Subgroups — C₂×C₄×#6092 #13131032

Order 1664.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6092	C₂	1	2	yes	maximal
2	C₂×C₄×#1055	C₂	1	1	yes	maximal, characteristic
3	C₄×#6092	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄²×C₁₃	C₄	1	1	yes	characteristic
5	C₂²×#1055	C₄	1	1	yes	characteristic
6	C₂²×#1055	C₂²	1	1	yes	characteristic
7	C₂×#6092	C₄	1	8	yes	direct product factor
8	C₂×#6092	C₂²	1	4	yes	—
9	C₄×#1055	C₄	1	2	yes	—
10	C₄×#1055	C₂²	1	2	yes	—
11	C₂²×C₄×C₁₃	C₈	1	2	yes	—
12	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₄²×C₁₃	C₈	1	2	yes	—
14	C₄²×C₁₃	C₂×C₄	1	2	yes	—
15	C₂×#1055	C₈	1	4	yes	—
16	C₂×#1055	C₂×C₄	1	1	yes	characteristic
17	C₂×#1055	C₂×C₄	1	4	yes	—
18	C₂×#1055	C₂×C₄	1	2	yes	—
19	C₂×#1055	C₂³	1	1	yes	characteristic
20	#6092	C₂×C₄	1	8	yes	direct product factor
21	C₂×C₄×C₁₆	—	13	1	no	maximal, Sylow
22	C₂³×C₁₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₁₃	C₁₆	1	8	yes	complemented
24	C₂×C₄×C₁₃	C₄²	1	2	yes	—
25	C₂×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₁₃	C₂×C₈	1	4	yes	—
28	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	#1055	C₄²	1	2	yes	—
30	#1055	C₂×C₈	1	4	yes	—
31	#1055	C₂²×C₄	1	2	yes	—
32	C₂²×C₁₆	—	13	2	no	—
33	C₂×C₄×C₈	—	13	1	no	—
34	C₄×C₁₆	—	13	4	no	—
35	C₂²×C₁₃	C₄×C₈	1	2	yes	—
36	C₂²×C₁₃	C₂×C₁₆	1	4	yes	—
37	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
38	C₄×C₁₃	C₄×C₈	1	2	yes	—
39	C₄×C₁₃	C₂×C₁₆	1	8	yes	complemented
40	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
41	C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
42	C₂²×C₈	—	13	1	no	—
43	C₂²×C₈	—	13	1	no	—
44	C₂×C₄²	#261	1	1	yes	characteristic
45	C₂×C₁₆	—	13	8	no	—
46	C₂×C₁₆	—	13	4	no	—
47	C₄×C₈	—	13	2	no	—
48	C₄×C₈	—	13	2	no	—
49	C₂×C₁₃	C₄×C₁₆	1	4	yes	complemented
50	C₂×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
51	C₂×C₁₃	C₂²×C₁₆	1	2	yes	—
52	C₂²×C₄	#1057	1	2	yes	—
53	C₂²×C₄	C₂×#261	1	1	yes	characteristic
54	C₂×C₈	—	13	4	no	—
55	C₂×C₈	—	13	4	no	—
56	C₂×C₈	—	13	1	no	—
57	C₂×C₈	—	13	2	no	—
58	C₂×C₈	—	13	1	no	—
59	C₄²	#1057	1	2	yes	—
60	C₄²	C₂×#261	1	2	yes	—
61	C₁₆	—	13	8	no	—
62	C₁₃	C₂×C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
63	C₂³	C₂×#1057	1	1	yes	characteristic
64	C₂×C₄	#6092	1	8	yes	direct product factor
65	C₂×C₄	D₁₃⋊C₈	1	2	yes	—
66	C₂×C₄	C₄×#261	1	2	yes	—
67	C₂×C₄	C₂×#1057	1	4	yes	—
68	C₂×C₄	C₂×#1057	1	1	yes	characteristic
69	C₂×C₄	C₂²×#261	1	1	yes	characteristic
70	C₈	—	13	4	no	—
71	C₈	—	13	2	no	—
72	C₈	—	13	2	no	—
73	C₂²	C₂×#6092	1	4	yes	—
74	C₂²	C₄×#1057	1	2	yes	—
75	C₂²	C₂²×#1057	1	1	yes	characteristic
76	C₄	C₂×#6092	1	8	yes	direct product factor
77	C₄	C₄×#1057	1	2	yes	—
78	C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
79	C₄	C₂×C₄×#261	1	1	yes	characteristic
80	C₂	C₄×#6092	1	4	yes	direct product factor
81	C₂	C₂²×#6092	1	2	yes	—
82	C₂	C₂×C₄×#1057	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄²	#261
commutator, hypocenter	C₁₃	C₂×C₄×C₁₆
Frattini	C₂×C₄	C₂²×#261
Fitting	C₂×C₄²×C₁₃	C₄
socle, prime radical	C₂³×C₁₃	C₂×C₈
cosocle	C₂×#1055	C₂³
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. C₄×#6092	C₂	direct (N × H)
7. C₂×#6092	C₄	direct (N × H)
20. #6092	C₂×C₄	direct (N × H)
23. C₂×C₄×C₁₃	C₁₆	semidirect
39. C₄×C₁₃	C₂×C₁₆	semidirect
49. C₂×C₁₃	C₄×C₁₆	semidirect
62. C₁₃	C₂×C₄×C₁₆	semidirect
64. C₂×C₄	#6092	direct (N × H)
76. C₄	C₂×#6092	direct (N × H)
80. C₂	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
C₂²×#6092	2
C₂×C₄×#1055	2
C₄×#6092	2
C₂×C₄×C₁₆	13

Subgroups — C2×C4×#6092 #13131032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#6092 #13131032