Subgroups — #14561839

Order 2432.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926374	C₂	1	2	yes	maximal
2	C₂×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
4	#10597276	—	2	2	no	—
5	C₁₉×C₃₂	C₄	1	2	yes	—
6	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
7	#64520	—	4	2	no	—
8	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₁₉	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
11	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
12	C₈×C₁₉	Q₁₆	1	1	yes	characteristic
13	C₁₉⋊C₈	—	8	2	no	—
14	#1425	—	19	1	no	maximal, Sylow
15	C₂²×C₁₉	Q₃₂	1	1	yes	characteristic
16	C₄×C₁₉	#107	1	1	yes	characteristic
17	C₄×C₁₉	D₁₆	1	1	yes	characteristic
18	C₂×C₃₂	D₁₉	1	1	yes	characteristic
19	#368	—	19	2	no	—
20	C₂×C₁₉	—	2	1	no	—
21	C₂×C₁₉	#366	1	1	yes	characteristic
22	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
23	#108	—	38	2	no	—
24	C₃₂	Dic₁₉	1	2	yes	—
25	C₁₉	#1425	1	1	yes	characteristic, complemented, Sylow
26	M₁₆	—	76	2	no	—
27	C₂×C₈	D₇₆	1	1	yes	characteristic
28	C₁₆	Dic₃₈	1	1	yes	characteristic
29	C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
30	C₂×C₄	D₁₅₂	1	1	yes	characteristic
31	C₈	—	152	2	no	—
32	C₈	Dic₇₆	1	1	yes	characteristic
33	C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
34	C₂²	Dic₁₅₂	1	1	yes	characteristic
35	C₄	D₃₀₄	1	1	yes	characteristic
36	C₄	#10597275	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#11926370	1	1	yes	characteristic

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

N	H ≅ G/N	type
25. C₁₉	#1425	semidirect

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