Subgroups — C₂×(C₇⋊C₉)⋊D₆₇ #30683067

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	2	yes	maximal, direct product factor
2	C₂×C₇⋊C₉×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₄₆₉	C₃	1	1	yes	maximal, characteristic
4	C₇⋊C₉×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₄₆₉	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇×C₆₇	C₂×C₃	1	1	yes	characteristic
7	C₂×C₉×D₆₇	—	7	1	no	maximal, Hall
8	C₂×D₄₆₉	C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₆₇	C₂²×C₃	1	1	yes	characteristic
10	C₂×C₉×C₆₇	—	7	1	no	—
11	C₉×D₆₇	—	7	2	no	—
12	C₂×C₇×C₆₇	C₂×C₉	1	1	yes	characteristic, complemented
13	D₄₆₉	C₂×C₉	1	2	yes	complemented
14	C₂×C₃×D₆₇	—	21	1	no	—
15	C₉×C₆₇	—	7	1	no	Hall
16	C₇×C₆₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₆₇	AGL(1,𝔽₇)	1	1	yes	characteristic
18	C₃×D₆₇	—	21	2	no	—
19	C₂×D₆₇	—	21	1	no	Hall
20	C₂×D₇⋊C₉	—	67	1	no	maximal, Hall
21	C₃×C₆₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
22	C₂×C₆₇	D₇⋊C₉	1	1	yes	characteristic, complemented
23	D₆₇	—	21	2	no	—
24	C₂×C₇⋊C₉	D₆₇	1	1	yes	characteristic, complemented
25	D₇⋊C₉	—	67	2	no	—
26	C₂×C₃×D₇	—	67	1	no	—
27	C₆₇	C₂×D₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
28	C₇⋊C₉	C₂×D₆₇	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇	C₃×D₆₇	1	1	yes	characteristic
30	C₃×D₇	—	67	2	no	—
31	C₂²×C₉	—	469	1	no	Hall
32	C₂×D₇	—	67	1	no	Hall
33	C₃×C₇	C₂×C₃×D₆₇	1	1	yes	characteristic
34	C₂×C₉	—	7	1	no	—
35	C₂×C₉	—	469	2	no	—
36	C₂×C₇	C₉×D₆₇	1	1	yes	characteristic, complemented
37	D₇	—	67	2	no	—
38	C₂²×C₃	—	1407	1	no	—
39	C₉	—	7	1	no	Sylow
40	C₇	C₂×C₉×D₆₇	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	1407	2	no	—
42	C₂×C₃	ΓL(1,𝔽₈)⋊D₆₇	1	1	yes	characteristic
43	C₂²	—	1407	1	no	Sylow
44	C₃	C₂×ΓL(1,𝔽₈)⋊D₆₇	1	1	yes	characteristic
45	C₂	—	1407	2	no	—
46	C₂	(C₇⋊C₉)⋊D₆₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	ΓL(1,𝔽₈)⋊D₆₇
commutator, hypocenter	C₇×C₆₇	C₂²×C₉
Frattini	C₃	C₂×ΓL(1,𝔽₈)⋊D₆₇
Fitting, socle	C₂×C₃×C₇×C₆₇	C₂×C₃
prime radical	C₂×C₃×D₄₆₉	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. (C₇⋊C₉)⋊D₆₇	C₂	direct (N × H)
2. C₂×C₇⋊C₉×C₆₇	C₂	semidirect
4. C₇⋊C₉×C₆₇	C₂²	semidirect
8. C₂×D₄₆₉	C₉	semidirect
12. C₂×C₇×C₆₇	C₂×C₉	semidirect
13. D₄₆₉	C₂×C₉	semidirect
16. C₇×C₆₇	C₂²×C₉	semidirect
22. C₂×C₆₇	D₇⋊C₉	semidirect
24. C₂×C₇⋊C₉	D₆₇	semidirect
27. C₆₇	C₂×D₇⋊C₉	semidirect
28. C₇⋊C₉	C₂×D₆₇	semidirect
36. C₂×C₇	C₉×D₆₇	semidirect
40. C₇	C₂×C₉×D₆₇	semidirect
46. C₂	(C₇⋊C₉)⋊D₆₇	direct (N × H)

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
C₂×C₇⋊C₉×C₆₇	2
C₂×C₃×D₄₆₉	3
C₂×C₉×D₆₇	7
C₂×D₇⋊C₉	67

Subgroups — C2×(C7⋊C9)⋊D67 #30683067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₇⋊C₉)⋊D₆₇ #30683067