Finite Group Databasebeta

← #15862448

Subgroups — #15862448

Order 3328.

1462 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719228C211yesmaximal, characteristic
2C2×#11718794C211yesmaximal, characteristic
3C2×#11718774C211yesmaximal, characteristic
4#13117459C211yesmaximal, characteristic, complemented
5#13114852C212yesmaximal, complemented
6#13114847C212yesmaximal, complemented
7#13114842C212yesmaximal, complemented
8#13114837C212yesmaximal, complemented
9#13114556C211yesmaximal, characteristic, complemented
10C2×#11718143C211yesmaximal, characteristic, complemented
11C2×C13×#424C211yesmaximal, characteristic, complemented
12C22×#6127C2211yescharacteristic
13C22×C13×M16C2211yescharacteristic
14C23×C8×C13C2211yescharacteristic
15C2×C13×#117C2211yescharacteristic
16C2×#88180C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19#11719228—24no—
20#11719228C418yescomplemented
21C2×#88146—21no—
22C2×C4⋊C4×D13—21no—
23C2×#88135—22no—
24C2×C4×D52C2212yes—
25C2×C4×Dic26C2212yes—
26C13×#424—24no—
27C2×C13×C4⋊C8C2212yes—
28C2×C13×C4⋊C8C2212yes—
29#11718794—24no—
30#11718774—24no—
31C2×#88061C2211yescharacteristic
32C2×#88061C2211yescharacteristic
33C2×#88061C2212yes—
34C2×#88056C2211yescharacteristic
35C2×#88056C2211yescharacteristic
36C2×#88056C2212yes—
37#11718646—21no—
38#11718646—21no—
39#11718611—22no—
40#11718597C2212yes—
41#11718596C2212yes—
42#11718143C2212yes—
43#11718143C2212yes—
44#11718143C2212yes—
45#11718143C2212yes—
46C23×C4×C13C2311yescharacteristic
47C22×C22⋊D13—21no—
48C23×Dic13—21no—
49C23×Dic13—21no—
50C2×#6127—22no—
51C2×#6127—22no—
52C2×#6127—22no—
53C2×#6127C2×C414yes—
54C2×#6127D414yes—
55C2×#6127Q814yes—
56C22×D52C2311yescharacteristic
57C22×C4×D13—21no—
58C22×C4×D13—22no—
59C22×Dic26C2311yescharacteristic
60C2×C13×M16—22no—
61C2×C13×M16—22no—
62C2×C13×M16—22no—
63C22×C8×C13—22no—
64C22×C8×C13—22no—
65C22×C8×C13—22no—
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2312yes—
69C13×#117C2×C414yes—
70C13×#117D414yes—
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C22⋊C4D412yes—
74C2×C42×C13C2312yes—
75C2×C22⋊Dic13—21no—
76C2×#6103—22no—
77#88180—22no—
78#88180—22no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13C2×C414yes—
87C2×C4⋊Dic13C2312yes—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2312yes—
91C2×#6101—22no—
92C2×C4×Dic13—22no—
93C2×C4×Dic13—21no—
94#88146—28no—
95C4⋊C4×D13—28no—
96#88135—216no—
97C4×D52—24no—
98C4×D52C2×C418yescomplemented
99C4×Dic26—24no—
100C4×Dic26C2×C418yescomplemented
101C13×C4⋊C8—24no—
102C13×C4⋊C8—24no—
103#88071—22no—
104#88071—22no—
105#88061—22no—
106#88061—22no—
107#88061—24no—
108#88056—22no—
109#88056—22no—
110#88056—24no—
111#20652—131nomaximal, Sylow
112C24×C13C2×D411yescharacteristic
113C23×D13—21no—
114C22×C4×C13C22×C412yes—
115C22×C4×C13C2×D412yes—
116C22×C4×C13C2×D412yes—
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2×D412yes—
119C22×C4×C13C2×D412yes—
120C22×C4×C13C2×Q812yes—
121C22×C4×C13#4112yes—
122C22×C4×C13#4112yes—
123C22×C4×C13C2411yescharacteristic
124C2×C22⋊D13—24no—
125C2×C22⋊D13—24no—
126C2×C22⋊D13—24no—
127C22×Dic13—21no—
128C22×Dic13—22no—
129C22×Dic13—24no—
130C22×Dic13—21no—
131C22×Dic13—22no—
132C22×Dic13—21no—
133C22×Dic13—42no—
134C22×Dic13—81no—
135C22×Dic13—81no—
136C22×Dic13—81no—
137C22×Dic13—81no—
138#6127—28no—
139#6127—28no—
