Subgroups — #20266227

Order 6464.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11717581	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#11717581	C₂	1	2	yes	maximal
3	#15692310	C₂	1	2	yes	maximal
4	C₄×#11717581	C₂	1	1	yes	maximal, characteristic
5	#15692220	C₂	1	1	yes	maximal, characteristic
6	C₂×#11717581	C₂²	1	1	yes	characteristic
7	C₂×#11717581	C₂²	1	2	yes	—
8	C₂×#11717581	C₂²	1	1	yes	characteristic
9	C₂×Dic₂₀₂	C₄	1	1	yes	characteristic
10	#13108053	C₄	1	2	yes	—
11	C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
12	C₄×Dic₁₀₁	C₂²	1	2	yes	—
13	C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₁₀₁	C₂×C₄	1	2	yes	—
18	C₂×Dic₁₀₁	C₂³	1	1	yes	characteristic
19	Dic₂₀₂	—	2	2	no	—
20	#11717581	—	2	1	no	—
21	#11717581	—	2	2	no	—
22	#11717581	Q₈	1	2	yes	complemented
23	C₂²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₁₀₁	—	2	2	no	—
25	C₄×C₁₀₁	M₁₆	1	2	yes	—
26	Dic₁₀₁	—	2	2	no	—
27	Dic₁₀₁	—	2	1	no	—
28	Dic₁₀₁	C₂×Q₈	1	1	yes	characteristic
29	Dic₁₀₁	#41	1	1	yes	characteristic
30	C₂×C₁₀₁	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₁₀₁	C₂×M₁₆	1	1	yes	characteristic
32	C₂×C₁₀₁	#131	1	1	yes	characteristic
33	C₁₀₁	#446	1	1	yes	characteristic, complemented, Sylow
34	#446	—	101	1	no	maximal, Sylow
35	C₄×Q₈	—	101	1	no	—
36	C₄⋊C₈	—	101	1	no	—
37	C₄⋊C₈	—	101	2	no	—
38	#97	—	101	2	no	—
39	C₄×C₈	—	101	1	no	—
40	C₂×Q₈	—	101	1	no	—
41	C₂×C₈	—	101	1	no	—
42	C₂×C₈	—	101	1	no	—
43	C₂×C₈	—	101	2	no	—
44	C₄⋊C₄	—	101	2	no	—
45	C₄⋊C₄	#87938	1	1	yes	characteristic
46	C₄²	—	101	1	no	—
47	C₄²	—	101	2	no	—
48	Q₈	—	202	2	no	—
49	C₂×C₄	—	101	1	no	—
50	C₂×C₄	—	101	1	no	—
51	C₂×C₄	—	101	2	no	—
52	C₂×C₄	C₂×#87938	1	2	yes	—
53	C₂×C₄	C₂×#87938	1	1	yes	characteristic
54	C₈	—	101	2	no	—
55	C₈	—	202	1	no	—
56	C₈	—	202	2	no	—
57	C₂²	C₂²×#87938	1	1	yes	characteristic
58	C₄	—	2	2	no	—
59	C₄	—	101	1	no	—
60	C₄	—	101	1	no	—
61	C₄	—	202	2	no	—
62	C₄	—	202	1	no	—
63	C₄	#13108084	1	2	yes	—
64	C₂	Q₈×#87938	1	1	yes	characteristic
65	C₂	C₂×#13108084	1	1	yes	characteristic
66	C₂	#15692342	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#87938
commutator, socle	C₂²×C₁₀₁	C₂²×C₄
Fitting	C₄⋊C₄×C₁₀₁	C₄
hypercenter	C₄⋊C₄	#87938
hypocenter	C₁₀₁	#446
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
22. #11717581	Q₈	semidirect
33. C₁₀₁	#446	semidirect