Subgroups — #45687849

Order 33344.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30659648	C₂	1	3	yes	maximal, complemented
2	C₂×#22552339	C₂	1	3	yes	maximal, complemented
3	#131×C₅₂₁	C₂	1	1	yes	maximal, characteristic
4	#22552339	C₂²	1	1	yes	characteristic
5	#22552339	C₂²	1	3	yes	—
6	#41×C₅₂₁	C₄	1	1	yes	characteristic
7	M₁₆×C₅₂₁	C₄	1	3	yes	—
8	C₂×C₈×C₅₂₁	C₂²	1	3	yes	—
9	Q₈×C₅₂₁	C₈	1	1	yes	characteristic
10	D₄×C₅₂₁	C₈	1	3	yes	—
11	C₂×C₄×C₅₂₁	C₂×C₄	1	3	yes	—
12	C₈×C₅₂₁	C₂×C₄	1	3	yes	—
13	C₈×C₅₂₁	C₂³	1	1	yes	characteristic
14	C₂²×C₅₂₁	C₂×C₈	1	3	yes	—
15	C₄×C₅₂₁	C₂×C₈	1	3	yes	—
16	C₄×C₅₂₁	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₅₂₁	—	2	3	no	—
18	C₂×C₅₂₁	C₂²×C₈	1	1	yes	characteristic
19	C₅₂₁	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	521	1	no	maximal, Sylow
21	#131	D₅₂₁	1	1	yes	characteristic
22	M₃₂	—	521	3	no	—
23	C₂×C₁₆	—	521	3	no	—
24	#41	Dic₅₂₁	1	1	yes	characteristic
25	M₁₆	Dic₅₂₁	1	3	yes	—
26	C₂×C₈	C₂×D₅₂₁	1	3	yes	—
27	C₁₆	—	521	1	no	—
28	C₁₆	—	521	3	no	—
29	Q₈	#16861960	1	1	yes	characteristic
30	D₄	#16861960	1	3	yes	—
31	C₂×C₄	C₂×Dic₅₂₁	1	3	yes	—
32	C₈	C₂×Dic₅₂₁	1	3	yes	—
33	C₈	C₂²×D₅₂₁	1	1	yes	characteristic
34	C₂²	C₂×#16861960	1	3	yes	—
35	C₄	C₂×#16861960	1	3	yes	—
36	C₄	C₂²×Dic₅₂₁	1	1	yes	characteristic
37	C₂	—	2	3	no	—
38	C₂	C₂²×#16861960	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.