Subgroups — #28357308

Order 13856.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20294107	C₂	1	3	yes	maximal, complemented
2	#20294105	C₂	1	3	yes	maximal, complemented
3	#20294098	C₂	1	1	yes	maximal, characteristic
4	#16812365	C₂²	1	1	yes	characteristic
5	#16812365	C₂²	1	3	yes	—
6	D₁₇₃₂	C₄	1	3	yes	—
7	C₄×D₄₃₃	C₂²	1	3	yes	—
8	Q₈×C₄₃₃	C₄	1	1	yes	characteristic
9	C₂×D₄₃₃	C₂×C₄	1	3	yes	—
10	C₄×C₄₃₃	C₂×C₄	1	3	yes	—
11	Dic₄₃₃	C₂³	1	1	yes	characteristic
12	C₂×C₄₃₃	C₂²×C₄	1	1	yes	characteristic
13	D₄₃₃	—	2	3	no	—
14	C₄₃₃	#131	1	1	yes	characteristic, complemented, Sylow
15	#131	—	433	1	no	maximal, Sylow
16	#41	—	433	1	no	—
17	M₁₆	—	433	3	no	—
18	C₂×C₈	—	433	3	no	—
19	Q₈	#13181884	1	1	yes	characteristic
20	D₄	—	433	3	no	—
21	C₂×C₄	—	433	3	no	—
22	C₈	—	433	1	no	—
23	C₈	—	433	3	no	—
24	C₂²	—	433	3	no	—
25	C₄	—	433	1	no	—
26	C₄	C₂×#13181884	1	3	yes	—
27	C₂	—	866	3	no	—
28	C₂	C₂²×#13181884	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.