Subgroups — #16840708

Order 3904.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#6923	C₂	1	6	yes	maximal
2	C₄²×D₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#6923	C₂²	1	4	yes	—
4	C₂×C₄×D₆₁	C₂²	1	3	yes	—
5	C₄⋊#6923	—	2	12	no	—
6	C₄²×C₆₁	C₄	1	1	yes	characteristic, complemented
7	C₄×Dic₆₁	C₄	1	3	yes	complemented
8	C₂²×D₆₁	C₂³	1	1	yes	characteristic
9	C₂×#6923	—	2	12	no	—
10	C₂×C₄×C₆₁	C₂×C₄	1	3	yes	—
11	C₂×Dic₆₁	C₂×C₄	1	3	yes	—
12	C₄×D₆₁	D₄	1	6	yes	—
13	C₄×D₆₁	Q₈	1	6	yes	—
14	C₂²×C₆₁	C₂²×C₄	1	1	yes	characteristic
15	C₂×D₆₁	C₂×D₄	1	3	yes	—
16	C₂×D₆₁	C₂×Q₈	1	3	yes	—
17	#6923	—	4	4	no	—
18	C₄×C₆₁	C₄⋊C₄	1	6	yes	complemented
19	Dic₆₁	C₄⋊C₄	1	6	yes	complemented
20	C₂×C₆₁	C₂×C₄⋊C₄	1	3	yes	—
21	D₆₁	#127	1	1	yes	characteristic
22	D₆₁	C₄⋊Q₈	1	3	yes	—
23	#384	—	61	1	no	maximal, Sylow
24	C₆₁	#384	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₄⋊C₄	—	61	6	no	—
26	C₂×C₄²	—	61	1	no	—
27	C₂²×C₄	—	61	3	no	—
28	C₂²×C₄	—	61	4	no	—
29	C₄⋊C₄	—	122	12	no	—
30	C₄²	—	61	3	no	—
31	C₄²	#6923	1	1	yes	characteristic, complemented
32	C₂³	—	61	1	no	—
33	C₂×C₄	—	61	3	no	—
34	C₂×C₄	—	61	6	no	—
35	C₂×C₄	—	61	6	no	—
36	C₂×C₄	—	122	12	no	—
37	C₂×C₄	C₂×#6923	1	3	yes	—
38	C₂²	—	61	3	no	—
39	C₂²	—	61	3	no	—
40	C₂²	C₂²×#6923	1	1	yes	characteristic
41	C₄	—	61	6	no	—
42	C₄	—	244	4	no	—
43	C₄	C₄⋊#6923	1	6	yes	complemented
44	C₂	—	61	1	no	—
45	C₂	—	61	3	no	—
46	C₂	C₂×C₄⋊#6923	1	3	yes	—

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.