Finite Group Databasebeta

← #15830728

Subgroups — #15830728

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128675C211yesmaximal, characteristic
2#13123865C211yesmaximal, characteristic, complemented
3#13113390C212yesmaximal, complemented
4#13113372C212yesmaximal, complemented
5#13113368C211yesmaximal, characteristic, complemented
6#13113364C211yesmaximal, characteristic, complemented
7#13113359C212yesmaximal, complemented
8#13113355C211yesmaximal, characteristic, complemented
9#13113351C211yesmaximal, characteristic, complemented
10#13113325C212yesmaximal, complemented
11C13×#2357C211yesmaximal, characteristic, complemented
12C2×C4×D4×C13C2211yescharacteristic
13#11719509—21no—
14#11719496C2212yes—
15C2×#88184C2211yescharacteristic
16C2×#88178C2211yescharacteristic
17#11719270C412yescomplemented
18#11719261—22no—
19#11719257C412yescomplemented
20#11719255C412yescomplemented
21#11719246C412yescomplemented
22#11719245—22no—
23#11719220—21no—
24#11719199—21no—
25#11719191—21no—
26#11719184C2212yes—
27C13×#390—21no—
28C13×#388—21no—
29C13×#388—21no—
30C13×#382C2211yescharacteristic, complemented
31C13×#381C2211yescharacteristic
32C13×#381C2211yescharacteristic, complemented
33C4×C13×C4⋊C4—21no—
34C4×C13×C4⋊C4C2211yescharacteristic, complemented
35C4×C13×C22⋊C4C2211yescharacteristic
36C4×C13×C22⋊C4C2211yescharacteristic, complemented
37#11718868C2211yescharacteristic
38#11718868C2211yescharacteristic
39C2×C22⋊#1055C2212yescomplemented
40#11718672—22no—
41#11718672—22no—
42#11718587C2212yescomplemented
43#11718044C2212yescomplemented
44#11718044C2212yescomplemented
45#11718044C2212yescomplemented
46#11718044C2212yescomplemented
47#11718043C2212yes—
48#11718043C2212yes—
49#11718043C2212yes—
50#11718043C2212yes—
51C22×D4×C13D411yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C22×C22⋊D13—21no—
55C2×#6127C2×C412yes—
56C22×D52C2×C411yescharacteristic
57C22×Dic26C2×C411yescharacteristic
58C4×D4×C13C2×C412yes—
59C4×D4×C13C2×C412yes—
60C4×D4×C13D412yes—
61C4×D4×C13D412yes—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4D411yescharacteristic
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4—21no—
68C2×C13×C22⋊C4—21no—
69C2×C13×C22⋊C4D411yescharacteristic
70C2×C13×C22⋊C4D411yescharacteristic
71C2×C42×C13—21no—
72C2×C42×C13—21no—
73C2×C42×C13—21no—
74C2×C42×C13C2311yescharacteristic
75#88207—22no—
76C2×C22⋊Dic13—21no—
77#88193—22no—
78#88193—22no—
79#88191—22no—
80#88189—22no—
81#88184—21no—
82#88184—21no—
83#88184C2×C412yes—
84#88184C2×C412yes—
85#88184C2312yes—
86#88183—22no—
87#88183—22no—
88C4×C22⋊D13—22no—
89C4×C22⋊D13—22no—
90C4×C22⋊D13—22no—
91C2×#6103—21no—
92#88180C2×C412yes—
93C2×C4⋊Dic13C2×C411yescharacteristic
94C2×C4⋊Dic13C2×C411yescharacteristic
95#88178—21no—
96#88178—21no—
97#88178C2×C412yes—
98#88178C2×C412yes—
99#88178C2312yes—
100C2×#6101—21no—
101C2×#6099—21no—
102C2×#6099—21no—
103C22×#1055—22no—
104#88152—22no—
105#88150—22no—
106#88148—22no—
107#88143—22no—
108#88139—22no—
109#88138—22no—
110#88137—22no—
111#88135—22no—
112#88135—22no—
113C22⋊C4×D13—22no—
114#88133—22no—
115#88131—22no—
116#88130—22no—
117#88129C2×C412yes—
118C4×D52C2×C412yes—
119#88126—22no—
120#88124C2×C412yes—
121C4×Dic26C2×C412yes—
122C13×#95—21no—
123C13×#95—21no—
124C13×#95—21no—
