C₂

C₂²×C₂₆₉

D₂₆₉

C₂₆₉

G ▷ C₄²×C₂₆₉ ▷ C₂²×C₂₆₉ ▷ C₂₆₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. #31771003	C₂	semidirect
2. #31770977	C₂	semidirect
3. #31770951	C₂	semidirect
4. #31770326	C₂	semidirect
38. C₈×C₂₆₉	SD₁₆	semidirect
51. C₂₆₉	#1715	semidirect
90. C₈	#16864390	semidirect

H ≅ G/N

type

1. #31771003

C₂

semidirect

2. #31770977

C₂

semidirect

3. #31770951

C₂

semidirect

4. #31770326

C₂

semidirect

38. C₈×C₂₆₉

SD₁₆

semidirect

51. C₂₆₉

#1715

semidirect

90. C₈

#16864390

semidirect

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

subgroup	index
#31771003	2
#31770977	2
#31770951	2
#31770326	2
#493×C₂₆₉	2
#1715	269

subgroup

index

#493×C₂₆₉

269

Subgroups — #46810511

Conjugacy classes of subgroups

Complements

Maximal subgroups