Group #46819267 — subgroups

Subgroups — #46819267

Order 34432.

408 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 165 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	#31770511	C₂	1	3	yes	maximal
2	#31770503	C₂	1	3	yes	maximal
3	#31770489	C₂	1	6	yes	maximal
4	#31770473	C₂	1	2	yes	maximal
5	C₄³×C₂₆₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₅₃₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₂₆₉	C₂²	1	3	yes	—
8	C₂×#16864381	C₂²	1	6	yes	—
9	#22575360	C₂²	1	6	yes	—
10	#22575360	C₂²	1	6	yes	—
11	#22575360	C₂²	1	6	yes	—
12	C₂×C₄²×C₂₆₉	C₂²	1	3	yes	—
13	C₂×C₄²×C₂₆₉	C₂²	1	3	yes	—
14	C₂×C₄²×C₂₆₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₅₃₈	—	2	6	no	—
16	C₂²×Dic₂₆₉	C₂³	1	2	yes	—
17	C₂²×Dic₂₆₉	C₂³	1	6	yes	—
18	C₄⋊Dic₂₆₉	—	2	6	no	—
19	#16864381	—	2	12	no	—
20	C₂²×C₄×C₂₆₉	C₂³	1	3	yes	—
21	C₂²×C₄×C₂₆₉	C₂³	1	3	yes	—
22	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
23	C₄²×C₂₆₉	—	2	6	no	—
24	C₄²×C₂₆₉	—	2	6	no	—
25	C₄²×C₂₆₉	Q₈	1	4	yes	complemented
26	Dic₅₃₈	—	4	4	no	—
27	C₂×Dic₂₆₉	—	2	12	no	—
28	C₂×Dic₂₆₉	—	2	6	no	—
29	C₂×Dic₂₆₉	—	2	6	no	—
30	C₂³×C₂₆₉	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₂₆₉	—	2	3	no	—
32	C₂×C₄×C₂₆₉	—	2	3	no	—
33	C₂×C₄×C₂₆₉	—	2	3	no	—
34	C₂×C₄×C₂₆₉	—	2	3	no	—
35	C₂×C₄×C₂₆₉	C₂×Q₈	1	6	yes	—
36	C₂×C₄×C₂₆₉	#41	1	6	yes	—
37	C₂×C₄×C₂₆₉	#41	1	6	yes	—
38	C₂²×C₂₆₉	C₂²×Q₈	1	1	yes	characteristic
39	C₂²×C₂₆₉	C₂×#41	1	3	yes	—
40	C₂²×C₂₆₉	C₂×#41	1	3	yes	—
41	C₄×C₂₆₉	—	2	6	no	—
42	C₄×C₂₆₉	—	2	6	no	—
43	C₄×C₂₆₉	#126	1	4	yes	—
44	Dic₂₆₉	—	4	2	no	—
45	Dic₂₆₉	—	4	6	no	—
46	C₂×C₂₆₉	C₂×#126	1	1	yes	characteristic
47	C₂×C₂₆₉	#529	1	3	yes	—
48	C₂×C₂₆₉	#533	1	3	yes	—
49	C₂₆₉	#2863	1	1	yes	characteristic, complemented, Sylow
50	#2863	—	269	1	no	maximal, Sylow
51	#391	—	269	3	no	—
52	#389	—	269	3	no	—
53	#387	—	269	6	no	—
54	#383	—	269	2	no	—
55	C₄³	D₂₆₉	1	1	yes	characteristic
56	C₂²×Q₈	—	269	1	no	—
57	C₂×C₄⋊C₄	—	269	6	no	—
58	C₂×C₄⋊C₄	—	269	3	no	—
59	C₂×C₄²	C₂×D₂₆₉	1	3	yes	—
60	C₂×C₄²	C₂×D₂₆₉	1	3	yes	—
61	C₂×C₄²	C₂×D₂₆₉	1	1	yes	characteristic
62	#95	—	269	6	no	—
63	#95	—	269	6	no	—
64	#95	—	269	6	no	—
65	C₂×Q₈	—	538	6	no	—
66	C₂²×C₄	—	269	2	no	—
67	C₂²×C₄	—	269	6	no	—
68	C₂²×C₄	C₂²×D₂₆₉	1	3	yes	—
69	C₂²×C₄	C₂²×D₂₆₉	1	3	yes	—
70	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
71	C₄⋊C₄	—	538	12	no	—
72	C₄⋊C₄	—	538	6	no	—
73	C₄²	—	2	6	no	—
74	C₄²	—	2	6	no	—
75	C₄²	Dic₅₃₈	1	4	yes	complemented
76	C₂³	C₂³×D₂₆₉	1	1	yes	characteristic
77	Q₈	—	1076	4	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	538	12	no	—
83	C₂×C₄	—	538	6	no	—
84	C₂×C₄	—	538	6	no	—
85	C₂×C₄	C₂×Dic₅₃₈	1	6	yes	—
86	C₂×C₄	#16864402	1	6	yes	—
87	C₂×C₄	#16864402	1	6	yes	—
88	C₂²	C₂²×Dic₅₃₈	1	1	yes	characteristic
89	C₂²	C₂×#16864402	1	3	yes	—
90	C₂²	C₂×#16864402	1	3	yes	—
91	C₄	—	2	6	no	—
92	C₄	—	2	6	no	—
93	C₄	—	1076	6	no	—
94	C₄	—	1076	2	no	—
95	C₄	#22575447	1	4	yes	—
96	C₂	C₂×#22575447	1	1	yes	characteristic
97	C₂	#31771139	1	3	yes	—
98	C₂	#31771162	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#31770511

