Subgroups — M₂₀₄₈ #72210197

Order 2048.

31 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₁₂	C₂	1	1	yes	maximal, characteristic
2	C₁₀₂₄	C₂	1	2	yes	maximal, complemented
3	C₂×C₂₅₆	C₄	1	1	yes	characteristic
4	C₅₁₂	C₄	1	1	yes	characteristic
5	C₅₁₂	C₂²	1	1	yes	characteristic
6	C₂×C₁₂₈	C₈	1	1	yes	characteristic
7	C₂₅₆	C₈	1	1	yes	characteristic
8	C₂₅₆	C₂×C₄	1	1	yes	characteristic
9	C₂×C₆₄	C₁₆	1	1	yes	characteristic
10	C₁₂₈	C₁₆	1	1	yes	characteristic
11	C₁₂₈	C₂×C₈	1	1	yes	characteristic
12	C₂×C₃₂	C₃₂	1	1	yes	characteristic
13	C₆₄	C₃₂	1	1	yes	characteristic
14	C₆₄	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₁₆	C₆₄	1	1	yes	characteristic
16	C₃₂	C₆₄	1	1	yes	characteristic
17	C₃₂	C₂×C₃₂	1	1	yes	characteristic
18	C₂×C₈	C₁₂₈	1	1	yes	characteristic
19	C₁₆	C₁₂₈	1	1	yes	characteristic
20	C₁₆	C₂×C₆₄	1	1	yes	characteristic
21	C₂×C₄	C₂₅₆	1	1	yes	characteristic
22	C₈	C₂₅₆	1	1	yes	characteristic
23	C₈	C₂×C₁₂₈	1	1	yes	characteristic
24	C₂²	C₅₁₂	1	1	yes	characteristic
25	C₄	C₅₁₂	1	1	yes	characteristic
26	C₄	C₂×C₂₅₆	1	1	yes	characteristic
27	C₂	—	2	1	no	—
28	C₂	C₂×C₅₁₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₁₀₂₄	C₂	semidirect

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

subgroup	index
C₂×C₅₁₂	2
C₁₀₂₄	2