Subgroups — C₄³×D₁₀₉ #28365353

Order 13952.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₁₀₉	C₂	1	7	yes	maximal
2	C₄²×Dic₁₀₉	C₂	1	7	yes	maximal, complemented
3	C₄³×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₁₀₉	C₂²	1	7	yes	—
5	C₂×C₄×Dic₁₀₉	C₂²	1	21	yes	—
6	C₄²×D₁₀₉	C₄	1	56	yes	direct product factor
7	C₂×C₄²×C₁₀₉	C₂²	1	7	yes	—
8	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
9	C₂²×Dic₁₀₉	C₂³	1	7	yes	—
10	C₂×C₄×D₁₀₉	C₂×C₄	1	84	yes	—
11	C₄×Dic₁₀₉	C₂×C₄	1	84	yes	complemented
12	C₂²×C₄×C₁₀₉	C₂³	1	7	yes	—
13	C₄²×C₁₀₉	C₂×C₄	1	28	yes	complemented
14	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
15	C₂²×D₁₀₉	C₂²×C₄	1	14	yes	—
16	C₂×C₄×C₁₀₉	C₂²×C₄	1	42	yes	—
17	C₂×Dic₁₀₉	C₂²×C₄	1	42	yes	—
18	C₄×D₁₀₉	C₄²	1	112	yes	direct product factor
19	C₂²×C₁₀₉	C₂³×C₄	1	7	yes	—
20	C₂×D₁₀₉	C₂×C₄²	1	28	yes	—
21	C₄×C₁₀₉	C₂×C₄²	1	28	yes	complemented
22	Dic₁₀₉	C₂×C₄²	1	28	yes	complemented
23	C₂×C₁₀₉	C₂²×C₄²	1	7	yes	—
24	D₁₀₉	C₄³	1	8	yes	direct product factor
25	C₂×C₄³	—	109	1	no	maximal, Sylow
26	C₁₀₉	C₂×C₄³	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₄²	—	109	7	no	—
28	C₄³	—	109	7	no	—
29	C₄³	D₁₀₉	1	1	yes	characteristic, direct product factor
30	C₂³×C₄	—	109	7	no	—
31	C₂×C₄²	—	109	21	no	—
32	C₂×C₄²	—	109	56	no	—
33	C₂×C₄²	C₂×D₁₀₉	1	7	yes	—
34	C₂⁴	—	109	1	no	—
35	C₂²×C₄	—	109	7	no	—
36	C₂²×C₄	—	109	84	no	—
37	C₂²×C₄	C₂²×D₁₀₉	1	7	yes	—
38	C₄²	—	109	84	no	—
39	C₄²	C₄×D₁₀₉	1	28	yes	direct product factor
40	C₂³	—	109	14	no	—
41	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
42	C₂×C₄	—	109	42	no	—
43	C₂×C₄	—	109	112	no	—
44	C₂×C₄	C₂×C₄×D₁₀₉	1	42	yes	—
45	C₂²	—	109	28	no	—
46	C₂²	C₂²×C₄×D₁₀₉	1	7	yes	—
47	C₄	—	109	28	no	—
48	C₄	C₄²×D₁₀₉	1	28	yes	direct product factor
49	C₂	—	109	8	no	—
50	C₂	C₂×C₄²×D₁₀₉	1	7	yes	—

	subgroup	G/H
center, hypercenter	C₄³	D₁₀₉
commutator, hypocenter	C₁₀₉	C₂×C₄³
Frattini	C₂³	C₂³×D₁₀₉
Fitting	C₄³×C₁₀₉	C₂
socle, cosocle	C₂³×C₁₀₉	C₂⁴
prime radical	C₂³×D₁₀₉	C₂³
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. C₄²×Dic₁₀₉	C₂	semidirect
3. C₄³×C₁₀₉	C₂	semidirect
6. C₄²×D₁₀₉	C₄	direct (N × H)
11. C₄×Dic₁₀₉	C₂×C₄	semidirect
13. C₄²×C₁₀₉	C₂×C₄	semidirect
18. C₄×D₁₀₉	C₄²	direct (N × H)
21. C₄×C₁₀₉	C₂×C₄²	semidirect
22. Dic₁₀₉	C₂×C₄²	semidirect
24. D₁₀₉	C₄³	direct (N × H)
26. C₁₀₉	C₂×C₄³	semidirect
29. C₄³	D₁₀₉	direct (N × H)
39. C₄²	C₄×D₁₀₉	direct (N × H)
48. C₄	C₄²×D₁₀₉	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×C₄²×D₁₀₉	2
C₄²×Dic₁₀₉	2
C₄³×C₁₀₉	2
C₂×C₄³	109

Subgroups — C43×D109 #28365353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×D₁₀₉ #28365353