Subgroups — #14269026

Order 1824.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	#11744894	C₂	1	2	yes	maximal, complemented
3	#10597291	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₁₉	C₄	1	1	yes	characteristic, complemented
5	C₂³×C₃×C₁₉	C₂²	1	1	yes	characteristic
6	C₃×D₄×C₁₉	—	2	2	no	—
7	C₂×C₃×C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
8	C₂×Dic₅₇	—	2	2	no	—
9	C₂×D₄×C₁₉	D₃	1	1	yes	characteristic
10	C₂²⋊Dic₁₉	—	3	2	no	—
11	C₂²×C₃×C₁₉	—	2	1	no	—
12	C₂²×C₃×C₁₉	—	4	1	no	—
13	C₂²×C₃×C₁₉	—	4	1	no	—
14	C₂²×C₃×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₃×C₁₉	D₄	1	2	yes	—
16	C₃×C₄×C₁₉	—	2	1	no	—
17	Dic₅₇	—	4	2	no	—
18	C₂³×C₁₉	Dic₃	1	1	yes	characteristic, complemented
19	C₂³×C₁₉	C₂×D₃	1	1	yes	characteristic
20	D₄×C₁₉	—	2	2	no	—
21	C₂×C₄×C₁₉	Dic₃	1	1	yes	characteristic, complemented
22	C₂×Dic₁₉	—	6	2	no	—
23	C₂×C₃×C₁₉	—	2	2	no	—
24	C₂×C₃×C₁₉	—	2	1	no	—
25	C₂×C₃×C₁₉	—	4	1	no	—
26	C₂×C₃×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
27	#834	—	19	1	no	maximal, Hall
28	C₂²×C₁₉	—	2	1	no	—
29	C₂²×C₁₉	—	4	1	no	—
30	C₂²×C₁₉	—	4	1	no	—
31	C₂²×C₁₉	C₂×Dic₃	1	1	yes	characteristic
32	C₂²×C₁₉	#67	1	2	yes	—
33	C₄×C₁₉	—	2	1	no	—
34	Dic₁₉	—	12	2	no	—
35	C₃×C₁₉	#99	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×D₄	D₁₉	1	1	yes	characteristic
37	#217	—	19	2	no	—
38	C₂×C₁₉	—	2	2	no	—
39	C₂×C₁₉	—	2	1	no	—
40	C₂×C₁₉	—	4	1	no	—
41	C₂×C₁₉	#217	1	1	yes	characteristic
42	#99	—	57	1	no	Sylow
43	C₂³×C₃	Dic₁₉	1	1	yes	characteristic, complemented
44	C₂³×C₃	C₂×D₁₉	1	1	yes	characteristic
45	C₃×D₄	—	2	2	no	—
46	C₂×C₃×C₄	Dic₁₉	1	1	yes	characteristic, complemented
47	C₂×Dic₃	—	38	2	no	—
48	C₁₉	#834	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₄	D₅₇	1	1	yes	characteristic
50	C₂²⋊C₄	—	57	2	no	—
51	C₂²×C₃	—	2	1	no	—
52	C₂²×C₃	—	4	1	no	—
53	C₂²×C₃	—	4	1	no	—
54	C₂²×C₃	C₂×Dic₁₉	1	1	yes	characteristic
55	C₂²×C₃	C₂²⋊D₁₉	1	2	yes	—
56	C₃×C₄	—	2	1	no	—
57	Dic₃	—	76	2	no	—
58	C₂³	Dic₅₇	1	1	yes	characteristic, complemented
59	C₂³	C₂×D₅₇	1	1	yes	characteristic
60	D₄	—	2	2	no	—
61	C₂×C₄	—	114	2	no	—
62	C₂×C₄	Dic₅₇	1	1	yes	characteristic, complemented
63	C₂×C₃	—	2	2	no	—
64	C₂×C₃	—	2	1	no	—
65	C₂×C₃	—	4	1	no	—
66	C₂×C₃	C₂²⋊Dic₁₉	1	1	yes	characteristic
67	C₂²	—	2	1	no	—
68	C₂²	—	4	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	C₂×Dic₅₇	1	1	yes	characteristic
71	C₂²	#90718	1	2	yes	—
72	C₄	—	2	1	no	—
73	C₄	—	228	2	no	—
74	C₃	#10597291	1	1	yes	characteristic, complemented, Sylow
75	C₂	—	2	2	no	—
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	C₂	#11744894	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11744894
commutator	C₂²×C₃×C₁₉	C₂×C₄
Frattini	C₂³	C₂×D₅₇
Fitting, prime radical	C₂×C₃×D₄×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂²⋊C₄
cosocle	C₂³×C₃×C₁₉	C₂²
hypercenter	C₂×D₄	D₅₇
hypocenter	C₃×C₁₉	#99
LCS	G ▷ C₂²×C₃×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. #11744894	C₂	semidirect
4. C₂³×C₃×C₁₉	C₄	semidirect
7. C₂×C₃×C₄×C₁₉	C₄	semidirect
18. C₂³×C₁₉	Dic₃	semidirect
21. C₂×C₄×C₁₉	Dic₃	semidirect
35. C₃×C₁₉	#99	semidirect
43. C₂³×C₃	Dic₁₉	semidirect
46. C₂×C₃×C₄	Dic₁₉	semidirect
48. C₁₉	#834	semidirect
58. C₂³	Dic₅₇	semidirect
62. C₂×C₄	Dic₅₇	semidirect
74. C₃	#10597291	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₄×C₁₉	2
#11744894	2
#10597291	3
#834	19