Subgroups — #27193344

Order 13184.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20267617	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₁₀₃	C₂	1	1	yes	maximal, characteristic
3	#15692955	—	2	2	no	—
4	C₂×C₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
5	C₃₂×C₁₀₃	C₄	1	2	yes	complemented
6	C₄⋊Dic₁₀₃	—	4	2	no	—
7	C₂×C₈×C₁₀₃	D₄	1	1	yes	characteristic
8	C₁₆×C₁₀₃	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₁₀₃	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₀₃	D₈	1	1	yes	characteristic
11	C₂×Dic₁₀₃	—	8	2	no	—
12	C₈×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₁₀₃	Q₁₆	1	1	yes	characteristic
14	C₂²×C₁₀₃	D₁₆	1	1	yes	characteristic
15	C₄×C₁₀₃	#107	1	1	yes	characteristic
16	C₄×C₁₀₃	Q₃₂	1	1	yes	characteristic
17	Dic₁₀₃	—	16	2	no	—
18	C₂×C₁₀₃	#366	1	1	yes	characteristic
19	C₂×C₁₀₃	D₃₂	1	1	yes	characteristic
20	C₂×C₁₀₃	Q₆₄	1	1	yes	characteristic
21	#1423	—	103	1	no	maximal, Sylow
22	C₁₀₃	#1423	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃₂	D₁₀₃	1	1	yes	characteristic
24	#366	—	103	2	no	—
25	C₂×C₁₆	C₂×D₁₀₃	1	1	yes	characteristic
26	#107	—	206	2	no	—
27	C₃₂	Dic₁₀₃	1	2	yes	complemented
28	C₂×C₈	D₄₁₂	1	1	yes	characteristic
29	C₄⋊C₄	—	412	2	no	—
30	C₁₆	Dic₂₀₆	1	1	yes	characteristic
31	C₁₆	C₂×Dic₁₀₃	1	1	yes	characteristic
32	C₂×C₄	—	824	2	no	—
33	C₂×C₄	D₈₂₄	1	1	yes	characteristic
34	C₈	C₄⋊Dic₁₀₃	1	1	yes	characteristic
35	C₈	Dic₄₁₂	1	1	yes	characteristic
36	C₂²	D₁₆₄₈	1	1	yes	characteristic
37	C₄	—	1648	2	no	—
38	C₄	#15692955	1	1	yes	characteristic
39	C₄	Dic₈₂₄	1	1	yes	characteristic
40	C₂	#20267617	1	1	yes	characteristic
41	C₂	D₃₂₉₆	1	1	yes	characteristic
42	C₂	Dic₁₆₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₆₄₈
commutator	C₁₆×C₁₀₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₀₃
Fitting	C₂×C₃₂×C₁₀₃	C₂
socle, prime radical	C₂²×C₁₀₃	D₁₆
cosocle	C₂×C₁₆×C₁₀₃	C₂²
hypercenter	C₂×C₃₂	D₁₀₃
hypocenter	C₁₀₃	#1423
LCS	G ▷ C₁₆×C₁₀₃ ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
5. C₃₂×C₁₀₃	C₄	semidirect
22. C₁₀₃	#1423	semidirect
27. C₃₂	Dic₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
#20267617	2
C₂×C₃₂×C₁₀₃	2
#1423	103