Subgroups — C₂×#41×C₁₇₃ #19149581

Order 5536.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₁₇₃	C₂	1	8	yes	maximal, direct product factor
2	C₂×Q₈×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄×C₁₇₃	C₂	1	3	yes	maximal, complemented
4	C₂²×C₄×C₁₇₃	C₂	1	3	yes	maximal, complemented
5	C₂³×C₁₇₃	C₂²	1	3	yes	—
6	Q₈×C₁₇₃	C₂²	1	4	yes	complemented
7	D₄×C₁₇₃	C₂²	1	12	yes	complemented
8	C₂×C₄×C₁₇₃	C₂²	1	3	yes	—
9	C₂×C₄×C₁₇₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₇₃	C₂²	1	12	yes	complemented
11	C₂²×C₁₇₃	—	2	6	no	—
12	C₂²×C₁₇₃	C₂³	1	6	yes	—
13	C₂²×C₁₇₃	C₂³	1	1	yes	characteristic
14	C₄×C₁₇₃	C₂³	1	6	yes	—
15	C₄×C₁₇₃	C₂³	1	2	yes	—
16	C₂×C₁₇₃	—	2	6	no	—
17	C₂×C₁₇₃	#41	1	2	yes	direct product factor
18	C₂×C₁₇₃	C₂⁴	1	1	yes	characteristic
19	C₁₇₃	C₂×#41	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×#41	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	#41	C₂×C₁₇₃	1	8	yes	direct product factor
22	C₂×Q₈	C₂×C₁₇₃	1	1	yes	characteristic, complemented
23	C₂×D₄	C₂×C₁₇₃	1	3	yes	complemented
24	C₂²×C₄	C₂×C₁₇₃	1	3	yes	complemented
25	C₂³	C₂²×C₁₇₃	1	3	yes	—
26	Q₈	C₂²×C₁₇₃	1	4	yes	complemented
27	D₄	C₂²×C₁₇₃	1	12	yes	complemented
28	C₂×C₄	C₂²×C₁₇₃	1	3	yes	—
29	C₂×C₄	C₂²×C₁₇₃	1	1	yes	characteristic
30	C₂×C₄	C₂²×C₁₇₃	1	12	yes	complemented
31	C₂²	—	2	6	no	—
32	C₂²	C₂³×C₁₇₃	1	6	yes	—
33	C₂²	C₂³×C₁₇₃	1	1	yes	characteristic
34	C₄	C₂³×C₁₇₃	1	2	yes	—
35	C₄	C₂³×C₁₇₃	1	6	yes	—
36	C₂	—	2	6	no	—
37	C₂	#41×C₁₇₃	1	2	yes	direct product factor
38	C₂	C₂⁴×C₁₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇₃	C₂²
commutator, Frattini, cosocle	C₂	C₂⁴×C₁₇₃
socle	C₂²×C₁₇₃	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. #41×C₁₇₃	C₂	direct (N × H)
2. C₂×Q₈×C₁₇₃	C₂	semidirect
3. C₂×D₄×C₁₇₃	C₂	semidirect
4. C₂²×C₄×C₁₇₃	C₂	semidirect
6. Q₈×C₁₇₃	C₂²	semidirect
7. D₄×C₁₇₃	C₂²	semidirect
10. C₂×C₄×C₁₇₃	C₂²	semidirect
17. C₂×C₁₇₃	#41	direct (N × H)
19. C₁₇₃	C₂×#41	direct (N × H)
20. C₂×#41	C₁₇₃	direct (N × H)
21. #41	C₂×C₁₇₃	direct (N × H)
22. C₂×Q₈	C₂×C₁₇₃	semidirect
23. C₂×D₄	C₂×C₁₇₃	semidirect
24. C₂²×C₄	C₂×C₁₇₃	semidirect
26. Q₈	C₂²×C₁₇₃	semidirect
27. D₄	C₂²×C₁₇₃	semidirect
30. C₂×C₄	C₂²×C₁₇₃	semidirect
37. C₂	#41×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
#41×C₁₇₃	2
C₂×Q₈×C₁₇₃	2
C₂×D₄×C₁₇₃	2
C₂²×C₄×C₁₇₃	2
C₂×#41	173

Subgroups — C2×#41×C173 #19149581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#41×C₁₇₃ #19149581