Group #46810513 — subgroups

Subgroups — #46810513

Order 34432.

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	#31771003	C₂	1	1	yes	maximal, characteristic, complemented
2	#31770982	C₂	1	1	yes	maximal, characteristic
3	#31770978	C₂	1	2	yes	maximal, complemented
4	#31770952	C₂	1	2	yes	maximal, complemented
5	#322×C₂₆₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864391	—	2	4	no	—
7	C₂×D₂₁₅₂	—	2	2	no	—
8	#22575453	C₂²	1	2	yes	—
9	#22575450	C₂²	1	1	yes	characteristic
10	#22575450	C₂²	1	1	yes	characteristic
11	#22575385	—	2	2	no	—
12	#22575375	—	2	4	no	—
13	C₄×C₈×C₂₆₉	C₂²	1	2	yes	—
14	C₄×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₅₃₈	—	2	2	no	—
16	C₂×D₁₀₇₆	—	2	2	no	—
17	C₂×D₁₀₇₆	—	2	1	no	—
18	C₂×D₁₀₇₆	—	2	1	no	—
19	C₂×D₁₀₇₆	—	2	2	no	—
20	#16864391	—	4	8	no	—
21	D₂₁₅₂	—	4	4	no	—
22	C₄⋊Dic₂₆₉	—	2	2	no	—
23	C₄⋊Dic₂₆₉	—	2	2	no	—
24	C₂×C₈×C₂₆₉	D₄	1	4	yes	—
25	C₂×C₈×C₂₆₉	D₄	1	2	yes	—
26	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
27	C₂²×D₂₆₉	—	4	1	no	—
28	C₂²×D₂₆₉	—	4	1	no	—
29	Dic₅₃₈	—	4	4	no	—
30	D₁₀₇₆	—	4	2	no	—
31	D₁₀₇₆	—	4	2	no	—
32	D₁₀₇₆	—	4	4	no	—
33	D₁₀₇₆	—	4	4	no	—
34	C₂×Dic₂₆₉	—	4	2	no	—
35	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₂₆₉	C₂×D₄	1	2	yes	—
37	C₈×C₂₆₉	—	2	4	no	—
38	C₈×C₂₆₉	SD₁₆	1	4	yes	complemented
39	C₂²×C₂₆₉	#127	1	1	yes	characteristic
40	C₂×D₂₆₉	—	8	1	no	—
41	C₂×D₂₆₉	—	8	1	no	—
42	C₂×D₂₆₉	—	8	2	no	—
43	C₂×D₂₆₉	—	8	2	no	—
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	#492	1	1	yes	characteristic
48	C₂×C₂₆₉	#496	1	2	yes	—
49	D₂₆₉	—	16	1	no	—
50	D₂₆₉	—	16	1	no	—
51	C₂₆₉	#1715	1	1	yes	characteristic, complemented, Sylow
52	#1715	—	269	1	no	maximal, Sylow
53	#498	—	269	1	no	—
54	#493	—	269	1	no	—
55	#492	—	269	2	no	—
56	#486	—	269	2	no	—
57	#322	D₂₆₉	1	1	yes	characteristic, complemented
58	C₂×SD₁₆	—	538	4	no	—
59	C₂×D₈	—	538	2	no	—
60	C₄⋊Q₈	—	269	2	no	—
61	#127	—	269	1	no	—
62	#127	—	269	1	no	—
63	#106	—	538	2	no	—
64	#102	—	538	4	no	—
65	C₄×C₈	C₂×D₂₆₉	1	2	yes	—
66	C₄×C₈	C₂×D₂₆₉	1	1	yes	characteristic
67	C₂×Q₈	—	538	2	no	—
68	C₂×D₄	—	538	2	no	—
69	C₂×D₄	—	538	1	no	—
70	C₂×D₄	—	538	1	no	—
71	C₂×D₄	—	538	2	no	—
72	SD₁₆	—	1076	8	no	—
73	D₈	—	1076	4	no	—
74	C₂×C₈	D₁₀₇₆	1	4	yes	—
75	C₂×C₈	D₁₀₇₆	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	—	1076	1	no	—
80	C₂³	—	1076	1	no	—
81	Q₈	—	1076	4	no	—
82	D₄	—	1076	2	no	—
83	D₄	—	1076	2	no	—
84	D₄	—	1076	4	no	—
85	D₄	—	1076	4	no	—
86	C₂×C₄	—	1076	2	no	—
87	C₂×C₄	C₂×D₁₀₇₆	1	1	yes	characteristic
88	C₂×C₄	C₂×D₁₀₇₆	1	2	yes	—
89	C₈	—	2	4	no	—
90	C₈	#16864391	1	4	yes	complemented
91	C₂²	—	2152	1	no	—
92	C₂²	—	2152	1	no	—
93	C₂²	—	2152	2	no	—
94	C₂²	—	2152	2	no	—
95	C₂²	#22575450	1	1	yes	characteristic
96	C₄	—	2152	2	no	—
97	C₄	C₂×#16864391	1	2	yes	—
98	C₄	#22575481	1	4	yes	—
99	C₂	—	4304	1	no	—
100	C₂	—	4304	1	no	—
101	C₂	#31770978	1	1	yes	characteristic
102	C₂	#31770994	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#31771003

