Subgroups — #405

Order 64.

65 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈	C₂	1	1	yes	maximal, characteristic
3	#117	C₂	1	1	yes	maximal, characteristic
4	#97	C₂	1	2	yes	maximal, complemented
5	C₄×C₈	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄	C₂²	1	1	yes	characteristic
7	M₁₆	C₄	1	4	yes	complemented
8	C₂×C₈	C₄	1	4	yes	complemented
9	C₂×C₈	C₂²	1	2	yes	—
10	C₂×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₈	C₂²	1	1	yes	characteristic
12	C₄⋊C₄	C₄	1	2	yes	—
13	C₂²⋊C₄	C₄	1	2	yes	—
14	C₄²	C₂²	1	2	yes	—
15	C₂³	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄	C₂×C₄	1	4	yes	—
17	C₂×C₄	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄	C₂×C₄	1	2	yes	—
19	C₂×C₄	C₂×C₄	1	2	yes	—
20	C₂×C₄	C₂³	1	1	yes	characteristic
21	C₈	C₂×C₄	1	2	yes	—
22	C₈	C₂×C₄	1	2	yes	—
23	C₈	C₂×C₄	1	4	yes	—
24	C₂²	—	2	2	no	—
25	C₂²	C₄²	1	2	yes	—
26	C₂²	C₂²×C₄	1	1	yes	characteristic
27	C₄	—	2	4	no	—
28	C₄	C₄²	1	2	yes	—
29	C₄	C₂²×C₄	1	1	yes	characteristic
30	C₄	C₂²×C₄	1	1	yes	characteristic
31	C₂	—	2	2	no	—
32	C₂	C₂×C₄²	1	1	yes	characteristic
33	C₂	#131	1	2	yes	—

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.