Subgroups — #15693041

Order 3296.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13110105	C₂	1	1	yes	maximal, characteristic, complemented
2	#13110095	C₂	1	1	yes	maximal, characteristic, complemented
3	#13110093	C₂	1	1	yes	maximal, characteristic, complemented
4	#13110092	C₂	1	1	yes	maximal, characteristic, complemented
5	#13110090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#41×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
9	D₄×C₁₀₃	—	2	1	no	—
10	D₄×C₁₀₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₀₃	—	2	1	no	—
12	C₂×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
13	C₂²⋊D₁₀₃	—	2	1	no	—
14	D₄₁₂	C₂²	1	1	yes	characteristic
15	C₄×D₁₀₃	—	2	1	no	—
16	Dic₂₀₆	C₂²	1	1	yes	characteristic
17	C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₁₀₃	—	2	1	no	—
20	C₂²×C₁₀₃	D₄	1	1	yes	characteristic
21	C₂×D₁₀₃	—	2	1	no	—
22	C₄×C₁₀₃	—	2	1	no	—
23	C₄×C₁₀₃	D₄	1	1	yes	characteristic
24	C₄×C₁₀₃	C₂³	1	1	yes	characteristic
25	Dic₁₀₃	—	2	1	no	—
26	C₂×C₁₀₃	—	2	1	no	—
27	C₂×C₁₀₃	—	4	1	no	—
28	C₂×C₁₀₃	C₂×D₄	1	1	yes	characteristic
29	D₁₀₃	—	4	1	no	—
30	C₁₀₃	#135	1	1	yes	characteristic, complemented, Sylow
31	#135	—	103	1	no	maximal, Sylow
32	#41	—	103	1	no	—
33	#41	D₁₀₃	1	1	yes	characteristic, complemented
34	Q₁₆	—	103	1	no	—
35	SD₁₆	—	103	1	no	—
36	SD₁₆	—	103	1	no	—
37	D₈	—	103	1	no	—
38	C₂×C₈	—	103	1	no	—
39	Q₈	—	103	1	no	—
40	Q₈	C₂×D₁₀₃	1	1	yes	characteristic
41	D₄	—	2	1	no	—
42	D₄	—	103	1	no	—
43	D₄	—	206	1	no	—
44	D₄	C₂×D₁₀₃	1	1	yes	characteristic
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	206	1	no	—
47	C₂×C₄	C₂×D₁₀₃	1	1	yes	characteristic
48	C₈	—	103	1	no	—
49	C₈	—	103	1	no	—
50	C₂²	—	2	1	no	—
51	C₂²	—	206	1	no	—
52	C₂²	C₂²⋊D₁₀₃	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	206	1	no	—
55	C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
56	C₄	C₂²×D₁₀₃	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	—	4	1	no	—
59	C₂	—	412	1	no	—
60	C₂	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊D₁₀₃
commutator, cosocle	C₄×C₁₀₃	C₂³
Frattini	C₄	C₂²×D₁₀₃
Fitting	#41×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂×D₄
hypercenter	#41	D₁₀₃
hypocenter	C₁₀₃	#135
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #13110105	C₂	semidirect
2. #13110095	C₂	semidirect
3. #13110093	C₂	semidirect
4. #13110092	C₂	semidirect
5. #13110090	C₂	semidirect
6. C₂×C₁₀₃⋊C₈	C₂	semidirect
7. #41×C₁₀₃	C₂	semidirect
30. C₁₀₃	#135	semidirect
33. #41	D₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
#13110105	2
#13110095	2
#13110093	2
#13110092	2
#13110090	2
C₂×C₁₀₃⋊C₈	2
#41×C₁₀₃	2
#135	103