Subgroups — #14269006

Order 1824.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₁₉⋊C₁₆)	C₂	1	2	yes	maximal, complemented
3	#10597269	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₁₉	C₄	1	1	yes	characteristic
5	C₃×C₈×C₁₉	C₄	1	1	yes	characteristic
6	C₃×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₉	D₃	1	1	yes	characteristic
8	C₁₉⋊C₁₆	—	3	2	no	—
9	C₂²×C₃×C₁₉	C₈	1	1	yes	characteristic
10	C₃×C₄×C₁₉	C₈	1	1	yes	characteristic
11	C₃×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₉	Dic₃	1	1	yes	characteristic
13	C₈×C₁₉	Dic₃	1	1	yes	characteristic
14	C₈×C₁₉	C₂×D₃	1	1	yes	characteristic
15	C₂×C₃×C₁₉	—	2	1	no	—
16	C₂×C₃×C₁₉	C₂×C₈	1	1	yes	characteristic
17	#812	—	19	1	no	maximal, Hall
18	C₂²×C₁₉	C₃⋊C₈	1	1	yes	characteristic
19	C₄×C₁₉	C₃⋊C₈	1	1	yes	characteristic
20	C₄×C₁₉	C₂×Dic₃	1	1	yes	characteristic
21	C₃×C₁₉	M₃₂	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₈	D₁₉	1	1	yes	characteristic
23	C₃⋊C₁₆	—	19	2	no	—
24	C₂×C₁₉	—	2	1	no	—
25	C₂×C₁₉	C₂×C₃⋊C₈	1	1	yes	characteristic
26	M₃₂	—	57	1	no	Sylow
27	C₂×C₃×C₄	Dic₁₉	1	1	yes	characteristic
28	C₃×C₈	Dic₁₉	1	1	yes	characteristic
29	C₃×C₈	C₂×D₁₉	1	1	yes	characteristic
30	C₁₉	#812	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₈	D₅₇	1	1	yes	characteristic
32	C₁₆	—	57	2	no	—
33	C₂²×C₃	C₁₉⋊C₈	1	1	yes	characteristic
34	C₃×C₄	C₁₉⋊C₈	1	1	yes	characteristic
35	C₃×C₄	C₂×Dic₁₉	1	1	yes	characteristic
36	C₂×C₄	Dic₅₇	1	1	yes	characteristic
37	C₈	Dic₅₇	1	1	yes	characteristic
38	C₈	C₂×D₅₇	1	1	yes	characteristic
39	C₂×C₃	—	2	1	no	—
40	C₂×C₃	C₂×C₁₉⋊C₈	1	1	yes	characteristic
41	C₂²	C₃⋊(C₁₉⋊C₈)	1	1	yes	characteristic
42	C₄	C₃⋊(C₁₉⋊C₈)	1	1	yes	characteristic
43	C₄	C₂×Dic₅₇	1	1	yes	characteristic
44	C₃	#10597269	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	2	1	no	—
46	C₂	C₂×C₃⋊(C₁₉⋊C₈)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂×D₅₇
commutator, socle	C₂×C₃×C₁₉	C₂×C₈
Fitting	C₂×C₃×C₈×C₁₉	C₂
prime radical	C₂²×C₃×C₁₉	C₈
cosocle	C₃×C₈×C₁₉	C₂²
hypercenter	C₂×C₈	D₅₇
hypocenter	C₃×C₁₉	M₃₂
LCS	G ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₁₉⋊C₁₆)	C₂	semidirect
21. C₃×C₁₉	M₃₂	semidirect
30. C₁₉	#812	semidirect
44. C₃	#10597269	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₈×C₁₉	2
C₃⋊(C₁₉⋊C₁₆)	2
#10597269	3
#812	19