Finite Group Databasebeta

← #15828955

Subgroups — #15828955

Order 3328.

984 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719269C211yesmaximal, characteristic
2#13123860C211yesmaximal, characteristic, complemented
3#13113206C212yesmaximal, complemented
4#13113201C212yesmaximal, complemented
5#13113193C212yesmaximal, complemented
6#13113185C212yesmaximal, complemented
7#13113152C212yesmaximal, complemented
8C2×#11718061C212yesmaximal, complemented
9C13×#2973C211yesmaximal, characteristic, complemented
10C2×C4×D4×C13C2211yescharacteristic
11C2×#88193C411yescharacteristic
12C2×#88189C411yescharacteristic
13C2×#88183C2211yescharacteristic
14C2×C4×C22⋊D13C2211yescharacteristic
15C2×#88178C2211yescharacteristic
16C22×#6101C2211yescharacteristic
17#11719269—24no—
18#11719269—24no—
19C2×#88150C411yescharacteristic
20C2×#88143C411yescharacteristic
21C2×#88140C411yescharacteristic
22C2×#88137C411yescharacteristic
23C2×#88133C411yescharacteristic
24C2×#88132C411yescharacteristic
25C2×#88130C2211yescharacteristic
26C2×#88124C2211yescharacteristic
27C13×#435—24no—
28C13×#432C2212yes—
29C13×#407C2212yes—
30C2×C13×C22⋊C8C2212yes—
31C2×C22⋊#1055C2212yes—
32C2×C22⋊#1055C2212yes—
33D4×#1055—24no—
34#11718586C2212yes—
35#11718061C2214yes—
36#11718061C2214yes—
37#11718061C2214yes—
38#11718060C2214yes—
39C22×D4×C13C2×C411yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C22×C22⋊D13C2×C411yescharacteristic
43C22×C22⋊D13C2×C411yescharacteristic
44C23×Dic13C2×C411yescharacteristic
45C23×Dic13C2×C411yescharacteristic
46C22×C4×D13C2×C411yescharacteristic
47C22×Dic26C2×C411yescharacteristic
48C2×C13×M16—22no—
49C22×C8×C13—22no—
50C4×D4×C13D414yes—
51C4×D4×C13D414yes—
52C2×C13×C4⋊C4C2×C411yescharacteristic
53C2×C13×C22⋊C4C2×C411yescharacteristic
54C2×C13×C22⋊C4C2×C411yescharacteristic
55C2×C42×C13C2311yescharacteristic
56C2×C22⋊Dic13C2×C411yescharacteristic
57C2×C22⋊Dic13C2×C411yescharacteristic
58C2×C22⋊Dic13C2×C411yescharacteristic
59C2×C22⋊Dic13C2×C411yescharacteristic
60#88193—24no—
61#88189—24no—
62#88183—22no—
63#88183—22no—
64C4×C22⋊D13—22no—
65C4×C22⋊D13—22no—
66C2×#6103C2×C411yescharacteristic
67C2×#6103C2×C411yescharacteristic
68C2×#6103C2×C411yescharacteristic
69C2×#6103C2311yescharacteristic
70C2×C4⋊Dic13C2×C411yescharacteristic
71C2×C4⋊Dic13C2×C411yescharacteristic
72C2×C4⋊Dic13C2×C411yescharacteristic
73#88178—22no—
74#88178—22no—
75C2×#6101—22no—
76C2×#6101—22no—
77C2×#6101C2×C411yescharacteristic
78C2×#6101C2×C411yescharacteristic
79C2×#6101C2×C411yescharacteristic
80C2×#6101C2×C411yescharacteristic
81C2×#6101C2×C411yescharacteristic
82C2×#6101C2×C411yescharacteristic
83C2×#6101C2×C411yescharacteristic
84C2×#6101C2311yescharacteristic
85C2×#6101C2311yescharacteristic
86C2×#6101C2311yescharacteristic
87C2×C4×Dic13C2×C411yescharacteristic
88C22×#1055—22no—
89C22×#1055—22no—
90#88150—24no—
91#88143—24no—
92#88140—24no—
93#88137—24no—
94#88133—24no—
95#88132—24no—
96#88130—22no—
97#88130—22no—
98#88124—22no—
99#88124—22no—
