Subgroups — #417

Order 64.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#103	C₂	1	2	yes	maximal, complemented
5	#102	C₂	1	2	yes	maximal, complemented
6	#41	—	2	2	no	—
7	#41	C₄	1	4	yes	complemented
8	C₂×Q₈	C₂²	1	1	yes	characteristic
9	C₂×D₄	—	2	1	no	—
10	C₂×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₄	—	2	1	no	—
12	C₂²×C₄	—	2	1	no	—
13	C₂²×C₄	C₂²	1	1	yes	characteristic
14	M₁₆	—	2	2	no	—
15	C₂×C₈	C₂²	1	2	yes	—
16	C₄⋊C₄	—	2	1	no	—
17	C₄⋊C₄	C₂²	1	2	yes	—
18	C₂³	—	2	1	no	—
19	C₂³	D₄	1	1	yes	characteristic
20	Q₈	—	2	1	no	—
21	Q₈	C₂×C₄	1	2	yes	complemented
22	D₄	—	2	4	no	—
23	D₄	—	2	1	no	—
24	D₄	C₂×C₄	1	2	yes	complemented
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	—	2	4	no	—
27	C₂×C₄	—	2	2	no	—
28	C₂×C₄	—	4	2	no	—
29	C₂×C₄	C₂×C₄	1	2	yes	—
30	C₂×C₄	D₄	1	1	yes	characteristic
31	C₂×C₄	D₄	1	2	yes	—
32	C₂×C₄	C₂³	1	1	yes	characteristic
33	C₈	—	2	2	no	—
34	C₂²	—	2	1	no	—
35	C₂²	—	2	1	no	—
36	C₂²	—	2	2	no	—
37	C₂²	—	4	1	no	—
38	C₂²	—	4	1	no	—
39	C₂²	C₂²⋊C₄	1	2	yes	—
40	C₂²	C₂×D₄	1	1	yes	characteristic
41	C₄	—	2	2	no	—
42	C₄	—	4	2	no	—
43	C₄	C₂²⋊C₄	1	2	yes	—
44	C₄	C₂²×C₄	1	1	yes	characteristic
45	C₄	C₂×D₄	1	1	yes	characteristic
46	C₂	—	2	2	no	—
47	C₂	—	4	2	no	—
48	C₂	C₂×C₂²⋊C₄	1	1	yes	characteristic
49	C₂	AGL(1,ℤ/8)	1	1	yes	characteristic
50	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.