Subgroups — C₂⁴×#11761640 #31771686

Order 17216.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11761640	C₂	1	30	yes	maximal, direct product factor
2	C₂⁴×D₂₆₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#11761640	C₂²	1	140	yes	direct product factor
4	C₂³×D₂₆₉	C₄	1	15	yes	complemented
5	C₂³×D₂₆₉	C₂²	1	15	yes	—
6	C₂⁴×C₂₆₉	C₄	1	1	yes	characteristic, complemented
7	C₂×#11761640	C₂³	1	120	yes	direct product factor
8	C₂²×D₂₆₉	C₂×C₄	1	105	yes	complemented
9	C₂²×D₂₆₉	C₂³	1	35	yes	—
10	C₂³×C₂₆₉	C₂×C₄	1	15	yes	complemented
11	C₂²×C₂₆₉	C₂²×C₄	1	35	yes	complemented
12	C₂×D₂₆₉	C₂²×C₄	1	105	yes	complemented
13	C₂×D₂₆₉	C₂⁴	1	15	yes	—
14	#11761640	C₂⁴	1	16	yes	direct product factor
15	C₂×C₂₆₉	C₂³×C₄	1	15	yes	complemented
16	D₂₆₉	C₂³×C₄	1	15	yes	complemented
17	D₂₆₉	C₂⁵	1	1	yes	characteristic
18	C₂₆₉	C₂⁴×C₄	1	1	yes	characteristic, complemented, Sylow
19	C₂⁴×C₄	—	269	1	no	maximal, Sylow
20	C₂⁵	—	269	1	no	—
21	C₂³×C₄	—	269	30	no	—
22	C₂⁴	—	269	15	no	—
23	C₂⁴	—	269	15	no	—
24	C₂⁴	#11761640	1	1	yes	characteristic, direct product factor
25	C₂²×C₄	—	269	140	no	—
26	C₂³	—	269	35	no	—
27	C₂³	—	269	105	no	—
28	C₂³	C₂×#11761640	1	15	yes	direct product factor
29	C₂×C₄	—	269	120	no	—
30	C₂²	—	269	15	no	—
31	C₂²	—	269	105	no	—
32	C₂²	C₂²×#11761640	1	35	yes	direct product factor
33	C₄	—	269	16	no	—
34	C₂	—	269	1	no	—
35	C₂	—	269	15	no	—
36	C₂	C₂³×#11761640	1	15	yes	direct product factor

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.