Subgroups — #11926292

Order 1216.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10597315	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₈	C₄	1	2	yes	—
5	C₂×C₈×C₁₉	—	2	1	no	—
6	C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₁₉	—	2	1	no	—
8	C₄⋊Dic₁₉	—	2	1	no	—
9	C₂×C₁₉⋊C₈	—	2	1	no	—
10	C₂×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
12	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
13	C₂×Dic₁₉	—	2	2	no	—
14	Dic₃₈	—	4	2	no	—
15	C₈×C₁₉	—	4	1	no	—
16	C₁₉⋊C₈	—	4	1	no	—
17	C₂²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
18	C₄×C₁₉	—	2	1	no	—
19	C₄×C₁₉	SD₁₆	1	1	yes	characteristic
20	C₄×C₁₉	SD₁₆	1	1	yes	characteristic
21	C₄×C₁₉	Q₁₆	1	1	yes	characteristic
22	C₄×C₁₉	Q₁₆	1	1	yes	characteristic
23	Dic₁₉	—	4	2	no	—
24	#333	—	19	1	no	maximal, Sylow
25	C₂×C₁₉	#100	1	1	yes	characteristic
26	C₂×C₁₉	#103	1	1	yes	characteristic
27	C₂×C₁₉	#103	1	1	yes	characteristic
28	C₄⋊Q₈	—	19	1	no	—
29	C₄⋊C₈	—	19	1	no	—
30	C₄⋊C₈	D₁₉	1	1	yes	characteristic
31	C₁₉	#333	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₈	—	19	2	no	—
33	C₂×C₈	—	2	1	no	—
34	C₂×C₈	—	38	1	no	—
35	C₄⋊C₄	—	38	1	no	—
36	C₄⋊C₄	—	38	1	no	—
37	C₄²	C₂×D₁₉	1	1	yes	characteristic
38	Q₈	—	76	2	no	—
39	C₂×C₄	—	38	2	no	—
40	C₂×C₄	C₄×D₁₉	1	1	yes	characteristic
41	C₂×C₄	D₇₆	1	1	yes	characteristic
42	C₂×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
43	C₈	—	4	1	no	—
44	C₈	—	76	1	no	—
45	C₂²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	76	2	no	—
48	C₄	#64516	1	1	yes	characteristic
49	C₄	Dic₇₆	1	1	yes	characteristic
50	C₄	#64526	1	1	yes	characteristic
51	C₄	#64528	1	1	yes	characteristic
52	C₂	#10597267	1	1	yes	characteristic
53	C₂	#10597273	1	1	yes	characteristic
54	C₂	#10597280	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₂×C₄
Frattini	C₄²	C₂×D₁₉
Fitting	C₁₉×C₄⋊C₈	C₂
socle, prime radical	C₂²×C₁₉	C₂²⋊C₄
cosocle	C₄²×C₁₉	C₂²
hypercenter	C₄⋊C₈	D₁₉
hypocenter	C₁₉	#333
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
31. C₁₉	#333	semidirect

Maximal subgroups

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

subgroup	index
#10597315	2
C₁₉×C₄⋊C₈	2
C₄⋊(C₁₉⋊C₈)	2
#333	19