Subgroups — #7457

Order 256.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1398	C₂	1	1	yes	maximal, characteristic
2	#1369	C₂	1	1	yes	maximal, characteristic
3	#1368	C₂	1	1	yes	maximal, characteristic
4	M₆₄	C₄	1	1	yes	characteristic
5	M₆₄	C₄	1	1	yes	characteristic
6	#364	—	2	1	no	—
7	#346	C₂²	1	1	yes	characteristic
8	#334	—	2	1	no	—
9	M₃₂	—	4	1	no	—
10	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
11	C₂×C₁₆	Q₈	1	1	yes	characteristic
12	C₄⋊C₈	—	4	1	no	—
13	C₄×C₈	D₄	1	1	yes	characteristic
14	C₃₂	—	2	1	no	—
15	C₃₂	C₈	1	2	yes	complemented
16	C₂×C₈	—	8	1	no	—
17	C₂×C₈	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈	SD₁₆	1	1	yes	characteristic
19	C₄²	SD₁₆	1	1	yes	characteristic
20	C₁₆	—	2	1	no	—
21	C₁₆	—	8	1	no	—
22	C₁₆	C₂×C₈	1	1	yes	characteristic
23	C₁₆	M₁₆	1	1	yes	characteristic
24	C₂×C₄	—	2	1	no	—
25	C₂×C₄	#106	1	1	yes	characteristic
26	C₈	—	2	1	no	—
27	C₈	—	16	1	no	—
28	C₈	C₄⋊C₈	1	1	yes	characteristic
29	C₈	#108	1	1	yes	characteristic
30	C₂²	#365	1	1	yes	characteristic
31	C₄	—	4	1	no	—
32	C₄	#334	1	1	yes	characteristic
33	C₄	#365	1	1	yes	characteristic
34	C₂	—	2	1	no	—
35	C₂	#1368	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₃₂	C₈	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.