Subgroups — #16840652

Order 3904.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14519852	C₂	1	1	yes	maximal, characteristic
2	#14519831	C₂	1	1	yes	maximal, characteristic
3	#14519716	C₂	1	1	yes	maximal, characteristic
4	C₄×#6923	C₄	1	1	yes	characteristic
5	D₆₁⋊C₈	C₄	1	1	yes	characteristic
6	C₈×D₆₁	C₂²	1	1	yes	characteristic
7	#11758187	C₄	1	2	yes	complemented
8	C₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
9	#11758185	C₄	1	1	yes	characteristic, complemented
10	C₂×#6923	—	2	1	no	—
11	C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
12	#92420	—	2	1	no	—
13	C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
14	#92418	C₂×C₄	1	1	yes	characteristic
15	C₂×D₆₁	M₁₆	1	1	yes	characteristic
16	#6923	—	4	1	no	—
17	C₄×C₆₁	C₄²	1	1	yes	characteristic
18	Dic₆₁	M₁₆	1	1	yes	characteristic
19	C₂×C₆₁	#97	1	1	yes	characteristic
20	D₆₁	—	2	1	no	—
21	#347	—	61	1	no	maximal, Sylow
22	C₆₁	#347	1	1	yes	characteristic, complemented, Sylow
23	M₃₂	—	61	1	no	—
24	M₃₂	—	61	1	no	—
25	#97	—	61	1	no	—
26	C₂×C₈	—	61	1	no	—
27	C₂×C₈	—	61	1	no	—
28	C₄²	—	61	1	no	—
29	C₁₆	—	61	2	no	—
30	C₁₆	—	61	1	no	—
31	C₁₆	#6923	1	1	yes	characteristic, complemented
32	C₂×C₄	—	61	1	no	—
33	C₂×C₄	—	122	1	no	—
34	C₈	—	61	1	no	—
35	C₈	—	122	1	no	—
36	C₈	C₂×#6923	1	1	yes	characteristic
37	C₂²	—	61	1	no	—
38	C₄	—	61	1	no	—
39	C₄	—	244	1	no	—
40	C₄	C₄×#6923	1	1	yes	characteristic
41	C₂	—	122	1	no	—
42	C₂	#14519831	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.