Finite Group Databasebeta

← #15866961

Subgroups — #15866961

Order 3328.

1562 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128165C211yesmaximal, characteristic
2C2×#11718666C211yesmaximal, characteristic, complemented
3C22×#88077C211yesmaximal, characteristic, complemented
4C22×#88065C211yesmaximal, characteristic, complemented
5#13123254C211yesmaximal, characteristic, complemented
6#13117318C211yesmaximal, characteristic, complemented
7#13115753C218yesmaximal, complemented
8C2×C13×#421C211yesmaximal, characteristic, complemented
9C22×C13×#41C2211yescharacteristic
10C22×#6127C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13#11719538—22no—
14#11719537C2214yes—
15#11719535C412yescomplemented
16#11719533—22no—
17#11719530C412yescomplemented
18#11719521C412yescomplemented
19#11719510C412yescomplemented
20#11719509—22no—
21#11719496—22no—
22C2×#88180C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C13×#421—24no—
26C2×C13×#104C2214yescomplemented
27C2×#88077—24no—
28C2×#88077C2214yescomplemented
29C2×#88065—24no—
30C2×#88065C2214yescomplemented
31#11718783—22no—
32M16×Dic13C2214yescomplemented
33#11718762—22no—
34#11718666—24no—
35#11718634—22no—
36#11718607—22no—
37C4×#6101C2214yescomplemented
38C2×#88045C2214yescomplemented
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C2×C13×#41—22no—
42C2×C13×#41—22no—
43C2×C13×#41—22no—
44C2×C13×#41—22no—
45C2×C13×#41C2×C412yes—
46C2×C13×#41C2312yes—
47C22×Q8×C13C2×C411yescharacteristic
48C22×D4×C13—21no—
49C22×D4×C13C2×C411yescharacteristic
50C23×C4×C13—21no—
51C23×C4×C13C2311yescharacteristic
52C22×C22⋊D13—21no—
53C23×Dic13—21no—
54C2×#6127—21no—
55C2×#6127—21no—
56C2×#6127—22no—
57C2×#6127—22no—
58C2×#6127—22no—
59C2×#6127—22no—
60C2×#6127C2×C412yes—
61C2×#6127C2312yes—
62C22×D52C2×C411yescharacteristic
63C22×C4×D13—21no—
64C22×Dic26C2×C411yescharacteristic
65C2×C13×M16—21no—
66C2×C13×M16—22no—
67C2×C13×M16D414yescomplemented
68C2×C13×M16C2312yes—
69C22×C8×C13—21no—
70C13×#117—22no—
71C13×#117—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C22⋊C4—21no—
74C2×C42×C13C2312yes—
75#88207—24no—
76C2×C22⋊Dic13D412yes—
77#88201C2×C414yescomplemented
78#88200—24no—
79#88198C2×C414yescomplemented
80#88194C2×C414yescomplemented
81#88193—28no—
82#88192—24no—
83#88191—24no—
84#88190C2×C414yescomplemented
85#88189—24no—
86#88184—24no—
87#88183—24no—
88C4×C22⋊D13—28no—
89#88180C2×C412yes—
90#88180C2×C412yes—
91#88180D412yes—
92#88180D412yes—
93C2×C4⋊Dic13D412yes—
94#88178—24no—
95C2×#6101—24no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13C2312yes—
100C2×C4×Dic13C2312yes—
101C2×#6099—21no—
102C2×#6099—22no—
103C2×#6099D414yescomplemented
104C2×#6099C2312yes—
105C22×#1055—21no—
106C13×#104—28no—
