Subgroups — #30657663

Order 16448.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22551661	C₂	1	2	yes	maximal
2	C₁₆×D₂₅₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11759967	—	2	2	no	—
4	C₈×D₂₅₇	C₂²	1	1	yes	characteristic
5	#16861593	C₄	1	1	yes	characteristic, complemented
6	C₁₆×C₂₅₇	C₄	1	1	yes	characteristic, complemented
7	C₂×#11759967	—	4	2	no	—
8	C₄×D₂₅₇	D₄	1	1	yes	characteristic
9	#14523339	Q₈	1	1	yes	characteristic
10	C₈×C₂₅₇	C₂×C₄	1	1	yes	characteristic
11	C₂×D₂₅₇	D₈	1	1	yes	characteristic
12	#11759967	—	8	2	no	—
13	C₄×C₂₅₇	C₄⋊C₄	1	1	yes	characteristic
14	Dic₂₅₇	Q₁₆	1	1	yes	characteristic
15	C₂×C₂₅₇	#107	1	1	yes	characteristic
16	D₂₅₇	D₁₆	1	1	yes	characteristic
17	D₂₅₇	Q₃₂	1	1	yes	characteristic
18	C₂₅₇	#366	1	1	yes	characteristic, complemented, Sylow
19	#366	—	257	1	no	maximal, Sylow
20	C₂×C₁₆	—	257	1	no	—
21	#107	—	257	2	no	—
22	C₂×C₈	—	257	1	no	—
23	C₄⋊C₄	—	514	2	no	—
24	C₁₆	—	257	1	no	—
25	C₁₆	#11759967	1	1	yes	characteristic, complemented
26	C₂×C₄	—	257	1	no	—
27	C₂×C₄	—	1028	2	no	—
28	C₈	—	257	1	no	—
29	C₈	C₂×#11759967	1	1	yes	characteristic
30	C₂²	—	257	1	no	—
31	C₄	—	257	1	no	—
32	C₄	—	2056	2	no	—
33	C₄	C₄⋊#11759967	1	1	yes	characteristic
34	C₂	—	257	1	no	—
35	C₂	—	257	1	no	—
36	C₂	#22551661	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.