Subgroups — #20294871

Order 6976.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₁₀₉	C₂	1	3	yes	maximal
2	#16812606	C₂	1	3	yes	maximal
3	#95×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₀₉	C₂²	1	3	yes	—
5	C₂²×Dic₁₀₉	C₂²	1	1	yes	characteristic
6	C₄×Dic₁₀₉	C₄	1	12	yes	complemented
7	C₂²×C₄×C₁₀₉	C₂²	1	3	yes	—
8	C₂³×C₁₀₉	C₂³	1	1	yes	characteristic
9	C₂×C₄×C₁₀₉	—	2	6	no	—
10	C₂×C₄×C₁₀₉	C₂×C₄	1	6	yes	—
11	C₂×Dic₁₀₉	—	2	3	no	—
12	C₂×Dic₁₀₉	—	2	3	no	—
13	C₂×Dic₁₀₉	C₂×C₄	1	6	yes	—
14	C₂×Dic₁₀₉	C₂×C₄	1	6	yes	—
15	C₂²×C₁₀₉	C₂²×C₄	1	3	yes	—
16	C₂²×C₁₀₉	#41	1	3	yes	—
17	C₂²×C₁₀₉	#41	1	1	yes	characteristic
18	C₄×C₁₀₉	—	2	6	no	—
19	Dic₁₀₉	—	2	6	no	—
20	Dic₁₀₉	C₄²	1	4	yes	—
21	C₂×C₁₀₉	C₂×C₄²	1	1	yes	characteristic
22	C₂×C₁₀₉	#117	1	3	yes	—
23	C₂×C₁₀₉	#117	1	3	yes	—
24	C₁₀₉	#376	1	1	yes	characteristic, complemented, Sylow
25	#376	—	109	1	no	maximal, Sylow
26	C₂×C₄²	—	109	3	no	—
27	#95	—	109	3	no	—
28	#95	D₁₀₉	1	1	yes	characteristic
29	C₂²×C₄	—	109	1	no	—
30	C₂²×C₄	—	109	3	no	—
31	C₂²×C₄	C₂×D₁₀₉	1	3	yes	—
32	C₄²	—	109	12	no	—
33	C₂³	C₂²×D₁₀₉	1	1	yes	characteristic
34	C₂×C₄	—	2	6	no	—
35	C₂×C₄	—	109	6	no	—
36	C₂×C₄	—	109	6	no	—
37	C₂×C₄	—	218	3	no	—
38	C₂×C₄	—	218	3	no	—
39	C₂×C₄	C₄×D₁₀₉	1	6	yes	—
40	C₂²	C₂×C₄×D₁₀₉	1	3	yes	—
41	C₂²	#13182028	1	3	yes	—
42	C₂²	#13182030	1	1	yes	characteristic
43	C₄	—	2	6	no	—
44	C₄	—	109	4	no	—
45	C₄	—	218	6	no	—
46	C₂	C₄²×D₁₀₉	1	1	yes	characteristic
47	C₂	#16812655	1	3	yes	—
48	C₂	#16812657	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₀₉
commutator	C₂×C₁₀₉	C₂×C₄²
Fitting	#95×C₁₀₉	C₂
socle	C₂³×C₁₀₉	C₂³
hypercenter	#95	D₁₀₉
hypocenter	C₁₀₉	#376
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
6. C₄×Dic₁₀₉	C₄	semidirect
24. C₁₀₉	#376	semidirect