Subgroups — C₄₉×C₃⋊#6157 #44528331

Order 31164.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₉×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₄₉×#6157	—	3	1	no	maximal, Hall
3	C₃×C₄₉×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄₉×D₅₃	D₃	1	1	yes	characteristic
5	C₇×C₃⋊#6157	C₇	1	1	yes	maximal, characteristic
6	C₄₉×C₅₃	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×D₅₃	C₂×C₇	1	1	yes	characteristic
8	C₇×#6157	—	3	1	no	—
9	C₃×C₇×C₅₃	C₄×C₇	1	1	yes	characteristic
10	C₇×D₅₃	D₃×C₇	1	1	yes	characteristic
11	C₃⋊#6157	C₄₉	1	1	yes	characteristic, direct product factor, Hall
12	Dic₃×C₄₉	—	53	1	no	maximal, Hall
13	C₇×C₅₃	C₇×Dic₃	1	1	yes	characteristic
14	C₃×D₅₃	C₂×C₄₉	1	1	yes	characteristic
15	C₂×C₃×C₄₉	—	53	1	no	—
16	#6157	—	3	1	no	Hall
17	C₄×C₄₉	—	159	1	no	Hall
18	C₃×C₅₃	C₄×C₄₉	1	1	yes	characteristic, complemented, Hall
19	C₃×C₄₉	#6157	1	1	yes	characteristic, complemented, Hall
20	D₅₃	D₃×C₄₉	1	1	yes	characteristic
21	C₂×C₄₉	—	53	1	no	—
22	C₇×Dic₃	—	53	1	no	—
23	C₅₃	Dic₃×C₄₉	1	1	yes	characteristic, complemented, Sylow
24	C₄₉	C₃⋊#6157	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃×C₇	—	53	1	no	—
26	C₄×C₇	—	159	1	no	—
27	C₃×C₇	C₇×#6157	1	1	yes	characteristic
28	C₂×C₇	—	53	1	no	—
29	Dic₃	—	53	1	no	Hall
30	C₇	C₇×C₃⋊#6157	1	1	yes	characteristic
31	C₂×C₃	—	53	1	no	—
32	C₄	—	159	1	no	Sylow
33	C₃	C₄₉×#6157	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	53	1	no	—

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.