Subgroups — #45688356

Order 33344.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30659778	C₂	1	1	yes	maximal, characteristic
2	#30659776	C₂	1	1	yes	maximal, characteristic
3	#30659647	C₂	1	1	yes	maximal, characteristic
4	#22552374	—	2	1	no	—
5	C₄⋊#14523438	—	2	1	no	—
6	C₈×D₅₂₁	C₂²	1	1	yes	characteristic
7	#22552339	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₅₂₁	C₄	1	1	yes	characteristic, complemented
9	C₂×#14523438	—	4	1	no	—
10	#16861967	—	4	1	no	—
11	C₄×D₅₂₁	D₄	1	1	yes	characteristic
12	#16861960	Q₈	1	1	yes	characteristic
13	C₈×C₅₂₁	C₂×C₄	1	1	yes	characteristic
14	C₂×D₅₂₁	SD₁₆	1	1	yes	characteristic
15	#14523438	—	8	1	no	—
16	C₄×C₅₂₁	C₄⋊C₄	1	1	yes	characteristic
17	Dic₅₂₁	SD₁₆	1	1	yes	characteristic
18	C₂×C₅₂₁	#106	1	1	yes	characteristic
19	D₅₂₁	—	2	1	no	—
20	C₅₂₁	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	521	1	no	maximal, Sylow
22	M₃₂	—	521	1	no	—
23	#108	—	521	1	no	—
24	#106	—	521	1	no	—
25	M₁₆	—	1042	1	no	—
26	C₂×C₈	—	521	1	no	—
27	C₄⋊C₄	—	1042	1	no	—
28	C₁₆	—	521	1	no	—
29	C₁₆	#14523438	1	1	yes	characteristic, complemented
30	C₂×C₄	—	521	1	no	—
31	C₂×C₄	—	2084	1	no	—
32	C₈	—	521	1	no	—
33	C₈	—	2084	1	no	—
34	C₈	C₂×#14523438	1	1	yes	characteristic
35	C₂²	—	521	1	no	—
36	C₄	—	521	1	no	—
37	C₄	—	4168	1	no	—
38	C₄	C₄⋊#14523438	1	1	yes	characteristic
39	C₂	—	1042	1	no	—
40	C₂	#30659776	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.