Subgroups — #18069153

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	2	yes	maximal
2	C₈×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉⋊C₁₆	C₄	1	4	yes	—
4	C₄×C₁₆×C₁₉	C₄	1	2	yes	—
5	C₈²×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₁₉	C₈	1	4	yes	—
7	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
8	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₉⋊C₁₆	C₈	1	8	yes	—
10	C₂×C₈×C₁₉	C₂×C₈	1	4	yes	—
11	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
12	C₄²×C₁₉	C₄²	1	1	yes	characteristic
13	C₁₆×C₁₉	C₁₆	1	8	yes	complemented
14	C₁₉⋊C₁₆	—	2	8	no	—
15	#7052	—	19	1	no	maximal, Sylow
16	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
17	C₂×C₄×C₁₉	C₄×C₈	1	2	yes	—
18	C₈×C₁₉	C₂×C₁₆	1	4	yes	—
19	C₈×C₁₉	M₃₂	1	8	yes	—
20	C₈×C₁₆	—	19	2	no	—
21	C₈×C₁₆	D₁₉	1	1	yes	characteristic
22	C₂²×C₁₉	C₈²	1	1	yes	characteristic
23	C₄×C₁₉	C₄×C₁₆	1	2	yes	—
24	C₄×C₁₉	#346	1	4	yes	—
25	C₄×C₁₆	—	19	4	no	—
26	C₄×C₁₆	Dic₁₉	1	2	yes	—
27	C₈²	C₂×D₁₉	1	1	yes	characteristic
28	C₂×C₁₉	C₈×C₁₆	1	1	yes	characteristic
29	C₂×C₁₉	#1311	1	2	yes	—
30	C₂×C₁₆	—	19	8	no	—
31	C₂×C₁₆	C₁₉⋊C₈	1	4	yes	—
32	C₄×C₈	C₄×D₁₉	1	2	yes	—
33	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
34	C₁₉	#7052	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₈	C₈×D₁₉	1	4	yes	—
36	C₂×C₈	C₂×C₁₉⋊C₈	1	2	yes	—
37	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
38	C₁₆	—	38	8	no	—
39	C₁₆	C₁₉⋊C₁₆	1	8	yes	complemented
40	C₂×C₄	C₄×C₁₉⋊C₈	1	1	yes	characteristic
41	C₂×C₄	C₈×Dic₁₉	1	2	yes	—
42	C₈	#10597255	1	8	yes	—
43	C₈	C₂×C₁₉⋊C₁₆	1	4	yes	—
44	C₂²	C₈×C₁₉⋊C₈	1	1	yes	characteristic
45	C₄	C₄×C₁₉⋊C₁₆	1	2	yes	—
46	C₄	#11926319	1	4	yes	—
47	C₂	C₈×C₁₉⋊C₁₆	1	1	yes	characteristic
48	C₂	#14561551	1	2	yes	—

	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
13. C₁₆×C₁₉	C₁₆	semidirect
34. C₁₉	#7052	semidirect
39. C₁₆	C₁₉⋊C₁₆	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