Subgroups — #27193347

Order 13184.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₀₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#20267621	C₂	1	1	yes	maximal, characteristic
3	#368×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	#15692957	—	2	1	no	—
5	C₁₀₃⋊C₃₂	C₄	1	2	yes	—
6	C₂×C₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
7	#108×C₁₀₃	—	2	1	no	—
8	#13110089	—	4	1	no	—
9	M₁₆×C₁₀₃	—	4	1	no	—
10	C₂×C₈×C₁₀₃	D₄	1	1	yes	characteristic
11	C₁₆×C₁₀₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₀₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₀₃	D₈	1	1	yes	characteristic
14	C₈×C₁₀₃	—	8	1	no	—
15	C₈×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₁₀₃	Q₁₆	1	1	yes	characteristic
17	C₁₀₃⋊C₈	—	8	1	no	—
18	C₂²×C₁₀₃	Q₃₂	1	1	yes	characteristic
19	C₄×C₁₀₃	#107	1	1	yes	characteristic
20	C₄×C₁₀₃	D₁₆	1	1	yes	characteristic
21	C₂×C₁₀₃	—	2	1	no	—
22	C₂×C₁₀₃	#366	1	1	yes	characteristic
23	#1425	—	103	1	no	maximal, Sylow
24	C₁₀₃	#1425	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃₂	—	103	1	no	—
26	#368	—	103	1	no	—
27	#368	D₁₀₃	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₁₀₃	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	206	1	no	—
31	C₃₂	—	103	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	412	1	no	—
34	C₂×C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
35	C₁₆	Dic₂₀₆	1	1	yes	characteristic
36	C₁₆	C₄×D₁₀₃	1	1	yes	characteristic
37	C₂×C₄	#13110090	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	824	1	no	—
40	C₈	Dic₁₀₃⋊C₄	1	1	yes	characteristic
41	C₈	#13110095	1	1	yes	characteristic
42	C₂²	#15692967	1	1	yes	characteristic
43	C₄	#15692954	1	1	yes	characteristic
44	C₄	#15692962	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#20267616	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15692962
commutator	C₁₆×C₁₀₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₀₃
Fitting	#368×C₁₀₃	C₂
socle	C₂×C₁₀₃	#366
prime radical	C₂²×C₁₀₃	Q₃₂
cosocle	C₂×C₁₆×C₁₀₃	C₂²
hypercenter	#368	D₁₀₃
hypocenter	C₁₀₃	#1425
LCS	G ▷ C₁₆×C₁₀₃ ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
24. C₁₀₃	#1425	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₀₃⋊C₃₂	2
#20267621	2
#368×C₁₀₃	2
#1425	103