Subgroups — #14565520

Order 2432.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926976	C₂	1	1	yes	maximal, characteristic
2	#11926660	C₂	1	2	yes	maximal, complemented
3	#11926350	C₂	1	2	yes	maximal, complemented
4	#11926319	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#368	C₂	1	1	yes	maximal, characteristic, complemented
6	#10597353	—	2	2	no	—
7	#10597350	C₂²	1	2	yes	—
8	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#108	C₂²	1	2	yes	—
10	#10597282	—	2	2	no	—
11	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
13	Dic₁₅₂	C₄	1	1	yes	characteristic, complemented
14	#10597257	C₄	1	2	yes	complemented
15	D₃₀₄	C₄	1	1	yes	characteristic, complemented
16	#64541	—	2	2	no	—
17	M₁₆×C₁₉	—	2	2	no	—
18	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
19	C₄×Dic₁₉	D₄	1	1	yes	characteristic
20	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
21	Dic₇₆	C₂×C₄	1	2	yes	—
22	D₁₅₂	C₂×C₄	1	2	yes	—
23	#64516	—	2	2	no	—
24	#64515	—	4	2	no	—
25	C₈×D₁₉	—	4	2	no	—
26	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₁₉⋊C₁₆	—	2	1	no	—
29	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
30	C₂²⋊D₁₉	—	4	2	no	—
31	C₂×Dic₁₉	—	2	1	no	—
32	D₇₆	—	2	2	no	—
33	C₄×D₁₉	—	4	2	no	—
34	Dic₃₈	—	2	2	no	—
35	C₈×C₁₉	—	4	2	no	—
36	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₁₉	#41	1	1	yes	characteristic
38	C₁₉⋊C₈	D₈	1	2	yes	—
39	#2179	—	19	1	no	maximal, Sylow
40	C₂²×C₁₉	#135	1	1	yes	characteristic
41	C₂×D₁₉	—	4	2	no	—
42	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
43	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
44	Dic₁₉	—	4	1	no	—
45	Dic₁₉	—	4	2	no	—
46	#508	—	19	1	no	—
47	#443	—	19	2	no	—
48	#368	D₁₉	1	1	yes	characteristic, complemented
49	#359	—	19	2	no	—
50	#346	—	19	1	no	—
51	C₂×C₁₉	—	2	1	no	—
52	C₂×C₁₉	C₄×D₈	1	1	yes	characteristic
53	D₁₉	—	8	2	no	—
54	#135	—	19	2	no	—
55	#131	—	38	2	no	—
56	Q₃₂	—	19	1	no	—
57	SD₃₂	—	19	2	no	—
58	D₁₆	—	19	1	no	—
59	C₂×C₁₆	—	19	1	no	—
60	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
61	#108	C₂×D₁₉	1	2	yes	—
62	#104	—	38	2	no	—
63	C₄×C₈	—	19	1	no	—
64	C₁₉	#2179	1	1	yes	characteristic, complemented, Sylow
65	#41	—	38	2	no	—
66	Q₁₆	—	19	2	no	—
67	SD₁₆	—	38	2	no	—
68	D₈	—	19	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	76	2	no	—
71	C₂×C₈	—	19	1	no	—
72	C₂×C₈	—	76	2	no	—
73	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
74	C₄²	—	19	1	no	—
75	C₁₆	—	38	1	no	—
76	C₁₆	C₄×D₁₉	1	1	yes	characteristic
77	C₁₆	C₄×D₁₉	1	1	yes	characteristic
78	Q₈	—	38	2	no	—
79	D₄	—	38	2	no	—
80	D₄	—	76	2	no	—
81	C₂×C₄	—	38	1	no	—
82	C₂×C₄	—	76	2	no	—
83	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
84	C₈	—	4	2	no	—
85	C₈	—	19	2	no	—
86	C₈	C₂×C₄×D₁₉	1	1	yes	characteristic
87	C₈	#64545	1	1	yes	characteristic
88	C₂²	—	76	2	no	—
89	C₂²	#10597365	1	1	yes	characteristic
90	C₄	—	76	1	no	—
91	C₄	—	76	2	no	—
92	C₄	#10597339	1	1	yes	characteristic
93	C₄	D₈×D₁₉	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	152	2	no	—
96	C₂	#11926626	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₁₉
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#368	C₂
socle	C₂×C₁₉	C₄×D₈
prime radical	#11926976	C₂
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	#368	D₁₉
hypocenter	C₁₉	#2179
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

Complements

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

N	H ≅ G/N	type
2. #11926660	C₂	semidirect
3. #11926350	C₂	semidirect
4. #11926319	C₂	semidirect
5. C₁₉×#368	C₂	semidirect
13. Dic₁₅₂	C₄	semidirect
14. #10597257	C₄	semidirect
15. D₃₀₄	C₄	semidirect
48. #368	D₁₉	semidirect
64. C₁₉	#2179	semidirect

Maximal subgroups

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

subgroup	index
#11926976	2
#11926660	2
#11926350	2
#11926319	2
C₁₉×#368	2
#2179	19