Subgroups — #14269021

Order 1824.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	Dic₂₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597284	—	3	1	no	maximal, Hall
5	C₃×D₄×C₁₉	—	2	1	no	—
6	Dic₁₁₄	—	2	1	no	—
7	C₃×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	D₈×C₁₉	D₃	1	1	yes	characteristic
9	Dic₇₆	—	3	1	no	—
10	C₁₉⋊C₁₆	—	3	1	no	—
11	C₂²×C₃×C₁₉	—	4	1	no	—
12	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
13	Dic₅₇	—	4	1	no	—
14	D₄×C₁₉	—	2	1	no	—
15	Dic₃₈	—	6	1	no	—
16	C₈×C₁₉	C₂×D₃	1	1	yes	characteristic
17	C₂×C₃×C₁₉	—	8	1	no	—
18	C₂×C₃×C₁₉	D₈	1	1	yes	characteristic
19	#827	—	19	1	no	maximal, Hall
20	C₂²×C₁₉	—	4	1	no	—
21	C₄×C₁₉	#67	1	1	yes	characteristic
22	Dic₁₉	—	12	1	no	—
23	C₃×C₁₉	SD₃₂	1	1	yes	characteristic, complemented, Hall
24	C₃×D₈	D₁₉	1	1	yes	characteristic
25	Dic₁₂	—	19	1	no	—
26	C₃⋊C₁₆	—	19	1	no	—
27	C₂×C₁₉	—	8	1	no	—
28	C₂×C₁₉	#213	1	1	yes	characteristic
29	SD₃₂	—	57	1	no	Sylow
30	C₃×D₄	—	2	1	no	—
31	Dic₆	—	38	1	no	—
32	C₃×C₈	C₂×D₁₉	1	1	yes	characteristic
33	C₁₉	#827	1	1	yes	characteristic, complemented, Sylow
34	Q₁₆	—	57	1	no	—
35	D₈	D₅₇	1	1	yes	characteristic
36	C₁₆	—	57	1	no	—
37	C₂²×C₃	—	4	1	no	—
38	C₃×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
39	Dic₃	—	76	1	no	—
40	Q₈	—	114	1	no	—
41	D₄	—	2	1	no	—
42	C₈	C₂×D₅₇	1	1	yes	characteristic
43	C₂×C₃	—	8	1	no	—
44	C₂×C₃	#64525	1	1	yes	characteristic
45	C₂²	—	4	1	no	—
46	C₄	—	228	1	no	—
47	C₄	#90718	1	1	yes	characteristic
48	C₃	#10597284	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	8	1	no	—
50	C₂	#11744890	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11744890
commutator, cosocle	C₃×C₈×C₁₉	C₂²
Frattini	C₈	C₂×D₅₇
Fitting, prime radical	C₃×D₈×C₁₉	C₂
socle	C₂×C₃×C₁₉	D₈
hypercenter	D₈	D₅₇
hypocenter	C₃×C₁₉	SD₃₂
LCS	G ▷ C₃×C₈×C₁₉ ▷ C₃×C₄×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
2. Dic₂₂₈	C₂	semidirect
3. C₃⋊(C₁₉⋊C₁₆)	C₂	semidirect
23. C₃×C₁₉	SD₃₂	semidirect
33. C₁₉	#827	semidirect
48. C₃	#10597284	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₈×C₁₉	2
Dic₂₂₈	2
C₃⋊(C₁₉⋊C₁₆)	2
#10597284	3
#827	19