Subgroups — #18076318

Order 4864.

390 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563763	C₂	1	6	yes	maximal
2	C₂×C₈²×C₁₉	C₂	1	1	yes	maximal, characteristic
3	#11926414	C₂²	1	4	yes	—
4	#11926307	—	2	12	no	—
5	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
6	C₈²×C₁₉	C₄	1	4	yes	complemented
7	C₂²×C₈×C₁₉	D₄	1	6	yes	—
8	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	—	2	12	no	—
10	C₄×C₈×C₁₉	C₂×C₄	1	6	yes	—
11	C₄×C₈×C₁₉	Q₈	1	6	yes	—
12	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
13	C₂²×Dic₁₉	—	4	4	no	—
14	C₂×C₈×C₁₉	—	2	12	no	—
15	C₂×C₈×C₁₉	C₄⋊C₄	1	12	yes	—
16	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
17	C₄²×C₁₉	C₂×Q₈	1	3	yes	—
18	C₄⋊Dic₁₉	—	4	24	no	—
19	#8817	—	19	1	no	maximal, Sylow
20	C₂³×C₁₉	#127	1	1	yes	characteristic
21	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	3	yes	—
22	C₂×C₄×C₁₉	C₄⋊Q₈	1	3	yes	—
23	C₂×C₄×C₁₉	#135	1	12	yes	—
24	C₂×Dic₁₉	—	8	12	no	—
25	C₈×C₁₉	—	2	12	no	—
26	#1834	—	19	6	no	—
27	C₂×C₈²	D₁₉	1	1	yes	characteristic
28	C₂²×C₁₉	#384	1	1	yes	characteristic
29	C₂²×C₁₉	#495	1	6	yes	—
30	C₄×C₁₉	#427	1	6	yes	—
31	C₄×C₁₉	#499	1	6	yes	—
32	Dic₁₉	—	16	4	no	—
33	C₂×C₄×C₈	C₂×D₁₉	1	3	yes	—
34	#384	—	19	4	no	—
35	#340	—	38	12	no	—
36	C₈²	Dic₁₉	1	4	yes	complemented
37	C₂×C₁₉	#1711	1	4	yes	—
38	C₂×C₁₉	#1846	1	3	yes	—
39	C₂²×C₈	D₇₆	1	6	yes	—
40	C₂×C₄⋊C₄	—	38	12	no	—
41	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
42	C₄×C₈	Dic₃₈	1	6	yes	—
43	C₄×C₈	C₂×Dic₁₉	1	6	yes	—
44	C₁₉	#8817	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₄	—	76	4	no	—
46	C₂²×C₄	C₂×D₇₆	1	3	yes	—
47	C₂×C₈	—	2	12	no	—
48	C₂×C₈	C₄⋊Dic₁₉	1	12	yes	—
49	C₄⋊C₄	—	76	24	no	—
50	C₄²	C₂×Dic₃₈	1	3	yes	—
51	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
52	C₂³	#10597320	1	1	yes	characteristic
53	C₂×C₄	—	152	12	no	—
54	C₂×C₄	#10597315	1	3	yes	—
55	C₂×C₄	#10597350	1	12	yes	—
56	C₂×C₄	C₂×C₄⋊Dic₁₉	1	3	yes	—
57	C₈	—	2	12	no	—
58	C₂²	#11926414	1	1	yes	characteristic
59	C₂²	#11926928	1	6	yes	—
60	C₄	—	304	4	no	—
61	C₄	#11926582	1	6	yes	—
62	C₄	#11926946	1	6	yes	—
63	C₂	#14563247	1	4	yes	—
64	C₂	#14563799	1	3	yes	—

	subgroup	G/H
center	C₂³	#10597320
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₈²×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×C₈²	D₁₉
hypocenter	C₁₉	#8817
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
6. C₈²×C₁₉	C₄	semidirect
36. C₈²	Dic₁₉	semidirect
44. C₁₉	#8817	semidirect

Maximal subgroups

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

subgroup	index
#14563763	2
C₂×C₈²×C₁₉	2
#8817	19