Finite Group Databasebeta

← #15872012

Subgroups — #15872012

Order 3328.

1518 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719535C211yesmaximal, characteristic
2C2×#11718895C211yesmaximal, characteristic, complemented
3#13115272C212yesmaximal, complemented
4#13115262C212yesmaximal, complemented
5#13115158C212yesmaximal, complemented
6#13115153C212yesmaximal, complemented
7#13114928C212yesmaximal, complemented
8#13114766C212yesmaximal, complemented
9C13×#2311C211yesmaximal, characteristic, complemented
10C22×C13×#41C2211yescharacteristic
11C23×D52C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic, complemented
13C22×C13×C4⋊C4C2211yescharacteristic, complemented
14#11719535—24no—
15#11719535C418yescomplemented
16C2×#88201—21no—
17C2×#88194—21no—
18C2×#88191—21no—
19C2×#88191—21no—
20C2×#88184C2212yes—
21C2×#88184C2212yes—
22C2×#88180C2211yescharacteristic
23C22×#6099C2211yescharacteristic, complemented
24C23×#1055C2211yescharacteristic, complemented
25C13×#391—21no—
26C13×#390—21no—
27C13×#386—21no—
28C13×#386—21no—
29C13×#380C2212yes—
30C13×#380C2212yescomplemented
31#11718895—24no—
32C2×C22⋊#1055C2212yes—
33C2×C22⋊#1055C2212yescomplemented
34C2×#88049C2212yes—
35C2×#88049C2212yes—
36C2×#88049C2212yes—
37C2×#88049C2212yes—
38#11718121C2212yescomplemented
39#11718121C2212yescomplemented
40#11718121C2212yescomplemented
41#11718121C2212yescomplemented
42C24×D13—21no—
43C2×C13×#41—41no—
44C2×C13×#41—41no—
45C2×C13×#41—41no—
46C2×C13×#41—41no—
47C2×C13×#41C2×C414yes—
48C2×C13×#41D414yes—
49C22×Q8×C13D411yescharacteristic
50C22×D4×C13D411yescharacteristic
51C22×D4×C13D411yescharacteristic
52C22×D4×C13D411yescharacteristic
53C23×C4×C13—21no—
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C22×C22⋊D13—22no—
58C22×C22⋊D13—22no—
59C22×D52—21no—
60C22×D52—22no—
61C22×D52—41no—
62C22×D52—41no—
63C22×D52—41no—
64C22×D52—41no—
65C22×D52C2×C414yescomplemented
66C22×D52C2312yes—
67C13×#117—41no—
68C13×#117—41no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—41no—
71C2×C13×C4⋊C4—41no—
72C2×C13×C4⋊C4C2312yes—
73C2×C13×C4⋊C4C2312yes—
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—22no—
76C2×C13×C22⋊C4—22no—
77C2×C42×C13—21no—
78C2×C22⋊Dic13—21no—
79#88201—28no—
80#88194—28no—
81#88191—28no—
82#88191—28no—
83#88184—24no—
84#88184—24no—
85#88184C2×C418yes—
86#88184C2×C418yescomplemented
87C2×#6103—22no—
88C2×#6103—22no—
89#88180—22no—
90#88180C2×C414yescomplemented
91C2×C4⋊Dic13C2312yes—
92C2×C4×Dic13—21no—
93C2×#6099—22no—
94C2×#6099—41no—
95C2×#6099—41no—
96C22×#1055—22no—
97C22×#1055—41no—
98C22×#1055—41no—
99C22×#1055C2312yes—
100C22×#1055C2312yes—
101C13×#95—22no—
102C13×#95—22no—
103C22⋊#1055—24no—
104C22⋊#1055—24no—
105#88049—42no—
106#88049—42no—
107#88049—42no—
108#88049—42no—
109#21770—131nomaximal, Sylow
110C24×C13C2×D411yescharacteristic
111C24×C13C2×D411yescharacteristic
112C24×C13C2×D411yescharacteristic
113C23×D13—22no—
114C23×D13—24no—
115C23×D13—42no—
116C23×D13—42no—
117C23×D13—82no—
118C23×D13—82no—
119C13×#41—44no—
120C13×#41—44no—
121C13×#41—44no—
122C13×#41—44no—
123C2×Q8×C13—41no—
124C2×Q8×C13—41no—
125C2×Q8×C13C22⋊C414yes—
126C2×D4×C13—41no—