107#88077—28no—
108#88071—24no—
109#88065—28no—
110#88055—24no—
111C8×Dic13—24no—
112#88045—28no—
113#21253—131nomaximal, Sylow
114C24×C13—21no—
115C24×C13C2×D411yescharacteristic
116C23×D13—21no—
117C13×#41—24no—
118C13×#41—24no—
119C13×#41—22no—
120C13×#41—22no—
121C13×#41—22no—
122C13×#41—22no—
123C13×#41—42no—
124C13×#41—42no—
125C13×#41—42no—
126C13×#41—42no—
127C2×Q8×C13—21no—
128C2×Q8×C13—22no—
129C2×Q8×C13—22no—
130C2×Q8×C13C22×C412yes—
131C2×D4×C13—22no—
132C2×D4×C13—22no—
133C2×D4×C13—21no—
134C2×D4×C13—22no—
135C2×D4×C13—22no—
136C2×D4×C13—42no—
137C2×D4×C13—42no—
138C2×D4×C13C22×C412yes—
139C22×C4×C13—21no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C22×C411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C22×C4×C13C2411yescharacteristic
155C2×C22⋊D13—22no—
156C2×C22⋊D13—22no—
157C2×C22⋊D13—28no—
158C2×C22⋊D13—42no—
159C2×C22⋊D13—42no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—44no—
163C22×Dic13—42no—
164C22×Dic13C2×D414yes—
165#6127—24no—
166#6127—24no—
167#6127—22no—
168#6127—22no—
169#6127—22no—
170#6127—22no—
171#6127—42no—
172#6127—42no—
173#6127—42no—
174#6127—42no—
175C2×D52—22no—
176C2×D52—22no—
177C2×D52—21no—
178C2×D52C22×C412yes—
179C2×C4×D13—22no—
180C2×C4×D13—22no—
181C2×C4×D13—42no—
182C2×C4×D13—42no—
183C2×Dic26—22no—
184C2×Dic26—22no—
185C2×Dic26—21no—
186C2×Dic26C22×C412yes—
187C13×M16—24no—
188C13×M16—22no—
189C13×M16C2×D414yes—
190C2×C8×C13—24no—
191C2×C8×C13—22no—
192C13×C4⋊C4—42no—
193C13×C22⋊C4—42no—
194C42×C13—22no—
195C42×C13—22no—
196C22⋊Dic13—28no—
197C22⋊Dic13C22⋊C414yes—
198C22⋊Dic13C22⋊C414yes—
199#6103—28no—
200C4⋊Dic13C22⋊C414yes—
201C4⋊Dic13C22⋊C414yes—
202#6101—28no—
203#6101—48no—
204C4×Dic13—22no—
205C4×Dic13—22no—
206C4×Dic13—42no—
207C4×Dic13C22×C414yes—
208C4×Dic13C2×D414yes—
209#6099—24no—
210#6099—22no—
211#6099C2×D414yes—
212C2×#1055—24no—
213C2×#1055—22no—
214#3449—131no—
215C2×#421—131no—
216C2×#421D1311yescharacteristic, complemented
217C22×#104—131no—
218C22×#104—131no—
219#2873—131no—
220#2296—131no—
221#1980—138no—
222C23×C13—22no—
223C23×C13—42no—
224C23×C13—42no—
225C23×C13—82no—
226C23×C13C2×C22⋊C411yescharacteristic
227C23×C13C2×C22⋊C411yescharacteristic
228C23×C13#12412yes—
229C23×C13#12712yes—
230C23×C13C22×D411yescharacteristic
231C22×D13—22no—
232C22×D13—42no—
233C22×D13—82no—
234Q8×C13—22no—
235Q8×C13—22no—
236Q8×C13—42no—
237D4×C13—22no—
238D4×C13—22no—
239D4×C13—42no—
240D4×C13—42no—
241D4×C13—44no—
242D4×C13—42no—
243C2×C4×C13—22no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—44no—
248C2×C4×C13—44no—
249C2×C4×C13—42no—
250C2×C4×C13C2×C22⋊C411yescharacteristic
251C2×C4×C13C2×C22⋊C411yescharacteristic
252C2×C4×C13C4×D412yes—
253C2×C4×C13C4×D412yes—
254C2×C4×C13C4×D412yes—
