Subgroups — #27193343

Order 13184.

56 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	#20267617	C₂	1	1	yes	maximal, characteristic
3	#366×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	#15692955	—	2	1	no	—
5	C₁₀₃⋊C₃₂	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
7	#107×C₁₀₃	—	2	1	no	—
8	C₄⋊Dic₁₀₃	—	4	1	no	—
9	C₂×C₈×C₁₀₃	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₁₀₃	—	4	1	no	—
11	C₁₆×C₁₀₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₀₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₀₃	—	8	1	no	—
14	C₂×C₄×C₁₀₃	D₈	1	1	yes	characteristic
15	C₂×Dic₁₀₃	—	8	1	no	—
16	C₈×C₁₀₃	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₀₃	Q₁₆	1	1	yes	characteristic
18	C₂²×C₁₀₃	D₁₆	1	1	yes	characteristic
19	C₄×C₁₀₃	—	16	1	no	—
20	C₄×C₁₀₃	#107	1	1	yes	characteristic
21	C₄×C₁₀₃	Q₃₂	1	1	yes	characteristic
22	Dic₁₀₃	—	16	1	no	—
23	C₂×C₁₀₃	#366	1	1	yes	characteristic
24	C₂×C₁₀₃	D₃₂	1	1	yes	characteristic
25	C₂×C₁₀₃	Q₆₄	1	1	yes	characteristic
26	#1423	—	103	1	no	maximal, Sylow
27	C₁₀₃	#1423	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃₂	—	103	1	no	—
29	#366	—	103	1	no	—
30	#366	D₁₀₃	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₁₀₃	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	206	1	no	—
34	C₃₂	—	103	2	no	—
35	C₂×C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	412	1	no	—
38	C₁₆	Dic₂₀₆	1	1	yes	characteristic
39	C₁₆	C₄×D₁₀₃	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	824	1	no	—
42	C₂×C₄	#13110090	1	1	yes	characteristic
43	C₈	Dic₁₀₃⋊C₄	1	1	yes	characteristic
44	C₈	#13110095	1	1	yes	characteristic
45	C₂²	#15692962	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	1648	1	no	—
48	C₄	#15692954	1	1	yes	characteristic
49	C₄	#15692967	1	1	yes	characteristic
50	C₂	#20267616	1	1	yes	characteristic
51	C₂	#20267626	1	1	yes	characteristic
52	C₂	#20267631	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15692962
commutator	C₁₆×C₁₀₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₀₃
Fitting	#366×C₁₀₃	C₂
socle, prime radical	C₂²×C₁₀₃	D₁₆
cosocle	C₂×C₁₆×C₁₀₃	C₂²
hypercenter	#366	D₁₀₃
hypocenter	C₁₀₃	#1423
LCS	G ▷ C₁₆×C₁₀₃ ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. C₁₀₃⋊C₃₂	C₄	semidirect
27. C₁₀₃	#1423	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
#20267617	2
#366×C₁₀₃	2
#1423	103