Subgroups — #7532

Order 256.

68 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	#1411	C₂	1	2	yes	maximal
3	#500	—	2	2	no	—
4	#494	C₄	1	1	yes	characteristic
5	#494	C₂²	1	1	yes	characteristic
6	#356	—	2	2	no	—
7	C₈²	C₄	1	1	yes	characteristic
8	C₂×Q₁₆	—	4	1	no	—
9	C₂×Q₁₆	—	4	1	no	—
10	C₄⋊Q₈	—	2	1	no	—
11	C₄⋊Q₈	D₄	1	2	yes	—
12	#107	—	4	4	no	—
13	#101	—	4	2	no	—
14	C₄×C₈	—	2	1	no	—
15	C₄×C₈	C₂×C₄	1	1	yes	characteristic
16	C₂×Q₈	—	2	2	no	—
17	C₂×Q₈	—	4	1	no	—
18	Q₁₆	—	8	2	no	—
19	Q₁₆	—	8	2	no	—
20	M₁₆	—	8	2	no	—
21	C₂×C₈	—	2	2	no	—
22	C₂×C₈	—	2	1	no	—
23	C₄⋊C₄	—	4	2	no	—
24	C₄⋊C₄	—	4	2	no	—
25	C₄²	C₂²⋊C₄	1	1	yes	characteristic
26	Q₈	—	8	2	no	—
27	Q₈	—	8	2	no	—
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	—	4	2	no	—
30	C₂×C₄	—	8	1	no	—
31	C₂×C₄	#99	1	1	yes	characteristic
32	C₈	—	2	4	no	—
33	C₈	—	2	2	no	—
34	C₈	—	16	2	no	—
35	C₂²	#353	1	1	yes	characteristic
36	C₄	—	2	2	no	—
37	C₄	—	2	1	no	—
38	C₄	—	8	2	no	—
39	C₄	—	16	1	no	—
40	C₂	—	2	1	no	—
41	C₂	#1408	1	1	yes	characteristic

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

subgroup	index
#1713	2
#1411	2