Subgroups — M₄₀₉₆ #72210198

Order 4096.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₀₂₄	C₂	1	1	yes	maximal, characteristic
2	C₂₀₄₈	C₂	1	2	yes	maximal, complemented
3	C₂×C₅₁₂	C₄	1	1	yes	characteristic
4	C₁₀₂₄	C₄	1	1	yes	characteristic
5	C₁₀₂₄	C₂²	1	1	yes	characteristic
6	C₂×C₂₅₆	C₈	1	1	yes	characteristic
7	C₅₁₂	C₈	1	1	yes	characteristic
8	C₅₁₂	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₂₈	C₁₆	1	1	yes	characteristic
10	C₂₅₆	C₁₆	1	1	yes	characteristic
11	C₂₅₆	C₂×C₈	1	1	yes	characteristic
12	C₂×C₆₄	C₃₂	1	1	yes	characteristic
13	C₁₂₈	C₃₂	1	1	yes	characteristic
14	C₁₂₈	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₃₂	C₆₄	1	1	yes	characteristic
16	C₆₄	C₆₄	1	1	yes	characteristic
17	C₆₄	C₂×C₃₂	1	1	yes	characteristic
18	C₂×C₁₆	C₁₂₈	1	1	yes	characteristic
19	C₃₂	C₁₂₈	1	1	yes	characteristic
20	C₃₂	C₂×C₆₄	1	1	yes	characteristic
21	C₂×C₈	C₂₅₆	1	1	yes	characteristic
22	C₁₆	C₂₅₆	1	1	yes	characteristic
23	C₁₆	C₂×C₁₂₈	1	1	yes	characteristic
24	C₂×C₄	C₅₁₂	1	1	yes	characteristic
25	C₈	C₅₁₂	1	1	yes	characteristic
26	C₈	C₂×C₂₅₆	1	1	yes	characteristic
27	C₂²	C₁₀₂₄	1	1	yes	characteristic
28	C₄	C₁₀₂₄	1	1	yes	characteristic
29	C₄	C₂×C₅₁₂	1	1	yes	characteristic
30	C₂	—	2	1	no	—
31	C₂	C₂×C₁₀₂₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₂₀₄₈	C₂	semidirect

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

subgroup	index
C₂×C₁₀₂₄	2
C₂₀₄₈	2