Finite Group Databasebeta

← #15760749

Subgroups — #15760749

Order 3328.

614 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 107 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#13117434C211yesmaximal, characteristic
2#13114935C212yesmaximal, complemented
3#13113163C211yesmaximal, characteristic
4#13112688C212yesmaximal, complemented
5C13×#2482C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C22×C13×C22⋊C4C2211yescharacteristic
8C13×#399C412yescomplemented
9C13×#397C412yescomplemented
10C13×#388—22no—
11C13×#385—21no—
12C13×#381C2211yescharacteristic
13C13×#379—21no—
14#11718908—21no—
15#11718873—21no—
16C4×C22⋊Dic13C2212yes—
17#11718868C2212yes—
18#11718612—24no—
19#11718124—24no—
20#11718117—22no—
21C25×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C13×#117—22no—
25C13×#117—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4—21no—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4C2×C412yes—
36C2×C13×C22⋊C4D412yes—
37C2×C42×C13—21no—
38C2×C22⋊Dic13—22no—
39C2×C22⋊Dic13—22no—
40C2×C22⋊Dic13—22no—
41C2×C4⋊Dic13—22no—
42C2×C4×Dic13D414yes—
43C2×#6099—22no—
44C13×#95—22no—
45C13×#95—21no—
46C13×#95C2×C412yes—
47#88071—22no—
48#88071—22no—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#9481—131nomaximal, Sylow
52C24×C13—21no—
53C24×C13—21no—
54C24×C13—42no—
55C24×C13—42no—
56C24×C13—81no—
57C24×C13C22⋊C412yes—
58C24×C13C2×D411yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—42no—
65C22×C4×C13—81no—
66C22×C4×C13C22⋊C412yes—
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D412yes—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13#4112yes—
71C22×Dic13—24no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—82no—
75C13×C22⋊C4—24no—
76C13×C22⋊C4—24no—
77C13×C22⋊C4—42no—
78C13×C22⋊C4—44no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—82no—
82C42×C13—42no—
83C22⋊Dic13—44no—
84C22⋊Dic13—82no—
85C22⋊Dic13—82no—
86C4⋊Dic13—82no—
87C4×Dic13—44no—
88#6099—44no—
89C2×#1055—42no—
90#2482D1311yescharacteristic
91#2312—131no—
92#1826—132no—
93#1462—131no—
94#1284—132no—
95C23×C13—22no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—41no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13—42no—
105C23×C13—42no—
106C23×C13—42no—
107C23×C13—81no—
108C23×C13—81no—
109C23×C13—88no—
110C23×C13C2×C22⋊C411yescharacteristic
111C23×C13#12011yescharacteristic
112C23×C13#12311yescharacteristic
113C2×C4×C13—24no—
114C2×C4×C13—22no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—81no—
128C2×C4×C13C4×D412yes—
129C2×C4×C13#12112yes—
130C2×Dic13—44no—
131C2×Dic13—44no—
132C2×Dic13—44no—
133#1055—82no—
134C2×#117C2×D1311yescharacteristic
135C22×C22⋊C4C2×D1311yescharacteristic
136#407—132no—
137#399Dic1312yescomplemented
138#397Dic1312yescomplemented
139#388—22no—
140#388—264no—
141#385—21no—
142#381C2×D1311yescharacteristic
143#380—261no—
144#379—21no—
145#379—261no—
146C4×C22⋊C4—132no—
147#339—264no—
148#323—262no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—44no—
157C22×C13—44no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—82no—
162C22×C13—84no—
163C22×C13—84no—
164C22×C13#38611yescharacteristic
165C22×C13#42112yes—
166C22×C13#45812yes—
167C4×C13—22no—
168C4×C13—22no—
169C4×C13—42no—
170C4×C13—82no—
171C4×C13—81no—
172C4×C13—81no—
173Dic13—84no—
174C25C22⋊D1311yescharacteristic
175C23×C4C22⋊D1311yescharacteristic
176C23×C4C22×D1311yescharacteristic
177C2×M16—262no—
178#117—22no—
179#117—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—262no—
182C2×C4⋊C4C2×Dic1311yescharacteristic
183C2×C4⋊C4C2×Dic1311yescharacteristic
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—21no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—262no—
191C2×C22⋊C4—262no—
192C2×C22⋊C4—262no—
193C2×C22⋊C4C2×Dic1312yes—
194C2×C22⋊C4C22⋊D1312yes—
195C2×C42—21no—
196C2×C42—134no—
197C22⋊C8—262no—
198C22⋊C8—262no—
199#95—22no—
200#95—21no—
201#95—262no—
202#95—262no—
203#95C2×Dic1312yes—
204C2×C13—22no—
205C2×C13—22no—
206C2×C13—41no—
207C2×C13—82no—
208C2×C13#189011yescharacteristic
209C2×C13#189711yescharacteristic
210C2×C13#191111yescharacteristic
211C24—21no—
212C24—21no—
213C24—42no—
214C24—42no—
215C24—81no—
216C24C22⋊Dic1312yes—
217C24C2×C22⋊D1311yescharacteristic
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—42no—
224C22×C4—81no—
225C22×C4—264no—
226C22×C4C22⋊Dic1312yes—
227C22×C4D4×D1312yes—
228C22×C4#612912yes—
229C22×C4C22×Dic1311yescharacteristic
230C22×C4C2×C22⋊D1311yescharacteristic
231M16—524no—
232C2×C8—522no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—82no—
236C4⋊C4—1042no—
237C22⋊C4—24no—
238C22⋊C4—24no—
239C22⋊C4—42no—
240C22⋊C4—44no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—82no—
244C22⋊C4—524no—
245C22⋊C4—1042no—
246C22⋊C4—1042no—
247C42—42no—
248C42—524no—
249C13#948111yescharacteristic, complemented, Sylow
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—41no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—81no—
263C23—81no—
264C23—88no—
265C23#8818911yescharacteristic
266C23#8819111yescharacteristic
267C23C2×C22⋊Dic1311yescharacteristic
268C2×C4—24no—
269C2×C4—22no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—81no—
283C2×C4—524no—
284C2×C4—524no—
285C2×C4—524no—
286C2×C4D4×Dic1312yes—
287C2×C4#8819312yes—
288C8—1042no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—44no—
297C22—44no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—82no—
302C22—84no—
303C22—84no—
304C22#1171871412yes—
305C22#1171888111yescharacteristic
306C22#1171889712yes—
307C4—22no—
308C4—22no—
309C4—42no—
310C4—82no—
311C4—81no—
312C4—81no—
313C4—1044no—
314C2—22no—
315C2—22no—
316C2—41no—
317C2—82no—
318C2#1311525011yescharacteristic
319C2#1311528511yescharacteristic
320C2#1311536911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2482C2
socleC22×C13#386
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenter#2482D13
hypocenterC13#9481
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
2. #13114935C2semidirect
4. #13112688C2semidirect
8. C13×#399C4semidirect
9. C13×#397C4semidirect
137. #399Dic13semidirect
138. #397Dic13semidirect
249. C13#9481semidirect

Maximal subgroups

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

subgroupindex
#131174342
#131149352
#131131632
#131126882
C13×#24822
#948113