Subgroups — #31771531

Order 17216.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22575522	C₂	1	2	yes	maximal
2	C₁₆×D₂₆₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11761640	—	2	2	no	—
4	C₈×D₂₆₉	C₂²	1	1	yes	characteristic
5	#16864377	C₄	1	1	yes	characteristic, complemented
6	C₁₆×C₂₆₉	C₄	1	1	yes	characteristic, complemented
7	C₂×#11761640	—	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	D₈	1	1	yes	characteristic
12	#11761640	—	8	2	no	—
13	C₄×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
14	Dic₂₆₉	Q₁₆	1	1	yes	characteristic
15	C₂×C₂₆₉	#107	1	1	yes	characteristic
16	D₂₆₉	D₁₆	1	1	yes	characteristic
17	D₂₆₉	Q₃₂	1	1	yes	characteristic
18	C₂₆₉	#366	1	1	yes	characteristic, complemented, Sylow
19	#366	—	269	1	no	maximal, Sylow
20	C₂×C₁₆	—	269	1	no	—
21	#107	—	269	2	no	—
22	C₂×C₈	—	269	1	no	—
23	C₄⋊C₄	—	538	2	no	—
24	C₁₆	—	269	1	no	—
25	C₁₆	#11761640	1	1	yes	characteristic, complemented
26	C₂×C₄	—	269	1	no	—
27	C₂×C₄	—	1076	2	no	—
28	C₈	—	269	1	no	—
29	C₈	C₂×#11761640	1	1	yes	characteristic
30	C₂²	—	269	1	no	—
31	C₄	—	269	1	no	—
32	C₄	—	2152	2	no	—
33	C₄	C₄⋊#11761640	1	1	yes	characteristic
34	C₂	—	269	1	no	—
35	C₂	—	269	1	no	—
36	C₂	#22575522	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.