Subgroups — #27187555

Order 12928.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266109	C₂	1	3	yes	maximal, complemented
2	C₂×#15692305	C₂	1	3	yes	maximal, complemented
3	#20265594	C₂	1	1	yes	maximal, characteristic
4	#15692305	C₂²	1	1	yes	characteristic
5	#15692305	C₂²	1	3	yes	—
6	#15692195	C₄	1	3	yes	—
7	C₂×#13108049	C₂²	1	3	yes	—
8	#131×C₁₀₁	C₄	1	1	yes	characteristic
9	#13108049	C₂×C₄	1	3	yes	—
10	#13108049	C₂³	1	1	yes	characteristic
11	#41×C₁₀₁	C₈	1	1	yes	characteristic
12	M₁₆×C₁₀₁	C₈	1	3	yes	—
13	C₂×C₈×C₁₀₁	C₂×C₄	1	3	yes	—
14	Q₈×C₁₀₁	C₁₆	1	1	yes	characteristic
15	D₄×C₁₀₁	C₁₆	1	3	yes	—
16	C₂×C₄×C₁₀₁	C₂×C₈	1	3	yes	—
17	C₈×C₁₀₁	C₂×C₈	1	3	yes	—
18	C₈×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₁₀₁	C₂×C₁₆	1	3	yes	—
20	C₄×C₁₀₁	C₂×C₁₆	1	3	yes	—
21	C₄×C₁₀₁	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₁₀₁	—	2	3	no	—
23	C₂×C₁₀₁	C₂²×C₁₆	1	1	yes	characteristic
24	#2258	—	101	1	no	maximal, Sylow
25	C₁₀₁	#2258	1	1	yes	characteristic, complemented, Sylow
26	#504	—	101	1	no	—
27	M₆₄	—	101	3	no	—
28	C₂×C₃₂	—	101	3	no	—
29	#131	#87938	1	1	yes	characteristic
30	M₃₂	—	101	3	no	—
31	C₂×C₁₆	—	101	3	no	—
32	C₃₂	—	101	1	no	—
33	C₃₂	—	101	3	no	—
34	#41	#11717581	1	1	yes	characteristic
35	M₁₆	#11717581	1	3	yes	—
36	C₂×C₈	C₂×#87938	1	3	yes	—
37	C₁₆	—	101	3	no	—
38	C₁₆	—	101	1	no	—
39	Q₈	#13108077	1	1	yes	characteristic
40	D₄	#13108077	1	3	yes	—
41	C₂×C₄	C₂×#11717581	1	3	yes	—
42	C₈	C₂×#11717581	1	3	yes	—
43	C₈	C₂²×#87938	1	1	yes	characteristic
44	C₂²	C₂×#13108077	1	3	yes	—
45	C₄	C₂×#13108077	1	3	yes	—
46	C₄	C₂²×#11717581	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×#13108077	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#87938
commutator, socle	C₂×C₁₀₁	C₂²×C₁₆
Fitting	#131×C₁₀₁	C₄
prime radical	#41×C₁₀₁	C₈
cosocle	#13108049	C₂³
hypercenter	#131	#87938
hypocenter	C₁₀₁	#2258
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₈ ◁ #131

Complements

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

N	H ≅ G/N	type
1. #20266109	C₂	semidirect
2. C₂×#15692305	C₂	semidirect
25. C₁₀₁	#2258	semidirect

Maximal subgroups

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

subgroup	index
#20266109	2
C₂×#15692305	2
#20265594	2
#2258	101