Subgroups — C₂²×#16864405 #31771658

Order 17216.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16864405	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#14524130	C₂	1	1	yes	maximal, characteristic
3	#16864405	C₂²	1	4	yes	direct product factor
4	C₂×#14524130	C₄	1	3	yes	—
5	C₂×#14524130	C₂²	1	3	yes	—
6	C₂²×C₄×C₂₆₉	C₄	1	1	yes	characteristic
7	#14524130	C₂×C₄	1	3	yes	—
8	#14524130	C₂³	1	1	yes	characteristic
9	C₂³×C₂₆₉	C₈	1	1	yes	characteristic
10	C₂×C₄×C₂₆₉	C₈	1	3	yes	—
11	C₂×C₄×C₂₆₉	C₂×C₄	1	3	yes	—
12	C₂²×C₂₆₉	C₁₆	1	4	yes	complemented
13	C₂²×C₂₆₉	C₂×C₈	1	3	yes	—
14	C₄×C₂₆₉	C₂×C₈	1	3	yes	—
15	C₄×C₂₆₉	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₂₆₉	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₂₆₉	C₂²×C₈	1	1	yes	characteristic
18	C₂₆₉	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₆	—	269	1	no	maximal, Sylow
20	C₂²×C₈	—	269	1	no	—
21	C₂×C₁₆	—	269	6	no	—
22	C₂²×C₄	#11761640	1	1	yes	characteristic
23	C₂×C₈	—	269	3	no	—
24	C₂×C₈	—	269	3	no	—
25	C₁₆	—	269	4	no	—
26	C₂³	#14524137	1	1	yes	characteristic
27	C₂×C₄	#14524137	1	3	yes	—
28	C₂×C₄	C₂×#11761640	1	3	yes	—
29	C₈	—	269	1	no	—
30	C₈	—	269	3	no	—
31	C₂²	#16864405	1	4	yes	direct product factor
32	C₂²	C₂×#14524137	1	3	yes	—
33	C₄	C₂×#14524137	1	3	yes	—
34	C₄	C₂²×#11761640	1	1	yes	characteristic
35	C₂	C₂×#16864405	1	6	yes	direct product factor
36	C₂	C₂²×#14524137	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.