255C2×C4×C13C4×D412yes—
256C2×C4×C13#12112yes—
257C2×C4×C13#12112yes—
258C2×C4×C13#12112yes—
259C2×C4×C13#12112yes—
260C2×C4×C13#12412yes—
261C2×C4×C13#12712yes—
262C2×C4×C13C23×C411yescharacteristic
263C2×C4×C13C22×D411yescharacteristic
264C2×C4×C13C22×D411yescharacteristic
265C2×C4×C13C22×D411yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C22⋊D13—42no—
269C22⋊D13—42no—
270C22⋊D13—44no—
271C22⋊D13—88no—
272C2×Dic13—24no—
273C2×Dic13—22no—
274C2×Dic13—44no—
275C2×Dic13—42no—
276C2×Dic13—48no—
277C2×Dic13—42no—
278C2×Dic13—42no—
279C2×Dic13C2×C22⋊C418yes—
280D52—22no—
281D52—22no—
282D52—42no—
283C4×D13—42no—
284C4×D13—42no—
285C4×D13—44no—
286Dic26—22no—
287Dic26—22no—
288Dic26—42no—
289C8×C13—24no—
290#1055—24no—
291C22×#41—131no—
292C22×#41C2×D1311yescharacteristic
293C22×M16—131no—
294C22×M16C2×D1311yescharacteristic
295#537—262no—
296#536—132no—
297#536—132no—
298#535—132no—
299#535—132no—
300#534—262no—
301#532—134no—
302#525—262no—
303#525—262no—
304C2×#117—131no—
305C2×#117C2×D1311yescharacteristic
306C22×C42—131no—
307#421—24no—
308#421—264no—
309C2×#104—134no—
310C2×#104—134no—
311C2×#104—134no—
312C2×#104—264no—
313C2×#104—264no—
314C2×#104C2×D1314yescomplemented
315#405—262no—
316#405—262no—
317C4×M16—134no—
318#389—262no—
319#385—262no—
320C4×C4⋊C4—134no—
321C22×C13—22no—
322C22×C13—22no—
323C22×C13—22no—
324C22×C13—42no—
325C22×C13—42no—
326C22×C13—44no—
327C22×C13—42no—
328C22×C13—84no—
329C22×C13#39012yes—
330C22×C13#39012yes—
331C22×C13C22×C22⋊C411yescharacteristic
332C22×C13C2×#12411yescharacteristic
333C22×C13C2×#12711yescharacteristic
334C2×D13—44no—
335C2×D13—42no—
336C2×D13—84no—
337C4×C13—42no—
338C4×C13—82no—
339C4×C13#39012yes—
340C4×C13#39012yes—
341C4×C13C2×C4×D411yescharacteristic
342C4×C13C2×C4×D411yescharacteristic
343C4×C13C2×#12111yescharacteristic
344C4×C13C2×#12111yescharacteristic
345Dic13—28no—
346Dic13—44no—
347Dic13—42no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41—22no—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41—132no—
355C2×#41—132no—
356C2×#41—261no—
357C2×#41—261no—
358C2×#41—262no—
359C2×#41—262no—
360C2×#41—262no—
361C2×#41—262no—
362C2×#41C4×D1312yes—
363C2×#41C22×D1312yes—
364C22×Q8—131no—
365C22×Q8C4×D1311yescharacteristic
366C22×D4—21no—
367C22×D4—131no—
368C22×D4—261no—
369C22×D4C4×D1311yescharacteristic
370C23×C4—21no—
371C23×C4—261no—
372C23×C4—261no—
373C23×C4C22×D1311yescharacteristic
374C2×M16—21no—
375C2×M16—22no—
376C2×M16—134no—
377C2×M16—132no—
378C2×M16—262no—
379C2×M16—261no—
380C2×M16C22⋊D1314yescomplemented
381C2×M16C22×D1312yes—
382C22×C8—21no—
383C22×C8—261no—
384C4⋊Q8—134no—
385#127—134no—
386#124—134no—
387#124—134no—
388#123—264no—
389#123—264no—
390C22⋊Q8—264no—
