Subgroups — #45688521

Order 33344.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#16861969	C₂	1	2	yes	maximal
2	C₈×#14523438	C₂	1	1	yes	maximal, characteristic
3	C₂×#16861969	—	2	2	no	—
4	#22552372	C₄	1	1	yes	characteristic
5	C₄×#14523438	C₂²	1	1	yes	characteristic
6	C₈×D₅₂₁	C₄	1	1	yes	characteristic
7	#16861969	—	4	2	no	—
8	C₂×#14523438	D₄	1	1	yes	characteristic
9	C₂×#14523438	Q₈	1	1	yes	characteristic
10	#16861967	—	2	1	no	—
11	C₄×D₅₂₁	C₂×C₄	1	1	yes	characteristic
12	#16861960	C₈	1	1	yes	characteristic, complemented
13	C₈×C₅₂₁	C₈	1	1	yes	characteristic, complemented
14	C₂×D₅₂₁	C₄⋊C₄	1	1	yes	characteristic
15	#14523438	—	2	1	no	—
16	#14523438	SD₁₆	1	2	yes	—
17	C₄×C₅₂₁	C₂×C₈	1	1	yes	characteristic
18	Dic₅₂₁	M₁₆	1	1	yes	characteristic
19	C₂×C₅₂₁	C₄⋊C₈	1	1	yes	characteristic
20	D₅₂₁	#106	1	1	yes	characteristic
21	D₅₂₁	#108	1	1	yes	characteristic
22	C₅₂₁	#334	1	1	yes	characteristic, complemented, Sylow
23	#334	—	521	1	no	maximal, Sylow
24	C₄⋊C₈	—	521	2	no	—
25	C₄×C₈	—	521	1	no	—
26	C₂×C₈	—	521	1	no	—
27	C₂×C₈	—	521	1	no	—
28	C₂×C₈	—	1042	2	no	—
29	C₄²	—	521	1	no	—
30	C₂×C₄	—	521	1	no	—
31	C₂×C₄	—	521	1	no	—
32	C₂×C₄	—	521	1	no	—
33	C₈	—	521	1	no	—
34	C₈	—	1042	1	no	—
35	C₈	—	2084	2	no	—
36	C₈	#16861969	1	1	yes	characteristic, complemented
37	C₂²	—	521	1	no	—
38	C₄	—	521	2	no	—
39	C₄	—	521	1	no	—
40	C₄	—	1042	1	no	—
41	C₄	C₂×#16861969	1	1	yes	characteristic
42	C₂	—	521	1	no	—
43	C₂	—	521	1	no	—
44	C₂	C₄⋊#16861969	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.