Subgroups — #18076320

Order 4864.

486 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14563795	C₂	1	6	yes	maximal
2	C₂×C₈²×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597275	—	2	12	no	—
4	#11926414	C₂²	1	4	yes	—
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	#10597275	—	4	24	no	—
13	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
14	C₂²×Dic₁₉	—	4	4	no	—
15	C₂×C₈×C₁₉	C₄⋊C₄	1	12	yes	—
16	C₂×C₈×C₁₉	D₈	1	12	yes	—
17	C₂×C₈×C₁₉	Q₁₆	1	12	yes	—
18	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
19	C₄²×C₁₉	C₂×Q₈	1	3	yes	—
20	C₄⋊Dic₁₉	—	4	24	no	—
21	#8818	—	19	1	no	maximal, Sylow
22	C₂³×C₁₉	#127	1	1	yes	characteristic
23	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	3	yes	—
24	C₂×C₄×C₁₉	C₄⋊Q₈	1	3	yes	—
25	C₂×C₄×C₁₉	C₂×D₈	1	6	yes	—
26	C₂×C₄×C₁₉	C₂×Q₁₆	1	6	yes	—
27	C₂×Dic₁₉	—	8	12	no	—
28	C₈×C₁₉	#107	1	24	yes	complemented
29	#1845	—	19	6	no	—
30	C₂×C₈²	D₁₉	1	1	yes	characteristic
31	C₂²×C₁₉	#384	1	1	yes	characteristic
32	C₂²×C₁₉	#493	1	3	yes	—
33	C₂²×C₁₉	#494	1	3	yes	—
34	C₄×C₁₉	C₂×#107	1	6	yes	—
35	C₄×C₁₉	#500	1	6	yes	—
36	Dic₁₉	—	16	4	no	—
37	C₂×#107	—	38	12	no	—
38	C₂×C₄×C₈	C₂×D₁₉	1	3	yes	—
39	#384	—	19	4	no	—
40	C₈²	Dic₁₉	1	4	yes	complemented
41	C₂×C₁₉	#1712	1	1	yes	characteristic
42	C₂×C₁₉	#1713	1	3	yes	—
43	C₂×C₁₉	#1845	1	3	yes	—
44	C₂²×C₈	D₇₆	1	6	yes	—
45	C₂×C₄⋊C₄	—	38	12	no	—
46	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
47	#107	—	76	24	no	—
48	C₄×C₈	Dic₃₈	1	6	yes	—
49	C₄×C₈	C₂×Dic₁₉	1	6	yes	—
50	C₁₉	#8818	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₄	—	76	4	no	—
52	C₂²×C₄	C₂×D₇₆	1	3	yes	—
53	C₂×C₈	D₁₅₂	1	12	yes	—
54	C₂×C₈	Dic₇₆	1	12	yes	—
55	C₂×C₈	C₄⋊Dic₁₉	1	12	yes	—
56	C₄⋊C₄	—	76	24	no	—
57	C₄²	C₂×Dic₃₈	1	3	yes	—
58	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
59	C₂³	#10597320	1	1	yes	characteristic
60	C₂×C₄	—	152	12	no	—
61	C₂×C₄	#10597315	1	3	yes	—
62	C₂×C₄	C₂×D₁₅₂	1	6	yes	—
63	C₂×C₄	C₂×Dic₇₆	1	6	yes	—
64	C₂×C₄	C₂×C₄⋊Dic₁₉	1	3	yes	—
65	C₈	#10597275	1	24	yes	complemented
66	C₂²	#11926414	1	1	yes	characteristic
67	C₂²	#11926921	1	3	yes	—
68	C₂²	#11926924	1	3	yes	—
69	C₄	—	304	4	no	—
70	C₄	C₂×#10597275	1	6	yes	—
71	C₄	#11926949	1	6	yes	—
72	C₂	#14563250	1	1	yes	characteristic
73	C₂	#14563253	1	3	yes	—
74	C₂	#14563795	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	#8818
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
28. C₈×C₁₉	#107	semidirect
40. C₈²	Dic₁₉	semidirect
50. C₁₉	#8818	semidirect
65. C₈	#10597275	semidirect

Maximal subgroups

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

subgroup	index
#14563795	2
C₂×C₈²×C₁₉	2
#8818	19