100C13×C4⋊C8—22no—
101C13×C22⋊C8—22no—
102C13×C22⋊C8—22no—
103C13×C22⋊C8C2314yes—
104C13×#97—22no—
105C22⋊#1055—22no—
106C22⋊#1055—22no—
107C22⋊#1055C2314yes—
108C4⋊#1055—22no—
109C4×#1055—22no—
110#17387—131nomaximal, Sylow
111C24×C13C22×C411yescharacteristic
112C24×C13C22×C411yescharacteristic
113C23×D13C22×C411yescharacteristic
114C2×D4×C13—24no—
115C2×D4×C13C22⋊C414yes—
116C22×C4×C13—81no—
117C22×C4×C13—81no—
118C22×C4×C13C22×C411yescharacteristic
119C22×C4×C13C22×C411yescharacteristic
120C22×C4×C13C22×C411yescharacteristic
121C22×C4×C13C22×C411yescharacteristic
122C22×C4×C13C2×D412yes—
123C22×C4×C13C2×D412yes—
124C22×C4×C13C2×D412yes—
125C22×C4×C13C2×D412yes—
126C22×C4×C13C2411yescharacteristic
127C2×C22⋊D13—22no—
128C2×C22⋊D13—24no—
129C2×C22⋊D13—22no—
130C2×C22⋊D13—81no—
131C22×Dic13—22no—
132C22×Dic13—24no—
133C22×Dic13—22no—
134C22×Dic13—81no—
135C22×Dic13C22×C411yescharacteristic
136C22×Dic13C22×C411yescharacteristic
137C22×Dic13C22×C411yescharacteristic
138C22×Dic13C22×C411yescharacteristic
139C22×Dic13C22×C411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C2×C4×D13—22no—
143C2×C4×D13—81no—
144C2×Dic26—22no—
145C2×Dic26—81no—
146C13×M16—82no—
147C2×C8×C13—24no—
148C2×C8×C13—82no—
149C13×C4⋊C4C22⋊C414yes—
150C13×C22⋊C4C22⋊C414yes—
151C13×C22⋊C4C22⋊C414yes—
152C42×C13C2×D412yes—
153C42×C13C2×D412yes—
154C22⋊Dic13—22no—
155C22⋊Dic13—22no—
156C22⋊Dic13—22no—
157C22⋊Dic13—22no—
158#6103—22no—
159#6103—22no—
160#6103—22no—
161#6103—21no—
162#6103—21no—
163C4⋊Dic13—22no—
164C4⋊Dic13—22no—
165C4⋊Dic13—22no—
166#6101—22no—
167#6101—22no—
168#6101—22no—
169#6101—22no—
170#6101—22no—
171#6101—22no—
172#6101—22no—
173#6101—21no—
174#6101—21no—
175#6101—21no—
176#6101—21no—
177#6101—21no—
178#6101—21no—
179C4×Dic13—22no—
180C2×#1055—24no—
181C2×#1055—82no—
182C2×#1055—82no—
183C2×#539—131no—
184#2973D1311yescharacteristic, complemented
185#2972—131no—
186#1473—132no—
187#1472—132no—
188#1470—132no—
189#1468—132no—
190#1459—132no—
191C2×#324—132no—
192C23×C13—22no—
193C23×C13—41no—
194C23×C13—41no—
195C23×C13—41no—
196C23×C13—41no—
197C23×C13C2×C22⋊C412yes—
198C23×C13C2×C22⋊C412yes—
199C23×C13#13114yes—
200C23×C13C23×C411yescharacteristic
201C22×D13—21no—
202C22×D13—22no—
203C22×D13—41no—
204C22×D13—41no—
205D4×C13—28no—
206C2×C4×C13—22no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13C2×C22⋊C412yes—
216C2×C4×C13C2×C22⋊C412yes—
217C2×C4×C13C2×C22⋊C412yes—
218C2×C4×C13C2×C22⋊C412yes—
219C2×C4×C13C22×D411yescharacteristic
220C2×C4×C13C22×D411yescharacteristic
221C22⋊D13—44no—
222C22⋊D13—82no—
223C2×Dic13—21no—
224C2×Dic13—21no—
225C2×Dic13—21no—
226C2×Dic13—21no—
227C2×Dic13—21no—
228C2×Dic13—21no—
229C2×Dic13—21no—
230C2×Dic13—22no—
231C2×Dic13—22no—
232C2×Dic13—22no—
233C2×Dic13—44no—
234C2×Dic13—41no—
235C2×Dic13—41no—
236C2×Dic13—41no—
237C2×Dic13—41no—
238C2×Dic13—82no—
239C4×D13—82no—
240Dic26—82no—
241C8×C13—44no—
242#1055—44no—
243#539—264no—
244#539—264no—
245C2×#126—131no—
246C2×#126—131no—
