Subgroups — D₇⋊C₉×D₆₇ #30683059

Order 16884.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₇⋊C₉)⋊D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×D₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇⋊C₉×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₇×D₆₇	C₃	1	1	yes	maximal, characteristic
5	C₇⋊C₉×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₄₆₉	C₂×C₃	1	1	yes	characteristic
7	C₃×D₇×C₆₇	C₂×C₃	1	1	yes	characteristic
8	C₃×C₇×D₆₇	C₂×C₃	1	1	yes	characteristic
9	C₂×C₉×D₆₇	—	7	1	no	maximal, Hall
10	D₇×D₆₇	C₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₆₇	C₂²×C₃	1	1	yes	characteristic
12	C₂×C₉×C₆₇	—	7	1	no	—
13	C₉×D₆₇	—	7	1	no	—
14	C₉×D₆₇	—	7	1	no	—
15	D₄₆₉	C₂×C₉	1	1	yes	characteristic, complemented
16	C₇×D₆₇	C₂×C₉	1	1	yes	characteristic, complemented
17	D₇×C₆₇	C₂×C₉	1	1	yes	characteristic, complemented
18	C₂×C₃×D₆₇	—	21	1	no	—
19	C₉×C₆₇	—	7	1	no	Hall
20	C₇×C₆₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₆₇	—	21	1	no	—
22	C₃×D₆₇	—	21	1	no	—
23	C₃×D₆₇	AGL(1,𝔽₇)	1	1	yes	characteristic
24	C₂×D₆₇	—	21	1	no	Hall
25	C₂×D₇⋊C₉	—	67	1	no	maximal, Hall
26	C₃×C₆₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
27	C₂×C₆₇	—	21	1	no	—
28	D₆₇	—	21	1	no	—
29	D₆₇	D₇⋊C₉	1	1	yes	characteristic, direct product factor
30	C₂×C₇⋊C₉	—	67	1	no	—
31	D₇⋊C₉	—	67	1	no	—
32	D₇⋊C₉	D₆₇	1	1	yes	characteristic, direct product factor
33	C₂×C₃×D₇	—	67	1	no	—
34	C₆₇	C₂×D₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
35	C₇⋊C₉	C₂×D₆₇	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₇	—	67	1	no	—
37	C₃×D₇	—	67	1	no	—
38	C₃×D₇	C₃×D₆₇	1	1	yes	characteristic
39	C₂²×C₉	—	469	1	no	Hall
40	C₂×D₇	—	67	1	no	Hall
41	C₃×C₇	C₂×C₃×D₆₇	1	1	yes	characteristic
42	C₂×C₉	—	7	1	no	—
43	C₂×C₉	—	469	1	no	—
44	C₂×C₉	—	469	1	no	—
45	C₂×C₇	—	67	1	no	—
46	D₇	—	67	1	no	—
47	D₇	C₉×D₆₇	1	1	yes	characteristic, complemented
48	C₂²×C₃	—	469	1	no	—
49	C₉	—	7	1	no	Sylow
50	C₇	C₂×C₉×D₆₇	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	7	1	no	—
52	C₂×C₃	—	67	1	no	—
53	C₂×C₃	—	1407	1	no	—
54	C₂²	—	469	1	no	Sylow
55	C₃	AGL(1,𝔽₇)×D₆₇	1	1	yes	characteristic
56	C₂	—	7	1	no	—
57	C₂	—	67	1	no	—
58	C₂	—	1407	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	AGL(1,𝔽₇)×D₆₇
commutator, hypocenter	C₇×C₆₇	C₂²×C₉
Fitting, socle, cosocle	C₃×C₇×C₆₇	C₂²×C₃
prime radical	C₃×D₇×D₆₇	C₃
LCS	G ▷ C₇×C₆₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. (C₇⋊C₉)⋊D₆₇	C₂	semidirect
2. C₆₇×D₇⋊C₉	C₂	semidirect
3. C₇⋊C₉×D₆₇	C₂	semidirect
5. C₇⋊C₉×C₆₇	C₂²	semidirect
10. D₇×D₆₇	C₉	semidirect
15. D₄₆₉	C₂×C₉	semidirect
16. C₇×D₆₇	C₂×C₉	semidirect
17. D₇×C₆₇	C₂×C₉	semidirect
20. C₇×C₆₇	C₂²×C₉	semidirect
29. D₆₇	D₇⋊C₉	direct (N × H)
32. D₇⋊C₉	D₆₇	direct (N × H)
34. C₆₇	C₂×D₇⋊C₉	semidirect
35. C₇⋊C₉	C₂×D₆₇	semidirect
47. D₇	C₉×D₆₇	semidirect
50. C₇	C₂×C₉×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
(C₇⋊C₉)⋊D₆₇	2
C₆₇×D₇⋊C₉	2
C₇⋊C₉×D₆₇	2
C₃×D₇×D₆₇	3
C₂×C₉×D₆₇	7
C₂×D₇⋊C₉	67

Subgroups — D7⋊C9×D67 #30683059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇⋊C₉×D₆₇ #30683059