127C2×D4×C13—41no—
128C2×D4×C13—41no—
129C2×D4×C13—41no—
130C2×D4×C13—41no—
131C2×D4×C13—41no—
132C2×D4×C13C22⋊C414yes—
133C2×D4×C13C22⋊C414yes—
134C2×D4×C13C22⋊C414yes—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—42no—
150C22×C4×C13—82no—
151C22×C4×C13C22×C412yes—
152C22×C4×C13C22×C412yes—
153C22×C4×C13C22×C412yes—
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2411yescharacteristic
161C2×C22⋊D13—28no—
162C2×C22⋊D13—28no—
163C2×C22⋊D13—82no—
164C2×C22⋊D13—82no—
165C2×C22⋊D13—82no—
166C2×C22⋊D13—82no—
167C22×Dic13—22no—
168C2×D52—22no—
169C2×D52—22no—
170C2×D52—22no—
171C2×D52—22no—
172C2×D52—24no—
173C2×D52—22no—
174C2×D52—44no—
175C2×D52—44no—
176C2×D52—42no—
177C2×D52—42no—
178C2×D52—44no—
179C2×D52—44no—
180C2×D52C22×C414yes—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—42no—
186C13×C22⋊C4—42no—
187C13×C22⋊C4—82no—
188C13×C22⋊C4—82no—
189C42×C13—42no—
190C22⋊Dic13—24no—
191#6103—28no—
192#6103—28no—
193C4⋊Dic13—22no—
194C4⋊Dic13C22×C414yes—
195C4×Dic13—24no—
196#6099—44no—
197C2×#1055—22no—
198C2×#1055—22no—
199C2×#1055—22no—
200C2×#1055—22no—
201C2×#1055—22no—
202C2×#1055—22no—
203C2×#1055—44no—
204C2×#535—131no—
205C2×#408—131no—
206#2311D1311yescharacteristic, complemented
207#1895—132no—
208#1893—132no—
209#1875—132no—
210#1874—132no—
211#1825—132no—
212#1786—132no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13C2×C22⋊C412yes—
226C23×C13C2×C22⋊C412yes—
227C23×C13C2×C22⋊C412yes—
228C23×C13C22×D411yescharacteristic
229C22×D13—24no—
230C22×D13—48no—
231C22×D13—42no—
232C22×D13—42no—
233C22×D13—42no—
234C22×D13—42no—
235C22×D13—42no—
236C22×D13—42no—
237C22×D13—88no—
238C22×D13—88no—
239C22×D13—84no—
240C22×D13—84no—
241Q8×C13—44no—
242D4×C13—44no—
243D4×C13—44no—
244D4×C13—44no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13—42no—
268C2×C4×C13—42no—
269C2×C4×C13—84no—
270C2×C4×C13C2×C22⋊C412yes—
271C2×C4×C13C2×C22⋊C412yes—
272C2×C4×C13C2×C22⋊C412yes—
273C2×C4×C13C23×C411yescharacteristic
274C2×C4×C13C22×D411yescharacteristic
275C2×C4×C13H(5,𝔽2)11yescharacteristic
276C2×C4×C13H(5,𝔽2)11yescharacteristic
277C2×C4×C13H(5,𝔽2)11yescharacteristic
278C2×C4×C13H(5,𝔽2)11yescharacteristic
279C22⋊D13—88no—
280C22⋊D13—88no—
281C2×Dic13—24no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284D52—24no—
285D52—24no—
286D52—48no—
287D52—42no—
288D52—42no—
289#1055—42no—
290#1055—42no—
291C22×#41C2×D1311yescharacteristic
292C23×D4—131no—
293C22×M16—131no—
294C23×C8—131no—
295#535—138no—
296#535—264no—
297C2×#127—261no—
298C2×#124—261no—
299C2×#121—132no—
300C2×#121—132no—
301C2×#120—261no—
302C2×#120—261no—
303C2×#117—131no—
304C2×#117C2×D1311yescharacteristic, complemented
305C22×C4⋊C4C2×D1311yescharacteristic, complemented
306C2×#102—132no—
307C2×#102—132no—
308C2×#102—132no—
309C2×#102—132no—
310#408—264no—
311C2×C22⋊C8—132no—
312C2×C22⋊C8—132no—
313#391—21no—
314#390—21no—
315#386—21no—
316#386—21no—
317#380C2×D1312yes—
318#380C2×D1312yescomplemented
319#340—132no—
320#340—132no—
321#340—132no—
322#340—132no—
323C22×C13—22no—
324C22×C13—22no—
325C22×C13—22no—
326C22×C13—24no—
327C22×C13—24no—
