Subgroups — #14269001

Order 1824.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₅₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#10597264	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₉	—	2	1	no	—
6	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×Dic₅₇	—	2	1	no	—
8	C₃⋊(C₁₉⋊C₈)	C₄	1	2	yes	complemented
9	C₄⋊C₄×C₁₉	D₃	1	1	yes	characteristic
10	C₄⋊Dic₁₉	—	3	1	no	—
11	C₂×C₁₉⋊C₈	—	3	1	no	—
12	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
13	C₃×C₄×C₁₉	—	4	1	no	—
14	C₃×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄×C₁₉	Q₈	1	1	yes	characteristic
16	Dic₅₇	—	4	1	no	—
17	C₂×C₄×C₁₉	—	2	1	no	—
18	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
19	C₂×Dic₁₉	—	6	1	no	—
20	C₁₉⋊C₈	—	3	2	no	—
21	C₂×C₃×C₁₉	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₃×C₁₉	D₈	1	1	yes	characteristic
23	C₂×C₃×C₁₉	Q₁₆	1	1	yes	characteristic
24	#807	—	19	1	no	maximal, Hall
25	C₂²×C₁₉	#67	1	1	yes	characteristic
26	C₄×C₁₉	—	4	1	no	—
27	C₄×C₁₉	Dic₆	1	1	yes	characteristic
28	C₄×C₁₉	C₄×D₃	1	1	yes	characteristic
29	Dic₁₉	—	12	1	no	—
30	C₃×C₁₉	#107	1	1	yes	characteristic, complemented, Hall
31	C₃×C₄⋊C₄	D₁₉	1	1	yes	characteristic
32	C₄⋊Dic₃	—	19	1	no	—
33	C₂×C₃⋊C₈	—	19	1	no	—
34	C₂×C₁₉	Dic₃⋊C₄	1	1	yes	characteristic
35	C₂×C₁₉	#213	1	1	yes	characteristic
36	C₂×C₁₉	#216	1	1	yes	characteristic
37	#107	—	57	1	no	Sylow
38	C₂×C₃×C₄	—	2	1	no	—
39	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
40	C₂×Dic₃	—	38	1	no	—
41	C₃⋊C₈	—	19	2	no	—
42	C₁₉	#807	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₈	—	57	1	no	—
44	C₄⋊C₄	—	57	1	no	—
45	C₄⋊C₄	D₅₇	1	1	yes	characteristic
46	C₂²×C₃	C₂²⋊D₁₉	1	1	yes	characteristic
47	C₃×C₄	—	4	1	no	—
48	C₃×C₄	Dic₃₈	1	1	yes	characteristic
49	C₃×C₄	C₄×D₁₉	1	1	yes	characteristic
50	Dic₃	—	76	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	114	1	no	—
53	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
54	C₈	—	57	2	no	—
55	C₂×C₃	Dic₁₉⋊C₄	1	1	yes	characteristic
56	C₂×C₃	#64525	1	1	yes	characteristic
57	C₂×C₃	#64528	1	1	yes	characteristic
58	C₂²	#90718	1	1	yes	characteristic
59	C₄	—	4	1	no	—
60	C₄	—	228	1	no	—
61	C₄	Dic₁₁₄	1	1	yes	characteristic
62	C₄	C₄×D₅₇	1	1	yes	characteristic
63	C₃	#10597264	1	1	yes	characteristic, complemented, Sylow
64	C₂	#11744887	1	1	yes	characteristic
65	C₂	#11744890	1	1	yes	characteristic
66	C₂	#11744893	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#90718
commutator	C₃×C₄×C₁₉	C₂×C₄
Frattini	C₂×C₄	C₂×D₅₇
Fitting	C₃×C₄⋊C₄×C₁₉	C₂
socle, prime radical	C₂²×C₃×C₁₉	D₄
cosocle	C₂×C₃×C₄×C₁₉	C₂²
hypercenter	C₄⋊C₄	D₅₇
hypocenter	C₃×C₁₉	#107
LCS	G ▷ C₃×C₄×C₁₉ ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
8. C₃⋊(C₁₉⋊C₈)	C₄	semidirect
30. C₃×C₁₉	#107	semidirect
42. C₁₉	#807	semidirect
63. C₃	#10597264	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄⋊C₄×C₁₉	2
C₄⋊Dic₅₇	2
C₂×C₃⋊(C₁₉⋊C₈)	2
#10597264	3
#807	19