Subgroups — #36378713

Order 22592.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26015061	C₂	1	2	yes	maximal
2	C₁₆×D₃₅₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#13083443	—	2	2	no	—
4	C₈×D₃₅₃	C₂²	1	1	yes	characteristic
5	#19150712	C₄	1	1	yes	characteristic, complemented
6	C₁₆×C₃₅₃	C₄	1	1	yes	characteristic, complemented
7	C₂×#13083443	—	4	2	no	—
8	C₄×D₃₅₃	D₄	1	1	yes	characteristic
9	#15667725	Q₈	1	1	yes	characteristic
10	C₈×C₃₅₃	C₂×C₄	1	1	yes	characteristic
11	C₂×D₃₅₃	D₈	1	1	yes	characteristic
12	#13083443	—	8	2	no	—
13	C₄×C₃₅₃	C₄⋊C₄	1	1	yes	characteristic
14	Dic₃₅₃	Q₁₆	1	1	yes	characteristic
15	C₂×C₃₅₃	#107	1	1	yes	characteristic
16	D₃₅₃	D₁₆	1	1	yes	characteristic
17	D₃₅₃	Q₃₂	1	1	yes	characteristic
18	C₃₅₃	#366	1	1	yes	characteristic, complemented, Sylow
19	#366	—	353	1	no	maximal, Sylow
20	C₂×C₁₆	—	353	1	no	—
21	#107	—	353	2	no	—
22	C₂×C₈	—	353	1	no	—
23	C₄⋊C₄	—	706	2	no	—
24	C₁₆	—	353	1	no	—
25	C₁₆	#13083443	1	1	yes	characteristic, complemented
26	C₂×C₄	—	353	1	no	—
27	C₂×C₄	—	1412	2	no	—
28	C₈	—	353	1	no	—
29	C₈	C₂×#13083443	1	1	yes	characteristic
30	C₂²	—	353	1	no	—
31	C₄	—	2824	2	no	—
32	C₄	—	353	1	no	—
33	C₄	C₄⋊#13083443	1	1	yes	characteristic
34	C₂	—	353	1	no	—
35	C₂	—	353	1	no	—
36	C₂	#26015061	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.