C₂

yes

maximal, characteristic, complemented

#31770982

C₂

yes

maximal, characteristic

#31770978

C₂

yes

maximal, complemented

#31770952

C₂

yes

maximal, complemented

#322×C₂₆₉

C₂

yes

maximal, characteristic, complemented

C₂×#16864391

—

C₂×D₂₁₅₂

—

#22575453

C₂²

yes

—

#22575450

C₂²

yes

characteristic

#22575450

C₂²

yes

characteristic

#22575385

—

#22575375

—

C₄×C₈×C₂₆₉

C₂²

yes

—

C₄×C₈×C₂₆₉

C₂²

yes

characteristic

C₂×Dic₅₃₈

—

C₂×D₁₀₇₆

—

C₂×D₁₀₇₆

—

C₂×D₁₀₇₆

—

C₂×D₁₀₇₆

—

#16864391

—

D₂₁₅₂

—

C₄⋊Dic₂₆₉

—

C₄⋊Dic₂₆₉

—

C₂×C₈×C₂₆₉

D₄

yes

—

C₂×C₈×C₂₆₉

D₄

yes

—

C₄²×C₂₆₉

C₂³

yes

characteristic

C₂²×D₂₆₉

—

C₂²×D₂₆₉

—

Dic₅₃₈

—

D₁₀₇₆

—

D₁₀₇₆

—

D₁₀₇₆

—

D₁₀₇₆

—

C₂×Dic₂₆₉

—

C₂×C₄×C₂₆₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₆₉

C₂×D₄

yes

—

C₈×C₂₆₉

—

C₈×C₂₆₉

SD₁₆

yes

complemented

C₂²×C₂₆₉

#127

yes

characteristic

C₂×D₂₆₉

—

C₂×D₂₆₉

—

C₂×D₂₆₉

—

C₂×D₂₆₉

—

C₄×C₂₆₉

C₂×SD₁₆

yes

—

C₄×C₂₆₉

AGL(1,ℤ/8)

yes

—

Dic₂₆₉

—

C₂×C₂₆₉

#492

yes

characteristic

C₂×C₂₆₉

#496

yes

—

D₂₆₉

—

D₂₆₉

—

C₂₆₉

#1715

yes

characteristic, complemented, Sylow

#1715

—

269

maximal, Sylow

#498

—

269

—

#493

—

269

—

#492

—

269

—

#486

—

269

—

#322

D₂₆₉

yes

characteristic, complemented

C₂×SD₁₆

—

538

—

C₂×D₈

—

538

—

C₄⋊Q₈

—

269

—

#127

—

269

—

#127

—

269

—

#106

—

538

—

#102

—

538

—

C₄×C₈

C₂×D₂₆₉

yes

—

C₄×C₈

C₂×D₂₆₉

yes

characteristic

C₂×Q₈

—

538

—

C₂×D₄

—

538

—

C₂×D₄

—

538

—

C₂×D₄

—

538

—

C₂×D₄

—

538

—

SD₁₆

—

1076

—

D₈

—

1076

—

C₂×C₈

D₁₀₇₆

yes

—

C₂×C₈

D₁₀₇₆

yes

—

C₄⋊C₄

—

538

—

C₄⋊C₄

—

538

—

C₄²

C₂²×D₂₆₉

yes

characteristic

C₂³

—

1076

—

C₂³

—

1076

—

Q₈

—

1076

—

D₄

—

1076

—

D₄

—

1076

—

D₄

—

1076

—

D₄

—

1076

—

C₂×C₄

—

1076

—

C₂×C₄

C₂×D₁₀₇₆

yes

characteristic

C₂×C₄

C₂×D₁₀₇₆

yes

—

C₈

—

C₈

#16864391

yes

complemented

C₂²

—

2152

—

C₂²

—

2152

—

C₂²

—

2152

—

C₂²

—

2152

—

C₂²

#22575450

yes

characteristic

C₄

—

2152

—

C₄

C₂×#16864391

yes

—

C₄

#22575481

yes

—

C₂

—

4304

—

100

C₂

—

4304

—

101

C₂

#31770978

yes

characteristic

102

C₂

#31770994

yes

—

	subgroup	G/H
center	C₂²	#22575450
commutator, cosocle	C₄²×C₂₆₉	C₂³
Frattini	C₄²	C₂²×D₂₆₉
Fitting	#322×C₂₆₉	C₂
socle	C₂²×C₂₆₉	#127
prime radical	#31770982	C₂
hypercenter	#322	D₂₆₉
hypocenter	C₂₆₉	#1715
LCS	G ▷ C₄²×C₂₆₉ ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

subgroup

G/H

center

C₂²

#22575450

commutator, cosocle

C₄²×C₂₆₉

C₂³

Frattini

C₄²

C₂²×D₂₆₉

Fitting

#322×C₂₆₉

C₂

C₂²×C₂₆₉

C₂

D₂₆₉

C₂₆₉

G ▷ C₄²×C₂₆₉ ▷ C₂²×C₂₆₉ ▷ C₂₆₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #322

N	H ≅ G/N	type
1. #31771003	C₂	semidirect
3. #31770978	C₂	semidirect
4. #31770952	C₂	semidirect
5. #322×C₂₆₉	C₂	semidirect
38. C₈×C₂₆₉	SD₁₆	semidirect
51. C₂₆₉	#1715	semidirect
57. #322	D₂₆₉	semidirect
90. C₈	#16864391	semidirect

H ≅ G/N

type

1. #31771003

C₂

semidirect

3. #31770978

C₂

semidirect

4. #31770952

C₂

semidirect

5. #322×C₂₆₉

C₂

semidirect

38. C₈×C₂₆₉

SD₁₆

semidirect

51. C₂₆₉

#1715

semidirect

57. #322

D₂₆₉

semidirect

90. C₈

#16864391

semidirect

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

subgroup	index
#31771003	2
#31770982	2
#31770978	2
#31770952	2
#322×C₂₆₉	2
#1715	269

subgroup

index

#322×C₂₆₉

269

Subgroups — #46810513

Conjugacy classes of subgroups

Complements

Maximal subgroups