Subgroups — C₄₇×C₁₉⋊#157 #44565323

Order 32148.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₁₉×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₉×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₁₉×C₄₇	—	6	2	no	—
4	C₄₇×Dic₁₉	—	9	1	no	maximal, Hall
5	C₃×C₁₉×C₄₇	—	2	2	no	—
6	C₂×C₁₉×C₄₇	—	9	1	no	—
7	#157×C₄₇	—	19	1	no	maximal, Hall
8	C₁₉×C₄₇	#157	1	1	yes	characteristic, complemented, Hall
9	C₃⋊D₃×C₄₇	D₁₉	1	1	yes	characteristic
10	C₁₉⋊#157	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃²×C₄₇	Dic₁₉	1	1	yes	characteristic, complemented, Hall
12	C₃⋊D₃×C₁₉	C₂×C₄₇	1	1	yes	characteristic
13	D₃×C₄₇	—	6	2	no	—
14	C₄×C₄₇	—	171	1	no	Hall
15	C₃²×C₁₉	C₄×C₄₇	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄₇	—	2	2	no	—
17	D₃×C₁₉	—	6	2	no	—
18	C₂×C₄₇	—	9	1	no	—
19	Dic₁₉	—	9	1	no	Hall
20	C₃×C₁₉	—	2	2	no	—
21	C₄₇	C₁₉⋊#157	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₁₉	—	9	1	no	—
23	#157	—	19	1	no	Hall
24	C₁₉	#157×C₄₇	1	1	yes	characteristic, complemented, Sylow
25	C₃⋊D₃	D₁₉×C₄₇	1	1	yes	characteristic
26	C₃²	C₄₇×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	171	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	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.