Subgroups — #46826048

Order 34432.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771533	C₂	1	2	yes	maximal
2	C₃₂×D₂₆₉	C₂	1	1	yes	maximal, characteristic
3	#22575524	—	2	2	no	—
4	C₁₆×D₂₆₉	C₂²	1	1	yes	characteristic
5	#22575359	C₄	1	1	yes	characteristic
6	C₃₂×C₂₆₉	C₄	1	1	yes	characteristic
7	#16864412	—	4	2	no	—
8	C₈×D₂₆₉	D₄	1	1	yes	characteristic
9	#16864377	Q₈	1	1	yes	characteristic
10	C₁₆×C₂₆₉	C₂×C₄	1	1	yes	characteristic
11	#14524137	—	8	2	no	—
12	C₄×D₂₆₉	D₈	1	1	yes	characteristic
13	#14524130	Q₁₆	1	1	yes	characteristic
14	C₈×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
15	C₂×D₂₆₉	Q₃₂	1	1	yes	characteristic
16	C₄×C₂₆₉	#107	1	1	yes	characteristic
17	Dic₂₆₉	D₁₆	1	1	yes	characteristic
18	C₂×C₂₆₉	#366	1	1	yes	characteristic
19	D₂₆₉	—	2	1	no	—
20	C₂₆₉	#1425	1	1	yes	characteristic, complemented, Sylow
21	#1425	—	269	1	no	maximal, Sylow
22	C₂×C₃₂	—	269	1	no	—
23	#368	—	269	2	no	—
24	C₂×C₁₆	—	269	1	no	—
25	#108	—	538	2	no	—
26	C₃₂	—	269	1	no	—
27	C₃₂	#11761640	1	1	yes	characteristic
28	M₁₆	—	1076	2	no	—
29	C₂×C₈	—	269	1	no	—
30	C₁₆	—	269	1	no	—
31	C₁₆	C₂×#11761640	1	1	yes	characteristic
32	C₂×C₄	—	269	1	no	—
33	C₈	—	269	1	no	—
34	C₈	—	2152	2	no	—
35	C₈	C₄⋊#11761640	1	1	yes	characteristic
36	C₂²	—	269	1	no	—
37	C₄	—	269	1	no	—
38	C₄	#22575522	1	1	yes	characteristic
39	C₂	—	538	1	no	—
40	C₂	#31771531	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. C₂₆₉	#1425	semidirect

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