Subgroups — #27194900

Order 13184.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20267749	C₂	1	3	yes	maximal
2	#20267548	C₂	1	3	yes	maximal
3	#338×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
5	#15692980	C₂²	1	3	yes	—
6	#15692931	C₄	1	6	yes	complemented
7	C₈×Dic₁₀₃	C₄	1	6	yes	complemented
8	C₂×M₁₆×C₁₀₃	C₂²	1	3	yes	—
9	C₂×C₁₀₃⋊C₈	C₂×C₄	1	3	yes	—
10	C₂×C₁₀₃⋊C₈	C₂×C₄	1	3	yes	—
11	C₄⋊Dic₁₀₃	—	2	3	no	—
12	C₂²⋊Dic₁₀₃	—	2	3	no	—
13	C₄×Dic₁₀₃	C₂×C₄	1	6	yes	—
14	C₂²×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
15	M₁₆×C₁₀₃	—	2	6	no	—
16	C₂×C₈×C₁₀₃	C₂×C₄	1	6	yes	—
17	C₂³×C₁₀₃	#41	1	1	yes	characteristic
18	C₂×C₄×C₁₀₃	C₂²×C₄	1	3	yes	—
19	C₂×C₄×C₁₀₃	#41	1	3	yes	—
20	C₂×Dic₁₀₃	—	2	6	no	—
21	C₈×C₁₀₃	—	2	6	no	—
22	C₁₀₃⋊C₈	C₄²	1	1	yes	characteristic
23	C₁₀₃⋊C₈	C₄²	1	3	yes	—
24	C₂²×C₁₀₃	—	4	1	no	—
25	C₂²×C₁₀₃	#117	1	3	yes	—
26	C₄×C₁₀₃	C₂×C₄²	1	1	yes	characteristic
27	C₄×C₁₀₃	#117	1	3	yes	—
28	Dic₁₀₃	—	4	6	no	—
29	C₂×C₁₀₃	—	2	3	no	—
30	C₂×C₁₀₃	#376	1	1	yes	characteristic
31	#1747	—	103	1	no	maximal, Sylow
32	C₁₀₃	#1747	1	1	yes	characteristic, complemented, Sylow
33	#405	—	103	3	no	—
34	#338	D₁₀₃	1	1	yes	characteristic
35	H(3,ℤ/4)	—	103	3	no	—
36	C₂×M₁₆	C₂×D₁₀₃	1	3	yes	—
37	C₂²×C₈	—	103	1	no	—
38	#117	—	103	3	no	—
39	#97	—	103	6	no	—
40	C₄×C₈	—	103	6	no	—
41	C₂²×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
42	M₁₆	—	2	6	no	—
43	C₂×C₈	—	103	3	no	—
44	C₂×C₈	—	103	3	no	—
45	C₂×C₈	C₄×D₁₀₃	1	6	yes	—
46	C₄⋊C₄	—	206	3	no	—
47	C₂²⋊C₄	—	206	3	no	—
48	C₄²	—	103	6	no	—
49	C₂³	#13110106	1	1	yes	characteristic
50	C₂×C₄	—	206	6	no	—
51	C₂×C₄	C₂×C₄×D₁₀₃	1	3	yes	—
52	C₂×C₄	#13110104	1	3	yes	—
53	C₈	—	2	6	no	—
54	C₈	—	103	1	no	—
55	C₈	—	103	3	no	—
56	C₂²	—	4	1	no	—
57	C₂²	#15692979	1	3	yes	—
58	C₄	—	412	6	no	—
59	C₄	C₄²×D₁₀₃	1	1	yes	characteristic
60	C₄	#15692977	1	3	yes	—
61	C₂	—	2	3	no	—
62	C₂	#20267636	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×D₁₀₃
commutator	C₄×C₁₀₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₀₃
Fitting	#338×C₁₀₃	C₂
socle	C₂×C₁₀₃	#376
prime radical	C₂³×C₁₀₃	#41
cosocle	C₂²×C₄×C₁₀₃	C₂³
hypercenter	#338	D₁₀₃
hypocenter	C₁₀₃	#1747
LCS	G ▷ C₄×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
6. #15692931	C₄	semidirect
7. C₈×Dic₁₀₃	C₄	semidirect
32. C₁₀₃	#1747	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20267749	2
#20267548	2
#338×C₁₀₃	2
#1747	103