Subgroups — #15750569

Order 3328.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117111	C₂	1	1	yes	maximal, characteristic
2	#13112908	C₂	1	1	yes	maximal, characteristic
3	C₁₃×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	#11718343	—	2	1	no	—
5	C₂×C₁₃×C₃₂	—	2	1	no	—
6	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	#11718096	—	2	1	no	—
8	#11718096	C₄	1	2	yes	—
9	#11718050	—	2	1	no	—
10	#88123	—	4	1	no	—
11	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
13	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
14	#88058	—	2	2	no	—
15	#88058	—	4	1	no	—
16	C₄⋊#1055	—	4	1	no	—
17	C₁₃×C₃₂	—	4	1	no	—
18	#7450	—	13	1	no	maximal, Sylow
19	C₂×Dic₂₆	—	8	1	no	—
20	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
22	C₄²×C₁₃	D₈	1	1	yes	characteristic
23	C₄⋊Dic₁₃	—	4	2	no	—
24	C₄⋊Dic₁₃	—	8	1	no	—
25	C₂×#1055	—	8	1	no	—
26	C₁₃×C₁₆	—	2	1	no	—
27	C₁₃×C₁₆	SD₁₆	1	1	yes	characteristic
28	C₁₃×C₁₆	Q₁₆	1	1	yes	characteristic
29	#2252	—	13	1	no	—
30	C₄⋊C₃₂	D₁₃	1	1	yes	characteristic
31	#1371	—	13	1	no	—
32	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
33	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
34	C₂×C₄×C₁₃	SD₃₂	1	1	yes	characteristic
35	C₂×Dic₁₃	—	8	2	no	—
36	Dic₂₆	—	16	1	no	—
37	Dic₂₆	—	16	1	no	—
38	C₈×C₁₃	—	2	1	no	—
39	C₈×C₁₃	#101	1	1	yes	characteristic
40	C₈×C₁₃	#103	1	1	yes	characteristic
41	#1055	—	16	1	no	—
42	#500	—	26	1	no	—
43	C₂×C₃₂	—	2	1	no	—
44	#366	—	13	2	no	—
45	#366	—	26	1	no	—
46	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
47	#335	—	26	1	no	—
48	C₂²×C₁₃	#357	1	1	yes	characteristic
49	C₄×C₁₃	—	2	1	no	—
50	C₄×C₁₃	#332	1	1	yes	characteristic
51	C₄×C₁₃	#362	1	1	yes	characteristic
52	C₄×C₁₃	D₃₂	1	1	yes	characteristic
53	C₄×C₁₃	SD₆₄	1	1	yes	characteristic
54	Dic₁₃	—	16	2	no	—
55	C₄⋊Q₈	—	52	1	no	—
56	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
57	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
58	#107	—	26	2	no	—
59	#107	—	52	1	no	—
60	C₄⋊C₈	—	52	1	no	—
61	C₄×C₈	D₅₂	1	1	yes	characteristic
62	C₃₂	—	4	1	no	—
63	C₂×C₁₃	#1364	1	1	yes	characteristic
64	C₂×C₁₃	#1415	1	1	yes	characteristic
65	C₂×C₁₃	#1420	1	1	yes	characteristic
66	C₂×Q₈	—	104	1	no	—
67	C₂×C₈	—	104	1	no	—
68	C₂×C₈	#6095	1	1	yes	characteristic
69	C₂×C₈	#6103	1	1	yes	characteristic
70	C₄⋊C₄	—	52	2	no	—
71	C₄⋊C₄	—	104	1	no	—
72	C₄²	D₁₀₄	1	1	yes	characteristic
73	C₁₆	—	2	1	no	—
74	C₁₆	#6105	1	1	yes	characteristic
75	C₁₆	#6107	1	1	yes	characteristic
76	C₁₃	#7450	1	1	yes	characteristic, complemented, Sylow
77	Q₈	—	208	1	no	—
78	Q₈	—	208	1	no	—
79	C₂×C₄	—	104	2	no	—
80	C₂×C₄	D₂₀₈	1	1	yes	characteristic
81	C₂×C₄	#88040	1	1	yes	characteristic
82	C₂×C₄	#88061	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	208	1	no	—
85	C₈	#88050	1	1	yes	characteristic
86	C₈	#88064	1	1	yes	characteristic
87	C₂²	#11718101	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	208	2	no	—
90	C₄	D₄₁₆	1	1	yes	characteristic
91	C₄	#11718041	1	1	yes	characteristic
92	C₄	#11718078	1	1	yes	characteristic
93	C₄	#11718109	1	1	yes	characteristic
94	C₂	#13112890	1	1	yes	characteristic
95	C₂	#13113015	1	1	yes	characteristic
96	C₂	#13113030	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11718101
commutator	C₂×C₁₃×C₁₆	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₃
Fitting	C₁₃×C₄⋊C₃₂	C₂
socle, prime radical	C₂²×C₁₃	#357
cosocle	C₄×C₁₃×C₁₆	C₂²
hypercenter	C₄⋊C₃₂	D₁₃
hypocenter	C₁₃	#7450
LCS	G ▷ C₂×C₁₃×C₁₆ ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄⋊C₃₂

Complements

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

N	H ≅ G/N	type
76. C₁₃	#7450	semidirect

Maximal subgroups

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

subgroup	index
#13117111	2
#13112908	2
C₁₃×C₄⋊C₃₂	2
#7450	13