Subgroups — #14269023

Order 1824.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	Dic₂₂₈	C₂	1	1	yes	maximal, characteristic
3	C₃⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
4	#10597286	—	3	1	no	maximal, Hall
5	C₃×Q₈×C₁₉	—	2	1	no	—
6	Dic₁₁₄	—	2	1	no	—
7	C₃×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	Q₁₆×C₁₉	D₃	1	1	yes	characteristic
9	Dic₇₆	—	3	1	no	—
10	C₁₉⋊C₁₆	—	3	1	no	—
11	C₃×C₄×C₁₉	—	4	1	no	—
12	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
13	Dic₅₇	—	4	1	no	—
14	Q₈×C₁₉	—	2	1	no	—
15	Dic₃₈	—	6	1	no	—
16	C₈×C₁₉	C₂×D₃	1	1	yes	characteristic
17	C₂×C₃×C₁₉	D₈	1	1	yes	characteristic
18	#829	—	19	1	no	maximal, Hall
19	C₄×C₁₉	—	4	1	no	—
20	C₄×C₁₉	#67	1	1	yes	characteristic
21	Dic₁₉	—	12	1	no	—
22	C₃×C₁₉	Q₃₂	1	1	yes	characteristic, complemented, Hall
23	C₃×Q₁₆	D₁₉	1	1	yes	characteristic
24	Dic₁₂	—	19	1	no	—
25	C₃⋊C₁₆	—	19	1	no	—
26	C₂×C₁₉	#213	1	1	yes	characteristic
27	Q₃₂	—	57	1	no	Sylow
28	C₃×Q₈	—	2	1	no	—
29	Dic₆	—	38	1	no	—
30	C₃×C₈	C₂×D₁₉	1	1	yes	characteristic
31	C₁₉	#829	1	1	yes	characteristic, complemented, Sylow
32	Q₁₆	—	57	1	no	—
33	Q₁₆	D₅₇	1	1	yes	characteristic
34	C₁₆	—	57	1	no	—
35	C₃×C₄	—	4	1	no	—
36	C₃×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
37	Dic₃	—	76	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	114	1	no	—
40	C₈	C₂×D₅₇	1	1	yes	characteristic
41	C₂×C₃	#64525	1	1	yes	characteristic
42	C₄	—	4	1	no	—
43	C₄	—	228	1	no	—
44	C₄	#90718	1	1	yes	characteristic
45	C₃	#10597286	1	1	yes	characteristic, complemented, Sylow
46	C₂	#11744890	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11744890
commutator, cosocle	C₃×C₈×C₁₉	C₂²
Frattini	C₈	C₂×D₅₇
Fitting	C₃×Q₁₆×C₁₉	C₂
socle, prime radical	C₂×C₃×C₁₉	D₈
hypercenter	Q₁₆	D₅₇
hypocenter	C₃×C₁₉	Q₃₂
LCS	G ▷ C₃×C₈×C₁₉ ▷ C₃×C₄×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
22. C₃×C₁₉	Q₃₂	semidirect
31. C₁₉	#829	semidirect
45. C₃	#10597286	semidirect

Maximal subgroups

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

subgroup	index
C₃×Q₁₆×C₁₉	2
Dic₂₂₈	2
C₃⋊(C₁₉⋊C₁₆)	2
#10597286	3
#829	19