Subgroups — #7014

Order 256.

169 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1744	C₂	1	3	yes	maximal
2	C₂×C₄×C₈	C₄	1	6	yes	—
3	C₄³	C₂²	1	1	yes	characteristic
4	#336	—	2	6	no	—
5	C₂²×C₈	—	2	6	no	—
6	C₂×C₄²	C₂×C₄	1	3	yes	—
7	C₂×C₄²	D₄	1	3	yes	—
8	C₂×C₄²	Q₈	1	1	yes	characteristic
9	C₄×C₈	—	2	6	no	—
10	C₄×C₈	C₈	1	12	yes	complemented
11	C₂²×C₄	C₄²	1	1	yes	characteristic
12	C₂²×C₄	C₂²⋊C₄	1	3	yes	—
13	C₂²×C₄	C₄⋊C₄	1	3	yes	—
14	C₂×C₈	—	2	12	no	—
15	C₂×C₈	—	4	12	no	—
16	C₄²	—	4	3	no	—
17	C₄²	—	4	1	no	—
18	C₄²	C₂×C₈	1	6	yes	—
19	C₄²	M₁₆	1	6	yes	—
20	C₂³	#95	1	1	yes	characteristic
21	C₂×C₄	—	2	6	no	—
22	C₂×C₄	—	2	3	no	—
23	C₂×C₄	—	2	3	no	—
24	C₂×C₄	C₄×C₈	1	3	yes	—
25	C₂×C₄	#97	1	3	yes	—
26	C₂×C₄	C₂²⋊C₈	1	6	yes	—
27	C₂×C₄	C₄⋊C₈	1	6	yes	—
28	C₈	—	4	12	no	—
29	C₂²	#336	1	3	yes	—
30	C₂²	H(3,ℤ/4)	1	3	yes	—
31	C₂²	#338	1	1	yes	characteristic
32	C₄	—	2	6	no	—
33	C₄	—	2	6	no	—
34	C₄	C₈²	1	1	yes	characteristic
35	C₄	#322	1	3	yes	—
36	C₂	#1273	1	1	yes	characteristic
37	C₂	#1274	1	3	yes	—
38	C₂	#1275	1	3	yes	—

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

N	H ≅ G/N	type
10. C₄×C₈	C₈	semidirect

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

subgroup	index
#1744	2