Finite Group Databasebeta

← #15760726

Subgroups — #15760726

Order 3328.

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

normal subgroups only

This group has 734 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#13119110C211yesmaximal, characteristic
2#13117189C211yesmaximal, characteristic
3#13114933C212yesmaximal, complemented
4#13112690C212yesmaximal, complemented
5C13×#1462C211yesmaximal, characteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C22×C22⋊Dic13—21no—
8C2×#88180C2211yescharacteristic
9C13×#407C2212yes—
10#11718908—21no—
11#11718872C2211yescharacteristic
12#11718871—21no—
13C4×C22⋊Dic13—21no—
14C4×C22⋊Dic13C2212yes—
15#11718614C412yescomplemented
16#11718610C412yescomplemented
17#11718605—22no—
18C22⋊C4×Dic13—24no—
19C13×#323—22no—
20#11718147—24no—
21C25×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C23×Dic13—22no—
25C2×C13×M16—22no—
26C2×C13×C22⋊C4—22no—
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4C2×C412yes—
29C2×C13×C22⋊C4D412yes—
30C2×C22⋊Dic13—28no—
31C2×C22⋊Dic13—22no—
32C2×C22⋊Dic13—22no—
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—22no—
37#88180—22no—
38#88180—22no—
39C2×C4⋊Dic13C2×C411yescharacteristic, complemented
40C2×C4⋊Dic13C2×C411yescharacteristic, complemented
41C2×#6101—22no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13—22no—
44C2×C4×Dic13D414yes—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—22no—
47#88071—22no—
48#88071—22no—
49#88071—22no—
50#88071—21no—
51#88071C2×C412yescomplemented
52#9477—131nomaximal, Sylow
53C24×C13—21no—
54C24×C13—24no—
55C24×C13—21no—
56C24×C13—42no—
57C24×C13—81no—
58C24×C13C22⋊C412yes—
59C24×C13C2×D411yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—42no—
63C22×C4×C13—81no—
64C22×C4×C13C22⋊C412yes—
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D412yes—
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13#4112yes—
69C22×Dic13—24no—
70C22×Dic13—28no—
71C22×Dic13—22no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—82no—
75C22×Dic13—82no—
76C13×M16—44no—
77C2×C8×C13—42no—
78C13×C22⋊C4—24no—
79C13×C22⋊C4—24no—
80C22⋊Dic13—28no—
81C22⋊Dic13—28no—
82C22⋊Dic13—42no—
83C22⋊Dic13—44no—
84C22⋊Dic13—41no—
85C22⋊Dic13—41no—
86C22⋊Dic13—82no—
87C4⋊Dic13—22no—
88C4⋊Dic13—22no—
89#6101—82no—
90C4×Dic13—42no—
91C4×Dic13—44no—
92C4×Dic13—82no—
93#2482—131no—
94#2273—131no—
95#1826—132no—
96#1462D1311yescharacteristic
97#1284—132no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—24no—
101C23×C13—22no—
102C23×C13—22no—
103C23×C13—22no—
104C23×C13—22no—
105C23×C13—41no—
106C23×C13—42no—
107C23×C13—42no—
108C23×C13—42no—
109C23×C13—42no—
110C23×C13—81no—
111C23×C13—81no—
112C23×C13—88no—
113C23×C13#10414yes—
114C23×C13C2×C22⋊C411yescharacteristic
115C23×C13#12011yescharacteristic
116C23×C13#12311yescharacteristic
117C2×C4×C13—24no—
118C2×C4×C13—22no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—81no—
125C2×C4×C13C4×D412yes—
126C2×C4×C13#12112yes—
127C2×Dic13—28no—
128C2×Dic13—44no—
129C2×Dic13—44no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13—88no—
138C8×C13—82no—
139C2×#117—131no—
140C22×C22⋊C4—261no—
141C22×C22⋊C4C2×D1311yescharacteristic
142#407C2×D1312yes—
143#399—132no—
144#397—132no—
145#388—262no—
146#385—261no—
147#381—131no—
148#379—261no—
149C4×C22⋊C4—132no—
150C4×C22⋊C4—264no—
151C4×C22⋊C4—261no—
152#339—264no—
153#323—22no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—24no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—44no—
163C22×C13—44no—
164C22×C13—44no—
