Subgroups — #14269708

Order 1824.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₅₇	C₂	1	2	yes	maximal
3	#11744887	C₂	1	4	yes	maximal
4	#10597316	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₉	C₂²	1	2	yes	—
6	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×Dic₅₇	C₂²	1	4	yes	—
8	C₄²×C₁₉	D₃	1	1	yes	characteristic
9	C₄⋊Dic₁₉	—	3	2	no	—
10	Dic₁₉⋊C₄	—	3	4	no	—
11	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
12	C₃×C₄×C₁₉	—	2	2	no	—
13	C₃×C₄×C₁₉	Q₈	1	2	yes	—
14	Dic₅₇	—	2	4	no	—
15	C₂×C₄×C₁₉	C₂×D₃	1	2	yes	—
16	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
17	C₂×Dic₁₉	—	3	4	no	—
18	C₂×C₃×C₁₉	C₂×Q₈	1	1	yes	characteristic
19	C₂×C₃×C₁₉	#41	1	2	yes	—
20	#870	—	19	1	no	maximal, Hall
21	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
22	C₄×C₁₉	—	2	2	no	—
23	C₄×C₁₉	Dic₆	1	2	yes	—
24	Dic₁₉	—	6	4	no	—
25	C₃×C₁₉	#125	1	1	yes	characteristic, complemented, Hall
26	C₃×C₄²	D₁₉	1	1	yes	characteristic
27	C₄⋊Dic₃	—	19	2	no	—
28	Dic₃⋊C₄	—	19	4	no	—
29	C₂×C₁₉	C₂×Dic₆	1	1	yes	characteristic
30	C₂×C₁₉	#235	1	2	yes	—
31	#125	—	57	1	no	Sylow
32	C₂×C₃×C₄	C₂×D₁₉	1	2	yes	—
33	C₂×C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
34	C₂×Dic₃	—	19	4	no	—
35	C₁₉	#870	1	1	yes	characteristic, complemented, Sylow
36	C₄⋊C₄	—	57	4	no	—
37	C₄⋊C₄	—	57	2	no	—
38	C₄²	D₅₇	1	1	yes	characteristic
39	C₂²×C₃	C₂²×D₁₉	1	1	yes	characteristic
40	C₃×C₄	—	2	2	no	—
41	C₃×C₄	Dic₃₈	1	2	yes	—
42	Dic₃	—	38	4	no	—
43	C₂×C₄	—	57	4	no	—
44	C₂×C₄	C₂×D₅₇	1	2	yes	—
45	C₂×C₄	C₂×D₅₇	1	1	yes	characteristic
46	C₂×C₃	C₂×Dic₃₈	1	1	yes	characteristic
47	C₂×C₃	#64541	1	2	yes	—
48	C₂²	C₂²×D₅₇	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	114	4	no	—
51	C₄	Dic₁₁₄	1	2	yes	—
52	C₃	#10597316	1	1	yes	characteristic, complemented, Sylow
53	C₂	C₂×Dic₁₁₄	1	1	yes	characteristic
54	C₂	#11744985	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₅₇
commutator, socle, prime radical, cosocle	C₂²×C₃×C₁₉	C₂³
Fitting	C₃×C₄²×C₁₉	C₂
hypercenter	C₄²	D₅₇
hypocenter	C₃×C₁₉	#125
LCS	G ▷ C₂²×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
25. C₃×C₁₉	#125	semidirect
35. C₁₉	#870	semidirect
52. C₃	#10597316	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₁₉	2
C₄⋊Dic₅₇	2
#11744887	2
#10597316	3
#870	19