Finite Group Databasebeta

← #15773773

Subgroups — #15773773

Order 3328.

280 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125581C211yesmaximal, characteristic
2#13114985C211yesmaximal, characteristic
3#13112831C212yesmaximal
4#13112825C212yesmaximal
5C13×#2165C211yesmaximal, characteristic
6#11719175—21no—
7C4×C13×M16C2211yescharacteristic
8#11718798—21no—
9#11718798C2212yes—
10#11718377—21no—
11#11718377C412yescomplemented
12#11718360C411yescharacteristic, complemented
13#11718342—21no—
14#11718341C411yescharacteristic, complemented
15C13×#364—21no—
16C13×#349C2212yes—
17C13×#347—21no—
18#11718152C2211yescharacteristic
19#11718149C2211yescharacteristic
20#11718148—21no—
21#11718115—21no—
22C2×C13×M16D411yescharacteristic
23C2×C13×M16C2311yescharacteristic
24C2×C42×C13D411yescharacteristic
25#88180—21no—
26#88180—41no—
27#88178—22no—
28#88178—41no—
29C2×#6099—21no—
30C2×Dic52—21no—
31C2×Dic52C2×C412yes—
32#88124—41no—
33#88123—21no—
34#88123—21no—
35C4×Dic26—22no—
36C4×Dic26—41no—
37C13×M32—22no—
38C13×#97C2×C411yescharacteristic
39C13×#97D411yescharacteristic
40C4×C8×C13C2×C411yescharacteristic
41C4×C8×C13D411yescharacteristic
42#88057—21no—
43#88057C2×C412yes—
44#88056—22no—
45#88056—22no—
46#11838—131nomaximal, Sylow
47C22×C4×C13—21no—
48C22×C4×C13C2×D411yescharacteristic
49C2×Dic26—22no—
50C2×Dic26—41no—
51C13×M16—41no—
52C13×M16—41no—
53C2×C8×C13C22⋊C411yescharacteristic
54C2×C8×C13C22⋊C411yescharacteristic
55C2×C8×C13C22×C411yescharacteristic
56C2×C8×C13C2×D411yescharacteristic
57C42×C13—21no—
58C42×C13C22⋊C411yescharacteristic
59C42×C13C22⋊C411yescharacteristic
60C22⋊Dic13—42no—
61C22⋊Dic13—41no—
62C4⋊Dic13—22no—
63C4⋊Dic13—41no—
64C4⋊Dic13—41no—
65C4⋊Dic13—41no—
66C4⋊Dic13—41no—
67#6101—42no—
68#6101—42no—
69C4×Dic13—42no—
70C4×Dic13—41no—
71#6099—41no—
72#6099—41no—
73C2×#1055—41no—
74Dic52—42no—
75Dic52—42no—
76C13×C16—42no—
77#3185—131no—
78#2165D1311yescharacteristic
79#1841—131no—
80#1342—132no—
81#1340—132no—
82C23×C13AGL(1,ℤ/8)11yescharacteristic
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—42no—
88C2×C4×C13C2×C22⋊C411yescharacteristic
89C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
90C2×Dic13—42no—
91C2×Dic13—42no—
92C2×Dic13—81no—
93Dic26—42no—
94Dic26—42no—
95Dic26—82no—
96C8×C13—21no—
97C8×C13—21no—
98C8×C13—21no—
99C8×C13—21no—
100#1055—81no—
101#533—261no—
102#498—131no—
103#494—131no—
104#487—261no—
105#470—132no—
106#470—261no—
107#441—132no—
108#441—261no—
109C4×M16C2×D1311yescharacteristic
110#364—21no—
111#349C2×D1312yes—
112#347—21no—
113#344—261no—
114#339—261no—
115#338—131no—
116H(3,ℤ/4)—131no—
117C22×C13—21no—
118C22×C13—41no—
119C22×C13#41811yescharacteristic
120C4×C13—22no—
121C4×C13—21no—
122C4×C13—41no—
123C4×C13#41011yescharacteristic
124C4×C13#42111yescharacteristic
125Dic13—82no—
126Dic13—82no—
127Dic13—161no—
128C2×Q16—132no—
129C2×Q16—261no—
130C2×M16—261no—
131C2×M16D5211yescharacteristic
132C2×M16C22×D1311yescharacteristic
133C4⋊Q8—261no—
134C4⋊Q8—261no—
135#125—521no—
136C22⋊Q8—262no—
137C22⋊Q8—521no—
138C4×Q8—262no—
139C4×Q8—521no—
140#117—261no—
141#117—521no—
142C2×C42D5211yescharacteristic
143M32—22no—
144#106—132no—
145#106—261no—
146#103—262no—
147#103—262no—
148#97C4×D1311yescharacteristic
149#97C22⋊D1311yescharacteristic
150C4×C8C4×D1311yescharacteristic
151C4×C8C22⋊D1311yescharacteristic
152C2×C13—21no—
153C2×C13—41no—
154C2×C13#151411yescharacteristic
155C2×Q8—262no—
156C2×Q8—521no—
157C22×C4—21no—
158C22×C4C2×D5211yescharacteristic
159Q16—522no—
160Q16—522no—
161M16—41no—
162M16—41no—
163M16—521no—
164M16—521no—
165C2×C8—521no—
166C2×C8#610311yescharacteristic
167C2×C8#610311yescharacteristic
168C2×C8C2×C4×D1311yescharacteristic
169C2×C8C2×C22⋊D1311yescharacteristic
170C4⋊C4—262no—
171C4⋊C4—521no—
172C4⋊C4—521no—
173C4⋊C4—522no—
174C4⋊C4—521no—
175C4⋊C4—521no—
176C4⋊C4—522no—
177C22⋊C4—522no—
178C22⋊C4—521no—
179C42—21no—
180C42—522no—
181C42—521no—
182C42#610311yescharacteristic
183C42#610311yescharacteristic
184C16—42no—
185C13#1183811yescharacteristic, complemented, Sylow
186C23#8816211yescharacteristic
187Q8—522no—
188Q8—522no—
189Q8—1042no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—522no—
196C2×C4—522no—
197C2×C4—1041no—
198C2×C4#8816211yescharacteristic
199C2×C4C2×#610311yescharacteristic
200C8—21no—
201C8—21no—
202C8—21no—
203C8—21no—
204C8—1041no—
205C22—21no—
206C22—41no—
207C22#1171879211yescharacteristic
208C4—22no—
209C4—21no—
210C4—41no—
211C4—1042no—
212C4—1042no—
213C4—2081no—
214C4#1171866711yescharacteristic
215C4#1171880011yescharacteristic
216C2—21no—
217C2—41no—
218C2#1311338411yescharacteristic
subgroupG/H
centerC2#13113384
commutatorC2×C8×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#2165C2
socleC2×C13#1514
prime radicalC23×C13AGL(1,ℤ/8)
cosocleC2×C13×M16C23
hypercenter#2165D13
hypocenterC13#11838
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
11. #11718377C4semidirect
12. #11718360C4semidirect
14. #11718341C4semidirect
185. C13#11838semidirect

Maximal subgroups

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

subgroupindex
#131255812
#131149852
#131128312
#131128252
C13×#21652
#1183813