165C22×C13—44no—
166C22×C13—42no—
167C22×C13—42no—
168C22×C13—82no—
169C22×C13—84no—
170C22×C13#38611yescharacteristic
171C22×C13C2×#10412yes—
172C22×C13#45812yes—
173C4×C13—22no—
174C4×C13—22no—
175C4×C13—42no—
176Dic13—48no—
177Dic13—82no—
178Dic13—81no—
179Dic13—81no—
180C25D5211yescharacteristic
181C23×C4—262no—
182C23×C4D5211yescharacteristic
183C23×C4C22×D1311yescharacteristic
184C2×M16—22no—
185#117—262no—
186#117—262no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—262no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—262no—
193C2×C22⋊C4—268no—
194C2×C22⋊C4—262no—
195C2×C22⋊C4—262no—
196C2×C22⋊C4—261no—
197C2×C22⋊C4—261no—
198C2×C22⋊C4—262no—
199C2×C22⋊C4C4×D1312yes—
200C2×C22⋊C4C22⋊D1312yes—
201C2×C42—134no—
202C2×C42—261no—
203C2×C42—262no—
204C22⋊C8—22no—
205C22⋊C8—22no—
206#95—132no—
207#95—262no—
208#95—262no—
209#95—262no—
210#95—261no—
211C2×C13—22no—
212C2×C13—22no—
213C2×C13—41no—
214C2×C13—44no—
215C2×C13#189011yescharacteristic
216C2×C13#189611yescharacteristic
217C2×C13#191111yescharacteristic
218C24—21no—
219C24—24no—
220C24—21no—
221C24—42no—
222C24—81no—
223C24#610312yes—
224C24C2×D5211yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—42no—
228C22×C4—81no—
229C22×C4—264no—
230C22×C4—268no—
231C22×C4—262no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4—1042no—
235C22×C4—1042no—
236C22×C4#610312yes—
237C22×C4C2×C4×D1311yescharacteristic
238C22×C4D4×D1312yes—
239C22×C4#612912yes—
240C22×C4C2×C22⋊D1311yescharacteristic
241M16—44no—
242C2×C8—42no—
243C4⋊C4—262no—
244C4⋊C4—262no—
245C4⋊C4—1042no—
246C22⋊C4—24no—
247C22⋊C4—24no—
248C22⋊C4—268no—
249C22⋊C4—268no—
250C22⋊C4—522no—
251C22⋊C4—524no—
252C22⋊C4—521no—
253C22⋊C4—521no—
254C22⋊C4—1042no—
255C42—524no—
256C42—522no—
257C42—1042no—
258C13#947711yescharacteristic, complemented, Sylow
259C23—22no—
260C23—22no—
261C23—24no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—41no—
267C23—42no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—81no—
272C23—81no—
273C23—88no—
274C23#8806514yes—
275C23#8813611yescharacteristic
276C23#8814011yescharacteristic
277C23C2×#610311yescharacteristic
278C2×C4—24no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—81no—
286C2×C4—268no—
287C2×C4—524no—
288C2×C4—524no—
289C2×C4—522no—
290C2×C4—522no—
291C2×C4—522no—
292C2×C4—522no—
293C2×C4—522no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—1048no—
297C2×C4#8813512yes—
298C2×C4#8819312yes—
299C8—82no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—24no—
306C22—21no—
307C22—21no—
308C22—44no—
309C22—44no—
310C22—44no—
311C22—44no—
312C22—42no—
313C22—42no—
314C22—82no—
315C22—84no—
316C22#1171840312yes—
317C22#1171861911yescharacteristic
318C22C2×#8806512yes—
319C4—22no—
320C4—22no—
321C4—42no—
322C4—528no—
323C4—1042no—
324C4—1041no—
325C4—1041no—
326C2—22no—
327C2—22no—
328C2—41no—
329C2—44no—
330C2#1311524711yescharacteristic
331C2#1311527711yescharacteristic
332C2#1311536611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1462C2
socleC22×C13#386
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenter#1462D13
hypocenterC13#9477
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
3. #13114933C2semidirect
4. #13112690C2semidirect
15. #11718614C4semidirect
16. #11718610C4semidirect
39. C2×C4⋊Dic13C2×C4semidirect
40. C2×C4⋊Dic13C2×C4semidirect
51. #88071C2×C4semidirect
258. C13#9477semidirect

Maximal subgroups

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

subgroupindex
#131191102
#131171892
#131149332
#131126902
C13×#14622
#947713