125C13×#95C2311yescharacteristic
126C13×#95C2311yescharacteristic
127C13×#95C2311yescharacteristic
128C13×#95C2311yescharacteristic
129C22⋊#1055—22no—
130C22⋊#1055—21no—
131C22⋊#1055—21no—
132C22⋊#1055C2312yes—
133C22⋊#1055C2312yes—
134C4⋊#1055—22no—
135#88043—22no—
136#17625—131nomaximal, Sylow
137C24×C13C2×D411yescharacteristic
138C24×C13C2×D411yescharacteristic
139C23×D13—21no—
140C2×D4×C13—41no—
141C2×D4×C13—41no—
142C2×D4×C13C22⋊C412yes—
143C2×D4×C13C22⋊C412yes—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—81no—
149C22×C4×C13—81no—
150C22×C4×C13C22×C411yescharacteristic
151C22×C4×C13C22×C412yes—
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C2×D412yes—
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2411yescharacteristic
161C2×C22⋊D13—22no—
162C2×C22⋊D13—22no—
163C2×C22⋊D13—22no—
164C2×C22⋊D13—22no—
165C2×C22⋊D13—42no—
166C2×C22⋊D13—42no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170#6127—82no—
171C2×D52—21no—
172C2×D52—81no—
173C2×D52C22×C412yes—
174C2×C4×D13—22no—
175C2×C4×D13—22no—
176C2×Dic26—21no—
177C2×Dic26—81no—
178C2×Dic26C22×C412yes—
179C13×C4⋊C4—42no—
180C13×C4⋊C4—42no—
181C13×C4⋊C4C22⋊C412yes—
182C13×C4⋊C4C22⋊C412yes—
183C13×C22⋊C4—42no—
184C13×C22⋊C4—42no—
185C13×C22⋊C4—81no—
186C13×C22⋊C4—81no—
187C13×C22⋊C4C22⋊C412yes—
188C13×C22⋊C4C22⋊C412yes—
189C13×C22⋊C4C22⋊C412yes—
190C13×C22⋊C4C22⋊C412yes—
191C42×C13—42no—
192C42×C13—81no—
193C42×C13—81no—
194C42×C13C22×C412yes—
195C42×C13C2×D412yes—
196C22⋊Dic13—22no—
197C22⋊Dic13—22no—
198C22⋊Dic13—22no—
199C22⋊Dic13—22no—
200#6103—22no—
201#6103—22no—
202#6103—22no—
203#6103—22no—
204#6103—22no—
205#6103—22no—
206C4⋊Dic13—21no—
207C4⋊Dic13—21no—
208C4⋊Dic13C22×C412yes—
209C4⋊Dic13C22×C412yes—
210#6101—22no—
211#6101—22no—
212#6101—22no—
213#6101—22no—
214#6101—22no—
215#6101—22no—
216C4×Dic13—22no—
217C4×Dic13—22no—
218#6099—81no—
219#6099—81no—
220C2×#1055—22no—
221C2×#1055—22no—
222C2×#1055—82no—
223#3505—131no—
224#2973—131no—
225#2357D1311yescharacteristic, complemented
226#1516—132no—
227#1512—132no—
228#1511—131no—
229#1510—131no—
230#1509—132no—
231#1508—131no—
232#1507—131no—
233#1501—132no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13C2×C22⋊C411yescharacteristic
243C23×C13C2×C22⋊C412yes—
244C23×C13C2×C22⋊C411yescharacteristic
245C23×C13C22×D411yescharacteristic
246C22×D13—22no—
247C22×D13—42no—
248C22×D13—81no—
249C22×D13—81no—
250D4×C13—42no—
251D4×C13—42no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—22no—
255C2×C4×C13—42no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—42no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13C2×C22⋊C412yes—
277C2×C4×C13C2×C22⋊C412yes—
278C2×C4×C13C2×C22⋊C411yescharacteristic
279C2×C4×C13C2×C22⋊C412yes—
280C2×C4×C13C2×C22⋊C411yescharacteristic
281C2×C4×C13C23×C411yescharacteristic
282C2×C4×C13C22×D411yescharacteristic
283C22⋊D13—44no—
284C22⋊D13—42no—
285C22⋊D13—42no—
286C22⋊D13—82no—
287C22⋊D13—82no—
288C2×Dic13—22no—
289C2×Dic13—22no—
290C2×Dic13—22no—
291C2×Dic13—42no—
292C2×Dic13—81no—
293C2×Dic13—81no—
294D52—42no—
295D52—81no—
296C4×D13—82no—
297C4×D13—82no—
298Dic26—42no—
299Dic26—81no—
300#1055—42no—
301#1055—42no—
302#553—132no—
303#553—262no—
304#552—132no—
305#551—262no—
306#548—132no—
307#546—132no—
308#539—261no—
309#538—261no—
