Subgroups — #11926879

Order 1216.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	#10597370	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#10597267	C₂	1	2	yes	maximal, complemented
5	#10597264	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₁₉	—	2	1	no	—
7	C₂²×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₁₉	—	2	1	no	—
10	C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂²⋊Dic₁₉	—	2	1	no	—
12	C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	Dic₁₉⋊C₄	—	2	1	no	—
14	C₂×C₁₉⋊C₈	C₂²	1	2	yes	—
15	C₂³×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄×C₁₉	—	2	2	no	—
17	C₂×C₄×C₁₉	—	2	2	no	—
18	C₂×C₄×C₁₉	—	4	2	no	—
19	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₉	—	2	1	no	—
22	C₂×Dic₁₉	—	2	1	no	—
23	Dic₃₈	—	2	2	no	—
24	C₁₉⋊C₈	—	2	2	no	—
25	C₂²×C₁₉	—	2	1	no	—
26	C₂²×C₁₉	—	2	1	no	—
27	C₂²×C₁₉	Q₁₆	1	2	yes	—
28	C₂²×C₁₉	C₂×D₄	1	1	yes	characteristic
29	C₄×C₁₉	—	2	1	no	—
30	C₄×C₁₉	—	4	2	no	—
31	C₄×C₁₉	#41	1	2	yes	—
32	Dic₁₉	—	4	1	no	—
33	Dic₁₉	—	4	1	no	—
34	#484	—	19	1	no	maximal, Sylow
35	C₂×C₁₉	—	2	2	no	—
36	C₂×C₁₉	#123	1	1	yes	characteristic
37	C₂×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
38	C₂×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
39	C₂²⋊Q₈	—	19	1	no	—
40	C₂×C₄⋊C₄	D₁₉	1	1	yes	characteristic
41	#107	—	19	2	no	—
42	#103	—	19	2	no	—
43	C₂²⋊C₈	—	19	1	no	—
44	C₁₉	#484	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	19	1	no	—
46	C₂²×C₄	—	2	1	no	—
47	C₂²×C₄	C₂×D₁₉	1	1	yes	characteristic
48	C₂×C₈	—	19	2	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	—	19	1	no	—
51	C₄⋊C₄	—	38	1	no	—
52	C₄⋊C₄	C₂×D₁₉	1	2	yes	—
53	C₂²⋊C₄	—	38	1	no	—
54	C₂³	C₂²⋊D₁₉	1	1	yes	characteristic
55	Q₈	—	38	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	4	2	no	—
59	C₂×C₄	—	38	1	no	—
60	C₂×C₄	—	38	1	no	—
61	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₁₉	1	1	yes	characteristic
63	C₈	—	38	2	no	—
64	C₂²	—	2	1	no	—
65	C₂²	—	2	1	no	—
66	C₂²	#64528	1	2	yes	—
67	C₂²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	4	2	no	—
70	C₄	—	76	1	no	—
71	C₄	—	76	1	no	—
72	C₄	#64541	1	2	yes	—
73	C₂	—	2	2	no	—
74	C₂	#10597375	1	1	yes	characteristic
75	C₂	#10597378	1	1	yes	characteristic
76	C₂	C₂×#64528	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₉
Fitting	C₂×C₄⋊C₄×C₁₉	C₂
socle	C₂²×C₁₉	C₂×D₄
prime radical	C₂³×C₁₉	D₄
hypercenter	C₂×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#484
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #10597267	C₂	semidirect
5. #10597264	C₂	semidirect
44. C₁₉	#484	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×C₁₉	2
#10597370	2
C₂²⋊(C₁₉⋊C₈)	2
#10597267	2
#10597264	2
#484	19