Subgroups — #31771528

Order 17216.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22575527	C₂	1	2	yes	maximal
2	C₄×#14524130	C₂	1	1	yes	maximal, characteristic
3	#16864405	—	2	2	no	—
4	C₂×#14524130	C₄	1	1	yes	characteristic
5	C₂×#14524130	C₂²	1	1	yes	characteristic
6	C₄²×C₂₆₉	C₄	1	1	yes	characteristic
7	#14524130	C₈	1	2	yes	—
8	#14524130	D₄	1	1	yes	characteristic
9	#14524130	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₂₆₉	—	2	1	no	—
11	C₂×C₄×C₂₆₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₂₆₉	M₁₆	1	1	yes	characteristic
13	C₄×C₂₆₉	—	2	2	no	—
14	C₄×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₂₆₉	C₂×C₈	1	1	yes	characteristic
16	C₂×C₂₆₉	—	2	1	no	—
17	C₂×C₂₆₉	C₄⋊C₈	1	1	yes	characteristic
18	C₂₆₉	#364	1	1	yes	characteristic, complemented, Sylow
19	#364	—	269	1	no	maximal, Sylow
20	M₃₂	—	269	2	no	—
21	C₄×C₈	—	269	1	no	—
22	C₂×C₈	—	269	1	no	—
23	C₂×C₈	—	269	1	no	—
24	C₄²	#11761640	1	1	yes	characteristic
25	C₁₆	—	538	2	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂×#11761640	1	1	yes	characteristic
28	C₈	—	269	1	no	—
29	C₈	—	269	1	no	—
30	C₈	—	269	2	no	—
31	C₂²	#16864411	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₄⋊#11761640	1	1	yes	characteristic
34	C₄	D₂₆₉⋊C₈	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#22575520	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
18. C₂₆₉	#364	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.