310#534—261no—
311#529—132no—
312#525—132no—
313C2×C22⋊Q8—131no—
314C2×#121—131no—
315#518—261no—
316C2×C4×D4C2×D1311yescharacteristic
317#435—262no—
318#435—262no—
319#432—132no—
320#407—131no—
321#407—131no—
322C2×C22⋊C8—132no—
323#390—21no—
324#388—21no—
325#388—21no—
326#382C2×D1311yescharacteristic, complemented
327#381C2×D1311yescharacteristic
328#381C2×D1311yescharacteristic, complemented
329C4×C4⋊C4—21no—
330C4×C4⋊C4C2×D1311yescharacteristic, complemented
331C4×C22⋊C4C2×D1311yescharacteristic
332C4×C22⋊C4C2×D1311yescharacteristic, complemented
333#328—132no—
334#328—132no—
335#328—132no—
336#328—132no—
337#327—132no—
338#327—132no—
339#327—132no—
340#327—132no—
341C22×C13—21no—
342C22×C13—21no—
343C22×C13—21no—
344C22×C13—22no—
345C22×C13—21no—
346C22×C13—21no—
347C22×C13—21no—
348C22×C13—22no—
349C22×C13—21no—
350C22×C13—22no—
351C22×C13—21no—
352C22×C13—81no—
353C22×C13—81no—
354C22×C13—81no—
355C22×C13—81no—
356C22×C13C22×C22⋊C411yescharacteristic
357C22×C13#57511yescharacteristic
358C22×C13#57511yescharacteristic
359C2×D13—42no—
360C2×D13—42no—
361C2×D13—42no—
362C2×D13—162no—
363C4×C13—21no—
364C4×C13—21no—
365C4×C13—21no—
366C4×C13—22no—
367C4×C13—21no—
368C4×C13—22no—
369C4×C13—22no—
370C4×C13—42no—
371C4×C13—81no—
372C4×C13—81no—
373C4×C13—81no—
374Dic13—42no—
375Dic13—42no—
376Dic13—42no—
377C2×#41—132no—
378C22×Q8—131no—
379C22×D4—131no—
380C22×D4—261no—
381C22×D4C22⋊D1311yescharacteristic
382C23×C4C22×D1311yescharacteristic
383C23×C4C22×D1311yescharacteristic
384C2×M16—261no—
385C2×M16—261no—
386C22×C8—262no—
387#126—262no—
388#126—262no—
389#126—262no—
390#125—132no—
391#125—262no—
392#124—132no—
393#124—262no—
394#123—262no—
395#123—262no—
396#123—262no—
397#123—262no—
398#123—262no—
399C22⋊Q8—132no—
400C22⋊Q8—132no—
401C22⋊Q8—132no—
402C22⋊Q8—261no—
403C22⋊Q8—261no—
404C22⋊Q8—262no—
405#121—132no—
406#121—132no—
407#121—132no—
408#121—262no—
409#121—262no—
410#121—261no—
411#121—261no—
412#121—262no—
413#120—262no—
414#120—262no—
415C4×Q8—132no—
416C4×D4—132no—
417C4×D4—262no—
418C4×D4—262no—
419C4×D4—262no—
420C4×D4—262no—
421C4×D4—262no—
422C4×D4C4×D1312yes—
423C4×D4C4×D1312yes—
424C4×D4D5212yes—
425C4×D4D5212yes—
426#117—132no—
427#117—262no—
428#117—262no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—131no—
432C2×C4⋊C4—131no—
433C2×C4⋊C4—261no—
434C2×C4⋊C4C22⋊D1311yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—261no—
440C2×C22⋊C4—261no—
441C2×C22⋊C4—262no—
442C2×C22⋊C4C22⋊D1311yescharacteristic
443C2×C22⋊C4C22⋊D1311yescharacteristic
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42C22×D1311yescharacteristic
448C4⋊C8—262no—
449C22⋊C8—132no—
450C22⋊C8—132no—
451C22⋊C8—262no—
452C22⋊C8—261no—
453C22⋊C8—261no—
454#97—262no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95C22×D1311yescharacteristic
459#95C22×D1311yescharacteristic
460#95C22×D1311yescharacteristic
461#95C22×D1311yescharacteristic
462C2×C13—21no—
463C2×C13—21no—
464C2×C13—41no—
465C2×C13—41no—
466C2×C13—42no—
467C2×C13#288311yescharacteristic
468C2×C13#289611yescharacteristic
469C2×C13#290111yescharacteristic
470D13—82no—
471C24—261no—
472C24C2×C22⋊D1311yescharacteristic
473C24C2×C22⋊D1311yescharacteristic
474#41—1042no—
475C2×Q8—132no—
476C2×Q8—261no—
