Group #46809705 — subgroups

Subgroups — #46809705

Order 34432.

160 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 73 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	C₈×Dic₅₃₈	C₂	1	2	yes	maximal
2	C₄×Dic₁₀₇₆	C₂	1	1	yes	maximal, characteristic
3	#31770356	C₂	1	1	yes	maximal, characteristic
4	#31770337	C₂	1	2	yes	maximal
5	#322×C₂₆₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₀₇₆	C₄	1	1	yes	characteristic
7	C₄×Dic₅₃₈	C₂²	1	2	yes	—
8	#22575387	C₄	1	1	yes	characteristic
9	C₄⋊#14524130	C₂²	1	2	yes	—
10	#22575382	—	2	2	no	—
11	#22575378	C₄	1	2	yes	—
12	C₈×Dic₂₆₉	—	2	2	no	—
13	C₄×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
16	C₂×Dic₅₃₈	C₂×C₄	1	2	yes	—
17	Dic₁₀₇₆	C₈	1	4	yes	complemented
18	C₂×#14524130	—	2	2	no	—
19	C₄⋊Dic₂₆₉	C₂×C₄	1	2	yes	—
20	#16864381	—	2	2	no	—
21	C₄×Dic₂₆₉	—	2	2	no	—
22	C₂×C₈×C₂₆₉	—	2	1	no	—
23	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₂₆₉	D₄	1	2	yes	—
26	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
27	Dic₅₃₈	—	2	2	no	—
28	Dic₅₃₈	C₂×C₈	1	4	yes	—
29	C₂×Dic₂₆₉	—	2	2	no	—
30	C₂×Dic₂₆₉	—	2	2	no	—
31	#14524130	—	4	2	no	—
32	C₂×C₄×C₂₆₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₂₆₉	#41	1	1	yes	characteristic
35	C₈×C₂₆₉	—	2	1	no	—
36	C₈×C₂₆₉	—	2	2	no	—
37	C₈×C₂₆₉	—	4	1	no	—
38	C₈×C₂₆₉	C₂×C₈	1	2	yes	—
39	C₂²×C₂₆₉	C₄×D₄	1	1	yes	characteristic
40	C₄×C₂₆₉	—	2	1	no	—
41	C₄×C₂₆₉	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₂₆₉	#131	1	1	yes	characteristic
43	C₄×C₂₆₉	#137	1	2	yes	—
44	Dic₂₆₉	—	2	4	no	—
45	Dic₂₆₉	—	4	2	no	—
46	C₂×C₂₆₉	C₈×D₄	1	1	yes	characteristic
47	C₂×C₂₆₉	#441	1	1	yes	characteristic
48	C₂×C₂₆₉	#444	1	1	yes	characteristic
49	C₂₆₉	#1579	1	1	yes	characteristic, complemented, Sylow
50	#1579	—	269	1	no	maximal, Sylow
51	C₈×Q₈	—	269	2	no	—
52	C₄×Q₁₆	—	269	1	no	—
53	#334	—	269	1	no	—
54	Q₈⋊C₈	—	269	2	no	—
55	#322	D₂₆₉	1	1	yes	characteristic
56	C₂×Q₁₆	—	269	1	no	—
57	C₄×Q₈	—	269	2	no	—
58	#107	—	269	1	no	—
59	C₄⋊C₈	—	269	2	no	—
60	C₄⋊C₈	—	538	2	no	—
61	#103	—	269	2	no	—
62	C₄×C₈	—	538	2	no	—
63	C₄×C₈	C₂×D₂₆₉	1	1	yes	characteristic
64	C₄×C₈	C₂×D₂₆₉	1	1	yes	characteristic
65	C₄×C₈	C₂×D₂₆₉	1	1	yes	characteristic
66	C₂×Q₈	—	269	2	no	—
67	Q₁₆	—	269	4	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	538	2	no	—
70	C₂×C₈	C₄×D₂₆₉	1	1	yes	characteristic
71	C₂×C₈	C₄×D₂₆₉	1	1	yes	characteristic
72	C₂×C₈	D₁₀₇₆	1	2	yes	—
73	C₄⋊C₄	—	269	2	no	—
74	C₄⋊C₄	—	538	2	no	—
75	C₄²	—	538	2	no	—
76	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
77	Q₈	—	269	4	no	—
78	Q₈	—	538	2	no	—
79	C₂×C₄	—	538	2	no	—
80	C₂×C₄	—	538	2	no	—
81	C₂×C₄	C₂×C₄×D₂₆₉	1	1	yes	characteristic
82	C₂×C₄	C₂×D₁₀₇₆	1	1	yes	characteristic
83	C₂×C₄	#16864402	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	2	2	no	—
86	C₈	—	4	1	no	—
87	C₈	—	1076	2	no	—
88	C₈	C₈×D₂₆₉	1	2	yes	—
89	C₂²	C₄×D₁₀₇₆	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	538	4	no	—
92	C₄	—	1076	2	no	—
93	C₄	C₂×C₈×D₂₆₉	1	1	yes	characteristic
94	C₄	#22575459	1	1	yes	characteristic
95	C₄	#22575486	1	2	yes	—
96	C₂	C₈×D₁₀₇₆	1	1	yes	characteristic
97	C₂	#31770713	1	1	yes	characteristic
98	C₂	#31770728	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×Dic₅₃₈

