Subgroups — #28417557

Order 14912.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21418632	C₂	1	3	yes	maximal, complemented
2	#21418630	C₂	1	3	yes	maximal, complemented
3	#21418623	C₂	1	1	yes	maximal, characteristic
4	#16836606	C₂²	1	1	yes	characteristic
5	#16836606	C₂²	1	3	yes	—
6	#16836604	C₄	1	3	yes	—
7	#16836602	C₂²	1	3	yes	—
8	#16836595	C₄	1	1	yes	characteristic
9	#14272345	C₂×C₄	1	3	yes	—
10	#14272345	C₂³	1	1	yes	characteristic
11	D₉₃₂	C₈	1	3	yes	—
12	C₄×D₂₃₃	C₂×C₄	1	3	yes	—
13	Q₈×C₂₃₃	C₈	1	1	yes	characteristic
14	C₂×D₂₃₃	C₂×C₈	1	3	yes	—
15	C₄×C₂₃₃	C₂×C₈	1	3	yes	—
16	Dic₂₃₃	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₂₃₃	C₂²×C₈	1	1	yes	characteristic
18	D₂₃₃	—	2	3	no	—
19	C₂₃₃	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	233	1	no	maximal, Sylow
21	#131	—	233	1	no	—
22	M₃₂	—	233	3	no	—
23	C₂×C₁₆	—	233	3	no	—
24	#41	—	233	1	no	—
25	M₁₆	—	233	3	no	—
26	C₂×C₈	—	233	3	no	—
27	C₁₆	—	233	1	no	—
28	C₁₆	—	233	3	no	—
29	Q₈	#14272347	1	1	yes	characteristic
30	D₄	—	233	3	no	—
31	C₂×C₄	—	233	3	no	—
32	C₈	—	233	1	no	—
33	C₈	—	233	3	no	—
34	C₂²	—	233	3	no	—
35	C₄	—	233	1	no	—
36	C₄	C₂×#14272347	1	3	yes	—
37	C₂	—	466	3	no	—
38	C₂	C₂²×#14272347	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.