Subgroups — #14561939

Order 2432.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#64515	C₂	1	2	yes	maximal
2	C₄×#64515	C₂	1	1	yes	maximal, characteristic
3	#11926266	C₂	1	2	yes	maximal, complemented
4	C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64515	C₄	1	2	yes	—
7	C₂×#64515	C₄	1	4	yes	—
8	C₄²×D₁₉	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₁₉	C₂²	1	2	yes	—
11	#10597272	C₄	1	2	yes	—
12	#10597272	C₄	1	4	yes	—
13	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
14	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₁₉	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
19	C₄²×C₁₉	C₂³	1	1	yes	characteristic
20	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
23	C₂×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
24	#64515	—	2	4	no	—
25	#64515	—	2	8	no	—
26	C₂²×D₁₉	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
29	C₂×Dic₁₉	C₄²	1	1	yes	characteristic
30	C₂×Dic₁₉	C₄²	1	2	yes	—
31	C₄×D₁₉	—	2	2	no	—
32	C₄×D₁₉	—	2	4	no	—
33	C₈×C₁₉	—	2	4	no	—
34	C₈×C₁₉	M₁₆	1	4	yes	complemented
35	C₁₉⋊C₈	—	2	2	no	—
36	C₁₉⋊C₈	M₁₆	1	8	yes	complemented
37	#1455	—	19	1	no	maximal, Sylow
38	C₂²×C₁₉	C₂×C₄²	1	1	yes	characteristic
39	C₂×D₁₉	—	2	1	no	—
40	C₂×D₁₉	—	2	2	no	—
41	C₄×C₁₉	C₂×M₁₆	1	2	yes	—
42	C₄×C₁₉	C₂×M₁₆	1	4	yes	—
43	Dic₁₉	—	2	1	no	—
44	Dic₁₉	—	2	2	no	—
45	C₄×M₁₆	—	19	2	no	—
46	C₄×M₁₆	—	19	1	no	—
47	#322	—	19	2	no	—
48	#322	D₁₉	1	1	yes	characteristic, complemented
49	C₈²	—	19	1	no	—
50	C₂×C₁₉	C₄×M₁₆	1	1	yes	characteristic
51	C₂×C₁₉	C₄×M₁₆	1	2	yes	—
52	D₁₉	—	4	1	no	—
53	C₂×M₁₆	—	19	4	no	—
54	C₂×M₁₆	—	19	2	no	—
55	C₂×C₄²	—	19	1	no	—
56	#97	—	19	4	no	—
57	#97	—	19	2	no	—
58	C₄×C₈	—	19	2	no	—
59	C₄×C₈	—	19	1	no	—
60	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
61	C₄×C₈	C₂×D₁₉	1	2	yes	—
62	C₁₉	#1455	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₄	—	19	1	no	—
64	C₂²×C₄	—	19	2	no	—
65	M₁₆	—	38	8	no	—
66	M₁₆	—	38	4	no	—
67	C₂×C₈	—	19	4	no	—
68	C₂×C₈	—	19	2	no	—
69	C₂×C₈	C₄×D₁₉	1	4	yes	—
70	C₂×C₈	C₄×D₁₉	1	2	yes	—
71	C₄²	—	19	1	no	—
72	C₄²	—	19	2	no	—
73	C₄²	C₂²×D₁₉	1	1	yes	characteristic
74	C₂³	—	19	1	no	—
75	C₂×C₄	—	19	1	no	—
76	C₂×C₄	—	19	2	no	—
77	C₂×C₄	—	38	2	no	—
78	C₂×C₄	—	38	4	no	—
79	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
80	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
81	C₈	—	2	4	no	—
82	C₈	—	19	8	no	—
83	C₈	—	38	2	no	—
84	C₈	#64515	1	4	yes	complemented
85	C₂²	—	38	1	no	—
86	C₂²	—	38	2	no	—
87	C₂²	C₄²×D₁₉	1	1	yes	characteristic
88	C₄	—	38	1	no	—
89	C₄	—	38	2	no	—
90	C₄	C₂×#64515	1	2	yes	—
91	C₄	M₁₆×D₁₉	1	4	yes	—
92	C₂	—	76	1	no	—
93	C₂	C₄×#64515	1	1	yes	characteristic
94	C₂	#11926496	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₁₉
commutator, socle	C₂²×C₁₉	C₂×C₄²
Fitting	C₁₉×#322	C₂
prime radical	C₂²×D₁₉	C₄²
cosocle	C₄²×C₁₉	C₂³
hypercenter	#322	D₁₉
hypocenter	C₁₉	#1455
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
3. #11926266	C₂	semidirect
4. C₈×C₁₉⋊C₈	C₂	semidirect
5. C₁₉×#322	C₂	semidirect
34. C₈×C₁₉	M₁₆	semidirect
36. C₁₉⋊C₈	M₁₆	semidirect
48. #322	D₁₉	semidirect
62. C₁₉	#1455	semidirect
84. C₈	#64515	semidirect

Maximal subgroups

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

subgroup	index
C₄×#64515	2
#11926266	2
C₈×C₁₉⋊C₈	2
C₁₉×#322	2
#1455	19