Subgroups — C₂×#11718041 #13117138

Order 1664.

112 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, complemented
2	C₂×D₂₀₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718041	C₂	1	4	yes	maximal, direct product factor
5	C₂×Dic₅₂	—	2	1	no	—
6	C₂×D₁₀₄	—	2	1	no	—
7	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	Dic₁₀₄	—	2	1	no	—
9	Dic₁₀₄	C₂²	1	2	yes	complemented
10	D₂₀₈	—	2	1	no	—
11	D₂₀₈	C₂²	1	2	yes	—
12	C₁₃×C₃₂	C₂²	1	2	yes	complemented
13	C₂×D₅₂	—	4	1	no	—
14	C₂×Dic₂₆	—	4	1	no	—
15	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
16	Dic₅₂	—	2	2	no	—
17	Dic₅₂	—	4	1	no	—
18	D₁₀₄	—	2	2	no	—
19	D₁₀₄	—	4	1	no	—
20	C₁₃×C₁₆	D₄	1	1	yes	characteristic
21	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
22	C₂×SD₆₄	—	13	1	no	maximal, Sylow
23	C₂²×D₁₃	—	8	1	no	—
24	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
25	C₂×Dic₁₃	—	8	1	no	—
26	D₅₂	—	4	2	no	—
27	D₅₂	—	8	1	no	—
28	Dic₂₆	—	4	2	no	—
29	Dic₂₆	—	8	1	no	—
30	C₈×C₁₃	D₈	1	1	yes	characteristic
31	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
32	C₂×Q₃₂	—	13	1	no	—
33	C₂×D₁₆	—	13	1	no	—
34	SD₆₄	—	13	4	no	—
35	C₂×C₃₂	D₁₃	1	1	yes	characteristic, complemented
36	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
37	C₂×D₁₃	—	8	2	no	—
38	C₂×D₁₃	—	16	2	no	—
39	C₄×C₁₃	D₁₆	1	1	yes	characteristic
40	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
41	Dic₁₃	—	8	2	no	—
42	C₂×Q₁₆	—	26	1	no	—
43	C₂×D₈	—	26	1	no	—
44	Q₃₂	—	13	2	no	—
45	Q₃₂	—	26	1	no	—
46	D₁₆	—	13	2	no	—
47	D₁₆	—	26	1	no	—
48	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
49	C₃₂	C₂×D₁₃	1	2	yes	complemented
50	C₂×C₁₃	SD₆₄	1	2	yes	complemented
51	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
52	D₁₃	—	16	2	no	—
53	C₂×Q₈	—	52	1	no	—
54	C₂×D₄	—	52	1	no	—
55	Q₁₆	—	26	2	no	—
56	Q₁₆	—	52	1	no	—
57	D₈	—	26	2	no	—
58	D₈	—	52	1	no	—
59	C₂×C₈	D₅₂	1	1	yes	characteristic
60	C₁₆	D₅₂	1	1	yes	characteristic
61	C₁₆	C₂²×D₁₃	1	1	yes	characteristic
62	C₁₃	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
63	C₂³	—	104	1	no	—
64	Q₈	—	52	2	no	—
65	Q₈	—	104	1	no	—
66	D₄	—	52	2	no	—
67	D₄	—	104	1	no	—
68	C₂×C₄	—	104	1	no	—
69	C₂×C₄	D₁₀₄	1	1	yes	characteristic
70	C₈	D₁₀₄	1	1	yes	characteristic
71	C₈	C₂×D₅₂	1	1	yes	characteristic
72	C₂²	—	104	2	no	—
73	C₂²	—	208	2	no	—
74	C₂²	D₂₀₈	1	1	yes	characteristic
75	C₄	—	104	2	no	—
76	C₄	D₂₀₈	1	1	yes	characteristic
77	C₄	C₂×D₁₀₄	1	1	yes	characteristic
78	C₂	—	208	2	no	—
79	C₂	#11718041	1	2	yes	direct product factor
80	C₂	C₂×D₂₀₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₀₈
commutator, cosocle	C₁₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₃
Fitting	C₂×C₁₃×C₃₂	C₂
socle	C₂²×C₁₃	D₁₆
prime radical	C₂×D₂₀₈	C₂
hypercenter	C₂×C₃₂	D₁₃
hypocenter	C₁₃	C₂×SD₆₄
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₀₄	C₂	semidirect
3. C₂×C₁₃×C₃₂	C₂	semidirect
4. #11718041	C₂	direct (N × H)
9. Dic₁₀₄	C₂²	semidirect
12. C₁₃×C₃₂	C₂²	semidirect
35. C₂×C₃₂	D₁₃	semidirect
49. C₃₂	C₂×D₁₃	semidirect
50. C₂×C₁₃	SD₆₄	semidirect
62. C₁₃	C₂×SD₆₄	semidirect
79. C₂	#11718041	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
C₂×D₂₀₈	2
C₂×C₁₃×C₃₂	2
#11718041	2
C₂×SD₆₄	13

Subgroups — C2×#11718041 #13117138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11718041 #13117138