Subgroups — #20267636

Order 6592.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₁₀₃	C₂	1	3	yes	maximal
2	C₁₀₃⋊#95	C₂	1	3	yes	maximal
3	#95×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₀₃	C₂²	1	3	yes	—
5	C₂²×Dic₁₀₃	C₂²	1	1	yes	characteristic
6	C₄×Dic₁₀₃	C₄	1	12	yes	complemented
7	C₂²×C₄×C₁₀₃	C₂²	1	3	yes	—
8	C₂³×C₁₀₃	C₂³	1	1	yes	characteristic
9	C₂×C₄×C₁₀₃	—	2	6	no	—
10	C₂×C₄×C₁₀₃	C₂×C₄	1	6	yes	—
11	C₂×Dic₁₀₃	—	2	3	no	—
12	C₂×Dic₁₀₃	—	2	3	no	—
13	C₂×Dic₁₀₃	C₂×C₄	1	6	yes	—
14	C₂×Dic₁₀₃	C₂×C₄	1	6	yes	—
15	C₂²×C₁₀₃	C₂²×C₄	1	3	yes	—
16	C₂²×C₁₀₃	#41	1	3	yes	—
17	C₂²×C₁₀₃	#41	1	1	yes	characteristic
18	C₄×C₁₀₃	—	2	6	no	—
19	Dic₁₀₃	—	2	6	no	—
20	Dic₁₀₃	C₄²	1	4	yes	—
21	C₂×C₁₀₃	C₂×C₄²	1	1	yes	characteristic
22	C₂×C₁₀₃	#117	1	3	yes	—
23	C₂×C₁₀₃	#117	1	3	yes	—
24	C₁₀₃	#376	1	1	yes	characteristic, complemented, Sylow
25	#376	—	103	1	no	maximal, Sylow
26	C₂×C₄²	—	103	3	no	—
27	#95	—	103	3	no	—
28	#95	D₁₀₃	1	1	yes	characteristic
29	C₂²×C₄	—	103	1	no	—
30	C₂²×C₄	—	103	3	no	—
31	C₂²×C₄	C₂×D₁₀₃	1	3	yes	—
32	C₄²	—	103	12	no	—
33	C₂³	C₂²×D₁₀₃	1	1	yes	characteristic
34	C₂×C₄	—	2	6	no	—
35	C₂×C₄	—	103	6	no	—
36	C₂×C₄	—	103	6	no	—
37	C₂×C₄	—	206	3	no	—
38	C₂×C₄	—	206	3	no	—
39	C₂×C₄	C₄×D₁₀₃	1	6	yes	—
40	C₂²	C₂×C₄×D₁₀₃	1	3	yes	—
41	C₂²	#13110104	1	3	yes	—
42	C₂²	#13110106	1	1	yes	characteristic
43	C₄	—	2	6	no	—
44	C₄	—	103	4	no	—
45	C₄	—	206	6	no	—
46	C₂	C₄²×D₁₀₃	1	1	yes	characteristic
47	C₂	#15692977	1	3	yes	—
48	C₂	#15692979	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₀₃
commutator	C₂×C₁₀₃	C₂×C₄²
Fitting	#95×C₁₀₃	C₂
socle	C₂³×C₁₀₃	C₂³
hypercenter	#95	D₁₀₃
hypocenter	C₁₀₃	#376
LCS	G ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
6. C₄×Dic₁₀₃	C₄	semidirect
24. C₁₀₃	#376	semidirect