Subgroups — #31773721

Order 17344.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22576100	C₂	1	1	yes	maximal, characteristic
2	#22576092	C₂	1	1	yes	maximal, characteristic
3	#108×C₂₇₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₂₇₁	—	2	1	no	—
5	C₂₇₁⋊C₁₆	C₄	1	2	yes	complemented
6	M₁₆×C₂₇₁	—	2	1	no	—
7	C₂×C₈×C₂₇₁	C₂²	1	1	yes	characteristic
8	C₂×Dic₂₇₁	—	4	1	no	—
9	C₂×C₄×C₂₇₁	D₄	1	1	yes	characteristic
10	C₈×C₂₇₁	—	4	1	no	—
11	C₈×C₂₇₁	C₂×C₄	1	1	yes	characteristic
12	C₈×C₂₇₁	Q₈	1	1	yes	characteristic
13	C₂²×C₂₇₁	SD₁₆	1	1	yes	characteristic
14	C₄×C₂₇₁	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₂₇₁	SD₁₆	1	1	yes	characteristic
16	Dic₂₇₁	—	8	1	no	—
17	C₂×C₂₇₁	—	2	1	no	—
18	C₂×C₂₇₁	#106	1	1	yes	characteristic
19	C₂₇₁	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	271	1	no	maximal, Sylow
21	M₃₂	—	271	1	no	—
22	#108	D₂₇₁	1	1	yes	characteristic
23	#106	—	271	1	no	—
24	M₁₆	—	2	1	no	—
25	C₂×C₈	C₂×D₂₇₁	1	1	yes	characteristic
26	C₄⋊C₄	—	542	1	no	—
27	C₁₆	—	271	2	no	—
28	C₂×C₄	—	1084	1	no	—
29	C₂×C₄	C₂²⋊D₂₇₁	1	1	yes	characteristic
30	C₈	—	4	1	no	—
31	C₈	C₄×D₂₇₁	1	1	yes	characteristic
32	C₈	Dic₅₄₂	1	1	yes	characteristic
33	C₂²	#16864641	1	1	yes	characteristic
34	C₄	—	2168	1	no	—
35	C₄	Dic₂₇₁⋊C₄	1	1	yes	characteristic
36	C₄	#16864642	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#22576091	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₂₇₁⋊C₁₆	C₄	semidirect
19. C₂₇₁	#365	semidirect

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