247C2×#125—131no—
248C2×#125—131no—
249C2×#123—131no—
250C2×#123—131no—
251C2×#123—131no—
252C2×#123—131no—
253C2×C22⋊Q8—131no—
254C2×C22⋊Q8—131no—
255C2×C22⋊Q8—131no—
256C2×#121—131no—
257C2×C4×D4—131no—
258C2×C4×D4C2×D1311yescharacteristic
259C22×C4⋊C4—131no—
260#435—24no—
261C8×D4—264no—
262#432C2×D1312yes—
263#431—132no—
264#407C2×D1312yes—
265C2×C22⋊C8—132no—
266C2×C22⋊C8—132no—
267C2×C22⋊C8C2×D1312yes—
268#324—134no—
269#324—134no—
270#324—134no—
271#323—134no—
272C22×C13—21no—
273C22×C13—22no—
274C22×C13—21no—
275C22×C13—22no—
276C22×C13—22no—
277C22×C13—22no—
278C22×C13—22no—
279C22×C13—44no—
280C22×C13—82no—
281C22×C13#40814yes—
282C22×C13C22×C22⋊C411yescharacteristic
283C22×C13C2×#13112yes—
284C2×D13—41no—
285C2×D13—41no—
286C2×D13—41no—
287C2×D13—82no—
288C4×C13—22no—
289C4×C13—21no—
290C4×C13—21no—
291C4×C13—22no—
292C4×C13—22no—
293C4×C13—22no—
294Dic13—41no—
295Dic13—41no—
296Dic13—41no—
297Dic13—41no—
298Dic13—41no—
299Dic13—41no—
300Dic13—41no—
301C22×Q8—131no—
302C22×D4—131no—
303C22×D4—131no—
304C22×D4C4×D1311yescharacteristic
305C23×C4—131no—
306C23×C4—131no—
307C23×C4—131no—
308C23×C4C22×D1311yescharacteristic
309C23×C4C22×D1311yescharacteristic
310C2×M16—22no—
311C22×C8—22no—
312C22×C8—262no—
313C22×C8—262no—
314#126—264no—
315#126—262no—
316#126—262no—
317#125—264no—
318#125—262no—
319#125—262no—
320#123—264no—
321#123—262no—
322#123—262no—
323#123—264no—
324#123—264no—
325C22⋊Q8—262no—
326C22⋊Q8—262no—
327C22⋊Q8—264no—
328C22⋊Q8—264no—
329#121—264no—
330C4×D4—262no—
331C4×D4—262no—
332C4×D4D5214yes—
333C4×D4C22⋊D1314yes—
334C2×C4⋊C4—131no—
335C2×C4⋊C4—131no—
336C2×C4⋊C4—131no—
337C2×C4⋊C4—131no—
338C2×C4⋊C4—131no—
339C2×C4⋊C4—131no—
340C2×C4⋊C4—131no—
341C2×C4⋊C4—131no—
342C2×C4⋊C4—131no—
343C2×C4⋊C4—131no—
344C2×C4⋊C4—131no—
345C2×C4⋊C4—131no—
346C2×C4⋊C4—131no—
347C2×C4⋊C4—262no—
348C2×C4⋊C4—262no—
349C2×C4⋊C4C4×D1311yescharacteristic
350C2×C22⋊C4—131no—
351C2×C22⋊C4—131no—
352C2×C22⋊C4—131no—
353C2×C22⋊C4—131no—
354C2×C22⋊C4—131no—
355C2×C22⋊C4—131no—
356C2×C22⋊C4—131no—
357C2×C22⋊C4—131no—
358C2×C22⋊C4C4×D1311yescharacteristic
359C2×C22⋊C4C4×D1311yescharacteristic
360C2×C42—131no—
361C2×C42C22×D1311yescharacteristic
362C4⋊C8—22no—
363C4⋊C8—262no—
364C22⋊C8—22no—
365C22⋊C8—22no—
366C22⋊C8—134no—
367C22⋊C8—262no—
368C22⋊C8—262no—
369C22⋊C8C22×D1314yes—
370#97—22no—
371C4×C8—262no—
372C2×C13—22no—
373C2×C13—24no—
374C2×C13—42no—
375C2×C13C2×#40811yescharacteristic
376C2×C13#288311yescharacteristic
377C2×C13#288911yescharacteristic
378D13—81no—
379C24—131no—
380C24C2×C4×D1311yescharacteristic
381C24C2×C4×D1311yescharacteristic
382C2×Q8—262no—
383C2×Q8—1041no—
384C2×D4—24no—
385C2×D4—264no—
386C2×D4—262no—
387C2×D4—262no—
388C2×D4—1041no—
389C2×D4#610314yes—
390C22×C4—81no—
391C22×C4—81no—
392C22×C4—131no—
393C22×C4—131no—
394C22×C4—131no—
395C22×C4—131no—
396C22×C4—131no—
397C22×C4—131no—
398C22×C4—131no—
399C22×C4—264no—
400C22×C4—262no—
401C22×C4—262no—
402C22×C4—262no—
403C22×C4—1041no—
404C22×C4—1041no—