477C2×Q8—1041no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—132no—
481C2×D4—262no—
482C2×D4—262no—
483C2×D4—262no—
484C2×D4—262no—
485C2×D4—261no—
486C2×D4—522no—
487C2×D4—522no—
488C2×D4—1041no—
489C2×D4#610312yes—
490C2×D4#610312yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4—261no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—262no—
501C22×C4—262no—
502C22×C4C2×C4×D1311yescharacteristic
503C22×C4C2×C4×D1311yescharacteristic
504C22×C4C2×C4×D1312yes—
505C22×C4C2×D5211yescharacteristic
506C22×C4C2×D5211yescharacteristic
507C22×C4C2×D5212yes—
508C22×C4C2×C22⋊D1311yescharacteristic
509C22×C4C2×C22⋊D1311yescharacteristic
510C22×C4C2×C22⋊D1311yescharacteristic
511C22×C4C2×C22⋊D1311yescharacteristic
512C22×C4C23×D1311yescharacteristic
513M16—1041no—
514M16—1041no—
515C2×C8—262no—
516C2×C8—262no—
517C2×C8—1042no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—132no—
521C4⋊C4—132no—
522C4⋊C4—261no—
523C4⋊C4—261no—
524C4⋊C4—262no—
525C4⋊C4—262no—
526C4⋊C4—262no—
527C4⋊C4—262no—
528C4⋊C4—262no—
529C4⋊C4—262no—
530C4⋊C4#610312yes—
531C4⋊C4#610312yes—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—81no—
535C22⋊C4—81no—
536C22⋊C4—262no—
537C22⋊C4—262no—
538C22⋊C4—262no—
539C22⋊C4—262no—
540C22⋊C4—262no—
541C22⋊C4—262no—
542C22⋊C4—262no—
543C22⋊C4—262no—
544C22⋊C4—262no—
545C22⋊C4—262no—
546C22⋊C4#610312yes—
547C22⋊C4#610312yes—
548C22⋊C4#610312yes—
549C22⋊C4#610312yes—
550C42—42no—
551C42—81no—
552C42—81no—
553C42—262no—
554C42—262no—
555C42C2×C4×D1312yes—
556C42C2×D5212yes—
557C13#1762511yescharacteristic, complemented, Sylow
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—262no—
567C23—522no—
568C23—1041no—
569C23—1041no—
570C23C2×#610311yescharacteristic
571C23C2×#610312yes—
572C23C2×#610311yescharacteristic
573C23C22×C22⋊D1311yescharacteristic
574Q8—522no—
575Q8—1041no—
576D4—42no—
577D4—42no—
578D4—522no—
579D4—524no—
580D4—522no—
581D4—522no—
582D4—1041no—
583D4—1042no—
584D4—1042no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—262no—
610C2×C4—262no—
611C2×C4—262no—
612C2×C4—522no—
613C2×C4—1042no—
614C2×C4—1042no—
615C2×C4—1041no—
616C2×C4—1041no—
617C2×C4C2×#610312yes—
618C2×C4C2×#610312yes—
619C2×C4C2×#610312yes—
620C2×C4C2×#610311yescharacteristic
621C2×C4C2×#610311yescharacteristic
622C2×C4C22×C4×D1311yescharacteristic
623C2×C4C22×D5211yescharacteristic
624C8—522no—
625C8—522no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—22no—
631C22—21no—
632C22—22no—
633C22—21no—
634C22—21no—
635C22—22no—
636C22—21no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—522no—
642C22—522no—
643C22—522no—
644C22—2082no—
645C22C22×#610311yescharacteristic
646C22#1171952711yescharacteristic
647C22#1171952711yescharacteristic
648C4—22no—
649C4—22no—
650C4—21no—
651C4—21no—
652C4—22no—
653C4—21no—
654C4—21no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—522no—
660C4—522no—
661C4—522no—
662C2—21no—
663C2—21no—
664C2—41no—
665C2—41no—
666C2—42no—
667C2—1042no—
668C2#1312329611yescharacteristic
669C2#1312335311yescharacteristic
670C2#1312338411yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2357C2
socleC22×C13C22×C22⋊C4
prime radical#13128675C2
cosocleC22×C4×C13C24
hypercenter#2357D13
hypocenterC13#17625
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2357

