Subgroups — C₂⁴×#3624 #14545767

Order 2176.

1976 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#3624	C₂	1	30	yes	maximal, direct product factor
2	C₂⁴×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂⁵×C₁₇	C₄	1	1	yes	characteristic
4	C₂³×Dic₁₇	C₄	1	15	yes	—
5	C₂³×Dic₁₇	C₂²	1	15	yes	—
6	C₂²×#3624	C₂²	1	140	yes	direct product factor
7	C₂⁴×C₁₇	C₈	1	16	yes	complemented
8	C₂⁴×C₁₇	C₂×C₄	1	15	yes	—
9	C₂²×Dic₁₇	C₂×C₄	1	105	yes	—
10	C₂²×Dic₁₇	C₂³	1	35	yes	—
11	C₂×#3624	C₂³	1	120	yes	direct product factor
12	C₂³×C₁₇	C₂×C₈	1	120	yes	complemented
13	C₂³×C₁₇	C₂²×C₄	1	35	yes	—
14	C₂×Dic₁₇	C₂²×C₄	1	105	yes	—
15	C₂×Dic₁₇	C₂⁴	1	15	yes	—
16	#3624	C₂⁴	1	16	yes	direct product factor
17	C₂⁴×C₈	—	17	1	no	maximal, Sylow
18	C₂²×C₁₇	C₂²×C₈	1	140	yes	complemented
19	C₂²×C₁₇	C₂³×C₄	1	15	yes	—
20	Dic₁₇	C₂³×C₄	1	15	yes	—
21	Dic₁₇	C₂⁵	1	1	yes	characteristic
22	C₂⁴×C₄	—	17	1	no	—
23	C₂³×C₈	—	17	30	no	—
24	C₂×C₁₇	C₂³×C₈	1	30	yes	complemented
25	C₂×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
26	C₂⁵	#595	1	1	yes	characteristic
27	C₂³×C₄	—	17	15	no	—
28	C₂³×C₄	—	17	15	no	—
29	C₂²×C₈	—	17	140	no	—
30	C₁₇	C₂⁴×C₈	1	1	yes	characteristic, complemented, Sylow
31	C₂⁴	#3624	1	16	yes	direct product factor
32	C₂⁴	C₂×#595	1	15	yes	—
33	C₂²×C₄	—	17	105	no	—
34	C₂²×C₄	—	17	35	no	—
35	C₂×C₈	—	17	120	no	—
36	C₂³	C₂×#3624	1	120	yes	direct product factor
37	C₂³	C₂²×#595	1	35	yes	—
38	C₂×C₄	—	17	15	no	—
39	C₂×C₄	—	17	105	no	—
40	C₈	—	17	16	no	—
41	C₂²	C₂²×#3624	1	140	yes	direct product factor
42	C₂²	C₂³×#595	1	15	yes	—
43	C₄	—	17	1	no	—
44	C₄	—	17	15	no	—
45	C₂	C₂³×#3624	1	30	yes	direct product factor
46	C₂	C₂⁴×#595	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁵	#595
commutator, hypocenter	C₁₇	C₂⁴×C₈
Frattini	C₂	C₂⁴×#595
Fitting, socle, prime radical	C₂⁵×C₁₇	C₄
cosocle	Dic₁₇	C₂⁵
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂³×#3624	C₂	direct (N × H)
6. C₂²×#3624	C₂²	direct (N × H)
7. C₂⁴×C₁₇	C₈	semidirect
11. C₂×#3624	C₂³	direct (N × H)
12. C₂³×C₁₇	C₂×C₈	semidirect
16. #3624	C₂⁴	direct (N × H)
18. C₂²×C₁₇	C₂²×C₈	semidirect
24. C₂×C₁₇	C₂³×C₈	semidirect
30. C₁₇	C₂⁴×C₈	semidirect
31. C₂⁴	#3624	direct (N × H)
36. C₂³	C₂×#3624	direct (N × H)
41. C₂²	C₂²×#3624	direct (N × H)
45. C₂	C₂³×#3624	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×#3624	2
C₂⁴×Dic₁₇	2
C₂⁴×C₈	17

Subgroups — C24×#3624 #14545767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×#3624 #14545767