Subgroups — D₃₉⋊(C₁₁⋊D₁₁) #34038457

Order 18876.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊(C₁₁⋊D₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁²×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁⋊D₁₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×C₁₁⋊D₁₁	—	3	1	no	maximal, Hall
5	C₃×C₁₁²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₁⋊D₁₄₃	D₃	1	1	yes	characteristic, complemented
7	C₁₃×C₁₁⋊D₁₁	—	3	1	no	—
8	C₁₁²×D₁₃	—	3	1	no	—
9	D₃₃⋊D₁₃	—	11	12	no	maximal
10	C₁₁²×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×C₁₁⋊D₁₁	—	13	1	no	maximal, Hall
12	C₁₃×D₃₃	—	11	12	no	—
13	C₁₁×D₃₉	D₁₁	1	12	yes	complemented
14	C₃×D₁₄₃	—	11	12	no	—
15	C₃⋊(C₁₁⋊D₁₁)	D₁₃	1	1	yes	characteristic, complemented
16	D₃×C₁₁²	—	13	1	no	—
17	C₃×C₁₁⋊D₁₁	—	13	1	no	—
18	D₁₁×D₁₃	—	33	12	no	—
19	C₂×C₁₁⋊D₁₁	—	39	1	no	Hall
20	C₃×C₁₁×C₁₃	C₂×D₁₁	1	12	yes	complemented
21	C₃×C₁₁²	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
22	D₁₄₃	—	11	12	no	—
23	C₁₁×D₁₃	—	3	12	no	—
24	C₁₃×D₁₁	—	33	12	no	—
25	C₂×C₁₁²	—	39	1	no	—
26	C₁₁⋊D₁₁	—	3	1	no	—
27	C₁₁⋊D₁₁	—	13	1	no	—
28	D₃×D₁₃	—	121	1	no	Hall
29	C₁₁×C₁₃	D₃×D₁₁	1	12	yes	complemented
30	D₃×D₁₁	—	143	12	no	—
31	C₁₁²	D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
32	D₃₉	C₁₁⋊D₁₁	1	1	yes	characteristic, complemented
33	C₃×D₁₃	—	121	1	no	—
34	D₃×C₁₃	—	121	1	no	—
35	D₃₃	—	11	12	no	—
36	C₃×D₁₁	—	143	12	no	—
37	D₃×C₁₁	—	13	12	no	—
38	C₂×D₁₃	—	363	1	no	Hall
39	C₂×D₁₁	—	429	12	no	—
40	C₃×C₁₃	C₂×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
41	C₃×C₁₁	D₁₁×D₁₃	1	12	yes	complemented
42	C₂×C₁₃	—	363	1	no	—
43	D₁₃	—	3	1	no	—
44	D₁₃	—	121	1	no	—
45	C₂×C₁₁	—	39	12	no	—
46	D₁₁	—	33	12	no	—
47	D₁₁	—	143	12	no	—
48	C₁₃	D₃×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₃	—	1573	1	no	Hall
50	C₁₁	D₃₃⋊D₁₃	1	12	yes	complemented
51	C₂×C₃	—	1573	1	no	—
52	D₃	—	13	1	no	—
53	D₃	—	121	1	no	—
54	C₂²	—	4719	1	no	Sylow
55	C₃	D₁₃×C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	1573	1	no	—
57	C₂	—	39	1	no	—
58	C₂	—	363	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁²×C₁₃	C₂²
LCS	G ▷ C₃×C₁₁²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊(C₁₁⋊D₁₁)	C₂	semidirect
2. C₁₁²×D₃₉	C₂	semidirect
3. C₃×C₁₁⋊D₁₄₃	C₂	semidirect
5. C₃×C₁₁²×C₁₃	C₂²	semidirect
6. C₁₁⋊D₁₄₃	D₃	semidirect
10. C₁₁²×C₁₃	C₂×D₃	semidirect
13. C₁₁×D₃₉	D₁₁	semidirect
15. C₃⋊(C₁₁⋊D₁₁)	D₁₃	semidirect
20. C₃×C₁₁×C₁₃	C₂×D₁₁	semidirect
21. C₃×C₁₁²	C₂×D₁₃	semidirect
29. C₁₁×C₁₃	D₃×D₁₁	semidirect
31. C₁₁²	D₃×D₁₃	semidirect
32. D₃₉	C₁₁⋊D₁₁	semidirect
40. C₃×C₁₃	C₂×C₁₁⋊D₁₁	semidirect
41. C₃×C₁₁	D₁₁×D₁₃	semidirect
48. C₁₃	D₃×C₁₁⋊D₁₁	semidirect
50. C₁₁	D₃₃⋊D₁₃	semidirect
55. C₃	D₁₃×C₁₁⋊D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₃⋊(C₁₁⋊D₁₁)	2
C₁₁²×D₃₉	2
C₃×C₁₁⋊D₁₄₃	2
D₁₃×C₁₁⋊D₁₁	3
D₃₃⋊D₁₃	11
D₃×C₁₁⋊D₁₁	13

Subgroups — D39⋊(C11⋊D11) #34038457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₉⋊(C₁₁⋊D₁₁) #34038457