Subgroups — #14564740

Order 2432.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927344	C₂	1	3	yes	maximal, complemented
2	#11926512	C₂	1	3	yes	maximal, complemented
3	C₁₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#64541	C₂²	1	3	yes	—
5	C₂×M₁₆×C₁₉	C₂²	1	3	yes	—
6	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
7	#10597355	—	2	6	no	—
8	#10597354	—	2	6	no	—
9	#10597350	—	2	6	no	—
10	(C₂×D₁₉)⋊C₈	—	2	6	no	—
11	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
12	C₂×C₂²⋊D₁₉	—	2	3	no	—
13	#64541	—	2	6	no	—
14	#64541	—	2	6	no	—
15	C₂×D₇₆	D₄	1	3	yes	—
16	C₂×C₄×D₁₉	—	2	3	no	—
17	C₂×Dic₃₈	D₄	1	3	yes	—
18	M₁₆×C₁₉	—	2	6	no	—
19	C₂×C₈×C₁₉	D₄	1	6	yes	—
20	C₂×C₁₉⋊C₈	—	2	3	no	—
21	Dic₇₆	—	2	6	no	—
22	D₁₅₂	—	2	6	no	—
23	#64516	—	2	12	no	—
24	C₂³×C₁₉	#41	1	1	yes	characteristic
25	C₂²×D₁₉	—	2	3	no	—
26	C₂×C₄×C₁₉	C₂×D₄	1	3	yes	—
27	C₂×C₄×C₁₉	C₂×D₄	1	3	yes	—
28	C₂²⋊D₁₉	—	4	6	no	—
29	C₂×Dic₁₉	—	2	3	no	—
30	D₇₆	—	2	6	no	—
31	C₄×D₁₉	—	4	3	no	—
32	C₄×D₁₉	—	4	3	no	—
33	Dic₃₈	—	2	6	no	—
34	C₈×C₁₉	—	2	6	no	—
35	C₁₉⋊C₈	—	4	1	no	—
36	#2017	—	19	1	no	maximal, Sylow
37	C₂²×C₁₉	—	4	1	no	—
38	C₂²×C₁₉	#121	1	3	yes	—
39	C₂×D₁₉	—	4	6	no	—
40	C₂×D₁₉	—	4	3	no	—
41	C₄×C₁₉	#120	1	3	yes	—
42	C₄×C₁₉	#127	1	1	yes	characteristic
43	Dic₁₉	—	4	3	no	—
44	#575	—	19	3	no	—
45	#408	—	19	3	no	—
46	#338	D₁₉	1	1	yes	characteristic, complemented
47	C₂×C₁₉	—	2	3	no	—
48	C₂×C₁₉	#392	1	1	yes	characteristic
49	D₁₉	—	8	3	no	—
50	C₂×#41	—	19	3	no	—
51	#137	—	38	6	no	—
52	AGL(1,ℤ/8)	—	38	6	no	—
53	#135	—	38	6	no	—
54	C₂×M₁₆	C₂×D₁₉	1	3	yes	—
55	C₂²×C₈	—	19	1	no	—
56	C₂²⋊C₈	—	38	6	no	—
57	C₁₉	#2017	1	1	yes	characteristic, complemented, Sylow
58	#41	—	38	6	no	—
59	#41	—	38	6	no	—
60	C₂×Q₈	—	19	3	no	—
61	C₂×D₄	—	19	3	no	—
62	C₂×D₄	—	38	3	no	—
63	C₂²×C₄	—	38	3	no	—
64	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
65	Q₁₆	—	38	6	no	—
66	SD₁₆	—	38	12	no	—
67	D₈	—	38	6	no	—
68	M₁₆	—	2	6	no	—
69	C₂×C₈	—	38	3	no	—
70	C₂×C₈	D₇₆	1	6	yes	—
71	C₂³	—	38	3	no	—
72	C₂³	#64545	1	1	yes	characteristic
73	Q₈	—	38	6	no	—
74	D₄	—	38	6	no	—
75	D₄	—	76	6	no	—
76	C₂×C₄	—	38	3	no	—
77	C₂×C₄	—	76	3	no	—
78	C₂×C₄	—	76	3	no	—
79	C₂×C₄	C₂×D₇₆	1	3	yes	—
80	C₂×C₄	D₄×D₁₉	1	3	yes	—
81	C₈	—	2	6	no	—
82	C₈	—	76	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	76	6	no	—
85	C₂²	—	76	3	no	—
86	C₂²	#10597341	1	3	yes	—
87	C₄	—	76	3	no	—
88	C₄	#10597320	1	1	yes	characteristic
89	C₄	#10597328	1	3	yes	—
90	C₂	—	2	3	no	—
91	C₂	—	152	3	no	—
92	C₂	#11926454	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10597320
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#338	C₂
socle	C₂×C₁₉	#392
hypercenter	#338	D₁₉
hypocenter	C₁₉	#2017
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
1. #11927344	C₂	semidirect
2. #11926512	C₂	semidirect
3. C₁₉×#338	C₂	semidirect
46. #338	D₁₉	semidirect
57. C₁₉	#2017	semidirect

Maximal subgroups

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

subgroup	index
#11927344	2
#11926512	2
C₁₉×#338	2
#2017	19