Subgroups — #32912701

Order 18272.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22603717	C₂	1	3	yes	maximal, complemented
2	C₂×C₅₇₁⋊C₈	C₂	1	3	yes	maximal, complemented
3	#41×C₅₇₁	C₂	1	1	yes	maximal, characteristic
4	C₅₇₁⋊C₈	C₂²	1	1	yes	characteristic
5	C₅₇₁⋊C₈	C₂²	1	3	yes	—
6	Q₈×C₅₇₁	C₄	1	1	yes	characteristic
7	D₄×C₅₇₁	C₄	1	3	yes	—
8	C₂×C₄×C₅₇₁	C₂²	1	3	yes	—
9	C₂²×C₅₇₁	C₂×C₄	1	3	yes	—
10	C₄×C₅₇₁	C₂×C₄	1	3	yes	—
11	C₄×C₅₇₁	C₂³	1	1	yes	characteristic
12	C₂×C₅₇₁	—	2	3	no	—
13	C₂×C₅₇₁	C₂²×C₄	1	1	yes	characteristic
14	C₅₇₁	#131	1	1	yes	characteristic, complemented, Sylow
15	#131	—	571	1	no	maximal, Sylow
16	#41	D₅₇₁	1	1	yes	characteristic
17	M₁₆	—	571	3	no	—
18	C₂×C₈	—	571	3	no	—
19	Q₈	Dic₅₇₁	1	1	yes	characteristic
20	D₄	Dic₅₇₁	1	3	yes	—
21	C₂×C₄	C₂×D₅₇₁	1	3	yes	—
22	C₈	—	571	1	no	—
23	C₈	—	571	3	no	—
24	C₂²	C₂×Dic₅₇₁	1	3	yes	—
25	C₄	C₂×Dic₅₇₁	1	3	yes	—
26	C₄	C₂²×D₅₇₁	1	1	yes	characteristic
27	C₂	—	2	3	no	—
28	C₂	C₂²×Dic₅₇₁	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.