Subgroups — #14565152

Order 2432.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926593	C₂	1	3	yes	maximal, complemented
2	#11926507	C₂	1	3	yes	maximal
3	C₁₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
5	C₂×M₁₆×C₁₉	C₂²	1	3	yes	—
6	C₂×#64520	C₂²	1	3	yes	—
7	(C₂×D₁₉)⋊C₈	—	2	6	no	—
8	#10597276	—	2	6	no	—
9	C₂³×D₁₉	Q₈	1	1	yes	characteristic
10	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
11	C₂²×Dic₁₉	Q₈	1	1	yes	characteristic
12	C₂×C₄×D₁₉	—	2	3	no	—
13	C₂×C₄×D₁₉	—	2	3	no	—
14	M₁₆×C₁₉	—	2	6	no	—
15	C₂×C₈×C₁₉	D₄	1	6	yes	—
16	#64520	—	2	6	no	—
17	C₂×C₁₉⋊C₈	—	2	3	no	—
18	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
19	C₂²×D₁₉	—	2	3	no	—
20	C₂²×D₁₉	—	4	2	no	—
21	C₂×C₄×C₁₉	C₂×D₄	1	3	yes	—
22	C₂×C₄×C₁₉	#41	1	3	yes	—
23	C₂×Dic₁₉	—	2	3	no	—
24	C₄×D₁₉	—	4	3	no	—
25	C₄×D₁₉	—	4	1	no	—
26	C₈×C₁₉	—	2	6	no	—
27	C₁₉⋊C₈	—	4	3	no	—
28	#2091	—	19	1	no	maximal, Sylow
29	C₂²×C₁₉	—	4	1	no	—
30	C₂²×C₁₉	C₂²⋊Q₈	1	3	yes	—
31	C₂×D₁₉	—	2	6	no	—
32	C₂×D₁₉	—	4	3	no	—
33	C₂×D₁₉	—	4	1	no	—
34	C₄×C₁₉	#123	1	3	yes	—
35	C₄×C₁₉	#127	1	1	yes	characteristic
36	Dic₁₉	—	4	1	no	—
37	#430	—	19	3	no	—
38	#407	—	19	3	no	—
39	#338	D₁₉	1	1	yes	characteristic, complemented
40	C₂×C₁₉	—	2	3	no	—
41	C₂×C₁₉	#399	1	1	yes	characteristic
42	D₁₉	—	4	2	no	—
43	C₂³×C₄	—	19	1	no	—
44	C₂×M₁₆	—	19	3	no	—
45	C₂×M₁₆	C₂×D₁₉	1	3	yes	—
46	#108	—	38	6	no	—
47	C₂²⋊C₈	—	38	6	no	—
48	C₁₉	#2091	1	1	yes	characteristic, complemented, Sylow
49	C₂⁴	—	19	1	no	—
50	C₂²×C₄	—	19	1	no	—
51	C₂²×C₄	—	38	3	no	—
52	C₂²×C₄	—	38	3	no	—
53	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
54	M₁₆	—	2	6	no	—
55	M₁₆	—	38	6	no	—
56	C₂×C₈	—	38	3	no	—
57	C₂×C₈	D₇₆	1	6	yes	—
58	C₂³	—	38	3	no	—
59	C₂³	—	76	2	no	—
60	C₂³	Q₈×D₁₉	1	1	yes	characteristic
61	C₂×C₄	—	38	3	no	—
62	C₂×C₄	—	76	1	no	—
63	C₂×C₄	—	76	3	no	—
64	C₂×C₄	C₂×D₇₆	1	3	yes	—
65	C₂×C₄	#64543	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	—	76	3	no	—
68	C₂²	—	4	1	no	—
69	C₂²	—	38	6	no	—
70	C₂²	—	76	3	no	—
71	C₂²	—	76	1	no	—
72	C₂²	#10597343	1	3	yes	—
73	C₄	—	76	1	no	—
74	C₄	#10597320	1	1	yes	characteristic
75	C₄	#10597332	1	3	yes	—
76	C₂	—	2	3	no	—
77	C₂	—	76	2	no	—
78	C₂	#11926481	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	#399
prime radical	C₂³×D₁₉	Q₈
hypercenter	#338	D₁₉
hypocenter	C₁₉	#2091
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. #11926593	C₂	semidirect
3. C₁₉×#338	C₂	semidirect
39. #338	D₁₉	semidirect
48. C₁₉	#2091	semidirect

Maximal subgroups

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

subgroup	index
#11926593	2
#11926507	2
C₁₉×#338	2
#2091	19