Subgroups — #20294853

Order 6976.

46 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	#16812633	C₂	1	1	yes	maximal, characteristic
3	#107×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₀₉	—	2	1	no	—
5	#13182004	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₀₉	—	2	1	no	—
8	C₂×C₄×C₁₀₉	—	4	1	no	—
9	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
10	C₂×Dic₁₀₉	—	4	1	no	—
11	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₀₉	Q₈	1	1	yes	characteristic
13	C₂²×C₁₀₉	D₈	1	1	yes	characteristic
14	C₄×C₁₀₉	—	8	1	no	—
15	C₄×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₀₉	Q₁₆	1	1	yes	characteristic
17	Dic₁₀₉	—	8	1	no	—
18	C₂×C₁₀₉	#107	1	1	yes	characteristic
19	C₂×C₁₀₉	SD₃₂	1	1	yes	characteristic
20	C₂×C₁₀₉	SD₃₂	1	1	yes	characteristic
21	C₁₀₉	#367	1	1	yes	characteristic, complemented, Sylow
22	#367	—	109	1	no	maximal, Sylow
23	C₂×C₁₆	—	109	1	no	—
24	#107	—	109	1	no	—
25	#107	D₁₀₉	1	1	yes	characteristic
26	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	218	1	no	—
29	C₁₆	—	109	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	436	1	no	—
32	C₂×C₄	C₂²⋊D₁₀₉	1	1	yes	characteristic
33	C₈	Dic₂₁₈	1	1	yes	characteristic
34	C₈	C₄×D₁₀₉	1	1	yes	characteristic
35	C₂²	#13182014	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	872	1	no	—
38	C₄	#13182008	1	1	yes	characteristic
39	C₄	#13182019	1	1	yes	characteristic
40	C₂	#16812632	1	1	yes	characteristic
41	C₂	#16812642	1	1	yes	characteristic
42	C₂	#16812643	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13182014
commutator	C₈×C₁₀₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₉
Fitting	#107×C₁₀₉	C₂
socle	C₂²×C₁₀₉	D₈
hypercenter	#107	D₁₀₉
hypocenter	C₁₀₉	#367
LCS	G ▷ C₈×C₁₀₉ ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. #13182004	C₄	semidirect
21. C₁₀₉	#367	semidirect