Finite Group Databasebeta

← #15760240

Subgroups — #15760240

Order 3328.

640 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123860C211yesmaximal, characteristic, complemented
2#13114824C211yesmaximal, characteristic, complemented
3#13113404C212yesmaximal, complemented
4#13112715C212yesmaximal, complemented
5C13×#2543C211yesmaximal, characteristic
6C2×C13×#121—21no—
7C2×C13×#121C2211yescharacteristic
8C2×C4×D4×C13C2211yescharacteristic
9C13×#398C411yescharacteristic, complemented
10C13×#397C411yescharacteristic, complemented
11C13×#394C411yescharacteristic, complemented
12C13×#392C411yescharacteristic, complemented
13C13×#388—21no—
14C13×#386—21no—
15C13×#386—21no—
16C2×C13×#95C2211yescharacteristic
17C2×#88074—21no—
18#11718873C2212yes—
19C2×C22⋊#1055—21no—
20C2×C22⋊#1055C2212yes—
21D4×#1055—24no—
22#11718586—21no—
23#11718129—24no—
24#11718118—21no—
25C22×D4×C13—21no—
26C22×D4×C13—21no—
27C22×D4×C13C2×C411yescharacteristic
28C22×D4×C13D411yescharacteristic
29C23×C4×C13—21no—
30C23×C4×C13D411yescharacteristic
31C23×C4×C13C2311yescharacteristic
32C13×#121—22no—
33C13×#121—22no—
34C13×#121—42no—
35C13×#121—42no—
36C4×D4×C13—22no—
37C4×D4×C13—22no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4C2×C411yescharacteristic
40C2×C13×C4⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4C2×C411yescharacteristic
47C2×C13×C22⋊C4D411yescharacteristic
48C2×C42×C13D411yescharacteristic
49C2×C22⋊Dic13—22no—
50C2×C4⋊Dic13—22no—
51C22×#1055—22no—
52C22×#1055—22no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95C2×C411yescharacteristic
57C13×#95C2×C411yescharacteristic
58#88074—42no—
59#88071—22no—
60C22⋊#1055—22no—
61C22⋊#1055—22no—
62C22⋊#1055D414yescomplemented
63C4⋊#1055—22no—
64C4×#1055—22no—
65#9384—131nomaximal, Sylow
66C24×C13—21no—
67C24×C13C22⋊C411yescharacteristic
68C24×C13C2×D411yescharacteristic
69C2×D4×C13—22no—
70C2×D4×C13—22no—
71C2×D4×C13—22no—
72C2×D4×C13—42no—
73C2×D4×C13—42no—
74C2×D4×C13—42no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—42no—
78C2×D4×C13—81no—
79C2×D4×C13—81no—
80C2×D4×C13D812yes—
81C2×D4×C13SD1612yes—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—42no—
88C22×C4×C13—41no—
89C22×C4×C13—41no—
90C22×C4×C13—81no—
91C22×C4×C13—81no—
92C22×C4×C13—81no—
93C22×C4×C13C22⋊C411yescharacteristic
94C22×C4×C13C22⋊C411yescharacteristic
95C22×C4×C13C22⋊C411yescharacteristic
96C22×C4×C13C22×C411yescharacteristic
97C22×C4×C13C2×D412yes—
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13#4112yes—
100C22×Dic13—42no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—42no—
104C13×C22⋊C4—22no—
105C13×C22⋊C4—22no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—42no—
108C13×C22⋊C4—42no—
109C13×C22⋊C4—41no—
110C13×C22⋊C4—41no—
111C13×C22⋊C4—81no—
112C42×C13—21no—
113C42×C13—21no—
114C22⋊Dic13—42no—
115C22⋊Dic13—42no—
116C4⋊Dic13—82no—
117C2×#1055—24no—
118C2×#1055—82no—
119C2×#1055—82no—
120#2972—131no—
121#2543D1311yescharacteristic
122#1799—131no—
123#1519—132no—
124#1294—132no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—41no—
135C23×C13—41no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13#10212yes—
139C23×C13C2×C22⋊C411yescharacteristic
140C23×C13#12112yes—
141C23×C13C2×D811yescharacteristic
142C23×C13C2×SD1611yescharacteristic
143C23×C13#13512yes—
144D4×C13—24no—
145D4×C13—24no—
146D4×C13—82no—
147D4×C13—84no—
148D4×C13—82no—
149D4×C13—82no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—22no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—42no—
156C2×C4×C13—42no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—42no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—81no—
171C2×C4×C13—82no—
172C2×C4×C13—82no—
173C2×C4×C13#10212yes—
174C2×C4×C13C4×D412yes—
175C2×C4×C13#12011yescharacteristic
176C2×C4×C13#12311yescharacteristic
177C2×Dic13—82no—
178C2×Dic13—82no—
179C2×Dic13—82no—
180#1055—44no—
181C2×#121—21no—
182C2×#121C2×D1311yescharacteristic
183C2×C4×D4C2×D1311yescharacteristic
184C8×D4—264no—
185#431—261no—
186C2×#99—261no—
187C2×C22⋊C8—132no—
188C2×C22⋊C8—261no—
189#398Dic1311yescharacteristic, complemented
190#397Dic1311yescharacteristic, complemented
191#394Dic1311yescharacteristic, complemented
192#392Dic1311yescharacteristic, complemented
193#388—21no—
194#386—21no—
195#386—21no—
196#380—132no—