140#6127—28no—
141#6127C4⋊C4116yescomplemented
142C2×D52—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52C22×C412yes—
146C2×D52C2×D412yes—
147C2×D52C2×Q812yes—
148C2×C4×D13—24no—
149C2×C4×D13—24no—
150C2×C4×D13—24no—
151C2×C4×D13—28no—
152C2×C4×D13—82no—
153C2×C4×D13—82no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26—21no—
157C2×Dic26C22×C412yes—
158C2×Dic26C2×D412yes—
159C2×Dic26C2×Q812yes—
160C13×M16—44no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—22no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—22no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—22no—
170C2×C8×C13—44no—
171C13×C4⋊C4C22⋊C414yes—
172C13×C4⋊C4C22⋊C414yes—
173C13×C22⋊C4C22⋊C418yes—
174C42×C13C22×C414yes—
175C42×C13C2×D414yes—
176C22⋊Dic13—42no—
177#6103—28no—
178C4⋊Dic13—24no—
179C4⋊Dic13—22no—
180C4⋊Dic13—22no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—22no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—42no—
187C4⋊Dic13—82no—
188C4⋊Dic13—82no—
189C4⋊Dic13C22×C414yes—
190#6101—28no—
191C4×Dic13—28no—
192C4×Dic13—42no—
193C2×#520—131no—
194C2×#424D1311yescharacteristic, complemented
195C2×#417—131no—
196C2×#416—131no—
197#2317—131no—
198#1805—132no—
199#1804—132no—
200#1803—132no—
201#1802—132no—
202#1736—131no—
203C2×#340—131no—
204C23×C13—21no—
205C23×C13—21no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13C2×C22⋊C412yes—
209C23×C13#12112yes—
210C23×C13C22⋊Q812yes—
211C23×C13C22×D411yescharacteristic
212C22×D13—22no—
213C22×D13—22no—
214C22×D13—22no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—41no—
218C22×D13—41no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13C2×C22⋊C414yes—
224C2×C4×C13C2×C22⋊C414yes—
225C2×C4×C13C2×C22⋊C412yes—
226C2×C4×C13C2×C4⋊C414yes—
227C2×C4×C13#11714yes—
228C2×C4×C13#12114yes—
229C2×C4×C13#12112yes—
230C2×C4×C13C22⋊Q814yes—
231C2×C4×C13C22⋊Q812yes—
232C2×C4×C13C23×C411yescharacteristic
233C2×C4×C13C22×D411yescharacteristic
234C2×C4×C13C22×D411yescharacteristic
235C2×C4×C13C22×Q811yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C22⋊D13—216no—
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—24no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—41no—
246C2×Dic13—41no—
247C2×Dic13—42no—
248C2×Dic13—41no—
249C2×Dic13—42no—
250C2×Dic13—41no—
251C2×Dic13—42no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—84no—
255C2×Dic13—84no—
256D52—22no—
257D52—22no—
258D52—22no—
259D52C2×C4⋊C414yes—
260C4×D13—216no—
261C4×D13—88no—
262Dic26—22no—
263Dic26—22no—
264Dic26—22no—
265Dic26C2×C4⋊C414yes—
266C8×C13—41no—
267C8×C13—41no—
268C8×C13—42no—
269C22×#41—131no—
270C22×M16C2×D1311yescharacteristic
271C23×C8C2×D1311yescharacteristic
272#520—138no—
273#520—264no—
274C2×C4×Q8—132no—
275C2×C4×D4—132no—
276C2×C4×D4—262no—
277C2×#117—131no—
278C2×#117—261no—
279C2×#117C2×D1311yescharacteristic
280C22×C4⋊C4—131no—
281C22×C4⋊C4—131no—
282C22×C4⋊C4—261no—
283#424—24no—
284C2×C4⋊C8C2×D1312yes—
285C2×C4⋊C8C2×D1312yes—
286#417—264no—
287#416—264no—
288C2×#103—131no—
289C2×#103—132no—
290C2×#103—131no—
291C2×#102—131no—
292C2×#102—132no—
293C2×#102—131no—
294#389—261no—
295#389—261no—
296#385—262no—
297#384—132no—
298#382—132no—
299#340—132no—
300#340—132no—
301#340—132no—
302#340—132no—
303C22×C13—22no—
304C22×C13—22no—
305C22×C13—22no—
306C22×C13—22no—
307C22×C13—22no—
308C22×C13—22no—
