Subgroups — #31773727

Order 17344.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22576096	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₂₇₁	C₂	1	1	yes	maximal, characteristic
3	#16864638	—	2	2	no	—
4	C₂×C₈×C₂₇₁	C₂²	1	1	yes	characteristic
5	C₁₆×C₂₇₁	C₄	1	2	yes	—
6	C₂₇₁⋊C₈	—	4	2	no	—
7	C₂×C₄×C₂₇₁	D₄	1	1	yes	characteristic
8	C₈×C₂₇₁	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₇₁	Q₈	1	1	yes	characteristic
10	C₂²×C₂₇₁	Q₁₆	1	1	yes	characteristic
11	C₄×C₂₇₁	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₂₇₁	D₈	1	1	yes	characteristic
13	C₂×C₂₇₁	—	2	1	no	—
14	C₂×C₂₇₁	#107	1	1	yes	characteristic
15	C₂₇₁	#368	1	1	yes	characteristic, complemented, Sylow
16	#368	—	271	1	no	maximal, Sylow
17	C₂×C₁₆	D₂₇₁	1	1	yes	characteristic
18	#108	—	271	2	no	—
19	M₁₆	—	542	2	no	—
20	C₂×C₈	C₂×D₂₇₁	1	1	yes	characteristic
21	C₁₆	Dic₂₇₁	1	2	yes	—
22	C₂×C₄	D₁₀₈₄	1	1	yes	characteristic
23	C₈	—	1084	2	no	—
24	C₈	C₂×Dic₂₇₁	1	1	yes	characteristic
25	C₈	Dic₅₄₂	1	1	yes	characteristic
26	C₂²	Dic₁₀₈₄	1	1	yes	characteristic
27	C₄	C₄⋊Dic₂₇₁	1	1	yes	characteristic
28	C₄	D₂₁₆₈	1	1	yes	characteristic
29	C₂	—	2	1	no	—
30	C₂	#22576094	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₂₇₁	#368	semidirect

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