Subgroups — #14269712

Order 1824.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₂₈	C₂	1	6	yes	maximal, complemented
2	C₃×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#10597320	—	3	1	no	maximal, Hall
4	C₂²×D₅₇	C₂²	1	4	yes	—
5	C₂×C₃×C₄×C₁₉	C₂²	1	3	yes	—
6	D₂₂₈	—	2	12	no	—
7	C₂×D₇₆	—	3	6	no	—
8	C₄²×C₁₉	D₃	1	1	yes	characteristic, complemented
9	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
10	C₂×D₅₇	—	2	12	no	—
11	C₃×C₄×C₁₉	D₄	1	6	yes	complemented
12	C₂²×D₁₉	—	3	4	no	—
13	C₂×C₄×C₁₉	C₂×D₃	1	3	yes	—
14	D₇₆	—	6	12	no	—
15	C₂×C₃×C₁₉	C₂×D₄	1	3	yes	—
16	D₅₇	—	4	4	no	—
17	#874	—	19	1	no	maximal, Hall
18	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
19	C₂×D₁₉	—	6	12	no	—
20	C₄×C₁₉	D₁₂	1	6	yes	complemented
21	C₃×C₁₉	#127	1	1	yes	characteristic, complemented, Hall
22	C₂×D₁₂	—	19	6	no	—
23	C₃×C₄²	D₁₉	1	1	yes	characteristic, complemented
24	C₂×C₁₉	C₂×D₁₂	1	3	yes	—
25	D₁₉	—	12	4	no	—
26	#127	—	57	1	no	Sylow
27	C₂²×D₃	—	19	4	no	—
28	C₂×C₃×C₄	C₂×D₁₉	1	3	yes	—
29	D₁₂	—	38	12	no	—
30	C₁₉	#874	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₄	—	57	6	no	—
32	C₄²	D₅₇	1	1	yes	characteristic, complemented
33	C₂²×C₃	C₂²×D₁₉	1	1	yes	characteristic
34	C₂×D₃	—	38	12	no	—
35	C₃×C₄	D₇₆	1	6	yes	complemented
36	C₂³	—	57	4	no	—
37	D₄	—	114	12	no	—
38	C₂×C₄	C₂×D₅₇	1	3	yes	—
39	C₂×C₃	C₂×D₇₆	1	3	yes	—
40	D₃	—	76	4	no	—
41	C₂²	—	114	12	no	—
42	C₂²	C₂²×D₅₇	1	1	yes	characteristic
43	C₄	D₂₂₈	1	6	yes	complemented
44	C₃	#10597320	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	228	4	no	—
46	C₂	C₂×D₂₂₈	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₅₇
commutator, socle, cosocle	C₂²×C₃×C₁₉	C₂³
Fitting	C₃×C₄²×C₁₉	C₂
hypercenter	C₄²	D₅₇
hypocenter	C₃×C₁₉	#127
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. C₂×D₂₂₈	C₂	semidirect
2. C₃×C₄²×C₁₉	C₂	semidirect
8. C₄²×C₁₉	D₃	semidirect
11. C₃×C₄×C₁₉	D₄	semidirect
20. C₄×C₁₉	D₁₂	semidirect
21. C₃×C₁₉	#127	semidirect
23. C₃×C₄²	D₁₉	semidirect
30. C₁₉	#874	semidirect
32. C₄²	D₅₇	semidirect
35. C₃×C₄	D₇₆	semidirect
43. C₄	D₂₂₈	semidirect
44. C₃	#10597320	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₂₈	2
C₃×C₄²×C₁₉	2
#10597320	3
#874	19