Subgroups — C₂×C₄³×C₁₇₃ #36350050

Order 22144.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₁₇₃	C₂	1	7	yes	maximal
2	C₄³×C₁₇₃	C₂	1	8	yes	maximal, direct product factor
3	C₂³×C₄×C₁₇₃	C₂²	1	7	yes	—
4	C₂×C₄²×C₁₇₃	C₄	1	56	yes	direct product factor
5	C₂×C₄²×C₁₇₃	C₂²	1	28	yes	—
6	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic
7	C₂²×C₄×C₁₇₃	C₂×C₄	1	84	yes	—
8	C₂²×C₄×C₁₇₃	C₂³	1	14	yes	—
9	C₄²×C₁₇₃	C₂×C₄	1	112	yes	direct product factor
10	C₂³×C₁₇₃	C₂²×C₄	1	14	yes	—
11	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
12	C₂×C₄×C₁₇₃	C₄²	1	112	yes	direct product factor
13	C₂×C₄×C₁₇₃	C₂²×C₄	1	84	yes	—
14	C₂²×C₁₇₃	C₂×C₄²	1	28	yes	—
15	C₂²×C₁₇₃	C₂³×C₄	1	7	yes	—
16	C₄×C₁₇₃	C₂×C₄²	1	56	yes	direct product factor
17	C₂×C₁₇₃	C₄³	1	8	yes	direct product factor
18	C₂×C₁₇₃	C₂²×C₄²	1	7	yes	—
19	C₁₇₃	C₂×C₄³	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₄³	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₄²	C₂×C₁₇₃	1	7	yes	—
22	C₄³	C₂×C₁₇₃	1	8	yes	direct product factor
23	C₂³×C₄	C₂²×C₁₇₃	1	7	yes	—
24	C₂×C₄²	C₄×C₁₇₃	1	56	yes	direct product factor
25	C₂×C₄²	C₂²×C₁₇₃	1	28	yes	—
26	C₂⁴	C₂³×C₁₇₃	1	1	yes	characteristic
27	C₂²×C₄	C₂×C₄×C₁₇₃	1	84	yes	—
28	C₂²×C₄	C₂³×C₁₇₃	1	14	yes	—
29	C₄²	C₂×C₄×C₁₇₃	1	112	yes	direct product factor
30	C₂³	C₂²×C₄×C₁₇₃	1	14	yes	—
31	C₂³	C₂⁴×C₁₇₃	1	1	yes	characteristic
32	C₂×C₄	C₄²×C₁₇₃	1	112	yes	direct product factor
33	C₂×C₄	C₂²×C₄×C₁₇₃	1	84	yes	—
34	C₂²	C₂×C₄²×C₁₇₃	1	28	yes	—
35	C₂²	C₂³×C₄×C₁₇₃	1	7	yes	—
36	C₄	C₂×C₄²×C₁₇₃	1	56	yes	direct product factor
37	C₂	C₄³×C₁₇₃	1	8	yes	direct product factor
38	C₂	C₂²×C₄²×C₁₇₃	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³	C₂⁴×C₁₇₃
socle, prime radical	C₂⁴×C₁₇₃	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄³×C₁₇₃	C₂	direct (N × H)
4. C₂×C₄²×C₁₇₃	C₄	direct (N × H)
9. C₄²×C₁₇₃	C₂×C₄	direct (N × H)
12. C₂×C₄×C₁₇₃	C₄²	direct (N × H)
16. C₄×C₁₇₃	C₂×C₄²	direct (N × H)
17. C₂×C₁₇₃	C₄³	direct (N × H)
19. C₁₇₃	C₂×C₄³	direct (N × H)
20. C₂×C₄³	C₁₇₃	direct (N × H)
22. C₄³	C₂×C₁₇₃	direct (N × H)
24. C₂×C₄²	C₄×C₁₇₃	direct (N × H)
29. C₄²	C₂×C₄×C₁₇₃	direct (N × H)
32. C₂×C₄	C₄²×C₁₇₃	direct (N × H)
36. C₄	C₂×C₄²×C₁₇₃	direct (N × H)
37. C₂	C₄³×C₁₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄²×C₁₇₃	2
C₄³×C₁₇₃	2
C₂×C₄³	173

Subgroups — C2×C43×C173 #36350050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄³×C₁₇₃ #36350050