Subgroups — #13129971

Order 1664.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718737	C₂	1	1	yes	maximal, characteristic
2	#11718227	C₂	1	2	yes	maximal, complemented
3	C₁₃×#127	C₄	1	1	yes	characteristic
4	C₂×#6105	—	2	2	no	—
5	#88123	C₂²	1	1	yes	characteristic
6	#88113	—	2	2	no	—
7	C₄×#1055	C₄	1	1	yes	characteristic
8	C₂×D₄×C₁₃	—	2	1	no	—
9	C₂×D₄×C₁₃	—	4	1	no	—
10	C₂×Dic₂₆	D₄	1	2	yes	—
11	#6122	—	4	2	no	—
12	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
13	#6105	—	4	4	no	—
14	C₄⋊Dic₁₃	—	4	1	no	—
15	C₂×#1055	—	2	1	no	—
16	#1410	—	13	1	no	maximal, Sylow
17	C₂³×C₁₃	—	4	1	no	—
18	D₄×C₁₃	—	4	2	no	—
19	D₄×C₁₃	—	8	2	no	—
20	C₂×C₄×C₁₃	—	2	1	no	—
21	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×Dic₁₃	—	2	2	no	—
23	Dic₂₆	—	4	2	no	—
24	#1057	—	8	2	no	—
25	#1055	—	2	2	no	—
26	#492	—	13	1	no	—
27	#356	—	13	2	no	—
28	C₂²×C₁₃	—	8	2	no	—
29	C₂²×C₁₃	—	8	1	no	—
30	C₂²×C₁₃	#99	1	1	yes	characteristic
31	C₄×C₁₃	—	2	2	no	—
32	C₄×C₁₃	—	2	1	no	—
33	Dic₁₃	—	4	2	no	—
34	C₂×SD₁₆	—	26	2	no	—
35	C₄⋊Q₈	—	13	1	no	—
36	#127	#261	1	1	yes	characteristic
37	#101	—	26	2	no	—
38	C₄×C₈	—	13	1	no	—
39	C₂×C₁₃	—	2	1	no	—
40	C₂×C₁₃	—	16	1	no	—
41	C₂×C₁₃	#353	1	1	yes	characteristic
42	C₂×Q₈	—	13	2	no	—
43	C₂×D₄	—	2	1	no	—
44	C₂×D₄	—	4	1	no	—
45	SD₁₆	—	52	4	no	—
46	M₁₆	—	52	2	no	—
47	C₂×C₈	—	26	1	no	—
48	C₄⋊C₄	—	52	1	no	—
49	C₄²	C₂×#261	1	1	yes	characteristic
50	C₁₃	#1410	1	1	yes	characteristic, complemented, Sylow
51	C₂³	—	4	1	no	—
52	Q₈	—	52	2	no	—
53	D₄	—	4	2	no	—
54	D₄	—	8	2	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	26	2	no	—
57	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
58	C₈	—	26	2	no	—
59	C₈	—	104	2	no	—
60	C₂²	—	8	2	no	—
61	C₂²	—	8	1	no	—
62	C₂²	#88119	1	1	yes	characteristic
63	C₄	—	2	2	no	—
64	C₄	—	2	1	no	—
65	C₄	—	52	2	no	—
66	C₂	—	2	1	no	—
67	C₂	—	16	1	no	—
68	C₂	#11718294	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718294
commutator	C₄²×C₁₃	C₂×C₄
Frattini	C₄²	C₂×#261
Fitting, prime radical	C₁₃×#127	C₄
socle	C₂×C₁₃	#353
cosocle	#88123	C₂²
hypercenter	#127	#261
hypocenter	C₁₃	#1410
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
2. #11718227	C₂	semidirect
50. C₁₃	#1410	semidirect

Maximal subgroups

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

subgroup	index
#11718737	2
#11718227	2
#1410	13