Subgroups — C₂⁴×C₄×Dic₁₇ #17940873

Order 4352.

24030 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×Dic₁₇	C₂	1	2	yes	maximal
2	C₂³×C₄×Dic₁₇	C₂	1	60	yes	maximal, direct product factor
3	C₂⁵×C₄×C₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂⁴×Dic₁₇	C₄	1	64	yes	direct product factor
5	C₂⁴×Dic₁₇	C₂²	1	60	yes	—
6	C₂²×C₄×Dic₁₇	C₂²	1	560	yes	direct product factor
7	C₂⁶×C₁₇	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₇	C₄	1	32	yes	complemented
9	C₂⁴×C₄×C₁₇	C₂²	1	30	yes	—
10	C₂⁵×C₁₇	C₂×C₄	1	32	yes	—
11	C₂⁵×C₁₇	C₂×C₄	1	16	yes	—
12	C₂⁵×C₁₇	C₂³	1	15	yes	—
13	C₂³×C₄×C₁₇	C₂×C₄	1	480	yes	complemented
14	C₂³×C₄×C₁₇	C₂³	1	140	yes	—
15	C₂³×Dic₁₇	C₂×C₄	1	960	yes	direct product factor
16	C₂³×Dic₁₇	C₂³	1	280	yes	—
17	C₂×C₄×Dic₁₇	C₂³	1	960	yes	direct product factor
18	C₂⁴×C₁₇	C₄²	1	256	yes	complemented
19	C₂⁴×C₁₇	C₂²×C₄	1	240	yes	—
20	C₂⁴×C₁₇	C₂²×C₄	1	120	yes	—
21	C₂⁴×C₁₇	C₂⁴	1	35	yes	—
22	C₂²×C₄×C₁₇	C₂²×C₄	1	1120	yes	complemented
23	C₂²×C₄×C₁₇	C₂⁴	1	120	yes	—
24	C₂²×Dic₁₇	C₂²×C₄	1	2240	yes	direct product factor
25	C₂²×Dic₁₇	C₂⁴	1	240	yes	—
26	C₄×Dic₁₇	C₂⁴	1	256	yes	direct product factor
27	C₂⁴×C₄²	—	17	1	no	maximal, Sylow
28	C₂³×C₁₇	C₂×C₄²	1	960	yes	complemented
29	C₂³×C₁₇	C₂³×C₄	1	280	yes	—
30	C₂³×C₁₇	C₂³×C₄	1	140	yes	—
31	C₂³×C₁₇	C₂⁵	1	15	yes	—
32	C₂×C₄×C₁₇	C₂³×C₄	1	480	yes	complemented
33	C₂×C₄×C₁₇	C₂⁵	1	16	yes	—
34	C₂×Dic₁₇	C₂³×C₄	1	960	yes	direct product factor
35	C₂×Dic₁₇	C₂⁵	1	32	yes	—
36	C₂⁵×C₄	—	17	2	no	—
37	C₂⁵×C₄	D₁₇	1	1	yes	characteristic
38	C₂³×C₄²	—	17	60	no	—
39	C₂²×C₁₇	C₂²×C₄²	1	560	yes	complemented
40	C₂²×C₁₇	C₂⁴×C₄	1	60	yes	—
41	C₂²×C₁₇	C₂⁴×C₄	1	30	yes	—
42	C₂²×C₁₇	C₂⁶	1	1	yes	characteristic
43	C₄×C₁₇	C₂⁴×C₄	1	32	yes	complemented
44	Dic₁₇	C₂⁴×C₄	1	64	yes	direct product factor
45	C₂⁶	C₂×D₁₇	1	1	yes	characteristic
46	C₂⁴×C₄	—	17	64	no	—
47	C₂⁴×C₄	—	17	60	no	—
48	C₂⁴×C₄	Dic₁₇	1	32	yes	direct product factor
49	C₂⁴×C₄	C₂×D₁₇	1	30	yes	—
50	C₂²×C₄²	—	17	560	no	—
51	C₂×C₁₇	C₂³×C₄²	1	60	yes	complemented
52	C₂×C₁₇	C₂⁵×C₄	1	2	yes	—
53	C₂×C₁₇	C₂⁵×C₄	1	1	yes	characteristic
54	C₂⁵	C₄×D₁₇	1	32	yes	—
55	C₂⁵	C₂×Dic₁₇	1	16	yes	—
56	C₂⁵	C₂²×D₁₇	1	15	yes	—
57	C₂³×C₄	—	17	960	no	—
58	C₂³×C₄	—	17	280	no	—
59	C₂³×C₄	C₂×Dic₁₇	1	480	yes	direct product factor
60	C₂³×C₄	C₂²×D₁₇	1	140	yes	—
61	C₂×C₄²	—	17	960	no	—
