Subgroups — #31771533

Order 17216.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22575524	C₂	1	2	yes	maximal
2	C₁₆×D₂₆₉	C₂	1	1	yes	maximal, characteristic
3	#16864412	—	2	2	no	—
4	C₈×D₂₆₉	C₂²	1	1	yes	characteristic
5	#16864377	C₄	1	1	yes	characteristic
6	C₁₆×C₂₆₉	C₄	1	1	yes	characteristic
7	#14524137	—	4	2	no	—
8	C₄×D₂₆₉	D₄	1	1	yes	characteristic
9	#14524130	Q₈	1	1	yes	characteristic
10	C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
11	C₂×D₂₆₉	Q₁₆	1	1	yes	characteristic
12	C₄×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
13	Dic₂₆₉	D₈	1	1	yes	characteristic
14	C₂×C₂₆₉	#107	1	1	yes	characteristic
15	D₂₆₉	—	2	1	no	—
16	C₂₆₉	#368	1	1	yes	characteristic, complemented, Sylow
17	#368	—	269	1	no	maximal, Sylow
18	C₂×C₁₆	—	269	1	no	—
19	#108	—	269	2	no	—
20	M₁₆	—	538	2	no	—
21	C₂×C₈	—	269	1	no	—
22	C₁₆	—	269	1	no	—
23	C₁₆	#11761640	1	1	yes	characteristic
24	C₂×C₄	—	269	1	no	—
25	C₈	—	269	1	no	—
26	C₈	—	1076	2	no	—
27	C₈	C₂×#11761640	1	1	yes	characteristic
28	C₂²	—	269	1	no	—
29	C₄	—	269	1	no	—
30	C₄	C₄⋊#11761640	1	1	yes	characteristic
31	C₂	—	538	1	no	—
32	C₂	#22575522	1	1	yes	characteristic

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

N	H ≅ G/N	type
16. C₂₆₉	#368	semidirect

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