Subgroups — #18069275

Order 4864.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14561705	C₂	1	2	yes	maximal
2	C₁₉×#1713	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₁₉×#500	—	2	2	no	—
5	C₁₉×#494	C₄	1	2	yes	—
6	C₈²×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×Q₁₆×C₁₉	—	4	2	no	—
8	C₁₉×C₄⋊Q₈	—	2	2	no	—
9	C₁₉×#107	—	4	2	no	—
10	C₁₉×#107	—	4	2	no	—
11	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₄×C₈×C₁₉	D₄	1	2	yes	—
13	C₂×C₁₉⋊C₁₆	—	4	2	no	—
14	C₂×Q₈×C₁₉	—	4	2	no	—
15	Q₁₆×C₁₉	—	8	4	no	—
16	C₂×C₈×C₁₉	—	2	1	no	—
17	C₂×C₈×C₁₉	D₈	1	2	yes	—
18	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
19	C₄⋊C₄×C₁₉	—	4	4	no	—
20	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₁₉⋊C₁₆	—	8	2	no	—
22	#7098	—	19	1	no	maximal, Sylow
23	Q₈×C₁₉	—	8	4	no	—
24	C₂×C₄×C₁₉	—	8	2	no	—
25	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
26	C₂×C₄×C₁₉	#102	1	2	yes	—
27	C₈×C₁₉	—	2	2	no	—
28	C₈×C₁₉	—	2	2	no	—
29	C₈×C₁₉	SD₃₂	1	2	yes	—
30	C₈×C₁₉	Q₃₂	1	2	yes	—
31	#1713	D₁₉	1	1	yes	characteristic
32	#1370	—	19	2	no	—
33	C₂²×C₁₉	#331	1	1	yes	characteristic
34	C₄×C₁₉	—	2	1	no	—
35	C₄×C₁₉	—	16	2	no	—
36	C₄×C₁₉	#358	1	2	yes	—
37	C₄×C₁₉	#362	1	2	yes	—
38	#500	—	2	2	no	—
39	#494	Dic₁₉	1	2	yes	—
40	C₄⋊C₁₆	—	38	2	no	—
41	C₈²	C₂×D₁₉	1	1	yes	characteristic
42	C₂×C₁₉	#1357	1	1	yes	characteristic
43	C₂×C₁₉	#1362	1	2	yes	—
44	C₂×Q₁₆	—	4	2	no	—
45	C₄⋊Q₈	—	2	2	no	—
46	C₂×C₁₆	—	76	2	no	—
47	#107	—	4	2	no	—
48	#107	—	4	2	no	—
49	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
50	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
51	C₁₉	#7098	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₈	—	4	2	no	—
53	Q₁₆	—	8	4	no	—
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	#64525	1	2	yes	—
56	C₂×C₈	#64526	1	2	yes	—
57	C₄⋊C₄	—	4	4	no	—
58	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
59	C₁₆	—	152	2	no	—
60	Q₈	—	8	4	no	—
61	C₂×C₄	—	8	2	no	—
62	C₂×C₄	#10597289	1	2	yes	—
63	C₂×C₄	#10597290	1	1	yes	characteristic
64	C₈	—	2	2	no	—
65	C₈	—	2	2	no	—
66	C₈	#10597285	1	2	yes	—
67	C₈	#10597286	1	2	yes	—
68	C₂²	#11926288	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	16	2	no	—
71	C₄	#11926348	1	2	yes	—
72	C₄	#11926360	1	2	yes	—
73	C₂	#14561672	1	1	yes	characteristic
74	C₂	#14561684	1	2	yes	—

	subgroup	G/H
center	C₂²	#11926288
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	C₈²	C₂×D₁₉
Fitting	C₁₉×#1713	C₂
socle, prime radical	C₂²×C₁₉	#331
cosocle	C₈²×C₁₉	C₂²
hypercenter	#1713	D₁₉
hypocenter	C₁₉	#7098
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1713

Complements

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

N	H ≅ G/N	type
51. C₁₉	#7098	semidirect

Maximal subgroups

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

subgroup	index
#14561705	2
C₁₉×#1713	2
#7098	19