Subgroups — C₈×C₁₆×C₁₀₉ #28358564

Order 13952.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₆×C₁₀₉	C₂	1	2	yes	maximal
2	C₈²×C₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₀₉	C₄	1	4	yes	—
4	C₄×C₈×C₁₀₉	C₄	1	2	yes	—
5	C₄×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₀₉	C₈	1	4	yes	—
7	C₂×C₈×C₁₀₉	C₂×C₄	1	2	yes	—
8	C₄²×C₁₀₉	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₁₀₉	C₈	1	8	yes	direct product factor
10	C₂×C₄×C₁₀₉	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₁₀₉	C₂×C₈	1	2	yes	—
12	C₈×C₁₀₉	C₁₆	1	8	yes	direct product factor
13	C₈×C₁₀₉	C₂×C₈	1	4	yes	—
14	C₂²×C₁₀₉	C₄×C₈	1	1	yes	characteristic
15	C₄×C₁₀₉	C₄×C₈	1	2	yes	—
16	C₄×C₁₀₉	C₂×C₁₆	1	4	yes	—
17	C₂×C₁₀₉	C₈²	1	1	yes	characteristic
18	C₂×C₁₀₉	C₄×C₁₆	1	2	yes	—
19	C₈×C₁₆	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₁₀₉	C₈×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
21	C₄×C₁₆	C₂×C₁₀₉	1	2	yes	—
22	C₈²	C₂×C₁₀₉	1	1	yes	characteristic
23	C₂×C₁₆	C₄×C₁₀₉	1	4	yes	—
24	C₄×C₈	C₄×C₁₀₉	1	2	yes	—
25	C₄×C₈	C₂²×C₁₀₉	1	1	yes	characteristic
26	C₂×C₈	C₈×C₁₀₉	1	4	yes	—
27	C₂×C₈	C₂×C₄×C₁₀₉	1	2	yes	—
28	C₄²	C₂×C₄×C₁₀₉	1	1	yes	characteristic
29	C₁₆	C₈×C₁₀₉	1	8	yes	direct product factor
30	C₂×C₄	C₄²×C₁₀₉	1	1	yes	characteristic
31	C₂×C₄	C₂×C₈×C₁₀₉	1	2	yes	—
32	C₈	C₁₆×C₁₀₉	1	8	yes	direct product factor
33	C₈	C₂×C₈×C₁₀₉	1	4	yes	—
34	C₂²	C₄×C₈×C₁₀₉	1	1	yes	characteristic
35	C₄	C₄×C₈×C₁₀₉	1	2	yes	—
36	C₄	C₂×C₁₆×C₁₀₉	1	4	yes	—
37	C₂	C₈²×C₁₀₉	1	1	yes	characteristic
38	C₂	C₄×C₁₆×C₁₀₉	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈	C₂²×C₁₀₉
socle, prime radical	C₂²×C₁₀₉	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₁₆×C₁₀₉	C₈	direct (N × H)
12. C₈×C₁₀₉	C₁₆	direct (N × H)
19. C₈×C₁₆	C₁₀₉	direct (N × H)
20. C₁₀₉	C₈×C₁₆	direct (N × H)
29. C₁₆	C₈×C₁₀₉	direct (N × H)
32. C₈	C₁₆×C₁₀₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₆×C₁₀₉	2
C₈²×C₁₀₉	2
C₈×C₁₆	109

Subgroups — C8×C16×C109 #28358564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₁₆×C₁₀₉ #28358564