Subgroups — C₂×#11718096 #13116613

Order 1664.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#88058	C₂	1	2	yes	maximal
3	#11718096	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×C₄⋊Dic₁₃	—	2	2	no	—
6	C₂×C₁₃×C₁₆	C₄	1	4	yes	complemented
7	C₂×C₁₃×C₁₆	C₂²	1	2	yes	—
8	#88058	—	2	2	no	—
9	#88058	C₂²	1	4	yes	—
10	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
11	C₂²×Dic₁₃	—	4	2	no	—
12	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₃	Q₈	1	2	yes	—
15	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
16	C₄⋊Dic₁₃	—	2	4	no	—
17	C₄⋊Dic₁₃	—	4	2	no	—
18	C₁₃×C₁₆	C₂×C₄	1	4	yes	complemented
19	C₂×#366	—	13	1	no	maximal, Sylow
20	C₂³×C₁₃	D₈	1	1	yes	characteristic
21	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
22	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
23	C₂×C₄×C₁₃	Q₁₆	1	2	yes	—
24	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
25	C₂×Dic₁₃	—	4	4	no	—
26	C₂×Dic₁₃	—	8	4	no	—
27	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
28	C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
30	C₂²×C₁₆	D₁₃	1	1	yes	characteristic
31	C₂×#107	—	13	2	no	—
32	#366	—	13	4	no	—
33	C₂²×C₁₃	#107	1	2	yes	—
34	C₂²×C₁₃	D₁₆	1	2	yes	—
35	C₂²×C₁₃	Q₃₂	1	2	yes	—
36	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
37	C₄×C₁₃	#107	1	2	yes	—
38	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
40	Dic₁₃	—	8	4	no	—
41	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
42	C₂×C₄⋊C₄	—	26	2	no	—
43	C₂×C₁₆	Dic₁₃	1	4	yes	complemented
44	C₂×C₁₆	C₂×D₁₃	1	2	yes	—
45	#107	—	13	4	no	—
46	#107	—	26	2	no	—
47	C₂×C₁₃	#366	1	4	yes	complemented
48	C₂×C₁₃	C₂×#107	1	1	yes	characteristic
49	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
50	C₂×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
51	C₂²×C₄	—	52	2	no	—
52	C₂²×C₄	D₅₂	1	1	yes	characteristic
53	C₂×C₈	Dic₂₆	1	2	yes	—
54	C₂×C₈	D₅₂	1	1	yes	characteristic
55	C₂×C₈	C₂×Dic₁₃	1	2	yes	—
56	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
57	C₄⋊C₄	—	26	4	no	—
58	C₄⋊C₄	—	52	2	no	—
59	C₁₆	C₂×Dic₁₃	1	4	yes	complemented
60	C₁₃	C₂×#366	1	1	yes	characteristic, complemented, Sylow
61	C₂³	D₁₀₄	1	1	yes	characteristic
62	C₂×C₄	—	52	4	no	—
63	C₂×C₄	—	104	4	no	—
64	C₂×C₄	D₁₀₄	1	1	yes	characteristic
65	C₂×C₄	Dic₅₂	1	2	yes	—
66	C₂×C₄	C₄⋊Dic₁₃	1	2	yes	—
67	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
68	C₈	C₄⋊Dic₁₃	1	2	yes	—
69	C₈	C₂×Dic₂₆	1	1	yes	characteristic
70	C₈	C₂²×Dic₁₃	1	1	yes	characteristic
71	C₂²	D₂₀₈	1	2	yes	—
72	C₂²	Dic₁₀₄	1	2	yes	—
73	C₂²	#88058	1	2	yes	—
74	C₂²	C₂×D₁₀₄	1	1	yes	characteristic
75	C₄	—	104	4	no	—
76	C₄	#88058	1	2	yes	—
77	C₄	C₂×Dic₅₂	1	1	yes	characteristic
78	C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
79	C₂	#11718096	1	4	yes	direct product factor
80	C₂	C₂×D₂₀₈	1	1	yes	characteristic
81	C₂	C₂×Dic₁₀₄	1	1	yes	characteristic
82	C₂	C₂×#88058	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₀₄
commutator	C₈×C₁₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₂²×C₁₃×C₁₆	C₂
socle, prime radical	C₂³×C₁₃	D₈
cosocle	C₂×C₈×C₁₃	C₂³
hypercenter	C₂²×C₁₆	D₁₃
hypocenter	C₁₃	C₂×#366
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. #11718096	C₂	direct (N × H)
6. C₂×C₁₃×C₁₆	C₄	semidirect
18. C₁₃×C₁₆	C₂×C₄	semidirect
43. C₂×C₁₆	Dic₁₃	semidirect
47. C₂×C₁₃	#366	semidirect
59. C₁₆	C₂×Dic₁₃	semidirect
60. C₁₃	C₂×#366	semidirect
79. C₂	#11718096	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×C₁₃×C₁₆	2
C₂×#88058	2
#11718096	2
C₂×#366	13

Subgroups — C2×#11718096 #13116613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11718096 #13116613