Subgroups — C₁₆×#89137 #20295910

Order 6976.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×#89137	C₂	1	1	yes	maximal, characteristic
3	C₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic
4	D₁₀₉⋊C₈	C₄	1	1	yes	characteristic
5	C₄×#89137	C₄	1	1	yes	characteristic
6	#13182032	C₄	1	2	yes	complemented
7	C₈×D₁₀₉	C₂²	1	1	yes	characteristic
8	#13182004	C₄	1	1	yes	characteristic, complemented
9	C₁₆×C₁₀₉	C₄	1	1	yes	characteristic, complemented
10	C₂×#89137	C₈	1	2	yes	—
11	C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic
12	#11724786	C₈	1	2	yes	—
13	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
14	#11724784	C₂×C₄	1	1	yes	characteristic
15	C₂×D₁₀₉	C₂×C₈	1	1	yes	characteristic
16	#89137	C₁₆	1	4	yes	direct product factor
17	C₄×C₁₀₉	C₄²	1	1	yes	characteristic
18	Dic₁₀₉	C₂×C₈	1	1	yes	characteristic
19	C₂×C₁₀₉	C₄×C₈	1	1	yes	characteristic
20	D₁₀₉	C₂×C₁₆	1	2	yes	—
21	C₁₀₉	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₆	—	109	1	no	maximal, Sylow
23	C₂×C₁₆	—	109	1	no	—
24	C₂×C₁₆	—	109	1	no	—
25	C₄×C₈	—	109	1	no	—
26	C₂×C₈	—	109	1	no	—
27	C₂×C₈	—	109	1	no	—
28	C₄²	—	109	1	no	—
29	C₁₆	—	109	2	no	—
30	C₁₆	—	109	1	no	—
31	C₁₆	#89137	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	109	2	no	—
33	C₂×C₄	—	109	1	no	—
34	C₈	—	109	2	no	—
35	C₈	—	109	1	no	—
36	C₈	C₂×#89137	1	1	yes	characteristic
37	C₂²	—	109	1	no	—
38	C₄	—	109	4	no	—
39	C₄	—	109	1	no	—
40	C₄	C₄×#89137	1	1	yes	characteristic
41	C₂	—	109	2	no	—
42	C₂	C₈×#89137	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₆	#89137
commutator, hypocenter	C₁₀₉	C₄×C₁₆
Frattini	C₈	C₂×#89137
Fitting	C₁₆×C₁₀₉	C₄
socle	C₂×C₁₀₉	C₄×C₈
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
6. #13182032	C₄	semidirect
8. #13182004	C₄	semidirect
9. C₁₆×C₁₀₉	C₄	semidirect
16. #89137	C₁₆	direct (N × H)
21. C₁₀₉	C₄×C₁₆	semidirect
31. C₁₆	#89137	direct (N × H)

Subgroups — C16×#89137 #20295910

Conjugacy classes of subgroups

Complements

Subgroups — C₁₆×#89137 #20295910