Subgroups — #14565881

Order 2432.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926946	C₂	1	1	yes	maximal, characteristic
2	#11926924	C₂	1	1	yes	maximal, characteristic
3	#11926349	C₂	1	4	yes	maximal
4	C₁₉×#346	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₇₆	—	2	1	no	—
6	C₂×Dic₇₆	C₂²	1	2	yes	—
7	#10597316	—	2	1	no	—
8	#10597315	—	2	1	no	—
9	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
10	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	#10597275	C₂²	1	2	yes	—
12	#10597274	—	2	1	no	—
13	C₂×Dic₃₈	—	2	2	no	—
14	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
15	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
16	C₄²×C₁₉	D₄	1	1	yes	characteristic
17	C₄⋊Dic₁₉	—	2	2	no	—
18	C₄⋊Dic₁₉	—	4	2	no	—
19	Dic₁₉⋊C₄	—	4	2	no	—
20	Dic₇₆	—	2	4	no	—
21	Dic₇₆	—	4	2	no	—
22	C₁₆×C₁₉	—	2	2	no	—
23	C₂×C₄×C₁₉	D₈	1	2	yes	—
24	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
25	C₂×Dic₁₉	—	4	2	no	—
26	C₂×Dic₁₉	—	4	2	no	—
27	Dic₃₈	—	4	2	no	—
28	Dic₃₈	—	4	2	no	—
29	C₈×C₁₉	SD₁₆	1	2	yes	—
30	C₈×C₁₉	#41	1	2	yes	—
31	#2245	—	19	1	no	maximal, Sylow
32	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
33	C₄×C₁₉	—	2	2	no	—
34	C₄×C₁₉	#124	1	1	yes	characteristic
35	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
36	Dic₁₉	—	8	2	no	—
37	Dic₁₉	—	8	2	no	—
38	#499	—	19	1	no	—
39	#494	—	19	1	no	—
40	#358	—	19	4	no	—
41	#346	D₁₉	1	1	yes	characteristic
42	C₂×C₁₉	#486	1	1	yes	characteristic
43	C₂×C₁₉	#510	1	2	yes	—
44	C₂×Q₁₆	—	19	2	no	—
45	C₂×Q₁₆	—	38	1	no	—
46	C₄⋊Q₈	—	38	1	no	—
47	#125	—	38	1	no	—
48	C₂×C₁₆	C₂×D₁₉	1	2	yes	—
49	#107	—	19	2	no	—
50	#106	—	38	1	no	—
51	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
52	C₁₉	#2245	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₈	—	38	2	no	—
54	Q₁₆	—	38	4	no	—
55	Q₁₆	—	76	2	no	—
56	C₂×C₈	D₇₆	1	1	yes	characteristic
57	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
58	C₄⋊C₄	—	38	2	no	—
59	C₄⋊C₄	—	76	2	no	—
60	C₄⋊C₄	—	76	2	no	—
61	C₄²	D₇₆	1	1	yes	characteristic
62	C₁₆	—	2	2	no	—
63	Q₈	—	76	2	no	—
64	Q₈	—	76	2	no	—
65	C₂×C₄	—	76	2	no	—
66	C₂×C₄	—	76	2	no	—
67	C₂×C₄	D₁₅₂	1	2	yes	—
68	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
69	C₈	#64516	1	2	yes	—
70	C₈	#64541	1	2	yes	—
71	C₂²	C₂×D₁₅₂	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	152	2	no	—
74	C₄	—	152	2	no	—
75	C₄	#10597321	1	1	yes	characteristic
76	C₄	C₂×#64516	1	1	yes	characteristic
77	C₂	#11926891	1	1	yes	characteristic
78	C₂	#11926987	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₅₂
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#346	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₈
hypercenter	#346	D₁₉
hypocenter	C₁₉	#2245
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
52. C₁₉	#2245	semidirect

Maximal subgroups

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

subgroup	index
#11926946	2
#11926924	2
#11926349	2
C₁₉×#346	2
#2245	19