Subgroups — #27193210

Order 13184.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20267542	C₂	1	2	yes	maximal
2	#346×C₁₀₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₀₃⋊C₈)	—	2	2	no	—
4	C₂×C₁₆×C₁₀₃	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₁₀₃	C₄	1	1	yes	characteristic
6	C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₀₃⋊C₈	—	4	2	no	—
8	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₀₃	Q₈	1	1	yes	characteristic
10	C₄²×C₁₀₃	D₄	1	1	yes	characteristic
11	C₁₆×C₁₀₃	—	2	1	no	—
12	C₁₆×C₁₀₃	C₈	1	2	yes	complemented
13	C₂×C₄×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₀₃	SD₁₆	1	2	yes	—
15	C₈×C₁₀₃	—	2	1	no	—
16	C₈×C₁₀₃	C₂×C₈	1	1	yes	characteristic
17	C₈×C₁₀₃	M₁₆	1	1	yes	characteristic
18	C₁₀₃⋊C₈	—	8	2	no	—
19	C₂²×C₁₀₃	#106	1	1	yes	characteristic
20	C₄×C₁₀₃	—	2	2	no	—
21	C₄×C₁₀₃	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₁₀₃	#108	1	1	yes	characteristic
23	C₂×C₁₀₃	#334	1	1	yes	characteristic
24	C₂×C₁₀₃	#365	1	2	yes	—
25	#1368	—	103	1	no	maximal, Sylow
26	C₁₀₃	#1368	1	1	yes	characteristic, complemented, Sylow
27	#346	D₁₀₃	1	1	yes	characteristic
28	#334	—	103	2	no	—
29	C₂×C₁₆	Dic₁₀₃	1	1	yes	characteristic
30	C₂×C₁₆	Dic₁₀₃	1	1	yes	characteristic
31	C₄⋊C₈	—	206	2	no	—
32	C₄×C₈	C₂×D₁₀₃	1	1	yes	characteristic
33	C₂×C₈	—	412	2	no	—
34	C₂×C₈	Dic₂₀₆	1	1	yes	characteristic
35	C₂×C₈	C₂×Dic₁₀₃	1	1	yes	characteristic
36	C₄²	D₄₁₂	1	1	yes	characteristic
37	C₁₆	—	2	1	no	—
38	C₁₆	C₁₀₃⋊C₈	1	2	yes	complemented
39	C₂×C₄	C₄⋊Dic₁₀₃	1	1	yes	characteristic
40	C₂×C₄	#13110094	1	2	yes	—
41	C₈	—	2	1	no	—
42	C₈	—	824	2	no	—
43	C₈	C₂×C₁₀₃⋊C₈	1	1	yes	characteristic
44	C₈	#13110089	1	1	yes	characteristic
45	C₂²	#15692953	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄⋊(C₁₀₃⋊C₈)	1	1	yes	characteristic
48	C₄	#15692957	1	1	yes	characteristic
49	C₂	#20267542	1	1	yes	characteristic
50	C₂	#20267614	1	2	yes	—

	subgroup	G/H
center	C₂²	#15692953
commutator	C₈×C₁₀₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₀₃
Fitting	#346×C₁₀₃	C₂
socle, prime radical	C₂²×C₁₀₃	#106
cosocle	C₄×C₈×C₁₀₃	C₂²
hypercenter	#346	D₁₀₃
hypocenter	C₁₀₃	#1368
LCS	G ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₁₀₃	C₈	semidirect
26. C₁₀₃	#1368	semidirect
38. C₁₆	C₁₀₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#20267542	2
#346×C₁₀₃	2
#1368	103