Subgroups — #11744985

Order 912.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#90718	C₂	1	2	yes	maximal, complemented
3	D₂₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₅₇	C₂	1	2	yes	maximal, complemented
5	Dic₁₁₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#64541	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×D₅₇	C₂²	1	2	yes	—
9	C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	Dic₅₇	C₂²	1	2	yes	—
12	C₂×C₄×C₁₉	D₃	1	1	yes	characteristic, complemented
13	C₂²⋊D₁₉	—	3	2	no	—
14	D₇₆	—	3	1	no	—
15	C₄×D₁₉	—	3	2	no	—
16	Dic₃₈	—	3	1	no	—
17	C₂×C₃×C₁₉	—	2	1	no	—
18	C₂×C₃×C₁₉	C₂³	1	1	yes	characteristic
19	D₅₇	—	2	2	no	—
20	C₂²×C₁₉	C₂×D₃	1	1	yes	characteristic
21	C₂×D₁₉	—	3	2	no	—
22	C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
23	C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
24	Dic₁₉	—	3	2	no	—
25	C₃×C₁₉	#41	1	1	yes	characteristic, complemented, Hall
26	#235	—	19	1	no	maximal, Hall
27	C₂×C₁₉	—	2	1	no	—
28	C₂×C₁₉	C₂²×D₃	1	1	yes	characteristic
29	D₁₉	—	6	2	no	—
30	C₂×C₃×C₄	D₁₉	1	1	yes	characteristic, complemented
31	#67	—	19	2	no	—
32	D₁₂	—	19	1	no	—
33	C₄×D₃	—	19	2	no	—
34	Dic₆	—	19	1	no	—
35	C₁₉	#235	1	1	yes	characteristic, complemented, Sylow
36	#41	—	57	1	no	Sylow
37	C₂²×C₃	C₂×D₁₉	1	1	yes	characteristic
38	C₂×D₃	—	19	2	no	—
39	C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
40	C₃×C₄	C₂×D₁₉	1	1	yes	characteristic
41	Dic₃	—	19	2	no	—
42	Q₈	—	57	1	no	—
43	D₄	—	57	2	no	—
44	D₄	—	57	1	no	—
45	C₂×C₄	—	57	2	no	—
46	C₂×C₄	D₅₇	1	1	yes	characteristic, complemented
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	C₂²×D₁₉	1	1	yes	characteristic
49	D₃	—	38	2	no	—
50	C₂²	—	57	2	no	—
51	C₂²	C₂×D₅₇	1	1	yes	characteristic
52	C₄	—	57	2	no	—
53	C₄	C₂×D₅₇	1	1	yes	characteristic
54	C₄	C₂×D₅₇	1	1	yes	characteristic
55	C₃	#64541	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	2	1	no	—
57	C₂	—	114	2	no	—
58	C₂	C₂²×D₅₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₅₇
commutator, socle, cosocle	C₂×C₃×C₁₉	C₂³
Frattini	C₂	C₂²×D₅₇
Fitting	C₂×C₃×C₄×C₁₉	C₂
hypercenter	C₂×C₄	D₅₇
hypocenter	C₃×C₁₉	#41
LCS	G ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₁₉	C₂	semidirect
2. #90718	C₂	semidirect
3. D₂₂₈	C₂	semidirect
4. C₄×D₅₇	C₂	semidirect
5. Dic₁₁₄	C₂	semidirect
12. C₂×C₄×C₁₉	D₃	semidirect
25. C₃×C₁₉	#41	semidirect
30. C₂×C₃×C₄	D₁₉	semidirect
35. C₁₉	#235	semidirect
46. C₂×C₄	D₅₇	semidirect
55. C₃	#64541	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₁₉	2
#90718	2
D₂₂₈	2
C₄×D₅₇	2
Dic₁₁₄	2
#64541	3
#235	19