Subgroups — #11926671

Order 1216.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#10597272	C₂	1	2	yes	maximal
4	Dic₁₉⋊C₈	C₂	1	2	yes	maximal
5	C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₈	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₉	C₂²	1	2	yes	—
8	C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
10	Dic₁₉⋊C₄	C₄	1	2	yes	—
11	C₄×Dic₁₉	C₂²	1	2	yes	—
12	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×Dic₁₉	C₂×C₄	1	2	yes	—
18	C₂×Dic₁₉	C₂×C₄	1	2	yes	—
19	Dic₃₈	—	2	2	no	—
20	C₈×C₁₉	—	2	2	no	—
21	C₁₉⋊C₈	—	2	1	no	—
22	C₁₉⋊C₈	Q₈	1	2	yes	complemented
23	C₂²×C₁₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₁₉	—	2	1	no	—
25	C₄×C₁₉	M₁₆	1	2	yes	—
26	C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
27	C₄×C₁₉	#41	1	1	yes	characteristic
28	Dic₁₉	—	2	2	no	—
29	Dic₁₉	—	2	2	no	—
30	#446	—	19	1	no	maximal, Sylow
31	C₂×C₁₉	C₄×Q₈	1	1	yes	characteristic
32	C₂×C₁₉	C₂×M₁₆	1	1	yes	characteristic
33	C₂×C₁₉	#131	1	1	yes	characteristic
34	C₄×Q₈	—	19	1	no	—
35	C₄⋊C₈	—	19	2	no	—
36	C₄⋊C₈	D₁₉	1	1	yes	characteristic
37	#97	—	19	2	no	—
38	C₄×C₈	—	19	1	no	—
39	C₁₉	#446	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	19	1	no	—
41	C₂×C₈	—	19	1	no	—
42	C₂×C₈	—	19	1	no	—
43	C₂×C₈	C₂×D₁₉	1	2	yes	—
44	C₄⋊C₄	—	19	2	no	—
45	C₄⋊C₄	—	19	1	no	—
46	C₄²	—	19	2	no	—
47	C₄²	C₂×D₁₉	1	1	yes	characteristic
48	Q₈	—	38	2	no	—
49	C₂×C₄	—	19	2	no	—
50	C₂×C₄	—	19	2	no	—
51	C₂×C₄	C₄×D₁₉	1	1	yes	characteristic
52	C₂×C₄	C₄×D₁₉	1	1	yes	characteristic
53	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	19	2	no	—
56	C₈	—	38	1	no	—
57	C₂²	C₂×C₄×D₁₉	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	38	2	no	—
60	C₄	—	38	2	no	—
61	C₄	#64515	1	2	yes	—
62	C₄	#64543	1	1	yes	characteristic
63	C₄	Q₈×D₁₉	1	1	yes	characteristic
64	C₂	#10597333	1	1	yes	characteristic
65	C₂	C₂×#64515	1	1	yes	characteristic
66	C₂	#10597353	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₉
commutator, socle, prime radical	C₂²×C₁₉	C₂²×C₄
Fitting	C₁₉×C₄⋊C₈	C₂
cosocle	C₂×C₄×C₁₉	C₂³
hypercenter	C₄⋊C₈	D₁₉
hypocenter	C₁₉	#446
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
22. C₁₉⋊C₈	Q₈	semidirect
39. C₁₉	#446	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₃₈	2
C₁₉×C₄⋊C₈	2
#10597272	2
Dic₁₉⋊C₈	2
C₄×C₁₉⋊C₈	2
#446	19