Subgroups — #11926953

Order 1216.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10597316	C₂	1	1	yes	maximal, characteristic
2	#10597315	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#97	C₂	1	1	yes	maximal, characteristic
4	#10597275	C₂	1	2	yes	maximal
5	#10597274	C₂	1	2	yes	maximal
6	C₂×Dic₃₈	—	2	1	no	—
7	C₂×C₈×C₁₉	C₂²	1	2	yes	—
8	C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₁₉	—	2	1	no	—
10	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₉	C₂²	1	2	yes	—
12	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	Dic₁₉⋊C₄	—	2	1	no	—
14	Dic₁₉⋊C₄	—	2	1	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	1	no	—
19	C₂×Dic₁₉	—	2	1	no	—
20	C₂×Dic₁₉	—	2	2	no	—
21	Dic₃₈	—	4	2	no	—
22	C₈×C₁₉	Q₈	1	4	yes	complemented
23	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
24	C₄×C₁₉	—	2	1	no	—
25	C₄×C₁₉	—	2	1	no	—
26	C₄×C₁₉	C₂×Q₈	1	2	yes	—
27	Dic₁₉	—	4	2	no	—
28	Dic₁₉	—	4	1	no	—
29	Dic₁₉	—	4	1	no	—
30	#501	—	19	1	no	maximal, Sylow
31	C₂×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
32	C₂×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
33	C₂×C₁₉	#137	1	1	yes	characteristic
34	C₄⋊Q₈	—	19	1	no	—
35	#125	—	19	1	no	—
36	#107	—	19	2	no	—
37	#106	—	19	2	no	—
38	#97	D₁₉	1	1	yes	characteristic
39	C₁₉	#501	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	38	1	no	—
41	C₂×C₈	C₂×D₁₉	1	2	yes	—
42	C₄⋊C₄	—	19	1	no	—
43	C₄⋊C₄	—	19	2	no	—
44	C₄⋊C₄	—	19	1	no	—
45	C₄⋊C₄	—	38	1	no	—
46	C₄⋊C₄	—	38	1	no	—
47	C₄⋊C₄	—	38	1	no	—
48	C₄²	C₂×D₁₉	1	1	yes	characteristic
49	Q₈	—	76	2	no	—
50	C₂×C₄	—	38	1	no	—
51	C₂×C₄	—	38	1	no	—
52	C₂×C₄	—	38	2	no	—
53	C₂×C₄	D₇₆	1	1	yes	characteristic
54	C₂×C₄	D₇₆	1	1	yes	characteristic
55	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
56	C₈	Dic₃₈	1	4	yes	complemented
57	C₂²	C₂×D₇₆	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	76	2	no	—
61	C₄	—	76	1	no	—
62	C₄	—	76	1	no	—
63	C₄	C₂×Dic₃₈	1	2	yes	—
64	C₂	#10597315	1	1	yes	characteristic
65	C₂	#10597354	1	1	yes	characteristic
66	C₂	#10597355	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₁₉×#97	C₂
socle, prime radical	C₂²×C₁₉	C₂×D₄
hypercenter	#97	D₁₉
hypocenter	C₁₉	#501
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
22. C₈×C₁₉	Q₈	semidirect
39. C₁₉	#501	semidirect
56. C₈	Dic₃₈	semidirect

Maximal subgroups

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

subgroup	index
#10597316	2
#10597315	2
C₁₉×#97	2
#10597275	2
#10597274	2
#501	19