Subgroups — #15750570

Order 3328.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#88034	C₂	1	1	yes	maximal, characteristic
2	#13112908	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2252	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#500	—	2	1	no	—
5	C₁₃×#366	—	2	1	no	—
6	C₁₃×#366	C₄	1	2	yes	—
7	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×#88034	—	2	1	no	—
9	#11718050	—	2	1	no	—
10	C₁₃×C₄⋊Q₈	—	4	1	no	—
11	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
13	C₁₃×#107	—	2	2	no	—
14	C₁₃×#107	—	4	1	no	—
15	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
16	C₄⋊#1055	—	4	1	no	—
17	#88034	—	4	1	no	—
18	#7450	—	13	1	no	maximal, Sylow
19	C₂×Q₈×C₁₃	—	8	1	no	—
20	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
22	C₁₃×C₄⋊C₄	—	4	2	no	—
23	C₁₃×C₄⋊C₄	—	8	1	no	—
24	C₄²×C₁₃	D₈	1	1	yes	characteristic
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	D₁₃	1	1	yes	characteristic
30	C₄⋊C₃₂	—	13	1	no	—
31	#1371	—	13	1	no	—
32	Q₈×C₁₃	—	16	1	no	—
33	Q₈×C₁₃	—	16	1	no	—
34	C₂×C₄×C₁₃	—	8	2	no	—
35	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
36	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
37	C₂×C₄×C₁₃	SD₃₂	1	1	yes	characteristic
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	—	2	1	no	—
43	C₂×C₃₂	—	26	1	no	—
44	#366	—	2	1	no	—
45	#366	Dic₁₃	1	2	yes	—
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	—	16	2	no	—
51	C₄×C₁₃	#332	1	1	yes	characteristic
52	C₄×C₁₃	#362	1	1	yes	characteristic
53	C₄×C₁₃	D₃₂	1	1	yes	characteristic
54	C₄×C₁₃	SD₆₄	1	1	yes	characteristic
55	C₄⋊Q₈	—	4	1	no	—
56	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
57	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
58	#107	—	2	2	no	—
59	#107	—	4	1	no	—
60	C₄⋊C₈	—	52	1	no	—
61	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
62	C₃₂	—	52	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	—	8	1	no	—
67	C₂×C₈	—	104	1	no	—
68	C₂×C₈	#6105	1	1	yes	characteristic
69	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
70	C₄⋊C₄	—	4	2	no	—
71	C₄⋊C₄	—	8	1	no	—
72	C₄²	#6104	1	1	yes	characteristic
73	C₁₆	—	2	1	no	—
74	C₁₆	#6106	1	1	yes	characteristic
75	C₁₆	#6107	1	1	yes	characteristic
76	C₁₃	#7450	1	1	yes	characteristic, complemented, Sylow
77	Q₈	—	16	1	no	—
78	Q₈	—	16	1	no	—
79	C₂×C₄	—	8	2	no	—
80	C₂×C₄	#88066	1	1	yes	characteristic
81	C₂×C₄	#88067	1	1	yes	characteristic
82	C₂×C₄	#88072	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	208	1	no	—
85	C₈	#88075	1	1	yes	characteristic
86	C₈	#88076	1	1	yes	characteristic
87	C₂²	#11718154	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	16	2	no	—
90	C₄	#11718111	1	1	yes	characteristic
91	C₄	#11718112	1	1	yes	characteristic
92	C₄	#11718139	1	1	yes	characteristic
93	C₄	#11718157	1	1	yes	characteristic
94	C₂	#13112891	1	1	yes	characteristic
95	C₂	#13113014	1	1	yes	characteristic
96	C₂	#13113029	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11718154
commutator	C₂×C₁₃×C₁₆	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₃
Fitting	C₁₃×#2252	C₂
socle, prime radical	C₂²×C₁₃	#357
cosocle	C₄×C₁₃×C₁₆	C₂²
hypercenter	#2252	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 ◁ #2252

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
C₄⋊#88034	2
#13112908	2
C₁₃×#2252	2
#7450	13