Subgroups — #41×D₁₀₃ #15693062

Order 3296.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13110106	C₂	1	1	yes	maximal, characteristic, complemented
2	#13110105	C₂	1	3	yes	maximal, complemented
3	#13110104	C₂	1	3	yes	maximal, complemented
4	Q₈×D₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×D₁₀₃	C₂	1	3	yes	maximal, complemented
6	C₂×C₄×D₁₀₃	C₂	1	3	yes	maximal, complemented
7	#41×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₁₀₃	C₂²	1	3	yes	—
9	Q₈×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
10	D₄×C₁₀₃	C₂²	1	3	yes	complemented
11	C₂×C₄×C₁₀₃	C₂²	1	3	yes	complemented
12	C₂²⋊D₁₀₃	C₂²	1	6	yes	complemented
13	C₂×Dic₁₀₃	C₂²	1	3	yes	complemented
14	D₄₁₂	C₂²	1	3	yes	complemented
15	C₄×D₁₀₃	C₂²	1	1	yes	characteristic
16	C₄×D₁₀₃	C₂²	1	3	yes	—
17	C₄×D₁₀₃	C₂²	1	3	yes	complemented
18	C₄×D₁₀₃	C₂²	1	3	yes	complemented
19	Dic₂₀₆	C₂²	1	3	yes	complemented
20	C₂²×C₁₀₃	C₂³	1	3	yes	—
21	C₂×D₁₀₃	—	2	6	no	—
22	C₂×D₁₀₃	C₂³	1	3	yes	—
23	C₂×D₁₀₃	C₂³	1	1	yes	characteristic
24	C₄×C₁₀₃	C₂³	1	3	yes	—
25	C₄×C₁₀₃	C₂³	1	1	yes	characteristic
26	Dic₁₀₃	C₂³	1	3	yes	—
27	Dic₁₀₃	C₂³	1	1	yes	characteristic
28	C₂×C₁₀₃	—	2	3	no	—
29	C₂×C₁₀₃	C₂⁴	1	1	yes	characteristic
30	D₁₀₃	—	2	3	no	—
31	D₁₀₃	#41	1	2	yes	direct product factor
32	C₁₀₃	C₂×#41	1	1	yes	characteristic, complemented, Sylow
33	C₂×#41	—	103	1	no	maximal, Sylow
34	#41	—	103	1	no	—
35	#41	—	103	3	no	—
36	#41	—	103	3	no	—
37	#41	D₁₀₃	1	1	yes	characteristic, direct product factor
38	C₂×Q₈	—	103	1	no	—
39	C₂×D₄	—	103	3	no	—
40	C₂²×C₄	—	103	3	no	—
41	C₂³	—	103	3	no	—
42	Q₈	—	103	3	no	—
43	Q₈	C₂×D₁₀₃	1	1	yes	characteristic, complemented
44	D₄	—	103	6	no	—
45	D₄	—	103	3	no	—
46	D₄	C₂×D₁₀₃	1	3	yes	complemented
47	C₂×C₄	—	103	3	no	—
48	C₂×C₄	—	103	3	no	—
49	C₂×C₄	—	103	3	no	—
50	C₂×C₄	—	103	1	no	—
51	C₂×C₄	—	103	3	no	—
52	C₂×C₄	C₂×D₁₀₃	1	3	yes	complemented
53	C₂²	—	103	1	no	—
54	C₂²	—	103	3	no	—
55	C₂²	—	206	6	no	—
56	C₂²	C₂²×D₁₀₃	1	3	yes	—
57	C₄	—	103	1	no	—
58	C₄	—	103	3	no	—
59	C₄	C₂²×D₁₀₃	1	3	yes	—
60	C₄	C₂²×D₁₀₃	1	1	yes	characteristic
61	C₂	—	2	3	no	—
62	C₂	—	103	2	no	—
63	C₂	—	206	3	no	—
64	C₂	C₂³×D₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₁₀₃
commutator, socle, cosocle	C₂×C₁₀₃	C₂⁴
Frattini	C₂	C₂³×D₁₀₃
Fitting	#41×C₁₀₃	C₂
hypercenter	#41	D₁₀₃
hypocenter	C₁₀₃	C₂×#41
LCS	G ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #13110106	C₂	semidirect
2. #13110105	C₂	semidirect
3. #13110104	C₂	semidirect
4. Q₈×D₁₀₃	C₂	semidirect
5. D₄×D₁₀₃	C₂	semidirect
6. C₂×C₄×D₁₀₃	C₂	semidirect
7. #41×C₁₀₃	C₂	semidirect
9. Q₈×C₁₀₃	C₂²	semidirect
10. D₄×C₁₀₃	C₂²	semidirect
11. C₂×C₄×C₁₀₃	C₂²	semidirect
12. C₂²⋊D₁₀₃	C₂²	semidirect
13. C₂×Dic₁₀₃	C₂²	semidirect
14. D₄₁₂	C₂²	semidirect
17. C₄×D₁₀₃	C₂²	semidirect
18. C₄×D₁₀₃	C₂²	semidirect
19. Dic₂₀₆	C₂²	semidirect
31. D₁₀₃	#41	direct (N × H)
32. C₁₀₃	C₂×#41	semidirect
37. #41	D₁₀₃	direct (N × H)
43. Q₈	C₂×D₁₀₃	semidirect
46. D₄	C₂×D₁₀₃	semidirect
52. C₂×C₄	C₂×D₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
#13110106	2
#13110105	2
#13110104	2
Q₈×D₁₀₃	2
D₄×D₁₀₃	2
C₂×C₄×D₁₀₃	2
#41×C₁₀₃	2
C₂×#41	103

Subgroups — #41×D103 #15693062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×D₁₀₃ #15693062