Subgroups — #31771538

Order 17216.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22575503	C₂	1	2	yes	maximal, complemented
2	C₁₆×D₂₆₉	C₂	1	1	yes	maximal, characteristic
3	C₈×D₂₆₉	C₄	1	1	yes	characteristic
4	#16864377	C₂²	1	1	yes	characteristic
5	C₁₆×C₂₆₉	C₄	1	1	yes	characteristic
6	C₄×D₂₆₉	C₈	1	1	yes	characteristic
7	#14524130	C₈	1	1	yes	characteristic
8	C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
9	C₂×D₂₆₉	C₁₆	1	1	yes	characteristic
10	C₄×C₂₆₉	C₂×C₈	1	1	yes	characteristic
11	Dic₂₆₉	C₁₆	1	1	yes	characteristic
12	C₂×C₂₆₉	C₂×C₁₆	1	1	yes	characteristic
13	D₂₆₉	—	2	1	no	—
14	C₂₆₉	M₆₄	1	1	yes	characteristic, complemented, Sylow
15	M₆₄	—	269	1	no	maximal, Sylow
16	C₂×C₁₆	—	269	1	no	—
17	C₃₂	—	269	2	no	—
18	C₂×C₈	—	269	1	no	—
19	C₁₆	—	269	1	no	—
20	C₁₆	#11761640	1	1	yes	characteristic
21	C₂×C₄	—	269	1	no	—
22	C₈	—	269	1	no	—
23	C₈	C₂×#11761640	1	1	yes	characteristic
24	C₂²	—	269	1	no	—
25	C₄	—	269	1	no	—
26	C₄	D₂₆₉⋊C₈	1	1	yes	characteristic
27	C₂	—	538	1	no	—
28	C₂	D₂₆₉⋊C₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #22575503	C₂	semidirect
14. C₂₆₉	M₆₄	semidirect

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