Subgroups — #13116235

Order 1664.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88063	C₂	1	3	yes	maximal
2	#11718785	C₂	1	3	yes	maximal, complemented
3	C₁₃×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₅₂	C₂²	1	1	yes	characteristic
5	C₂×C₁₃×M₁₆	C₂²	1	3	yes	—
6	C₂×#6099	C₂²	1	3	yes	—
7	#88063	—	2	6	no	—
8	#88062	—	2	6	no	—
9	C₂³×D₁₃	Q₈	1	2	yes	—
10	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
11	C₂×D₅₂	—	2	3	no	—
12	C₂×D₅₂	—	2	3	no	—
13	C₁₃×M₁₆	—	2	3	no	—
14	C₁₃×M₁₆	—	2	3	no	—
15	C₂×C₈×C₁₃	—	2	3	no	—
16	#6099	—	2	3	no	—
17	#6099	D₄	1	6	yes	—
18	C₂×#1055	—	2	3	no	—
19	#2069	—	13	1	no	maximal, Sylow
20	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
21	C₂²×D₁₃	—	2	6	no	—
22	C₂²×D₁₃	—	8	2	no	—
23	C₂×C₄×C₁₃	C₂×D₄	1	3	yes	—
24	C₂×C₄×C₁₃	#41	1	3	yes	—
25	D₅₂	—	4	3	no	—
26	D₅₂	—	4	1	no	—
27	C₈×C₁₃	—	4	3	no	—
28	#1055	—	2	6	no	—
29	#430	—	13	3	no	—
30	C₂×#100	—	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	—	4	2	no	—
35	C₂×D₁₃	—	8	6	no	—
36	C₄×C₁₃	#121	1	3	yes	—
37	C₄×C₁₃	#126	1	1	yes	characteristic
38	C₂²×D₄	—	13	1	no	—
39	C₂×M₁₆	—	13	3	no	—
40	C₂×M₁₆	C₂×D₁₃	1	3	yes	—
41	#108	—	26	6	no	—
42	#100	—	26	6	no	—
43	C₂×C₁₃	—	2	3	no	—
44	C₂×C₁₃	#396	1	1	yes	characteristic
45	D₁₃	—	8	2	no	—
46	C₂⁴	—	13	2	no	—
47	C₂×D₄	—	26	3	no	—
48	C₂×D₄	—	26	3	no	—
49	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
50	M₁₆	—	2	3	no	—
51	M₁₆	—	2	3	no	—
52	M₁₆	—	13	6	no	—
53	M₁₆	—	26	3	no	—
54	C₂×C₈	—	2	3	no	—
55	C₂×C₈	—	26	3	no	—
56	C₁₃	#2069	1	1	yes	characteristic, complemented, Sylow
57	C₂³	—	26	6	no	—
58	C₂³	—	104	2	no	—
59	C₂³	Q₈×D₁₃	1	1	yes	characteristic
60	D₄	—	52	1	no	—
61	D₄	—	52	3	no	—
62	C₂×C₄	#6127	1	3	yes	—
63	C₂×C₄	D₄×D₁₃	1	3	yes	—
64	C₈	—	4	3	no	—
65	C₈	—	26	6	no	—
66	C₂²	—	4	1	no	—
67	C₂²	—	52	2	no	—
68	C₂²	—	104	6	no	—
69	C₂²	#88150	1	3	yes	—
70	C₄	#88130	1	1	yes	characteristic
71	C₄	#88138	1	3	yes	—
72	C₂	—	2	3	no	—
73	C₂	—	104	2	no	—
74	C₂	#11718337	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718337
commutator, cosocle	C₂²×C₄×C₁₃	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#338	C₂
socle	C₂×C₁₃	#396
prime radical	C₂²×D₅₂	C₂²
hypercenter	#338	D₁₃
hypocenter	C₁₃	#2069
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
2. #11718785	C₂	semidirect
3. C₁₃×#338	C₂	semidirect
31. #338	D₁₃	semidirect
56. C₁₃	#2069	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88063	2
#11718785	2
C₁₃×#338	2
#2069	13