Subgroups — #44569571

Order 32416.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30633798	C₂	1	2	yes	maximal
2	C₂×Q₈×C₁₀₁₃	C₂	1	1	yes	maximal, characteristic
3	#22549201	—	2	2	no	—
4	Q₈×C₁₀₁₃	—	2	2	no	—
5	C₂×C₄×C₁₀₁₃	C₄	1	2	yes	—
6	C₂×C₄×C₁₀₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₁₀₁₃	C₂×C₄	1	1	yes	characteristic
8	C₄×C₁₀₁₃	—	2	2	no	—
9	C₄×C₁₀₁₃	D₄	1	2	yes	—
10	C₂×C₁₀₁₃	—	2	1	no	—
11	C₂×C₁₀₁₃	C₂²⋊C₄	1	1	yes	characteristic
12	C₁₀₁₃	#101	1	1	yes	characteristic, complemented, Sylow
13	#101	—	1013	1	no	maximal, Sylow
14	C₂×Q₈	D₁₀₁₃	1	1	yes	characteristic
15	M₁₆	—	1013	2	no	—
16	Q₈	—	2	2	no	—
17	C₂×C₄	Dic₁₀₁₃	1	2	yes	—
18	C₂×C₄	C₂×D₁₀₁₃	1	1	yes	characteristic
19	C₈	—	2026	2	no	—
20	C₂²	C₂×Dic₁₀₁₃	1	1	yes	characteristic
21	C₄	—	2	2	no	—
22	C₄	C₂²⋊D₁₀₁₃	1	2	yes	—
23	C₂	—	2	1	no	—
24	C₂	C₂²⋊Dic₁₀₁₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₁₀₁₃	#101	semidirect

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