Subgroups — #13117122

Order 1664.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718344	C₂	1	1	yes	maximal, characteristic
2	#11718343	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#346	C₂	1	1	yes	maximal, characteristic
4	#11718097	C₂	1	2	yes	maximal
5	#11718096	C₂	1	2	yes	maximal
6	#88124	—	2	1	no	—
7	#88123	—	2	1	no	—
8	C₂×C₁₃×C₁₆	C₂²	1	2	yes	—
9	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	#88058	—	2	1	no	—
11	#88058	C₂²	1	2	yes	—
12	#88058	C₂²	1	1	yes	characteristic
13	#88058	C₂²	1	1	yes	characteristic
14	#88057	—	2	1	no	—
15	C₂×Dic₂₆	—	4	1	no	—
16	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₄²×C₁₃	D₄	1	1	yes	characteristic
19	C₄⋊Dic₁₃	—	2	2	no	—
20	C₄⋊Dic₁₃	—	2	1	no	—
21	C₄⋊Dic₁₃	—	2	1	no	—
22	C₄⋊Dic₁₃	—	4	1	no	—
23	#6101	—	4	1	no	—
24	#6101	—	4	1	no	—
25	C₁₃×C₁₆	Q₈	1	4	yes	complemented
26	#2255	—	13	1	no	maximal, Sylow
27	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
28	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
29	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₁₃	—	4	1	no	—
31	C₂×Dic₁₃	—	4	1	no	—
32	C₂×Dic₁₃	—	4	2	no	—
33	Dic₂₆	—	8	2	no	—
34	C₈×C₁₃	Q₁₆	1	2	yes	—
35	C₈×C₁₃	C₂×Q₈	1	2	yes	—
36	#500	—	13	1	no	—
37	#499	—	13	1	no	—
38	#367	—	13	2	no	—
39	#366	—	13	2	no	—
40	#346	D₁₃	1	1	yes	characteristic
41	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
42	C₄×C₁₃	—	2	1	no	—
43	C₄×C₁₃	—	2	1	no	—
44	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
45	C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
46	Dic₁₃	—	8	2	no	—
47	Dic₁₃	—	8	1	no	—
48	Dic₁₃	—	8	1	no	—
49	C₄⋊Q₈	—	26	1	no	—
50	#125	—	26	1	no	—
51	C₂×C₁₆	C₂×D₁₃	1	2	yes	—
52	#107	—	13	1	no	—
53	#107	—	13	2	no	—
54	#107	—	13	1	no	—
55	#107	—	26	1	no	—
56	#106	—	26	1	no	—
57	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
58	C₂×C₁₃	#500	1	1	yes	characteristic
59	C₂×C₁₃	#509	1	1	yes	characteristic
60	C₂×C₁₃	#510	1	1	yes	characteristic
61	C₂×Q₈	—	52	1	no	—
62	C₂×C₈	D₅₂	1	1	yes	characteristic
63	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
64	C₄⋊C₄	—	26	1	no	—
65	C₄⋊C₄	—	26	1	no	—
66	C₄⋊C₄	—	26	2	no	—
67	C₄⋊C₄	—	52	1	no	—
68	C₄⋊C₄	—	52	1	no	—
69	C₄⋊C₄	—	52	1	no	—
70	C₄²	D₅₂	1	1	yes	characteristic
71	C₁₆	Dic₂₆	1	4	yes	complemented
72	C₁₃	#2255	1	1	yes	characteristic, complemented, Sylow
73	Q₈	—	104	2	no	—
74	C₂×C₄	—	52	1	no	—
75	C₂×C₄	—	52	1	no	—
76	C₂×C₄	—	52	2	no	—
77	C₂×C₄	D₁₀₄	1	1	yes	characteristic
78	C₂×C₄	D₁₀₄	1	1	yes	characteristic
79	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
80	C₈	Dic₅₂	1	2	yes	—
81	C₈	C₂×Dic₂₆	1	2	yes	—
82	C₂²	C₂×D₁₀₄	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	104	1	no	—
86	C₄	—	104	2	no	—
87	C₄	—	104	1	no	—
88	C₄	#88123	1	1	yes	characteristic
89	C₄	C₂×Dic₅₂	1	1	yes	characteristic
90	C₂	#11718343	1	1	yes	characteristic
91	C₂	#11718569	1	1	yes	characteristic
92	C₂	#11718570	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₀₄
commutator, cosocle	C₂×C₈×C₁₃	C₂³
Frattini	C₂×C₈	C₂²×D₁₃
Fitting	C₁₃×#346	C₂
socle, prime radical	C₂²×C₁₃	C₂×D₈
hypercenter	#346	D₁₃
hypocenter	C₁₃	#2255
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
25. C₁₃×C₁₆	Q₈	semidirect
71. C₁₆	Dic₂₆	semidirect
72. C₁₃	#2255	semidirect

Maximal subgroups

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

subgroup	index
#11718344	2
#11718343	2
C₁₃×#346	2
#11718097	2
#11718096	2
#2255	13