Subgroups — #45688322

Order 33344.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30659783	C₂	1	1	yes	maximal, characteristic
2	#30659762	C₂	1	1	yes	maximal, characteristic
3	#30659647	C₂	1	1	yes	maximal, characteristic
4	#22552372	C₄	1	1	yes	characteristic
5	C₄×#14523438	C₄	1	1	yes	characteristic
6	#22552367	C₄	1	2	yes	complemented
7	C₈×D₅₂₁	C₂²	1	1	yes	characteristic
8	#22552339	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₅₂₁	C₄	1	1	yes	characteristic, complemented
10	C₂×#14523438	—	2	1	no	—
11	#16861967	—	2	1	no	—
12	C₄×D₅₂₁	C₂×C₄	1	1	yes	characteristic
13	#16861960	C₂×C₄	1	1	yes	characteristic
14	C₈×C₅₂₁	C₂×C₄	1	1	yes	characteristic
15	C₂×D₅₂₁	M₁₆	1	1	yes	characteristic
16	#14523438	—	4	1	no	—
17	C₄×C₅₂₁	C₄²	1	1	yes	characteristic
18	Dic₅₂₁	M₁₆	1	1	yes	characteristic
19	C₂×C₅₂₁	#97	1	1	yes	characteristic
20	D₅₂₁	—	2	1	no	—
21	C₅₂₁	#347	1	1	yes	characteristic, complemented, Sylow
22	#347	—	521	1	no	maximal, Sylow
23	M₃₂	—	521	1	no	—
24	M₃₂	—	521	1	no	—
25	#97	—	521	1	no	—
26	C₂×C₈	—	521	1	no	—
27	C₂×C₈	—	521	1	no	—
28	C₄²	—	521	1	no	—
29	C₁₆	—	521	2	no	—
30	C₁₆	—	521	1	no	—
31	C₁₆	#14523438	1	1	yes	characteristic, complemented
32	C₂×C₄	—	521	1	no	—
33	C₂×C₄	—	1042	1	no	—
34	C₈	—	521	1	no	—
35	C₈	—	1042	1	no	—
36	C₈	C₂×#14523438	1	1	yes	characteristic
37	C₂²	—	521	1	no	—
38	C₄	—	521	1	no	—
39	C₄	—	2084	1	no	—
40	C₄	C₄×#14523438	1	1	yes	characteristic
41	C₂	—	1042	1	no	—
42	C₂	#30659762	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.