Subgroups — #31771663

Order 17216.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22575527	C₂	1	3	yes	maximal, complemented
2	C₂×#16864405	C₂	1	3	yes	maximal, complemented
3	#22575460	C₂	1	1	yes	maximal, characteristic
4	#16864405	C₂²	1	1	yes	characteristic
5	#16864405	C₂²	1	3	yes	—
6	#16864386	C₄	1	3	yes	—
7	C₂×#14524130	C₂²	1	3	yes	—
8	#41×C₂₆₉	C₄	1	1	yes	characteristic
9	#14524130	C₂×C₄	1	3	yes	—
10	#14524130	C₂³	1	1	yes	characteristic
11	Q₈×C₂₆₉	C₈	1	1	yes	characteristic
12	D₄×C₂₆₉	C₈	1	3	yes	—
13	C₂×C₄×C₂₆₉	C₂×C₄	1	3	yes	—
14	C₂²×C₂₆₉	C₂×C₈	1	3	yes	—
15	C₄×C₂₆₉	C₂×C₈	1	3	yes	—
16	C₄×C₂₆₉	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₂₆₉	—	2	3	no	—
18	C₂×C₂₆₉	C₂²×C₈	1	1	yes	characteristic
19	C₂₆₉	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	269	1	no	maximal, Sylow
21	#131	—	269	1	no	—
22	M₃₂	—	269	3	no	—
23	C₂×C₁₆	—	269	3	no	—
24	#41	#11761640	1	1	yes	characteristic
25	M₁₆	—	269	3	no	—
26	C₂×C₈	—	269	3	no	—
27	C₁₆	—	269	1	no	—
28	C₁₆	—	269	3	no	—
29	Q₈	#14524137	1	1	yes	characteristic
30	D₄	#14524137	1	3	yes	—
31	C₂×C₄	C₂×#11761640	1	3	yes	—
32	C₈	—	269	1	no	—
33	C₈	—	269	3	no	—
34	C₂²	C₂×#14524137	1	3	yes	—
35	C₄	C₂×#14524137	1	3	yes	—
36	C₄	C₂²×#11761640	1	1	yes	characteristic
37	C₂	—	2	3	no	—
38	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.