Subgroups — #7333

Order 256.

44 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	#1398	C₂	1	1	yes	maximal, characteristic
3	#1313	C₂	1	1	yes	maximal, characteristic
4	M₆₄	C₄	1	2	yes	—
5	M₆₄	C₄	1	2	yes	—
6	#346	C₄	1	1	yes	characteristic
7	#346	C₂²	1	1	yes	characteristic
8	#322	C₄	1	1	yes	characteristic
9	C₂×C₁₆	—	2	1	no	—
10	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
11	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₄×C₈	—	2	1	no	—
13	C₄×C₈	C₂×C₄	1	1	yes	characteristic
14	C₃₂	—	2	2	no	—
15	C₃₂	C₈	1	4	yes	complemented
16	C₂×C₈	—	4	1	no	—
17	C₂×C₈	C₄²	1	1	yes	characteristic
18	C₂×C₈	M₁₆	1	1	yes	characteristic
19	C₄²	M₁₆	1	1	yes	characteristic
20	C₁₆	—	4	1	no	—
21	C₁₆	C₂×C₈	1	2	yes	—
22	C₁₆	M₁₆	1	2	yes	—
23	C₂×C₄	—	2	1	no	—
24	C₂×C₄	#97	1	1	yes	characteristic
25	C₈	—	2	1	no	—
26	C₈	—	8	1	no	—
27	C₈	C₄×C₈	1	1	yes	characteristic
28	C₈	#97	1	1	yes	characteristic
29	C₂²	#347	1	1	yes	characteristic
30	C₄	—	4	1	no	—
31	C₄	#322	1	1	yes	characteristic
32	C₄	#347	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#1313	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.

subgroup	index
#1398	2
#1313	2