Subgroups — #14561573

Order 2432.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926326	C₂	1	2	yes	maximal, complemented
2	C₁₉×#408	C₂	1	1	yes	maximal, characteristic
3	C₂×#41×C₁₉	C₄	1	1	yes	characteristic
4	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
5	C₂²×C₈×C₁₉	C₄	1	1	yes	characteristic
6	C₁₉×C₂²⋊C₈	—	2	2	no	—
7	#10597269	—	2	2	no	—
8	#41×C₁₉	—	4	1	no	—
9	#41×C₁₉	—	4	1	no	—
10	C₂×Q₈×C₁₉	C₈	1	1	yes	characteristic
11	C₂×D₄×C₁₉	—	2	1	no	—
12	C₂×D₄×C₁₉	C₈	1	1	yes	characteristic
13	C₂²×C₄×C₁₉	—	2	1	no	—
14	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	M₁₆×C₁₉	—	4	1	no	—
16	C₂×C₈×C₁₉	—	2	1	no	—
17	C₂×C₈×C₁₉	—	4	1	no	—
18	C₂×C₈×C₁₉	D₄	1	2	yes	—
19	C₁₉⋊C₁₆	—	4	2	no	—
20	C₂³×C₁₉	—	2	1	no	—
21	C₂³×C₁₉	M₁₆	1	1	yes	characteristic
22	Q₈×C₁₉	—	4	1	no	—
23	D₄×C₁₉	—	4	1	no	—
24	D₄×C₁₉	—	4	2	no	—
25	C₂×C₄×C₁₉	—	2	1	no	—
26	C₂×C₄×C₁₉	—	2	1	no	—
27	C₂×C₄×C₁₉	—	2	1	no	—
28	C₂×C₄×C₁₉	—	4	1	no	—
29	C₂×C₄×C₁₉	—	4	1	no	—
30	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₉	—	2	2	no	—
33	C₈×C₁₉	—	4	1	no	—
34	#1321	—	19	1	no	maximal, Sylow
35	C₂²×C₁₉	—	2	1	no	—
36	C₂²×C₁₉	—	4	1	no	—
37	C₂²×C₁₉	—	4	2	no	—
38	C₂²×C₁₉	—	4	1	no	—
39	C₂²×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₁₉	—	2	1	no	—
41	C₄×C₁₉	—	4	1	no	—
42	C₄×C₁₉	#99	1	1	yes	characteristic
43	C₄×C₁₉	#100	1	1	yes	characteristic
44	#408	D₁₉	1	1	yes	characteristic
45	#349	—	19	2	no	—
46	C₂×C₁₉	—	2	1	no	—
47	C₂×C₁₉	—	4	1	no	—
48	C₂×C₁₉	—	8	1	no	—
49	C₂×C₁₉	#323	1	1	yes	characteristic
50	C₂×#41	Dic₁₉	1	1	yes	characteristic
51	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
52	C₂²×C₈	Dic₁₉	1	1	yes	characteristic
53	M₃₂	—	38	2	no	—
54	C₂²⋊C₈	—	2	2	no	—
55	C₁₉	#1321	1	1	yes	characteristic, complemented, Sylow
56	#41	—	4	1	no	—
57	#41	—	4	1	no	—
58	C₂×Q₈	C₁₉⋊C₈	1	1	yes	characteristic
59	C₂×D₄	—	2	1	no	—
60	C₂×D₄	C₁₉⋊C₈	1	1	yes	characteristic
61	C₂²×C₄	—	2	1	no	—
62	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
63	M₁₆	—	4	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	4	1	no	—
66	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
67	C₁₆	—	76	2	no	—
68	C₂³	—	2	1	no	—
69	C₂³	#64520	1	1	yes	characteristic
70	Q₈	—	4	1	no	—
71	D₄	—	4	1	no	—
72	D₄	—	4	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
79	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
80	C₈	—	2	2	no	—
81	C₈	—	4	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	4	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	4	1	no	—
89	C₄	#10597290	1	1	yes	characteristic
90	C₄	#10597291	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	4	1	no	—
93	C₂	—	8	1	no	—
94	C₂	#11926268	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10597291
commutator	C₂×C₄×C₁₉	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₁₉
Fitting	C₁₉×#408	C₂
socle	C₂×C₁₉	#323
prime radical	C₂×#41×C₁₉	C₄
cosocle	C₂×M₁₆×C₁₉	C₂²
hypercenter	#408	D₁₉
hypocenter	C₁₉	#1321
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #408

Complements

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

N	H ≅ G/N	type
1. #11926326	C₂	semidirect
55. C₁₉	#1321	semidirect

Maximal subgroups

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

subgroup	index
#11926326	2
C₁₉×#408	2
#1321	19