Subgroups — C₂³×Dic₁₀₄ #16769401

Order 3328.

2078 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₅₂	C₂	1	2	yes	maximal
2	C₂²×Dic₁₀₄	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₂₆	—	2	2	no	—
5	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×Dic₅₂	—	2	14	no	—
7	C₂²×Dic₅₂	C₂²	1	28	yes	—
8	C₂²×C₁₃×C₁₆	C₂²	1	14	yes	—
9	C₂×Dic₁₀₄	C₂²	1	112	yes	direct product factor
10	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
11	C₂³×Dic₁₃	—	4	2	no	—
12	C₂²×Dic₂₆	—	2	28	no	—
13	C₂²×Dic₂₆	—	4	14	no	—
14	C₂²×C₈×C₁₃	D₄	1	7	yes	—
15	C₂²×C₈×C₁₃	C₂³	1	7	yes	—
16	C₂×Dic₅₂	—	2	84	no	—
17	C₂×Dic₅₂	C₂³	1	56	yes	—
18	C₂×C₁₃×C₁₆	C₂³	1	28	yes	—
19	Dic₁₀₄	C₂³	1	64	yes	direct product factor
20	C₂³×Q₃₂	—	13	1	no	maximal, Sylow
21	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
22	C₂²×C₄×C₁₃	D₈	1	7	yes	—
23	C₂²×C₄×C₁₃	C₂×D₄	1	7	yes	—
24	C₂²×Dic₁₃	—	4	28	no	—
25	C₂×Dic₂₆	—	2	56	no	—
26	C₂×Dic₂₆	—	4	84	no	—
27	C₂×C₈×C₁₃	C₂×D₄	1	21	yes	—
28	C₂×C₈×C₁₃	C₂⁴	1	7	yes	—
29	Dic₅₂	—	2	56	no	—
30	Dic₅₂	C₂⁴	1	16	yes	—
31	C₁₃×C₁₆	C₂⁴	1	8	yes	—
32	C₂³×Q₁₆	—	13	2	no	—
33	C₂²×Q₃₂	—	13	28	no	—
34	C₂³×C₁₆	D₁₃	1	1	yes	characteristic
35	C₂³×C₁₃	Q₃₂	1	8	yes	complemented
36	C₂³×C₁₃	C₂×D₈	1	7	yes	—
37	C₂×C₄×C₁₃	C₂×D₈	1	21	yes	—
38	C₂×C₄×C₁₃	C₂²×D₄	1	7	yes	—
39	C₂×Dic₁₃	—	4	56	no	—
40	Dic₂₆	—	2	16	no	—
41	Dic₂₆	—	4	56	no	—
42	C₈×C₁₃	C₂²×D₄	1	7	yes	—
43	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
44	C₂³×Q₈	—	26	2	no	—
45	C₂²×Q₁₆	—	13	28	no	—
46	C₂²×Q₁₆	—	26	14	no	—
47	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
48	C₂×Q₃₂	—	13	112	no	—
49	C₂²×C₁₆	C₂×D₁₃	1	14	yes	—
50	C₂²×C₁₃	C₂×Q₃₂	1	28	yes	complemented
51	C₂²×C₁₃	C₂²×D₈	1	7	yes	—
52	C₄×C₁₃	C₂²×D₈	1	7	yes	—
53	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
54	Dic₁₃	—	4	16	no	—
55	C₂²×Q₈	—	26	28	no	—
56	C₂²×Q₈	—	52	14	no	—
57	C₂³×C₄	—	52	2	no	—
58	C₂³×C₄	D₅₂	1	1	yes	characteristic
59	C₂×Q₁₆	—	13	56	no	—
60	C₂×Q₁₆	—	26	84	no	—
61	C₂²×C₈	D₅₂	1	7	yes	—
62	C₂²×C₈	C₂²×D₁₃	1	7	yes	—
63	Q₃₂	—	13	64	no	—
64	C₂×C₁₆	C₂²×D₁₃	1	28	yes	—
65	C₂×C₁₃	C₂²×Q₃₂	1	14	yes	complemented
66	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
67	C₂⁴	D₁₀₄	1	1	yes	characteristic
68	C₂×Q₈	—	26	56	no	—
69	C₂×Q₈	—	52	84	no	—
70	C₂²×C₄	—	52	28	no	—
71	C₂²×C₄	D₁₀₄	1	7	yes	—
72	C₂²×C₄	C₂×D₅₂	1	7	yes	—
73	Q₁₆	—	13	16	no	—
74	Q₁₆	—	26	56	no	—
75	C₂×C₈	C₂×D₅₂	1	21	yes	—
76	C₂×C₈	C₂³×D₁₃	1	7	yes	—
77	C₁₆	C₂³×D₁₃	1	8	yes	—
78	C₁₃	C₂³×Q₃₂	1	1	yes	characteristic, complemented, Sylow
79	C₂³	Dic₁₀₄	1	8	yes	direct product factor
80	C₂³	C₂×D₁₀₄	1	7	yes	—
81	Q₈	—	26	16	no	—
82	Q₈	—	52	56	no	—
83	C₂×C₄	—	52	56	no	—
84	C₂×C₄	C₂×D₁₀₄	1	21	yes	—
85	C₂×C₄	C₂²×D₅₂	1	7	yes	—
86	C₈	C₂²×D₅₂	1	7	yes	—
87	C₈	C₂⁴×D₁₃	1	1	yes	characteristic
88	C₂²	C₂×Dic₁₀₄	1	28	yes	direct product factor
89	C₂²	C₂²×D₁₀₄	1	7	yes	—
90	C₄	—	52	16	no	—
91	C₄	C₂²×D₁₀₄	1	7	yes	—
92	C₄	C₂³×D₅₂	1	1	yes	characteristic
93	C₂	C₂²×Dic₁₀₄	1	14	yes	direct product factor
94	C₂	C₂³×D₁₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₁₀₄
commutator, cosocle	C₈×C₁₃	C₂⁵
Frattini	C₈	C₂⁴×D₁₃
Fitting	C₂³×C₁₃×C₁₆	C₂
socle, prime radical	C₂⁴×C₁₃	D₈
hypercenter	C₂³×C₁₆	D₁₃
hypocenter	C₁₃	C₂³×Q₃₂
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂³×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₁₀₄	C₂	direct (N × H)
9. C₂×Dic₁₀₄	C₂²	direct (N × H)
19. Dic₁₀₄	C₂³	direct (N × H)
35. C₂³×C₁₃	Q₃₂	semidirect
50. C₂²×C₁₃	C₂×Q₃₂	semidirect
65. C₂×C₁₃	C₂²×Q₃₂	semidirect
78. C₁₃	C₂³×Q₃₂	semidirect
79. C₂³	Dic₁₀₄	direct (N × H)
88. C₂²	C₂×Dic₁₀₄	direct (N × H)
93. C₂	C₂²×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
C₂³×Dic₅₂	2
C₂²×Dic₁₀₄	2
C₂³×C₁₃×C₁₆	2
C₂³×Q₃₂	13

Subgroups — C23×Dic104 #16769401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×Dic₁₀₄ #16769401