Subgroups — #29567925

Order 15616.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₉₀₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#21443638	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×D₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉₅₂	—	2	1	no	—
5	C₆₁×D₃₂	—	2	1	no	—
6	C₆₁×C₆₄	C₂²	1	1	yes	characteristic
7	D₉₇₆	—	4	1	no	—
8	D₁₆×C₆₁	—	4	1	no	—
9	C₃₂×C₆₁	D₄	1	1	yes	characteristic
10	D₈×C₆₁	—	8	1	no	—
11	D₄₈₈	—	8	1	no	—
12	C₁₆×C₆₁	D₈	1	1	yes	characteristic
13	D₄×C₆₁	—	16	1	no	—
14	D₂₄₄	—	16	1	no	—
15	C₈×C₆₁	D₁₆	1	1	yes	characteristic
16	D₁₂₈	—	61	1	no	maximal, Sylow
17	C₂²×C₆₁	—	32	1	no	—
18	C₂×D₆₁	—	32	1	no	—
19	C₄×C₆₁	D₃₂	1	1	yes	characteristic
20	D₆₄	—	61	1	no	—
21	D₆₄	D₆₁	1	1	yes	characteristic, complemented
22	C₁₂₈	—	61	1	no	—
23	C₂×C₆₁	—	64	1	no	—
24	C₂×C₆₁	D₆₄	1	1	yes	characteristic
25	D₆₁	—	64	1	no	—
26	D₃₂	—	2	1	no	—
27	D₃₂	—	122	1	no	—
28	C₆₄	C₂×D₆₁	1	1	yes	characteristic
29	C₆₁	D₁₂₈	1	1	yes	characteristic, complemented, Sylow
30	D₁₆	—	4	1	no	—
31	D₁₆	—	244	1	no	—
32	C₃₂	C₂²⋊D₆₁	1	1	yes	characteristic
33	D₈	—	8	1	no	—
34	D₈	—	488	1	no	—
35	C₁₆	#11758199	1	1	yes	characteristic
36	D₄	—	16	1	no	—
37	D₄	—	976	1	no	—
38	C₈	#14519718	1	1	yes	characteristic
39	C₂²	—	32	1	no	—
40	C₂²	—	1952	1	no	—
41	C₄	#16839597	1	1	yes	characteristic
42	C₂	—	64	1	no	—
43	C₂	—	3904	1	no	—
44	C₂	#21444031	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.