Subgroups — #22551649

Order 8224.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14523346	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×D₂₅₇	C₂	1	1	yes	maximal, characteristic
3	#14523346	—	2	2	no	—
4	C₂²×D₂₅₇	C₄	1	1	yes	characteristic
5	C₂×Dic₂₅₇	C₂²	1	1	yes	characteristic
6	C₄×D₂₅₇	—	2	2	no	—
7	C₂×C₄×C₂₅₇	C₄	1	1	yes	characteristic
8	C₂²×C₂₅₇	C₂×C₄	1	1	yes	characteristic
9	C₂×D₂₅₇	—	2	1	no	—
10	C₂×D₂₅₇	—	2	1	no	—
11	C₂×D₂₅₇	C₈	1	2	yes	complemented
12	C₄×C₂₅₇	—	2	1	no	—
13	Dic₂₅₇	D₄	1	2	yes	—
14	C₂×C₂₅₇	C₂²⋊C₄	1	1	yes	characteristic
15	C₂×C₂₅₇	C₂×C₈	1	1	yes	characteristic
16	C₂×C₂₅₇	M₁₆	1	1	yes	characteristic
17	D₂₅₇	—	2	2	no	—
18	C₂₅₇	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂²⋊C₈	—	257	1	no	maximal, Sylow
20	C₂²×C₄	—	257	1	no	—
21	C₂×C₈	—	257	2	no	—
22	C₂³	—	257	1	no	—
23	C₂×C₄	—	257	1	no	—
24	C₂×C₄	—	514	2	no	—
25	C₂×C₄	#11759967	1	1	yes	characteristic
26	C₈	—	514	2	no	—
27	C₂²	—	257	2	no	—
28	C₂²	—	514	1	no	—
29	C₂²	—	514	1	no	—
30	C₂²	C₂×#11759967	1	1	yes	characteristic
31	C₄	—	257	2	no	—
32	C₄	—	2	1	no	—
33	C₂	—	514	2	no	—
34	C₂	C₂²⋊#11759967	1	1	yes	characteristic
35	C₂	#16861626	1	1	yes	characteristic
36	C₂	#16861628	1	1	yes	characteristic

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