Subgroups — C₂⁵×#3866 #18011593

Order 4736.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×#3866	C₂	1	62	yes	maximal, direct product factor
2	C₂⁵×D₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂³×#3866	C₂²	1	620	yes	direct product factor
4	C₂⁴×D₃₇	C₄	1	31	yes	complemented
5	C₂⁴×D₃₇	C₂²	1	31	yes	—
6	C₂⁵×C₃₇	C₄	1	1	yes	characteristic, complemented
7	C₂⁴×C₃₇	C₂×C₄	1	31	yes	complemented
8	C₂³×D₃₇	C₂×C₄	1	465	yes	complemented
9	C₂³×D₃₇	C₂³	1	155	yes	—
10	C₂²×#3866	C₂³	1	1240	yes	direct product factor
11	C₂³×C₃₇	C₂²×C₄	1	155	yes	complemented
12	C₂²×D₃₇	C₂²×C₄	1	1085	yes	complemented
13	C₂²×D₃₇	C₂⁴	1	155	yes	—
14	C₂×#3866	C₂⁴	1	496	yes	direct product factor
15	C₂²×C₃₇	C₂³×C₄	1	155	yes	complemented
16	C₂×D₃₇	C₂³×C₄	1	465	yes	complemented
17	C₂×D₃₇	C₂⁵	1	31	yes	—
18	#3866	C₂⁵	1	32	yes	direct product factor
19	C₂⁵×C₄	—	37	1	no	maximal, Sylow
20	C₂×C₃₇	C₂⁴×C₄	1	31	yes	complemented
21	D₃₇	C₂⁴×C₄	1	31	yes	complemented
22	D₃₇	C₂⁶	1	1	yes	characteristic
23	C₂⁶	—	37	1	no	—
24	C₂⁴×C₄	—	37	62	no	—
25	C₃₇	C₂⁵×C₄	1	1	yes	characteristic, complemented, Sylow
26	C₂⁵	—	37	31	no	—
27	C₂⁵	—	37	31	no	—
28	C₂⁵	#3866	1	1	yes	characteristic, direct product factor
29	C₂³×C₄	—	37	620	no	—
30	C₂⁴	—	37	465	no	—
31	C₂⁴	—	37	155	no	—
32	C₂⁴	C₂×#3866	1	31	yes	direct product factor
33	C₂²×C₄	—	37	1240	no	—
34	C₂³	—	37	155	no	—
35	C₂³	—	37	1085	no	—
36	C₂³	C₂²×#3866	1	155	yes	direct product factor
37	C₂×C₄	—	37	496	no	—
38	C₂²	—	37	31	no	—
39	C₂²	—	37	465	no	—
40	C₂²	C₂³×#3866	1	155	yes	direct product factor
41	C₄	—	37	32	no	—
42	C₂	—	37	1	no	—
43	C₂	—	37	31	no	—
44	C₂	C₂⁴×#3866	1	31	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁵	#3866
commutator, hypocenter	C₃₇	C₂⁵×C₄
Frattini	C₁	G
Fitting, socle	C₂⁵×C₃₇	C₄
prime radical	C₂⁵×D₃₇	C₂
cosocle	D₃₇	C₂⁶
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂⁴×#3866	C₂	direct (N × H)
3. C₂³×#3866	C₂²	direct (N × H)
4. C₂⁴×D₃₇	C₄	semidirect
6. C₂⁵×C₃₇	C₄	semidirect
7. C₂⁴×C₃₇	C₂×C₄	semidirect
8. C₂³×D₃₇	C₂×C₄	semidirect
10. C₂²×#3866	C₂³	direct (N × H)
11. C₂³×C₃₇	C₂²×C₄	semidirect
12. C₂²×D₃₇	C₂²×C₄	semidirect
14. C₂×#3866	C₂⁴	direct (N × H)
15. C₂²×C₃₇	C₂³×C₄	semidirect
16. C₂×D₃₇	C₂³×C₄	semidirect
18. #3866	C₂⁵	direct (N × H)
20. C₂×C₃₇	C₂⁴×C₄	semidirect
21. D₃₇	C₂⁴×C₄	semidirect
25. C₃₇	C₂⁵×C₄	semidirect
28. C₂⁵	#3866	direct (N × H)
32. C₂⁴	C₂×#3866	direct (N × H)
36. C₂³	C₂²×#3866	direct (N × H)
40. C₂²	C₂³×#3866	direct (N × H)
44. C₂	C₂⁴×#3866	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×#3866	2
C₂⁵×D₃₇	2
C₂⁵×C₄	37

Subgroups — C25×#3866 #18011593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×#3866 #18011593