Subgroups — #11926352

Order 1216.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10597350	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#10597276	C₂	1	1	yes	maximal, characteristic, complemented
4	#64541	—	2	1	no	—
5	C₂×C₈×C₁₉	C₂²	1	1	yes	characteristic
6	#64520	—	2	1	no	—
7	Dic₇₆	C₄	1	1	yes	characteristic
8	D₁₅₂	C₄	1	1	yes	characteristic
9	#64516	—	2	1	no	—
10	C₁₆×C₁₉	—	2	1	no	—
11	C₂×C₄×C₁₉	D₄	1	1	yes	characteristic
12	C₂²⋊D₁₉	—	4	1	no	—
13	D₇₆	—	2	1	no	—
14	C₄×D₁₉	—	4	1	no	—
15	Dic₃₈	—	2	1	no	—
16	C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₁₉⋊C₈	—	4	1	no	—
19	C₂²×C₁₉	SD₁₆	1	1	yes	characteristic
20	C₂×D₁₉	—	4	1	no	—
21	C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₁₉	D₈	1	1	yes	characteristic
23	Dic₁₉	—	4	1	no	—
24	#359	—	19	1	no	maximal, Sylow
25	C₂×C₁₉	—	2	1	no	—
26	C₂×C₁₉	#102	1	1	yes	characteristic
27	D₁₉	—	8	1	no	—
28	#135	—	19	1	no	—
29	C₂×C₁₆	D₁₉	1	1	yes	characteristic, complemented
30	#108	—	19	1	no	—
31	C₁₉	#359	1	1	yes	characteristic, complemented, Sylow
32	#41	—	38	1	no	—
33	Q₁₆	—	19	1	no	—
34	SD₁₆	—	38	1	no	—
35	D₈	—	19	1	no	—
36	M₁₆	—	38	1	no	—
37	C₂×C₈	C₂×D₁₉	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	Q₈	—	38	1	no	—
40	D₄	—	38	1	no	—
41	D₄	—	76	1	no	—
42	C₂×C₄	—	76	1	no	—
43	C₂×C₄	D₇₆	1	1	yes	characteristic
44	C₈	—	76	1	no	—
45	C₈	C₄×D₁₉	1	1	yes	characteristic
46	C₈	C₂²⋊D₁₉	1	1	yes	characteristic
47	C₂²	—	76	1	no	—
48	C₂²	#64516	1	1	yes	characteristic
49	C₄	—	76	1	no	—
50	C₄	D₁₅₂	1	1	yes	characteristic
51	C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	152	1	no	—
54	C₂	#10597278	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₅₂
commutator	C₈×C₁₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₉
Fitting	C₂×C₁₆×C₁₉	C₂
socle	C₂×C₁₉	#102
prime radical	#10597350	C₂
cosocle	C₂×C₈×C₁₉	C₂²
hypercenter	C₂×C₁₆	D₁₉
hypocenter	C₁₉	#359
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₆×C₁₉	C₂	semidirect
3. #10597276	C₂	semidirect
29. C₂×C₁₆	D₁₉	semidirect
31. C₁₉	#359	semidirect

Maximal subgroups

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

subgroup	index
#10597350	2
C₂×C₁₆×C₁₉	2
#10597276	2
#359	19