Subgroups — #42122869

Order 27712.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28357294	C₂	1	3	yes	maximal, complemented
2	C₂×#20294100	C₂	1	3	yes	maximal, complemented
3	#28357227	C₂	1	1	yes	maximal, characteristic
4	#20294100	C₂²	1	1	yes	characteristic
5	#20294100	C₂²	1	3	yes	—
6	#20294081	C₄	1	3	yes	—
7	C₂×#16812358	C₂²	1	3	yes	—
8	#41×C₄₃₃	C₄	1	1	yes	characteristic
9	#16812358	C₂×C₄	1	3	yes	—
10	#16812358	C₂³	1	1	yes	characteristic
11	Q₈×C₄₃₃	C₈	1	1	yes	characteristic
12	D₄×C₄₃₃	C₈	1	3	yes	—
13	C₂×C₄×C₄₃₃	C₂×C₄	1	3	yes	—
14	C₂²×C₄₃₃	C₂×C₈	1	3	yes	—
15	C₄×C₄₃₃	C₂×C₈	1	3	yes	—
16	C₄×C₄₃₃	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₄₃₃	—	2	3	no	—
18	C₂×C₄₃₃	C₂²×C₈	1	1	yes	characteristic
19	C₄₃₃	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	433	1	no	maximal, Sylow
21	#131	—	433	1	no	—
22	M₃₂	—	433	3	no	—
23	C₂×C₁₆	—	433	3	no	—
24	#41	#13181884	1	1	yes	characteristic
25	M₁₆	—	433	3	no	—
26	C₂×C₈	—	433	3	no	—
27	C₁₆	—	433	1	no	—
28	C₁₆	—	433	3	no	—
29	Q₈	#16812365	1	1	yes	characteristic
30	D₄	#16812365	1	3	yes	—
31	C₂×C₄	C₂×#13181884	1	3	yes	—
32	C₈	—	433	1	no	—
33	C₈	—	433	3	no	—
34	C₂²	C₂×#16812365	1	3	yes	—
35	C₄	C₂×#16812365	1	3	yes	—
36	C₄	C₂²×#13181884	1	1	yes	characteristic
37	C₂	—	2	3	no	—
38	C₂	C₂²×#16812365	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.