Subgroups — #31773736

Order 17344.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₁₆₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₃₃₆	C₂	1	1	yes	maximal, characteristic
3	C₃₂×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₁₀₈₄	—	2	1	no	—
5	D₂₁₆₈	—	2	1	no	—
6	C₁₆×C₂₇₁	C₂²	1	1	yes	characteristic
7	Dic₅₄₂	—	4	1	no	—
8	D₁₀₈₄	—	4	1	no	—
9	C₈×C₂₇₁	D₄	1	1	yes	characteristic
10	C₂×D₂₇₁	—	8	1	no	—
11	C₄×C₂₇₁	D₈	1	1	yes	characteristic
12	Dic₂₇₁	—	8	1	no	—
13	C₂×C₂₇₁	D₁₆	1	1	yes	characteristic
14	D₂₇₁	—	16	1	no	—
15	C₂₇₁	SD₆₄	1	1	yes	characteristic, complemented, Sylow
16	SD₆₄	—	271	1	no	maximal, Sylow
17	Q₃₂	—	271	1	no	—
18	D₁₆	—	271	1	no	—
19	C₃₂	D₂₇₁	1	1	yes	characteristic, complemented
20	Q₁₆	—	542	1	no	—
21	D₈	—	542	1	no	—
22	C₁₆	C₂×D₂₇₁	1	1	yes	characteristic
23	Q₈	—	1084	1	no	—
24	D₄	—	1084	1	no	—
25	C₈	D₁₀₈₄	1	1	yes	characteristic
26	C₂²	—	2168	1	no	—
27	C₄	—	2168	1	no	—
28	C₄	D₂₁₆₈	1	1	yes	characteristic
29	C₂	—	4336	1	no	—
30	C₂	D₄₃₃₆	1	1	yes	characteristic

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.