Subgroups — C₄×#17985113 #31823237

Order 17984.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17985113	C₂	1	2	yes	maximal
2	C₄×C₈×C₂₈₁	C₂	1	1	yes	maximal, characteristic
3	#17985113	C₄	1	4	yes	direct product factor
4	C₂×C₈×C₂₈₁	C₄	1	1	yes	characteristic
5	C₂×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
6	C₄²×C₂₈₁	C₄	1	1	yes	characteristic
7	C₂×C₄×C₂₈₁	C₈	1	2	yes	—
8	C₂×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₈₁	C₈	1	2	yes	—
10	C₈×C₂₈₁	C₂×C₄	1	2	yes	—
11	C₂²×C₂₈₁	C₂×C₈	1	1	yes	characteristic
12	C₄×C₂₈₁	C₁₆	1	4	yes	complemented
13	C₄×C₂₈₁	C₄²	1	1	yes	characteristic
14	C₄×C₂₈₁	C₂×C₈	1	1	yes	characteristic
15	C₂×C₂₈₁	C₄×C₈	1	1	yes	characteristic
16	C₂×C₂₈₁	C₂×C₁₆	1	2	yes	—
17	C₂₈₁	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₁₆	—	281	1	no	maximal, Sylow
19	C₂×C₁₆	—	281	2	no	—
20	C₄×C₈	D₂₈₁	1	1	yes	characteristic
21	C₂×C₈	Dic₂₈₁	1	1	yes	characteristic
22	C₂×C₈	C₂×D₂₈₁	1	1	yes	characteristic
23	C₄²	Dic₂₈₁	1	1	yes	characteristic
24	C₁₆	—	281	4	no	—
25	C₂×C₄	#14555886	1	2	yes	—
26	C₂×C₄	C₂×Dic₂₈₁	1	1	yes	characteristic
27	C₈	#14555886	1	2	yes	—
28	C₈	C₄×D₂₈₁	1	2	yes	—
29	C₂²	C₂×#14555886	1	1	yes	characteristic
30	C₄	#17985113	1	4	yes	direct product factor
31	C₄	C₄×Dic₂₈₁	1	1	yes	characteristic
32	C₄	C₂×#14555886	1	1	yes	characteristic
33	C₂	C₄×#14555886	1	1	yes	characteristic
34	C₂	C₂×#17985113	1	2	yes	—

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

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