Subgroups — #31771532

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	SD₃₂	1	2	yes	—
17	C₂₆₉	#367	1	1	yes	characteristic, complemented, Sylow
18	#367	—	269	1	no	maximal, Sylow
19	C₂×C₁₆	—	269	1	no	—
20	#107	—	269	2	no	—
21	C₂×C₈	—	269	1	no	—
22	C₄⋊C₄	—	538	2	no	—
23	C₁₆	—	269	1	no	—
24	C₁₆	#11761640	1	1	yes	characteristic, complemented
25	C₂×C₄	—	269	1	no	—
26	C₂×C₄	—	1076	2	no	—
27	C₈	—	269	1	no	—
28	C₈	C₂×#11761640	1	1	yes	characteristic
29	C₂²	—	269	1	no	—
30	C₄	—	269	1	no	—
31	C₄	—	2152	2	no	—
32	C₄	C₄⋊#11761640	1	1	yes	characteristic
33	C₂	—	269	2	no	—
34	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.