Finite Group Databasebeta

← #15896828

Subgroups — #15896828

Order 3328.

1218 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718745C211yesmaximal, characteristic, complemented
2C2×C4×#6106C211yesmaximal, characteristic, complemented
3#13119749C211yesmaximal, characteristic
4#13116029C212yesmaximal, complemented
5#13115837C212yesmaximal, complemented
6#13115798C211yesmaximal, characteristic, complemented
7#13115631C211yesmaximal, characteristic, complemented
8#13115153C212yesmaximal, complemented
9#13115029C212yesmaximal, complemented
10#13114841C211yesmaximal, characteristic, complemented
11C2×C13×#554C211yesmaximal, characteristic, complemented
12C13×#554—24no—
13C13×#554—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#125—21no—
16C2×C13×C22⋊Q8—22no—
17C2×C13×C22⋊Q8C2212yes—
18C2×C4×Q8×C13C2211yescharacteristic
19C2×C4×D4×C13—21no—
20C2×C4×D4×C13C2211yescharacteristic
21C22×C13×C4⋊C4C2212yes—
22C22×#6106C2211yescharacteristic
23C2×#88192—21no—
24C2×#88184C2212yes—
25C2×C4×D52C2211yescharacteristic
26C2×#88075C2211yescharacteristic
27C2×#88075C2212yes—
28#11718873C2212yes—
29C2×C22⋊#1055C2212yes—
30C2×C22⋊#1055C2212yes—
31#11718745—24no—
32C4×#6106—24no—
33#11718648—21no—
34C2×#88049C2211yescharacteristic
35C2×#88049C2212yes—
36C2×#88048C2211yescharacteristic
37C2×#88048C2212yes—
38#11718622—22no—
39#11718596C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41C2×C4×#1055C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45C22×Q8×C13—21no—
46C22×Q8×C13C2311yescharacteristic
47C22×D4×C13D411yescharacteristic
48C23×C4×C13—22no—
49C23×C4×C13C2312yes—
50C22×C22⋊D13—22no—
51C22×D52C2311yescharacteristic
52C22×C4×D13—21no—
53C13×C4⋊Q8—22no—
54C13×C4⋊Q8D414yescomplemented
55C13×#125—28no—
56C13×C22⋊Q8—216no—
57C13×C22⋊Q8—24no—
58C13×C22⋊Q8—24no—
59C4×Q8×C13—22no—
60C4×Q8×C13D414yescomplemented
61C4×D4×C13—28no—
62C4×D4×C13—22no—
63C4×D4×C13—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—24no—
69C2×C13×C4⋊C4—24no—
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2312yes—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4D412yes—
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C22⋊Dic13—22no—
78C2×#6106—22no—
79C2×#6106—22no—
80C2×#6106—22no—
81#88192—44no—
82#88184—24no—
83#88184—42no—
84C2×#6103—21no—
85C2×#6103—22no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2312yes—
90C22×#1055C2311yescharacteristic
91C22×#1055C2312yes—
92C22×#1055C2311yescharacteristic
93C4×D52—22no—
94C4×D52—22no—
95#88075—22no—
96#88075—42no—
97#88071—22no—
98C22⋊#1055—24no—
99C22⋊#1055—42no—
100#88049—22no—
101#88049—24no—
102#88048—22no—
103#88048—24no—
104C4⋊#1055—22no—
105C4×#1055—22no—
106#24118—131nomaximal, Sylow
107C24×C13C2×D412yes—
108C23×D13—21no—
109C2×Q8×C13—24no—
110C2×Q8×C13—21no—
111C2×Q8×C13—21no—
112C2×Q8×C13—21no—
113C2×Q8×C13—21no—
114C2×Q8×C13—21no—
115C2×Q8×C13—81no—
116C2×Q8×C13—81no—
117C2×Q8×C13C2×D412yes—
118C2×D4×C13—22no—
119C2×D4×C13—22no—
120C2×D4×C13SD1614yescomplemented
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—22no—
