Subgroups — #14565416

Order 2432.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₁₉	C₂	1	1	yes	maximal, characteristic
2	#11926581	C₂	1	2	yes	maximal
3	#11926371	C₂	1	2	yes	maximal, complemented
4	#11926370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
7	#10597338	—	2	2	no	—
8	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#107	C₂²	1	2	yes	—
10	#10597275	C₂²	1	2	yes	—
11	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
12	#10597265	—	2	2	no	—
13	C₁₆×D₁₉	C₄	1	4	yes	complemented
14	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
15	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₁₉	—	2	2	no	—
17	(C₂×D₁₉)⋊C₄	—	4	2	no	—
18	C₄⋊Dic₁₉	—	2	2	no	—
19	C₄×Dic₁₉	—	4	2	no	—
20	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
21	C₈×D₁₉	C₂×C₄	1	2	yes	—
22	C₈×D₁₉	Q₈	1	2	yes	—
23	C₁₆×C₁₉	C₂×C₄	1	2	yes	—
24	C₁₉⋊C₁₆	C₂×C₄	1	2	yes	—
25	C₂²×D₁₉	D₈	1	1	yes	characteristic
26	C₂×C₄×C₁₉	—	4	2	no	—
27	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₁₉	—	4	2	no	—
29	C₂×Dic₁₉	D₈	1	1	yes	characteristic
30	C₄×D₁₉	C₄⋊C₄	1	2	yes	—
31	C₄×D₁₉	Q₁₆	1	2	yes	—
32	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
34	C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
35	#2158	—	19	1	no	maximal, Sylow
36	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
37	C₂×D₁₉	—	2	1	no	—
38	C₂×D₁₉	—	2	1	no	—
39	C₂×D₁₉	#107	1	2	yes	—
40	C₄×C₁₉	—	8	2	no	—
41	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
43	Dic₁₉	—	8	2	no	—
44	Dic₁₉	#107	1	2	yes	—
45	C₂²×C₁₆	—	19	1	no	—
46	#427	—	19	2	no	—
47	#367	—	19	2	no	—
48	#366	—	19	1	no	—
49	#366	D₁₉	1	1	yes	characteristic, complemented
50	C₂×C₁₉	C₂×#107	1	1	yes	characteristic
51	C₂×C₁₉	#508	1	1	yes	characteristic
52	C₂×C₁₉	#508	1	1	yes	characteristic
53	D₁₉	—	2	2	no	—
54	C₂²×C₈	—	19	1	no	—
55	#117	—	38	2	no	—
56	C₂×C₁₆	—	19	1	no	—
57	C₂×C₁₆	—	19	4	no	—
58	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
59	#107	—	19	2	no	—
60	#107	C₂×D₁₉	1	2	yes	—
61	#106	—	38	2	no	—
62	C₁₉	#2158	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₄	—	19	1	no	—
64	C₂×C₈	—	19	1	no	—
65	C₂×C₈	—	19	2	no	—
66	C₂×C₈	—	19	2	no	—
67	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
68	C₄⋊C₄	—	2	2	no	—
69	C₄⋊C₄	—	38	2	no	—
70	C₂²⋊C₄	—	76	2	no	—
71	C₄²	—	76	2	no	—
72	C₁₆	—	19	2	no	—
73	C₁₆	C₄×D₁₉	1	2	yes	—
74	C₂³	—	19	1	no	—
75	C₂×C₄	—	4	2	no	—
76	C₂×C₄	—	19	1	no	—
77	C₂×C₄	—	19	2	no	—
78	C₂×C₄	—	19	2	no	—
79	C₂×C₄	—	76	2	no	—
80	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
81	C₈	—	19	2	no	—
82	C₈	C₂×C₄×D₁₉	1	1	yes	characteristic
83	C₈	Q₈×D₁₉	1	1	yes	characteristic
84	C₂²	—	19	2	no	—
85	C₂²	—	38	1	no	—
86	C₂²	—	38	1	no	—
87	C₂²	D₈×D₁₉	1	1	yes	characteristic
88	C₄	—	8	2	no	—
89	C₄	—	19	2	no	—
90	C₄	—	152	2	no	—
91	C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
92	C₄	Q₁₆×D₁₉	1	1	yes	characteristic
93	C₂	—	38	2	no	—
94	C₂	#107×D₁₉	1	1	yes	characteristic
95	C₂	#11926973	1	1	yes	characteristic
96	C₂	#11926977	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#366	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂²×D₁₉	D₈
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	#366	D₁₉
hypocenter	C₁₉	#2158
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

Complements

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

N	H ≅ G/N	type
3. #11926371	C₂	semidirect
4. #11926370	C₂	semidirect
5. C₁₉×#366	C₂	semidirect
13. C₁₆×D₁₉	C₄	semidirect
49. #366	D₁₉	semidirect
62. C₁₉	#2158	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₆×D₁₉	2
#11926581	2
#11926371	2
#11926370	2
C₁₉×#366	2
#2158	19