Subgroups — #419

Order 64.

75 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆	C₂	1	1	yes	maximal, characteristic
3	#117	C₂	1	1	yes	maximal, characteristic
4	#103	C₂	1	4	yes	maximal, complemented
5	C₂×Q₈	—	2	2	no	—
6	C₂×Q₈	—	2	1	no	—
7	C₂×Q₈	C₄	1	4	yes	complemented
8	C₂×Q₈	C₂²	1	2	yes	—
9	C₂²×C₄	—	2	1	no	—
10	C₂²×C₄	C₂²	1	1	yes	characteristic
11	M₁₆	—	2	2	no	—
12	C₂×C₈	C₂²	1	2	yes	—
13	C₄⋊C₄	C₂²	1	2	yes	—
14	C₂²⋊C₄	—	2	1	no	—
15	C₄²	—	2	1	no	—
16	C₂³	D₄	1	1	yes	characteristic
17	Q₈	—	2	4	no	—
18	Q₈	—	2	2	no	—
19	Q₈	C₂×C₄	1	4	yes	—
20	C₂×C₄	—	2	4	no	—
21	C₂×C₄	—	2	2	no	—
22	C₂×C₄	—	2	2	no	—
23	C₂×C₄	C₂×C₄	1	2	yes	—
24	C₂×C₄	D₄	1	1	yes	characteristic
25	C₂×C₄	D₄	1	2	yes	—
26	C₂×C₄	C₂³	1	1	yes	characteristic
27	C₈	—	2	2	no	—
28	C₂²	—	2	2	no	—
29	C₂²	C₂²⋊C₄	1	2	yes	—
30	C₂²	C₂×D₄	1	1	yes	characteristic
31	C₄	—	2	4	no	—
32	C₄	—	4	2	no	—
33	C₄	C₂²⋊C₄	1	2	yes	—
34	C₄	C₂²×C₄	1	1	yes	characteristic
35	C₄	C₂×D₄	1	1	yes	characteristic
36	C₂	—	2	2	no	—
37	C₂	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₂	#137	1	2	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #103	C₂	semidirect
7. C₂×Q₈	C₄	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.