124C22×C4×C13—28no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—82no—
132C22×C4×C13—82no—
133C22×C4×C13C2×D412yes—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2411yescharacteristic
137C2×C22⋊D13—44no—
138C2×C22⋊D13—44no—
139C2×C22⋊D13—82no—
140C22×Dic13—21no—
141C22×Dic13—22no—
142C2×D52—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52#4112yes—
148C2×C4×D13—42no—
149C2×C4×D13—42no—
150C2×C4×D13—42no—
151C13×C4⋊C4—28no—
152C13×C4⋊C4—28no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4C2×D412yes—
159C13×C4⋊C4C2×D414yes—
160C13×C22⋊C4—28no—
161C13×C22⋊C4—24no—
162C42×C13—24no—
163C42×C13C2×D412yes—
164C42×C13C2×D412yes—
165C22⋊Dic13—44no—
166#6106—28no—
167#6103—44no—
168#6103—42no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—22no—
172C4⋊Dic13—22no—
173C4⋊Dic13—42no—
174C4⋊Dic13—81no—
175C2×#1055—21no—
176C2×#1055—21no—
177C2×#1055—21no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055—21no—
181C2×#1055—22no—
182C2×#1055—21no—
183C2×#1055#4112yes—
184C2×#554D1311yescharacteristic, complemented
185C2×#476—131no—
186C2×C4×SD16—131no—
187#2537—131no—
188#2035—132no—
189#2000—132no—
190#1990—131no—
191#1954—131no—
192#1874—132no—
193#1853—132no—
194#1803—131no—
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13C2×SD1614yes—
202C23×C13C22×D411yescharacteristic
203C22×D13—22no—
204C22×D13—41no—
205C22×D13—41no—
206C22×D13—41no—
207C22×D13—41no—
208C22×D13—41no—
209C22×D13—41no—
210Q8×C13—22no—
211Q8×C13—22no—
212Q8×C13—41no—
213Q8×C13—41no—
214Q8×C13—84no—
215D4×C13—28no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—24no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—42no—
228C2×C4×C13—41no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—88no—
235C2×C4×C13#12012yes—
236C2×C4×C13#12012yes—
237C2×C4×C13C2×SD1612yes—
238C2×C4×C13#13712yes—
239C2×C4×C13C22×D411yescharacteristic
240C2×C4×C13C22×D411yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C2×C4×C13H(5,𝔽2)11yescharacteristic
244C2×C4×C132−1+411yescharacteristic
245C22⋊D13—88no—
246C2×Dic13—41no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—42no—
252D52—22no—
253D52—22no—
254D52—41no—
255D52—41no—
256C4×D13—84no—
257#1055—22no—
258#1055—41no—
259#1055—42no—
260C22×SD16—131no—
261#554—24no—
262#554—24no—
263C2×C4⋊Q8C2×D1311yescharacteristic
264C2×#125—21no—
265C2×C22⋊Q8—22no—
266C2×C22⋊Q8C2×D1312yes—
267C2×#121—132no—
268C2×#121—261no—
269C2×C4×Q8C2×D1311yescharacteristic
270C2×C4×D4—21no—
271C2×C4×D4—131no—
272C2×C4×D4C2×D1311yescharacteristic
273C22×C4⋊C4C2×D1312yes—
274#476—264no—
275C4×SD16—264no—
276C2×#106—131no—
277C2×#106—132no—
278C2×C4⋊C8—131no—
279C2×#103—131no—
280C2×#103—132no—
281C2×#102—131no—
282C2×#102—132no—
283C2×C22⋊C8—132no—
284C2×C22⋊C8—132no—
285C2×C4×C8—131no—
286#394—262no—
287#384—131no—
288#380—132no—
289#380—261no—
290#340—132no—
291#340—132no—
292#340—132no—
293C22×C13—24no—
294C22×C13—24no—
295C22×C13—24no—
296C22×C13—42no—
297C22×C13—42no—
298C22×C13—42no—
299C22×C13—42no—
