Subgroups — #31770431

Order 17216.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22575387	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₂₆₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₂₆₉	—	2	2	no	—
4	C₂×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
5	C₁₆×C₂₆₉	C₄	1	2	yes	complemented
6	C₂×Dic₂₆₉	—	4	2	no	—
7	C₂×C₄×C₂₆₉	D₄	1	1	yes	characteristic
8	C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₆₉	Q₈	1	1	yes	characteristic
10	C₂²×C₂₆₉	D₈	1	1	yes	characteristic
11	C₄×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₂₆₉	Q₁₆	1	1	yes	characteristic
13	Dic₂₆₉	—	8	2	no	—
14	C₂×C₂₆₉	#107	1	1	yes	characteristic
15	C₂×C₂₆₉	D₁₆	1	1	yes	characteristic
16	C₂×C₂₆₉	Q₃₂	1	1	yes	characteristic
17	C₂₆₉	#366	1	1	yes	characteristic, complemented, Sylow
18	#366	—	269	1	no	maximal, Sylow
19	C₂×C₁₆	D₂₆₉	1	1	yes	characteristic
20	#107	—	269	2	no	—
21	C₂×C₈	C₂×D₂₆₉	1	1	yes	characteristic
22	C₄⋊C₄	—	538	2	no	—
23	C₁₆	Dic₂₆₉	1	2	yes	complemented
24	C₂×C₄	—	1076	2	no	—
25	C₂×C₄	D₁₀₇₆	1	1	yes	characteristic
26	C₈	C₂×Dic₂₆₉	1	1	yes	characteristic
27	C₈	Dic₅₃₈	1	1	yes	characteristic
28	C₂²	D₂₁₅₂	1	1	yes	characteristic
29	C₄	—	2152	2	no	—
30	C₄	C₄⋊Dic₂₆₉	1	1	yes	characteristic
31	C₄	Dic₁₀₇₆	1	1	yes	characteristic
32	C₂	#22575387	1	1	yes	characteristic
33	C₂	D₄₃₀₄	1	1	yes	characteristic
34	C₂	Dic₂₁₅₂	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.