Subgroups — #14561796

Order 2432.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926939	C₂	1	1	yes	maximal, characteristic
2	#11926339	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#355	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#124	C₂²	1	1	yes	characteristic
5	C₂×#64528	—	2	1	no	—
6	C₂×#64526	—	2	1	no	—
7	#10597315	C₄	1	1	yes	characteristic, complemented
8	C₁₉×#101	—	2	1	no	—
9	#10597291	—	2	1	no	—
10	#10597260	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
12	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
13	C₂×Dic₃₈	—	2	1	no	—
14	M₁₆×C₁₉	—	4	1	no	—
15	C₂²⋊C₄×C₁₉	—	4	1	no	—
16	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂²⋊Dic₁₉	—	4	1	no	—
18	#64528	—	4	2	no	—
19	#64526	—	4	2	no	—
20	C₄⋊Dic₁₉	—	4	1	no	—
21	C₂×C₁₉⋊C₈	—	2	1	no	—
22	C₂³×C₁₉	—	2	1	no	—
23	Q₈×C₁₉	—	4	1	no	—
24	D₄×C₁₉	—	4	1	no	—
25	C₂×C₄×C₁₉	—	2	1	no	—
26	C₂×C₄×C₁₉	—	2	1	no	—
27	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₁₉	—	4	1	no	—
29	C₂×Dic₁₉	—	8	1	no	—
30	Dic₃₈	—	4	1	no	—
31	Dic₃₈	—	4	1	no	—
32	C₈×C₁₉	—	8	1	no	—
33	C₁₉⋊C₈	—	2	2	no	—
34	#1407	—	19	1	no	maximal, Sylow
35	C₂²×C₁₉	—	4	1	no	—
36	C₂²×C₁₉	—	8	1	no	—
37	C₂²×C₁₉	#99	1	1	yes	characteristic
38	C₄×C₁₉	—	2	1	no	—
39	C₄×C₁₉	—	4	1	no	—
40	C₄×C₁₉	—	4	1	no	—
41	Dic₁₉	—	8	1	no	—
42	Dic₁₉	—	16	1	no	—
43	#497	—	19	1	no	—
44	#355	D₁₉	1	1	yes	characteristic
45	#354	—	19	1	no	—
46	C₂×C₁₉	—	2	1	no	—
47	C₂×C₁₉	—	8	1	no	—
48	C₂×C₁₉	#353	1	1	yes	characteristic
49	C₂×Q₁₆	—	38	1	no	—
50	C₂×SD₁₆	—	38	1	no	—
51	C₄⋊Q₈	—	19	1	no	—
52	#124	C₂×D₁₉	1	1	yes	characteristic
53	#101	—	2	1	no	—
54	#99	—	38	1	no	—
55	#97	—	19	1	no	—
56	C₁₉	#1407	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	38	1	no	—
58	C₂×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
59	C₂×D₄	D₇₆	1	1	yes	characteristic
60	Q₁₆	—	76	2	no	—
61	SD₁₆	—	76	2	no	—
62	M₁₆	—	4	1	no	—
63	C₂×C₈	—	38	1	no	—
64	C₄⋊C₄	—	76	1	no	—
65	C₂²⋊C₄	—	4	1	no	—
66	C₂²⋊C₄	—	76	1	no	—
67	C₄²	C₄×D₁₉	1	1	yes	characteristic
68	C₂³	—	2	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	76	1	no	—
71	Q₈	—	76	1	no	—
72	D₄	—	4	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	76	1	no	—
76	C₂×C₄	—	152	1	no	—
77	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
78	C₈	—	8	1	no	—
79	C₈	—	38	2	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	8	1	no	—
82	C₂²	#10597263	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	304	1	no	—
87	C₄	—	152	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	8	1	no	—
90	C₂	#11926336	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11926336
commutator	C₄²×C₁₉	C₂×C₄
Frattini	#124	C₂×D₁₉
Fitting	C₁₉×#355	C₂
socle	C₂×C₁₉	#353
prime radical	C₂×D₄×C₁₉	D₄
cosocle	C₁₉×#124	C₂²
hypercenter	#355	D₁₉
hypocenter	C₁₉	#1407
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #355

Complements

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

N	H ≅ G/N	type
7. #10597315	C₄	semidirect
10. #10597260	C₄	semidirect
56. C₁₉	#1407	semidirect

Maximal subgroups

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

subgroup	index
#11926939	2
#11926339	2
C₁₉×#355	2
#1407	19