Subgroups — #14269020

Order 1824.

56 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, complemented
2	D₄₅₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597283	—	3	1	no	maximal, Hall
5	C₃×D₄×C₁₉	—	2	1	no	—
6	D₂₂₈	—	2	1	no	—
7	C₃×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	D₈×C₁₉	D₃	1	1	yes	characteristic, complemented
9	D₁₅₂	—	3	1	no	—
10	C₁₉⋊C₁₆	—	3	1	no	—
11	C₂²×C₃×C₁₉	—	4	1	no	—
12	C₂×D₅₇	—	4	1	no	—
13	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
14	D₄×C₁₉	—	2	1	no	—
15	D₇₆	—	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	D₅₇	—	8	1	no	—
20	#826	—	19	1	no	maximal, Hall
21	C₂²×C₁₉	—	4	1	no	—
22	C₂×D₁₉	—	12	1	no	—
23	C₄×C₁₉	#67	1	1	yes	characteristic
24	C₃×C₁₉	D₁₆	1	1	yes	characteristic, complemented, Hall
25	C₃×D₈	D₁₉	1	1	yes	characteristic, complemented
26	D₂₄	—	19	1	no	—
27	C₃⋊C₁₆	—	19	1	no	—
28	C₂×C₁₉	—	8	1	no	—
29	C₂×C₁₉	#213	1	1	yes	characteristic
30	D₁₉	—	24	1	no	—
31	D₁₆	—	57	1	no	Sylow
32	C₃×D₄	—	2	1	no	—
33	D₁₂	—	38	1	no	—
34	C₃×C₈	C₂×D₁₉	1	1	yes	characteristic
35	C₁₉	#826	1	1	yes	characteristic, complemented, Sylow
36	D₈	—	57	1	no	—
37	D₈	D₅₇	1	1	yes	characteristic, complemented
38	C₁₆	—	57	1	no	—
39	C₂²×C₃	—	4	1	no	—
40	C₂×D₃	—	76	1	no	—
41	C₃×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
42	D₄	—	2	1	no	—
43	D₄	—	114	1	no	—
44	C₈	C₂×D₅₇	1	1	yes	characteristic
45	C₂×C₃	—	8	1	no	—
46	C₂×C₃	#64525	1	1	yes	characteristic
47	D₃	—	152	1	no	—
48	C₂²	—	4	1	no	—
49	C₂²	—	228	1	no	—
50	C₄	#90718	1	1	yes	characteristic
51	C₃	#10597283	1	1	yes	characteristic, complemented, Sylow
52	C₂	—	8	1	no	—
53	C₂	—	456	1	no	—
54	C₂	#11744890	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11744890
commutator, cosocle	C₃×C₈×C₁₉	C₂²
Frattini	C₈	C₂×D₅₇
Fitting	C₃×D₈×C₁₉	C₂
socle	C₂×C₃×C₁₉	D₈
hypercenter	D₈	D₅₇
hypocenter	C₃×C₁₉	D₁₆
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
1. C₃×D₈×C₁₉	C₂	semidirect
2. D₄₅₆	C₂	semidirect
3. C₃⋊(C₁₉⋊C₁₆)	C₂	semidirect
8. D₈×C₁₉	D₃	semidirect
24. C₃×C₁₉	D₁₆	semidirect
25. C₃×D₈	D₁₉	semidirect
35. C₁₉	#826	semidirect
37. D₈	D₅₇	semidirect
51. C₃	#10597283	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
D₄₅₆	2
C₃⋊(C₁₉⋊C₁₆)	2
#10597283	3
#826	19