Finite Group Databasebeta

← #15760864

Subgroups — #15760864

Order 3328.

878 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 878 conjugacy classes of subgroups — too many to draw. Only its 111 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, complemented
2#13114757C212yesmaximal, complemented
3#13113174C211yesmaximal, characteristic, complemented
4#13112742C212yesmaximal, complemented
5C13×#2408C211yesmaximal, characteristic
6C23×D4×C13C2211yescharacteristic
7C2×C13×#121—21no—
8C2×C13×#120C412yes—
9C2×C4×D4×C13C2211yescharacteristic
10C13×#394—21no—
11C13×#392—21no—
12C13×#390—21no—
13C13×#380C2211yescharacteristic
14C13×#379C412yes—
15C2×#88073—24no—
16#11718868—21no—
17#11718868C2212yes—
18#11718868C2212yes—
19#11718673—24no—
20#11718586—21no—
21#11718120—21no—
22#11718117—21no—
23C25×C13C2×C412yes—
24C22×D4×C13—22no—
25C22×D4×C13—21no—
26C22×D4×C13—22no—
27C22×D4×C13—21no—
28C22×D4×C13—22no—
29C22×D4×C13—44no—
30C22×D4×C13C2×C411yescharacteristic
31C23×C4×C13D411yescharacteristic
32C23×C4×C13C2311yescharacteristic
33C13×#121—44no—
34C13×#120—44no—
35C4×D4×C13—22no—
36C4×D4×C13—22no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4C2×C412yes—
44C2×C13×C22⋊C4D411yescharacteristic
45C2×C42×C13D411yescharacteristic
46C2×#6099—22no—
47C2×#6099—22no—
48C2×#6099D414yescomplemented
49C13×#95—21no—
50#88073—48no—
51C22⋊#1055—22no—
52C22⋊#1055—22no—
53C22⋊#1055—22no—
54C22⋊#1055—22no—
55C22⋊#1055—22no—
56C4⋊#1055—22no—
57C4×#1055—22no—
58#9504—131nomaximal, Sylow
59C24×C13—22no—
60C24×C13—24no—
61C24×C13—44no—
62C24×C13—42no—
63C24×C13—42no—
64C24×C13—82no—
65C24×C13C22⋊C411yescharacteristic
66C24×C13C22×C411yescharacteristic
67C2×D4×C13—28no—
68C2×D4×C13—24no—
69C2×D4×C13—22no—
70C2×D4×C13—22no—
71C2×D4×C13—41no—
72C2×D4×C13—44no—
73C2×D4×C13—42no—
74C2×D4×C13—44no—
75C2×D4×C13—48no—
76C2×D4×C13—44no—
77C2×D4×C13—44no—
78C2×D4×C13—41no—
79C2×D4×C13—42no—
80C2×D4×C13—41no—
81C2×D4×C13—82no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—22no—
85C22×C4×C13—42no—
86C22×C4×C13—42no—
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22⋊C411yescharacteristic
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C2×D412yes—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13#4112yes—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—42no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—22no—
98C13×C22⋊C4—44no—
99C13×C22⋊C4—44no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—82no—
102C42×C13—21no—
103C42×C13—21no—
104#6099—44no—
105#6099—44no—
106#6099—82no—
107C2×#1055—24no—
108C2×#1055—42no—
109#2975—131no—
110#2408D1311yescharacteristic
111#1783—132no—
112#1465—131no—
113#1305—132no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—24no—
117C23×C13—28no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13—44no—
128C23×C13—42no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—42no—
132C23×C13—84no—
133C23×C13—84no—
134C23×C13—88no—
135C23×C13—88no—
136C23×C13C2×C22⋊C411yescharacteristic
137C23×C13C4×D412yes—
138D4×C13—44no—
139D4×C13—48no—
140D4×C13—44no—
141D4×C13—44no—
142D4×C13—88no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—24no—
146C2×C4×C13—22no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—41no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—81no—
158C2×C4×C13#10012yescomplemented
159C2×C4×C13#12011yescharacteristic
160C2×C4×C13#12112yes—
161C2×C4×C13#12311yescharacteristic
162#1055—44no—
163#1055—82no—
164C23×D4C2×D1311yescharacteristic
165C2×#121—21no—
166C2×#120Dic1312yes—
167C2×C4×D4C2×D1311yescharacteristic
168#436—264no—
169#431—261no—
170C2×#100—264no—
171#407—132no—
172#407—132no—
173#407—261no—
174#394—21no—
175#392—21no—
176#390—21no—
177#380C2×D1311yescharacteristic
178#379Dic1312yes—
179#324—261no—
180#323—261no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—22no—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—42no—
187C22×C13—42no—
188C22×C13—42no—
189C22×C13—44no—
190C22×C13—44no—
191C22×C13—41no—