328C22×C13—24no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—42no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13C22×C22⋊C411yescharacteristic
339C22×C13#53411yescharacteristic
340C22×C13#53411yescharacteristic
341C22×C13#57612yes—
342C22×C13#57712yes—
343C2×D13—44no—
344C2×D13—44no—
345C2×D13—44no—
346C2×D13—816no—
347C2×D13—82no—
348C2×D13—82no—
349C2×D13—82no—
350C2×D13—82no—
351C4×C13—22no—
352C4×C13—22no—
353C4×C13—22no—
354C4×C13—82no—
355C4×C13—82no—
356C4×C13#51811yescharacteristic
357C4×C13#51811yescharacteristic
358C4×C13#53411yescharacteristic
359C4×C13#53411yescharacteristic
360Dic13—44no—
361C25—261no—
362C2×#41—41no—
363C2×#41—41no—
364C2×#41—41no—
365C2×#41—41no—
366C2×#41C4×D1314yes—
367C2×#41D5214yes—
368C22×Q8C22⋊D1311yescharacteristic
369C22×D4—134no—
370C22×D4—132no—
371C22×D4—262no—
372C22×D4—262no—
373C22×D4—262no—
374C22×D4—261no—
375C22×D4—521no—
376C22×D4—521no—
377C22×D4—521no—
378C22×D4—521no—
379C22×D4C22⋊D1311yescharacteristic
380C22×D4C22⋊D1311yescharacteristic
381C22×D4C22⋊D1311yescharacteristic
382C23×C4—21no—
383C23×C4C22×D1311yescharacteristic
384C23×C4C22×D1311yescharacteristic
385C23×C4C22×D1311yescharacteristic
386C2×M16—262no—
387C2×M16—521no—
388C2×M16—521no—
389C22×C8—132no—
390C22×C8—132no—
391C22×C8—262no—
392C22×C8—521no—
393C22×C8—521no—
394#127—268no—
395#124—268no—
396#121—138no—
397#121—138no—
398#121—264no—
399#121—264no—
400#120—268no—
401#120—268no—
402#117—41no—
403#117—41no—
404#117—134no—
405#117—262no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—41no—
408C2×C4⋊C4—41no—
409C2×C4⋊C4—132no—
410C2×C4⋊C4C22×D1312yes—
411C2×C4⋊C4C22×D1312yes—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—261no—
416C2×C22⋊C4—262no—
417C2×C22⋊C4—262no—
418C2×C42—21no—
419C2×C42—261no—
420#102—522no—
421#102—522no—
422#102—522no—
423#102—522no—
424C22⋊C8—264no—
425C22⋊C8—264no—
426#95—22no—
427#95—22no—
428C2×C13—42no—
429C2×C13—42no—
430C2×C13—42no—
431C2×C13#230811yescharacteristic
432C2×C13#289712yes—
433C2×C13#319812yes—
434C2×C13#319911yescharacteristic
435C2×C13#320011yescharacteristic
436D13—84no—
437C24—262no—
438C24—264no—
439C24—522no—
440C24—522no—
441C24—1042no—
442C24—1042no—
443C24C2×C22⋊D1311yescharacteristic
444C24C2×C22⋊D1311yescharacteristic
445C24C2×C22⋊D1311yescharacteristic
446#41—44no—
447#41—44no—
448#41—44no—
449#41—44no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8#610314yes—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—134no—
460C2×D4—268no—
461C2×D4—268no—
462C2×D4—264no—
463C2×D4—262no—
464C2×D4—262no—
465C2×D4—262no—
466C2×D4—262no—
467C2×D4—262no—
468C2×D4—524no—
469C2×D4—524no—
470C2×D4—522no—
471C2×D4—522no—
472C2×D4—524no—
473C2×D4—524no—
474C2×D4—1042no—
475C2×D4—1042no—
476C2×D4—1042no—
477C2×D4—1042no—
478C2×D4#610314yes—
479C2×D4#610314yes—
480C2×D4#610314yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—42no—
496C22×C4—82no—
497C22×C4—262no—
498C22×C4C2×C4×D1312yes—
499C22×C4C2×C4×D1312yes—
500C22×C4C2×C4×D1312yes—
501C22×C4C2×D5212yes—
502C22×C4C2×D5212yes—
503C22×C4C2×D5212yes—
504C22×C4C2×C22⋊D1311yescharacteristic
505C22×C4C2×C22⋊D1311yescharacteristic
506C22×C4C2×C22⋊D1311yescharacteristic
507C22×C4C23×D1311yescharacteristic