Complements

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

NH ≅ G/Ntype
2. #13123865C2semidirect
3. #13113390C2semidirect
4. #13113372C2semidirect
5. #13113368C2semidirect
6. #13113364C2semidirect
7. #13113359C2semidirect
8. #13113355C2semidirect
9. #13113351C2semidirect
10. #13113325C2semidirect
11. C13×#2357C2semidirect
17. #11719270C4semidirect
19. #11719257C4semidirect
20. #11719255C4semidirect
21. #11719246C4semidirect
30. C13×#382C22semidirect
32. C13×#381C22semidirect
34. C4×C13×C4⋊C4C22semidirect
36. C4×C13×C22⋊C4C22semidirect
39. C2×C22⋊#1055C22semidirect
42. #11718587C22semidirect
43. #11718044C22semidirect
44. #11718044C22semidirect
45. #11718044C22semidirect
46. #11718044C22semidirect
225. #2357D13semidirect
326. #382C2×D13semidirect
328. #381C2×D13semidirect
330. C4×C4⋊C4C2×D13semidirect
332. C4×C22⋊C4C2×D13semidirect
557. C13#17625semidirect

Maximal subgroups

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

subgroupindex
#131286752
#131238652
#131133902
#131133722
#131133682
#131133642
#131133592
#131133552
#131133512
#131133252
C13×#23572
#1762513