C₂

yes

maximal

C₄×Dic₁₀₇₆

C₂

yes

maximal, characteristic

#31770356

C₂

yes

maximal, characteristic

#31770337

C₂

yes

maximal

#322×C₂₆₉

C₂

yes

maximal, characteristic

C₂×Dic₁₀₇₆

C₄

yes

characteristic

C₄×Dic₅₃₈

C₂²

yes

—

#22575387

C₄

yes

characteristic

C₄⋊#14524130

C₂²

yes

—

#22575382

—

#22575378

C₄

yes

—

C₈×Dic₂₆₉

—

C₄×C₈×C₂₆₉

C₂²

yes

characteristic

C₄×C₈×C₂₆₉

C₂²

yes

characteristic

C₄×C₈×C₂₆₉

C₂²

yes

characteristic

C₂×Dic₅₃₈

C₂×C₄

yes

—

Dic₁₀₇₆

C₈

yes

complemented

C₂×#14524130

—

C₄⋊Dic₂₆₉

C₂×C₄

yes

—

#16864381

—

C₄×Dic₂₆₉

—

C₂×C₈×C₂₆₉

—

C₂×C₈×C₂₆₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₆₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₆₉

D₄

yes

—

C₄²×C₂₆₉

C₂³

yes

characteristic

Dic₅₃₈

—

Dic₅₃₈

C₂×C₈

yes

—

C₂×Dic₂₆₉

—

C₂×Dic₂₆₉

—

#14524130

—

C₂×C₄×C₂₆₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₆₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₆₉

#41

yes

characteristic

C₈×C₂₆₉

—

C₈×C₂₆₉

—

C₈×C₂₆₉

—

C₈×C₂₆₉

C₂×C₈

yes

—

C₂²×C₂₆₉

C₄×D₄

yes

characteristic

C₄×C₂₆₉

—

C₄×C₂₆₉

C₂²×C₈

yes

C₄×C₂₆₉

yes

C₄×C₂₆₉

yes

—

Dic₂₆₉

—

Dic₂₆₉

—

C₂×C₂₆₉

C₈×D₄

yes

C₂×C₂₆₉

yes

C₂×C₂₆₉

yes

C₂₆₉

yes

characteristic, complemented, Sylow

#1579

—

269

maximal, Sylow

C₈×Q₈

—

269

—

C₄×Q₁₆

—

269

—

#334

—

269

—

Q₈⋊C₈

—

269

—

#322

D₂₆₉

yes

characteristic

C₂×Q₁₆

—

269

—

C₄×Q₈

—

269

—

#107

—

269

—

C₄⋊C₈

—

269

—

C₄⋊C₈

—

538

—

#103

—

269

—

C₄×C₈

—

538

—

C₄×C₈

C₂×D₂₆₉

yes

characteristic

C₄×C₈

C₂×D₂₆₉

yes

characteristic

C₄×C₈

C₂×D₂₆₉

yes

characteristic

C₂×Q₈

—

269

—

Q₁₆

—

269

—

C₂×C₈

—

C₂×C₈

—

538

—

C₂×C₈

C₄×D₂₆₉

yes

characteristic

C₂×C₈

C₄×D₂₆₉

yes

characteristic

C₂×C₈

D₁₀₇₆

yes

—

C₄⋊C₄

—

269

—

C₄⋊C₄

—

538

—

C₄²

—

538

—

C₄²

C₂²×D₂₆₉

yes

characteristic

Q₈

—

269

—

Q₈

—

538

—

C₂×C₄

—

538

—

C₂×C₄

—

538

—

C₂×C₄

C₂×C₄×D₂₆₉

yes

characteristic

C₂×C₄

C₂×D₁₀₇₆

yes

characteristic

C₂×C₄

#16864402

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

1076

—

C₈

C₈×D₂₆₉

yes

—

C₂²

C₄×D₁₀₇₆

yes

characteristic

C₄

—

C₄

—

538

—

C₄

—

1076

—

C₄

C₂×C₈×D₂₆₉

yes

C₄

yes

C₄

yes

—

C₂

C₈×D₁₀₇₆

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	C₂×D₁₀₇₆
commutator	C₄×C₂₆₉	C₂²×C₈
Frattini	C₄²	C₂²×D₂₆₉
Fitting	#322×C₂₆₉	C₂
socle, prime radical	C₂²×C₂₆₉	C₄×D₄
cosocle	C₄²×C₂₆₉	C₂³
hypercenter	#322	D₂₆₉
hypocenter	C₂₆₉	#1579
LCS	G ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

subgroup

G/H

center

C₂×C₄

C₂×D₁₀₇₆

commutator

C₄×C₂₆₉

C₂²×C₈

Frattini

C₄²

C₂²×D₂₆₉

Fitting

#322×C₂₆₉

C₂

socle, prime radical

C₂²×C₂₆₉

C₄×D₄

cosocle

C₄²×C₂₆₉

C₂³

D₂₆₉

C₂₆₉

G ▷ C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

N	H ≅ G/N	type
17. Dic₁₀₇₆	C₈	semidirect
49. C₂₆₉	#1579	semidirect

H ≅ G/N

type

17. Dic₁₀₇₆

C₈

semidirect

49. C₂₆₉

#1579

semidirect

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

subgroup	index
C₈×Dic₅₃₈	2
C₄×Dic₁₀₇₆	2
#31770356	2
#31770337	2
#322×C₂₆₉	2
#1579	269

subgroup

index

C₈×Dic₅₃₈

C₄×Dic₁₀₇₆

#31770356

#31770337

#322×C₂₆₉

#1579

269

Subgroups — #46809705

Conjugacy classes of subgroups

Complements

Maximal subgroups