197C2×#95C2×D1311yescharacteristic
198#342—261no—
199#327—264no—
200C22×C13—22no—
201C22×C13—21no—
202C22×C13—22no—
203C22×C13—21no—
204C22×C13—22no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13—81no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13#38611yescharacteristic
220C22×C13C2×#10211yescharacteristic
221C22×C13#41611yescharacteristic
222C22×C13#46512yes—
223C22×C13#46612yes—
224C4×C13—22no—
225C4×C13—21no—
226C4×C13—21no—
227C4×C13—22no—
228C4×C13—42no—
229C4×C13—41no—
230C4×C13—41no—
231C4×C13—81no—
232C4×C13—81no—
233Dic13—162no—
234C22×D4—21no—
235C22×D4—21no—
236C22×D4C2×Dic1311yescharacteristic
237C22×D4C22⋊D1311yescharacteristic
238C23×C4—21no—
239C23×C4C22⋊D1311yescharacteristic
240C23×C4C22×D1311yescharacteristic
241C22×C8—262no—
242C22×C8—262no—
243#121—22no—
244#121—22no—
245#121—42no—
246#121—42no—
247C4×D4—22no—
248C4×D4—22no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—262no—
251C2×C4⋊C4C2×Dic1311yescharacteristic
252C2×C4⋊C4C2×Dic1311yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—262no—
259C2×C22⋊C4C2×Dic1311yescharacteristic
260C2×C22⋊C4C22⋊D1311yescharacteristic
261C2×C42C22⋊D1311yescharacteristic
262C4⋊C8—262no—
263#99—522no—
264C22⋊C8—134no—
265C22⋊C8—262no—
266C22⋊C8—262no—
267C4×C8—262no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—262no—
272#95C2×Dic1311yescharacteristic
273#95C2×Dic1311yescharacteristic
274C2×C13—22no—
275C2×C13—21no—
276C2×C13—21no—
277C2×C13—22no—
278C2×C13—42no—
279C2×C13—161no—
280C2×C13#188411yescharacteristic
281C2×C13#189311yescharacteristic
282C2×C13#191311yescharacteristic
283C24—21no—
284C24C22⋊Dic1311yescharacteristic
285C24C2×C22⋊D1311yescharacteristic
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—81no—
296C2×D4—81no—
297C2×D4#610412yes—
298C2×D4#610512yes—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—81no—
308C22×C4—81no—
309C22×C4—81no—
310C22×C4—522no—
311C22×C4C22⋊Dic1311yescharacteristic
312C22×C4C22⋊Dic1311yescharacteristic
313C22×C4C22⋊Dic1311yescharacteristic
314C22×C4D4×D1312yes—
315C22×C4#612912yes—
316C22×C4C22×Dic1311yescharacteristic
317C22×C4C2×C22⋊D1311yescharacteristic
318C2×C8—264no—
319C2×C8—1042no—
320C2×C8—1042no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—42no—
324C4⋊C4—1042no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—42no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—81no—
333C22⋊C4—522no—
334C22⋊C4—522no—
335C42—21no—
336C42—21no—
337C13#938411yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23#8807212yes—
352C23C2×#610411yescharacteristic
353C23C2×#610511yescharacteristic
354C23#8819312yes—
355C23#8820412yes—
356C23C2×C22⋊Dic1311yescharacteristic
357D4—24no—
358D4—24no—
359D4—82no—
360D4—84no—
361D4—82no—
362D4—82no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—1042no—
387C2×C4—1042no—
388C2×C4—1042no—
389C2×C4#8807212yes—
390C2×C4D4×Dic1312yes—
391C2×C4#8818911yescharacteristic
392C2×C4#8819111yescharacteristic
393C8—524no—
394C22—21no—
395C22—22no—
396C22—21no—
397C22—22no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22#1171869912yes—
414C22#1171870212yes—
415C22C2×#8807211yescharacteristic
416C22#1171888111yescharacteristic
417C22#1171889411yescharacteristic
418C4—22no—
419C4—21no—
420C4—21no—
421C4—22no—
422C4—42no—
423C4—41no—
424C4—41no—
425C4—81no—
426C4—81no—
427C4—2082no—
428C2—21no—
429C2—22no—
430C2—21no—
431C2—22no—
432C2—42no—
433C2—161no—
434C2#1311522011yescharacteristic
435C2#1311526511yescharacteristic
436C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC13×#2543C2
socleC22×C13#386
cosocleC23×C4×C13C23
hypercenter#2543D13
hypocenterC13#9384
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2543

Complements

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

NH ≅ G/Ntype
1. #13123860C2semidirect
2. #13114824C2semidirect
3. #13113404C2semidirect
4. #13112715C2semidirect
9. C13×#398C4semidirect
10. C13×#397C4semidirect
11. C13×#394C4semidirect
12. C13×#392C4semidirect
62. C22⋊#1055D4semidirect
189. #398Dic13semidirect
190. #397Dic13semidirect
191. #394Dic13semidirect
192. #392Dic13semidirect
337. C13#9384semidirect

Maximal subgroups

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

subgroupindex
#131238602
#131148242
#131134042
#131127152
C13×#25432
#938413