Subgroups — #433

Order 64.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#117	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂²⋊C₈	C₂	1	2	yes	maximal
4	#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₈	C₂²	1	2	yes	—
8	C₂×C₈	C₂²	1	2	yes	—
9	C₄⋊C₄	C₄	1	2	yes	—
10	C₂²⋊C₄	C₄	1	2	yes	—
11	C₄²	C₂²	1	1	yes	characteristic
12	C₄²	C₂²	1	1	yes	characteristic
13	C₂³	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄	—	2	2	no	—
15	C₂×C₄	C₂×C₄	1	2	yes	—
16	C₂×C₄	C₂×C₄	1	2	yes	—
17	C₂×C₄	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄	C₂³	1	1	yes	characteristic
19	C₈	—	2	2	no	—
20	C₈	—	2	2	no	—
21	C₂²	—	2	1	no	—
22	C₂²	—	2	2	no	—
23	C₂²	C₂²×C₄	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	—	2	2	no	—
26	C₄	—	2	2	no	—
27	C₄	#41	1	2	yes	—
28	C₂	—	4	1	no	—
29	C₂	#117	1	1	yes	characteristic
30	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.