Subgroups — C₂×C₁₁²×D₇⋊C₉ #44478939

Order 30492.

420 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁²×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁²×D₇⋊C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₁₁²×D₇	C₃	1	1	yes	maximal, characteristic
4	C₁₁²×C₇⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁²×D₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇×C₁₁²	C₂×C₃	1	1	yes	characteristic
7	C₂²×C₉×C₁₁²	—	7	1	no	maximal, Hall
8	C₂×C₁₁²×D₇	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₁×D₇⋊C₉	C₁₁	1	12	yes	maximal, direct product factor
10	C₃×C₇×C₁₁²	C₂²×C₃	1	1	yes	characteristic
11	C₂×C₉×C₁₁²	—	7	2	no	—
12	C₂×C₉×C₁₁²	—	7	1	no	—
13	C₂×C₇×C₁₁²	C₂×C₉	1	1	yes	characteristic, complemented
14	C₁₁²×D₇	C₂×C₉	1	2	yes	complemented
15	C₂²×C₃×C₁₁²	—	7	1	no	—
16	C₂×C₁₁×C₇⋊C₉	C₂×C₁₁	1	12	yes	complemented
17	C₁₁×D₇⋊C₉	C₂×C₁₁	1	24	yes	direct product factor
18	C₉×C₁₁²	—	7	1	no	Hall
19	C₂×C₃×C₁₁×D₇	C₃×C₁₁	1	12	yes	—
20	C₇×C₁₁²	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₁²	—	7	2	no	—
22	C₂×C₃×C₁₁²	AGL(1,𝔽₇)	1	1	yes	characteristic
23	C₁₁×C₇⋊C₉	C₂²×C₁₁	1	12	yes	complemented
24	C₂²×C₁₁²	—	7	1	no	Hall
25	C₂×C₃×C₇×C₁₁	C₂×C₃×C₁₁	1	12	yes	—
26	C₃×C₁₁×D₇	C₂×C₃×C₁₁	1	24	yes	—
27	C₂²×C₉×C₁₁	—	7	12	no	—
28	C₃×C₁₁²	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
29	C₂×C₁₁×D₇	C₉×C₁₁	1	12	yes	complemented
30	C₂×D₇⋊C₉	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₁₁²	—	7	2	no	—
32	C₂×C₁₁²	D₇⋊C₉	1	1	yes	characteristic, direct product factor
33	C₃×C₇×C₁₁	C₂²×C₃×C₁₁	1	12	yes	—
34	C₂×C₉×C₁₁	—	7	24	no	—
35	C₂×C₉×C₁₁	—	7	12	no	—
36	C₂×C₇×C₁₁	C₂×C₉×C₁₁	1	12	yes	complemented
37	C₁₁×D₇	C₂×C₉×C₁₁	1	24	yes	complemented
38	C₂²×C₃×C₁₁	—	7	12	no	—
39	C₂×C₇⋊C₉	C₂×C₁₁²	1	1	yes	characteristic, complemented
40	D₇⋊C₉	C₂×C₁₁²	1	2	yes	direct product factor
41	C₁₁²	C₂×D₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₉×C₁₁	—	7	12	no	—
43	C₂×C₃×D₇	C₃×C₁₁²	1	1	yes	characteristic
44	C₇×C₁₁	C₂²×C₉×C₁₁	1	12	yes	complemented
45	C₂×C₃×C₁₁	—	7	24	no	—
46	C₂×C₃×C₁₁	C₁₁×AGL(1,𝔽₇)	1	12	yes	—
47	C₇⋊C₉	C₂²×C₁₁²	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₁₁	—	7	12	no	—
49	C₂×C₃×C₇	C₂×C₃×C₁₁²	1	1	yes	characteristic
50	C₃×D₇	C₂×C₃×C₁₁²	1	2	yes	—
51	C₂²×C₉	—	7	1	no	Hall
52	C₃×C₁₁	C₂×C₁₁×AGL(1,𝔽₇)	1	12	yes	—
53	C₂×D₇	C₉×C₁₁²	1	1	yes	characteristic, complemented, Hall
54	C₂×C₁₁	—	7	24	no	—
55	C₂×C₁₁	C₁₁×D₇⋊C₉	1	12	yes	direct product factor
56	C₃×C₇	C₂²×C₃×C₁₁²	1	1	yes	characteristic
57	C₂×C₉	—	7	2	no	—
58	C₂×C₉	—	7	1	no	—
59	C₂×C₇	C₂×C₉×C₁₁²	1	1	yes	characteristic, complemented
60	D₇	C₂×C₉×C₁₁²	1	2	yes	complemented
61	C₂²×C₃	—	7	1	no	—
62	C₁₁	C₂×C₁₁×D₇⋊C₉	1	12	yes	direct product factor
63	C₉	—	7	1	no	Sylow
64	C₇	C₂²×C₉×C₁₁²	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	7	2	no	—
66	C₂×C₃	C₁₁²×AGL(1,𝔽₇)	1	1	yes	characteristic
67	C₂²	—	7	1	no	Sylow
68	C₃	C₂×C₁₁²×AGL(1,𝔽₇)	1	1	yes	characteristic
69	C₂	—	7	2	no	—
70	C₂	C₁₁²×D₇⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁²	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂²×C₉×C₁₁²
Frattini	C₃	C₂×C₁₁²×AGL(1,𝔽₇)
Fitting, socle	C₂×C₃×C₇×C₁₁²	C₂×C₃
prime radical	C₂×C₃×C₁₁²×D₇	C₃
cosocle	C₃×C₇	C₂²×C₃×C₁₁²
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₁₁²

