Subgroups — #16777961

Order 3328.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129996	C₂	1	1	yes	maximal, characteristic
2	#13129872	C₂	1	1	yes	maximal, characteristic
3	#13117114	C₂	1	1	yes	maximal, characteristic
4	#11718539	—	2	1	no	—
5	#11718261	—	2	1	no	—
6	#11718249	—	2	1	no	—
7	C₁₃×#367	C₄	1	1	yes	characteristic
8	#11718097	C₄	1	1	yes	characteristic
9	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
10	#11718081	—	2	1	no	—
11	#88144	—	4	1	no	—
12	#88106	—	4	1	no	—
13	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
14	C₁₃×#107	—	2	1	no	—
15	#88058	—	2	1	no	—
16	C₈×Dic₁₃	D₄	1	1	yes	characteristic
17	C₂×#6090	D₄	1	1	yes	characteristic
18	#88048	—	4	1	no	—
19	#88036	—	4	1	no	—
20	#7454	—	13	1	no	maximal, Sylow
21	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₁₃×C₄⋊C₄	—	4	1	no	—
23	C₄⋊Dic₁₃	—	4	1	no	—
24	C₄⋊Dic₁₃	—	8	1	no	—
25	#6101	—	8	1	no	—
26	C₄×Dic₁₃	SD₁₆	1	1	yes	characteristic
27	C₂×#1055	D₈	1	1	yes	characteristic
28	#6092	—	8	1	no	—
29	C₁₃×C₁₆	—	2	1	no	—
30	#6090	SD₁₆	1	1	yes	characteristic
31	#6090	Q₁₆	1	1	yes	characteristic
32	#2253	—	13	1	no	—
33	#1422	—	13	1	no	—
34	#1373	—	13	1	no	—
35	C₂×C₄×C₁₃	—	8	1	no	—
36	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
37	C₂×Dic₁₃	—	2	1	no	—
38	C₂×Dic₁₃	—	8	1	no	—
39	C₈×C₁₃	#101	1	1	yes	characteristic
40	C₈×C₁₃	#103	1	1	yes	characteristic
41	#1055	SD₃₂	1	1	yes	characteristic
42	#1055	Q₃₂	1	1	yes	characteristic
43	#499	—	26	1	no	—
44	M₆₄	—	26	1	no	—
45	#367	—	13	1	no	—
46	#367	#261	1	1	yes	characteristic
47	#366	—	26	1	no	—
48	#364	—	26	1	no	—
49	C₄×C₁₆	—	13	1	no	—
50	C₂²×C₁₃	#361	1	1	yes	characteristic
51	C₄×C₁₃	—	16	1	no	—
52	C₄×C₁₃	#332	1	1	yes	characteristic
53	C₄×C₁₃	#358	1	1	yes	characteristic
54	Dic₁₃	—	4	1	no	—
55	Dic₁₃	—	16	1	no	—
56	#125	—	52	1	no	—
57	M₃₂	—	52	1	no	—
58	C₂×C₁₆	—	13	1	no	—
59	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
60	#107	—	2	1	no	—
61	#107	—	26	1	no	—
62	#106	—	52	1	no	—
63	C₄×C₈	—	13	1	no	—
64	C₃₂	—	52	1	no	—
65	C₂×C₁₃	—	2	1	no	—
66	C₂×C₁₃	#1365	1	1	yes	characteristic
67	C₂×C₈	—	13	1	no	—
68	C₂×C₈	C₂²⋊#261	1	1	yes	characteristic
69	C₄⋊C₄	—	4	1	no	—
70	C₄⋊C₄	—	52	1	no	—
71	C₄⋊C₄	—	104	1	no	—
72	C₄⋊C₄	—	104	1	no	—
73	C₄²	—	13	1	no	—
74	C₁₆	—	2	1	no	—
75	C₁₆	—	13	1	no	—
76	C₁₆	—	13	1	no	—
77	C₁₆	—	104	1	no	—
78	C₁₃	#7454	1	1	yes	characteristic, complemented, Sylow
79	C₂×C₄	—	8	1	no	—
80	C₂×C₄	—	26	1	no	—
81	C₂×C₄	—	104	1	no	—
82	C₂×C₄	#88115	1	1	yes	characteristic
83	C₈	—	13	1	no	—
84	C₈	—	13	1	no	—
85	C₈	#88113	1	1	yes	characteristic
86	C₈	#88117	1	1	yes	characteristic
87	C₂²	#11718278	1	1	yes	characteristic
88	C₄	—	16	1	no	—
89	C₄	—	52	1	no	—
90	C₄	—	208	1	no	—
91	C₄	#11718245	1	1	yes	characteristic
92	C₄	#11718280	1	1	yes	characteristic
93	C₂	—	2	1	no	—
94	C₂	#13129855	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13129855
commutator	C₂×C₁₃×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×#261
Fitting	C₁₃×#367	C₄
socle	C₂×C₁₃	#1365
prime radical	C₂²×C₁₃	#361
cosocle	C₁₆×Dic₁₃	C₂²
hypercenter	#367	#261
hypocenter	C₁₃	#7454
LCS	G ▷ C₂×C₁₃×C₁₆ ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #367

Complements

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

N	H ≅ G/N	type
78. C₁₃	#7454	semidirect

Maximal subgroups

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

subgroup	index
#13129996	2
#13129872	2
#13117114	2
#7454	13