Subgroups — #14563776

Order 2432.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926568	C₂	1	2	yes	maximal
2	#11926309	C₂	1	4	yes	maximal
3	C₂×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
5	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×#64520	C₂²	1	4	yes	—
7	C₁₉×#97	C₄	1	4	yes	—
8	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
9	C₂²×C₄×C₁₉	Q₈	1	2	yes	—
10	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
11	C₂×C₈×C₁₉	—	2	4	no	—
12	C₂×C₈×C₁₉	C₂×C₄	1	4	yes	—
13	C₄²×C₁₉	C₂×C₄	1	2	yes	—
14	C₄²×C₁₉	D₄	1	2	yes	—
15	#64520	—	2	8	no	—
16	C₂×C₁₉⋊C₈	—	2	4	no	—
17	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
18	C₂×C₄×C₁₉	—	4	2	no	—
19	C₂×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
20	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
22	C₂×C₄×C₁₉	#41	1	4	yes	—
23	C₈×C₁₉	—	2	4	no	—
24	C₁₉⋊C₈	—	4	4	no	—
25	#1838	—	19	1	no	maximal, Sylow
26	C₂²×C₁₉	—	2	2	no	—
27	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₁₉	#125	1	2	yes	—
29	C₄×C₁₉	—	2	4	no	—
30	C₄×C₁₉	#117	1	2	yes	—
31	C₄×C₁₉	#124	1	2	yes	—
32	#423	—	19	2	no	—
33	C₂×#97	D₁₉	1	1	yes	characteristic
34	#341	—	19	4	no	—
35	C₂×C₁₉	—	2	2	no	—
36	C₂×C₁₉	#382	1	1	yes	characteristic
37	C₂×C₁₉	#430	1	2	yes	—
38	C₂×M₁₆	—	19	4	no	—
39	C₂²×C₈	C₂×D₁₉	1	2	yes	—
40	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
41	C₄⋊C₈	—	38	4	no	—
42	#97	Dic₁₉	1	4	yes	—
43	C₁₉	#1838	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₄	Dic₃₈	1	2	yes	—
45	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
46	M₁₆	—	38	8	no	—
47	C₂×C₈	—	2	4	no	—
48	C₂×C₈	—	38	4	no	—
49	C₂×C₈	C₂×Dic₁₉	1	4	yes	—
50	C₄²	D₇₆	1	2	yes	—
51	C₄²	C₂×Dic₁₉	1	2	yes	—
52	C₂³	C₂×Dic₃₈	1	1	yes	characteristic
53	C₂×C₄	—	4	2	no	—
54	C₂×C₄	C₄⋊Dic₁₉	1	4	yes	—
55	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
56	C₂×C₄	#64541	1	4	yes	—
57	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
58	C₈	—	2	4	no	—
59	C₈	—	76	4	no	—
60	C₂²	—	2	2	no	—
61	C₂²	#10597316	1	2	yes	—
62	C₂²	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
63	C₄	—	2	4	no	—
64	C₄	#10597321	1	2	yes	—
65	C₄	#10597372	1	2	yes	—
66	C₂	—	2	2	no	—
67	C₂	#11926410	1	1	yes	characteristic
68	C₂	#11926593	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#97	C₂
socle	C₂²×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×C₁₉	C₂×Q₈
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#97	D₁₉
hypocenter	C₁₉	#1838
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
43. C₁₉	#1838	semidirect

Maximal subgroups

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

subgroup	index
#11926568	2
#11926309	2
C₂×C₁₉×#97	2
#1838	19