Subgroups — #42122737

Order 27712.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28357289	C₂	1	2	yes	maximal
2	C₁₆×D₄₃₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#13181884	—	2	2	no	—
4	C₈×D₄₃₃	C₂²	1	1	yes	characteristic
5	#20294072	C₄	1	1	yes	characteristic, complemented
6	C₁₆×C₄₃₃	C₄	1	1	yes	characteristic, complemented
7	C₂×#13181884	—	4	2	no	—
8	C₄×D₄₃₃	D₄	1	1	yes	characteristic
9	#16812358	Q₈	1	1	yes	characteristic
10	C₈×C₄₃₃	C₂×C₄	1	1	yes	characteristic
11	C₂×D₄₃₃	D₈	1	1	yes	characteristic
12	#13181884	—	8	2	no	—
13	C₄×C₄₃₃	C₄⋊C₄	1	1	yes	characteristic
14	Dic₄₃₃	Q₁₆	1	1	yes	characteristic
15	C₂×C₄₃₃	#107	1	1	yes	characteristic
16	D₄₃₃	D₁₆	1	1	yes	characteristic
17	D₄₃₃	Q₃₂	1	1	yes	characteristic
18	C₄₃₃	#366	1	1	yes	characteristic, complemented, Sylow
19	#366	—	433	1	no	maximal, Sylow
20	C₂×C₁₆	—	433	1	no	—
21	#107	—	433	2	no	—
22	C₂×C₈	—	433	1	no	—
23	C₄⋊C₄	—	866	2	no	—
24	C₁₆	—	433	1	no	—
25	C₁₆	#13181884	1	1	yes	characteristic, complemented
26	C₂×C₄	—	433	1	no	—
27	C₂×C₄	—	1732	2	no	—
28	C₈	—	433	1	no	—
29	C₈	C₂×#13181884	1	1	yes	characteristic
30	C₂²	—	433	1	no	—
31	C₄	—	3464	2	no	—
32	C₄	—	433	1	no	—
33	C₄	C₄⋊#13181884	1	1	yes	characteristic
34	C₂	—	433	1	no	—
35	C₂	—	433	1	no	—
36	C₂	#28357289	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.