Subgroups — #418

Order 64.

95 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#117	C₂	1	1	yes	maximal, characteristic, complemented
4	#102	C₂	1	4	yes	maximal, complemented
5	C₂⁴	—	2	1	no	—
6	C₂×D₄	—	2	1	no	—
7	C₂×D₄	—	2	2	no	—
8	C₂×D₄	C₄	1	4	yes	complemented
9	C₂×D₄	C₂²	1	2	yes	—
10	C₂²×C₄	C₂²	1	1	yes	characteristic
11	M₁₆	—	2	2	no	—
12	C₂×C₈	C₂²	1	2	yes	complemented
13	C₄⋊C₄	C₂²	1	2	yes	complemented
14	C₂²⋊C₄	—	2	1	no	—
15	C₄²	—	2	1	no	—
16	C₂³	—	2	4	no	—
17	C₂³	—	2	2	no	—
18	C₂³	—	4	4	no	—
19	C₂³	D₄	1	1	yes	characteristic
20	D₄	—	2	4	no	—
21	D₄	—	2	2	no	—
22	D₄	C₂×C₄	1	4	yes	—
23	C₂×C₄	—	2	2	no	—
24	C₂×C₄	C₂×C₄	1	2	yes	—
25	C₂×C₄	D₄	1	1	yes	characteristic
26	C₂×C₄	D₄	1	2	yes	—
27	C₂×C₄	C₂³	1	1	yes	characteristic
28	C₈	—	2	2	no	—
29	C₂²	—	2	2	no	—
30	C₂²	—	2	4	no	—
31	C₂²	—	4	8	no	—
32	C₂²	—	4	4	no	—
33	C₂²	C₂²⋊C₄	1	2	yes	—
34	C₂²	C₂×D₄	1	1	yes	characteristic
35	C₄	—	4	2	no	—
36	C₄	C₂²⋊C₄	1	2	yes	—
37	C₄	C₂²×C₄	1	1	yes	characteristic
38	C₄	C₂×D₄	1	1	yes	characteristic
39	C₂	—	2	2	no	—
40	C₂	—	4	4	no	—
41	C₂	C₂×C₂²⋊C₄	1	1	yes	characteristic
42	C₂	AGL(1,ℤ/8)	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.