Subgroups — C₄×Dic₁₀₄ #13116696

Order 1664.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₀₄	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₅₂	C₂	1	2	yes	maximal
3	C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	#11718096	C₂	1	1	yes	maximal, characteristic
5	#11718095	C₂	1	2	yes	maximal
6	C₂×Dic₅₂	C₂²	1	2	yes	—
7	C₄×Dic₂₆	—	2	2	no	—
8	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	#88058	C₂²	1	2	yes	—
12	#88056	—	2	2	no	—
13	Dic₁₀₄	C₄	1	4	yes	direct product factor
14	C₂×Dic₂₆	—	2	2	no	—
15	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
17	C₄²×C₁₃	D₄	1	1	yes	characteristic
18	C₄⋊Dic₁₃	—	2	2	no	—
19	#6101	—	4	2	no	—
20	C₄×Dic₁₃	—	4	2	no	—
21	Dic₅₂	—	2	2	no	—
22	Dic₅₂	C₂×C₄	1	4	yes	—
23	C₁₃×C₁₆	—	2	1	no	—
24	C₁₃×C₁₆	C₂×C₄	1	2	yes	—
25	C₄×Q₃₂	—	13	1	no	maximal, Sylow
26	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
27	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
28	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₁₃	—	4	2	no	—
30	C₂×Dic₁₃	—	4	2	no	—
31	Dic₂₆	—	2	4	no	—
32	Dic₂₆	—	4	2	no	—
33	C₈×C₁₃	—	2	1	no	—
34	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₁₃	#41	1	1	yes	characteristic
36	C₂×Q₃₂	—	13	1	no	—
37	C₄×Q₁₆	—	13	2	no	—
38	#366	—	13	1	no	—
39	#358	—	13	2	no	—
40	C₄×C₁₆	D₁₃	1	1	yes	characteristic
41	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
42	C₄×C₁₃	—	2	1	no	—
43	C₄×C₁₃	Q₃₂	1	2	yes	complemented
44	C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
45	C₄×C₁₃	#135	1	1	yes	characteristic
46	Dic₁₃	—	4	4	no	—
47	Dic₁₃	—	8	2	no	—
48	C₂×Q₁₆	—	13	2	no	—
49	C₄×Q₈	—	26	2	no	—
50	Q₃₂	—	13	4	no	—
51	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
52	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
53	#107	—	13	2	no	—
54	#103	—	26	2	no	—
55	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
56	C₂×C₁₃	C₄×D₈	1	1	yes	characteristic
57	C₂×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
58	C₂×C₁₃	#508	1	1	yes	characteristic
59	C₂×Q₈	—	26	2	no	—
60	Q₁₆	—	13	4	no	—
61	Q₁₆	—	26	2	no	—
62	C₂×C₈	D₅₂	1	1	yes	characteristic
63	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
64	C₄⋊C₄	—	26	2	no	—
65	C₄⋊C₄	—	52	2	no	—
66	C₄²	—	52	2	no	—
67	C₄²	D₅₂	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	C₄×D₁₃	1	2	yes	—
70	C₁₃	C₄×Q₃₂	1	1	yes	characteristic, complemented, Sylow
71	Q₈	—	26	4	no	—
72	Q₈	—	52	2	no	—
73	C₂×C₄	—	52	2	no	—
74	C₂×C₄	—	52	2	no	—
75	C₂×C₄	D₁₀₄	1	1	yes	characteristic
76	C₂×C₄	D₁₀₄	1	1	yes	characteristic
77	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
80	C₈	#6127	1	1	yes	characteristic
81	C₂²	C₂×D₁₀₄	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	52	4	no	—
84	C₄	—	104	2	no	—
85	C₄	Dic₁₀₄	1	2	yes	direct product factor
86	C₄	C₄×D₅₂	1	1	yes	characteristic
87	C₄	#88158	1	1	yes	characteristic
88	C₂	C₄×D₁₀₄	1	1	yes	characteristic
89	C₂	#11718565	1	1	yes	characteristic
90	C₂	C₂×Dic₁₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₀₄
commutator	C₈×C₁₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₄×C₁₃×C₁₆	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₈
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	C₄×C₁₆	D₁₃
hypocenter	C₁₃	C₄×Q₃₂
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
13. Dic₁₀₄	C₄	direct (N × H)
43. C₄×C₁₃	Q₃₂	semidirect
70. C₁₃	C₄×Q₃₂	semidirect
85. C₄	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
C₂×Dic₁₀₄	2
C₄×Dic₅₂	2
C₄×C₁₃×C₁₆	2
#11718096	2
#11718095	2
C₄×Q₃₂	13

Subgroups — C4×Dic104 #13116696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Dic₁₀₄ #13116696