Subgroups — #443

Order 64.

53 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#135	C₂	1	1	yes	maximal, characteristic
2	#131	C₂	1	2	yes	maximal, complemented
3	#108	C₂	1	1	yes	maximal, characteristic, complemented
4	#104	C₂	1	2	yes	maximal, complemented
5	C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#41	C₂²	1	2	yes	—
7	Q₁₆	C₄	1	1	yes	characteristic, complemented
8	SD₁₆	C₄	1	2	yes	complemented
9	D₈	C₄	1	1	yes	characteristic, complemented
10	M₁₆	—	2	2	no	—
11	M₁₆	C₂²	1	2	yes	—
12	C₂×C₈	—	2	2	no	—
13	C₂×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₈	C₂²	1	1	yes	characteristic
15	C₄²	C₂²	1	1	yes	characteristic
16	Q₈	C₂×C₄	1	2	yes	—
17	D₄	—	2	2	no	—
18	D₄	C₂×C₄	1	2	yes	—
19	C₂×C₄	—	2	1	no	—
20	C₂×C₄	—	2	2	no	—
21	C₂×C₄	C₂³	1	1	yes	characteristic
22	C₈	—	2	2	no	—
23	C₈	C₂×C₄	1	1	yes	characteristic
24	C₈	C₂×C₄	1	1	yes	characteristic
25	C₈	D₄	1	1	yes	characteristic
26	C₈	D₄	1	1	yes	characteristic
27	C₂²	—	2	2	no	—
28	C₂²	#41	1	1	yes	characteristic
29	C₄	—	2	2	no	—
30	C₄	—	2	2	no	—
31	C₄	C₂²×C₄	1	1	yes	characteristic
32	C₄	C₂×D₄	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	—	4	2	no	—
35	C₂	C₄×D₄	1	1	yes	characteristic

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.