Subgroups — C₂×#22582825 #31823890

Order 17984.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₂₄	C₂	1	1	yes	maximal, characteristic
2	#22582825	C₂	1	4	yes	maximal, direct product factor
3	C₂×#17985113	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₂₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₅₆₂	—	2	1	no	—
6	Dic₁₁₂₄	—	2	1	no	—
7	Dic₁₁₂₄	C₂²	1	2	yes	—
8	#17985113	C₂²	1	2	yes	—
9	C₂×Q₈×C₂₈₁	—	2	1	no	—
10	Q₁₆×C₂₈₁	—	2	1	no	—
11	Q₁₆×C₂₈₁	C₂²	1	2	yes	—
12	C₂×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
13	Dic₅₆₂	—	2	2	no	—
14	Dic₅₆₂	—	4	1	no	—
15	C₂×Dic₂₈₁	—	4	1	no	—
16	Q₈×C₂₈₁	—	2	2	no	—
17	Q₈×C₂₈₁	—	4	1	no	—
18	C₂×C₄×C₂₈₁	—	4	1	no	—
19	C₂×C₄×C₂₈₁	D₄	1	1	yes	characteristic
20	C₈×C₂₈₁	D₄	1	1	yes	characteristic
21	C₈×C₂₈₁	C₂³	1	1	yes	characteristic
22	C₂²×C₂₈₁	D₈	1	1	yes	characteristic
23	C₄×C₂₈₁	—	4	2	no	—
24	C₄×C₂₈₁	D₈	1	1	yes	characteristic
25	C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
26	Dic₂₈₁	—	4	2	no	—
27	C₂×C₂₈₁	Q₃₂	1	2	yes	complemented
28	C₂×C₂₈₁	C₂×D₈	1	1	yes	characteristic
29	C₂₈₁	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
30	C₂×Q₃₂	—	281	1	no	maximal, Sylow
31	C₂×Q₁₆	—	281	1	no	—
32	C₂×Q₁₆	D₂₈₁	1	1	yes	characteristic
33	Q₃₂	—	281	4	no	—
34	C₂×C₁₆	—	281	1	no	—
35	C₂×Q₈	—	2	1	no	—
36	C₂×Q₈	—	562	1	no	—
37	Q₁₆	—	2	1	no	—
38	Q₁₆	—	281	2	no	—
39	Q₁₆	—	562	1	no	—
40	Q₁₆	C₂×D₂₈₁	1	2	yes	—
41	C₂×C₈	C₂×D₂₈₁	1	1	yes	characteristic
42	C₁₆	—	281	2	no	—
43	Q₈	—	2	2	no	—
44	Q₈	—	4	1	no	—
45	Q₈	—	562	2	no	—
46	Q₈	—	1124	1	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	—	1124	1	no	—
49	C₂×C₄	C₂²⋊D₂₈₁	1	1	yes	characteristic
50	C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
51	C₈	C₂²×D₂₈₁	1	1	yes	characteristic
52	C₂²	#17985123	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	1124	2	no	—
55	C₄	#17985123	1	1	yes	characteristic
56	C₄	C₂×C₂²⋊D₂₈₁	1	1	yes	characteristic
57	C₂	#22582825	1	2	yes	direct product factor
58	C₂	C₂×#17985123	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#17985123
commutator, cosocle	C₈×C₂₈₁	C₂³
Frattini	C₈	C₂²×D₂₈₁
Fitting	C₂×Q₁₆×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	D₈
hypercenter	C₂×Q₁₆	D₂₈₁
hypocenter	C₂₈₁	C₂×Q₃₂
LCS	G ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #22582825	C₂	direct (N × H)
27. C₂×C₂₈₁	Q₃₂	semidirect
29. C₂₈₁	C₂×Q₃₂	semidirect
57. C₂	#22582825	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×Dic₁₁₂₄	2
#22582825	2
C₂×#17985113	2
C₂×Q₁₆×C₂₈₁	2
C₂×Q₃₂	281

Subgroups — C2×#22582825 #31823890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22582825 #31823890