Subgroups — C₄²×#6092 #16789010

Order 3328.

558 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6092	C₂	1	6	yes	maximal
2	C₄²×#1055	C₂	1	1	yes	maximal, characteristic
3	C₂²×#6092	C₂²	1	4	yes	—
4	C₄³×C₁₃	C₄	1	1	yes	characteristic
5	C₂×C₄×#1055	C₄	1	3	yes	—
6	C₂×C₄×#1055	C₂²	1	3	yes	—
7	C₄×#6092	C₄	1	24	yes	direct product factor
8	C₂×C₄²×C₁₃	C₈	1	4	yes	—
9	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
10	C₂²×#1055	C₂×C₄	1	3	yes	—
11	C₂²×#1055	C₂³	1	1	yes	characteristic
12	C₂×#6092	C₂×C₄	1	24	yes	—
13	C₄×#1055	C₈	1	12	yes	—
14	C₄×#1055	C₂×C₄	1	12	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	C₄²×C₁₃	C₁₆	1	16	yes	complemented
19	C₄²×C₁₃	C₄²	1	6	yes	—
20	C₄²×C₁₃	C₂×C₈	1	6	yes	—
21	C₂×#1055	C₄²	1	6	yes	—
22	C₂×#1055	C₂×C₈	1	12	yes	—
23	C₂×#1055	C₂²×C₄	1	6	yes	—
24	#6092	C₄²	1	16	yes	direct product factor
25	C₂×C₄×C₁₆	—	13	6	no	—
26	C₄²×C₈	—	13	1	no	—
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	#1055	C₄×C₈	1	12	yes	—
33	#1055	C₂×C₄²	1	4	yes	—
34	C₂²×C₁₆	—	13	4	no	—
35	C₂×C₄×C₈	—	13	3	no	—
36	C₂×C₄×C₈	—	13	3	no	—
37	C₄³	#261	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	—	13	3	no	—
45	C₂²×C₈	—	13	1	no	—
46	C₂×C₄²	#1057	1	4	yes	—
47	C₂×C₄²	C₂×#261	1	3	yes	—
48	C₂×C₁₆	—	13	24	no	—
49	C₄×C₈	—	13	12	no	—
50	C₄×C₈	—	13	12	no	—
51	C₂×C₁₃	C₄²×C₈	1	1	yes	characteristic
52	C₂×C₁₃	C₂×C₄×C₁₆	1	6	yes	—
53	C₂²×C₄	C₂×#1057	1	6	yes	—
54	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
55	C₂×C₈	—	13	12	no	—
56	C₂×C₈	—	13	6	no	—
57	C₂×C₈	—	13	6	no	—
58	C₄²	#6092	1	16	yes	direct product factor
59	C₄²	D₁₃⋊C₈	1	6	yes	—
60	C₄²	C₄×#261	1	6	yes	—
61	C₁₆	—	13	16	no	—
62	C₁₃	C₄²×C₁₆	1	1	yes	characteristic, complemented, Sylow
63	C₂³	C₂²×#1057	1	1	yes	characteristic
64	C₂×C₄	C₂×#6092	1	24	yes	—
65	C₂×C₄	C₄×#1057	1	12	yes	—
66	C₂×C₄	C₂×D₁₃⋊C₈	1	3	yes	—
67	C₂×C₄	C₂×C₄×#261	1	3	yes	—
68	C₈	—	13	12	no	—
69	C₈	—	13	4	no	—
70	C₂²	C₂²×#6092	1	4	yes	—
71	C₂²	C₂×C₄×#1057	1	3	yes	—
72	C₄	C₄×#6092	1	24	yes	direct product factor
73	C₄	C₄×D₁₃⋊C₈	1	3	yes	—
74	C₄	C₄²×#261	1	1	yes	characteristic
75	C₂	C₄²×#1057	1	1	yes	characteristic
76	C₂	C₂×C₄×#6092	1	6	yes	—

	subgroup	G/H
center, hypercenter	C₄³	#261
commutator, hypocenter	C₁₃	C₄²×C₁₆
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₄³×C₁₃	C₄
socle, prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂²×#1055	C₂³
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
7. C₄×#6092	C₄	direct (N × H)
18. C₄²×C₁₃	C₁₆	semidirect
24. #6092	C₄²	direct (N × H)
41. C₄×C₁₃	C₄×C₁₆	semidirect
58. C₄²	#6092	direct (N × H)
62. C₁₃	C₄²×C₁₆	semidirect
72. C₄	C₄×#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
C₂×C₄×#6092	2
C₄²×#1055	2
C₄²×C₁₆	13

Subgroups — C42×#6092 #16789010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×#6092 #16789010