Subgroups — C₂³×#6092 #13131795

Order 1664.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#1055	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6092	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₄×C₁₃	C₄	1	1	yes	characteristic
4	C₂²×#1055	C₄	1	7	yes	—
5	C₂²×#1055	C₂²	1	7	yes	—
6	C₂×#6092	C₂²	1	28	yes	direct product factor
7	C₂⁴×C₁₃	C₈	1	1	yes	characteristic
8	C₂²×C₄×C₁₃	C₈	1	7	yes	—
9	C₂²×C₄×C₁₃	C₂×C₄	1	7	yes	—
10	C₂×#1055	C₂×C₄	1	21	yes	—
11	C₂×#1055	C₂³	1	7	yes	—
12	#6092	C₂³	1	8	yes	direct product factor
13	C₂³×C₁₆	—	13	1	no	maximal, Sylow
14	C₂³×C₁₃	C₁₆	1	8	yes	complemented
15	C₂³×C₁₃	C₂×C₈	1	7	yes	—
16	C₂×C₄×C₁₃	C₂×C₈	1	21	yes	—
17	C₂×C₄×C₁₃	C₂²×C₄	1	7	yes	—
18	#1055	C₂²×C₄	1	7	yes	—
19	#1055	C₂⁴	1	1	yes	characteristic
20	C₂³×C₈	—	13	1	no	—
21	C₂²×C₁₆	—	13	14	no	—
22	C₂²×C₁₃	C₂×C₁₆	1	28	yes	complemented
23	C₂²×C₁₃	C₂²×C₈	1	7	yes	—
24	C₄×C₁₃	C₂²×C₈	1	7	yes	—
25	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
26	C₂³×C₄	#261	1	1	yes	characteristic
27	C₂²×C₈	—	13	7	no	—
28	C₂²×C₈	—	13	7	no	—
29	C₂×C₁₆	—	13	28	no	—
30	C₂×C₁₃	C₂²×C₁₆	1	14	yes	complemented
31	C₂×C₁₃	C₂³×C₈	1	1	yes	characteristic
32	C₂⁴	#1057	1	1	yes	characteristic
33	C₂²×C₄	#1057	1	7	yes	—
34	C₂²×C₄	C₂×#261	1	7	yes	—
35	C₂×C₈	—	13	7	no	—
36	C₂×C₈	—	13	21	no	—
37	C₁₆	—	13	8	no	—
38	C₁₃	C₂³×C₁₆	1	1	yes	characteristic, complemented, Sylow
39	C₂³	#6092	1	8	yes	direct product factor
40	C₂³	C₂×#1057	1	7	yes	—
41	C₂×C₄	C₂×#1057	1	21	yes	—
42	C₂×C₄	C₂²×#261	1	7	yes	—
43	C₈	—	13	1	no	—
44	C₈	—	13	7	no	—
45	C₂²	C₂×#6092	1	28	yes	direct product factor
46	C₂²	C₂²×#1057	1	7	yes	—
47	C₄	C₂²×#1057	1	7	yes	—
48	C₄	C₂³×#261	1	1	yes	characteristic
49	C₂	C₂²×#6092	1	14	yes	direct product factor
50	C₂	C₂³×#1057	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	#261
commutator, hypocenter	C₁₃	C₂³×C₁₆
Frattini	C₄	C₂³×#261
Fitting	C₂³×C₄×C₁₃	C₄
socle, prime radical	C₂⁴×C₁₃	C₈
cosocle	#1055	C₂⁴
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×#6092	C₂	direct (N × H)
6. C₂×#6092	C₂²	direct (N × H)
12. #6092	C₂³	direct (N × H)
14. C₂³×C₁₃	C₁₆	semidirect
22. C₂²×C₁₃	C₂×C₁₆	semidirect
30. C₂×C₁₃	C₂²×C₁₆	semidirect
38. C₁₃	C₂³×C₁₆	semidirect
39. C₂³	#6092	direct (N × H)
45. C₂²	C₂×#6092	direct (N × H)
49. C₂	C₂²×#6092	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×#1055	2
C₂²×#6092	2
C₂³×C₁₆	13

Subgroups — C23×#6092 #13131795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#6092 #13131795