Subgroups — #16840683

Order 3904.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758187	C₂	1	2	yes	maximal
2	C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₆₁	C₄	1	1	yes	characteristic
4	C₄×Dic₆₁	C₄	1	1	yes	characteristic
5	C₂×#92418	C₂²	1	1	yes	characteristic
6	#11758187	—	2	2	no	—
7	C₂×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₆₁	C₈	1	1	yes	characteristic
9	C₂×Dic₆₁	C₈	1	1	yes	characteristic
10	C₈×C₆₁	—	2	1	no	—
11	#92418	D₄	1	1	yes	characteristic
12	#92418	Q₈	1	1	yes	characteristic
13	C₂²×C₆₁	C₂×C₈	1	1	yes	characteristic
14	C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₆₁	M₁₆	1	1	yes	characteristic
16	Dic₆₁	—	2	1	no	—
17	Dic₆₁	C₁₆	1	2	yes	complemented
18	C₂×C₆₁	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₆₁	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₆₁	M₃₂	1	1	yes	characteristic
21	C₄⋊C₁₆	—	61	1	no	maximal, Sylow
22	C₆₁	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	—	61	2	no	—
24	C₄×C₈	—	61	1	no	—
25	C₂×C₈	—	61	1	no	—
26	C₂×C₈	#6923	1	1	yes	characteristic
27	C₄²	—	61	1	no	—
28	C₁₆	—	122	2	no	—
29	C₂×C₄	—	61	1	no	—
30	C₂×C₄	—	61	1	no	—
31	C₂×C₄	C₂×#6923	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	61	1	no	—
34	C₈	—	61	1	no	—
35	C₂²	D₆₁⋊C₈	1	1	yes	characteristic
36	C₄	—	61	2	no	—
37	C₄	—	122	1	no	—
38	C₄	C₄⋊#6923	1	1	yes	characteristic
39	C₄	#11758217	1	1	yes	characteristic
40	C₂	#14519844	1	1	yes	characteristic
41	C₂	D₆₁⋊C₁₆	1	1	yes	characteristic
42	C₂	#14519852	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. Dic₆₁	C₁₆	semidirect
22. C₆₁	C₄⋊C₁₆	semidirect

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