Subgroups — C₂³×#11764049 #22578526

Order 8768.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11764049	C₂	1	14	yes	maximal, direct product factor
2	C₂³×#10587739	C₂	1	1	yes	maximal, characteristic
3	C₂×#11764049	C₂²	1	28	yes	direct product factor
4	C₂²×#10587739	C₄	1	7	yes	—
5	C₂²×#10587739	C₂²	1	7	yes	—
6	C₂³×D₁₃₇	C₄	1	1	yes	characteristic
7	#11764049	C₂³	1	8	yes	direct product factor
8	C₂×#10587739	C₂×C₄	1	21	yes	—
9	C₂×#10587739	C₂³	1	7	yes	—
10	C₂²×D₁₃₇	C₈	1	7	yes	complemented
11	C₂²×D₁₃₇	C₂×C₄	1	7	yes	—
12	C₂³×C₁₃₇	C₈	1	1	yes	characteristic, complemented
13	C₂²×C₁₃₇	C₂×C₈	1	7	yes	complemented
14	C₂×D₁₃₇	C₂×C₈	1	21	yes	complemented
15	C₂×D₁₃₇	C₂²×C₄	1	7	yes	—
16	#10587739	C₂²×C₄	1	7	yes	—
17	#10587739	C₂⁴	1	1	yes	characteristic
18	C₂×C₁₃₇	C₂²×C₈	1	7	yes	complemented
19	D₁₃₇	C₂²×C₈	1	7	yes	complemented
20	D₁₃₇	C₂³×C₄	1	1	yes	characteristic
21	C₁₃₇	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
22	C₂³×C₈	—	137	1	no	maximal, Sylow
23	C₂³×C₄	—	137	1	no	—
24	C₂²×C₈	—	137	14	no	—
25	C₂⁴	—	137	1	no	—
26	C₂²×C₄	—	137	7	no	—
27	C₂²×C₄	—	137	7	no	—
28	C₂×C₈	—	137	28	no	—
29	C₂³	—	137	7	no	—
30	C₂³	—	137	7	no	—
31	C₂³	#11764049	1	1	yes	characteristic, direct product factor
32	C₂×C₄	—	137	7	no	—
33	C₂×C₄	—	137	21	no	—
34	C₈	—	137	8	no	—
35	C₂²	—	137	7	no	—
36	C₂²	—	137	21	no	—
37	C₂²	C₂×#11764049	1	7	yes	direct product factor
38	C₄	—	137	1	no	—
39	C₄	—	137	7	no	—
40	C₂	—	137	1	no	—
41	C₂	—	137	7	no	—
42	C₂	C₂²×#11764049	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	#11764049
commutator, hypocenter	C₁₃₇	C₂³×C₈
Frattini	C₁	G
Fitting, socle	C₂³×C₁₃₇	C₈
LCS	G ▷ C₁₃₇
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂²×#11764049	C₂	direct (N × H)
3. C₂×#11764049	C₂²	direct (N × H)
7. #11764049	C₂³	direct (N × H)
10. C₂²×D₁₃₇	C₈	semidirect
12. C₂³×C₁₃₇	C₈	semidirect
13. C₂²×C₁₃₇	C₂×C₈	semidirect
14. C₂×D₁₃₇	C₂×C₈	semidirect
18. C₂×C₁₃₇	C₂²×C₈	semidirect
19. D₁₃₇	C₂²×C₈	semidirect
21. C₁₃₇	C₂³×C₈	semidirect
31. C₂³	#11764049	direct (N × H)
37. C₂²	C₂×#11764049	direct (N × H)
42. C₂	C₂²×#11764049	direct (N × H)

Subgroups — C23×#11764049 #22578526

Conjugacy classes of subgroups

Complements

Subgroups — C₂³×#11764049 #22578526