Subgroups — #18069154

Order 4864.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₈×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₉⋊C₁₆	C₄	1	2	yes	—
5	C₄×C₁₉⋊C₁₆	C₄	1	2	yes	—
6	C₄×C₁₆×C₁₉	C₄	1	2	yes	—
7	C₈²×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₁₉	C₈	1	4	yes	—
9	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₉⋊C₁₆	C₈	1	4	yes	—
13	C₂×C₁₉⋊C₁₆	C₈	1	4	yes	—
14	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
15	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
16	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
17	C₄²×C₁₉	C₄²	1	1	yes	characteristic
18	C₁₆×C₁₉	—	2	4	no	—
19	C₁₉⋊C₁₆	—	2	4	no	—
20	C₁₉⋊C₁₆	C₁₆	1	8	yes	complemented
21	#7052	—	19	1	no	maximal, Sylow
22	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
23	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
24	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
25	C₈×C₁₉	C₂×C₁₆	1	4	yes	—
26	C₈×C₁₉	M₃₂	1	4	yes	—
27	C₈×C₁₉	M₃₂	1	4	yes	—
28	C₈×C₁₆	—	19	1	no	—
29	C₈×C₁₆	—	19	1	no	—
30	C₈×C₁₆	D₁₉	1	1	yes	characteristic
31	C₂²×C₁₉	C₈²	1	1	yes	characteristic
32	C₄×C₁₉	C₄×C₁₆	1	2	yes	—
33	C₄×C₁₉	#346	1	2	yes	—
34	C₄×C₁₉	#346	1	2	yes	—
35	C₄×C₁₆	—	19	2	no	—
36	C₄×C₁₆	—	19	2	no	—
37	C₄×C₁₆	Dic₁₉	1	2	yes	—
38	C₈²	C₂×D₁₉	1	1	yes	characteristic
39	C₂×C₁₉	C₈×C₁₆	1	1	yes	characteristic
40	C₂×C₁₉	#1311	1	1	yes	characteristic
41	C₂×C₁₉	#1311	1	1	yes	characteristic
42	C₂×C₁₆	—	19	4	no	—
43	C₂×C₁₆	—	19	4	no	—
44	C₂×C₁₆	C₁₉⋊C₈	1	4	yes	—
45	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
46	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
47	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
48	C₁₉	#7052	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₈	C₈×D₁₉	1	2	yes	—
50	C₂×C₈	C₈×D₁₉	1	2	yes	—
51	C₂×C₈	C₂×C₁₉⋊C₈	1	2	yes	—
52	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
53	C₁₆	—	2	4	no	—
54	C₁₆	—	19	8	no	—
55	C₁₆	—	38	4	no	—
56	C₂×C₄	C₄×C₁₉⋊C₈	1	1	yes	characteristic
57	C₂×C₄	C₈×Dic₁₉	1	1	yes	characteristic
58	C₂×C₄	C₈×Dic₁₉	1	1	yes	characteristic
59	C₈	C₁₆×D₁₉	1	4	yes	—
60	C₈	#10597255	1	4	yes	—
61	C₈	#10597269	1	4	yes	—
62	C₂²	C₈×C₁₉⋊C₈	1	1	yes	characteristic
63	C₄	C₁₆×Dic₁₉	1	2	yes	—
64	C₄	#11926319	1	2	yes	—
65	C₄	#11926320	1	2	yes	—
66	C₂	C₁₆×C₁₉⋊C₈	1	1	yes	characteristic
67	C₂	#14561551	1	1	yes	characteristic
68	C₂	#14561552	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈²	C₂×D₁₉
commutator	C₂×C₁₉	C₈×C₁₆
Fitting	C₈×C₁₆×C₁₉	C₂
socle, prime radical	C₂²×C₁₉	C₈²
cosocle	C₈²×C₁₉	C₂²
hypercenter	C₈×C₁₆	D₁₉
hypocenter	C₁₉	#7052
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈² ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
20. C₁₉⋊C₁₆	C₁₆	semidirect
48. C₁₉	#7052	semidirect

Maximal subgroups

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

subgroup	index
C₈×C₁₉⋊C₁₆	2
C₈×C₁₆×C₁₉	2
#7052	19