Subgroups — C₂²×C₁₁⋊C₅×ΓL(1,𝔽₃₂) #46802060

Order 34100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁⋊C₅×ΓL(1,𝔽₃₂)	C₂	1	3	yes	maximal, direct product factor
2	C₁₁⋊C₅×ΓL(1,𝔽₃₂)	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₁×ΓL(1,𝔽₃₂)	C₅	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃₁×C₁₁⋊C₅	C₅	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13133723	C₅	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13133722	C₅	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13133724	C₅	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13133721	C₅	1	1	yes	maximal, characteristic, complemented
9	C₂×#13133724	C₂×C₅	1	3	yes	complemented
10	C₂×#13133722	C₂×C₅	1	3	yes	complemented
11	C₂×#13133723	C₂×C₅	1	3	yes	complemented
12	C₂×#13133721	C₂×C₅	1	3	yes	complemented
13	C₂×C₃₁×C₁₁⋊C₅	C₂×C₅	1	3	yes	complemented
14	C₂×C₁₁×ΓL(1,𝔽₃₂)	C₂×C₅	1	3	yes	complemented
15	C₂²×C₅×ΓL(1,𝔽₃₂)	—	11	1	no	maximal, Hall
16	#13133724	C₂²×C₅	1	1	yes	characteristic, complemented
17	#13133723	C₂²×C₅	1	1	yes	characteristic, complemented
18	#13133722	C₂²×C₅	1	1	yes	characteristic, complemented
19	#13133721	C₂²×C₅	1	1	yes	characteristic, complemented
20	C₁₁×ΓL(1,𝔽₃₂)	C₂²×C₅	1	1	yes	characteristic, complemented
21	C₃₁×C₁₁⋊C₅	C₂²×C₅	1	1	yes	characteristic, complemented
22	C₂×C₅×ΓL(1,𝔽₃₂)	—	11	3	no	—
23	C₂²×C₁₁×C₃₁	C₅²	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₅×C₁₁⋊C₅	—	31	1	no	maximal, Hall
25	C₅×ΓL(1,𝔽₃₂)	—	11	1	no	Hall
26	C₂×C₁₁×C₃₁	C₂×C₅²	1	3	yes	complemented
27	C₂²×C₅×C₃₁	—	11	1	no	—
28	C₂²×ΓL(1,𝔽₃₂)	—	11	1	no	—
29	C₂²×ΓL(1,𝔽₃₂)	—	11	1	no	—
30	C₂²×ΓL(1,𝔽₃₂)	—	11	1	no	—
31	C₂²×ΓL(1,𝔽₃₂)	—	11	1	no	—
32	C₂²×ΓL(1,𝔽₃₂)	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
33	C₂×C₅×C₁₁⋊C₅	—	31	3	no	—
34	C₁₁×C₃₁	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
35	C₂×C₅×C₃₁	—	11	3	no	—
36	C₂×ΓL(1,𝔽₃₂)	—	11	3	no	—
37	C₂×ΓL(1,𝔽₃₂)	—	11	3	no	—
38	C₂×ΓL(1,𝔽₃₂)	—	11	3	no	—
39	C₂×ΓL(1,𝔽₃₂)	—	11	3	no	—
40	C₂×ΓL(1,𝔽₃₂)	C₂×C₁₁⋊C₅	1	3	yes	direct product factor
41	C₅×C₁₁⋊C₅	—	31	1	no	Hall
42	C₂²×C₅×C₁₁	—	31	1	no	—
43	C₂²×C₁₁⋊C₅	—	31	1	no	—
44	C₂²×C₁₁⋊C₅	—	31	1	no	—
45	C₂²×C₁₁⋊C₅	—	31	1	no	—
46	C₂²×C₁₁⋊C₅	—	31	1	no	—
47	C₂²×C₁₁⋊C₅	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor
48	C₅×C₃₁	—	11	1	no	—
49	ΓL(1,𝔽₃₂)	—	11	1	no	—
50	ΓL(1,𝔽₃₂)	—	11	1	no	—
51	ΓL(1,𝔽₃₂)	—	11	1	no	—
52	ΓL(1,𝔽₃₂)	—	11	1	no	—
53	ΓL(1,𝔽₃₂)	C₂²×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
54	C₂²×C₃₁	C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
55	C₂×C₅×C₁₁	—	31	3	no	—
56	C₂×C₁₁⋊C₅	—	31	3	no	—
57	C₂×C₁₁⋊C₅	—	31	3	no	—
58	C₂×C₁₁⋊C₅	—	31	3	no	—
59	C₂×C₁₁⋊C₅	—	31	3	no	—
60	C₂×C₁₁⋊C₅	C₂×ΓL(1,𝔽₃₂)	1	3	yes	direct product factor
61	C₂²×C₅²	—	341	1	no	Hall
62	C₂×C₃₁	C₂×C₅×C₁₁⋊C₅	1	3	yes	complemented
63	C₅×C₁₁	—	31	1	no	—
64	C₁₁⋊C₅	—	31	1	no	—
