Subgroups — #27169050

Order 12928.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13108049	C₂	1	2	yes	maximal
2	C₈²×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#13108049	C₄	1	4	yes	—
4	C₄×C₈×C₁₀₁	C₄	1	1	yes	characteristic
5	C₄×C₈×C₁₀₁	C₄	1	1	yes	characteristic
6	C₄×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
7	#13108049	—	2	4	no	—
8	C₂×C₈×C₁₀₁	C₈	1	2	yes	—
9	C₂×C₈×C₁₀₁	C₈	1	2	yes	—
10	C₂×C₈×C₁₀₁	C₂×C₄	1	2	yes	—
11	C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₀₁	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₀₁	—	2	2	no	—
16	C₈×C₁₀₁	C₁₆	1	4	yes	complemented
17	C₈×C₁₀₁	M₁₆	1	4	yes	—
18	C₂²×C₁₀₁	C₄×C₈	1	1	yes	characteristic
19	C₄×C₁₀₁	#97	1	2	yes	—
20	C₄×C₁₀₁	C₂×C₁₆	1	2	yes	—
21	C₄×C₁₀₁	M₃₂	1	2	yes	—
22	C₂×C₁₀₁	#322	1	1	yes	characteristic
23	C₂×C₁₀₁	C₄×C₁₆	1	1	yes	characteristic
24	C₂×C₁₀₁	#346	1	1	yes	characteristic
25	#1312	—	101	1	no	maximal, Sylow
26	C₁₀₁	#1312	1	1	yes	characteristic, complemented, Sylow
27	C₄×C₁₆	—	101	2	no	—
28	C₈²	D₁₀₁	1	1	yes	characteristic
29	C₂×C₁₆	—	101	4	no	—
30	C₄×C₈	Dic₁₀₁	1	1	yes	characteristic
31	C₄×C₈	Dic₁₀₁	1	1	yes	characteristic
32	C₄×C₈	C₂×D₁₀₁	1	1	yes	characteristic
33	C₂×C₈	#11717579	1	2	yes	—
34	C₂×C₈	#11717579	1	2	yes	—
35	C₂×C₈	C₄×D₁₀₁	1	2	yes	—
36	C₄²	C₂×Dic₁₀₁	1	1	yes	characteristic
37	C₁₆	—	202	4	no	—
38	C₂×C₄	C₄×Dic₁₀₁	1	1	yes	characteristic
39	C₂×C₄	C₂×#11717579	1	1	yes	characteristic
40	C₂×C₄	C₂×#11717579	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₈	#13108049	1	4	yes	complemented
43	C₈	#13108057	1	4	yes	—
44	C₂²	C₄×#11717579	1	1	yes	characteristic
45	C₄	#15692165	1	2	yes	—
46	C₄	C₂×#13108049	1	2	yes	—
47	C₄	#15692195	1	2	yes	—
48	C₂	#20264898	1	1	yes	characteristic
49	C₂	C₄×#13108049	1	1	yes	characteristic
50	C₂	#20264953	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₁₀₁
commutator	C₂×C₁₀₁	C₄×C₁₆
Fitting	C₈²×C₁₀₁	C₂
socle, prime radical	C₂²×C₁₀₁	C₄×C₈
cosocle	C₄×C₈×C₁₀₁	C₂²
hypercenter	C₈²	D₁₀₁
hypocenter	C₁₀₁	#1312
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
16. C₈×C₁₀₁	C₁₆	semidirect
26. C₁₀₁	#1312	semidirect
42. C₈	#13108049	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13108049	2
C₈²×C₁₀₁	2
#1312	101