Finite Group Databasebeta

← #15760344

Subgroups — #15760344

Order 3328.

706 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 119 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#13119782C211yesmaximal, characteristic
2#13114828C211yesmaximal, characteristic, complemented
3#13113503C212yesmaximal, complemented
4#13112738C212yesmaximal, complemented
5C13×#2975C211yesmaximal, characteristic, complemented
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88194—21no—
8C2×#88184—22no—
9C2×#88128C2211yescharacteristic
10C13×#436—24no—
11C13×#431C2212yes—
12C13×#407—22no—
13C2×#88073—21no—
14#11718649—21no—
15#11718621C414yes—
16C4×C4⋊Dic13C2211yescharacteristic
17#11718585C2212yes—
18#11718122—21no—
19#11718077—24no—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13D412yes—
22C22×C22⋊D13—24no—
23C22×D52—21no—
24C22×D52—21no—
25C22×D52C2×C412yes—
26C2×C13×M16—24no—
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C22⋊C4C2×C412yes—
31C2×C42×C13C2311yescharacteristic
32#88194—44no—
33#88184—48no—
34C2×#6103—24no—
35C2×C4⋊Dic13—21no—
36C2×C4×Dic13—21no—
37C2×#6099—22no—
38#88128—22no—
39#88128—22no—
40C13×C4⋊C8D414yescomplemented
41C13×C22⋊C8—24no—
42C13×C22⋊C8—22no—
43C4×C8×C13—22no—
44#88073—42no—
45#88071C2×C412yes—
46C4⋊#1055—22no—
47C4⋊#1055—22no—
48#9405—131nomaximal, Sylow
49C24×C13C22⋊C412yes—
50C23×D13—22no—
51C2×D4×C13—22no—
52C2×D4×C13—21no—
53C2×D4×C13—22no—
54C2×D4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—44no—
58C22×C4×C13C22⋊C412yes—
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C2×C22⋊D13—48no—
63C2×C22⋊D13—48no—
64C2×C22⋊D13—84no—
65C22×Dic13—22no—
66C2×D52—24no—
67C2×D52—44no—
68C2×D52—41no—
69C2×D52—42no—
70C2×D52—41no—
71C2×D52—42no—
72C2×D52—41no—
73C2×D52—41no—
74C2×D52—82no—
75C13×M16—84no—
76C2×C8×C13—24no—
77C13×C4⋊C4—22no—
78C13×C22⋊C4—24no—
79C42×C13C2×D412yes—
80C42×C13#4112yes—
81#6103—48no—
82C4⋊Dic13—24no—
83C4×Dic13—42no—
84#6099—42no—
85#6099—42no—
86C2×#1055—42no—
87#2975D1311yescharacteristic, complemented
88#2541—131no—
89#1800—131no—
90#1545—132no—
91#1303—132no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13C2×C22⋊C411yescharacteristic
98C22×D13—44no—
99C22×D13—44no—
100C22×D13—42no—
101C22×D13—42no—
102C22×D13—42no—
103D4×C13—42no—
104D4×C13—42no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—41no—
108C2×C4×C13—44no—
109C2×C4×C13—42no—
110C2×C4×C13—82no—
111C2×C4×C13C4×D412yes—
112C2×C4×C13#12011yescharacteristic
113C2×C4×C13#12112yes—
114C2×C4×C13#12311yescharacteristic
115C2×C4×C13AGL(1,ℤ/8)12yes—
116C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C13#13711yescharacteristic
118C22⋊D13—816no—
119C2×Dic13—24no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122D52—82no—
123D52—84no—
124D52—82no—
125D52—82no—
126D52—82no—
127C8×C13—44no—
128#1055—82no—
129C2×#127—131no—
130C2×#127—261no—
131C2×#121—262no—
132C2×C4×D4C2×D1311yescharacteristic
133#436—24no—
134#431C2×D1312yes—
135#423—132no—
136C2×#100—261no—
137#407—22no—
138#392—134no—
139#390—261no—
140C4×C4⋊C4—131no—
141#343—261no—
142#331—264no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—44no—
146C22×C13—42no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13—82no—
150C22×C13#38611yescharacteristic
151C22×C13#41711yescharacteristic
152C22×C13#41811yescharacteristic
153C2×D13—84no—
154C2×D13—84no—
155C2×D13—82no—
156C2×D13—82no—
157C2×D13—82no—
158C4×C13—21no—
159C4×C13—22no—