65	C₁₁⋊C₅	—	31	1	no	—
66	C₁₁⋊C₅	—	31	1	no	—
67	C₁₁⋊C₅	—	31	1	no	—
68	C₁₁⋊C₅	C₂²×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor
69	C₂×C₅²	—	341	3	no	—
70	C₂²×C₁₁	C₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
71	C₃₁	C₂²×C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
72	C₅²	—	341	1	no	Sylow
73	C₂×C₁₁	C₂×C₅×ΓL(1,𝔽₃₂)	1	3	yes	complemented
74	C₂²×C₅	—	11	1	no	—
75	C₂²×C₅	—	31	1	no	—
76	C₂²×C₅	—	341	1	no	—
77	C₂²×C₅	—	341	1	no	—
78	C₂²×C₅	—	341	1	no	—
79	C₂²×C₅	—	341	1	no	—
80	C₁₁	C₂²×C₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₅	—	11	3	no	—
82	C₂×C₅	—	31	3	no	—
83	C₂×C₅	—	341	3	no	—
84	C₂×C₅	—	341	3	no	—
85	C₂×C₅	—	341	3	no	—
86	C₂×C₅	—	341	3	no	—
87	C₅	—	11	1	no	—
88	C₅	—	31	1	no	—
89	C₅	—	341	1	no	—
90	C₅	—	341	1	no	—
91	C₅	—	341	1	no	—
92	C₅	—	341	1	no	—
93	C₂²	C₁₁⋊C₅×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow
94	C₂	C₂×C₁₁⋊C₅×ΓL(1,𝔽₃₂)	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	C₁₁⋊C₅×ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₁₁×C₃₁	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₂²×C₁₁×C₃₁	C₅²
LCS	G ▷ C₁₁×C₃₁
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁⋊C₅×ΓL(1,𝔽₃₂)	C₂	direct (N × H)
2. C₁₁⋊C₅×ΓL(1,𝔽₃₂)	C₂²	direct (N × H)
3. C₂²×C₁₁×ΓL(1,𝔽₃₂)	C₅	semidirect
4. C₂²×C₃₁×C₁₁⋊C₅	C₅	semidirect
5. C₂²×#13133723	C₅	semidirect
6. C₂²×#13133722	C₅	semidirect
7. C₂²×#13133724	C₅	semidirect
8. C₂²×#13133721	C₅	semidirect
9. C₂×#13133724	C₂×C₅	semidirect
10. C₂×#13133722	C₂×C₅	semidirect
11. C₂×#13133723	C₂×C₅	semidirect
12. C₂×#13133721	C₂×C₅	semidirect
13. C₂×C₃₁×C₁₁⋊C₅	C₂×C₅	semidirect
14. C₂×C₁₁×ΓL(1,𝔽₃₂)	C₂×C₅	semidirect
16. #13133724	C₂²×C₅	semidirect
17. #13133723	C₂²×C₅	semidirect
18. #13133722	C₂²×C₅	semidirect
19. #13133721	C₂²×C₅	semidirect
20. C₁₁×ΓL(1,𝔽₃₂)	C₂²×C₅	semidirect
21. C₃₁×C₁₁⋊C₅	C₂²×C₅	semidirect
23. C₂²×C₁₁×C₃₁	C₅²	semidirect
26. C₂×C₁₁×C₃₁	C₂×C₅²	semidirect
32. C₂²×ΓL(1,𝔽₃₂)	C₁₁⋊C₅	direct (N × H)
34. C₁₁×C₃₁	C₂²×C₅²	semidirect
40. C₂×ΓL(1,𝔽₃₂)	C₂×C₁₁⋊C₅	direct (N × H)
47. C₂²×C₁₁⋊C₅	ΓL(1,𝔽₃₂)	direct (N × H)
53. ΓL(1,𝔽₃₂)	C₂²×C₁₁⋊C₅	direct (N × H)
54. C₂²×C₃₁	C₅×C₁₁⋊C₅	semidirect
60. C₂×C₁₁⋊C₅	C₂×ΓL(1,𝔽₃₂)	direct (N × H)
62. C₂×C₃₁	C₂×C₅×C₁₁⋊C₅	semidirect
68. C₁₁⋊C₅	C₂²×ΓL(1,𝔽₃₂)	direct (N × H)
70. C₂²×C₁₁	C₅×ΓL(1,𝔽₃₂)	semidirect
71. C₃₁	C₂²×C₅×C₁₁⋊C₅	semidirect
73. C₂×C₁₁	C₂×C₅×ΓL(1,𝔽₃₂)	semidirect
80. C₁₁	C₂²×C₅×ΓL(1,𝔽₃₂)	semidirect
93. C₂²	C₁₁⋊C₅×ΓL(1,𝔽₃₂)	direct (N × H)
94. C₂	C₂×C₁₁⋊C₅×ΓL(1,𝔽₃₂)	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×C₁₁⋊C₅×ΓL(1,𝔽₃₂)	2
C₂²×C₁₁×ΓL(1,𝔽₃₂)	5
C₂²×C₃₁×C₁₁⋊C₅	5
C₂²×#13133723	5
C₂²×#13133722	5
C₂²×#13133724	5
C₂²×#13133721	5
C₂²×C₅×ΓL(1,𝔽₃₂)	11
C₂²×C₅×C₁₁⋊C₅	31

Subgroups — C22×C11⋊C5×ΓL(1,𝔽32) #46802060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁⋊C₅×ΓL(1,𝔽₃₂) #46802060