Subgroups — #413

Order 64.

75 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	2	yes	maximal, complemented
3	#101	C₂	1	2	yes	maximal, complemented
4	#100	C₂	1	2	yes	maximal, complemented
5	#41	—	2	2	no	—
6	#41	—	2	2	no	—
7	C₂×Q₈	C₂²	1	1	yes	characteristic
8	C₂×D₄	C₄	1	2	yes	—
9	C₂×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₄	C₄	1	2	yes	—
11	C₂²×C₄	C₂²	1	1	yes	characteristic
12	M₁₆	—	2	2	no	—
13	M₁₆	C₂²	1	4	yes	—
14	C₂×C₈	—	2	2	no	—
15	C₂³	C₂×C₄	1	2	yes	—
16	C₂³	C₂×C₄	1	1	yes	characteristic
17	Q₈	—	2	2	no	—
18	D₄	—	2	4	no	—
19	D₄	—	2	2	no	—
20	C₂×C₄	—	2	2	no	—
21	C₂×C₄	—	2	2	no	—
22	C₂×C₄	C₂×C₄	1	2	yes	—
23	C₂×C₄	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄	D₄	1	2	yes	—
25	C₂×C₄	D₄	1	2	yes	—
26	C₂×C₄	C₂³	1	1	yes	characteristic
27	C₈	—	2	4	no	—
28	C₂²	—	2	2	no	—
29	C₂²	—	4	1	no	—
30	C₂²	—	4	2	no	—
31	C₂²	C₂²⋊C₄	1	2	yes	—
32	C₂²	C₂²×C₄	1	1	yes	characteristic
33	C₄	—	2	2	no	—
34	C₄	C₂²⋊C₄	1	1	yes	characteristic
35	C₄	C₂²⋊C₄	1	1	yes	characteristic
36	C₄	C₂×D₄	1	2	yes	—
37	C₂	—	2	1	no	—
38	C₂	—	2	2	no	—
39	C₂	—	4	2	no	—
40	C₂	C₂×C₂²⋊C₄	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.