Subgroups — C₂³×#14524137 #31771675

Order 17216.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14524137	C₂	1	14	yes	maximal, direct product factor
2	C₂³×Dic₂₆₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#14524137	C₂²	1	28	yes	direct product factor
4	C₂²×Dic₂₆₉	C₄	1	7	yes	—
5	C₂²×Dic₂₆₉	C₂²	1	7	yes	—
6	C₂⁴×C₂₆₉	C₄	1	1	yes	characteristic
7	#14524137	C₂³	1	8	yes	direct product factor
8	C₂×Dic₂₆₉	C₂×C₄	1	21	yes	—
9	C₂×Dic₂₆₉	C₂³	1	7	yes	—
10	C₂³×C₂₆₉	C₈	1	8	yes	complemented
11	C₂³×C₂₆₉	C₂×C₄	1	7	yes	—
12	C₂²×C₂₆₉	C₂×C₈	1	28	yes	complemented
13	C₂²×C₂₆₉	C₂²×C₄	1	7	yes	—
14	Dic₂₆₉	C₂²×C₄	1	7	yes	—
15	Dic₂₆₉	C₂⁴	1	1	yes	characteristic
16	C₂×C₂₆₉	C₂²×C₈	1	14	yes	complemented
17	C₂×C₂₆₉	C₂³×C₄	1	1	yes	characteristic
18	C₂₆₉	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂³×C₈	—	269	1	no	maximal, Sylow
20	C₂³×C₄	—	269	1	no	—
21	C₂²×C₈	—	269	14	no	—
22	C₂⁴	#11761640	1	1	yes	characteristic
23	C₂²×C₄	—	269	7	no	—
24	C₂²×C₄	—	269	7	no	—
25	C₂×C₈	—	269	28	no	—
26	C₂³	#14524137	1	8	yes	direct product factor
27	C₂³	C₂×#11761640	1	7	yes	—
28	C₂×C₄	—	269	7	no	—
29	C₂×C₄	—	269	21	no	—
30	C₈	—	269	8	no	—
31	C₂²	C₂×#14524137	1	28	yes	direct product factor
32	C₂²	C₂²×#11761640	1	7	yes	—
33	C₄	—	269	1	no	—
34	C₄	—	269	7	no	—
35	C₂	C₂²×#14524137	1	14	yes	direct product factor
36	C₂	C₂³×#11761640	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.