Subgroups — #22576088

Order 8672.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864654	C₂	1	1	yes	maximal, characteristic
2	#16864638	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₅₄₂	C₄	1	1	yes	characteristic, complemented
5	D₁₀₈₄	C₄	1	1	yes	characteristic, complemented
6	C₂²⋊D₂₇₁	—	2	1	no	—
7	C₄×D₂₇₁	—	2	1	no	—
8	C₂₇₁⋊C₈	—	2	1	no	—
9	C₂×C₄×C₂₇₁	—	2	1	no	—
10	C₂×C₄×C₂₇₁	C₂²	1	1	yes	characteristic
11	C₂²×C₂₇₁	D₄	1	1	yes	characteristic
12	C₂×D₂₇₁	—	2	1	no	—
13	C₄×C₂₇₁	—	2	2	no	—
14	C₄×C₂₇₁	C₂×C₄	1	1	yes	characteristic
15	C₄×C₂₇₁	D₄	1	1	yes	characteristic
16	Dic₂₇₁	—	2	1	no	—
17	C₂×C₂₇₁	—	2	1	no	—
18	C₂×C₂₇₁	C₂²⋊C₄	1	1	yes	characteristic
19	D₂₇₁	—	4	1	no	—
20	C₂₇₁	#104	1	1	yes	characteristic, complemented, Sylow
21	#104	—	271	1	no	maximal, Sylow
22	#41	—	271	1	no	—
23	M₁₆	—	271	1	no	—
24	C₄²	D₂₇₁	1	1	yes	characteristic, complemented
25	Q₈	—	271	1	no	—
26	D₄	—	271	1	no	—
27	D₄	—	542	1	no	—
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	—	542	1	no	—
30	C₂×C₄	C₂×D₂₇₁	1	1	yes	characteristic
31	C₈	—	542	1	no	—
32	C₂²	—	542	1	no	—
33	C₂²	C₂²⋊D₂₇₁	1	1	yes	characteristic
34	C₄	—	2	2	no	—
35	C₄	—	542	1	no	—
36	C₄	C₄×D₂₇₁	1	1	yes	characteristic
37	C₄	D₁₀₈₄	1	1	yes	characteristic
38	C₂	—	2	1	no	—
39	C₂	—	1084	1	no	—
40	C₂	(C₂×D₂₇₁)⋊C₄	1	1	yes	characteristic

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