300C22×C13C2×#12011yescharacteristic
301C22×C13#54611yescharacteristic
302C22×C13#54711yescharacteristic
303C22×C13C22×SD1611yescharacteristic
304C22×C13C2×#13711yescharacteristic
305C22×C13#57611yescharacteristic
306C22×C13#57711yescharacteristic
307C2×D13—42no—
308C2×D13—42no—
309C2×D13—42no—
310C2×D13—81no—
311C2×D13—81no—
312C2×D13—81no—
313C2×D13—81no—
314C4×C13—22no—
315C4×C13—42no—
316C4×C13—42no—
317C4×C13—42no—
318C4×C13—44no—
319C4×C13#44814yes—
320C4×C13#52511yescharacteristic
321C4×C13#53711yescharacteristic
322C4×C13#54811yescharacteristic
323C4×C13#55011yescharacteristic
324Dic13—81no—
325Dic13—82no—
326C22×Q8—21no—
327C22×Q8C22×D1311yescharacteristic
328C22×D4—131no—
329C22×D4—262no—
330C22×D4C22⋊D1311yescharacteristic
331C23×C4—22no—
332C23×C4—261no—
333C23×C4C22×D1312yes—
334C2×SD16—262no—
335C2×SD16—262no—
336C2×SD16—262no—
337C22×C8—131no—
338C22×C8—131no—
339C22×C8—132no—
340C4⋊Q8—22no—
341C4⋊Q8C22⋊D1314yescomplemented
342#125—28no—
343C22⋊Q8—216no—
344C22⋊Q8—24no—
345C22⋊Q8—24no—
346#121—264no—
347#121—522no—
348#121—524no—
349C4×Q8—22no—
350C4×Q8C22⋊D1314yescomplemented
351C4×D4—28no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—262no—
355C4×D4—262no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—132no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4C22⋊D1311yescharacteristic
367C2×C4⋊C4C22×D1311yescharacteristic
368C2×C4⋊C4C22×D1312yes—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—262no—
371C2×C22⋊C4—261no—
372C2×C22⋊C4—262no—
373C2×C22⋊C4C22⋊D1312yes—
374C2×C42—21no—
375C2×C42C22×D1311yescharacteristic
376#106—262no—
377#106—264no—
378C4⋊C8—262no—
379#103—262no—
380#103—522no—
381#102—262no—
382#102—264no—
383C22⋊C8—264no—
384C22⋊C8—522no—
385C4×C8—262no—
386#95—262no—
387C2×C13—44no—
388C2×C13#240711yescharacteristic
389C2×C13C2×#44811yescharacteristic
390C2×C13#301211yescharacteristic
391C2×C13#329511yescharacteristic
392C2×C13#333111yescharacteristic
393C2×C13#333511yescharacteristic
394C2×C13#335711yescharacteristic
395D13—82no—
396C24—261no—
397C24C2×C22⋊D1312yes—
398C2×Q8—24no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—81no—
405C2×Q8—81no—
406C2×Q8C2×C22⋊D1312yes—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—132no—
410C2×D4—261no—
411C2×D4—261no—
412C2×D4—261no—
413C2×D4—261no—
414C2×D4—261no—
415C2×D4—524no—
416C2×D4—524no—
417C2×D4—1042no—
418C2×D4#610614yescomplemented
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—28no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—82no—
430C22×C4—82no—
431C22×C4—261no—
432C22×C4—262no—
433C22×C4—522no—
434C22×C4—522no—
435C22×C4—522no—
436C22×C4C2×C22⋊D1312yes—
437C22×C4C2×C22⋊D1311yescharacteristic
438C22×C4C2×C22⋊D1311yescharacteristic
439C22×C4C23×D1311yescharacteristic
440SD16—268no—
441C2×C8—132no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8—262no—
445C2×C8—261no—
446C2×C8—262no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—262no—
450C4⋊C4—28no—
451C4⋊C4—28no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—262no—
