Subgroups — #336

Order 64.

59 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈	C₂	1	2	yes	maximal
2	C₂×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄	C₄	1	2	yes	—
4	C₂²×C₄	C₂²	1	1	yes	characteristic
5	C₂×C₈	—	2	2	no	—
6	C₂×C₈	—	2	2	no	—
7	C₂×C₈	C₄	1	4	yes	complemented
8	C₄²	—	2	2	no	—
9	C₂³	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄	—	2	2	no	—
11	C₂×C₄	—	2	2	no	—
12	C₂×C₄	C₈	1	4	yes	complemented
13	C₂×C₄	C₂×C₄	1	2	yes	—
14	C₂×C₄	D₄	1	1	yes	characteristic
15	C₂×C₄	D₄	1	2	yes	—
16	C₂×C₄	Q₈	1	1	yes	characteristic
17	C₈	—	2	4	no	—
18	C₂²	C₄²	1	1	yes	characteristic
19	C₂²	C₂²⋊C₄	1	1	yes	characteristic
20	C₂²	C₄⋊C₄	1	1	yes	characteristic
21	C₂²	C₂×C₈	1	2	yes	—
22	C₂²	M₁₆	1	2	yes	—
23	C₄	—	2	4	no	—
24	C₄	C₂²⋊C₄	1	2	yes	—
25	C₄	C₄⋊C₄	1	2	yes	—
26	C₂	#95	1	1	yes	characteristic
27	C₂	C₄×C₈	1	1	yes	characteristic
28	C₂	#97	1	1	yes	characteristic
29	C₂	C₂²⋊C₈	1	2	yes	—
30	C₂	C₄⋊C₈	1	2	yes	—

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

N	H ≅ G/N	type
7. C₂×C₈	C₄	semidirect
12. C₂×C₄	C₈	semidirect

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

subgroup	index
C₂²×C₈	2
C₂×C₄²	2