Subgroups — C₂×D₇×C₆₇⋊C₉ #30683072

Order 16884.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃	D₇×C₆₇⋊C₃
commutator, hypocenter	C₇×C₆₇	C₂²×C₉
Frattini	C₃	C₂×D₇×C₆₇⋊C₃
Fitting, socle	C₂×C₃×C₇×C₆₇	C₂×C₃
prime radical	C₂×C₃×D₇×C₆₇	C₃
cosocle	C₃×C₇×C₆₇	C₂²×C₃
LCS	G ▷ C₇×C₆₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. D₇×C₆₇⋊C₉	C₂	direct (N × H)
2. C₂×C₇×C₆₇⋊C₉	C₂	semidirect
4. C₇×C₆₇⋊C₉	C₂²	semidirect
8. C₂×D₇×C₆₇	C₉	semidirect
11. C₂×C₆₇⋊C₉	D₇	direct (N × H)
12. C₂×C₇×C₆₇	C₂×C₉	semidirect
13. D₇×C₆₇	C₂×C₉	semidirect
15. C₆₇⋊C₉	C₂×D₇	direct (N × H)
16. C₇×C₆₇	C₂²×C₉	semidirect
23. C₂×C₆₇	C₉×D₇	semidirect
27. C₆₇	C₂×C₉×D₇	semidirect
32. C₂×D₇	C₆₇⋊C₉	direct (N × H)
36. C₂×C₇	C₂×C₆₇⋊C₉	semidirect
37. D₇	C₂×C₆₇⋊C₉	direct (N × H)
40. C₇	C₂²×C₆₇⋊C₉	semidirect
46. C₂	D₇×C₆₇⋊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
D₇×C₆₇⋊C₉	2
C₂×C₇×C₆₇⋊C₉	2
C₂×C₃×D₇×C₆₇	3
C₂²×C₆₇⋊C₉	7
C₂×C₉×D₇	67

Subgroups — C2×D7×C67⋊C9 #30683072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₇×C₆₇⋊C₉ #30683072