Subgroups — #7845

Order 256.

243 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1744	C₂	1	3	yes	maximal
2	C₂×#322	C₂	1	3	yes	maximal
3	C₂×C₈²	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈	C₂²	1	3	yes	—
5	C₂×C₄×C₈	C₂²	1	3	yes	—
6	C₄³	C₂²	1	1	yes	characteristic
7	#336	C₄	1	12	yes	—
8	#322	C₄	1	12	yes	complemented
9	C₈²	C₄	1	4	yes	complemented
10	C₂²×C₈	C₂×C₄	1	6	yes	—
11	C₂²×C₈	C₂×C₄	1	6	yes	—
12	C₂×C₄²	C₂×C₄	1	6	yes	—
13	C₂×C₄²	C₂³	1	1	yes	characteristic
14	C₄×C₈	C₂×C₄	1	6	yes	—
15	C₄×C₈	C₂×C₄	1	6	yes	—
16	C₄×C₈	C₂×C₄	1	12	yes	—
17	C₂²×C₄	C₄²	1	4	yes	—
18	C₂²×C₄	C₂²×C₄	1	3	yes	—
19	C₂×C₈	—	2	12	no	—
20	C₂×C₈	—	2	12	no	—
21	C₂×C₈	C₄²	1	12	yes	—
22	C₂×C₈	C₄²	1	12	yes	—
23	C₄²	—	2	12	no	—
24	C₄²	C₂²×C₄	1	1	yes	characteristic
25	C₄²	C₂²×C₄	1	3	yes	—
26	C₂³	C₂×C₄²	1	1	yes	characteristic
27	C₂×C₄	—	2	12	no	—
28	C₂×C₄	C₂×C₄²	1	3	yes	—
29	C₂×C₄	C₂×C₄²	1	3	yes	—
30	C₂×C₄	#131	1	12	yes	—
31	C₈	—	2	12	no	—
32	C₈	—	2	12	no	—
33	C₂²	C₄³	1	1	yes	characteristic
34	C₂²	#405	1	6	yes	—
35	C₄	—	4	4	no	—
36	C₄	#405	1	6	yes	—
37	C₄	#405	1	6	yes	—
38	C₂	#1454	1	4	yes	—
39	C₂	#1726	1	3	yes	—

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

N	H ≅ G/N	type
8. #322	C₄	semidirect
9. C₈²	C₄	semidirect

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