Subgroups — #11926947

Order 1216.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	#10597315	C₂	1	1	yes	maximal, characteristic
3	#10597264	C₂	1	4	yes	maximal
4	C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₁₉	—	2	1	no	—
6	C₂×Dic₃₈	—	2	1	no	—
7	C₄⋊C₄×C₁₉	—	2	1	no	—
8	C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₉	—	2	1	no	—
11	C₄⋊Dic₁₉	C₂²	1	2	yes	—
12	C₂×C₁₉⋊C₈	C₂²	1	2	yes	—
13	Q₈×C₁₉	—	4	2	no	—
14	C₂×C₄×C₁₉	—	2	2	no	—
15	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂×Dic₁₉	—	2	2	no	—
19	Dic₃₈	—	4	2	no	—
20	C₁₉⋊C₈	Q₈	1	4	yes	complemented
21	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
22	C₄×C₁₉	—	4	2	no	—
23	C₄×C₁₉	D₈	1	2	yes	—
24	C₄×C₁₉	Q₁₆	1	2	yes	—
25	C₄×C₁₉	C₂×Q₈	1	2	yes	—
26	Dic₁₉	—	4	2	no	—
27	#500	—	19	1	no	maximal, Sylow
28	C₂×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
29	C₂×C₁₉	C₂×D₈	1	1	yes	characteristic
30	C₂×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
31	C₄⋊Q₈	—	19	1	no	—
32	C₄⋊Q₈	D₁₉	1	1	yes	characteristic
33	#107	—	19	4	no	—
34	C₄×C₈	—	19	1	no	—
35	C₁₉	#500	1	1	yes	characteristic, complemented, Sylow
36	C₂×Q₈	—	2	1	no	—
37	C₂×Q₈	—	38	1	no	—
38	C₂×C₈	—	19	2	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	19	2	no	—
41	C₄⋊C₄	—	38	1	no	—
42	C₄⋊C₄	C₂×D₁₉	1	2	yes	—
43	C₄²	C₂×D₁₉	1	1	yes	characteristic
44	Q₈	—	4	2	no	—
45	Q₈	—	76	2	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	38	2	no	—
48	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
51	C₈	—	19	4	no	—
52	C₂²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	76	2	no	—
55	C₄	#64525	1	2	yes	—
56	C₄	#64528	1	2	yes	—
57	C₄	Q₈×D₁₉	1	2	yes	—
58	C₂	C₂×#64525	1	1	yes	characteristic
59	C₂	C₂×#64528	1	1	yes	characteristic
60	C₂	#10597390	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₁₉×C₄⋊Q₈	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₄
hypercenter	C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#500
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
20. C₁₉⋊C₈	Q₈	semidirect
35. C₁₉	#500	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×C₄⋊Q₈	2
#10597315	2
#10597264	2
C₄×C₁₉⋊C₈	2
#500	19