Subgroups — #11926922

Order 1216.

122 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	#10597390	C₂	1	2	yes	maximal
3	C₂×#64528	C₂	1	2	yes	maximal
4	C₂×Dic₇₆	C₂	1	1	yes	maximal, characteristic
5	C₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₁₉	C₂²	1	2	yes	—
7	C₂×Dic₃₈	C₂²	1	2	yes	—
8	Q₁₆×C₁₉	—	2	2	no	—
9	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	#64528	—	2	4	no	—
11	Dic₁₉⋊C₄	—	2	4	no	—
12	C₄×Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	Dic₇₆	—	2	2	no	—
15	Q₈×C₁₉	—	2	2	no	—
16	Q₈×C₁₉	—	2	2	no	—
17	C₂×C₄×C₁₉	—	2	2	no	—
18	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₉	—	2	2	no	—
20	C₂×Dic₁₉	D₄	1	2	yes	—
21	Dic₃₈	—	2	2	no	—
22	Dic₃₈	—	2	2	no	—
23	C₈×C₁₉	D₄	1	2	yes	—
24	C₁₉⋊C₈	D₄	1	2	yes	—
25	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
26	C₄×C₁₉	—	4	2	no	—
27	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
28	C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
29	Dic₁₉	—	4	2	no	—
30	Dic₁₉	Q₁₆	1	4	yes	complemented
31	#494	—	19	1	no	maximal, Sylow
32	C₂×C₁₉	#127	1	1	yes	characteristic
33	C₂×C₁₉	C₂×Q₁₆	1	2	yes	—
34	C₂×Q₁₆	—	19	2	no	—
35	C₂×Q₁₆	—	19	1	no	—
36	C₂×Q₁₆	D₁₉	1	1	yes	characteristic
37	C₄⋊Q₈	—	19	2	no	—
38	C₄×C₈	—	19	1	no	—
39	C₁₉	#494	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	19	2	no	—
41	C₂×Q₈	C₂×D₁₉	1	2	yes	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	38	4	no	—
44	Q₁₆	—	38	2	no	—
45	C₂×C₈	—	19	1	no	—
46	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
47	C₄⋊C₄	—	38	4	no	—
48	C₄²	—	19	1	no	—
49	Q₈	—	2	2	no	—
50	Q₈	—	2	2	no	—
51	Q₈	—	38	2	no	—
52	Q₈	—	38	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	19	2	no	—
55	C₂×C₄	—	38	2	no	—
56	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
57	C₈	—	19	2	no	—
58	C₈	C₂²⋊D₁₉	1	2	yes	—
59	C₂²	D₄×D₁₉	1	1	yes	characteristic
60	C₄	—	4	2	no	—
61	C₄	—	19	4	no	—
62	C₄	—	76	2	no	—
63	C₄	D₄×D₁₉	1	1	yes	characteristic
64	C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
65	C₂	Q₁₆×D₁₉	1	2	yes	—
66	C₂	#10597386	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	#494
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
30. Dic₁₉	Q₁₆	semidirect
39. C₁₉	#494	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
#10597390	2
C₂×#64528	2
C₂×Dic₇₆	2
C₈×Dic₁₉	2
#494	19