Subgroups — #14565522

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	#11926662	C₂	1	2	yes	maximal, complemented
3	#11926374	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926352	C₂	1	2	yes	maximal, complemented
5	C₁₉×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	#10597350	C₂²	1	2	yes	—
7	#10597347	—	2	2	no	—
8	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	#10597276	C₂²	1	2	yes	—
12	#10597262	—	2	2	no	—
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	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
19	C₄²×C₁₉	D₄	1	1	yes	characteristic
20	#64520	—	2	2	no	—
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	—	2	1	no	—
27	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₉	—	2	1	no	—
30	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂²⋊D₁₉	—	4	2	no	—
32	D₇₆	—	2	2	no	—
33	C₄×D₁₉	—	4	2	no	—
34	Dic₃₈	—	2	2	no	—
35	C₈×C₁₉	D₈	1	2	yes	—
36	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₁₉	#41	1	1	yes	characteristic
38	C₁₉⋊C₈	—	4	2	no	—
39	#2179	—	19	1	no	maximal, Sylow
40	C₂²×C₁₉	#135	1	1	yes	characteristic
41	C₂×D₁₉	—	4	2	no	—
42	C₄×C₁₉	—	4	1	no	—
43	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
44	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
45	Dic₁₉	—	4	2	no	—
46	#508	—	19	1	no	—
47	#443	—	19	2	no	—
48	#368	—	19	1	no	—
49	#359	—	19	2	no	—
50	#346	D₁₉	1	1	yes	characteristic, complemented
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	C₂×D₁₉	1	1	yes	characteristic
60	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
61	#108	—	19	2	no	—
62	#104	—	38	2	no	—
63	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
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	—	38	2	no	—
70	M₁₆	—	76	2	no	—
71	C₂×C₈	—	76	2	no	—
72	C₂×C₈	D₇₆	1	1	yes	characteristic
73	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
74	C₄²	D₇₆	1	1	yes	characteristic
75	C₁₆	—	2	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	—	2	1	no	—
82	C₂×C₄	—	76	2	no	—
83	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
84	C₈	—	76	2	no	—
85	C₈	D₁₅₂	1	2	yes	—
86	C₈	C₂×C₄×D₁₉	1	1	yes	characteristic
87	C₈	#64541	1	1	yes	characteristic
88	C₂²	—	76	2	no	—
89	C₂²	#10597350	1	1	yes	characteristic
90	C₄	—	4	1	no	—
91	C₄	—	76	2	no	—
92	C₄	C₄×D₇₆	1	1	yes	characteristic
93	C₄	C₂×D₁₅₂	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	152	2	no	—
96	C₂	C₄×D₁₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₁₅₂
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#346	C₂
socle	C₂×C₁₉	C₄×D₈
prime radical	#11926976	C₂
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	#346	D₁₉
hypocenter	C₁₉	#2179
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. #11926662	C₂	semidirect
3. #11926374	C₂	semidirect
4. #11926352	C₂	semidirect
5. C₁₉×#346	C₂	semidirect
13. Dic₁₅₂	C₄	semidirect
14. #10597257	C₄	semidirect
15. D₃₀₄	C₄	semidirect
50. #346	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
#11926662	2
#11926374	2
#11926352	2
C₁₉×#346	2
#2179	19