Subgroups — #13116353

Order 1664.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718787	C₂	1	3	yes	maximal
2	#11718786	C₂	1	3	yes	maximal, complemented
3	C₁₃×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
5	C₂×C₁₃×M₁₆	C₂²	1	3	yes	—
6	C₂×#6099	C₂²	1	3	yes	—
7	#88060	—	2	6	no	—
8	#88059	—	2	6	no	—
9	C₂³×D₁₃	Q₈	1	1	yes	characteristic
10	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
11	C₂²×Dic₁₃	Q₈	1	1	yes	characteristic
12	C₂×C₄×D₁₃	—	2	3	no	—
13	C₂×C₄×D₁₃	—	2	3	no	—
14	C₁₃×M₁₆	—	2	6	no	—
15	C₂×C₈×C₁₃	D₄	1	6	yes	—
16	#6099	—	2	6	no	—
17	C₂×#1055	—	2	3	no	—
18	#2091	—	13	1	no	maximal, Sylow
19	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
20	C₂²×D₁₃	—	2	3	no	—
21	C₂²×D₁₃	—	4	2	no	—
22	C₂×C₄×C₁₃	C₂×D₄	1	3	yes	—
23	C₂×C₄×C₁₃	#41	1	3	yes	—
24	C₂×Dic₁₃	—	2	3	no	—
25	C₄×D₁₃	—	4	3	no	—
26	C₄×D₁₃	—	4	1	no	—
27	C₈×C₁₃	—	2	6	no	—
28	#1055	—	4	3	no	—
29	#430	—	13	3	no	—
30	#407	—	13	3	no	—
31	#338	D₁₃	1	1	yes	characteristic, complemented
32	C₂²×C₁₃	—	4	1	no	—
33	C₂²×C₁₃	C₂²⋊Q₈	1	3	yes	—
34	C₂×D₁₃	—	2	6	no	—
35	C₂×D₁₃	—	4	3	no	—
36	C₂×D₁₃	—	4	1	no	—
37	C₄×C₁₃	#123	1	3	yes	—
38	C₄×C₁₃	#127	1	1	yes	characteristic
39	Dic₁₃	—	4	1	no	—
40	C₂³×C₄	—	13	1	no	—
41	C₂×M₁₆	—	13	3	no	—
42	C₂×M₁₆	C₂×D₁₃	1	3	yes	—
43	#108	—	26	6	no	—
44	C₂²⋊C₈	—	26	6	no	—
45	C₂×C₁₃	—	2	3	no	—
46	C₂×C₁₃	#399	1	1	yes	characteristic
47	D₁₃	—	4	2	no	—
48	C₂⁴	—	13	1	no	—
49	C₂²×C₄	—	13	1	no	—
50	C₂²×C₄	—	26	3	no	—
51	C₂²×C₄	—	26	3	no	—
52	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
53	M₁₆	—	2	6	no	—
54	M₁₆	—	26	6	no	—
55	C₂×C₈	—	26	3	no	—
56	C₂×C₈	D₅₂	1	6	yes	—
57	C₁₃	#2091	1	1	yes	characteristic, complemented, Sylow
58	C₂³	—	26	3	no	—
59	C₂³	—	52	2	no	—
60	C₂³	Q₈×D₁₃	1	1	yes	characteristic
61	C₂×C₄	—	26	3	no	—
62	C₂×C₄	—	52	1	no	—
63	C₂×C₄	—	52	3	no	—
64	C₂×C₄	C₂×D₅₂	1	3	yes	—
65	C₂×C₄	#6129	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	—	52	3	no	—
68	C₂²	—	4	1	no	—
69	C₂²	—	26	6	no	—
70	C₂²	—	52	3	no	—
71	C₂²	—	52	1	no	—
72	C₂²	#88151	1	3	yes	—
73	C₄	—	52	1	no	—
74	C₄	#88128	1	1	yes	characteristic
75	C₄	#88140	1	3	yes	—
76	C₂	—	2	3	no	—
77	C₂	—	52	2	no	—
78	C₂	#11718338	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#88128
commutator, cosocle	C₂²×C₄×C₁₃	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#338	C₂
socle	C₂×C₁₃	#399
prime radical	C₂³×D₁₃	Q₈
hypercenter	#338	D₁₃
hypocenter	C₁₃	#2091
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
2. #11718786	C₂	semidirect
3. C₁₃×#338	C₂	semidirect
31. #338	D₁₃	semidirect
57. C₁₃	#2091	semidirect

Maximal subgroups

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

subgroup	index
#11718787	2
#11718786	2
C₁₃×#338	2
#2091	13