Subgroups — C₂⁶×#64408 #34032724

Order 18688.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×#64408	C₂	1	126	yes	maximal, direct product factor
2	C₂⁶×D₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂⁴×#64408	C₂²	1	2604	yes	direct product factor
4	C₂⁵×D₇₃	C₄	1	63	yes	complemented
5	C₂⁵×D₇₃	C₂²	1	63	yes	—
6	C₂⁶×C₇₃	C₄	1	1	yes	characteristic, complemented
7	C₂³×#64408	C₂³	1	11160	yes	direct product factor
8	C₂⁴×D₇₃	C₂×C₄	1	1953	yes	complemented
9	C₂⁴×D₇₃	C₂³	1	651	yes	—
10	C₂⁵×C₇₃	C₂×C₄	1	63	yes	complemented
11	C₂²×#64408	C₂⁴	1	10416	yes	direct product factor
12	C₂³×D₇₃	C₂²×C₄	1	9765	yes	complemented
13	C₂³×D₇₃	C₂⁴	1	1395	yes	—
14	C₂⁴×C₇₃	C₂²×C₄	1	651	yes	complemented
15	C₂³×C₇₃	C₂³×C₄	1	1395	yes	complemented
16	C₂²×D₇₃	C₂³×C₄	1	9765	yes	complemented
17	C₂²×D₇₃	C₂⁵	1	651	yes	—
18	C₂×#64408	C₂⁵	1	2016	yes	direct product factor
19	C₂²×C₇₃	C₂⁴×C₄	1	651	yes	complemented
20	C₂×D₇₃	C₂⁴×C₄	1	1953	yes	complemented
21	C₂×D₇₃	C₂⁶	1	63	yes	—
22	#64408	C₂⁶	1	64	yes	direct product factor
23	C₂⁶×C₄	—	73	1	no	maximal, Sylow
24	C₂×C₇₃	C₂⁵×C₄	1	63	yes	complemented
25	D₇₃	C₂⁵×C₄	1	63	yes	complemented
26	D₇₃	C₂⁷	1	1	yes	characteristic
27	C₂⁷	—	73	1	no	—
28	C₂⁵×C₄	—	73	126	no	—
29	C₇₃	C₂⁶×C₄	1	1	yes	characteristic, complemented, Sylow
30	C₂⁶	—	73	63	no	—
31	C₂⁶	—	73	63	no	—
32	C₂⁶	#64408	1	1	yes	characteristic, direct product factor
33	C₂⁴×C₄	—	73	2604	no	—
34	C₂⁵	—	73	651	no	—
35	C₂⁵	—	73	1953	no	—
36	C₂⁵	C₂×#64408	1	63	yes	direct product factor
37	C₂³×C₄	—	73	11160	no	—
38	C₂⁴	—	73	9765	no	—
39	C₂⁴	—	73	1395	no	—
40	C₂⁴	C₂²×#64408	1	651	yes	direct product factor
41	C₂²×C₄	—	73	10416	no	—
42	C₂³	—	73	651	no	—
43	C₂³	—	73	9765	no	—
44	C₂³	C₂³×#64408	1	1395	yes	direct product factor
45	C₂×C₄	—	73	2016	no	—
46	C₂²	—	73	63	no	—
47	C₂²	—	73	1953	no	—
48	C₂²	C₂⁴×#64408	1	651	yes	direct product factor
49	C₄	—	73	64	no	—
50	C₂	—	73	1	no	—
51	C₂	—	73	63	no	—
52	C₂	C₂⁵×#64408	1	63	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁶	#64408
commutator, hypocenter	C₇₃	C₂⁶×C₄
Frattini	C₁	G
Fitting, socle	C₂⁶×C₇₃	C₄
prime radical	C₂⁶×D₇₃	C₂
cosocle	D₇₃	C₂⁷
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
1. C₂⁵×#64408	C₂	direct (N × H)
3. C₂⁴×#64408	C₂²	direct (N × H)
4. C₂⁵×D₇₃	C₄	semidirect
6. C₂⁶×C₇₃	C₄	semidirect
7. C₂³×#64408	C₂³	direct (N × H)
8. C₂⁴×D₇₃	C₂×C₄	semidirect
10. C₂⁵×C₇₃	C₂×C₄	semidirect
11. C₂²×#64408	C₂⁴	direct (N × H)
12. C₂³×D₇₃	C₂²×C₄	semidirect
14. C₂⁴×C₇₃	C₂²×C₄	semidirect
15. C₂³×C₇₃	C₂³×C₄	semidirect
16. C₂²×D₇₃	C₂³×C₄	semidirect
18. C₂×#64408	C₂⁵	direct (N × H)
19. C₂²×C₇₃	C₂⁴×C₄	semidirect
20. C₂×D₇₃	C₂⁴×C₄	semidirect
22. #64408	C₂⁶	direct (N × H)
24. C₂×C₇₃	C₂⁵×C₄	semidirect
25. D₇₃	C₂⁵×C₄	semidirect
29. C₇₃	C₂⁶×C₄	semidirect
32. C₂⁶	#64408	direct (N × H)
36. C₂⁵	C₂×#64408	direct (N × H)
40. C₂⁴	C₂²×#64408	direct (N × H)
44. C₂³	C₂³×#64408	direct (N × H)
48. C₂²	C₂⁴×#64408	direct (N × H)
52. C₂	C₂⁵×#64408	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×#64408	2
C₂⁶×D₇₃	2
C₂⁶×C₄	73

Subgroups — C26×#64408 #34032724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×#64408 #34032724