Subgroups — #440

Order 64.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄	C₂	1	1	yes	maximal, characteristic
4	#107	C₂	1	1	yes	maximal, characteristic, complemented
5	#103	C₂	1	1	yes	maximal, characteristic, complemented
6	#102	C₂	1	1	yes	maximal, characteristic
7	#97	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈	C₂²	1	1	yes	characteristic
9	C₂×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₄	—	2	1	no	—
11	SD₁₆	C₄	1	4	yes	complemented
12	C₂×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₈	C₂²	1	1	yes	characteristic
14	C₄⋊C₄	—	2	1	no	—
15	C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²⋊C₄	—	2	1	no	—
18	C₄²	—	2	1	no	—
19	C₄²	C₂²	1	1	yes	characteristic
20	C₂³	—	2	1	no	—
21	Q₈	—	2	1	no	—
22	Q₈	C₂×C₄	1	2	yes	complemented
23	D₄	—	2	1	no	—
24	D₄	C₂×C₄	1	2	yes	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	—	2	1	no	—
28	C₂×C₄	—	4	2	no	—
29	C₂×C₄	D₄	1	1	yes	characteristic
30	C₂×C₄	D₄	1	1	yes	characteristic
31	C₂×C₄	C₂³	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	C₂×C₄	1	2	yes	complemented
34	C₂²	—	2	2	no	—
35	C₂²	—	4	1	no	—
36	C₂²	—	4	1	no	—
37	C₂²	C₂×D₄	1	1	yes	characteristic
38	C₄	—	2	2	no	—
39	C₄	—	2	1	no	—
40	C₄	—	2	1	no	—
41	C₄	—	4	1	no	—
42	C₄	—	4	1	no	—
43	C₄	C₂²×C₄	1	1	yes	characteristic
44	C₄	#41	1	1	yes	characteristic
45	C₂	—	4	2	no	—
46	C₂	C₄×D₄	1	1	yes	characteristic
47	C₂	AGL(1,ℤ/8)	1	1	yes	characteristic
48	C₂	#137	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.