Subgroups — C₂³×D₁₄₉₂ #37560244

Order 23872.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₃₇₃	C₂	1	2	yes	maximal, complemented
2	C₂²×D₁₄₉₂	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₄×C₃₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₃₇₃	—	2	16	no	—
5	C₂³×D₃₇₃	C₂²	1	28	yes	complemented
6	C₂×D₁₄₉₂	C₂²	1	112	yes	direct product factor
7	C₂⁴×C₃₇₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₃₇₃	C₂²	1	14	yes	complemented
9	C₂²×D₃₇₃	—	2	112	no	—
10	C₂²×D₃₇₃	C₂³	1	56	yes	complemented
11	D₁₄₉₂	C₂³	1	64	yes	direct product factor
12	C₂³×C₃₇₃	D₄	1	8	yes	complemented
13	C₂³×C₃₇₃	C₂³	1	7	yes	—
14	C₂×C₄×C₃₇₃	C₂³	1	28	yes	complemented
15	C₂²×C₃₇₃	C₂×D₄	1	28	yes	complemented
16	C₂²×C₃₇₃	C₂⁴	1	7	yes	—
17	C₂×D₃₇₃	—	2	112	no	—
18	C₂×D₃₇₃	C₂⁴	1	16	yes	complemented
19	C₄×C₃₇₃	C₂⁴	1	8	yes	complemented
20	C₂×C₃₇₃	C₂²×D₄	1	14	yes	complemented
21	C₂×C₃₇₃	C₂⁵	1	1	yes	characteristic
22	D₃₇₃	—	2	16	no	—
23	C₃₇₃	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
24	C₂³×D₄	—	373	1	no	maximal, Sylow
25	C₂⁵	—	373	2	no	—
26	C₂²×D₄	—	373	28	no	—
27	C₂³×C₄	D₃₇₃	1	1	yes	characteristic, complemented
28	C₂⁴	—	373	28	no	—
29	C₂⁴	—	746	16	no	—
30	C₂⁴	C₂×D₃₇₃	1	1	yes	characteristic
31	C₂×D₄	—	373	112	no	—
32	C₂²×C₄	C₂×D₃₇₃	1	14	yes	complemented
33	C₂³	—	373	56	no	—
34	C₂³	—	746	112	no	—
35	C₂³	D₁₄₉₂	1	8	yes	direct product factor
36	C₂³	C₂²×D₃₇₃	1	7	yes	—
37	D₄	—	373	64	no	—
38	C₂×C₄	C₂²×D₃₇₃	1	28	yes	complemented
39	C₂²	—	373	16	no	—
40	C₂²	—	746	112	no	—
41	C₂²	C₂×D₁₄₉₂	1	28	yes	direct product factor
42	C₂²	C₂³×D₃₇₃	1	7	yes	—
43	C₄	C₂³×D₃₇₃	1	8	yes	complemented
44	C₂	—	746	16	no	—
45	C₂	C₂²×D₁₄₉₂	1	14	yes	direct product factor
46	C₂	C₂⁴×D₃₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃₇₃
commutator, cosocle	C₂×C₃₇₃	C₂⁵
Frattini	C₂	C₂⁴×D₃₇₃
Fitting	C₂³×C₄×C₃₇₃	C₂
socle	C₂⁴×C₃₇₃	C₂²
hypercenter	C₂³×C₄	D₃₇₃
hypocenter	C₃₇₃	C₂³×D₄
LCS	G ▷ C₂×C₃₇₃ ▷ C₃₇₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₃₇₃	C₂	semidirect
2. C₂²×D₁₄₉₂	C₂	direct (N × H)
3. C₂³×C₄×C₃₇₃	C₂	semidirect
5. C₂³×D₃₇₃	C₂²	semidirect
6. C₂×D₁₄₉₂	C₂²	direct (N × H)
8. C₂²×C₄×C₃₇₃	C₂²	semidirect
10. C₂²×D₃₇₃	C₂³	semidirect
11. D₁₄₉₂	C₂³	direct (N × H)
12. C₂³×C₃₇₃	D₄	semidirect
14. C₂×C₄×C₃₇₃	C₂³	semidirect
15. C₂²×C₃₇₃	C₂×D₄	semidirect
18. C₂×D₃₇₃	C₂⁴	semidirect
19. C₄×C₃₇₃	C₂⁴	semidirect
20. C₂×C₃₇₃	C₂²×D₄	semidirect
23. C₃₇₃	C₂³×D₄	semidirect
27. C₂³×C₄	D₃₇₃	semidirect
32. C₂²×C₄	C₂×D₃₇₃	semidirect
35. C₂³	D₁₄₉₂	direct (N × H)
38. C₂×C₄	C₂²×D₃₇₃	semidirect
41. C₂²	C₂×D₁₄₉₂	direct (N × H)
43. C₄	C₂³×D₃₇₃	semidirect
45. C₂	C₂²×D₁₄₉₂	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×D₃₇₃	2
C₂²×D₁₄₉₂	2
C₂³×C₄×C₃₇₃	2
C₂³×D₄	373

Subgroups — C23×D1492 #37560244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×D₁₄₉₂ #37560244