Subgroups — C₁₉×#944 #14269693

Order 1824.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₁₉×Dic₃⋊C₄	C₂	1	4	yes	maximal
4	C₄×Dic₃×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×C₄⋊Q₈	—	3	1	no	maximal, Hall
6	C₃×Q₈×C₁₉	—	2	2	no	—
7	C₂×C₃×C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₃×C₁₉	C₂²	1	2	yes	—
10	C₂×Dic₃×C₁₉	C₂²	1	2	yes	—
11	C₁₉×Dic₆	—	2	2	no	—
12	C₂×Q₈×C₁₉	—	3	1	no	—
13	C₂×Q₈×C₁₉	D₃	1	1	yes	characteristic
14	C₄⋊C₄×C₁₉	—	3	4	no	—
15	C₄²×C₁₉	—	3	1	no	—
16	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
17	C₃×C₄×C₁₉	—	2	2	no	—
18	C₃×C₄×C₁₉	D₄	1	2	yes	—
19	Dic₃×C₁₉	—	2	2	no	—
20	Dic₃×C₁₉	Q₈	1	4	yes	complemented
21	Q₈×C₁₉	—	2	2	no	—
22	Q₈×C₁₉	—	6	2	no	—
23	C₂×C₄×C₁₉	—	3	2	no	—
24	C₂×C₄×C₁₉	—	3	2	no	—
25	C₂×C₄×C₁₉	C₂×D₃	1	2	yes	—
26	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
27	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₃×C₁₉	C₂×Q₈	1	2	yes	—
29	#944	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
31	C₄×C₁₉	—	2	2	no	—
32	C₄×C₁₉	—	3	4	no	—
33	C₄×C₁₉	—	6	2	no	—
34	C₄×C₁₉	#67	1	2	yes	—
35	C₃×C₁₉	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×Q₈	C₂×C₁₉	1	1	yes	characteristic
37	C₂×Dic₆	C₂×C₁₉	1	1	yes	characteristic
38	Dic₃⋊C₄	C₂×C₁₉	1	4	yes	—
39	C₄×Dic₃	C₂×C₁₉	1	1	yes	characteristic
40	C₂×C₁₉	D₃×Q₈	1	2	yes	—
41	C₂×C₁₉	C₂×#67	1	1	yes	characteristic
42	C₄⋊Q₈	—	3	1	no	Sylow
43	C₃×Q₈	—	2	2	no	—
44	C₂×C₃×C₄	C₂²×C₁₉	1	2	yes	—
45	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
46	C₂×Dic₃	C₂²×C₁₉	1	2	yes	—
47	C₂×Dic₃	C₂²×C₁₉	1	2	yes	—
48	Dic₆	—	2	2	no	—
49	C₁₉	#944	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×Q₈	—	3	1	no	—
51	C₂×Q₈	D₃×C₁₉	1	1	yes	characteristic
52	C₄⋊C₄	—	3	4	no	—
53	C₄²	—	3	1	no	—
54	C₂²×C₃	C₂³×C₁₉	1	1	yes	characteristic
55	C₃×C₄	—	2	2	no	—
56	C₃×C₄	D₄×C₁₉	1	2	yes	—
57	Dic₃	—	2	2	no	—
58	Dic₃	Q₈×C₁₉	1	4	yes	complemented
59	Q₈	—	2	2	no	—
60	Q₈	—	6	2	no	—
61	C₂×C₄	—	3	2	no	—
62	C₂×C₄	—	3	2	no	—
63	C₂×C₄	C₂×D₃×C₁₉	1	2	yes	—
64	C₂×C₄	C₂×D₃×C₁₉	1	1	yes	characteristic
65	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
66	C₂×C₃	C₂×Q₈×C₁₉	1	2	yes	—
67	C₂²	C₂²×D₃×C₁₉	1	1	yes	characteristic
68	C₄	—	2	2	no	—
69	C₄	—	3	4	no	—
70	C₄	—	6	2	no	—
71	C₄	C₁₉×#67	1	2	yes	—
72	C₃	C₁₉×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
73	C₂	D₃×Q₈×C₁₉	1	2	yes	—
74	C₂	C₂×C₁₉×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₉	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₂×C₃×Q₈×C₁₉	C₂
socle, prime radical	C₂²×C₃×C₁₉	C₂³
hypercenter	C₂×Q₈×C₁₉	D₃
hypocenter	C₃	C₁₉×C₄⋊Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×Q₈×C₁₉

Complements

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

N	H ≅ G/N	type
20. Dic₃×C₁₉	Q₈	semidirect
29. #944	C₁₉	direct (N × H)
35. C₃×C₁₉	C₄⋊Q₈	semidirect
49. C₁₉	#944	direct (N × H)
58. Dic₃	Q₈×C₁₉	semidirect
72. C₃	C₁₉×C₄⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×Q₈×C₁₉	2
C₂×C₁₉×Dic₆	2
C₁₉×Dic₃⋊C₄	2
C₄×Dic₃×C₁₉	2
C₁₉×C₄⋊Q₈	3
#944	19

Subgroups — C19×#944 #14269693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#944 #14269693