Subgroups — C₂×D₄₂₂₁ #30683095

Order 16884.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₂₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₉×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₄₀₇	—	3	1	no	maximal
4	C₇×C₉×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₄₀₇	—	3	2	no	—
6	C₂×C₃×C₇×C₆₇	D₃	1	1	yes	characteristic
7	C₂×D₆₀₃	—	7	1	no	maximal, Hall
8	C₂×D₄₆₉	—	9	1	no	Hall
9	C₃×C₇×C₆₇	C₂×D₃	1	1	yes	characteristic
10	C₂×C₉×C₆₇	D₇	1	1	yes	characteristic, complemented
11	D₆₀₃	—	7	2	no	—
12	C₂×C₇×C₆₇	D₉	1	1	yes	characteristic, complemented
13	D₄₆₉	—	9	2	no	—
14	C₂×D₂₀₁	—	21	1	no	—
15	C₉×C₆₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₆₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₆₇	D₂₁	1	1	yes	characteristic
18	D₂₀₁	—	21	2	no	—
19	C₂×D₆₇	—	63	1	no	Hall
20	C₂×D₆₃	—	67	1	no	maximal, Hall
21	C₃×C₆₇	C₂×D₂₁	1	1	yes	characteristic
22	C₂×C₆₇	D₆₃	1	1	yes	characteristic, complemented
23	D₆₇	—	63	2	no	—
24	C₂×C₇×C₉	D₆₇	1	1	yes	characteristic, complemented
25	D₆₃	—	67	2	no	—
26	C₂×D₂₁	—	201	1	no	—
27	C₆₇	C₂×D₆₃	1	1	yes	characteristic, complemented, Sylow
28	C₇×C₉	C₂×D₆₇	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇	D₂₀₁	1	1	yes	characteristic
30	D₂₁	—	201	2	no	—
31	C₂×D₉	—	469	1	no	Hall
32	C₂×D₇	—	603	1	no	Hall
33	C₃×C₇	C₂×D₂₀₁	1	1	yes	characteristic
34	C₂×C₉	D₄₆₉	1	1	yes	characteristic, complemented
35	D₉	—	469	2	no	—
36	C₂×C₇	D₆₀₃	1	1	yes	characteristic, complemented
37	D₇	—	603	2	no	—
38	C₂×D₃	—	1407	1	no	—
39	C₉	C₂×D₄₆₉	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×D₆₀₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₁₄₀₇	1	1	yes	characteristic
42	D₃	—	1407	2	no	—
43	C₂²	—	4221	1	no	Sylow
44	C₃	C₂×D₁₄₀₇	1	1	yes	characteristic
45	C₂	—	4221	2	no	—
46	C₂	D₄₂₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₄₂₂₁
commutator, cosocle, hypocenter	C₇×C₉×C₆₇	C₂²
Frattini	C₃	C₂×D₁₄₀₇
Fitting	C₂×C₇×C₉×C₆₇	C₂
socle	C₂×C₃×C₇×C₆₇	D₃
LCS	G ▷ C₇×C₉×C₆₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₄₂₂₁	C₂	direct (N × H)
2. C₂×C₇×C₉×C₆₇	C₂	semidirect
4. C₇×C₉×C₆₇	C₂²	semidirect
10. C₂×C₉×C₆₇	D₇	semidirect
12. C₂×C₇×C₆₇	D₉	semidirect
15. C₉×C₆₇	C₂×D₇	semidirect
16. C₇×C₆₇	C₂×D₉	semidirect
22. C₂×C₆₇	D₆₃	semidirect
24. C₂×C₇×C₉	D₆₇	semidirect
27. C₆₇	C₂×D₆₃	semidirect
28. C₇×C₉	C₂×D₆₇	semidirect
34. C₂×C₉	D₄₆₉	semidirect
36. C₂×C₇	D₆₀₃	semidirect
39. C₉	C₂×D₄₆₉	semidirect
40. C₇	C₂×D₆₀₃	semidirect
46. C₂	D₄₂₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
D₄₂₂₁	2
C₂×C₇×C₉×C₆₇	2
C₂×D₁₄₀₇	3
C₂×D₆₀₃	7
C₂×D₆₃	67

Subgroups — C2×D4221 #30683095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄₂₂₁ #30683095