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁²×C₇⋊C₉	C₂	semidirect
2. C₁₁²×D₇⋊C₉	C₂	direct (N × H)
4. C₁₁²×C₇⋊C₉	C₂²	semidirect
8. C₂×C₁₁²×D₇	C₉	semidirect
9. C₂×C₁₁×D₇⋊C₉	C₁₁	direct (N × H)
13. C₂×C₇×C₁₁²	C₂×C₉	semidirect
14. C₁₁²×D₇	C₂×C₉	semidirect
16. C₂×C₁₁×C₇⋊C₉	C₂×C₁₁	semidirect
17. C₁₁×D₇⋊C₉	C₂×C₁₁	direct (N × H)
20. C₇×C₁₁²	C₂²×C₉	semidirect
23. C₁₁×C₇⋊C₉	C₂²×C₁₁	semidirect
29. C₂×C₁₁×D₇	C₉×C₁₁	semidirect
30. C₂×D₇⋊C₉	C₁₁²	direct (N × H)
32. C₂×C₁₁²	D₇⋊C₉	direct (N × H)
36. C₂×C₇×C₁₁	C₂×C₉×C₁₁	semidirect
37. C₁₁×D₇	C₂×C₉×C₁₁	semidirect
39. C₂×C₇⋊C₉	C₂×C₁₁²	semidirect
40. D₇⋊C₉	C₂×C₁₁²	direct (N × H)
41. C₁₁²	C₂×D₇⋊C₉	direct (N × H)
44. C₇×C₁₁	C₂²×C₉×C₁₁	semidirect
47. C₇⋊C₉	C₂²×C₁₁²	semidirect
53. C₂×D₇	C₉×C₁₁²	semidirect
55. C₂×C₁₁	C₁₁×D₇⋊C₉	direct (N × H)
59. C₂×C₇	C₂×C₉×C₁₁²	semidirect
60. D₇	C₂×C₉×C₁₁²	semidirect
62. C₁₁	C₂×C₁₁×D₇⋊C₉	direct (N × H)
64. C₇	C₂²×C₉×C₁₁²	semidirect
70. C₂	C₁₁²×D₇⋊C₉	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×C₁₁²×C₇⋊C₉	2
C₁₁²×D₇⋊C₉	2
C₂×C₃×C₁₁²×D₇	3
C₂²×C₉×C₁₁²	7
C₂×C₁₁×D₇⋊C₉	11

Subgroups — C2×C112×D7⋊C9 #44478939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁²×D₇⋊C₉ #44478939