508M16—524no—
509C2×C8—262no—
510C2×C8—262no—
511C2×C8—262no—
512C2×C8—262no—
513C2×C8—262no—
514C2×C8—262no—
515C2×C8—524no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—42no—
521C4⋊C4—134no—
522C4⋊C4—262no—
523C22⋊C4—42no—
524C22⋊C4—82no—
525C22⋊C4—82no—
526C22⋊C4—264no—
527C22⋊C4—268no—
528C22⋊C4—268no—
529C42—42no—
530C42—264no—
531C13#2177011yescharacteristic, complemented, Sylow
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—264no—
545C23—528no—
546C23—522no—
547C23—522no—
548C23—522no—
549C23—522no—
550C23—522no—
551C23—522no—
552C23—1048no—
553C23—1048no—
554C23—1044no—
555C23—1044no—
556C23C2×#610312yes—
557C23C2×#610312yes—
558C23C2×#610312yes—
559C23C22×C22⋊D1311yescharacteristic
560Q8—44no—
561D4—44no—
562D4—44no—
563D4—44no—
564D4—264no—
565D4—264no—
566D4—528no—
567D4—522no—
568D4—522no—
569D4—1048no—
570D4—1048no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—84no—
596C2×C4—264no—
597C2×C4—522no—
598C2×C4—522no—
599C2×C4C2×#610312yes—
600C2×C4C2×#610312yes—
601C2×C4C2×#610312yes—
602C2×C4C22×C4×D1311yescharacteristic
603C2×C4C22×D5211yescharacteristic
604C2×C4#8825111yescharacteristic
605C2×C4#8825111yescharacteristic
606C2×C4#8825111yescharacteristic
607C2×C4#8825111yescharacteristic
608C8—522no—
609C8—522no—
610C22—24no—
611C22—24no—
612C22—24no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—524no—
626C22—524no—
627C22—524no—
628C22—10416no—
629C22—1042no—
630C22—1042no—
631C22—1042no—
632C22—1042no—
633C22C22×#610311yescharacteristic
634C22#1171950911yescharacteristic
635C22#1171950911yescharacteristic
636C22#1171954012yes—
637C22#1171954212yes—
638C4—22no—
639C4—22no—
640C4—22no—
641C4—82no—
642C4—82no—
643C4—524no—
644C4#1171919111yescharacteristic
645C4#1171919111yescharacteristic
646C4#1171919811yescharacteristic
647C4#1171919811yescharacteristic
648C2—42no—
649C2—42no—
650C2—42no—
651C2—1044no—
652C2#1311741111yescharacteristic
653C2#1312335912yes—
654C2#1312568212yes—
655C2#1312569711yescharacteristic
656C2#1312570311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2311C2
socleC23×C13C22×D4
prime radicalC2×#11719535C2
cosocleC22×C4×C13C24
hypercenter#2311D13
hypocenterC13#21770
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#11718895C2semidirect
3. #13115272C2semidirect
4. #13115262C2semidirect
5. #13115158C2semidirect
6. #13115153C2semidirect
7. #13114928C2semidirect
8. #13114766C2semidirect
9. C13×#2311C2semidirect
12. C2×C13×#117C22semidirect
13. C22×C13×C4⋊C4C22semidirect
15. #11719535C4semidirect
23. C22×#6099C22semidirect
24. C23×#1055C22semidirect
30. C13×#380C22semidirect
33. C2×C22⋊#1055C22semidirect
38. #11718121C22semidirect
39. #11718121C22semidirect
40. #11718121C22semidirect
41. #11718121C22semidirect
65. C22×D52C2×C4semidirect
86. #88184C2×C4semidirect
90. #88180C2×C4semidirect
206. #2311D13semidirect
304. C2×#117C2×D13semidirect
305. C22×C4⋊C4C2×D13semidirect
318. #380C2×D13semidirect
531. C13#21770semidirect

Maximal subgroups

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

subgroupindex
C2×#117195352
C2×#117188952
#131152722
#131152622
#131151582
#131151532
#131149282
#131147662
C13×#23112
#2177013