Subgroups — C₆₄×D₂₄₁ #44505653

Order 30848.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₂×D₂₄₁	C₂	1	1	yes	maximal, characteristic
2	#29507436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₄×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₂₄₁	C₄	1	1	yes	characteristic
5	#21440548	C₄	1	1	yes	characteristic
6	C₃₂×C₂₄₁	C₂²	1	1	yes	characteristic
7	C₈×D₂₄₁	C₈	1	1	yes	characteristic
8	#16838745	C₈	1	1	yes	characteristic
9	C₁₆×C₂₄₁	C₂×C₄	1	1	yes	characteristic
10	C₄×D₂₄₁	C₁₆	1	1	yes	characteristic
11	#14515349	C₁₆	1	1	yes	characteristic
12	C₈×C₂₄₁	C₂×C₈	1	1	yes	characteristic
13	C₂×D₂₄₁	C₃₂	1	1	yes	characteristic
14	C₄×C₂₄₁	C₂×C₁₆	1	1	yes	characteristic
15	Dic₂₄₁	C₃₂	1	1	yes	characteristic
16	C₂×C₂₄₁	C₂×C₃₂	1	1	yes	characteristic
17	D₂₄₁	C₆₄	1	2	yes	direct product factor
18	C₂₄₁	C₂×C₆₄	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₆₄	—	241	1	no	maximal, Sylow
20	C₂×C₃₂	—	241	1	no	—
21	C₆₄	—	241	1	no	—
22	C₆₄	D₂₄₁	1	1	yes	characteristic, direct product factor
23	C₂×C₁₆	—	241	1	no	—
24	C₃₂	—	241	1	no	—
25	C₃₂	C₂×D₂₄₁	1	1	yes	characteristic
26	C₂×C₈	—	241	1	no	—
27	C₁₆	—	241	1	no	—
28	C₁₆	C₄×D₂₄₁	1	1	yes	characteristic
29	C₂×C₄	—	241	1	no	—
30	C₈	—	241	1	no	—
31	C₈	C₈×D₂₄₁	1	1	yes	characteristic
32	C₂²	—	241	1	no	—
33	C₄	—	241	1	no	—
34	C₄	C₁₆×D₂₄₁	1	1	yes	characteristic
35	C₂	—	241	2	no	—
36	C₂	C₃₂×D₂₄₁	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.