Subgroups — C₂⁵×#3624 #17981046

Order 4352.

15454 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×#3624	C₂	1	62	yes	maximal, direct product factor
2	C₂⁵×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂³×#3624	C₂²	1	620	yes	direct product factor
4	C₂⁴×Dic₁₇	C₄	1	31	yes	—
5	C₂⁴×Dic₁₇	C₂²	1	31	yes	—
6	C₂⁶×C₁₇	C₄	1	1	yes	characteristic
7	C₂⁵×C₁₇	C₈	1	32	yes	complemented
8	C₂⁵×C₁₇	C₂×C₄	1	31	yes	—
9	C₂³×Dic₁₇	C₂×C₄	1	465	yes	—
10	C₂³×Dic₁₇	C₂³	1	155	yes	—
11	C₂²×#3624	C₂³	1	1240	yes	direct product factor
12	C₂⁴×C₁₇	C₂×C₈	1	496	yes	complemented
13	C₂⁴×C₁₇	C₂²×C₄	1	155	yes	—
14	C₂²×Dic₁₇	C₂²×C₄	1	1085	yes	—
15	C₂²×Dic₁₇	C₂⁴	1	155	yes	—
16	C₂×#3624	C₂⁴	1	496	yes	direct product factor
17	C₂⁵×C₈	—	17	1	no	maximal, Sylow
18	C₂³×C₁₇	C₂²×C₈	1	1240	yes	complemented
19	C₂³×C₁₇	C₂³×C₄	1	155	yes	—
20	C₂×Dic₁₇	C₂³×C₄	1	465	yes	—
21	C₂×Dic₁₇	C₂⁵	1	31	yes	—
22	#3624	C₂⁵	1	32	yes	direct product factor
23	C₂⁵×C₄	—	17	1	no	—
24	C₂⁴×C₈	—	17	62	no	—
25	C₂²×C₁₇	C₂³×C₈	1	620	yes	complemented
26	C₂²×C₁₇	C₂⁴×C₄	1	31	yes	—
27	Dic₁₇	C₂⁴×C₄	1	31	yes	—
28	Dic₁₇	C₂⁶	1	1	yes	characteristic
29	C₂⁶	#595	1	1	yes	characteristic
30	C₂⁴×C₄	—	17	31	no	—
31	C₂⁴×C₄	—	17	31	no	—
32	C₂³×C₈	—	17	620	no	—
33	C₂×C₁₇	C₂⁴×C₈	1	62	yes	complemented
34	C₂×C₁₇	C₂⁵×C₄	1	1	yes	characteristic
35	C₂⁵	#3624	1	32	yes	direct product factor
36	C₂⁵	C₂×#595	1	31	yes	—
37	C₂³×C₄	—	17	465	no	—
38	C₂³×C₄	—	17	155	no	—
39	C₂²×C₈	—	17	1240	no	—
40	C₁₇	C₂⁵×C₈	1	1	yes	characteristic, complemented, Sylow
41	C₂⁴	C₂×#3624	1	496	yes	direct product factor
42	C₂⁴	C₂²×#595	1	155	yes	—
43	C₂²×C₄	—	17	1085	no	—
44	C₂²×C₄	—	17	155	no	—
45	C₂×C₈	—	17	496	no	—
46	C₂³	C₂²×#3624	1	1240	yes	direct product factor
47	C₂³	C₂³×#595	1	155	yes	—
48	C₂×C₄	—	17	31	no	—
49	C₂×C₄	—	17	465	no	—
50	C₈	—	17	32	no	—
51	C₂²	C₂³×#3624	1	620	yes	direct product factor
52	C₂²	C₂⁴×#595	1	31	yes	—
53	C₄	—	17	1	no	—
54	C₄	—	17	31	no	—
55	C₂	C₂⁴×#3624	1	62	yes	direct product factor
56	C₂	C₂⁵×#595	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁶	#595
commutator, hypocenter	C₁₇	C₂⁵×C₈
Frattini	C₂	C₂⁵×#595
Fitting, socle, prime radical	C₂⁶×C₁₇	C₄
cosocle	Dic₁₇	C₂⁶
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁴×#3624	C₂	direct (N × H)
3. C₂³×#3624	C₂²	direct (N × H)
7. C₂⁵×C₁₇	C₈	semidirect
11. C₂²×#3624	C₂³	direct (N × H)
12. C₂⁴×C₁₇	C₂×C₈	semidirect
16. C₂×#3624	C₂⁴	direct (N × H)
18. C₂³×C₁₇	C₂²×C₈	semidirect
22. #3624	C₂⁵	direct (N × H)
25. C₂²×C₁₇	C₂³×C₈	semidirect
33. C₂×C₁₇	C₂⁴×C₈	semidirect
35. C₂⁵	#3624	direct (N × H)
40. C₁₇	C₂⁵×C₈	semidirect
41. C₂⁴	C₂×#3624	direct (N × H)
46. C₂³	C₂²×#3624	direct (N × H)
51. C₂²	C₂³×#3624	direct (N × H)
55. C₂	C₂⁴×#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
C₂⁴×#3624	2
C₂⁵×Dic₁₇	2
C₂⁵×C₈	17

Subgroups — C25×#3624 #17981046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×#3624 #17981046