391C22⋊Q8—264no—
392#121—264no—
393#121—264no—
394#121—268no—
395#120—264no—
396#120—264no—
397C4×D4—268no—
398#117—22no—
399#117—22no—
400#117—132no—
401#117—132no—
402#117—132no—
403#117—132no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—132no—
406C2×C4⋊C4—264no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—132no—
409C2×C42—132no—
410C2×C42—132no—
411C2×C42—262no—
412C2×C42—262no—
413C2×C42—261no—
414C2×C42C22×D1312yes—
415#104—28no—
416#104—268no—
417#104—268no—
418#104—268no—
419#97—264no—
420C4×C8—264no—
421#95—264no—
422C2×C13—21no—
423C2×C13—22no—
424C2×C13—22no—
425C2×C13—21no—
426C2×C13—82no—
427C2×C13C2×#39011yescharacteristic
428C2×C13#290112yes—
429D13—82no—
430C24—21no—
431C24—261no—
432C24D4×D1311yescharacteristic
433#41—24no—
434#41—24no—
435#41—22no—
436#41—22no—
437#41—22no—
438#41—22no—
439#41—42no—
440#41—42no—
441#41—42no—
442#41—42no—
443#41—264no—
444#41—264no—
445#41—262no—
446#41—262no—
447#41—262no—
448#41—262no—
449#41—522no—
450#41—522no—
451#41—522no—
452#41—522no—
453C2×Q8—21no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—132no—
457C2×Q8—261no—
458C2×Q8—262no—
459C2×Q8—262no—
460C2×Q8C2×C4×D1312yes—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—132no—
469C2×D4—268no—
470C2×D4—262no—
471C2×D4—262no—
472C2×D4—261no—
473C2×D4—262no—
474C2×D4—262no—
475C2×D4—522no—
476C2×D4—522no—
477C2×D4C2×C4×D1312yes—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—134no—
485C22×C4—261no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—524no—
490C22×C4—522no—
491C22×C4—522no—
492C22×C4—522no—
493C22×C4C2×C4×D1311yescharacteristic
494C22×C4C2×C4×D1311yescharacteristic
495C22×C4#612712yes—
496C22×C4D4×D1311yescharacteristic
497C22×C4D4×D1311yescharacteristic
498C22×C4D4×D1311yescharacteristic
499C22×C4D4×D1312yes—
500C22×C4#612912yes—
501C22×C4C2×C22⋊D1312yes—
502C22×C4C23×D1311yescharacteristic
503M16—24no—
504M16—22no—
505M16—134no—
506M16—264no—
507M16—262no—
508M16C2×C22⋊D1314yes—
509C2×C8—24no—
510C2×C8—22no—
511C2×C8—264no—
512C2×C8—262no—
513C4⋊C4—42no—
514C4⋊C4—134no—
515C4⋊C4—134no—
516C4⋊C4—268no—
517C4⋊C4—528no—
518C22⋊C4—42no—
519C22⋊C4—134no—
520C22⋊C4—134no—
521C22⋊C4—268no—
522C22⋊C4—268no—
523C42—22no—
524C42—22no—
525C42—134no—
526C42—134no—
527C42—262no—
528C42—262no—
529C42—522no—
530C13#2125311yescharacteristic, complemented, Sylow
531C23—22no—
532C23—42no—
533C23—42no—
534C23—82no—
535C23—262no—
536C23—522no—
537C23—1042no—
538C23C22⋊C4×D1311yescharacteristic
539C23C22⋊C4×D1311yescharacteristic
540C23#8813912yes—
541C23#8819412yes—
542C23C2×D4×D1311yescharacteristic
543Q8—22no—
544Q8—22no—
545Q8—42no—
546Q8—262no—
547Q8—262no—
548Q8—522no—
549D4—22no—
550D4—22no—
551D4—42no—
552D4—42no—