458C4⋊C4—262no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—522no—
462C4⋊C4—1041no—
463C4⋊C4C2×C22⋊D1312yes—
464C4⋊C4C2×C22⋊D1314yes—
465C22⋊C4—28no—
466C22⋊C4—24no—
467C22⋊C4—524no—
468C22⋊C4—524no—
469C22⋊C4—522no—
470C42—24no—
471C42C2×C22⋊D1312yes—
472C42C2×C22⋊D1312yes—
473C13#2411811yescharacteristic, complemented, Sylow
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—262no—
481C23—521no—
482C23—521no—
483C23—521no—
484C23—521no—
485C23—521no—
486C23—521no—
487C23C2×#610614yes—
488C23C22×C22⋊D1311yescharacteristic
489Q8—22no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493Q8—84no—
494D4—28no—
495D4—262no—
496D4—262no—
497D4—521no—
498D4—521no—
499D4—1048no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—88no—
519C2×C4—521no—
520C2×C4—522no—
521C2×C4—521no—
522C2×C4—522no—
523C2×C4—522no—
524C2×C4—521no—
525C2×C4—1044no—
526C2×C4C2×#610612yes—
527C2×C4#8819612yes—
528C2×C4#8820712yes—
529C2×C4#8820712yes—
530C2×C4#41×D1311yescharacteristic
531C2×C4#41×D1311yescharacteristic
532C2×C4#8825611yescharacteristic
533C2×C4#8825711yescharacteristic
534C2×C4C22×C22⋊D1311yescharacteristic
535C2×C4C22×C22⋊D1311yescharacteristic
536C8—262no—
537C8—521no—
538C8—522no—
539C22—24no—
540C22—24no—
541C22—24no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—522no—
547C22—522no—
548C22—522no—
549C22—1041no—
550C22—1041no—
551C22—1041no—
552C22—1041no—
553C22C22×#610611yescharacteristic
554C22C2×#8819611yescharacteristic
555C22#1171952911yescharacteristic
556C22#1171953411yescharacteristic
557C22#1171954011yescharacteristic
558C22#1171954111yescharacteristic
559C22C2×#8820711yescharacteristic
560C4—22no—
561C4—42no—
562C4—44no—
563C4—42no—
564C4—42no—
565C4—1041no—
566C4—1042no—
567C4#1171888814yes—
568C4#1171953311yescharacteristic
569C4#1171953611yescharacteristic
570C4#1171953811yescharacteristic
571C4#1171953911yescharacteristic
572C2—44no—
573C2—1042no—
574C2#1311817511yescharacteristic
575C2C2×#1171888811yescharacteristic
576C2#1312414011yescharacteristic
577C2#1312665411yescharacteristic
578C2#1312714611yescharacteristic
579C2#1312718711yescharacteristic
580C2#1312746211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#554C2
socleC23×C13C22×D4
prime radical#13119749C2
hypercenterC2×#554D13
hypocenterC13#24118
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#11718745C2semidirect
2. C2×C4×#6106C2semidirect
4. #13116029C2semidirect
5. #13115837C2semidirect
6. #13115798C2semidirect
7. #13115631C2semidirect
8. #13115153C2semidirect
9. #13115029C2semidirect
10. #13114841C2semidirect
11. C2×C13×#554C2semidirect
54. C13×C4⋊Q8D4semidirect
60. C4×Q8×C13D4semidirect
120. C2×D4×C13SD16semidirect
184. C2×#554D13semidirect
341. C4⋊Q8C22⋊D13semidirect
350. C4×Q8C22⋊D13semidirect
418. C2×D4#6106semidirect
473. C13#24118semidirect

Maximal subgroups

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

subgroupindex
C2×#117187452
C2×C4×#61062
#131197492
#131160292
#131158372
#131157982
#131156312
#131151532
#131150292
#131148412
C2×C13×#5542
#2411813