Subgroups — #41003763

Order 26944.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27212440	C₂	1	2	yes	maximal
2	C₄×#16809890	C₂	1	1	yes	maximal, characteristic
3	#20269774	—	2	2	no	—
4	C₂×#16809890	C₄	1	1	yes	characteristic
5	C₂×#16809890	C₂²	1	1	yes	characteristic
6	C₄²×C₄₂₁	C₄	1	1	yes	characteristic
7	#16809890	C₈	1	2	yes	—
8	#16809890	D₄	1	1	yes	characteristic
9	#16809890	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₄₂₁	—	2	1	no	—
11	C₂×C₄×C₄₂₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄₂₁	M₁₆	1	1	yes	characteristic
13	C₄×C₄₂₁	—	2	2	no	—
14	C₄×C₄₂₁	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₄₂₁	C₂×C₈	1	1	yes	characteristic
16	C₂×C₄₂₁	—	2	1	no	—
17	C₂×C₄₂₁	C₄⋊C₈	1	1	yes	characteristic
18	C₄₂₁	#364	1	1	yes	characteristic, complemented, Sylow
19	#364	—	421	1	no	maximal, Sylow
20	M₃₂	—	421	2	no	—
21	C₄×C₈	—	421	1	no	—
22	C₂×C₈	—	421	1	no	—
23	C₂×C₈	—	421	1	no	—
24	C₄²	#13132997	1	1	yes	characteristic
25	C₁₆	—	842	2	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂×#13132997	1	1	yes	characteristic
28	C₈	—	421	1	no	—
29	C₈	—	421	1	no	—
30	C₈	—	421	2	no	—
31	C₂²	#20269780	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₄⋊#13132997	1	1	yes	characteristic
34	C₄	D₄₂₁⋊C₈	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#27212433	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₄₂₁	#364	semidirect

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