Subgroups — #22576151

Order 8672.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Dic₂₇₁	C₂	1	2	yes	maximal
2	C₄⋊Dic₂₇₁	C₂	1	1	yes	maximal, characteristic
3	Dic₂₇₁⋊C₄	C₂	1	2	yes	maximal
4	C₄×Dic₂₇₁	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₄×C₂₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₇₁	C₂²	1	1	yes	characteristic
7	C₂×Dic₂₇₁	C₂²	1	1	yes	characteristic
8	C₂×Dic₂₇₁	C₂²	1	2	yes	—
9	C₂×C₄×C₂₇₁	C₂²	1	2	yes	—
10	C₂×C₄×C₂₇₁	C₂²	1	1	yes	characteristic
11	C₂²×C₂₇₁	C₂³	1	1	yes	characteristic
12	C₄×C₂₇₁	—	2	2	no	—
13	C₄×C₂₇₁	Q₈	1	2	yes	—
14	Dic₂₇₁	—	2	1	no	—
15	Dic₂₇₁	—	2	1	no	—
16	Dic₂₇₁	—	2	2	no	—
17	C₂×C₂₇₁	C₂×Q₈	1	1	yes	characteristic
18	C₂×C₂₇₁	#41	1	1	yes	characteristic
19	C₂×C₂₇₁	#41	1	1	yes	characteristic
20	C₂₇₁	#125	1	1	yes	characteristic, complemented, Sylow
21	#125	—	271	1	no	maximal, Sylow
22	C₄⋊C₄	—	271	2	no	—
23	C₄⋊C₄	—	271	2	no	—
24	C₄⋊C₄	—	271	1	no	—
25	C₄⋊C₄	D₂₇₁	1	1	yes	characteristic
26	C₄²	—	271	1	no	—
27	C₂×C₄	—	271	1	no	—
28	C₂×C₄	—	271	1	no	—
29	C₂×C₄	—	271	2	no	—
30	C₂×C₄	C₂×D₂₇₁	1	2	yes	—
31	C₂×C₄	C₂×D₂₇₁	1	1	yes	characteristic
32	C₂²	C₂²×D₂₇₁	1	1	yes	characteristic
33	C₄	—	2	2	no	—
34	C₄	—	542	1	no	—
35	C₄	—	542	1	no	—
36	C₄	—	542	2	no	—
37	C₄	Dic₅₄₂	1	2	yes	—
38	C₂	C₂×Dic₅₄₂	1	1	yes	characteristic
39	C₂	#16864653	1	1	yes	characteristic
40	C₂	#16864655	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
20. C₂₇₁	#125	semidirect