160C4×C13—42no—
161C4×C13#45312yes—
162C4×C13#46812yes—
163C4×C13#46912yes—
164Dic13—44no—
165C22×D4—132no—
166C22×D4—264no—
167C22×D4—261no—
168C22×D4—261no—
169C22×D4D5211yescharacteristic
170C23×C4C22⋊D1312yes—
171C2×M16—24no—
172C2×M16—262no—
173#127—262no—
174#127—262no—
175#127—524no—
176#121—528no—
177C4×D4—22no—
178C4×D4—22no—
179C2×C4⋊C4—261no—
180C2×C4⋊C4D5211yescharacteristic
181C2×C22⋊C4—264no—
182C2×C22⋊C4C4×D1312yes—
183C2×C42—261no—
184C2×C42C22×D1311yescharacteristic
185C4⋊C8—262no—
186C4⋊C8—262no—
187C4⋊C8C22⋊D1314yescomplemented
188#100—522no—
189C22⋊C8—24no—
190C22⋊C8—22no—
191C4×C8—22no—
192#95—132no—
193C2×C13—21no—
194C2×C13—21no—
195C2×C13—82no—
196C2×C13#188711yescharacteristic
197C2×C13#189511yescharacteristic
198C2×C13#191411yescharacteristic
199D13—162no—
200C24—262no—
201C24#610312yes—
202C2×D4—21no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—22no—
206C2×D4—264no—
207C2×D4—524no—
208C2×D4—528no—
209C2×D4—528no—
210C2×D4—522no—
211C2×D4—521no—
212C2×D4—521no—
213C2×D4—521no—
214C2×D4—522no—
215C2×D4—521no—
216C2×D4—1042no—
217C2×D4—1044no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—44no—
221C22×C4—262no—
222C22×C4#610312yes—
223C22×C4C2×C4×D1311yescharacteristic
224C22×C4C2×D5211yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226M16—84no—
227M16—522no—
228M16—522no—
229C2×C8—24no—
230C2×C8—522no—
231C4⋊C4—22no—
232C4⋊C4—264no—
233C22⋊C4—24no—
234C22⋊C4—528no—
235C42—522no—
236C42#612712yes—
237C42C2×C22⋊D1312yes—
238C13#940511yescharacteristic, complemented, Sylow
239C23—22no—
240C23—22no—
241C23—22no—
242C23—42no—
243C23—42no—
244C23—524no—
245C23—524no—
246C23—522no—
247C23—522no—
248C23—522no—
249C23C2×#610311yescharacteristic
250D4—42no—
251D4—42no—
252D4—1044no—
253D4—1042no—
254D4—10416no—
255D4—1042no—
256D4—1042no—
257D4—1042no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—41no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—82no—
264C2×C4—264no—
265C2×C4—522no—
266C2×C4—522no—
267C2×C4#8816212yes—
268C2×C4#8816211yescharacteristic
269C2×C4#8816311yescharacteristic
270C2×C4C4×C22⋊D1312yes—
271C2×C4#8818311yescharacteristic
272C2×C4#8818412yes—
273C2×C4#8820711yescharacteristic
274C8—44no—
275C8—1042no—
276C22—21no—
277C22—21no—
278C22—44no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—82no—
283C22—1044no—
284C22—1044no—
285C22—1042no—
286C22—1042no—
287C22—1042no—
288C22#1171879211yescharacteristic
289C22#1171879411yescharacteristic
290C22#1171887411yescharacteristic
291C4—21no—
292C4—22no—
293C4—42no—
294C4—524no—
295C4#1171879512yes—
296C4#1171879612yes—
297C4#1171890212yes—
298C2—21no—
299C2—21no—
300C2—82no—
301C2—2082no—
302C2#1311523411yescharacteristic
303C2#1311527411yescharacteristic
304C2#1311538311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2975C2
socleC22×C13#386
prime radical#13119782C2
cosocleC2×C42×C13C23
hypercenter#2975D13
hypocenterC13#9405
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2975

Complements

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

NH ≅ G/Ntype
2. #13114828C2semidirect
3. #13113503C2semidirect
4. #13112738C2semidirect
5. C13×#2975C2semidirect
40. C13×C4⋊C8D4semidirect
87. #2975D13semidirect
187. C4⋊C8C22⋊D13semidirect
238. C13#9405semidirect

Maximal subgroups

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

subgroupindex
#131197822
#131148282
#131135032
#131127382
C13×#29752
#940513