Subgroups — #14269714

Order 1824.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#11744889	C₂	1	3	yes	maximal
3	#11744887	C₂	1	3	yes	maximal, complemented
4	#10597322	—	3	1	no	maximal, Hall
5	C₂²×D₅₇	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₉	C₂²	1	3	yes	—
7	C₂×Dic₅₇	C₂²	1	3	yes	—
8	C₄²×C₁₉	D₃	1	1	yes	characteristic, complemented
9	(C₂×D₁₉)⋊C₄	—	3	3	no	—
10	Dic₁₉⋊C₄	—	3	3	no	—
11	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
12	C₂×D₅₇	—	2	3	no	—
13	C₃×C₄×C₁₉	—	2	3	no	—
14	Dic₅₇	—	2	3	no	—
15	C₂²×D₁₉	—	3	1	no	—
16	C₂×C₄×C₁₉	C₂×D₃	1	3	yes	—
17	C₂×Dic₁₉	—	3	3	no	—
18	C₂×C₃×C₁₉	#41	1	3	yes	—
19	D₅₇	—	4	1	no	—
20	#876	—	19	1	no	maximal, Hall
21	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
22	C₂×D₁₉	—	6	3	no	—
23	C₄×C₁₉	—	2	3	no	—
24	Dic₁₉	—	6	3	no	—
25	C₃×C₁₉	#126	1	1	yes	characteristic, complemented, Hall
26	C₃×C₄²	D₁₉	1	1	yes	characteristic, complemented
27	(C₂×D₃)⋊C₄	—	19	3	no	—
28	Dic₃⋊C₄	—	19	3	no	—
29	C₂×C₁₉	#235	1	3	yes	—
30	D₁₉	—	12	1	no	—
31	#126	—	57	1	no	Sylow
32	C₂²×D₃	—	19	1	no	—
33	C₂×C₃×C₄	C₂×D₁₉	1	3	yes	—
34	C₂×Dic₃	—	19	3	no	—
35	C₁₉	#876	1	1	yes	characteristic, complemented, Sylow
36	C₄⋊C₄	—	57	3	no	—
37	C₂²⋊C₄	—	57	3	no	—
38	C₄²	D₅₇	1	1	yes	characteristic, complemented
39	C₂²×C₃	C₂²×D₁₉	1	1	yes	characteristic
40	C₂×D₃	—	38	3	no	—
41	C₃×C₄	—	2	3	no	—
42	Dic₃	—	38	3	no	—
43	C₂³	—	57	1	no	—
44	C₂×C₄	—	57	3	no	—
45	C₂×C₄	C₂×D₅₇	1	3	yes	—
46	C₂×C₃	#64541	1	3	yes	—
47	D₃	—	76	1	no	—
48	C₂²	—	114	3	no	—
49	C₂²	C₂²×D₅₇	1	1	yes	characteristic
50	C₄	—	2	3	no	—
51	C₄	—	114	3	no	—
52	C₃	#10597322	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	228	1	no	—
54	C₂	#11744985	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₅₇
commutator, socle, cosocle	C₂²×C₃×C₁₉	C₂³
Fitting	C₃×C₄²×C₁₉	C₂
prime radical	C₂²×D₅₇	C₂²
hypercenter	C₄²	D₅₇
hypocenter	C₃×C₁₉	#126
LCS	G ▷ C₂²×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
1. C₃×C₄²×C₁₉	C₂	semidirect
3. #11744887	C₂	semidirect
8. C₄²×C₁₉	D₃	semidirect
25. C₃×C₁₉	#126	semidirect
26. C₃×C₄²	D₁₉	semidirect
35. C₁₉	#876	semidirect
38. C₄²	D₅₇	semidirect
52. C₃	#10597322	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₁₉	2
#11744889	2
#11744887	2
#10597322	3
#876	19