Subgroups — #11926752

Order 1216.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	#10597390	C₂	1	1	yes	maximal, characteristic
4	C₂×#64528	C₂	1	1	yes	maximal, characteristic
5	#10597292	C₂	1	1	yes	maximal, characteristic
6	#10597273	C₂	1	1	yes	maximal, characteristic
7	Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₃₈	C₂²	1	1	yes	characteristic
11	Q₁₆×C₁₉	—	2	2	no	—
12	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	#64528	—	2	2	no	—
14	C₄⋊Dic₁₉	—	2	1	no	—
15	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
16	Dic₁₉⋊C₄	—	2	1	no	—
17	Dic₁₉⋊C₄	—	2	1	no	—
18	C₄×Dic₁₉	—	2	1	no	—
19	C₄×Dic₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
21	Q₈×C₁₉	—	2	1	no	—
22	Q₈×C₁₉	—	2	1	no	—
23	Q₈×C₁₉	—	2	1	no	—
24	Q₈×C₁₉	D₄	1	2	yes	—
25	C₂×C₄×C₁₉	—	2	1	no	—
26	C₂×C₄×C₁₉	—	2	1	no	—
27	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×Dic₁₉	—	2	1	no	—
29	C₂×Dic₁₉	—	2	1	no	—
30	C₂×Dic₁₉	D₄	1	1	yes	characteristic
31	C₂×Dic₁₉	D₄	1	1	yes	characteristic
32	Dic₃₈	—	2	1	no	—
33	Dic₃₈	—	2	1	no	—
34	C₈×C₁₉	—	2	1	no	—
35	C₁₉⋊C₈	—	2	1	no	—
36	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₄×C₁₉	—	2	2	no	—
38	C₄×C₁₉	—	4	1	no	—
39	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₄×C₁₉	#41	1	1	yes	characteristic
41	Dic₁₉	—	2	1	no	—
42	Dic₁₉	—	4	1	no	—
43	Dic₁₉	—	4	1	no	—
44	Dic₁₉	Q₁₆	1	2	yes	complemented
45	#462	—	19	1	no	maximal, Sylow
46	C₂×C₁₉	#121	1	1	yes	characteristic
47	C₂×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
48	C₂×C₁₉	#137	1	1	yes	characteristic
49	C₂×Q₁₆	—	19	1	no	—
50	C₂×Q₁₆	D₁₉	1	1	yes	characteristic
51	C₄⋊Q₈	—	19	1	no	—
52	C₄×Q₈	—	19	1	no	—
53	C₄⋊C₈	—	19	1	no	—
54	#103	—	19	1	no	—
55	#103	—	19	1	no	—
56	C₁₉	#462	1	1	yes	characteristic, complemented, Sylow
57	C₂×Q₈	—	19	1	no	—
58	C₂×Q₈	C₂×D₁₉	1	1	yes	characteristic
59	C₂×Q₈	C₂×D₁₉	1	1	yes	characteristic
60	Q₁₆	—	2	2	no	—
61	Q₁₆	—	38	2	no	—
62	C₂×C₈	—	19	1	no	—
63	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
64	C₄⋊C₄	—	19	1	no	—
65	C₄⋊C₄	—	38	1	no	—
66	C₄⋊C₄	—	38	1	no	—
67	C₄⋊C₄	—	38	1	no	—
68	C₄²	—	19	1	no	—
69	C₄²	—	38	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	—	2	1	no	—
73	Q₈	—	38	1	no	—
74	Q₈	—	38	1	no	—
75	Q₈	C₂²⋊D₁₉	1	2	yes	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	19	1	no	—
79	C₂×C₄	—	19	1	no	—
80	C₂×C₄	—	38	1	no	—
81	C₂×C₄	—	38	1	no	—
82	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	38	1	no	—
85	C₂²	D₄×D₁₉	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	4	1	no	—
88	C₄	—	19	2	no	—
89	C₄	—	38	1	no	—
90	C₄	—	76	1	no	—
91	C₄	—	76	1	no	—
92	C₄	#64543	1	1	yes	characteristic
93	C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
94	C₂	Q₁₆×D₁₉	1	1	yes	characteristic
95	C₂	#10597364	1	1	yes	characteristic
96	C₂	#10597385	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₂×Q₁₆×C₁₉	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₄
hypercenter	C₂×Q₁₆	D₁₉
hypocenter	C₁₉	#462
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
44. Dic₁₉	Q₁₆	semidirect
56. C₁₉	#462	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₁₉	2
Q₈×Dic₁₉	2
#10597390	2
C₂×#64528	2
#10597292	2
#10597273	2
Dic₁₉⋊C₈	2
#462	19