Subgroups — C₄×M₁₆×C₄₉₁ #44536261

Order 31424.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₄₉₁	C₂	1	2	yes	maximal
2	C₂×C₄²×C₄₉₁	C₂	1	1	yes	maximal, characteristic
3	#97×C₄₉₁	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×C₄₉₁	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×C₄₉₁	C₄	1	2	yes	—
6	C₂²×C₄×C₄₉₁	C₂²	1	1	yes	characteristic
7	M₁₆×C₄₉₁	C₄	1	8	yes	direct product factor
8	C₂×C₈×C₄₉₁	C₂²	1	4	yes	—
9	C₄²×C₄₉₁	C₄	1	2	yes	—
10	C₄²×C₄₉₁	C₂²	1	1	yes	characteristic
11	C₄²×C₄₉₁	C₂²	1	1	yes	characteristic
12	C₂³×C₄₉₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₄₉₁	—	2	4	no	—
14	C₂×C₄×C₄₉₁	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₄₉₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₄₉₁	C₂×C₄	1	4	yes	—
17	C₂×C₄×C₄₉₁	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₄₉₁	C₂³	1	1	yes	characteristic
19	C₈×C₄₉₁	C₂×C₄	1	8	yes	complemented
20	C₂²×C₄₉₁	—	2	2	no	—
21	C₂²×C₄₉₁	C₄²	1	2	yes	—
22	C₂²×C₄₉₁	C₂²×C₄	1	1	yes	characteristic
23	C₄×C₄₉₁	—	2	2	no	—
24	C₄×C₄₉₁	C₄²	1	2	yes	—
25	C₄×C₄₉₁	M₁₆	1	4	yes	direct product factor
26	C₄×C₄₉₁	C₂²×C₄	1	2	yes	—
27	C₂×C₄₉₁	—	2	2	no	—
28	C₂×C₄₉₁	C₂×C₄²	1	1	yes	characteristic
29	C₂×C₄₉₁	C₂×M₁₆	1	2	yes	—
30	C₄₉₁	C₄×M₁₆	1	1	yes	characteristic, direct product factor, Sylow
31	C₄×M₁₆	C₄₉₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂×M₁₆	C₂×C₄₉₁	1	2	yes	—
33	C₂×C₄²	C₂×C₄₉₁	1	1	yes	characteristic
34	#97	C₂×C₄₉₁	1	2	yes	complemented
35	C₄×C₈	C₂×C₄₉₁	1	2	yes	complemented
36	C₂²×C₄	C₄×C₄₉₁	1	2	yes	—
37	C₂²×C₄	C₂²×C₄₉₁	1	1	yes	characteristic
38	M₁₆	C₄×C₄₉₁	1	8	yes	direct product factor
39	C₂×C₈	C₂²×C₄₉₁	1	4	yes	—
40	C₄²	C₄×C₄₉₁	1	2	yes	—
41	C₄²	C₂²×C₄₉₁	1	1	yes	characteristic
42	C₄²	C₂²×C₄₉₁	1	1	yes	characteristic
43	C₂³	C₂×C₄×C₄₉₁	1	1	yes	characteristic
44	C₂×C₄	—	2	4	no	—
45	C₂×C₄	C₂×C₄×C₄₉₁	1	2	yes	—
46	C₂×C₄	C₂×C₄×C₄₉₁	1	4	yes	—
47	C₂×C₄	C₂×C₄×C₄₉₁	1	1	yes	characteristic
48	C₂×C₄	C₂×C₄×C₄₉₁	1	2	yes	—
49	C₂×C₄	C₂³×C₄₉₁	1	1	yes	characteristic
50	C₈	C₂×C₄×C₄₉₁	1	8	yes	complemented
51	C₂²	—	2	2	no	—
52	C₂²	C₄²×C₄₉₁	1	2	yes	—
53	C₂²	C₂²×C₄×C₄₉₁	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	C₄²×C₄₉₁	1	2	yes	—
56	C₄	M₁₆×C₄₉₁	1	4	yes	direct product factor
57	C₄	C₂²×C₄×C₄₉₁	1	2	yes	—
58	C₂	—	2	2	no	—
59	C₂	C₂×C₄²×C₄₉₁	1	1	yes	characteristic
60	C₂	C₂×M₁₆×C₄₉₁	1	2	yes	—

	subgroup	G/H
center	C₄²×C₄₉₁	C₂²
commutator	C₂	C₂×C₄²×C₄₉₁
Frattini, cosocle	C₂×C₄	C₂³×C₄₉₁
socle	C₂²×C₄₉₁	C₂²×C₄
prime radical	C₂³×C₄₉₁	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₄₉₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #97×C₄₉₁	C₂	semidirect
4. C₄×C₈×C₄₉₁	C₂	semidirect
7. M₁₆×C₄₉₁	C₄	direct (N × H)
19. C₈×C₄₉₁	C₂×C₄	semidirect
25. C₄×C₄₉₁	M₁₆	direct (N × H)
30. C₄₉₁	C₄×M₁₆	direct (N × H)
31. C₄×M₁₆	C₄₉₁	direct (N × H)
34. #97	C₂×C₄₉₁	semidirect
35. C₄×C₈	C₂×C₄₉₁	semidirect
38. M₁₆	C₄×C₄₉₁	direct (N × H)
50. C₈	C₂×C₄×C₄₉₁	semidirect
56. C₄	M₁₆×C₄₉₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₄₉₁	2
C₂×C₄²×C₄₉₁	2
#97×C₄₉₁	2
C₄×C₈×C₄₉₁	2
C₄×M₁₆	491

Subgroups — C4×M16×C491 #44536261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×M₁₆×C₄₉₁ #44536261