Subgroups — #344

Order 64.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆	C₂	1	1	yes	maximal, characteristic
3	#117	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄	C₂²	1	1	yes	characteristic
5	M₁₆	—	2	1	no	—
6	M₁₆	—	2	1	no	—
7	M₁₆	—	2	1	no	—
8	M₁₆	C₄	1	2	yes	complemented
9	C₂×C₈	—	2	1	no	—
10	C₂×C₈	C₄	1	2	yes	complemented
11	C₄⋊C₄	—	2	1	no	—
12	C₂²⋊C₄	C₄	1	2	yes	—
13	C₄²	—	2	1	no	—
14	C₂³	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄	—	2	2	no	—
16	C₂×C₄	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄	D₄	1	1	yes	characteristic
19	C₂×C₄	D₄	1	1	yes	characteristic
20	C₂×C₄	D₄	1	1	yes	characteristic
21	C₂×C₄	Q₈	1	1	yes	characteristic
22	C₈	—	2	2	no	—
23	C₈	—	2	2	no	—
24	C₂²	—	4	1	no	—
25	C₂²	C₄²	1	1	yes	characteristic
26	C₂²	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²	C₄⋊C₄	1	1	yes	characteristic
28	C₄	—	4	2	no	—
29	C₄	C₂²⋊C₄	1	1	yes	characteristic
30	C₄	C₂²⋊C₄	1	1	yes	characteristic
31	C₄	C₄⋊C₄	1	1	yes	characteristic
32	C₄	C₄⋊C₄	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	—	2	1	no	—
35	C₂	—	2	1	no	—
36	C₂	#95	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. M₁₆	C₄	semidirect
10. C₂×C₈	C₄	semidirect

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

subgroup	index
C₂×M₁₆	2
#117	2