Subgroups — #339

Order 64.

55 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	#117	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄	—	2	1	no	—
5	C₂²×C₄	C₂²	1	1	yes	characteristic
6	M₁₆	—	2	1	no	—
7	M₁₆	C₄	1	2	yes	complemented
8	C₂×C₈	—	2	1	no	—
9	C₄⋊C₄	C₄	1	2	yes	complemented
10	C₂²⋊C₄	—	2	1	no	—
11	C₄²	—	2	1	no	—
12	C₄²	—	2	1	no	—
13	C₄²	C₄	1	2	yes	complemented
14	C₂³	D₄	1	1	yes	characteristic
15	C₂×C₄	—	2	4	no	—
16	C₂×C₄	—	2	2	no	—
17	C₂×C₄	—	2	2	no	—
18	C₂×C₄	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄	D₄	1	1	yes	characteristic
22	C₂×C₄	D₄	1	1	yes	characteristic
23	C₂×C₄	Q₈	1	1	yes	characteristic
24	C₈	—	2	2	no	—
25	C₂²	—	2	2	no	—
26	C₂²	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²	C₂²⋊C₄	1	1	yes	characteristic
28	C₂²	C₄⋊C₄	1	1	yes	characteristic
29	C₄	—	2	4	no	—
30	C₄	—	4	2	no	—
31	C₄	C₄²	1	1	yes	characteristic
32	C₄	C₂²⋊C₄	1	1	yes	characteristic
33	C₄	C₄⋊C₄	1	1	yes	characteristic
34	C₄	C₄⋊C₄	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	—	2	1	no	—
37	C₂	#95	1	1	yes	characteristic
38	C₂	#104	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.