Subgroups — #14269019

Order 1824.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11744985	C₂	1	1	yes	maximal, characteristic
2	C₃×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₅₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597282	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
6	#90718	—	2	1	no	—
7	C₂×Dic₅₇	—	2	1	no	—
8	D₂₂₈	C₄	1	1	yes	characteristic, complemented
9	C₄×D₅₇	—	2	1	no	—
10	Dic₁₁₄	C₄	1	1	yes	characteristic, complemented
11	C₃×C₈×C₁₉	—	2	1	no	—
12	#64541	—	3	1	no	—
13	M₁₆×C₁₉	D₃	1	1	yes	characteristic, complemented
14	C₄×Dic₁₉	—	3	1	no	—
15	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
16	C₂×D₅₇	—	2	1	no	—
17	C₃×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
19	Dic₅₇	—	2	2	no	—
20	Dic₅₇	—	2	1	no	—
21	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
22	C₂²⋊D₁₉	—	6	1	no	—
23	C₂×Dic₁₉	—	6	1	no	—
24	D₇₆	—	3	1	no	—
25	C₄×D₁₉	—	6	1	no	—
26	Dic₃₈	—	3	1	no	—
27	C₈×C₁₉	—	2	1	no	—
28	C₂×C₃×C₁₉	—	2	1	no	—
29	C₂×C₃×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	D₅₇	—	4	1	no	—
31	#825	—	19	1	no	maximal, Hall
32	C₂²×C₁₉	D₁₂	1	1	yes	characteristic
33	C₂×D₁₉	—	6	1	no	—
34	C₄×C₁₉	C₄×D₃	1	1	yes	characteristic
35	C₄×C₁₉	#67	1	1	yes	characteristic
36	Dic₁₉	—	6	2	no	—
37	Dic₁₉	—	6	1	no	—
38	C₃×C₁₉	#104	1	1	yes	characteristic, complemented, Hall
39	#235	—	19	1	no	—
40	C₃×M₁₆	D₁₉	1	1	yes	characteristic, complemented
41	C₄×Dic₃	—	19	1	no	—
42	C₂×C₁₉	—	2	1	no	—
43	C₂×C₁₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
44	D₁₉	—	12	1	no	—
45	#104	—	57	1	no	Sylow
46	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
47	#67	—	38	1	no	—
48	C₂×Dic₃	—	38	1	no	—
49	D₁₂	—	19	1	no	—
50	C₄×D₃	—	38	1	no	—
51	Dic₆	—	19	1	no	—
52	C₃×C₈	—	2	1	no	—
53	C₁₉	#825	1	1	yes	characteristic, complemented, Sylow
54	#41	—	57	1	no	—
55	M₁₆	D₅₇	1	1	yes	characteristic, complemented
56	C₄²	—	57	1	no	—
57	C₂²×C₃	D₇₆	1	1	yes	characteristic
58	C₂×D₃	—	38	1	no	—
59	C₃×C₄	C₄×D₁₉	1	1	yes	characteristic
60	C₃×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
61	Dic₃	—	38	2	no	—
62	Dic₃	—	38	1	no	—
63	Q₈	—	57	1	no	—
64	D₄	—	57	1	no	—
65	D₄	—	114	1	no	—
66	C₂×C₄	—	114	1	no	—
67	C₂×C₄	—	114	1	no	—
68	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₂×C₃	—	2	1	no	—
71	C₂×C₃	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
72	D₃	—	76	1	no	—
73	C₂²	—	114	1	no	—
74	C₂²	D₂₂₈	1	1	yes	characteristic
75	C₄	—	114	2	no	—
76	C₄	—	114	1	no	—
77	C₄	C₄×D₅₇	1	1	yes	characteristic
78	C₄	#90718	1	1	yes	characteristic
79	C₃	#10597282	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	2	1	no	—
81	C₂	—	228	1	no	—
82	C₂	#11744889	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#90718
commutator	C₃×C₄×C₁₉	C₂×C₄
Frattini	C₂×C₄	C₂×D₅₇
Fitting	C₃×M₁₆×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂²⋊C₄
prime radical	#11744985	C₂
cosocle	C₂×C₃×C₄×C₁₉	C₂²
hypercenter	M₁₆	D₅₇
hypocenter	C₃×C₁₉	#104
LCS	G ▷ C₃×C₄×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×M₁₆×C₁₉	C₂	semidirect
3. C₄×Dic₅₇	C₂	semidirect
8. D₂₂₈	C₄	semidirect
10. Dic₁₁₄	C₄	semidirect
13. M₁₆×C₁₉	D₃	semidirect
38. C₃×C₁₉	#104	semidirect
40. C₃×M₁₆	D₁₉	semidirect
53. C₁₉	#825	semidirect
55. M₁₆	D₅₇	semidirect
79. C₃	#10597282	semidirect

Maximal subgroups

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

subgroup	index
#11744985	2
C₃×M₁₆×C₁₉	2
C₄×Dic₅₇	2
#10597282	3
#825	19