Subgroups — C₂×C₁₁⋊((C₁₃⋊C₃)⋊D₇) #26046530

Order 12012.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊((C₁₃⋊C₃)⋊D₇)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₁₁×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₀₀₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×C₁₁×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₀₀₁	C₂×C₃	1	2	yes	complemented
6	C₂×C₇×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₁₁⋊(D₁₃⋊C₃)	—	7	1	no	maximal, Hall
8	C₂×(C₁₃⋊C₃)⋊D₇	—	11	1	no	maximal, Hall
9	C₇×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×D₇₇	—	13	1	no	maximal, Hall
11	C₂×C₁₁×C₁₃⋊C₃	D₇	1	1	yes	characteristic, complemented
12	C₁₁⋊(D₁₃⋊C₃)	—	7	2	no	—
13	C₂×D₁₄₃	—	7	1	no	Hall
14	C₂×C₇×C₁₃⋊C₃	D₁₁	1	1	yes	characteristic, complemented
15	(C₁₃⋊C₃)⋊D₇	—	11	2	no	—
16	C₂×C₃×C₇×C₁₁	—	13	1	no	—
17	C₃×D₇₇	—	13	2	no	—
18	C₁₁×C₁₃⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
19	C₂×D₉₁	—	11	1	no	Hall
20	C₂×D₇₇	—	13	1	no	Hall
21	C₂×C₁₁×C₁₃	C₃×D₇	1	1	yes	characteristic, complemented
22	D₁₄₃	—	7	2	no	—
23	C₇×C₁₃⋊C₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₇×C₁₁	—	13	1	no	Hall
25	C₂×C₇×C₁₃	C₃×D₁₁	1	1	yes	characteristic, complemented
26	D₉₁	—	11	2	no	—
27	C₂×D₁₃⋊C₃	—	77	1	no	Hall
28	C₂×C₇×C₁₁	D₁₃⋊C₃	1	1	yes	characteristic, complemented
29	D₇₇	—	13	2	no	—
30	C₁₁×C₁₃	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃×D₁₁	—	91	1	no	Hall
32	C₇×C₁₃	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×D₇	—	143	1	no	Hall
34	C₂×C₁₃⋊C₃	D₇₇	1	1	yes	characteristic, complemented
35	D₁₃⋊C₃	—	77	2	no	—
36	C₇×C₁₁	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₁₁	—	13	1	no	—
38	C₃×D₁₁	—	91	2	no	—
39	C₂×D₁₃	—	77	1	no	Hall
40	C₂×D₁₁	—	91	1	no	Hall
41	C₂×C₃×C₇	—	13	1	no	—
42	C₃×D₇	—	143	2	no	—
43	C₁₃⋊C₃	C₂×D₇₇	1	1	yes	characteristic, complemented, Hall
44	C₃×C₁₁	—	13	1	no	Hall
45	C₂×D₇	—	143	1	no	Hall
46	C₂×C₁₃	C₃×D₇₇	1	1	yes	characteristic, complemented
47	D₁₃	—	77	2	no	—
48	C₂×C₁₁	(C₁₃⋊C₃)⋊D₇	1	1	yes	characteristic, complemented
49	D₁₁	—	91	2	no	—
50	C₃×C₇	—	13	1	no	Hall
51	C₂×C₇	C₁₁⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented
52	D₇	—	143	2	no	—
53	C₁₃	C₂×C₃×D₇₇	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₃	—	1001	1	no	Hall
55	C₁₁	C₂×(C₁₃⋊C₃)⋊D₇	1	1	yes	characteristic, complemented, Sylow
56	C₇	C₂×C₁₁⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	—	13	1	no	—
58	C₂×C₃	—	1001	2	no	—
59	C₂²	—	1001	1	no	Sylow
60	C₃	—	13	1	no	Sylow
61	C₂	—	1001	2	no	—
62	C₂	C₁₁⋊((C₁₃⋊C₃)⋊D₇)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₁⋊((C₁₃⋊C₃)⋊D₇)
commutator, cosocle, hypocenter	C₇×C₁₁×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₁×C₁₃	C₂×C₃
LCS	G ▷ C₇×C₁₁×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₁₁⋊((C₁₃⋊C₃)⋊D₇)	C₂	direct (N × H)
2. C₂×C₇×C₁₁×C₁₃⋊C₃	C₂	semidirect
3. C₂×D₁₀₀₁	C₃	semidirect
4. C₇×C₁₁×C₁₃⋊C₃	C₂²	semidirect
5. D₁₀₀₁	C₂×C₃	semidirect
6. C₂×C₇×C₁₁×C₁₃	C₂×C₃	semidirect
9. C₇×C₁₁×C₁₃	C₂²×C₃	semidirect
11. C₂×C₁₁×C₁₃⋊C₃	D₇	semidirect
14. C₂×C₇×C₁₃⋊C₃	D₁₁	semidirect
18. C₁₁×C₁₃⋊C₃	C₂×D₇	semidirect
21. C₂×C₁₁×C₁₃	C₃×D₇	semidirect
23. C₇×C₁₃⋊C₃	C₂×D₁₁	semidirect
25. C₂×C₇×C₁₃	C₃×D₁₁	semidirect
28. C₂×C₇×C₁₁	D₁₃⋊C₃	semidirect
30. C₁₁×C₁₃	C₂×C₃×D₇	semidirect
32. C₇×C₁₃	C₂×C₃×D₁₁	semidirect
34. C₂×C₁₃⋊C₃	D₇₇	semidirect
36. C₇×C₁₁	C₂×D₁₃⋊C₃	semidirect
43. C₁₃⋊C₃	C₂×D₇₇	semidirect
46. C₂×C₁₃	C₃×D₇₇	semidirect
48. C₂×C₁₁	(C₁₃⋊C₃)⋊D₇	semidirect
51. C₂×C₇	C₁₁⋊(D₁₃⋊C₃)	semidirect
53. C₁₃	C₂×C₃×D₇₇	semidirect
55. C₁₁	C₂×(C₁₃⋊C₃)⋊D₇	semidirect
56. C₇	C₂×C₁₁⋊(D₁₃⋊C₃)	semidirect
62. C₂	C₁₁⋊((C₁₃⋊C₃)⋊D₇)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁⋊((C₁₃⋊C₃)⋊D₇)	2
C₂×C₇×C₁₁×C₁₃⋊C₃	2
C₂×D₁₀₀₁	3
C₂×C₁₁⋊(D₁₃⋊C₃)	7
C₂×(C₁₃⋊C₃)⋊D₇	11
C₂×C₃×D₇₇	13

Subgroups — C2×C11⋊((C13⋊C3)⋊D7) #26046530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁⋊((C₁₃⋊C₃)⋊D₇) #26046530