Subgroups — #14561815

Order 2432.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₅₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#366	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₆	—	2	1	no	—
5	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
6	C₁₉×#107	—	2	1	no	—
7	Dic₁₅₂	—	2	1	no	—
8	Dic₁₅₂	C₄	1	2	yes	complemented
9	C₁₉⋊C₃₂	—	2	1	no	—
10	C₂×Dic₃₈	—	4	1	no	—
11	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
12	C₄⋊C₄×C₁₉	—	4	1	no	—
13	Dic₇₆	—	2	2	no	—
14	Dic₇₆	—	4	1	no	—
15	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₉	—	8	1	no	—
18	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
19	C₂×Dic₁₉	—	8	1	no	—
20	Dic₃₈	—	4	2	no	—
21	Dic₃₈	—	8	1	no	—
22	C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
24	#1416	—	19	1	no	maximal, Sylow
25	C₂²×C₁₉	D₁₆	1	1	yes	characteristic
26	C₄×C₁₉	—	16	1	no	—
27	C₄×C₁₉	#102	1	1	yes	characteristic
28	C₄×C₁₉	SD₃₂	1	1	yes	characteristic
29	Dic₁₉	—	8	2	no	—
30	C₂×Q₃₂	—	19	1	no	—
31	C₂×C₃₂	—	19	1	no	—
32	#366	D₁₉	1	1	yes	characteristic
33	C₂×C₁₉	#357	1	1	yes	characteristic
34	C₂×C₁₉	SD₆₄	1	1	yes	characteristic
35	C₂×C₁₉	Q₆₄	1	1	yes	characteristic
36	C₂×Q₁₆	—	38	1	no	—
37	Q₃₂	—	19	2	no	—
38	Q₃₂	—	38	1	no	—
39	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
40	#107	—	2	1	no	—
41	C₃₂	—	38	1	no	—
42	C₁₉	#1416	1	1	yes	characteristic, complemented, Sylow
43	C₂×Q₈	—	76	1	no	—
44	Q₁₆	—	38	2	no	—
45	Q₁₆	—	76	1	no	—
46	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
47	C₄⋊C₄	—	4	1	no	—
48	C₁₆	C₄×D₁₉	1	1	yes	characteristic
49	C₁₆	D₇₆	1	1	yes	characteristic
50	Q₈	—	76	2	no	—
51	Q₈	—	152	1	no	—
52	C₂×C₄	—	8	1	no	—
53	C₂×C₄	—	152	1	no	—
54	C₂×C₄	#64525	1	1	yes	characteristic
55	C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
56	C₈	#64527	1	1	yes	characteristic
57	C₂²	#10597283	1	1	yes	characteristic
58	C₄	—	16	1	no	—
59	C₄	—	152	2	no	—
60	C₄	#10597266	1	1	yes	characteristic
61	C₄	#10597285	1	1	yes	characteristic
62	C₂	#11926344	1	1	yes	characteristic
63	C₂	#11926382	1	1	yes	characteristic
64	C₂	#11926384	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10597283
commutator	C₁₆×C₁₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₉
Fitting	C₁₉×#366	C₂
socle, prime radical	C₂²×C₁₉	D₁₆
cosocle	C₂×C₁₆×C₁₉	C₂²
hypercenter	#366	D₁₉
hypocenter	C₁₉	#1416
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
8. Dic₁₅₂	C₄	semidirect
42. C₁₉	#1416	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₅₂	2
C₂×C₁₉⋊C₃₂	2
C₁₉×#366	2
#1416	19