Subgroups — C₂⁴×#13063443 #36370546

Order 22144.

1976 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#13063443	C₂	1	30	yes	maximal, direct product factor
2	C₂⁴×Dic₁₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13063443	C₂²	1	140	yes	direct product factor
4	C₂³×Dic₁₇₃	C₄	1	15	yes	—
5	C₂³×Dic₁₇₃	C₂²	1	15	yes	—
6	C₂⁵×C₁₇₃	C₄	1	1	yes	characteristic
7	C₂×#13063443	C₂³	1	120	yes	direct product factor
8	C₂²×Dic₁₇₃	C₂×C₄	1	105	yes	—
9	C₂²×Dic₁₇₃	C₂³	1	35	yes	—
10	C₂⁴×C₁₇₃	C₈	1	16	yes	complemented
11	C₂⁴×C₁₇₃	C₂×C₄	1	15	yes	—
12	#13063443	C₂⁴	1	16	yes	direct product factor
13	C₂×Dic₁₇₃	C₂²×C₄	1	105	yes	—
14	C₂×Dic₁₇₃	C₂⁴	1	15	yes	—
15	C₂³×C₁₇₃	C₂×C₈	1	120	yes	complemented
16	C₂³×C₁₇₃	C₂²×C₄	1	35	yes	—
17	C₂²×C₁₇₃	C₂²×C₈	1	140	yes	complemented
18	C₂²×C₁₇₃	C₂³×C₄	1	15	yes	—
19	Dic₁₇₃	C₂³×C₄	1	15	yes	—
20	Dic₁₇₃	C₂⁵	1	1	yes	characteristic
21	C₂×C₁₇₃	C₂³×C₈	1	30	yes	complemented
22	C₂×C₁₇₃	C₂⁴×C₄	1	1	yes	characteristic
23	C₁₇₃	C₂⁴×C₈	1	1	yes	characteristic, complemented, Sylow
24	C₂⁴×C₈	—	173	1	no	maximal, Sylow
25	C₂⁴×C₄	—	173	1	no	—
26	C₂³×C₈	—	173	30	no	—
27	C₂⁵	#10621924	1	1	yes	characteristic
28	C₂³×C₄	—	173	15	no	—
29	C₂³×C₄	—	173	15	no	—
30	C₂²×C₈	—	173	140	no	—
31	C₂⁴	#13063443	1	16	yes	direct product factor
32	C₂⁴	C₂×#10621924	1	15	yes	—
33	C₂²×C₄	—	173	105	no	—
34	C₂²×C₄	—	173	35	no	—
35	C₂×C₈	—	173	120	no	—
36	C₂³	C₂×#13063443	1	120	yes	direct product factor
37	C₂³	C₂²×#10621924	1	35	yes	—
38	C₂×C₄	—	173	105	no	—
39	C₂×C₄	—	173	15	no	—
40	C₈	—	173	16	no	—
41	C₂²	C₂²×#13063443	1	140	yes	direct product factor
42	C₂²	C₂³×#10621924	1	15	yes	—
43	C₄	—	173	1	no	—
44	C₄	—	173	15	no	—
45	C₂	C₂³×#13063443	1	30	yes	direct product factor
46	C₂	C₂⁴×#10621924	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁵	#10621924
commutator, hypocenter	C₁₇₃	C₂⁴×C₈
Frattini	C₂	C₂⁴×#10621924
Fitting, socle, prime radical	C₂⁵×C₁₇₃	C₄
cosocle	Dic₁₇₃	C₂⁵
LCS	G ▷ C₁₇₃
UCS	C₁ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂³×#13063443	C₂	direct (N × H)
3. C₂²×#13063443	C₂²	direct (N × H)
7. C₂×#13063443	C₂³	direct (N × H)
10. C₂⁴×C₁₇₃	C₈	semidirect
12. #13063443	C₂⁴	direct (N × H)
15. C₂³×C₁₇₃	C₂×C₈	semidirect
17. C₂²×C₁₇₃	C₂²×C₈	semidirect
21. C₂×C₁₇₃	C₂³×C₈	semidirect
23. C₁₇₃	C₂⁴×C₈	semidirect
31. C₂⁴	#13063443	direct (N × H)
36. C₂³	C₂×#13063443	direct (N × H)
41. C₂²	C₂²×#13063443	direct (N × H)
45. C₂	C₂³×#13063443	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#13063443	2
C₂⁴×Dic₁₇₃	2
C₂⁴×C₈	173

Subgroups — C24×#13063443 #36370546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×#13063443 #36370546