Subgroups — #14561852

Order 2432.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₀₄	C₂	1	1	yes	maximal, characteristic
2	C₁₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic
3	C₁₉×Q₆₄	C₂	1	1	yes	maximal, characteristic
4	C₁₉×Q₃₂	—	2	1	no	—
5	Dic₁₅₂	—	2	1	no	—
6	C₁₉×C₃₂	C₂²	1	1	yes	characteristic
7	Q₁₆×C₁₉	—	4	1	no	—
8	Dic₇₆	—	4	1	no	—
9	C₁₆×C₁₉	D₄	1	1	yes	characteristic
10	Q₈×C₁₉	—	8	1	no	—
11	Dic₃₈	—	8	1	no	—
12	C₈×C₁₉	D₈	1	1	yes	characteristic
13	Q₁₂₈	—	19	1	no	maximal, Sylow
14	C₄×C₁₉	—	16	1	no	—
15	C₄×C₁₉	D₁₆	1	1	yes	characteristic
16	Dic₁₉	—	16	1	no	—
17	Q₆₄	—	19	1	no	—
18	Q₆₄	D₁₉	1	1	yes	characteristic
19	C₆₄	—	19	1	no	—
20	C₂×C₁₉	D₃₂	1	1	yes	characteristic
21	Q₃₂	—	2	1	no	—
22	Q₃₂	—	38	1	no	—
23	C₃₂	C₂×D₁₉	1	1	yes	characteristic
24	C₁₉	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
25	Q₁₆	—	4	1	no	—
26	Q₁₆	—	76	1	no	—
27	C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
28	Q₈	—	8	1	no	—
29	Q₈	—	152	1	no	—
30	C₈	#64525	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	304	1	no	—
33	C₄	#10597283	1	1	yes	characteristic
34	C₂	#11926379	1	1	yes	characteristic

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

N	H ≅ G/N	type
24. C₁₉	Q₁₂₈	semidirect

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