Subgroups — C₂×#63143 #10587249

Order 528.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×Dic₁₁	C₂	1	1	yes	maximal, characteristic
4	#63143	C₂	1	4	yes	maximal, direct product factor
5	C₂×Dic₂₂	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₁₁	C₂²	1	1	yes	characteristic
7	Dic₃₃	C₂²	1	2	yes	—
8	C₃×Dic₁₁	C₂²	1	2	yes	—
9	C₁₁×Dic₃	C₂²	1	2	yes	—
10	C₂×C₄×C₁₁	—	3	1	no	—
11	C₂×Dic₁₁	—	3	1	no	—
12	C₂×Dic₁₁	D₃	1	1	yes	characteristic
13	Dic₂₂	—	3	4	no	—
14	C₂×C₃×C₁₁	Q₈	1	2	yes	complemented
15	C₂×C₃×C₁₁	C₂³	1	1	yes	characteristic
16	C₂×Dic₆	—	11	1	no	maximal, Hall
17	C₂²×C₁₁	C₂×D₃	1	1	yes	characteristic
18	C₄×C₁₁	—	3	2	no	—
19	Dic₁₁	—	3	2	no	—
20	Dic₁₁	C₂×D₃	1	2	yes	—
21	C₃×C₁₁	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₄	—	11	1	no	—
23	C₂×Dic₃	—	11	1	no	—
24	C₂×Dic₃	D₁₁	1	1	yes	characteristic
25	Dic₆	—	11	4	no	—
26	C₂×C₁₁	Dic₆	1	2	yes	complemented
27	C₂×C₁₁	C₂²×D₃	1	1	yes	characteristic
28	C₂×Q₈	—	33	1	no	Sylow
29	C₂²×C₃	C₂×D₁₁	1	1	yes	characteristic
30	C₃×C₄	—	11	2	no	—
31	Dic₃	—	11	2	no	—
32	Dic₃	C₂×D₁₁	1	2	yes	—
33	C₁₁	C₂×Dic₆	1	1	yes	characteristic, complemented, Sylow
34	Q₈	—	33	4	no	—
35	C₂×C₄	—	3	1	no	—
36	C₂×C₄	—	11	1	no	—
37	C₂×C₄	—	33	1	no	—
38	C₂×C₃	Dic₂₂	1	2	yes	complemented
39	C₂×C₃	C₂²×D₁₁	1	1	yes	characteristic
40	C₂²	D₃×D₁₁	1	1	yes	characteristic
41	C₄	—	3	2	no	—
42	C₄	—	11	2	no	—
43	C₄	—	33	2	no	—
44	C₃	C₂×Dic₂₂	1	1	yes	characteristic, complemented, Sylow
45	C₂	#63143	1	2	yes	direct product factor
46	C₂	C₂×D₃×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×D₁₁
commutator, cosocle	C₂×C₃×C₁₁	C₂³
Frattini	C₂	C₂×D₃×D₁₁
Fitting, socle, prime radical	C₂²×C₃×C₁₁	C₂²
hypocenter	C₃×C₁₁	C₂×Q₈
LCS	G ▷ C₂×C₃×C₁₁ ▷ C₃×C₁₁
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
4. #63143	C₂	direct (N × H)
14. C₂×C₃×C₁₁	Q₈	semidirect
21. C₃×C₁₁	C₂×Q₈	semidirect
26. C₂×C₁₁	Dic₆	semidirect
33. C₁₁	C₂×Dic₆	semidirect
38. C₂×C₃	Dic₂₂	semidirect
44. C₃	C₂×Dic₂₂	semidirect
45. C₂	#63143	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₃₃	2
C₂×C₁₁×Dic₃	2
C₂×C₃×Dic₁₁	2
#63143	2
C₂×Dic₂₂	3
C₂×Dic₆	11

Subgroups — C2×#63143 #10587249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#63143 #10587249