C₂

yes

maximal

#31770503

C₂

yes

maximal

#31770489

C₂

yes

maximal

#31770473

C₂

yes

maximal

C₄³×C₂₆₉

C₂

yes

maximal, characteristic

C₂²×Dic₅₃₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₆₉

C₂²

yes

—

C₂×#16864381

C₂²

yes

—

#22575360

C₂²

yes

—

#22575360

C₂²

yes

—

#22575360

C₂²

yes

—

C₂×C₄²×C₂₆₉

C₂²

yes

—

C₂×C₄²×C₂₆₉

C₂²

yes

—

C₂×C₄²×C₂₆₉

C₂²

yes

characteristic

C₂×Dic₅₃₈

—

C₂²×Dic₂₆₉

C₂³

yes

—

C₂²×Dic₂₆₉

C₂³

yes

—

C₄⋊Dic₂₆₉

—

#16864381

—

C₂²×C₄×C₂₆₉

C₂³

yes

—

C₂²×C₄×C₂₆₉

C₂³

yes

—

C₂²×C₄×C₂₆₉

C₂³

yes

characteristic

C₄²×C₂₆₉

—

C₄²×C₂₆₉

—

C₄²×C₂₆₉

Q₈

yes

complemented

Dic₅₃₈

—

C₂×Dic₂₆₉

—

C₂×Dic₂₆₉

—

C₂×Dic₂₆₉

—

C₂³×C₂₆₉

C₂⁴

yes

characteristic

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

C₂×Q₈

yes

—

C₂×C₄×C₂₆₉

#41

yes

—

C₂×C₄×C₂₆₉

#41

yes

—

C₂²×C₂₆₉

C₂²×Q₈

yes

characteristic

C₂²×C₂₆₉

C₂×#41

yes

—

C₂²×C₂₆₉

C₂×#41

yes

—

C₄×C₂₆₉

—

C₄×C₂₆₉

—

C₄×C₂₆₉

#126

yes

—

Dic₂₆₉

—

Dic₂₆₉

—

C₂×C₂₆₉

C₂×#126

yes

characteristic

C₂×C₂₆₉

#529

yes

—

C₂×C₂₆₉

#533

yes

—

C₂₆₉

#2863

yes

characteristic, complemented, Sylow

#2863

—

269

maximal, Sylow

#391

—

269

—

#389

—

269

—

#387

—

269

—

#383

—

269

—

C₄³

D₂₆₉

yes

characteristic

C₂²×Q₈

—

269

—

C₂×C₄⋊C₄

—

269

—

C₂×C₄⋊C₄

—

269

—

C₂×C₄²

C₂×D₂₆₉

yes

—

C₂×C₄²

C₂×D₂₆₉

yes

—

C₂×C₄²

C₂×D₂₆₉

yes

characteristic

#95

—

269

—

#95

—

269

—

#95

—

269

—

C₂×Q₈

—

538

—

C₂²×C₄

—

269

—

C₂²×C₄

—

269

—

C₂²×C₄

C₂²×D₂₆₉

yes

—

C₂²×C₄

C₂²×D₂₆₉

yes

—

C₂²×C₄

C₂²×D₂₆₉

yes

characteristic

C₄⋊C₄

—

538

—

C₄⋊C₄

—

538

—

C₄²

—

C₄²

—

C₄²

Dic₅₃₈

yes

complemented

C₂³

C₂³×D₂₆₉

yes

characteristic

Q₈

—

1076

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

538

—

C₂×C₄

—

538

—

C₂×C₄

—

538

—

C₂×C₄

C₂×Dic₅₃₈

yes

—

C₂×C₄

#16864402

yes

—

C₂×C₄

#16864402

yes

—

C₂²

C₂²×Dic₅₃₈

yes

characteristic

C₂²

C₂×#16864402

yes

—

C₂²

C₂×#16864402

yes

—

C₄

—

C₄

—

C₄

—

1076

—

C₄

—

1076

—

C₄

#22575447

yes

—

C₂

C₂×#22575447

yes

characteristic

C₂

#31771139

yes

—

C₂

#31771162

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₆₉
commutator, socle, prime radical, cosocle	C₂³×C₂₆₉	C₂⁴
Fitting	C₄³×C₂₆₉	C₂
hypercenter	C₄³	D₂₆₉
hypocenter	C₂₆₉	#2863
LCS	G ▷ C₂³×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₂₆₉

commutator, socle, prime radical, cosocle

C₂³×C₂₆₉

C₂⁴

Fitting

C₄³×C₂₆₉

C₂

hypercenter

C₄³

D₂₆₉

C₂₆₉

G ▷ C₂³×C₂₆₉ ▷ C₂₆₉

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
25. C₄²×C₂₆₉	Q₈	semidirect
49. C₂₆₉	#2863	semidirect
75. C₄²	Dic₅₃₈	semidirect

H ≅ G/N

type

25. C₄²×C₂₆₉

Q₈

semidirect

49. C₂₆₉

#2863

semidirect

75. C₄²

Dic₅₃₈

semidirect

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

subgroup	index
#31770511	2
#31770503	2
#31770489	2
#31770473	2
C₄³×C₂₆₉	2
#2863	269

subgroup

index

C₄³×C₂₆₉

269

Subgroups — #46819267

Conjugacy classes of subgroups

Complements

Maximal subgroups