Subgroups — #29567930

Order 15616.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₉₅₂	C₂	1	1	yes	maximal, characteristic
2	#21443638	C₂	1	1	yes	maximal, characteristic
3	C₆₁×Q₁₂₈	C₂	1	1	yes	maximal, characteristic
4	Dic₉₇₆	—	2	1	no	—
5	C₆₁×Q₆₄	—	2	1	no	—
6	C₆₁×C₆₄	C₂²	1	1	yes	characteristic
7	Dic₄₈₈	—	4	1	no	—
8	Q₃₂×C₆₁	—	4	1	no	—
9	C₃₂×C₆₁	D₄	1	1	yes	characteristic
10	Q₁₆×C₆₁	—	8	1	no	—
11	Dic₂₄₄	—	8	1	no	—
12	C₁₆×C₆₁	D₈	1	1	yes	characteristic
13	Q₈×C₆₁	—	16	1	no	—
14	Dic₁₂₂	—	16	1	no	—
15	C₈×C₆₁	D₁₆	1	1	yes	characteristic
16	Q₂₅₆	—	61	1	no	maximal, Sylow
17	C₄×C₆₁	—	32	1	no	—
18	C₄×C₆₁	D₃₂	1	1	yes	characteristic
19	Dic₆₁	—	32	1	no	—
20	Q₁₂₈	—	61	1	no	—
21	Q₁₂₈	D₆₁	1	1	yes	characteristic
22	C₁₂₈	—	61	1	no	—
23	C₂×C₆₁	D₆₄	1	1	yes	characteristic
24	Q₆₄	—	2	1	no	—
25	Q₆₄	—	122	1	no	—
26	C₆₄	C₂×D₆₁	1	1	yes	characteristic
27	C₆₁	Q₂₅₆	1	1	yes	characteristic, complemented, Sylow
28	Q₃₂	—	4	1	no	—
29	Q₃₂	—	244	1	no	—
30	C₃₂	C₂²⋊D₆₁	1	1	yes	characteristic
31	Q₁₆	—	8	1	no	—
32	Q₁₆	—	488	1	no	—
33	C₁₆	#11758199	1	1	yes	characteristic
34	Q₈	—	16	1	no	—
35	Q₈	—	976	1	no	—
36	C₈	#14519718	1	1	yes	characteristic
37	C₄	—	32	1	no	—
38	C₄	—	1952	1	no	—
39	C₄	#16839597	1	1	yes	characteristic
40	C₂	#21444031	1	1	yes	characteristic

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

N	H ≅ G/N	type
27. C₆₁	Q₂₅₆	semidirect

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