405C22×C4C2×C4×D1311yescharacteristic
406C22×C4C2×C4×D1311yescharacteristic
407C22×C4C2×C4×D1311yescharacteristic
408C22×C4C2×C4×D1311yescharacteristic
409C22×C4C2×D5212yes—
410C22×C4C2×D5212yes—
411C22×C4C2×C22⋊D1312yes—
412C22×C4C2×C22⋊D1312yes—
413C22×C4C23×D1311yescharacteristic
414M16—82no—
415C2×C8—24no—
416C2×C8—82no—
417C2×C8—264no—
418C2×C8—1042no—
419C2×C8—1042no—
420C4⋊C4—262no—
421C4⋊C4—262no—
422C4⋊C4—262no—
423C4⋊C4—262no—
424C4⋊C4—262no—
425C4⋊C4—262no—
426C4⋊C4—262no—
427C4⋊C4—262no—
428C4⋊C4—262no—
429C4⋊C4—262no—
430C4⋊C4—261no—
431C4⋊C4—261no—
432C4⋊C4—261no—
433C4⋊C4—261no—
434C4⋊C4—261no—
435C4⋊C4—261no—
436C4⋊C4#610314yes—
437C22⋊C4—262no—
438C22⋊C4—262no—
439C22⋊C4—262no—
440C22⋊C4—262no—
441C22⋊C4—262no—
442C22⋊C4—262no—
443C22⋊C4—262no—
444C22⋊C4—261no—
445C22⋊C4—261no—
446C22⋊C4#610314yes—
447C22⋊C4#610314yes—
448C42—262no—
449C42C2×D5212yes—
450C42C2×C22⋊D1312yes—
451C13#1738711yescharacteristic, complemented, Sylow
452C23—22no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—261no—
458C23—262no—
459C23—521no—
460C23—521no—
461C23#8816114yes—
462C23C2×#610312yes—
463C23C2×#610312yes—
464C23C22×C4×D1311yescharacteristic
465Q8—1042no—
466D4—28no—
467D4—524no—
468D4—1042no—
469C2×C4—22no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—262no—
479C2×C4—262no—
480C2×C4—262no—
481C2×C4—261no—
482C2×C4—261no—
483C2×C4—261no—
484C2×C4—261no—
485C2×C4—261no—
486C2×C4—261no—
487C2×C4—261no—
488C2×C4—524no—
489C2×C4—521no—
490C2×C4—521no—
491C2×C4—521no—
492C2×C4—521no—
493C2×C4—1042no—
494C2×C4—1042no—
495C2×C4C2×#610312yes—
496C2×C4C2×#610312yes—
497C2×C4C2×#610312yes—
498C2×C4C2×#610312yes—
499C2×C4C22×D5211yescharacteristic
500C2×C4C22×C22⋊D1311yescharacteristic
501C8—44no—
502C8—524no—
503C22—21no—
504C22—22no—
505C22—21no—
506C22—22no—
507C22—22no—
508C22—22no—
509C22—22no—
510C22—44no—
511C22—82no—
512C22—521no—
513C22—521no—
514C22—521no—
515C22—1042no—
516C22#1171879014yes—
517C22C2×#8816112yes—
518C22C22×#610311yescharacteristic
519C4—22no—
520C4—21no—
521C4—21no—
522C4—22no—
523C4—22no—
524C4—22no—
525C4—521no—
526C4—521no—
527C4—521no—
528C4—521no—
529C4—521no—
530C4—521no—
531C4—521no—
532C2—22no—
533C2—24no—
534C2—42no—
535C2—1041no—
536C2C2×#1171879011yescharacteristic
537C2#1312329611yescharacteristic
538C2#1312331811yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2973C2
socleC22×C13C22×C22⋊C4
prime radicalC2×#88193C4
cosocleC22×C4×C13C24
hypercenter#2973D13
hypocenterC13#17387
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13123860C2semidirect
3. #13113206C2semidirect
4. #13113201C2semidirect
5. #13113193C2semidirect
6. #13113185C2semidirect
7. #13113152C2semidirect
8. C2×#11718061C2semidirect
9. C13×#2973C2semidirect
184. #2973D13semidirect
451. C13#17387semidirect

Maximal subgroups

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

subgroupindex
C2×#117192692
#131238602
#131132062
#131132012
#131131932
#131131852
#131131522
C2×#117180612
C13×#29732
#1738713