Subgroups — D₄₁×C₃⋊(C₇⋊D₇) #37563156

Order 24108.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×C₃⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₇⋊D₂₈₇)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄₁×C₇⋊D₇	—	3	1	no	maximal, Hall
5	C₃×C₇²×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₂₈₇	—	3	1	no	—
7	C₄₁×C₇⋊D₇	—	3	1	no	—
8	C₇²×D₄₁	D₃	1	1	yes	characteristic, complemented
9	D₂₁×D₄₁	—	7	8	no	maximal
10	C₇²×C₄₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₈₆₁	—	7	8	no	—
12	C₄₁×D₂₁	—	7	8	no	—
13	C₃×C₇×D₄₁	D₇	1	8	yes	complemented
14	D₇×D₄₁	—	21	8	no	—
15	C₃×C₇×C₄₁	C₂×D₇	1	8	yes	complemented
16	C₂×C₃⋊(C₇⋊D₇)	—	41	1	no	maximal, Hall
17	D₂₈₇	—	21	8	no	—
18	C₇×D₄₁	D₂₁	1	8	yes	complemented
19	D₇×C₄₁	—	21	8	no	—
20	D₃×D₄₁	—	49	1	no	Hall
21	C₂×C₃×C₇²	—	41	1	no	—
22	C₃⋊(C₇⋊D₇)	—	41	1	no	—
23	C₃⋊(C₇⋊D₇)	D₄₁	1	1	yes	characteristic, direct product factor
24	C₇×C₄₁	C₂×D₂₁	1	8	yes	complemented
25	D₁₂₃	—	49	1	no	—
26	C₃×D₄₁	C₇⋊D₇	1	1	yes	characteristic, complemented
27	D₃×C₄₁	—	49	1	no	—
28	C₂×C₇⋊D₇	—	123	1	no	Hall
29	C₂×D₄₁	—	147	1	no	Hall
30	C₃×C₇²	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
31	C₃×C₄₁	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
32	C₂×C₇²	—	41	1	no	—
33	C₇⋊D₇	—	3	1	no	—
34	C₇⋊D₇	—	123	1	no	—
35	C₂×D₂₁	—	287	8	no	—
36	C₂×C₄₁	—	147	1	no	—
37	D₄₁	—	147	1	no	—
38	D₄₁	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor
39	C₇²	D₃×D₄₁	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃×C₇	—	41	8	no	—
41	D₂₁	—	7	8	no	—
42	D₂₁	—	287	8	no	—
43	C₄₁	C₂×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₇	—	861	8	no	—
45	C₃×C₇	D₇×D₄₁	1	8	yes	complemented
46	C₂×C₇	—	41	8	no	—
47	D₇	—	21	8	no	—
48	D₇	—	861	8	no	—
49	C₂×D₃	—	2009	1	no	Hall
50	C₇	D₂₁×D₄₁	1	8	yes	complemented
51	C₂×C₃	—	41	1	no	—
52	D₃	—	49	1	no	—
53	D₃	—	2009	1	no	—
54	C₂²	—	6027	1	no	Sylow
55	C₃	D₄₁×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	41	1	no	—
57	C₂	—	6027	1	no	—
58	C₂	—	147	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇²×C₄₁	C₂²
LCS	G ▷ C₃×C₇²×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇²×D₄₁	C₂	semidirect
2. C₄₁×C₃⋊(C₇⋊D₇)	C₂	semidirect
3. C₃⋊(C₇⋊D₂₈₇)	C₂	semidirect
5. C₃×C₇²×C₄₁	C₂²	semidirect
8. C₇²×D₄₁	D₃	semidirect
10. C₇²×C₄₁	C₂×D₃	semidirect
13. C₃×C₇×D₄₁	D₇	semidirect
15. C₃×C₇×C₄₁	C₂×D₇	semidirect
18. C₇×D₄₁	D₂₁	semidirect
23. C₃⋊(C₇⋊D₇)	D₄₁	direct (N × H)
24. C₇×C₄₁	C₂×D₂₁	semidirect
26. C₃×D₄₁	C₇⋊D₇	semidirect
30. C₃×C₇²	C₂×D₄₁	semidirect
31. C₃×C₄₁	C₂×C₇⋊D₇	semidirect
38. D₄₁	C₃⋊(C₇⋊D₇)	direct (N × H)
39. C₇²	D₃×D₄₁	semidirect
43. C₄₁	C₂×C₃⋊(C₇⋊D₇)	semidirect
45. C₃×C₇	D₇×D₄₁	semidirect
50. C₇	D₂₁×D₄₁	semidirect
55. C₃	D₄₁×C₇⋊D₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇²×D₄₁	2
C₄₁×C₃⋊(C₇⋊D₇)	2
C₃⋊(C₇⋊D₂₈₇)	2
D₄₁×C₇⋊D₇	3
D₂₁×D₄₁	7
C₂×C₃⋊(C₇⋊D₇)	41

Subgroups — D41×C3⋊(C7⋊D7) #37563156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₁×C₃⋊(C₇⋊D₇) #37563156