Subgroups — #42122915

Order 27712.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28357317	C₂	1	2	yes	maximal
2	C₈×#13181884	C₂	1	1	yes	maximal, characteristic
3	#20294109	—	2	2	no	—
4	#20294105	C₂²	1	1	yes	characteristic
5	C₄×#13181884	C₄	1	1	yes	characteristic
6	C₈×D₄₃₃	C₄	1	1	yes	characteristic
7	C₂×#13181884	—	2	1	no	—
8	#16812365	D₄	1	1	yes	characteristic
9	#16812365	Q₈	1	1	yes	characteristic
10	C₄×D₄₃₃	C₂×C₄	1	1	yes	characteristic
11	#16812358	C₈	1	1	yes	characteristic
12	C₈×C₄₃₃	C₈	1	1	yes	characteristic
13	C₂×D₄₃₃	M₁₆	1	1	yes	characteristic
14	#13181884	—	2	2	no	—
15	C₄×C₄₃₃	C₂×C₈	1	1	yes	characteristic
16	Dic₄₃₃	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₄₃₃	C₄⋊C₈	1	1	yes	characteristic
18	D₄₃₃	—	2	1	no	—
19	C₄₃₃	#364	1	1	yes	characteristic, complemented, Sylow
20	#364	—	433	1	no	maximal, Sylow
21	M₃₂	—	433	2	no	—
22	C₄×C₈	—	433	1	no	—
23	C₂×C₈	—	433	1	no	—
24	C₂×C₈	—	433	1	no	—
25	C₄²	—	433	1	no	—
26	C₁₆	—	866	2	no	—
27	C₂×C₄	—	866	1	no	—
28	C₂×C₄	—	433	1	no	—
29	C₈	—	433	1	no	—
30	C₈	—	433	1	no	—
31	C₈	—	433	1	no	—
32	C₈	#16812367	1	1	yes	characteristic
33	C₂²	—	433	1	no	—
34	C₄	—	866	2	no	—
35	C₄	—	433	1	no	—
36	C₄	C₂×#16812367	1	1	yes	characteristic
37	C₂	—	866	1	no	—
38	C₂	C₄⋊#16812367	1	1	yes	characteristic

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

N	H ≅ G/N	type
19. C₄₃₃	#364	semidirect

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