Subgroups — #13112806

Order 1664.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	#11718053	C₂	1	1	yes	maximal, characteristic
3	#11718049	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×Q₁₆	C₄	1	1	yes	characteristic
5	C₄×Q₈×C₁₃	—	2	1	no	—
6	C₁₃×#107	C₄	1	1	yes	characteristic
7	C₁₃×#103	—	2	1	no	—
8	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×#6090	—	2	1	no	—
10	C₄⋊#1055	—	2	1	no	—
11	C₂×Q₈×C₁₃	—	2	1	no	—
12	C₁₃×Q₁₆	—	2	1	no	—
13	C₁₃×Q₁₆	C₈	1	2	yes	complemented
14	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
16	C₁₃×C₄⋊C₄	—	2	1	no	—
17	C₁₃×C₄⋊C₄	—	4	1	no	—
18	C₄²×C₁₃	—	4	1	no	—
19	C₄²×C₁₃	D₄	1	1	yes	characteristic
20	C₂×#1055	—	4	1	no	—
21	#6090	—	2	2	no	—
22	#1334	—	13	1	no	maximal, Sylow
23	Q₈×C₁₃	—	2	2	no	—
24	Q₈×C₁₃	—	4	1	no	—
25	C₂×C₄×C₁₃	—	4	1	no	—
26	C₂×C₄×C₁₃	—	4	1	no	—
27	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
29	C₂×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
30	C₈×C₁₃	—	2	1	no	—
31	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₃	M₁₆	1	1	yes	characteristic
33	#1055	—	8	1	no	—
34	C₄×Q₁₆	D₁₃	1	1	yes	characteristic
35	#346	—	13	1	no	—
36	#334	—	13	1	no	—
37	C₂²×C₁₃	#102	1	1	yes	characteristic
38	C₄×C₁₃	—	2	1	no	—
39	C₄×C₁₃	—	2	1	no	—
40	C₄×C₁₃	—	4	2	no	—
41	C₄×C₁₃	—	8	1	no	—
42	C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
43	C₄×C₁₃	#104	1	1	yes	characteristic
44	C₂×Q₁₆	Dic₁₃	1	1	yes	characteristic
45	C₄×Q₈	—	2	1	no	—
46	C₂×C₁₆	—	26	1	no	—
47	#107	Dic₁₃	1	1	yes	characteristic
48	C₄⋊C₈	—	26	1	no	—
49	#103	—	2	1	no	—
50	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
51	C₂×C₁₃	D₄⋊C₈	1	1	yes	characteristic
52	C₂×C₁₃	#360	1	1	yes	characteristic
53	C₂×C₁₃	#362	1	1	yes	characteristic
54	C₂×Q₈	—	2	1	no	—
55	Q₁₆	—	2	1	no	—
56	Q₁₆	#1055	1	2	yes	complemented
57	C₂×C₈	—	52	1	no	—
58	C₂×C₈	C₂×Dic₁₃	1	1	yes	characteristic
59	C₂×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
60	C₄⋊C₄	—	2	1	no	—
61	C₄⋊C₄	—	4	1	no	—
62	C₄²	—	4	1	no	—
63	C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
64	C₁₆	—	26	2	no	—
65	C₁₃	#1334	1	1	yes	characteristic, complemented, Sylow
66	Q₈	—	2	2	no	—
67	Q₈	—	4	1	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	4	1	no	—
70	C₂×C₄	#6104	1	1	yes	characteristic
71	C₂×C₄	#6105	1	1	yes	characteristic
72	C₂×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	104	1	no	—
75	C₈	C₂×#1055	1	1	yes	characteristic
76	C₈	#6099	1	1	yes	characteristic
77	C₂²	#88072	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	2	1	no	—
80	C₄	—	4	2	no	—
81	C₄	—	8	1	no	—
82	C₄	C₂²⋊#1055	1	1	yes	characteristic
83	C₄	#88077	1	1	yes	characteristic
84	C₂	D₄⋊#1055	1	1	yes	characteristic
85	C₂	#11718157	1	1	yes	characteristic
86	C₂	#11718158	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#88072
commutator	C₈×C₁₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₃
Fitting	C₄×C₁₃×Q₁₆	C₂
socle, prime radical	C₂²×C₁₃	#102
cosocle	C₄×C₈×C₁₃	C₂²
hypercenter	C₄×Q₁₆	D₁₃
hypocenter	C₁₃	#1334
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
13. C₁₃×Q₁₆	C₈	semidirect
56. Q₁₆	#1055	semidirect
65. C₁₃	#1334	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₃×Q₁₆	2
#11718053	2
#11718049	2
#1334	13