Subgroups — #423

Order 64.

63 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈	C₂	1	4	yes	maximal, complemented
4	C₂²×C₄	C₄	1	2	yes	—
5	C₂²×C₄	C₂²	1	1	yes	characteristic
6	M₁₆	—	2	4	no	—
7	C₂×C₈	C₂²	1	4	yes	—
8	C₄²	C₄	1	1	yes	characteristic
9	C₄²	C₄	1	1	yes	characteristic
10	C₄²	C₂²	1	2	yes	—
11	C₂³	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄	—	2	4	no	—
13	C₂×C₄	C₂×C₄	1	2	yes	—
14	C₂×C₄	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄	C₂×C₄	1	2	yes	—
16	C₂×C₄	D₄	1	2	yes	—
17	C₂×C₄	Q₈	1	2	yes	—
18	C₂×C₄	C₂³	1	1	yes	characteristic
19	C₈	—	2	4	no	—
20	C₂²	—	2	2	no	—
21	C₂²	C₄⋊C₄	1	2	yes	—
22	C₂²	C₂²×C₄	1	1	yes	characteristic
23	C₄	—	2	2	no	—
24	C₄	C₄⋊C₄	1	2	yes	—
25	C₄	M₁₆	1	4	yes	complemented
26	C₄	C₂×D₄	1	1	yes	characteristic
27	C₄	C₂×Q₈	1	1	yes	characteristic
28	C₂	—	2	2	no	—
29	C₂	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂	C₂×M₁₆	1	2	yes	—

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

N	H ≅ G/N	type
3. C₄⋊C₈	C₂	semidirect
25. C₄	M₁₆	semidirect

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