Subgroups — #442×C₁₃₁ #22552886

Order 8384.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₄×D₄×C₁₃₁	C₂	1	2	yes	maximal, complemented
3	#106×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#102×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#97×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₁₃₁	C₂²	1	2	yes	—
7	C₂²×C₄×C₁₃₁	—	2	2	no	—
8	D₈×C₁₃₁	C₄	1	4	yes	complemented
9	C₂×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₁₃₁	C₂²	1	2	yes	—
12	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
13	C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂³×C₁₃₁	—	2	2	no	—
15	D₄×C₁₃₁	—	2	2	no	—
16	D₄×C₁₃₁	C₂×C₄	1	4	yes	complemented
17	C₂×C₄×C₁₃₁	—	2	2	no	—
18	C₂×C₄×C₁₃₁	—	4	4	no	—
19	C₂×C₄×C₁₃₁	D₄	1	2	yes	—
20	C₂×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
21	C₈×C₁₃₁	—	2	1	no	—
22	C₈×C₁₃₁	C₂×C₄	1	2	yes	complemented
23	C₂²×C₁₃₁	—	2	4	no	—
24	C₂²×C₁₃₁	—	4	2	no	—
25	C₂²×C₁₃₁	—	4	2	no	—
26	C₂²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
27	C₄×C₁₃₁	—	2	2	no	—
28	C₄×C₁₃₁	—	4	2	no	—
29	C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₁₃₁	#41	1	1	yes	characteristic
31	C₂×C₁₃₁	—	4	4	no	—
32	C₂×C₁₃₁	C₄×D₄	1	1	yes	characteristic
33	C₂×C₁₃₁	AGL(1,ℤ/8)	1	2	yes	—
34	C₁₃₁	#442	1	1	yes	characteristic, direct product factor, Sylow
35	#442	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂×D₈	C₂×C₁₃₁	1	1	yes	characteristic
37	C₄×D₄	C₂×C₁₃₁	1	2	yes	complemented
38	#106	C₂×C₁₃₁	1	1	yes	characteristic, complemented
39	#102	C₂×C₁₃₁	1	2	yes	complemented
40	#97	C₂×C₁₃₁	1	1	yes	characteristic, complemented
41	C₂×D₄	C₂²×C₁₃₁	1	2	yes	—
42	C₂²×C₄	—	2	2	no	—
43	D₈	C₄×C₁₃₁	1	4	yes	complemented
44	C₂×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
45	C₂×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
46	C₄⋊C₄	C₂²×C₁₃₁	1	2	yes	—
47	C₂²⋊C₄	—	2	2	no	—
48	C₄²	C₂²×C₁₃₁	1	1	yes	characteristic
49	C₂³	—	2	2	no	—
50	D₄	—	2	2	no	—
51	D₄	C₂×C₄×C₁₃₁	1	4	yes	complemented
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	4	4	no	—
54	C₂×C₄	D₄×C₁₃₁	1	2	yes	—
55	C₂×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	C₂×C₄×C₁₃₁	1	2	yes	complemented
58	C₂²	—	2	4	no	—
59	C₂²	—	4	2	no	—
60	C₂²	—	4	2	no	—
61	C₂²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
62	C₄	—	2	2	no	—
63	C₄	—	4	2	no	—
64	C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
65	C₄	#41×C₁₃₁	1	1	yes	characteristic
66	C₂	—	4	4	no	—
67	C₂	C₄×D₄×C₁₃₁	1	1	yes	characteristic
68	C₂	AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂×D₄
commutator	C₄	C₂²×C₄×C₁₃₁
Frattini, cosocle	C₂×C₄	C₂³×C₁₃₁
prime radical	C₂×D₈×C₁₃₁	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×D₄×C₁₃₁	C₂	semidirect
3. #106×C₁₃₁	C₂	semidirect
4. #102×C₁₃₁	C₂	semidirect
5. #97×C₁₃₁	C₂	semidirect
8. D₈×C₁₃₁	C₄	semidirect
16. D₄×C₁₃₁	C₂×C₄	semidirect
22. C₈×C₁₃₁	C₂×C₄	semidirect
34. C₁₃₁	#442	direct (N × H)
35. #442	C₁₃₁	direct (N × H)
37. C₄×D₄	C₂×C₁₃₁	semidirect
38. #106	C₂×C₁₃₁	semidirect
39. #102	C₂×C₁₃₁	semidirect
40. #97	C₂×C₁₃₁	semidirect
43. D₈	C₄×C₁₃₁	semidirect
51. D₄	C₂×C₄×C₁₃₁	semidirect
57. C₈	C₂×C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₈×C₁₃₁	2
C₄×D₄×C₁₃₁	2
#106×C₁₃₁	2
#102×C₁₃₁	2
#97×C₁₃₁	2
#442	131

Subgroups — #442×C131 #22552886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #442×C₁₃₁ #22552886