Subgroups — C₄²×#6090 #15777738

Order 3328.

558 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6090	C₂	1	6	yes	maximal
2	C₄²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×C₁₃	C₄	1	3	yes	—
4	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
5	C₄³×C₁₃	C₄	1	1	yes	characteristic
6	C₂²×#6090	C₂²	1	4	yes	—
7	C₄×#6090	C₄	1	24	yes	direct product factor
8	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
9	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
10	C₂×C₄²×C₁₃	C₈	1	4	yes	—
11	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
12	C₄×C₈×C₁₃	C₈	1	12	yes	—
13	C₄×C₈×C₁₃	C₂×C₄	1	12	yes	—
14	C₂×#6090	C₂×C₄	1	24	yes	—
15	C₄²×C₁₆	—	13	1	no	maximal, Sylow
16	C₂²×C₄×C₁₃	C₂×C₈	1	6	yes	—
17	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₃	C₄²	1	6	yes	—
19	C₂×C₈×C₁₃	C₂×C₈	1	12	yes	—
20	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
21	C₄²×C₁₃	C₁₆	1	16	yes	complemented
22	C₄²×C₁₃	C₄²	1	6	yes	—
23	C₄²×C₁₃	C₂×C₈	1	6	yes	—
24	#6090	C₄²	1	16	yes	direct product factor
25	C₂×C₄×C₁₆	—	13	6	no	—
26	C₄²×C₈	D₁₃	1	1	yes	characteristic
27	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
28	C₂×C₄×C₁₃	C₄×C₈	1	12	yes	—
29	C₂×C₄×C₁₃	C₂×C₁₆	1	24	yes	—
30	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
31	C₂×C₄×C₁₃	C₂²×C₈	1	3	yes	—
32	C₈×C₁₃	C₄×C₈	1	12	yes	—
33	C₈×C₁₃	C₂×C₄²	1	4	yes	—
34	C₂²×C₁₆	—	13	4	no	—
35	C₂×C₄×C₈	Dic₁₃	1	3	yes	—
36	C₂×C₄×C₈	C₂×D₁₃	1	3	yes	—
37	C₄³	Dic₁₃	1	1	yes	characteristic
38	C₄×C₁₆	—	13	24	no	—
39	C₂²×C₁₃	C₂×C₄×C₈	1	3	yes	—
40	C₂²×C₁₃	C₂²×C₁₆	1	4	yes	—
41	C₄×C₁₃	C₄×C₁₆	1	24	yes	complemented
42	C₄×C₁₃	C₄³	1	1	yes	characteristic
43	C₄×C₁₃	C₂×C₄×C₈	1	3	yes	—
44	C₂²×C₈	C₂×Dic₁₃	1	3	yes	—
45	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
46	C₂×C₄²	#1055	1	4	yes	—
47	C₂×C₄²	C₂×Dic₁₃	1	3	yes	—
48	C₂×C₁₆	—	13	24	no	—
49	C₄×C₈	#1055	1	12	yes	—
50	C₄×C₈	C₄×D₁₃	1	12	yes	—
51	C₂×C₁₃	C₄²×C₈	1	1	yes	characteristic
52	C₂×C₁₃	C₂×C₄×C₁₆	1	6	yes	—
53	C₂²×C₄	C₂×#1055	1	6	yes	—
54	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
55	C₂×C₈	C₂×#1055	1	12	yes	—
56	C₂×C₈	C₄×Dic₁₃	1	6	yes	—
57	C₂×C₈	C₂×C₄×D₁₃	1	6	yes	—
58	C₄²	#6090	1	16	yes	direct product factor
59	C₄²	C₂×#1055	1	6	yes	—
60	C₄²	C₄×Dic₁₃	1	6	yes	—
61	C₁₆	—	13	16	no	—
62	C₁₃	C₄²×C₁₆	1	1	yes	characteristic, complemented, Sylow
63	C₂³	C₂²×#1055	1	1	yes	characteristic
64	C₂×C₄	C₄×#1055	1	12	yes	—
65	C₂×C₄	C₂×#6090	1	24	yes	—
66	C₂×C₄	C₂²×#1055	1	3	yes	—
67	C₂×C₄	C₂×C₄×Dic₁₃	1	3	yes	—
68	C₈	C₄×#1055	1	12	yes	—
69	C₈	C₄²×D₁₃	1	4	yes	—
70	C₂²	C₂×C₄×#1055	1	3	yes	—
71	C₂²	C₂²×#6090	1	4	yes	—
72	C₄	C₄×#6090	1	24	yes	direct product factor
73	C₄	C₂×C₄×#1055	1	3	yes	—
74	C₄	C₄²×Dic₁₃	1	1	yes	characteristic
75	C₂	C₄²×#1055	1	1	yes	characteristic
76	C₂	C₂×C₄×#6090	1	6	yes	—

	subgroup	G/H
center, hypercenter	C₄²×C₈	D₁₃
commutator, hypocenter	C₁₃	C₄²×C₁₆
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₄²×C₈×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂²×C₈×C₁₃	C₂³
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
7. C₄×#6090	C₄	direct (N × H)
21. C₄²×C₁₃	C₁₆	semidirect
24. #6090	C₄²	direct (N × H)
41. C₄×C₁₃	C₄×C₁₆	semidirect
58. C₄²	#6090	direct (N × H)
62. C₁₃	C₄²×C₁₆	semidirect
72. C₄	C₄×#6090	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×C₄×#6090	2
C₄²×C₈×C₁₃	2
C₄²×C₁₆	13

Subgroups — C42×#6090 #15777738

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×#6090 #15777738