Subgroups — #343

Order 64.

49 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×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄	C₄	1	2	yes	—
4	C₂²×C₄	C₂²	1	1	yes	characteristic
5	M₁₆	—	2	2	no	—
6	M₁₆	C₄	1	4	yes	complemented
7	C₂×C₈	—	2	2	no	—
8	C₄⋊C₄	—	2	2	no	—
9	C₂³	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄	—	2	2	no	—
11	C₂×C₄	—	4	2	no	—
12	C₂×C₄	C₂×C₄	1	2	yes	—
13	C₂×C₄	D₄	1	1	yes	characteristic
14	C₂×C₄	D₄	1	2	yes	—
15	C₂×C₄	Q₈	1	1	yes	characteristic
16	C₈	—	2	4	no	—
17	C₂²	—	2	1	no	—
18	C₂²	—	2	1	no	—
19	C₂²	C₄²	1	1	yes	characteristic
20	C₂²	C₂²⋊C₄	1	1	yes	characteristic
21	C₂²	C₄⋊C₄	1	1	yes	characteristic
22	C₄	—	4	2	no	—
23	C₄	C₂²⋊C₄	1	2	yes	—
24	C₄	C₄⋊C₄	1	2	yes	—
25	C₂	—	2	1	no	—
26	C₂	—	2	1	no	—
27	C₂	#95	1	1	yes	characteristic
28	C₂	#100	1	1	yes	characteristic
29	C₂	#101	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. M₁₆	C₄	semidirect

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

subgroup	index
C₂×M₁₆	2
C₂×C₄⋊C₄	2