309C22×C13#38014yes—
310C22×C13C22×C22⋊C411yescharacteristic
311C22×C13C2×#12111yescharacteristic
312C22×C13C2×C22⋊Q811yescharacteristic
313C22×C13#57611yescharacteristic
314C22×C13#57711yescharacteristic
315C22×C13#57711yescharacteristic
316C22×C13#57811yescharacteristic
317C2×D13—24no—
318C2×D13—42no—
319C2×D13—42no—
320C2×D13—42no—
321C2×D13—42no—
322C2×D13—42no—
323C2×D13—42no—
324C4×C13—24no—
325C4×C13—24no—
326C4×C13#38014yes—
327C4×C13C22×C4⋊C411yescharacteristic
328C4×C13C2×#11711yescharacteristic
329C4×C13C2×#12111yescharacteristic
330C4×C13C2×C22⋊Q811yescharacteristic
331Dic13—24no—
332Dic13—44no—
333Dic13—81no—
334Dic13—82no—
335Dic13—81no—
336C2×#41—134no—
337C2×#41—134no—
338C2×#41—134no—
339C2×#41—262no—
340C2×#41—262no—
341C2×#41—262no—
342C22×Q8—131no—
343C22×D4—131no—
344C22×D4—261no—
345C23×C4—261no—
346C23×C4—261no—
347C23×C4—262no—
348C23×C4—261no—
349C23×C4C22×D1311yescharacteristic
350C2×M16—22no—
351C2×M16—22no—
352C2×M16—22no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—22no—
356C22×C8C22×D1311yescharacteristic
357C22×C8C22×D1311yescharacteristic
358C22×C8C22×D1312yes—
359C4×Q8—138no—
360C4×Q8—264no—
361C4×D4—138no—
362C4×D4—2616no—
363C4×D4—264no—
364#117—268no—
365#117—262no—
366#117—262no—
367#117C4×D1314yes—
368#117C22⋊D1314yes—
369C2×C4⋊C4—134no—
370C2×C4⋊C4—132no—
371C2×C4⋊C4—132no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—262no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—268no—
378C2×C4⋊C4—262no—
379C2×C4⋊C4—262no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—262no—
382C2×C4⋊C4—262no—
383C2×C4⋊C4D5211yescharacteristic
384C2×C4⋊C4D5211yescharacteristic
385C2×C22⋊C4—262no—
386C2×C22⋊C4—261no—
387C2×C22⋊C4D5212yes—
388C2×C42—262no—
389C2×C42—261no—
390C2×C42C22×D1312yes—
391C4⋊C8—24no—
392C4⋊C8—24no—
393#103—262no—
394#103—262no—
395#103—264no—
396#102—262no—
397#102—262no—
398#102—264no—
399#95—262no—
400#95—262no—
401C2×C13—24no—
402C2×C13C2×#38011yescharacteristic
403C2×C13#289711yescharacteristic
404C2×C13#289811yescharacteristic
405C2×C13#304511yescharacteristic
406C2×C13#304611yescharacteristic
407C2×C13#308311yescharacteristic
408C2×C13#308411yescharacteristic
409D13—44no—
410C24—261no—
411C24C2×D5211yescharacteristic
412#41—1316no—
413#41—268no—
414#41—268no—
415#41—268no—
416C2×Q8—132no—
417C2×Q8—132no—
418C2×Q8—132no—
419C2×Q8—261no—
420C2×Q8—261no—
421C2×Q8—261no—
422C2×D4—132no—
423C2×D4—132no—
424C2×D4—132no—
425C2×D4—264no—
426C2×D4—264no—
427C2×D4—264no—
428C2×D4—261no—
429C2×D4—261no—
430C2×D4—261no—
431C22×C4—261no—
432C22×C4—264no—
433C22×C4—264no—
434C22×C4—264no—
435C22×C4—262no—
436C22×C4—264no—
437C22×C4—268no—
438C22×C4—261no—
439C22×C4—262no—
440C22×C4—261no—
441C22×C4—522no—
442C22×C4—1042no—
443C22×C4—1042no—
444C22×C4—1041no—
445C22×C4—1041no—
446C22×C4—1041no—
447C22×C4—1041no—
448C22×C4C2×C4×D1312yes—
449C22×C4C2×D5212yes—
450C22×C4C2×D5212yes—
451C22×C4C2×D5211yescharacteristic
452C22×C4D4×D1312yes—
453C22×C4#612912yes—
454C22×C4Q8×D1312yes—
455C22×C4#613112yes—
456C22×C4C2×C22⋊D1312yes—
457C22×C4C23×D1311yescharacteristic
458M16—44no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—22no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—22no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—22no—
468C2×C8—44no—
469C4⋊C4—134no—
470C4⋊C4—264no—
