Subgroups — #27194731

Order 13184.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20268189	C₂	1	3	yes	maximal, complemented
2	#20268164	C₂	1	3	yes	maximal
3	C₈²×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13110094	—	2	6	no	—
5	#15693021	C₂²	1	3	yes	—
6	#15693018	C₂²	1	1	yes	characteristic
7	#15692953	—	2	6	no	—
8	C₄×C₈×C₁₀₃	C₂²	1	3	yes	—
9	C₂×Dic₂₀₆	—	2	3	no	—
10	C₂×D₄₁₂	—	2	3	no	—
11	#13110094	—	4	12	no	—
12	C₄⋊Dic₁₀₃	—	2	6	no	—
13	C₂×C₈×C₁₀₃	D₄	1	6	yes	—
14	C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
15	C₂²×D₁₀₃	—	4	1	no	—
16	C₂×C₄×C₁₀₃	C₂×D₄	1	3	yes	—
17	C₂×Dic₁₀₃	—	4	3	no	—
18	D₄₁₂	—	4	6	no	—
19	Dic₂₀₆	—	4	6	no	—
20	C₈×C₁₀₃	SD₁₆	1	12	yes	complemented
21	C₂²×C₁₀₃	#127	1	1	yes	characteristic
22	C₂×D₁₀₃	—	8	3	no	—
23	C₄×C₁₀₃	C₂×SD₁₆	1	6	yes	—
24	Dic₁₀₃	—	8	3	no	—
25	C₂×C₁₀₃	#492	1	3	yes	—
26	D₁₀₃	—	16	1	no	—
27	#1705	—	103	1	no	maximal, Sylow
28	C₁₀₃	#1705	1	1	yes	characteristic, complemented, Sylow
29	#498	—	103	3	no	—
30	#492	—	103	3	no	—
31	C₈²	D₁₀₃	1	1	yes	characteristic, complemented
32	C₂×SD₁₆	—	206	6	no	—
33	C₄⋊Q₈	—	103	3	no	—
34	#127	—	103	1	no	—
35	#106	—	206	6	no	—
36	C₄×C₈	C₂×D₁₀₃	1	3	yes	—
37	C₂×Q₈	—	206	3	no	—
38	C₂×D₄	—	206	3	no	—
39	SD₁₆	—	412	12	no	—
40	C₂×C₈	D₄₁₂	1	6	yes	—
41	C₄⋊C₄	—	206	6	no	—
42	C₄²	C₂²×D₁₀₃	1	1	yes	characteristic
43	C₂³	—	412	1	no	—
44	Q₈	—	412	6	no	—
45	D₄	—	412	6	no	—
46	C₂×C₄	—	412	3	no	—
47	C₂×C₄	C₂×D₄₁₂	1	3	yes	—
48	C₈	#13110094	1	12	yes	complemented
49	C₂²	—	824	3	no	—
50	C₂²	#15693018	1	1	yes	characteristic
51	C₄	—	824	3	no	—
52	C₄	C₂×#13110094	1	6	yes	—
53	C₂	—	1648	1	no	—
54	C₂	#20268164	1	3	yes	—

	subgroup	G/H
center	C₂²	#15693018
commutator, cosocle	C₄²×C₁₀₃	C₂³
Frattini	C₄²	C₂²×D₁₀₃
Fitting	C₈²×C₁₀₃	C₂
socle	C₂²×C₁₀₃	#127
prime radical	#15693018	C₂²
hypercenter	C₈²	D₁₀₃
hypocenter	C₁₀₃	#1705
LCS	G ▷ C₄²×C₁₀₃ ▷ C₂²×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #20268189	C₂	semidirect
3. C₈²×C₁₀₃	C₂	semidirect
20. C₈×C₁₀₃	SD₁₆	semidirect
28. C₁₀₃	#1705	semidirect
31. C₈²	D₁₀₃	semidirect
48. C₈	#13110094	semidirect

Maximal subgroups

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

subgroup	index
#20268189	2
#20268164	2
C₈²×C₁₀₃	2
#1705	103