Subgroups — #7098

Order 256.

71 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1713	C₂	1	1	yes	maximal, characteristic
2	#1370	C₂	1	2	yes	maximal
3	#500	—	2	2	no	—
4	#494	C₄	1	2	yes	—
5	C₄⋊C₁₆	—	2	2	no	—
6	C₈²	C₂²	1	1	yes	characteristic
7	C₂×Q₁₆	—	4	2	no	—
8	C₄⋊Q₈	—	2	2	no	—
9	C₂×C₁₆	—	4	2	no	—
10	#107	—	4	2	no	—
11	#107	—	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	Q₁₆	—	8	4	no	—
16	C₂×C₈	—	2	1	no	—
17	C₂×C₈	D₈	1	2	yes	—
18	C₂×C₈	SD₁₆	1	2	yes	—
19	C₄⋊C₄	—	4	4	no	—
20	C₄²	C₂²⋊C₄	1	1	yes	characteristic
21	C₁₆	—	8	2	no	—
22	Q₈	—	8	4	no	—
23	C₂×C₄	—	8	2	no	—
24	C₂×C₄	#100	1	1	yes	characteristic
25	C₂×C₄	#102	1	2	yes	—
26	C₈	—	2	2	no	—
27	C₈	—	2	2	no	—
28	C₈	SD₃₂	1	2	yes	—
29	C₈	Q₃₂	1	2	yes	—
30	C₂²	#331	1	1	yes	characteristic
31	C₄	—	2	1	no	—
32	C₄	—	16	2	no	—
33	C₄	#358	1	2	yes	—
34	C₄	#362	1	2	yes	—
35	C₂	#1357	1	1	yes	characteristic
36	C₂	#1362	1	2	yes	—

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

subgroup	index
#1713	2
#1370	2