Subgroups — #27193443

Order 13184.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20267842	C₂	1	3	yes	maximal
2	#20267513	C₂	1	3	yes	maximal, complemented
3	C₈²×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×D₁₀₃	C₂²	1	1	yes	characteristic
5	Dic₁₀₃⋊C₈	C₄	1	6	yes	—
6	(C₂×D₁₀₃)⋊C₈	C₄	1	6	yes	—
7	C₄×C₁₀₃⋊C₈	C₂²	1	3	yes	—
8	C₄×C₈×C₁₀₃	C₂²	1	3	yes	—
9	C₂×C₄×D₁₀₃	C₂×C₄	1	3	yes	—
10	C₂×C₁₀₃⋊C₈	C₂×C₄	1	6	yes	—
11	C₄×Dic₁₀₃	C₂×C₄	1	3	yes	—
12	C₂×C₈×C₁₀₃	C₂×C₄	1	6	yes	—
13	C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
14	C₂²×D₁₀₃	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₁₀₃	C₂²×C₄	1	3	yes	—
16	C₂×Dic₁₀₃	C₄²	1	3	yes	—
17	C₄×D₁₀₃	—	2	6	no	—
18	C₈×C₁₀₃	—	2	6	no	—
19	C₁₀₃⋊C₈	—	2	6	no	—
20	C₂²×C₁₀₃	C₂×C₄²	1	1	yes	characteristic
21	C₂×D₁₀₃	—	2	3	no	—
22	C₄×C₁₀₃	#131	1	6	yes	—
23	Dic₁₀₃	—	2	3	no	—
24	C₂×C₁₀₃	#405	1	3	yes	—
25	D₁₀₃	—	4	1	no	—
26	#1454	—	103	1	no	maximal, Sylow
27	C₁₀₃	#1454	1	1	yes	characteristic, complemented, Sylow
28	#431	—	103	3	no	—
29	#322	—	103	3	no	—
30	C₈²	D₁₀₃	1	1	yes	characteristic, complemented
31	C₂×C₄²	—	103	1	no	—
32	C₄⋊C₈	—	103	6	no	—
33	C₂²⋊C₈	—	103	6	no	—
34	C₄×C₈	—	103	3	no	—
35	C₄×C₈	C₂×D₁₀₃	1	3	yes	—
36	C₂²×C₄	—	103	3	no	—
37	C₂×C₈	—	103	6	no	—
38	C₂×C₈	C₄×D₁₀₃	1	6	yes	—
39	C₄²	—	103	3	no	—
40	C₄²	C₂²×D₁₀₃	1	1	yes	characteristic
41	C₂³	—	103	1	no	—
42	C₂×C₄	—	103	3	no	—
43	C₂×C₄	—	206	6	no	—
44	C₂×C₄	C₂×C₄×D₁₀₃	1	3	yes	—
45	C₈	—	2	6	no	—
46	C₈	—	206	6	no	—
47	C₂²	—	206	3	no	—
48	C₂²	C₄²×D₁₀₃	1	1	yes	characteristic
49	C₄	—	206	3	no	—
50	C₄	#15693027	1	6	yes	—
51	C₂	—	412	1	no	—
52	C₂	#20267745	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₁₀₃
commutator, socle	C₂²×C₁₀₃	C₂×C₄²
Fitting	C₈²×C₁₀₃	C₂
prime radical	C₂²×D₁₀₃	C₄²
cosocle	C₄²×C₁₀₃	C₂³
hypercenter	C₈²	D₁₀₃
hypocenter	C₁₀₃	#1454
LCS	G ▷ C₂²×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #20267513	C₂	semidirect
3. C₈²×C₁₀₃	C₂	semidirect
27. C₁₀₃	#1454	semidirect
30. C₈²	D₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
#20267842	2
#20267513	2
C₈²×C₁₀₃	2
#1454	103