Subgroups — C₂²×Dic₁₀₄ #13127949

Order 1664.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₅₂	C₂	1	2	yes	maximal
2	C₂²×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₁₀₄	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Dic₂₆	—	2	2	no	—
5	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×Dic₅₂	—	2	6	no	—
7	C₂×Dic₅₂	C₂²	1	12	yes	—
8	C₂×C₁₃×C₁₆	C₂²	1	6	yes	—
9	Dic₁₀₄	C₂²	1	16	yes	direct product factor
10	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
11	C₂²×Dic₁₃	—	4	2	no	—
12	C₂×Dic₂₆	—	2	12	no	—
13	C₂×Dic₂₆	—	4	6	no	—
14	C₂×C₈×C₁₃	D₄	1	3	yes	—
15	C₂×C₈×C₁₃	C₂³	1	3	yes	—
16	Dic₅₂	—	2	12	no	—
17	Dic₅₂	C₂³	1	8	yes	—
18	C₁₃×C₁₆	C₂³	1	4	yes	—
19	C₂²×Q₃₂	—	13	1	no	maximal, Sylow
20	C₂³×C₁₃	D₈	1	1	yes	characteristic
21	C₂×C₄×C₁₃	D₈	1	3	yes	—
22	C₂×C₄×C₁₃	C₂×D₄	1	3	yes	—
23	C₂×Dic₁₃	—	4	12	no	—
24	Dic₂₆	—	2	8	no	—
25	Dic₂₆	—	4	12	no	—
26	C₈×C₁₃	C₂×D₄	1	3	yes	—
27	C₈×C₁₃	C₂⁴	1	1	yes	characteristic
28	C₂²×Q₁₆	—	13	2	no	—
29	C₂×Q₃₂	—	13	12	no	—
30	C₂²×C₁₆	D₁₃	1	1	yes	characteristic
31	C₂²×C₁₃	Q₃₂	1	4	yes	complemented
32	C₂²×C₁₃	C₂×D₈	1	3	yes	—
33	C₄×C₁₃	C₂×D₈	1	3	yes	—
34	C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
35	Dic₁₃	—	4	8	no	—
36	C₂²×Q₈	—	26	2	no	—
37	C₂×Q₁₆	—	13	12	no	—
38	C₂×Q₁₆	—	26	6	no	—
39	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
40	Q₃₂	—	13	16	no	—
41	C₂×C₁₆	C₂×D₁₃	1	6	yes	—
42	C₂×C₁₃	C₂×Q₃₂	1	6	yes	complemented
43	C₂×C₁₃	C₂²×D₈	1	1	yes	characteristic
44	C₂×Q₈	—	26	12	no	—
45	C₂×Q₈	—	52	6	no	—
46	C₂²×C₄	—	52	2	no	—
47	C₂²×C₄	D₅₂	1	1	yes	characteristic
48	Q₁₆	—	13	8	no	—
49	Q₁₆	—	26	12	no	—
50	C₂×C₈	D₅₂	1	3	yes	—
51	C₂×C₈	C₂²×D₁₃	1	3	yes	—
52	C₁₆	C₂²×D₁₃	1	4	yes	—
53	C₁₃	C₂²×Q₃₂	1	1	yes	characteristic, complemented, Sylow
54	C₂³	D₁₀₄	1	1	yes	characteristic
55	Q₈	—	26	8	no	—
56	Q₈	—	52	12	no	—
57	C₂×C₄	—	52	12	no	—
58	C₂×C₄	D₁₀₄	1	3	yes	—
59	C₂×C₄	C₂×D₅₂	1	3	yes	—
60	C₈	C₂×D₅₂	1	3	yes	—
61	C₈	C₂³×D₁₃	1	1	yes	characteristic
62	C₂²	Dic₁₀₄	1	4	yes	direct product factor
63	C₂²	C₂×D₁₀₄	1	3	yes	—
64	C₄	—	52	8	no	—
65	C₄	C₂×D₁₀₄	1	3	yes	—
66	C₄	C₂²×D₅₂	1	1	yes	characteristic
67	C₂	C₂×Dic₁₀₄	1	6	yes	direct product factor
68	C₂	C₂²×D₁₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₀₄
commutator, cosocle	C₈×C₁₃	C₂⁴
Frattini	C₈	C₂³×D₁₃
Fitting	C₂²×C₁₃×C₁₆	C₂
socle, prime radical	C₂³×C₁₃	D₈
hypercenter	C₂²×C₁₆	D₁₃
hypocenter	C₁₃	C₂²×Q₃₂
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₁₀₄	C₂	direct (N × H)
9. Dic₁₀₄	C₂²	direct (N × H)
31. C₂²×C₁₃	Q₃₂	semidirect
42. C₂×C₁₃	C₂×Q₃₂	semidirect
53. C₁₃	C₂²×Q₃₂	semidirect
62. C₂²	Dic₁₀₄	direct (N × H)
67. C₂	C₂×Dic₁₀₄	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×Dic₅₂	2
C₂²×C₁₃×C₁₆	2
C₂×Dic₁₀₄	2
C₂²×Q₃₂	13

Subgroups — C22×Dic104 #13127949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₁₀₄ #13127949