Subgroups — #7093

Order 256.

65 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1710	C₂	1	1	yes	maximal, characteristic
2	#1367	C₂	1	2	yes	maximal
3	#500	C₄	1	2	yes	—
4	#487	—	2	2	no	—
5	C₄⋊C₁₆	—	2	2	no	—
6	C₈²	C₂²	1	1	yes	characteristic
7	C₄⋊Q₈	—	2	2	no	—
8	C₂×C₁₆	—	4	2	no	—
9	#107	—	4	2	no	—
10	#103	—	4	2	no	—
11	#103	—	4	2	no	—
12	C₄×C₈	C₂×C₄	1	1	yes	characteristic
13	C₄×C₈	D₄	1	2	yes	—
14	C₂×Q₈	—	4	2	no	—
15	C₂×C₈	—	2	1	no	—
16	C₂×C₈	D₈	1	2	yes	—
17	C₂×C₈	SD₁₆	1	2	yes	—
18	C₄⋊C₄	—	4	2	no	—
19	C₄⋊C₄	—	4	2	no	—
20	C₄²	C₂²⋊C₄	1	1	yes	characteristic
21	C₁₆	—	8	2	no	—
22	Q₈	—	8	2	no	—
23	Q₈	—	8	2	no	—
24	C₂×C₄	—	8	2	no	—
25	C₂×C₄	#100	1	1	yes	characteristic
26	C₂×C₄	#102	1	2	yes	—
27	C₈	—	2	2	no	—
28	C₈	—	2	2	no	—
29	C₈	—	2	2	no	—
30	C₂²	#331	1	1	yes	characteristic
31	C₄	—	2	1	no	—
32	C₄	—	16	2	no	—
33	C₄	#359	1	2	yes	—
34	C₄	#360	1	2	yes	—
35	C₂	#1358	1	1	yes	characteristic
36	C₂	#1360	1	2	yes	—

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

subgroup	index
#1710	2
#1367	2