471C4⋊C4—268no—
472C4⋊C4—262no—
473C4⋊C4—262no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—262no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—522no—
480C4⋊C4—1042no—
481C4⋊C4—1042no—
482C4⋊C4#610314yes—
483C4⋊C4#610314yes—
484C22⋊C4—268no—
485C22⋊C4—522no—
486C22⋊C4#610318yes—
487C42—268no—
488C42—522no—
489C42C2×C4×D1314yes—
490C42C2×C22⋊D1314yes—
491C13#2065211yescharacteristic, complemented, Sylow
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—262no—
497C23—262no—
498C23—262no—
499C23—521no—
500C23—521no—
501C23—521no—
502C23—521no—
503C23#8814912yes—
504C23#8815112yes—
505C23C2×#610312yes—
506C23C22×D5211yescharacteristic
507Q8—134no—
508Q8—262no—
509Q8—262no—
510Q8—262no—
511D4—134no—
512D4—2616no—
513D4—262no—
514D4—262no—
515D4—262no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—262no—
521C2×C4—262no—
522C2×C4—262no—
523C2×C4—2616no—
524C2×C4—264no—
525C2×C4—522no—
526C2×C4—522no—
527C2×C4—521no—
528C2×C4—522no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—522no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—522no—
536C2×C4—1048no—
537C2×C4—1044no—
538C2×C4—1044no—
539C2×C4C4⋊C4×D1314yes—
540C2×C4#8814614yes—
541C2×C4#8814912yes—
542C2×C4#8815112yes—
543C2×C4C2×#610314yes—
544C2×C4C2×#610314yes—
545C2×C4C2×#610312yes—
546C2×C4#8819214yes—
547C2×C4#8820014yes—
548C2×C4C22×C4×D1311yescharacteristic
549C2×C4C2×D4×D1311yescharacteristic
550C2×C4C2×#612911yescharacteristic
551C2×C4C2×Q8×D1311yescharacteristic
552C2×C4C2×#613111yescharacteristic
553C2×C4C22×C22⋊D1311yescharacteristic
554C8—41no—
555C8—41no—
556C8—42no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—264no—
564C22—522no—
565C22—522no—
566C22—522no—
567C22—522no—
568C22—522no—
569C22—522no—
570C22#1171864814yes—
571C22C2×#8814911yescharacteristic
572C22C2×#8815111yescharacteristic
573C22#1171945611yescharacteristic
574C22#1171945611yescharacteristic
575C22#1171945711yescharacteristic
576C22#1171945811yescharacteristic
577C22C22×#610311yescharacteristic
578C4—24no—
579C4—24no—
580C4—264no—
581C4—524no—
582C4—1041no—
583C4—1042no—
584C4—1041no—
585C4#1171864814yes—
586C4C2×C4⋊C4×D1311yescharacteristic
587C4C2×#8814611yescharacteristic
588C4C2×#8819211yescharacteristic
589C4C2×#8820011yescharacteristic
590C2—24no—
591C2—524no—
592C2C2×#1171864811yescharacteristic
593C2#1312336311yescharacteristic
594C2#1312337011yescharacteristic
595C2#1312437711yescharacteristic
596C2#1312438811yescharacteristic
597C2#1312468911yescharacteristic
598C2#1312470011yescharacteristic
subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#424C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC2×#424D13
hypocenterC13#20652
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
4. #13117459C2semidirect
5. #13114852C2semidirect
6. #13114847C2semidirect
7. #13114842C2semidirect
8. #13114837C2semidirect
9. #13114556C2semidirect
10. C2×#11718143C2semidirect
11. C2×C13×#424C2semidirect
20. #11719228C4semidirect
98. C4×D52C2×C4semidirect
100. C4×Dic26C2×C4semidirect
141. #6127C4⋊C4semidirect
194. C2×#424D13semidirect
491. C13#20652semidirect

Maximal subgroups

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

subgroupindex
C2×#117192282
C2×#117187942
C2×#117187742
#131174592
#131148522
#131148472
#131148422
#131148372
#131145562
C2×#117181432
C2×C13×#4242
#2065213