Subgroups — #7053

Order 256.

61 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1312	C₂	1	2	yes	maximal
2	#1311	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆	C₄	1	4	yes	—
4	C₄×C₁₆	C₄	1	1	yes	characteristic
5	C₄×C₁₆	C₄	1	1	yes	characteristic
6	C₈²	C₂²	1	1	yes	characteristic
7	C₂×C₁₆	—	2	4	no	—
8	C₂×C₁₆	C₈	1	2	yes	—
9	C₂×C₁₆	C₈	1	2	yes	—
10	C₄×C₈	C₂×C₄	1	1	yes	characteristic
11	C₄×C₈	C₂×C₄	1	2	yes	—
12	C₂×C₈	C₂×C₈	1	1	yes	characteristic
13	C₂×C₈	C₂×C₈	1	1	yes	characteristic
14	C₂×C₈	M₁₆	1	4	yes	—
15	C₄²	C₄²	1	1	yes	characteristic
16	C₁₆	—	2	2	no	—
17	C₁₆	—	4	4	no	—
18	C₁₆	C₁₆	1	4	yes	complemented
19	C₂×C₄	C₄×C₈	1	1	yes	characteristic
20	C₂×C₄	#97	1	2	yes	—
21	C₈	—	2	4	no	—
22	C₈	C₂×C₁₆	1	2	yes	—
23	C₈	M₃₂	1	2	yes	—
24	C₂²	#322	1	1	yes	characteristic
25	C₄	C₄×C₁₆	1	1	yes	characteristic
26	C₄	#346	1	1	yes	characteristic
27	C₄	#347	1	4	yes	—
28	C₂	#1312	1	1	yes	characteristic
29	C₂	#1313	1	2	yes	—

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

N	H ≅ G/N	type
18. C₁₆	C₁₆	semidirect

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

subgroup	index
#1312	2
#1311	2