Finite Group Databasebeta

← #15760315

Subgroups — #15760315

Order 3328.

514 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 123 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#13123877C211yesmaximal, characteristic
2#13114828C211yesmaximal, characteristic
3#13113517C212yesmaximal, complemented
4#13112739C212yesmaximal, complemented
5C13×#2563C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#393C414yes—
9C13×#390—21no—
10C13×#382—21no—
11C13×#380—22no—
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88073—21no—
14#11718868—22no—
15#11718673—24no—
16#11718586C2212yes—
17#11718585C2212yes—
18#11718138—24no—
19#11718122—21no—
20C22×Q8×C13C2×C412yes—
21C22×D4×C13D411yescharacteristic
22C23×C4×C13D412yes—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8—22no—
25C4×D4×C13—22no—
26C4×D4×C13—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C22⋊C4—24no—
32C2×C13×C22⋊C4C2×C412yes—
33C2×C42×C13—21no—
34C2×C42×C13C2311yescharacteristic
35C2×#6099—24no—
36C2×#6099—22no—
37C13×#95—24no—
38C13×#95C2×C412yes—
39#88073—42no—
40C22⋊#1055—24no—
41C22⋊#1055—22no—
42C4⋊#1055—22no—
43C4⋊#1055—22no—
44C4⋊#1055D414yes—
45C4×#1055—22no—
46#9399—131nomaximal, Sylow
47C24×C13C22⋊C412yes—
48C2×Q8×C13—24no—
49C2×Q8×C13—82no—
50C2×D4×C13—22no—
51C2×D4×C13—21no—
52C2×D4×C13—22no—
53C2×D4×C13—21no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—44no—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C13×C4⋊C4—22no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—41no—
68C13×C22⋊C4—24no—
69C13×C22⋊C4—84no—
70C42×C13—41no—
71C42×C13—41no—
72C42×C13C2×D412yes—
73C42×C13#4112yes—
74#6099—42no—
75#6099—42no—
76#6099—84no—
77C2×#1055—24no—
78C2×#1055—42no—
79#2975—131no—
80#2563D1311yescharacteristic
81#1800—131no—
82#1548—132no—
83#1303—132no—
84C23×C13—22no—
85C23×C13—22no—
86C23×C13—22no—
87C23×C13—42no—
88C23×C13—42no—
89C23×C13C2×C22⋊C411yescharacteristic
90Q8×C13—84no—
91D4×C13—42no—
92D4×C13—42no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—41no—
96C2×C4×C13—44no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—44no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—82no—
104C2×C4×C13C4×D412yes—
105C2×C4×C13#12011yescharacteristic
106C2×C4×C13#12112yes—
107C2×C4×C13#12311yescharacteristic
108C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
109C2×C4×C13#13712yes—
110C2×C4×C13#13711yescharacteristic
111#1055—44no—
112#1055—82no—
113C2×C4⋊Q8C2×D1311yescharacteristic
114C2×C4×D4C2×D1311yescharacteristic
115#436—264no—
116#431—132no—
117#423—132no—
118C2×#100—261no—
119#407—262no—
120#393Dic1314yes—
121#390—21no—
122#382—21no—
123#380—22no—
124C4×C4⋊C4C2×D1311yescharacteristic
125#343—261no—
126#333—264no—
127C22×C13—21no—
128C22×C13—21no—
129C22×C13—44no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13—82no—
134C22×C13#38611yescharacteristic
135C22×C13#41711yescharacteristic
136C22×C13#41911yescharacteristic
137C4×C13—21no—
138C4×C13—22no—
139C4×C13—42no—
140C4×C13—82no—
141C4×C13—82no—
142C4×C13#45512yes—
143C4×C13#46812yes—
144C4×C13#47012yes—
145C22×Q8C2×Dic1312yes—
146C22×D4C22⋊D1311yescharacteristic
147C23×C4C22⋊D1312yes—
148C2×M16—264no—
149C2×M16—262no—
150C4⋊Q8—22no—
151C4⋊Q8—22no—
152C4×D4—22no—
153C4×D4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C22⋊D1311yescharacteristic
158C2×C22⋊C4—24no—
159C2×C22⋊C4C2×Dic1312yes—
160C2×C42—21no—
161C2×C42C22×D1311yescharacteristic
162C4⋊C8—134no—
163C4⋊C8—262no—
164C4⋊C8—262no—
165#100—522no—
166C22⋊C8—264no—
167C22⋊C8—262no—
168C4×C8—262no—
169#95—24no—
170#95C2×Dic1312yes—
171C2×C13—21no—
172C2×C13—21no—
173C2×C13—82no—
174C2×C13#188511yescharacteristic
175C2×C13#189411yescharacteristic
176C2×C13#191411yescharacteristic
177C24C22⋊Dic1312yes—
178C2×Q8—24no—
179C2×Q8—82no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—21no—
183C2×D4—21no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—44no—
189C22×C4C22⋊Dic1312yes—
190C22×C4C22×Dic1311yescharacteristic
191C22×C4C2×C22⋊D1311yescharacteristic
192C22×C4C2×C22⋊D1311yescharacteristic
193M16—522no—
194M16—522no—
195M16—1044no—
196C2×C8—264no—
197C2×C8—522no—
198C4⋊C4—22no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—42no—
203C22⋊C4—24no—
204C22⋊C4—84no—
205C42—41no—
206C42—41no—
207C42D4×D1312yes—
208C42#612912yes—
209C13#939911yescharacteristic, complemented, Sylow
210C23—22no—
211C23—22no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23C2×C22⋊Dic1311yescharacteristic
216Q8—84no—
217D4—42no—
218D4—42no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—44no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—82no—
230C2×C4D4×Dic1312yes—
231C2×C4#8818911yescharacteristic
232C2×C4#8819111yescharacteristic
233C2×C4#8819312yes—
234C2×C4#8819612yes—
235C2×C4#8820311yescharacteristic
236C2×C4#8820511yescharacteristic
237C8—524no—
238C8—1042no—
239C22—21no—
240C22—21no—
241C22—44no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—82no—
246C22#1171888111yescharacteristic
247C22#1171888611yescharacteristic
248C22#1171889311yescharacteristic
249C4—21no—
250C4—22no—
251C4—42no—
252C4—82no—
253C4—82no—
254C4#1171871012yes—
255C4#1171871312yes—
256C4#1171872212yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2#1311522511yescharacteristic
261C2#1311527011yescharacteristic
262C2#1311538411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2563C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenter#2563D13
hypocenterC13#9399
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2563

Complements

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

NH ≅ G/Ntype
3. #13113517C2semidirect
4. #13112739C2semidirect
209. C13#9399semidirect

Maximal subgroups

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

subgroupindex
#131238772
#131148282
#131135172
#131127392
C13×#25632
#939913