Subgroups — #30657830

Order 16448.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22551687	C₂	1	2	yes	maximal
2	C₈×#11759967	C₂	1	1	yes	maximal, characteristic
3	#16861630	C₄	1	4	yes	complemented
4	#16861626	C₂²	1	1	yes	characteristic
5	C₄×#11759967	C₄	1	1	yes	characteristic
6	C₈×D₂₅₇	C₄	1	1	yes	characteristic
7	C₂×#11759967	C₈	1	2	yes	—
8	#14523346	C₂×C₄	1	2	yes	—
9	C₄×D₂₅₇	C₂×C₄	1	1	yes	characteristic
10	#14523339	C₈	1	1	yes	characteristic
11	C₈×C₂₅₇	C₈	1	1	yes	characteristic
12	C₂×D₂₅₇	C₂×C₈	1	1	yes	characteristic
13	#11759967	C₁₆	1	4	yes	complemented
14	C₄×C₂₅₇	C₂×C₈	1	1	yes	characteristic
15	Dic₂₅₇	C₄²	1	1	yes	characteristic
16	C₂×C₂₅₇	C₄×C₈	1	1	yes	characteristic
17	D₂₅₇	C₂×C₁₆	1	2	yes	—
18	C₂₅₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₄×C₁₆	—	257	1	no	maximal, Sylow
20	C₂×C₁₆	—	257	2	no	—
21	C₄×C₈	—	257	1	no	—
22	C₂×C₈	—	257	1	no	—
23	C₂×C₈	—	257	1	no	—
24	C₄²	—	257	1	no	—
25	C₁₆	—	257	4	no	—
26	C₂×C₄	—	257	2	no	—
27	C₂×C₄	—	257	1	no	—
28	C₈	—	257	2	no	—
29	C₈	—	257	1	no	—
30	C₈	#14523348	1	1	yes	characteristic
31	C₂²	—	257	1	no	—
32	C₄	—	257	4	no	—
33	C₄	—	257	1	no	—
34	C₄	C₂×#14523348	1	1	yes	characteristic
35	C₂	—	257	2	no	—
36	C₂	C₄×#14523348	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.