Subgroups — C₁₀₁×#1369 #27166723

Order 12928.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#364×C₁₀₁	C₂	1	2	yes	maximal
2	#346×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₁₀₁	—	2	2	no	—
4	C₂×C₁₆×C₁₀₁	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₁₀₁	C₄	1	1	yes	characteristic
6	C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₁₀₁	D₄	1	1	yes	characteristic
9	C₄²×C₁₀₁	Q₈	1	1	yes	characteristic
10	C₁₆×C₁₀₁	—	2	1	no	—
11	C₁₆×C₁₀₁	—	4	2	no	—
12	C₁₆×C₁₀₁	C₈	1	2	yes	—
13	C₂×C₄×C₁₀₁	—	2	1	no	—
14	C₂×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
15	C₈×C₁₀₁	C₂×C₈	1	1	yes	characteristic
16	C₈×C₁₀₁	M₁₆	1	1	yes	characteristic
17	C₈×C₁₀₁	SD₁₆	1	2	yes	—
18	C₂²×C₁₀₁	#108	1	1	yes	characteristic
19	C₄×C₁₀₁	—	4	1	no	—
20	C₄×C₁₀₁	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₁₀₁	#106	1	1	yes	characteristic
22	C₂×C₁₀₁	—	2	1	no	—
23	C₂×C₁₀₁	#334	1	1	yes	characteristic
24	#1369	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₁₀₁	#1369	1	1	yes	characteristic, direct product factor, Sylow
26	#364	C₂×C₁₀₁	1	2	yes	—
27	#346	C₂×C₁₀₁	1	1	yes	characteristic
28	M₃₂	—	2	2	no	—
29	C₂×C₁₆	C₄×C₁₀₁	1	1	yes	characteristic
30	C₂×C₁₆	C₄×C₁₀₁	1	1	yes	characteristic
31	C₄×C₈	C₂²×C₁₀₁	1	1	yes	characteristic
32	C₂×C₈	C₂×C₄×C₁₀₁	1	1	yes	characteristic
33	C₂×C₈	D₄×C₁₀₁	1	1	yes	characteristic
34	C₄²	Q₈×C₁₀₁	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₁₆	—	4	2	no	—
37	C₁₆	C₈×C₁₀₁	1	2	yes	—
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₄⋊C₄×C₁₀₁	1	1	yes	characteristic
40	C₈	C₂×C₈×C₁₀₁	1	1	yes	characteristic
41	C₈	M₁₆×C₁₀₁	1	1	yes	characteristic
42	C₈	SD₁₆×C₁₀₁	1	2	yes	—
43	C₂²	#108×C₁₀₁	1	1	yes	characteristic
44	C₄	—	4	1	no	—
45	C₄	C₄⋊C₈×C₁₀₁	1	1	yes	characteristic
46	C₄	#106×C₁₀₁	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#334×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₀₁	#106
commutator	C₈	C₂×C₈×C₁₀₁
Frattini, cosocle	C₄×C₈	C₂²×C₁₀₁
socle	C₂×C₁₀₁	#334
prime radical	C₂²×C₁₀₁	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₁ ◁ C₂×C₈×C₁₀₁ ◁ C₄×C₈×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
24. #1369	C₁₀₁	direct (N × H)
25. C₁₀₁	#1369	direct (N × H)

Maximal subgroups

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

subgroup	index
#364×C₁₀₁	2
#346×C₁₀₁	2
#1369	101

Subgroups — C101×#1369 #27166723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₁×#1369 #27166723