Subgroups — #20294801

Order 6976.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182004	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11724784	C₄	1	1	yes	characteristic
5	C₄×Dic₁₀₉	C₄	1	1	yes	characteristic
6	#13182004	C₄	1	2	yes	complemented
7	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₀₉	C₄	1	2	yes	complemented
9	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₁₀₉	C₈	1	2	yes	—
11	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
13	#11724784	C₈	1	2	yes	—
14	C₂²×C₁₀₉	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₀₉	C₄²	1	1	yes	characteristic
16	C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
17	Dic₁₀₉	—	2	2	no	—
18	C₂×C₁₀₉	C₄×C₈	1	1	yes	characteristic
19	C₂×C₁₀₉	M₃₂	1	2	yes	—
20	C₁₀₉	#346	1	1	yes	characteristic, complemented, Sylow
21	#346	—	109	1	no	maximal, Sylow
22	C₂×C₁₆	—	109	1	no	—
23	C₂×C₁₆	D₁₀₉	1	1	yes	characteristic
24	C₄×C₈	—	109	1	no	—
25	C₂×C₈	—	109	1	no	—
26	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
27	C₄²	—	109	1	no	—
28	C₁₆	—	109	2	no	—
29	C₁₆	Dic₁₀₉	1	2	yes	complemented
30	C₂×C₄	—	109	2	no	—
31	C₂×C₄	C₄×D₁₀₉	1	1	yes	characteristic
32	C₈	—	109	2	no	—
33	C₈	C₄×D₁₀₉	1	1	yes	characteristic
34	C₈	C₂×Dic₁₀₉	1	1	yes	characteristic
35	C₂²	C₈×D₁₀₉	1	1	yes	characteristic
36	C₄	—	218	2	no	—
37	C₄	C₄×Dic₁₀₉	1	1	yes	characteristic
38	C₄	C₈×D₁₀₉	1	1	yes	characteristic
39	C₂	C₈×Dic₁₀₉	1	1	yes	characteristic
40	C₂	#16812638	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₀₉
commutator	C₂×C₁₀₉	C₄×C₈
Fitting	C₂×C₁₆×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂×C₈
hypercenter	C₂×C₁₆	D₁₀₉
hypocenter	C₁₀₉	#346
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
6. #13182004	C₄	semidirect
8. C₁₆×C₁₀₉	C₄	semidirect
20. C₁₀₉	#346	semidirect
29. C₁₆	Dic₁₀₉	semidirect