Subgroups — M₁₆×#87938 #20266137

Order 6464.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₁⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#87938	C₂	1	1	yes	maximal, characteristic
3	#15692309	C₂	1	2	yes	maximal, complemented
4	C₈×#87938	C₂	1	2	yes	maximal, complemented
5	M₁₆×D₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×#87938	C₄	1	2	yes	—
7	#13108084	C₄	1	2	yes	complemented
8	#13108083	C₄	1	2	yes	complemented
9	D₁₀₁⋊C₈	C₂²	1	2	yes	—
10	C₄×#87938	C₄	1	2	yes	—
11	C₄×#87938	C₂²	1	1	yes	characteristic
12	C₄×#87938	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
14	#13108058	C₄	1	1	yes	characteristic, complemented
15	#13108057	C₄	1	2	yes	complemented
16	C₈×D₁₀₁	C₂²	1	2	yes	—
17	M₁₆×C₁₀₁	C₄	1	1	yes	characteristic, complemented
18	C₂²×D₁₀₁	C₂×C₄	1	1	yes	characteristic
19	C₂×#87938	—	2	4	no	—
20	C₂×#87938	C₂×C₄	1	2	yes	—
21	C₂×#87938	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
24	C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
25	C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
26	C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
27	C₄×D₁₀₁	C₂³	1	1	yes	characteristic
28	#11717581	C₂×C₄	1	4	yes	complemented
29	C₈×C₁₀₁	C₂×C₄	1	2	yes	complemented
30	#11717579	C₂×C₄	1	2	yes	complemented
31	C₂²×C₁₀₁	C₄²	1	1	yes	characteristic
32	C₂×D₁₀₁	—	2	2	no	—
33	C₂×D₁₀₁	C₄²	1	1	yes	characteristic
34	C₂×D₁₀₁	C₂²×C₄	1	1	yes	characteristic
35	#87938	—	2	2	no	—
36	#87938	M₁₆	1	4	yes	direct product factor
37	C₄×C₁₀₁	C₄²	1	1	yes	characteristic
38	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
39	Dic₁₀₁	C₄²	1	1	yes	characteristic
40	Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₁₀₁	—	2	1	no	—
42	C₂×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
43	D₁₀₁	—	2	1	no	—
44	D₁₀₁	C₂×M₁₆	1	2	yes	—
45	C₁₀₁	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
46	C₄×M₁₆	—	101	1	no	maximal, Sylow
47	C₂×M₁₆	—	101	1	no	—
48	C₂×M₁₆	—	101	1	no	—
49	C₂×C₄²	—	101	1	no	—
50	#97	—	101	2	no	—
51	C₄×C₈	—	101	2	no	—
52	C₂²×C₄	—	101	1	no	—
53	C₂²×C₄	—	101	2	no	—
54	M₁₆	—	101	2	no	—
55	M₁₆	—	101	2	no	—
56	M₁₆	—	101	1	no	—
57	M₁₆	—	101	2	no	—
58	M₁₆	#87938	1	1	yes	characteristic, direct product factor
59	C₂×C₈	—	101	2	no	—
60	C₂×C₈	—	101	2	no	—
61	C₄²	—	101	1	no	—
62	C₄²	—	101	1	no	—
63	C₄²	—	101	2	no	—
64	C₂³	—	101	1	no	—
65	C₂×C₄	—	101	2	no	—
66	C₂×C₄	—	101	1	no	—
67	C₂×C₄	—	101	1	no	—
68	C₂×C₄	—	101	1	no	—
69	C₂×C₄	—	101	1	no	—
70	C₂×C₄	—	101	1	no	—
71	C₂×C₄	—	101	2	no	—
72	C₂×C₄	—	202	4	no	—
73	C₂×C₄	C₂×#87938	1	1	yes	characteristic
74	C₈	—	101	4	no	—
75	C₈	—	101	2	no	—
76	C₈	C₂×#87938	1	2	yes	complemented
77	C₂²	—	101	1	no	—
78	C₂²	—	101	1	no	—
79	C₂²	—	202	2	no	—
80	C₂²	C₄×#87938	1	1	yes	characteristic
81	C₄	—	101	4	no	—
82	C₄	—	101	1	no	—
83	C₄	—	101	1	no	—
84	C₄	—	202	2	no	—
85	C₄	C₄×#87938	1	1	yes	characteristic
86	C₄	C₂²×#87938	1	1	yes	characteristic
87	C₂	—	2	1	no	—
88	C₂	—	101	2	no	—
89	C₂	—	202	1	no	—
90	C₂	C₂×C₄×#87938	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#87938
commutator, socle	C₂×C₁₀₁	C₂×C₄²
Fitting	M₁₆×C₁₀₁	C₄
hypercenter	M₁₆	#87938
hypocenter	C₁₀₁	C₄×M₁₆
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
3. #15692309	C₂	semidirect
4. C₈×#87938	C₂	semidirect
7. #13108084	C₄	semidirect
8. #13108083	C₄	semidirect
14. #13108058	C₄	semidirect
15. #13108057	C₄	semidirect
17. M₁₆×C₁₀₁	C₄	semidirect
28. #11717581	C₂×C₄	semidirect
29. C₈×C₁₀₁	C₂×C₄	semidirect
30. #11717579	C₂×C₄	semidirect
36. #87938	M₁₆	direct (N × H)
45. C₁₀₁	C₄×M₁₆	semidirect
58. M₁₆	#87938	direct (N × H)
76. C₈	C₂×#87938	semidirect

Subgroups — M16×#87938 #20266137

Conjugacy classes of subgroups

Complements

Subgroups — M₁₆×#87938 #20266137