Subgroups — C₂⁴×#64438 #18011579

Order 4736.

1976 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#64438	C₂	1	30	yes	maximal, direct product factor
2	C₂⁴×Dic₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#64438	C₂²	1	140	yes	direct product factor
4	C₂³×Dic₃₇	C₄	1	15	yes	—
5	C₂³×Dic₃₇	C₂²	1	15	yes	—
6	C₂⁵×C₃₇	C₄	1	1	yes	characteristic
7	C₂⁴×C₃₇	C₈	1	16	yes	complemented
8	C₂⁴×C₃₇	C₂×C₄	1	15	yes	—
9	C₂²×Dic₃₇	C₂×C₄	1	105	yes	—
10	C₂²×Dic₃₇	C₂³	1	35	yes	—
11	C₂×#64438	C₂³	1	120	yes	direct product factor
12	C₂³×C₃₇	C₂×C₈	1	120	yes	complemented
13	C₂³×C₃₇	C₂²×C₄	1	35	yes	—
14	C₂×Dic₃₇	C₂²×C₄	1	105	yes	—
15	C₂×Dic₃₇	C₂⁴	1	15	yes	—
16	#64438	C₂⁴	1	16	yes	direct product factor
17	C₂²×C₃₇	C₂²×C₈	1	140	yes	complemented
18	C₂²×C₃₇	C₂³×C₄	1	15	yes	—
19	Dic₃₇	C₂³×C₄	1	15	yes	—
20	Dic₃₇	C₂⁵	1	1	yes	characteristic
21	C₂⁴×C₈	—	37	1	no	maximal, Sylow
22	C₂×C₃₇	C₂³×C₈	1	30	yes	complemented
23	C₂×C₃₇	C₂⁴×C₄	1	1	yes	characteristic
24	C₂⁴×C₄	—	37	1	no	—
25	C₂³×C₈	—	37	30	no	—
26	C₃₇	C₂⁴×C₈	1	1	yes	characteristic, complemented, Sylow
27	C₂⁵	#3866	1	1	yes	characteristic
28	C₂³×C₄	—	37	15	no	—
29	C₂³×C₄	—	37	15	no	—
30	C₂²×C₈	—	37	140	no	—
31	C₂⁴	#64438	1	16	yes	direct product factor
32	C₂⁴	C₂×#3866	1	15	yes	—
33	C₂²×C₄	—	37	105	no	—
34	C₂²×C₄	—	37	35	no	—
35	C₂×C₈	—	37	120	no	—
36	C₂³	C₂×#64438	1	120	yes	direct product factor
37	C₂³	C₂²×#3866	1	35	yes	—
38	C₂×C₄	—	37	15	no	—
39	C₂×C₄	—	37	105	no	—
40	C₈	—	37	16	no	—
41	C₂²	C₂²×#64438	1	140	yes	direct product factor
42	C₂²	C₂³×#3866	1	15	yes	—
43	C₄	—	37	1	no	—
44	C₄	—	37	15	no	—
45	C₂	C₂³×#64438	1	30	yes	direct product factor
46	C₂	C₂⁴×#3866	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁵	#3866
commutator, hypocenter	C₃₇	C₂⁴×C₈
Frattini	C₂	C₂⁴×#3866
Fitting, socle, prime radical	C₂⁵×C₃₇	C₄
cosocle	Dic₃₇	C₂⁵
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂³×#64438	C₂	direct (N × H)
3. C₂²×#64438	C₂²	direct (N × H)
7. C₂⁴×C₃₇	C₈	semidirect
11. C₂×#64438	C₂³	direct (N × H)
12. C₂³×C₃₇	C₂×C₈	semidirect
16. #64438	C₂⁴	direct (N × H)
17. C₂²×C₃₇	C₂²×C₈	semidirect
22. C₂×C₃₇	C₂³×C₈	semidirect
26. C₃₇	C₂⁴×C₈	semidirect
31. C₂⁴	#64438	direct (N × H)
36. C₂³	C₂×#64438	direct (N × H)
41. C₂²	C₂²×#64438	direct (N × H)
45. C₂	C₂³×#64438	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#64438	2
C₂⁴×Dic₃₇	2
C₂⁴×C₈	37

Subgroups — C24×#64438 #18011579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×#64438 #18011579