62	C₁₇	C₂⁴×C₄²	1	1	yes	characteristic, complemented, Sylow
63	C₂⁴	C₄×Dic₁₇	1	256	yes	direct product factor
64	C₂⁴	C₂×C₄×D₁₇	1	240	yes	—
65	C₂⁴	C₂²×Dic₁₇	1	120	yes	—
66	C₂⁴	C₂³×D₁₇	1	35	yes	—
67	C₂²×C₄	—	17	2240	no	—
68	C₂²×C₄	—	17	240	no	—
69	C₂²×C₄	C₂²×Dic₁₇	1	1120	yes	direct product factor
70	C₂²×C₄	C₂³×D₁₇	1	120	yes	—
71	C₄²	—	17	256	no	—
72	C₂³	C₂×C₄×Dic₁₇	1	960	yes	direct product factor
73	C₂³	C₂²×C₄×D₁₇	1	280	yes	—
74	C₂³	C₂³×Dic₁₇	1	140	yes	—
75	C₂³	C₂⁴×D₁₇	1	15	yes	—
76	C₂×C₄	—	17	960	no	—
77	C₂×C₄	—	17	32	no	—
78	C₂×C₄	C₂³×Dic₁₇	1	480	yes	direct product factor
79	C₂×C₄	C₂⁴×D₁₇	1	16	yes	—
80	C₂²	C₂²×C₄×Dic₁₇	1	560	yes	direct product factor
81	C₂²	C₂³×C₄×D₁₇	1	60	yes	—
82	C₂²	C₂⁴×Dic₁₇	1	30	yes	—
83	C₂²	C₂⁵×D₁₇	1	1	yes	characteristic
84	C₄	—	17	64	no	—
85	C₄	C₂⁴×Dic₁₇	1	32	yes	direct product factor
86	C₂	C₂³×C₄×Dic₁₇	1	60	yes	direct product factor
87	C₂	C₂⁴×C₄×D₁₇	1	2	yes	—
88	C₂	C₂⁵×Dic₁₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁵×C₄	D₁₇
commutator, hypocenter	C₁₇	C₂⁴×C₄²
Frattini	C₂²	C₂⁵×D₁₇
Fitting	C₂⁵×C₄×C₁₇	C₂
socle, prime radical	C₂⁶×C₁₇	C₂²
cosocle	C₂²×C₁₇	C₂⁶
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄×Dic₁₇	C₂	direct (N × H)
4. C₂⁴×Dic₁₇	C₄	direct (N × H)
6. C₂²×C₄×Dic₁₇	C₂²	direct (N × H)
8. C₂⁴×C₄×C₁₇	C₄	semidirect
13. C₂³×C₄×C₁₇	C₂×C₄	semidirect
15. C₂³×Dic₁₇	C₂×C₄	direct (N × H)
17. C₂×C₄×Dic₁₇	C₂³	direct (N × H)
18. C₂⁴×C₁₇	C₄²	semidirect
22. C₂²×C₄×C₁₇	C₂²×C₄	semidirect
24. C₂²×Dic₁₇	C₂²×C₄	direct (N × H)
26. C₄×Dic₁₇	C₂⁴	direct (N × H)
28. C₂³×C₁₇	C₂×C₄²	semidirect
32. C₂×C₄×C₁₇	C₂³×C₄	semidirect
34. C₂×Dic₁₇	C₂³×C₄	direct (N × H)
39. C₂²×C₁₇	C₂²×C₄²	semidirect
43. C₄×C₁₇	C₂⁴×C₄	semidirect
44. Dic₁₇	C₂⁴×C₄	direct (N × H)
48. C₂⁴×C₄	Dic₁₇	direct (N × H)
51. C₂×C₁₇	C₂³×C₄²	semidirect
59. C₂³×C₄	C₂×Dic₁₇	direct (N × H)
62. C₁₇	C₂⁴×C₄²	semidirect
63. C₂⁴	C₄×Dic₁₇	direct (N × H)
69. C₂²×C₄	C₂²×Dic₁₇	direct (N × H)
72. C₂³	C₂×C₄×Dic₁₇	direct (N × H)
78. C₂×C₄	C₂³×Dic₁₇	direct (N × H)
80. C₂²	C₂²×C₄×Dic₁₇	direct (N × H)
85. C₄	C₂⁴×Dic₁₇	direct (N × H)
86. C₂	C₂³×C₄×Dic₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×Dic₁₇	2
C₂³×C₄×Dic₁₇	2
C₂⁵×C₄×C₁₇	2
C₂⁴×C₄²	17

Subgroups — C24×C4×Dic17 #17940873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₄×Dic₁₇ #17940873