Subgroups — #15750574

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	C₄⋊#88034	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1371	C₂	1	1	yes	maximal, characteristic
4	#11718343	—	2	1	no	—
5	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₁₃×#335	—	2	1	no	—
7	#11718096	—	2	1	no	—
8	#11718096	C₄	1	2	yes	—
9	C₂×#88034	—	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	C₁₃×C₄⋊C₈	—	4	1	no	—
14	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
15	#88058	—	2	2	no	—
16	#88058	—	4	1	no	—
17	#88034	—	4	1	no	—
18	#7451	—	13	1	no	maximal, Sylow
19	C₂×Dic₂₆	—	8	1	no	—
20	C₂×C₈×C₁₃	—	8	1	no	—
21	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
23	C₄²×C₁₃	D₈	1	1	yes	characteristic
24	C₄⋊Dic₁₃	—	4	2	no	—
25	C₄⋊Dic₁₃	—	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	—	13	1	no	—
31	#1371	D₁₃	1	1	yes	characteristic
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	2	no	—
37	C₈×C₁₃	—	2	1	no	—
38	C₈×C₁₃	—	16	1	no	—
39	C₈×C₁₃	#101	1	1	yes	characteristic
40	C₈×C₁₃	#103	1	1	yes	characteristic
41	#500	—	26	1	no	—
42	C₂×C₃₂	—	26	1	no	—
43	#366	—	13	2	no	—
44	#366	—	26	1	no	—
45	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
46	#335	—	2	1	no	—
47	C₂²×C₁₃	#357	1	1	yes	characteristic
48	C₄×C₁₃	—	2	1	no	—
49	C₄×C₁₃	#332	1	1	yes	characteristic
50	C₄×C₁₃	#362	1	1	yes	characteristic
51	C₄×C₁₃	SD₆₄	1	1	yes	characteristic
52	C₄×C₁₃	Q₆₄	1	1	yes	characteristic
53	Dic₁₃	—	16	2	no	—
54	C₄⋊Q₈	—	52	1	no	—
55	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
56	C₂×C₁₆	D₅₂	1	1	yes	characteristic
57	#107	—	26	2	no	—
58	#107	—	52	1	no	—
59	C₄⋊C₈	—	4	1	no	—
60	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
61	C₃₂	—	52	1	no	—
62	C₂×C₁₃	#1364	1	1	yes	characteristic
63	C₂×C₁₃	#1416	1	1	yes	characteristic
64	C₂×C₁₃	#1419	1	1	yes	characteristic
65	C₂×Q₈	—	104	1	no	—
66	C₂×C₈	—	8	1	no	—
67	C₂×C₈	#6103	1	1	yes	characteristic
68	C₂×C₈	#6106	1	1	yes	characteristic
69	C₄⋊C₄	—	52	2	no	—
70	C₄⋊C₄	—	104	1	no	—
71	C₄²	#6104	1	1	yes	characteristic
72	C₁₆	—	2	1	no	—
73	C₁₆	#6095	1	1	yes	characteristic
74	C₁₆	Dic₅₂	1	1	yes	characteristic
75	C₁₃	#7451	1	1	yes	characteristic, complemented, Sylow
76	Q₈	—	208	2	no	—
77	C₂×C₄	—	104	2	no	—
78	C₂×C₄	#88049	1	1	yes	characteristic
79	C₂×C₄	#88066	1	1	yes	characteristic
80	C₂×C₄	#88068	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	16	1	no	—
83	C₈	#88056	1	1	yes	characteristic
84	C₈	#88064	1	1	yes	characteristic
85	C₂²	#11718083	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	208	2	no	—
88	C₄	#11718074	1	1	yes	characteristic
89	C₄	#11718088	1	1	yes	characteristic
90	C₄	#11718112	1	1	yes	characteristic
91	C₄	#11718114	1	1	yes	characteristic
92	C₂	#13112892	1	1	yes	characteristic
93	C₂	#13113016	1	1	yes	characteristic
94	C₂	#13113025	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11718083
commutator	C₂×C₁₃×C₁₆	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₃
Fitting	C₁₃×#1371	C₂
socle, prime radical	C₂²×C₁₃	#357
cosocle	C₄×C₁₃×C₁₆	C₂²
hypercenter	#1371	D₁₃
hypocenter	C₁₃	#7451
LCS	G ▷ C₂×C₁₃×C₁₆ ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1371

Complements

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

N	H ≅ G/N	type
75. C₁₃	#7451	semidirect

Maximal subgroups

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

subgroup	index
#13117111	2
C₄⋊#88034	2
C₁₃×#1371	2
#7451	13