Subgroups — C₂⁴×#6092 #16809610

Order 3328.

2590 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6092	C₂	1	30	yes	maximal, direct product factor
2	C₂⁴×#1055	C₂	1	1	yes	maximal, characteristic
3	C₂⁴×C₄×C₁₃	C₄	1	1	yes	characteristic
4	C₂³×#1055	C₄	1	15	yes	—
5	C₂³×#1055	C₂²	1	15	yes	—
6	C₂²×#6092	C₂²	1	140	yes	direct product factor
7	C₂⁵×C₁₃	C₈	1	1	yes	characteristic
8	C₂³×C₄×C₁₃	C₈	1	15	yes	—
9	C₂³×C₄×C₁₃	C₂×C₄	1	15	yes	—
10	C₂²×#1055	C₂×C₄	1	105	yes	—
11	C₂²×#1055	C₂³	1	35	yes	—
12	C₂×#6092	C₂³	1	120	yes	direct product factor
13	C₂⁴×C₁₆	—	13	1	no	maximal, Sylow
14	C₂⁴×C₁₃	C₁₆	1	16	yes	complemented
15	C₂⁴×C₁₃	C₂×C₈	1	15	yes	—
16	C₂²×C₄×C₁₃	C₂×C₈	1	105	yes	—
17	C₂²×C₄×C₁₃	C₂²×C₄	1	35	yes	—
18	C₂×#1055	C₂²×C₄	1	105	yes	—
19	C₂×#1055	C₂⁴	1	15	yes	—
20	#6092	C₂⁴	1	16	yes	direct product factor
21	C₂⁴×C₈	—	13	1	no	—
22	C₂³×C₁₆	—	13	30	no	—
23	C₂³×C₁₃	C₂×C₁₆	1	120	yes	complemented
24	C₂³×C₁₃	C₂²×C₈	1	35	yes	—
25	C₂×C₄×C₁₃	C₂²×C₈	1	105	yes	—
26	C₂×C₄×C₁₃	C₂³×C₄	1	15	yes	—
27	#1055	C₂³×C₄	1	15	yes	—
28	#1055	C₂⁵	1	1	yes	characteristic
29	C₂⁴×C₄	#261	1	1	yes	characteristic
30	C₂³×C₈	—	13	15	no	—
31	C₂³×C₈	—	13	15	no	—
32	C₂²×C₁₆	—	13	140	no	—
33	C₂²×C₁₃	C₂²×C₁₆	1	140	yes	complemented
34	C₂²×C₁₃	C₂³×C₈	1	15	yes	—
35	C₄×C₁₃	C₂³×C₈	1	15	yes	—
36	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
37	C₂⁵	#1057	1	1	yes	characteristic
38	C₂³×C₄	#1057	1	15	yes	—
39	C₂³×C₄	C₂×#261	1	15	yes	—
40	C₂²×C₈	—	13	105	no	—
41	C₂²×C₈	—	13	35	no	—
42	C₂×C₁₆	—	13	120	no	—
43	C₂×C₁₃	C₂³×C₁₆	1	30	yes	complemented
44	C₂×C₁₃	C₂⁴×C₈	1	1	yes	characteristic
45	C₂⁴	#6092	1	16	yes	direct product factor
46	C₂⁴	C₂×#1057	1	15	yes	—
47	C₂²×C₄	C₂×#1057	1	105	yes	—
48	C₂²×C₄	C₂²×#261	1	35	yes	—
49	C₂×C₈	—	13	15	no	—
50	C₂×C₈	—	13	105	no	—
51	C₁₆	—	13	16	no	—
52	C₁₃	C₂⁴×C₁₆	1	1	yes	characteristic, complemented, Sylow
53	C₂³	C₂×#6092	1	120	yes	direct product factor
54	C₂³	C₂²×#1057	1	35	yes	—
55	C₂×C₄	C₂²×#1057	1	105	yes	—
56	C₂×C₄	C₂³×#261	1	15	yes	—
57	C₈	—	13	1	no	—
58	C₈	—	13	15	no	—
59	C₂²	C₂²×#6092	1	140	yes	direct product factor
60	C₂²	C₂³×#1057	1	15	yes	—
61	C₄	C₂³×#1057	1	15	yes	—
62	C₄	C₂⁴×#261	1	1	yes	characteristic
63	C₂	C₂³×#6092	1	30	yes	direct product factor
64	C₂	C₂⁴×#1057	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₄	#261
commutator, hypocenter	C₁₃	C₂⁴×C₁₆
Frattini	C₄	C₂⁴×#261
Fitting	C₂⁴×C₄×C₁₃	C₄
socle, prime radical	C₂⁵×C₁₃	C₈
cosocle	#1055	C₂⁵
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#6092	C₂	direct (N × H)
6. C₂²×#6092	C₂²	direct (N × H)
12. C₂×#6092	C₂³	direct (N × H)
14. C₂⁴×C₁₃	C₁₆	semidirect
20. #6092	C₂⁴	direct (N × H)
23. C₂³×C₁₃	C₂×C₁₆	semidirect
33. C₂²×C₁₃	C₂²×C₁₆	semidirect
43. C₂×C₁₃	C₂³×C₁₆	semidirect
45. C₂⁴	#6092	direct (N × H)
52. C₁₃	C₂⁴×C₁₆	semidirect
53. C₂³	C₂×#6092	direct (N × H)
59. C₂²	C₂²×#6092	direct (N × H)
63. C₂	C₂³×#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×#6092	2
C₂⁴×#1055	2
C₂⁴×C₁₆	13

Subgroups — C24×#6092 #16809610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×#6092 #16809610