Subgroups — #27193279

Order 13184.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20267625	C₂	1	1	yes	maximal, characteristic
2	#20267566	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₀₃⋊C₁₆	C₄	1	1	yes	characteristic
5	C₈×Dic₁₀₃	C₄	1	1	yes	characteristic
6	C₁₀₃⋊C₃₂	C₄	1	2	yes	complemented
7	C₂×C₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
8	C₃₂×C₁₀₃	C₄	1	2	yes	complemented
9	C₂×C₁₀₃⋊C₈	C₈	1	1	yes	characteristic
10	C₄×Dic₁₀₃	C₈	1	1	yes	characteristic
11	C₁₀₃⋊C₁₆	C₈	1	2	yes	—
12	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₁₀₃	C₂×C₄	1	1	yes	characteristic
14	C₁₆×C₁₀₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₃	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₁₀₃	—	2	1	no	—
17	C₈×C₁₀₃	C₄²	1	1	yes	characteristic
18	C₈×C₁₀₃	C₂×C₈	1	1	yes	characteristic
19	C₁₀₃⋊C₈	—	2	1	no	—
20	C₂²×C₁₀₃	M₃₂	1	1	yes	characteristic
21	C₄×C₁₀₃	C₄×C₈	1	1	yes	characteristic
22	C₄×C₁₀₃	M₃₂	1	1	yes	characteristic
23	Dic₁₀₃	—	4	1	no	—
24	C₂×C₁₀₃	—	2	1	no	—
25	C₂×C₁₀₃	#346	1	1	yes	characteristic
26	#1398	—	103	1	no	maximal, Sylow
27	C₁₀₃	#1398	1	1	yes	characteristic, complemented, Sylow
28	M₆₄	—	103	1	no	—
29	M₆₄	D₁₀₃	1	1	yes	characteristic
30	#346	—	103	1	no	—
31	C₂×C₁₆	—	103	1	no	—
32	C₂×C₁₆	C₂×D₁₀₃	1	1	yes	characteristic
33	C₄×C₈	—	103	1	no	—
34	C₃₂	—	103	2	no	—
35	C₃₂	Dic₁₀₃	1	2	yes	complemented
36	C₂×C₈	—	103	1	no	—
37	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
38	C₄²	—	103	1	no	—
39	C₁₆	—	103	2	no	—
40	C₁₆	C₄×D₁₀₃	1	1	yes	characteristic
41	C₁₆	C₂×Dic₁₀₃	1	1	yes	characteristic
42	C₂×C₄	—	206	1	no	—
43	C₂×C₄	C₈×D₁₀₃	1	1	yes	characteristic
44	C₈	—	206	1	no	—
45	C₈	C₄×Dic₁₀₃	1	1	yes	characteristic
46	C₈	C₈×D₁₀₃	1	1	yes	characteristic
47	C₂²	#15692960	1	1	yes	characteristic
48	C₄	—	412	1	no	—
49	C₄	C₈×Dic₁₀₃	1	1	yes	characteristic
50	C₄	#15692960	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	#20267566	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×Dic₁₀₃
commutator	C₄×C₁₀₃	C₄×C₈
Frattini	C₂×C₁₆	C₂×D₁₀₃
Fitting	M₆₄×C₁₀₃	C₂
socle	C₂×C₁₀₃	#346
prime radical	C₂²×C₁₀₃	M₃₂
cosocle	C₂×C₁₆×C₁₀₃	C₂²
hypercenter	M₆₄	D₁₀₃
hypocenter	C₁₀₃	#1398
LCS	G ▷ C₄×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₈ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
6. C₁₀₃⋊C₃₂	C₄	semidirect
8. C₃₂×C₁₀₃	C₄	semidirect
27. C₁₀₃	#1398	semidirect
35. C₃₂	Dic₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
#20267625	2
#20267566	2
M₆₄×C₁₀₃	2
#1398	103