Subgroups — #7538

Order 256.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₄	C₂	1	1	yes	maximal, characteristic
3	#1423	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₃₂	—	2	1	no	—
5	Q₆₄	—	2	1	no	—
6	Q₆₄	C₄	1	2	yes	complemented
7	C₂×C₃₂	C₂²	1	1	yes	characteristic
8	#366	—	2	1	no	—
9	C₆₄	—	2	1	no	—
10	C₂×Q₁₆	—	4	1	no	—
11	Q₃₂	—	2	2	no	—
12	Q₃₂	—	4	1	no	—
13	C₂×C₁₆	D₄	1	1	yes	characteristic
14	#107	—	4	1	no	—
15	C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₃₂	D₄	1	1	yes	characteristic
17	C₂×Q₈	—	8	1	no	—
18	Q₁₆	—	4	2	no	—
19	Q₁₆	—	8	1	no	—
20	C₂×C₈	D₈	1	1	yes	characteristic
21	C₄⋊C₄	—	8	1	no	—
22	C₁₆	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆	SD₁₆	1	1	yes	characteristic
24	Q₈	—	8	2	no	—
25	Q₈	—	16	1	no	—
26	C₂×C₄	—	16	1	no	—
27	C₂×C₄	—	16	1	no	—
28	C₂×C₄	D₁₆	1	1	yes	characteristic
29	C₈	#102	1	1	yes	characteristic
30	C₈	SD₃₂	1	1	yes	characteristic
31	C₂²	D₃₂	1	1	yes	characteristic
32	C₄	—	16	2	no	—
33	C₄	—	32	1	no	—
34	C₄	#357	1	1	yes	characteristic
35	C₄	SD₆₄	1	1	yes	characteristic
36	C₂	#1415	1	1	yes	characteristic
37	C₂	SD₁₂₈	1	1	yes	characteristic
38	C₂	Q₁₂₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. Q₆₄	C₄	semidirect

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