Subgroups — #7548

Order 256.

31 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₂₈	C₂	1	1	yes	maximal, characteristic
2	#1425	C₂	1	1	yes	maximal, characteristic
3	#1424	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₂	C₂²	1	1	yes	characteristic
5	#368	—	2	1	no	—
6	#366	—	2	1	no	—
7	C₆₄	C₄	1	2	yes	complemented
8	C₂×C₁₆	D₄	1	1	yes	characteristic
9	#108	—	4	1	no	—
10	#107	—	4	1	no	—
11	C₃₂	C₂×C₄	1	1	yes	characteristic
12	C₃₂	Q₈	1	1	yes	characteristic
13	M₁₆	—	8	1	no	—
14	C₂×C₈	D₈	1	1	yes	characteristic
15	C₄⋊C₄	—	8	1	no	—
16	C₁₆	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆	Q₁₆	1	1	yes	characteristic
18	C₂×C₄	—	16	1	no	—
19	C₂×C₄	D₁₆	1	1	yes	characteristic
20	C₈	—	16	1	no	—
21	C₈	#107	1	1	yes	characteristic
22	C₈	Q₃₂	1	1	yes	characteristic
23	C₂²	SD₆₄	1	1	yes	characteristic
24	C₄	—	32	1	no	—
25	C₄	#366	1	1	yes	characteristic
26	C₄	SD₆₄	1	1	yes	characteristic
27	C₂	—	2	1	no	—
28	C₂	#1424	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₆₄	C₄	semidirect

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