Subgroups — C₄³×D₁₇₃ #36355884

Order 22144.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₁₇₃	C₂	1	7	yes	maximal
2	C₄²×Dic₁₇₃	C₂	1	7	yes	maximal, complemented
3	C₄³×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₁₇₃	C₂²	1	7	yes	—
5	C₂×C₄×Dic₁₇₃	C₂²	1	21	yes	—
6	C₄²×D₁₇₃	C₄	1	56	yes	direct product factor
7	C₂×C₄²×C₁₇₃	C₂²	1	7	yes	—
8	C₂³×D₁₇₃	C₂³	1	1	yes	characteristic
9	C₂²×Dic₁₇₃	C₂³	1	7	yes	—
10	C₂×C₄×D₁₇₃	C₂×C₄	1	84	yes	—
11	C₄×Dic₁₇₃	C₂×C₄	1	84	yes	complemented
12	C₂²×C₄×C₁₇₃	C₂³	1	7	yes	—
13	C₄²×C₁₇₃	C₂×C₄	1	28	yes	complemented
14	C₂²×D₁₇₃	C₂²×C₄	1	14	yes	—
15	C₂×Dic₁₇₃	C₂²×C₄	1	42	yes	—
16	C₄×D₁₇₃	C₄²	1	112	yes	direct product factor
17	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
18	C₂×C₄×C₁₇₃	C₂²×C₄	1	42	yes	—
19	C₂²×C₁₇₃	C₂³×C₄	1	7	yes	—
20	C₂×D₁₇₃	C₂×C₄²	1	28	yes	—
21	C₄×C₁₇₃	C₂×C₄²	1	28	yes	complemented
22	Dic₁₇₃	C₂×C₄²	1	28	yes	complemented
23	C₂×C₁₇₃	C₂²×C₄²	1	7	yes	—
24	D₁₇₃	C₄³	1	8	yes	direct product factor
25	C₁₇₃	C₂×C₄³	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₄³	—	173	1	no	maximal, Sylow
27	C₂²×C₄²	—	173	7	no	—
28	C₄³	—	173	7	no	—
29	C₄³	D₁₇₃	1	1	yes	characteristic, direct product factor
30	C₂³×C₄	—	173	7	no	—
31	C₂×C₄²	—	173	21	no	—
32	C₂×C₄²	—	173	56	no	—
33	C₂×C₄²	C₂×D₁₇₃	1	7	yes	—
34	C₂⁴	—	173	1	no	—
35	C₂²×C₄	—	173	7	no	—
36	C₂²×C₄	—	173	84	no	—
37	C₂²×C₄	C₂²×D₁₇₃	1	7	yes	—
38	C₄²	—	173	84	no	—
39	C₄²	C₄×D₁₇₃	1	28	yes	direct product factor
40	C₂³	—	173	14	no	—
41	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
42	C₂×C₄	—	173	42	no	—
43	C₂×C₄	—	173	112	no	—
44	C₂×C₄	C₂×C₄×D₁₇₃	1	42	yes	—
45	C₂²	—	173	28	no	—
46	C₂²	C₂²×C₄×D₁₇₃	1	7	yes	—
47	C₄	—	173	28	no	—
48	C₄	C₄²×D₁₇₃	1	28	yes	direct product factor
49	C₂	—	173	8	no	—
50	C₂	C₂×C₄²×D₁₇₃	1	7	yes	—

	subgroup	G/H
center, hypercenter	C₄³	D₁₇₃
commutator, hypocenter	C₁₇₃	C₂×C₄³
Frattini	C₂³	C₂³×D₁₇₃
Fitting	C₄³×C₁₇₃	C₂
socle, cosocle	C₂³×C₁₇₃	C₂⁴
prime radical	C₂³×D₁₇₃	C₂³
LCS	G ▷ C₁₇₃
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. C₄²×Dic₁₇₃	C₂	semidirect
3. C₄³×C₁₇₃	C₂	semidirect
6. C₄²×D₁₇₃	C₄	direct (N × H)
11. C₄×Dic₁₇₃	C₂×C₄	semidirect
13. C₄²×C₁₇₃	C₂×C₄	semidirect
16. C₄×D₁₇₃	C₄²	direct (N × H)
21. C₄×C₁₇₃	C₂×C₄²	semidirect
22. Dic₁₇₃	C₂×C₄²	semidirect
24. D₁₇₃	C₄³	direct (N × H)
25. C₁₇₃	C₂×C₄³	semidirect
29. C₄³	D₁₇₃	direct (N × H)
39. C₄²	C₄×D₁₇₃	direct (N × H)
48. C₄	C₄²×D₁₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄²×D₁₇₃	2
C₄²×Dic₁₇₃	2
C₄³×C₁₇₃	2
C₂×C₄³	173

Subgroups — C43×D173 #36355884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×D₁₇₃ #36355884