Subgroups — #36378204

Order 22592.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26014932	C₂	1	3	yes	maximal, complemented
2	C₂×#19150712	C₂	1	3	yes	maximal, complemented
3	#131×C₃₅₃	C₂	1	1	yes	maximal, characteristic
4	#19150712	C₂²	1	1	yes	characteristic
5	#19150712	C₂²	1	3	yes	—
6	#41×C₃₅₃	C₄	1	1	yes	characteristic
7	M₁₆×C₃₅₃	C₄	1	3	yes	—
8	C₂×C₈×C₃₅₃	C₂²	1	3	yes	—
9	Q₈×C₃₅₃	C₈	1	1	yes	characteristic
10	D₄×C₃₅₃	C₈	1	3	yes	—
11	C₂×C₄×C₃₅₃	C₂×C₄	1	3	yes	—
12	C₈×C₃₅₃	C₂×C₄	1	3	yes	—
13	C₈×C₃₅₃	C₂³	1	1	yes	characteristic
14	C₂²×C₃₅₃	C₂×C₈	1	3	yes	—
15	C₄×C₃₅₃	C₂×C₈	1	3	yes	—
16	C₄×C₃₅₃	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₃₅₃	—	2	3	no	—
18	C₂×C₃₅₃	C₂²×C₈	1	1	yes	characteristic
19	C₃₅₃	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	353	1	no	maximal, Sylow
21	#131	D₃₅₃	1	1	yes	characteristic
22	M₃₂	—	353	3	no	—
23	C₂×C₁₆	—	353	3	no	—
24	#41	Dic₃₅₃	1	1	yes	characteristic
25	M₁₆	Dic₃₅₃	1	3	yes	—
26	C₂×C₈	C₂×D₃₅₃	1	3	yes	—
27	C₁₆	—	353	1	no	—
28	C₁₆	—	353	3	no	—
29	Q₈	#15667725	1	1	yes	characteristic
30	D₄	#15667725	1	3	yes	—
31	C₂×C₄	C₂×Dic₃₅₃	1	3	yes	—
32	C₈	C₂×Dic₃₅₃	1	3	yes	—
33	C₈	C₂²×D₃₅₃	1	1	yes	characteristic
34	C₂²	C₂×#15667725	1	3	yes	—
35	C₄	C₂×#15667725	1	3	yes	—
36	C₄	C₂²×Dic₃₅₃	1	1	yes	characteristic
37	C₂	—	2	3	no	—
38	C₂	C₂²×#15667725	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.