Subgroups — C₂×#11718111 #13117133

Order 1664.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₂₀₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718111	C₂	1	4	yes	maximal, direct product factor
4	C₂×#88034	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×D₈	—	2	1	no	—
6	C₂×D₁₀₄	—	2	1	no	—
7	C₁₃×D₁₆	—	2	1	no	—
8	C₁₃×D₁₆	C₂²	1	2	yes	complemented
9	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
10	D₂₀₈	—	2	1	no	—
11	D₂₀₈	C₂²	1	2	yes	complemented
12	#88034	C₂²	1	2	yes	complemented
13	C₂×D₄×C₁₃	—	4	1	no	—
14	C₂×D₅₂	—	4	1	no	—
15	C₁₃×D₈	—	2	2	no	—
16	C₁₃×D₈	—	4	1	no	—
17	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
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×D₃₂	—	13	1	no	maximal, Sylow
23	C₂³×C₁₃	—	8	1	no	—
24	C₂²×D₁₃	—	8	1	no	—
25	D₄×C₁₃	—	4	2	no	—
26	D₄×C₁₃	—	8	1	no	—
27	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
28	D₅₂	—	4	2	no	—
29	D₅₂	—	8	1	no	—
30	C₈×C₁₃	D₈	1	1	yes	characteristic
31	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
32	C₂×D₁₆	—	13	1	no	—
33	C₂×D₁₆	D₁₃	1	1	yes	characteristic, complemented
34	D₃₂	—	13	4	no	—
35	C₂×C₃₂	—	13	1	no	—
36	C₂²×C₁₃	—	8	2	no	—
37	C₂²×C₁₃	—	16	2	no	—
38	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
39	C₂×D₁₃	—	8	2	no	—
40	C₂×D₁₃	—	16	2	no	—
41	C₄×C₁₃	D₁₆	1	1	yes	characteristic
42	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
43	C₂×D₈	—	2	1	no	—
44	C₂×D₈	—	26	1	no	—
45	D₁₆	—	2	1	no	—
46	D₁₆	—	13	2	no	—
47	D₁₆	—	26	1	no	—
48	D₁₆	C₂×D₁₃	1	2	yes	complemented
49	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
50	C₃₂	—	13	2	no	—
51	C₂×C₁₃	—	16	2	no	—
52	C₂×C₁₃	D₃₂	1	2	yes	complemented
53	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
54	D₁₃	—	16	2	no	—
55	C₂×D₄	—	4	1	no	—
56	C₂×D₄	—	52	1	no	—
57	D₈	—	2	2	no	—
58	D₈	—	4	1	no	—
59	D₈	—	26	2	no	—
60	D₈	—	52	1	no	—
61	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
62	C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
63	C₁₆	C₂²×D₁₃	1	1	yes	characteristic
64	C₁₃	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
65	C₂³	—	8	1	no	—
66	C₂³	—	104	1	no	—
67	D₄	—	4	2	no	—
68	D₄	—	8	1	no	—
69	D₄	—	52	2	no	—
70	D₄	—	104	1	no	—
71	C₂×C₄	#6104	1	1	yes	characteristic
72	C₈	#6104	1	1	yes	characteristic
73	C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
74	C₂²	—	8	2	no	—
75	C₂²	—	16	2	no	—
76	C₂²	—	104	2	no	—
77	C₂²	—	208	2	no	—
78	C₂²	#88066	1	1	yes	characteristic
79	C₄	#88066	1	1	yes	characteristic
80	C₄	C₂×#6104	1	1	yes	characteristic
81	C₂	—	16	2	no	—
82	C₂	—	208	2	no	—
83	C₂	#11718111	1	2	yes	direct product factor
84	C₂	C₂×#88066	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#88066
commutator, cosocle	C₁₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₃
Fitting	C₂×C₁₃×D₁₆	C₂
socle	C₂²×C₁₃	D₁₆
hypercenter	C₂×D₁₆	D₁₃
hypocenter	C₁₃	C₂×D₃₂
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×D₁₆	C₂	semidirect
2. C₂×D₂₀₈	C₂	semidirect
3. #11718111	C₂	direct (N × H)
4. C₂×#88034	C₂	semidirect
8. C₁₃×D₁₆	C₂²	semidirect
11. D₂₀₈	C₂²	semidirect
12. #88034	C₂²	semidirect
33. C₂×D₁₆	D₁₃	semidirect
48. D₁₆	C₂×D₁₃	semidirect
52. C₂×C₁₃	D₃₂	semidirect
64. C₁₃	C₂×D₃₂	semidirect
83. C₂	#11718111	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×C₁₃×D₁₆	2
C₂×D₂₀₈	2
#11718111	2
C₂×#88034	2
C₂×D₃₂	13

Subgroups — C2×#11718111 #13117133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11718111 #13117133