Subgroups — #46826055

Order 34432.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771444	C₂	1	2	yes	maximal, complemented
2	C₃₂×D₂₆₉	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₂₆₉	C₄	1	1	yes	characteristic
4	#22575359	C₂²	1	1	yes	characteristic
5	C₃₂×C₂₆₉	C₄	1	1	yes	characteristic
6	C₈×D₂₆₉	C₈	1	1	yes	characteristic
7	#16864377	C₈	1	1	yes	characteristic
8	C₁₆×C₂₆₉	C₂×C₄	1	1	yes	characteristic
9	C₄×D₂₆₉	C₁₆	1	1	yes	characteristic
10	#14524130	C₁₆	1	1	yes	characteristic
11	C₈×C₂₆₉	C₂×C₈	1	1	yes	characteristic
12	C₂×D₂₆₉	C₃₂	1	1	yes	characteristic
13	C₄×C₂₆₉	C₂×C₁₆	1	1	yes	characteristic
14	Dic₂₆₉	C₃₂	1	1	yes	characteristic
15	C₂×C₂₆₉	C₂×C₃₂	1	1	yes	characteristic
16	D₂₆₉	—	2	1	no	—
17	C₂₆₉	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
18	M₁₂₈	—	269	1	no	maximal, Sylow
19	C₂×C₃₂	—	269	1	no	—
20	C₆₄	—	269	2	no	—
21	C₂×C₁₆	—	269	1	no	—
22	C₃₂	—	269	1	no	—
23	C₃₂	#11761640	1	1	yes	characteristic
24	C₂×C₈	—	269	1	no	—
25	C₁₆	—	269	1	no	—
26	C₁₆	C₂×#11761640	1	1	yes	characteristic
27	C₂×C₄	—	269	1	no	—
28	C₈	—	269	1	no	—
29	C₈	D₂₆₉⋊C₈	1	1	yes	characteristic
30	C₂²	—	269	1	no	—
31	C₄	—	269	1	no	—
32	C₄	D₂₆₉⋊C₁₆	1	1	yes	characteristic
33	C₂	—	538	1	no	—
34	C₂	D₂₆₉⋊C₃₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #31771444	C₂	semidirect
17. C₂₆₉	M₁₂₈	semidirect

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