Subgroups — C₂×#11718047 #13113111

Order 1664.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#1055	C₂	1	2	yes	maximal
3	#11718047	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₃	C₄	1	2	yes	—
5	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×#1055	C₄	1	4	yes	—
7	C₄×C₈×C₁₃	C₄	1	2	yes	—
8	C₄×C₈×C₁₃	C₂²	1	2	yes	—
9	C₄×#1055	C₄	1	4	yes	—
10	C₄×#1055	C₂²	1	4	yes	—
11	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₁₃	C₈	1	8	yes	complemented
14	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
15	C₄²×C₁₃	C₂×C₄	1	2	yes	—
16	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×#1055	—	2	8	no	—
19	C₂×#1055	C₂×C₄	1	8	yes	—
20	C₂×#322	—	13	1	no	maximal, Sylow
21	C₂³×C₁₃	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₁₃	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₁₃	C₄²	1	2	yes	—
24	C₂×C₄×C₁₃	C₂×C₈	1	4	yes	—
25	C₂×C₄×C₁₃	M₁₆	1	8	yes	—
26	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
28	C₈×C₁₃	C₂×C₈	1	8	yes	complemented
29	#1055	—	2	8	no	—
30	C₂×C₄×C₈	—	13	2	no	—
31	C₂×C₄×C₈	D₁₃	1	1	yes	characteristic
32	#322	—	13	4	no	—
33	C₂²×C₁₃	C₄×C₈	1	2	yes	—
34	C₂²×C₁₃	#97	1	4	yes	—
35	C₂²×C₁₃	C₂×C₄²	1	1	yes	characteristic
36	C₄×C₁₃	C₄×C₈	1	2	yes	—
37	C₄×C₁₃	#97	1	4	yes	—
38	C₄×C₁₃	C₂²×C₈	1	2	yes	—
39	C₄×C₁₃	C₂×M₁₆	1	4	yes	—
40	C₂²×C₈	—	13	4	no	—
41	C₂²×C₈	Dic₁₃	1	2	yes	—
42	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
43	C₄×C₈	—	13	4	no	—
44	C₄×C₈	—	13	4	no	—
45	C₄×C₈	Dic₁₃	1	2	yes	—
46	C₄×C₈	C₂×D₁₃	1	2	yes	—
47	C₂×C₁₃	#322	1	4	yes	complemented
48	C₂×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
49	C₂×C₁₃	C₂×#97	1	2	yes	—
50	C₂²×C₄	C₄×D₁₃	1	2	yes	—
51	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
52	C₂×C₈	—	13	8	no	—
53	C₂×C₈	—	26	8	no	—
54	C₂×C₈	#1055	1	8	yes	complemented
55	C₂×C₈	C₂×Dic₁₃	1	4	yes	—
56	C₄²	C₄×D₁₃	1	2	yes	—
57	C₄²	C₂×Dic₁₃	1	1	yes	characteristic
58	C₄²	C₂²×D₁₃	1	1	yes	characteristic
59	C₁₃	C₂×#322	1	1	yes	characteristic, complemented, Sylow
60	C₂³	C₄×Dic₁₃	1	1	yes	characteristic
61	C₂×C₄	#6094	1	8	yes	—
62	C₂×C₄	C₂×#1055	1	4	yes	—
63	C₂×C₄	C₄×Dic₁₃	1	1	yes	characteristic
64	C₂×C₄	C₄×Dic₁₃	1	2	yes	—
65	C₂×C₄	C₂×C₄×D₁₃	1	2	yes	—
66	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
67	C₈	—	26	8	no	—
68	C₈	C₂×#1055	1	8	yes	complemented
69	C₂²	C₄×#1055	1	2	yes	—
70	C₂²	#88055	1	4	yes	—
71	C₂²	C₂×C₄×Dic₁₃	1	1	yes	characteristic
72	C₄	C₄×#1055	1	2	yes	—
73	C₄	#88055	1	4	yes	—
74	C₄	C₂×#6094	1	4	yes	—
75	C₄	C₂²×#1055	1	2	yes	—
76	C₂	#11718047	1	4	yes	direct product factor
77	C₂	C₂×C₄×#1055	1	1	yes	characteristic
78	C₂	C₂×#88055	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₄×C₈
Frattini	C₄²	C₂²×D₁₃
Fitting	C₂×C₄×C₈×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₄²
cosocle	C₄²×C₁₃	C₂³
hypercenter	C₂×C₄×C₈	D₁₃
hypocenter	C₁₃	C₂×#322
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #11718047	C₂	direct (N × H)
13. C₂×C₈×C₁₃	C₈	semidirect
28. C₈×C₁₃	C₂×C₈	semidirect
47. C₂×C₁₃	#322	semidirect
54. C₂×C₈	#1055	semidirect
59. C₁₃	C₂×#322	semidirect
68. C₈	C₂×#1055	semidirect
76. C₂	#11718047	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×C₄×C₈×C₁₃	2
C₂×C₄×#1055	2
#11718047	2
C₂×#322	13

Subgroups — C2×#11718047 #13113111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11718047 #13113111