Subgroups — C₄×#22551498 #45662452

Order 32896.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22551498	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₂₅₇	C₂	1	1	yes	maximal, characteristic
3	#22551498	C₄	1	4	yes	direct product factor
4	C₂×C₁₆×C₂₅₇	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₂₅₇	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₂₅₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₂₅₇	C₈	1	1	yes	characteristic
8	C₂×C₈×C₂₅₇	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₂₅₇	C₈	1	1	yes	characteristic
10	C₁₆×C₂₅₇	C₈	1	2	yes	—
11	C₁₆×C₂₅₇	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₂₅₇	C₁₆	1	2	yes	—
13	C₂×C₄×C₂₅₇	C₂×C₈	1	1	yes	characteristic
14	C₈×C₂₅₇	C₁₆	1	2	yes	—
15	C₈×C₂₅₇	C₄²	1	1	yes	characteristic
16	C₈×C₂₅₇	C₂×C₈	1	1	yes	characteristic
17	C₂²×C₂₅₇	C₂×C₁₆	1	1	yes	characteristic
18	C₄×C₂₅₇	C₃₂	1	4	yes	complemented
19	C₄×C₂₅₇	C₄×C₈	1	1	yes	characteristic
20	C₄×C₂₅₇	C₂×C₁₆	1	1	yes	characteristic
21	C₂×C₂₅₇	C₄×C₁₆	1	1	yes	characteristic
22	C₂×C₂₅₇	C₂×C₃₂	1	2	yes	—
23	C₂₅₇	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
24	C₄×C₃₂	—	257	1	no	maximal, Sylow
25	C₂×C₃₂	—	257	2	no	—
26	C₄×C₁₆	D₂₅₇	1	1	yes	characteristic
27	C₂×C₁₆	Dic₂₅₇	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₂₅₇	1	1	yes	characteristic
29	C₄×C₈	Dic₂₅₇	1	1	yes	characteristic
30	C₃₂	—	257	4	no	—
31	C₂×C₈	#14523339	1	1	yes	characteristic
32	C₂×C₈	C₂×Dic₂₅₇	1	1	yes	characteristic
33	C₄²	#14523339	1	1	yes	characteristic
34	C₁₆	#14523339	1	2	yes	—
35	C₁₆	C₄×D₂₅₇	1	2	yes	—
36	C₂×C₄	#16861593	1	2	yes	—
37	C₂×C₄	C₂×#14523339	1	1	yes	characteristic
38	C₈	#16861593	1	2	yes	—
39	C₈	C₄×Dic₂₅₇	1	1	yes	characteristic
40	C₈	C₂×#14523339	1	1	yes	characteristic
41	C₂²	C₂×#16861593	1	1	yes	characteristic
42	C₄	#22551498	1	4	yes	direct product factor
43	C₄	C₄×#14523339	1	1	yes	characteristic
44	C₄	C₂×#16861593	1	1	yes	characteristic
45	C₂	C₄×#16861593	1	1	yes	characteristic
46	C₂	C₂×#22551498	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₁₆	D₂₅₇
commutator, hypocenter	C₂₅₇	C₄×C₃₂
Frattini	C₂×C₁₆	C₂×D₂₅₇
Fitting	C₄×C₁₆×C₂₅₇	C₂
socle, prime radical	C₂²×C₂₅₇	C₂×C₁₆
cosocle	C₂×C₁₆×C₂₅₇	C₂²
LCS	G ▷ C₂₅₇
UCS	C₁ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
3. #22551498	C₄	direct (N × H)
18. C₄×C₂₅₇	C₃₂	semidirect
23. C₂₅₇	C₄×C₃₂	semidirect
42. C₄	#22551498	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#22551498	2
C₄×C₁₆×C₂₅₇	2
C₄×C₃₂	257

Subgroups — C4×#22551498 #45662452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#22551498 #45662452