Subgroups — #11926832

Order 1216.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	#10597334	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#102	C₂	1	1	yes	maximal, characteristic
4	#10597289	C₂	1	1	yes	maximal, characteristic
5	#10597274	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#10597265	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₉	—	2	1	no	—
10	C₂×Dic₃₈	—	2	1	no	—
11	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²⋊Dic₁₉	—	2	1	no	—
14	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
16	Dic₁₉⋊C₄	—	2	1	no	—
17	C₄×Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₁₉	—	2	1	no	—
20	D₄×C₁₉	—	2	1	no	—
21	D₄×C₁₉	Q₈	1	2	yes	complemented
22	C₂×C₄×C₁₉	—	2	1	no	—
23	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×Dic₁₉	—	2	1	no	—
25	C₂×Dic₁₉	—	2	1	no	—
26	C₂×Dic₁₉	—	4	2	no	—
27	C₂×Dic₁₉	D₄	1	1	yes	characteristic
28	C₂×Dic₁₉	D₄	1	1	yes	characteristic
29	Dic₃₈	—	4	2	no	—
30	C₈×C₁₉	—	2	1	no	—
31	C₁₉⋊C₈	—	2	1	no	—
32	C₂²×C₁₉	—	2	2	no	—
33	C₂²×C₁₉	—	4	1	no	—
34	C₂²×C₁₉	—	4	1	no	—
35	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₄×C₁₉	—	4	1	no	—
37	C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	C₄×C₁₉	#41	1	1	yes	characteristic
39	Dic₁₉	—	2	1	no	—
40	Dic₁₉	—	4	1	no	—
41	Dic₁₉	—	4	1	no	—
42	Dic₁₉	SD₁₆	1	2	yes	—
43	#476	—	19	1	no	maximal, Sylow
44	C₂×C₁₉	—	4	2	no	—
45	C₂×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
46	C₂×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
47	C₂×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
48	C₄⋊Q₈	—	19	1	no	—
49	C₄×D₄	—	19	1	no	—
50	#106	—	19	1	no	—
51	#106	—	19	1	no	—
52	C₄⋊C₈	—	19	1	no	—
53	#102	—	19	1	no	—
54	#102	D₁₉	1	1	yes	characteristic
55	C₁₉	#476	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₈	—	38	1	no	—
57	C₂×D₄	C₂×D₁₉	1	1	yes	characteristic
58	C₂²×C₄	—	38	1	no	—
59	C₂×C₈	—	19	1	no	—
60	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
61	C₄⋊C₄	—	19	1	no	—
62	C₄⋊C₄	—	19	1	no	—
63	C₄⋊C₄	—	38	1	no	—
64	C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
65	C₂²⋊C₄	—	38	1	no	—
66	C₄²	—	19	1	no	—
67	C₂³	—	2	1	no	—
68	Q₈	—	76	2	no	—
69	D₄	—	2	1	no	—
70	D₄	Dic₃₈	1	2	yes	complemented
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	19	1	no	—
73	C₂×C₄	—	19	1	no	—
74	C₂×C₄	—	38	1	no	—
75	C₂×C₄	—	38	1	no	—
76	C₂×C₄	—	76	2	no	—
77	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	38	1	no	—
80	C₂²	—	2	2	no	—
81	C₂²	—	4	1	no	—
82	C₂²	—	4	1	no	—
83	C₂²	D₄×D₁₉	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	19	2	no	—
86	C₄	—	38	1	no	—
87	C₄	—	76	1	no	—
88	C₄	—	76	1	no	—
89	C₄	C₂×Dic₃₈	1	1	yes	characteristic
90	C₄	#64543	1	1	yes	characteristic
91	C₂	—	4	2	no	—
92	C₂	#10597324	1	1	yes	characteristic
93	C₂	#10597357	1	1	yes	characteristic
94	C₂	SD₁₆×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₁₉×#102	C₂
socle	C₂²×C₁₉	C₂×D₄
prime radical	C₂×D₄×C₁₉	C₂²
hypercenter	#102	D₁₉
hypocenter	C₁₉	#476
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

Complements

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

N	H ≅ G/N	type
2. #10597334	C₂	semidirect
5. #10597274	C₂	semidirect
6. Dic₁₉⋊C₈	C₂	semidirect
7. #10597265	C₂	semidirect
21. D₄×C₁₉	Q₈	semidirect
55. C₁₉	#476	semidirect
70. D₄	Dic₃₈	semidirect

Maximal subgroups

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

subgroup	index
D₄×Dic₁₉	2
#10597334	2
C₁₉×#102	2
#10597289	2
#10597274	2
Dic₁₉⋊C₈	2
#10597265	2
#476	19