553D4—44no—
554D4—42no—
555D4—262no—
556D4—262no—
557D4—522no—
558D4—522no—
559D4—524no—
560D4—522no—
561D4—1048no—
562C2×C4—22no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—42no—
569C2×C4—138no—
570C2×C4—264no—
571C2×C4—262no—
572C2×C4—524no—
573C2×C4—522no—
574C2×C4—528no—
575C2×C4—522no—
576C2×C4—522no—
577C2×C4—522no—
578C2×C4—522no—
579C2×C4—524no—
580C2×C4C22⋊C4×D1311yescharacteristic
581C2×C4C22⋊C4×D1311yescharacteristic
582C2×C4#8813512yes—
583C2×C4#8813512yes—
584C2×C4#8813812yes—
585C2×C4#8813812yes—
586C2×C4#8813912yes—
587C2×C4C4×C22⋊D1312yes—
588C2×C4C4×C22⋊D1312yes—
589C2×C4#8819312yes—
590C2×C4#8819312yes—
591C2×C4#8819412yes—
592C2×C4C22×C4×D1311yescharacteristic
593C2×C4C2×#612711yescharacteristic
594C2×C4C2×D4×D1311yescharacteristic
595C2×C4C2×D4×D1311yescharacteristic
596C2×C4C2×#612911yescharacteristic
597C2×C4C22×C22⋊D1311yescharacteristic
598C8—24no—
599C8—264no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—42no—
604C22—42no—
605C22—44no—
606C22—42no—
607C22—84no—
608C22—524no—
609C22—522no—
610C22—1044no—
611C22#1171861812yes—
612C22#1171861812yes—
613C22C2×C22⋊C4×D1311yescharacteristic
614C22C2×#8813911yescharacteristic
615C22C2×#8819411yescharacteristic
616C4—42no—
617C4—82no—
618C4—268no—
619C4—524no—
620C4—522no—
621C4#1171861812yes—
622C4#1171861812yes—
623C4C2×#8813511yescharacteristic
624C4C2×#8813811yescharacteristic
625C4C2×C4×C22⋊D1311yescharacteristic
626C4C2×#8819311yescharacteristic
627C2—21no—
628C2—22no—
629C2—22no—
630C2—21no—
631C2—82no—
632C2—1042no—
633C2C2×#1171861811yescharacteristic
634C2#1312338212yes—
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#421C2
socleC22×C13C22×C22⋊C4
prime radical#13128165C2
cosocleC22×C4×C13C24
hypercenterC2×#421D13
hypocenterC13#21253
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#11718666C2semidirect
3. C22×#88077C2semidirect
4. C22×#88065C2semidirect
5. #13123254C2semidirect
6. #13117318C2semidirect
7. #13115753C2semidirect
8. C2×C13×#421C2semidirect
15. #11719535C4semidirect
17. #11719530C4semidirect
18. #11719521C4semidirect
19. #11719510C4semidirect
26. C2×C13×#104C22semidirect
28. C2×#88077C22semidirect
30. C2×#88065C22semidirect
32. M16×Dic13C22semidirect
37. C4×#6101C22semidirect
38. C2×#88045C22semidirect
67. C2×C13×M16D4semidirect
77. #88201C2×C4semidirect
79. #88198C2×C4semidirect
80. #88194C2×C4semidirect
84. #88190C2×C4semidirect
103. C2×#6099D4semidirect
216. C2×#421D13semidirect
314. C2×#104C2×D13semidirect
380. C2×M16C22⋊D13semidirect
530. C13#21253semidirect

Maximal subgroups

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

subgroupindex
#131281652
C2×#117186662
C22×#880772
C22×#880652
#131232542
#131173182
#131157532
C2×C13×#4212
#2125313