192C22×C13—44no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—81no—
196C22×C13—82no—
197C22×C13—82no—
198C22×C13—88no—
199C22×C13—88no—
200C22×C13—82no—
201C22×C13—82no—
202C22×C13#38611yescharacteristic
203C22×C13C2×#10011yescharacteristic
204C22×C13#41311yescharacteristic
205C4×C13—22no—
206C4×C13—21no—
207C4×C13—22no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—82no—
211C4×C13B(4,𝔽2)12yes—
212C25C2×Dic1312yes—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4—44no—
219C22×D4C2×Dic1311yescharacteristic
220C23×C4C22⋊D1311yescharacteristic
221C23×C4C22×D1311yescharacteristic
222C2×M16—134no—
223C2×M16—262no—
224C2×M16—262no—
225#121—44no—
226#120—44no—
227C4×D4—22no—
228C4×D4—22no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C22⋊D1311yescharacteristic
231C2×C22⋊C4—22no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4C2×Dic1311yescharacteristic
235C2×C22⋊C4C2×Dic1312yes—
236C2×C22⋊C4C22⋊D1311yescharacteristic
237C2×C42C22⋊D1311yescharacteristic
238C4⋊C8—262no—
239#100—528no—
240C22⋊C8—262no—
241C22⋊C8—262no—
242C22⋊C8—262no—
243C22⋊C8—262no—
244C22⋊C8—262no—
245C4×C8—262no—
246#95—21no—
247C2×C13—21no—
248C2×C13—21no—
249C2×C13—42no—
250C2×C13—81no—
251C2×C13—84no—
252C2×C13#188911yescharacteristic
253C2×C13#190011yescharacteristic
254C2×C13#191411yescharacteristic
255C24—22no—
256C24—24no—
257C24—44no—
258C24—42no—
259C24—42no—
260C24—82no—
261C24C22⋊Dic1311yescharacteristic
262C24C22×Dic1311yescharacteristic
263C2×D4—28no—
264C2×D4—24no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—41no—
268C2×D4—42no—
269C2×D4—44no—
270C2×D4—48no—
271C2×D4—44no—
272C2×D4—44no—
273C2×D4—44no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—42no—
277C2×D4—82no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4C22⋊Dic1311yescharacteristic
284C22×C4C22⋊Dic1311yescharacteristic
285C22×C4C22⋊Dic1311yescharacteristic
286C22×C4D4×D1312yes—
287C22×C4#612912yes—
288C22×C4C2×C22⋊D1311yescharacteristic
289C22×C4C2×C22⋊D1311yescharacteristic
290M16—524no—
291M16—524no—
292M16—1042no—
293C2×C8—264no—
294C2×C8—522no—
295C4⋊C4—22no—
296C4⋊C4—42no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—44no—
300C22⋊C4—44no—
301C22⋊C4—42no—
302C22⋊C4—82no—
303C42—21no—
304C42—21no—
305C13#950411yescharacteristic, complemented, Sylow
306C23—21no—
307C23—21no—
308C23—24no—
309C23—28no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—42no—
318C23—42no—
319C23—44no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—84no—
325C23—84no—
326C23—88no—
327C23—88no—
328C23D4×Dic1312yes—
329C23C2×C22⋊Dic1311yescharacteristic
330D4—44no—
331D4—48no—
332D4—44no—
333D4—44no—
334D4—88no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—81no—
350C2×C4#8807312yescomplemented
351C2×C4#8818911yescharacteristic
352C2×C4#8819111yescharacteristic
353C2×C4#8819312yes—
354C8—524no—
355C8—1042no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—44no—
365C22—44no—
366C22—41no—
367C22—44no—
368C22—41no—
369C22—41no—
370C22—81no—
371C22—82no—
372C22—82no—
373C22—88no—
374C22—88no—
375C22—82no—
376C22—82no—
377C22C2×#8807311yescharacteristic
378C22#1171888111yescharacteristic
379C22#1171889811yescharacteristic
380C4—22no—
381C4—21no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—82no—
386C4#1171869312yes—
387C2—21no—
388C2—21no—
389C2—42no—
390C2—81no—
391C2—84no—
392C2#1311524511yescharacteristic
393C2#1311530011yescharacteristic
394C2#1311538411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC13×#2408C2
socleC22×C13#386
cosocleC23×C4×C13C23
hypercenter#2408D13
hypocenterC13#9504
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. #13123877C2semidirect
2. #13114757C2semidirect
3. #13113174C2semidirect
4. #13112742C2semidirect
48. C2×#6099D4semidirect
158. C2×C4×C13#100semidirect
305. C13#9504semidirect
350. C2×C4#88073semidirect

Maximal subgroups

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

subgroupindex
#131238772
#131147572
#131131742
#131127422
C13×#24082
#950413