Subgroups — C₂₅₇⋊#564 #30657492

Order 16448.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22551584	C₂	1	2	yes	maximal
2	#22551583	C₂	1	4	yes	maximal
3	#22551582	C₂	1	4	yes	maximal
4	#22551582	C₂	1	4	yes	maximal
5	#125×C₂₅₇	C₂	1	1	yes	maximal, characteristic
6	C₄⋊Dic₂₅₇	C₂²	1	2	yes	—
7	C₄⋊Dic₂₅₇	C₂²	1	4	yes	—
8	C₄⋊Dic₂₅₇	C₂²	1	2	yes	—
9	#16861597	C₂²	1	4	yes	—
10	#16861597	C₂²	1	4	yes	—
11	#16861597	C₂²	1	4	yes	—
12	#16861597	C₂²	1	4	yes	—
13	C₄×Dic₂₅₇	C₂²	1	4	yes	—
14	C₄⋊C₄×C₂₅₇	C₂²	1	2	yes	—
15	C₄⋊C₄×C₂₅₇	C₂²	1	4	yes	—
16	C₄²×C₂₅₇	C₂²	1	1	yes	characteristic
17	C₂×Dic₂₅₇	C₂³	1	4	yes	—
18	C₂×Dic₂₅₇	C₂³	1	4	yes	—
19	C₂×C₄×C₂₅₇	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₂₅₇	C₂³	1	2	yes	—
21	C₂×C₄×C₂₅₇	C₂³	1	4	yes	—
22	C₂²×C₂₅₇	C₂⁴	1	1	yes	characteristic
23	C₄×C₂₅₇	—	2	2	no	—
24	C₄×C₂₅₇	—	2	4	no	—
25	C₄×C₂₅₇	—	2	1	no	—
26	Dic₂₅₇	—	2	4	no	—
27	Dic₂₅₇	—	2	4	no	—
28	C₂×C₂₅₇	2₋¹⁺⁴	1	2	yes	—
29	C₂×C₂₅₇	2₋¹⁺⁴	1	1	yes	characteristic
30	C₂₅₇	#564	1	1	yes	characteristic, complemented, Sylow
31	#564	—	257	1	no	maximal, Sylow
32	#125	—	257	4	no	—
33	#125	—	257	4	no	—
34	#125	—	257	4	no	—
35	#125	—	257	2	no	—
36	#125	D₂₅₇	1	1	yes	characteristic
37	C₄⋊C₄	—	257	4	no	—
38	C₄⋊C₄	—	257	4	no	—
39	C₄⋊C₄	—	257	4	no	—
40	C₄⋊C₄	—	257	4	no	—
41	C₄⋊C₄	—	257	4	no	—
42	C₄⋊C₄	—	257	2	no	—
43	C₄⋊C₄	—	257	2	no	—
44	C₄⋊C₄	C₂×D₂₅₇	1	2	yes	—
45	C₄⋊C₄	C₂×D₂₅₇	1	4	yes	—
46	C₄²	—	257	4	no	—
47	C₄²	C₂×D₂₅₇	1	1	yes	characteristic
48	C₂×C₄	—	257	4	no	—
49	C₂×C₄	—	257	4	no	—
50	C₂×C₄	C₂²×D₂₅₇	1	4	yes	—
51	C₂×C₄	C₂²×D₂₅₇	1	2	yes	—
52	C₂×C₄	C₂²×D₂₅₇	1	1	yes	characteristic
53	C₂²	C₂³×D₂₅₇	1	1	yes	characteristic
54	C₄	—	2	4	no	—
55	C₄	—	2	2	no	—
56	C₄	—	2	1	no	—
57	C₄	—	514	4	no	—
58	C₄	—	514	4	no	—
59	C₂	#22551639	1	2	yes	—
60	C₂	#22551640	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₅₇
commutator, socle, prime radical, cosocle	C₂²×C₂₅₇	C₂⁴
Fitting	#125×C₂₅₇	C₂
hypercenter	#125	D₂₅₇
hypocenter	C₂₅₇	#564
LCS	G ▷ C₂²×C₂₅₇ ▷ C₂₅₇
UCS	C₁ ◁ C₂² ◁ #125

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
30. C₂₅₇	#564	semidirect

Maximal subgroups

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

subgroup	index
#22551584	2
#22551583	2
#22551582	2
#125×C₂₅₇	2
#564	257

Subgroups — C257⋊#564 #30657492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅₇⋊#564 #30657492