Subgroups — D₁₁×D₇₃₇ #44569845

Order 32428.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₁₁×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₇₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁⋊D₇₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁²×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₇₃₇	—	11	1	no	maximal
6	D₁₁×D₆₇	—	11	1	no	maximal
7	C₂×C₁₁×C₆₇	—	11	1	no	—
8	D₇₃₇	—	11	1	no	—
9	D₇₃₇	—	11	1	no	—
10	D₇₃₇	—	22	5	no	—
11	D₇₃₇	D₁₁	1	1	yes	characteristic, direct product factor
12	C₁₁×D₆₇	—	11	1	no	—
13	D₁₁×C₆₇	D₁₁	1	1	yes	characteristic, complemented
14	C₁₁×C₆₇	—	2	5	no	—
15	C₁₁×C₆₇	C₂×D₁₁	1	1	yes	characteristic, complemented
16	C₁₁×C₆₇	C₂×D₁₁	1	1	yes	characteristic, complemented
17	D₁₁²	—	67	1	no	maximal, Hall
18	C₂×D₆₇	—	121	1	no	Hall
19	C₁₁⋊D₁₁	—	67	1	no	—
20	C₁₁×D₁₁	—	67	1	no	—
21	C₁₁×D₁₁	D₆₇	1	1	yes	characteristic, complemented
22	C₂×C₆₇	—	11	1	no	—
23	D₆₇	—	11	1	no	—
24	D₆₇	—	121	1	no	—
25	C₁₁²	C₂×D₆₇	1	1	yes	characteristic, complemented, Sylow
26	C₆₇	D₁₁²	1	1	yes	characteristic, complemented, Sylow
27	C₂×D₁₁	—	737	1	no	—
28	C₂×D₁₁	—	737	1	no	—
29	C₂×C₁₁	—	11	1	no	—
30	C₂×C₁₁	—	737	1	no	—
31	D₁₁	—	67	1	no	—
32	D₁₁	—	1474	5	no	—
33	D₁₁	—	737	1	no	—
34	D₁₁	—	737	1	no	—
35	D₁₁	D₇₃₇	1	1	yes	characteristic, direct product factor
36	C₁₁	—	2	5	no	—
37	C₁₁	D₁₁×D₆₇	1	1	yes	characteristic, complemented
38	C₁₁	C₂×D₇₃₇	1	1	yes	characteristic, complemented
39	C₂²	—	8107	1	no	Sylow
40	C₂	—	11	1	no	—
41	C₂	—	8107	1	no	—
42	C₂	—	737	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₆₇	C₂²
LCS	G ▷ C₁₁²×C₆₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₁₁×C₆₇	C₂	semidirect
2. C₁₁×D₇₃₇	C₂	semidirect
3. C₁₁⋊D₇₃₇	C₂	semidirect
4. C₁₁²×C₆₇	C₂²	semidirect
11. D₇₃₇	D₁₁	direct (N × H)
13. D₁₁×C₆₇	D₁₁	semidirect
15. C₁₁×C₆₇	C₂×D₁₁	semidirect
16. C₁₁×C₆₇	C₂×D₁₁	semidirect
21. C₁₁×D₁₁	D₆₇	semidirect
25. C₁₁²	C₂×D₆₇	semidirect
26. C₆₇	D₁₁²	semidirect
35. D₁₁	D₇₃₇	direct (N × H)
37. C₁₁	D₁₁×D₆₇	semidirect
38. C₁₁	C₂×D₇₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×D₁₁×C₆₇	2
C₁₁×D₇₃₇	2
C₁₁⋊D₇₃₇	2
C₂×D₇₃₇	11
D₁₁×D₆₇	11
D₁₁²	67

Subgroups — D11×D737 #44569845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×D₇₃₇ #44569845