Subgroups — #436

Order 64.

61 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆	C₂	1	2	yes	maximal, complemented
2	C₄×D₄	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄	C₄	1	1	yes	characteristic
7	C₂²×C₄	C₂²	1	2	yes	—
8	M₁₆	—	2	4	no	—
9	C₂×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₈	C₂²	1	2	yes	—
11	C₂×C₈	C₂²	1	1	yes	characteristic
12	C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₂²⋊C₄	C₄	1	2	yes	—
14	C₄²	C₂²	1	1	yes	characteristic
15	C₂³	C₂×C₄	1	2	yes	—
16	D₄	—	2	2	no	—
17	C₂×C₄	—	2	2	no	—
18	C₂×C₄	—	2	2	no	—
19	C₂×C₄	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄	C₂×C₄	1	2	yes	—
21	C₂×C₄	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄	C₂³	1	1	yes	characteristic
23	C₈	—	2	2	no	—
24	C₈	—	2	1	no	—
25	C₈	D₄	1	2	yes	complemented
26	C₂²	—	2	2	no	—
27	C₂²	—	2	2	no	—
28	C₂²	—	2	2	no	—
29	C₂²	C₂²×C₄	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	—	2	1	no	—
32	C₄	M₁₆	1	2	yes	complemented
33	C₄	C₂×D₄	1	1	yes	characteristic
34	C₄	#41	1	1	yes	characteristic
35	C₂	—	4	2	no	—
36	C₂	C₄×D₄	1	1	yes	characteristic
37	C₂	C₂×M₁₆	1	1	yes	characteristic
38	C₂	#131	1	1	yes	characteristic

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

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