Subgroups — #101×C₁₀₄₉ #46776813

Order 33568.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₀₄₉	C₂	1	1	yes	maximal, characteristic
2	M₁₆×C₁₀₄₉	C₂	1	2	yes	maximal
3	Q₈×C₁₀₄₉	—	2	2	no	—
4	C₂×C₄×C₁₀₄₉	C₄	1	2	yes	—
5	C₂×C₄×C₁₀₄₉	C₂²	1	1	yes	characteristic
6	C₈×C₁₀₄₉	—	2	2	no	—
7	C₂²×C₁₀₄₉	C₂×C₄	1	1	yes	characteristic
8	C₄×C₁₀₄₉	—	2	2	no	—
9	C₄×C₁₀₄₉	D₄	1	2	yes	—
10	C₂×C₁₀₄₉	—	2	1	no	—
11	C₂×C₁₀₄₉	C₂²⋊C₄	1	1	yes	characteristic
12	C₁₀₄₉	#101	1	1	yes	characteristic, direct product factor, Sylow
13	#101	C₁₀₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂×Q₈	C₂×C₁₀₄₉	1	1	yes	characteristic
15	M₁₆	C₂×C₁₀₄₉	1	2	yes	—
16	Q₈	—	2	2	no	—
17	C₂×C₄	C₄×C₁₀₄₉	1	2	yes	—
18	C₂×C₄	C₂²×C₁₀₄₉	1	1	yes	characteristic
19	C₈	—	2	2	no	—
20	C₂²	C₂×C₄×C₁₀₄₉	1	1	yes	characteristic
21	C₄	—	2	2	no	—
22	C₄	D₄×C₁₀₄₉	1	2	yes	—
23	C₂	—	2	1	no	—
24	C₂	C₂²⋊C₄×C₁₀₄₉	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₁₀₄₉	#101	direct (N × H)
13. #101	C₁₀₄₉	direct (N × H)

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