Subgroups — C₈×#14523348 #30657820

Order 16448.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14523348	C₂	1	2	yes	maximal
2	C₈×#11759967	C₂	1	1	yes	maximal, characteristic
3	C₂×#14523348	C₄	1	4	yes	—
4	#16861626	C₄	1	1	yes	characteristic
5	C₄×#11759967	C₂²	1	1	yes	characteristic
6	C₈×D₂₅₇	C₄	1	1	yes	characteristic
7	#14523348	C₈	1	8	yes	direct product factor
8	C₂×#11759967	C₂×C₄	1	2	yes	—
9	#14523346	C₈	1	2	yes	complemented
10	C₄×D₂₅₇	C₂×C₄	1	1	yes	characteristic
11	#14523339	C₈	1	1	yes	characteristic, complemented
12	C₈×C₂₅₇	C₈	1	1	yes	characteristic, complemented
13	C₂×D₂₅₇	C₄²	1	1	yes	characteristic
14	#11759967	C₂×C₈	1	4	yes	—
15	C₄×C₂₅₇	C₂×C₈	1	1	yes	characteristic
16	Dic₂₅₇	C₂×C₈	1	1	yes	characteristic
17	C₂×C₂₅₇	C₄×C₈	1	1	yes	characteristic
18	D₂₅₇	C₄×C₈	1	2	yes	—
19	C₂₅₇	C₈²	1	1	yes	characteristic, complemented, Sylow
20	C₈²	—	257	1	no	maximal, Sylow
21	C₄×C₈	—	257	1	no	—
22	C₄×C₈	—	257	2	no	—
23	C₂×C₈	—	257	1	no	—
24	C₂×C₈	—	257	4	no	—
25	C₂×C₈	—	257	1	no	—
26	C₄²	—	257	1	no	—
27	C₂×C₄	—	257	2	no	—
28	C₂×C₄	—	257	1	no	—
29	C₈	—	257	2	no	—
30	C₈	—	257	8	no	—
31	C₈	—	257	1	no	—
32	C₈	#14523348	1	1	yes	characteristic, direct product factor
33	C₂²	—	257	1	no	—
34	C₄	—	257	4	no	—
35	C₄	—	257	1	no	—
36	C₄	C₂×#14523348	1	1	yes	characteristic
37	C₂	—	257	2	no	—
38	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.