Subgroups — #41003729

Order 26944.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20269774	C₂	1	2	yes	maximal
2	C₈×Dic₄₂₁	C₂	1	1	yes	maximal, characteristic
3	#20269774	C₄	1	4	yes	complemented
4	C₂×#16809890	C₂²	1	1	yes	characteristic
5	C₄×Dic₄₂₁	C₄	1	1	yes	characteristic
6	C₂×C₈×C₄₂₁	C₄	1	1	yes	characteristic
7	C₂×Dic₄₂₁	C₈	1	2	yes	—
8	#16809890	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₄₂₁	C₂×C₄	1	1	yes	characteristic
10	C₈×C₄₂₁	C₈	1	2	yes	—
11	C₂²×C₄₂₁	C₂×C₈	1	1	yes	characteristic
12	C₄×C₄₂₁	C₄²	1	1	yes	characteristic
13	C₄×C₄₂₁	C₂×C₈	1	1	yes	characteristic
14	Dic₄₂₁	—	2	2	no	—
15	C₂×C₄₂₁	C₄×C₈	1	1	yes	characteristic
16	C₂×C₄₂₁	M₃₂	1	2	yes	—
17	C₄₂₁	#346	1	1	yes	characteristic, complemented, Sylow
18	#346	—	421	1	no	maximal, Sylow
19	C₂×C₁₆	—	421	2	no	—
20	C₄×C₈	—	421	1	no	—
21	C₂×C₈	—	421	1	no	—
22	C₂×C₈	#13132997	1	1	yes	characteristic
23	C₄²	—	421	1	no	—
24	C₁₆	—	421	4	no	—
25	C₂×C₄	—	421	2	no	—
26	C₂×C₄	C₂×#13132997	1	1	yes	characteristic
27	C₈	—	421	2	no	—
28	C₈	#16809897	1	2	yes	—
29	C₂²	D₄₂₁⋊C₈	1	1	yes	characteristic
30	C₄	—	842	2	no	—
31	C₄	C₄×#13132997	1	1	yes	characteristic
32	C₄	C₂×#16809897	1	1	yes	characteristic
33	C₂	C₄×#16809897	1	1	yes	characteristic
34	C₂	#27212441	1	2	yes	—

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

N	H ≅ G/N	type
3. #20269774	C₄	semidirect
17. C₄₂₁	#346	semidirect

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