Subgroups — #41×D₁₁ #67041

Order 352.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	#4343	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#4341	C₂	1	3	yes	maximal, complemented
5	D₄×D₁₁	C₂	1	3	yes	maximal, complemented
6	#4339	C₂	1	3	yes	maximal, complemented
7	C₂×C₄×D₁₁	C₂	1	3	yes	maximal, complemented
8	C₂²×D₁₁	C₂²	1	3	yes	—
9	Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
10	D₄×C₁₁	C₂²	1	3	yes	complemented
11	C₂×C₄×C₁₁	C₂²	1	3	yes	complemented
12	C₂²⋊D₁₁	C₂²	1	6	yes	complemented
13	C₂×Dic₁₁	C₂²	1	3	yes	complemented
14	D₄₄	C₂²	1	3	yes	complemented
15	C₄×D₁₁	C₂²	1	1	yes	characteristic
16	C₄×D₁₁	C₂²	1	3	yes	—
17	C₄×D₁₁	C₂²	1	3	yes	complemented
18	C₄×D₁₁	C₂²	1	3	yes	complemented
19	Dic₂₂	C₂²	1	3	yes	complemented
20	C₂²×C₁₁	C₂³	1	3	yes	—
21	C₂×D₁₁	—	2	6	no	—
22	C₂×D₁₁	C₂³	1	3	yes	—
23	C₂×D₁₁	C₂³	1	1	yes	characteristic
24	C₄×C₁₁	C₂³	1	3	yes	—
25	C₄×C₁₁	C₂³	1	1	yes	characteristic
26	Dic₁₁	C₂³	1	3	yes	—
27	Dic₁₁	C₂³	1	1	yes	characteristic
28	C₂×#41	—	11	1	no	maximal, Sylow
29	C₂×C₁₁	—	2	3	no	—
30	C₂×C₁₁	C₂⁴	1	1	yes	characteristic
31	D₁₁	—	2	3	no	—
32	D₁₁	#41	1	2	yes	direct product factor
33	#41	—	11	1	no	—
34	#41	—	11	3	no	—
35	#41	—	11	3	no	—
36	#41	D₁₁	1	1	yes	characteristic, direct product factor
37	C₂×Q₈	—	11	1	no	—
38	C₂×D₄	—	11	3	no	—
39	C₂²×C₄	—	11	3	no	—
40	C₁₁	C₂×#41	1	1	yes	characteristic, complemented, Sylow
41	C₂³	—	11	3	no	—
42	Q₈	—	11	3	no	—
43	Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
44	D₄	—	11	6	no	—
45	D₄	—	11	3	no	—
46	D₄	C₂×D₁₁	1	3	yes	complemented
47	C₂×C₄	—	11	3	no	—
48	C₂×C₄	—	11	3	no	—
49	C₂×C₄	—	11	3	no	—
50	C₂×C₄	—	11	1	no	—
51	C₂×C₄	—	11	3	no	—
52	C₂×C₄	C₂×D₁₁	1	3	yes	complemented
53	C₂²	—	11	1	no	—
54	C₂²	—	11	3	no	—
55	C₂²	—	22	6	no	—
56	C₂²	C₂²×D₁₁	1	3	yes	—
57	C₄	—	11	1	no	—
58	C₄	—	11	3	no	—
59	C₄	C₂²×D₁₁	1	3	yes	—
60	C₄	C₂²×D₁₁	1	1	yes	characteristic
61	C₂	—	2	3	no	—
62	C₂	—	11	2	no	—
63	C₂	—	22	3	no	—
64	C₂	C₂³×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₁₁
commutator, socle, cosocle	C₂×C₁₁	C₂⁴
Frattini	C₂	C₂³×D₁₁
Fitting	C₁₁×#41	C₂
hypercenter	#41	D₁₁
hypocenter	C₁₁	C₂×#41
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. C₁₁×#41	C₂	semidirect
2. #4343	C₂	semidirect
3. Q₈×D₁₁	C₂	semidirect
4. #4341	C₂	semidirect
5. D₄×D₁₁	C₂	semidirect
6. #4339	C₂	semidirect
7. C₂×C₄×D₁₁	C₂	semidirect
9. Q₈×C₁₁	C₂²	semidirect
10. D₄×C₁₁	C₂²	semidirect
11. C₂×C₄×C₁₁	C₂²	semidirect
12. C₂²⋊D₁₁	C₂²	semidirect
13. C₂×Dic₁₁	C₂²	semidirect
14. D₄₄	C₂²	semidirect
17. C₄×D₁₁	C₂²	semidirect
18. C₄×D₁₁	C₂²	semidirect
19. Dic₂₂	C₂²	semidirect
32. D₁₁	#41	direct (N × H)
36. #41	D₁₁	direct (N × H)
40. C₁₁	C₂×#41	semidirect
43. Q₈	C₂×D₁₁	semidirect
46. D₄	C₂×D₁₁	semidirect
52. C₂×C₄	C₂×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#41	2
#4343	2
Q₈×D₁₁	2
#4341	2
D₄×D₁₁	2
#4339	2
C₂×C₄×D₁₁	2
C₂×#41	11

Subgroups — #41×D11 #67041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×D₁₁ #67041