Subgroups — #41003764

Order 26944.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27212436	C₂	1	1	yes	maximal, characteristic
2	#27212434	C₂	1	1	yes	maximal, characteristic
3	#27212305	C₂	1	1	yes	maximal, characteristic
4	#20269781	—	2	1	no	—
5	C₄⋊#13132997	—	2	1	no	—
6	C₈×D₄₂₁	C₂²	1	1	yes	characteristic
7	#20269746	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₄₂₁	C₄	1	1	yes	characteristic, complemented
9	C₂×#13132997	—	4	1	no	—
10	#16809897	—	4	1	no	—
11	C₄×D₄₂₁	D₄	1	1	yes	characteristic
12	#16809890	Q₈	1	1	yes	characteristic
13	C₈×C₄₂₁	C₂×C₄	1	1	yes	characteristic
14	C₂×D₄₂₁	SD₁₆	1	1	yes	characteristic
15	#13132997	—	8	1	no	—
16	C₄×C₄₂₁	C₄⋊C₄	1	1	yes	characteristic
17	Dic₄₂₁	SD₁₆	1	1	yes	characteristic
18	C₂×C₄₂₁	#106	1	1	yes	characteristic
19	D₄₂₁	—	2	1	no	—
20	C₄₂₁	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	421	1	no	maximal, Sylow
22	M₃₂	—	421	1	no	—
23	#108	—	421	1	no	—
24	#106	—	421	1	no	—
25	M₁₆	—	842	1	no	—
26	C₂×C₈	—	421	1	no	—
27	C₄⋊C₄	—	842	1	no	—
28	C₁₆	—	421	1	no	—
29	C₁₆	#13132997	1	1	yes	characteristic, complemented
30	C₂×C₄	—	1684	1	no	—
31	C₂×C₄	—	421	1	no	—
32	C₈	—	1684	1	no	—
33	C₈	—	421	1	no	—
34	C₈	C₂×#13132997	1	1	yes	characteristic
35	C₂²	—	421	1	no	—
36	C₄	—	3368	1	no	—
37	C₄	—	421	1	no	—
38	C₄	C₄⋊#13132997	1	1	yes	characteristic
39	C₂	—	842	1	no	—
40	C₂	#27212434	1	1	yes	characteristic

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

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