Subgroups — #46826046

Order 34432.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771531	C₂	1	2	yes	maximal
2	C₃₂×D₂₆₉	C₂	1	1	yes	maximal, characteristic
3	#22575522	—	2	2	no	—
4	C₁₆×D₂₆₉	C₂²	1	1	yes	characteristic
5	#22575359	C₄	1	1	yes	characteristic, complemented
6	C₃₂×C₂₆₉	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#11761640	—	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	C₂×#11761640	—	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	D₁₆	1	1	yes	characteristic
16	#11761640	—	16	2	no	—
17	C₄×C₂₆₉	#107	1	1	yes	characteristic
18	Dic₂₆₉	Q₃₂	1	1	yes	characteristic
19	C₂×C₂₆₉	#366	1	1	yes	characteristic
20	D₂₆₉	D₃₂	1	1	yes	characteristic
21	D₂₆₉	Q₆₄	1	1	yes	characteristic
22	C₂₆₉	#1423	1	1	yes	characteristic, complemented, Sylow
23	#1423	—	269	1	no	maximal, Sylow
24	C₂×C₃₂	—	269	1	no	—
25	#366	—	269	2	no	—
26	C₂×C₁₆	—	269	1	no	—
27	#107	—	538	2	no	—
28	C₃₂	—	269	1	no	—
29	C₃₂	#11761640	1	1	yes	characteristic, complemented
30	C₂×C₈	—	269	1	no	—
31	C₄⋊C₄	—	1076	2	no	—
32	C₁₆	—	269	1	no	—
33	C₁₆	C₂×#11761640	1	1	yes	characteristic
34	C₂×C₄	—	269	1	no	—
35	C₂×C₄	—	2152	2	no	—
36	C₈	—	269	1	no	—
37	C₈	C₄⋊#11761640	1	1	yes	characteristic
38	C₂²	—	269	1	no	—
39	C₄	—	269	1	no	—
40	C₄	—	4304	2	no	—
41	C₄	#22575522	1	1	yes	characteristic
42	C₂	—	269	1	no	—
43	C₂	—	269	1	no	—
44	C₂	#31771531	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.