Finite Group Databasebeta

← #15872600

Subgroups — #15872600

Order 3328.

1222 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719283C211yesmaximal, characteristic
2C2×#11718494C211yesmaximal, characteristic
3D13×#384C211yesmaximal, characteristic
4#13115795C212yesmaximal, complemented
5#13115636C212yesmaximal, complemented
6#13115142C212yesmaximal
7#13115140C212yesmaximal
8#13114842C211yesmaximal, characteristic, complemented
9#13114841C211yesmaximal, characteristic, complemented
10#13114838C211yesmaximal, characteristic, complemented
11C13×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C13C2211yescharacteristic
13C2×#88200C2211yescharacteristic
14C2×#88198C2211yescharacteristic
15#11719283—24no—
16#11719283C418yescomplemented
17C2×#88151C2211yescharacteristic
18C2×#88150—21no—
19C2×C4⋊C4×D13—21no—
20C2×C4⋊C4×D13—21no—
21C2×C4⋊C4×D13C2212yes—
22C2×#88143—21no—
23C2×#88142C2211yescharacteristic
24C2×#88126—21no—
25C2×C42×D13C2211yescharacteristic
26C2×C4×Dic26—21no—
27C2×C4×Dic26C2211yescharacteristic
28C2×C13×C4⋊C8C2211yescharacteristic
29C2×C13×#103C2212yes—
30C13×#384C2211yescharacteristic
31C2×#88075C2212yes—
32C2×#88060C2212yes—
33C2×#88056C2212yes—
34C2×C8×Dic13C2212yes—
35#11718637—21no—
36#11718637—21no—
37#11718637C2212yes—
38C2×#88050C2212yes—
39#11718596C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41#11718494—24no—
42C13×#340C2212yes—
43#11718143C2212yes—
44#11718121C2212yes—
45#11718121C2212yes—
46C22×Q8×C13C2311yescharacteristic
47C22×C4×D13—22no—
48C22×C4×D13D411yescharacteristic
49C22×C4×D13D411yescharacteristic
50C22×C4×D13C2311yescharacteristic
51C22×Dic26—21no—
52C22×Dic26C2311yescharacteristic
53C22×C8×C13C2312yes—
54C4×Q8×C13—22no—
55C4×Q8×C13C2×C414yescomplemented
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4C2312yes—
60C2×C13×C4⋊C4C2311yescharacteristic
61C2×C42×C13—21no—
62C2×C42×C13C2311yescharacteristic
63#88200—22no—
64#88200C2×C414yes—
65#88198—22no—
66#88198C2×C414yescomplemented
67C2×#6103—21no—
68C2×#6103—21no—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13—21no—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13C2312yes—
73C2×C4⋊Dic13C2311yescharacteristic
74C2×#6101—21no—
75C2×#6101—21no—
76C2×#6101—21no—
77C2×#6101—21no—
78C2×#6101—21no—
79C2×#6101—22no—
80C2×#6101—22no—
81C2×#6101—22no—
82C2×C4×Dic13—21no—
83C2×C4×Dic13D411yescharacteristic
84C2×C4×Dic13D411yescharacteristic
85C2×C4×Dic13C2311yescharacteristic
86C22×#1055C2312yes—
87#88151—22no—
88#88151C2×C414yes—
89#88150—28no—
90C4⋊C4×D13—42no—
91C4⋊C4×D13—42no—
92C4⋊C4×D13—44no—
93C4⋊C4×D13—44no—
94#88143—28no—
95#88142—22no—
96#88142C2×C414yescomplemented
97#88126—28no—
98C42×D13C2×C414yes—
99C42×D13D414yes—
100C4×Dic26—22no—
101C4×Dic26—28no—
102C4×Dic26C2×C414yescomplemented
103C13×C4⋊C8—22no—
104C13×#103—42no—
105#88075—42no—
106#88060—24no—
107#88056—42no—
108C8×Dic13—24no—
109#88050—42no—
110C4⋊#1055—22no—
111#21860—131nomaximal, Sylow
112C23×D13C2×D411yescharacteristic
113C2×Q8×C13—21no—
114C2×Q8×C13—21no—
115C2×Q8×C13—21no—
116C2×Q8×C13—21no—
117C2×Q8×C13—21no—
118C2×Q8×C13C22×C412yes—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—22no—
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13C2411yescharacteristic
125C22×Dic13—21no—
126C22×Dic13—21no—
127C22×Dic13—22no—
128C22×Dic13C2×D411yescharacteristic
129C22×Dic13C2×D411yescharacteristic
130C22×Dic13C2×D411yescharacteristic
131C2×C4×D13—21no—
132C2×C4×D13—21no—
133C2×C4×D13—21no—
134C2×C4×D13—21no—
135C2×C4×D13—22no—
136C2×C4×D13—22no—
137C2×C4×D13—44no—
138C2×C4×D13—44no—
139C2×C4×D13—44no—
140C2×C4×D13C22⋊C414yes—
141C2×C4×D13C22⋊C414yes—
142C2×C4×D13SD1614yes—
143C2×C4×D13Q1614yes—
144C2×C4×D13C22×C412yes—
145C2×C4×D13C2×D412yes—
146C2×Dic26—21no—
147C2×Dic26—21no—
148C2×Dic26—21no—
149C2×Dic26—21no—
150C2×Dic26—21no—
151C2×Dic26—24no—
152C2×Dic26—42no—
153C2×Dic26—42no—
154C2×Dic26C22×C412yes—
155C2×C8×C13—22no—
156C2×C8×C13—22no—
157C2×C8×C13—22no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—42no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4C22×C412yes—
165C42×C13—24no—
166C42×C13C22×C412yes—
167C42×C13C2×D412yes—
168#6103—24no—
169#6103—24no—
170C4⋊Dic13—21no—
171C4⋊Dic13—24no—
172C4⋊Dic13—22no—
173C4⋊Dic13—22no—
174C4⋊Dic13—42no—
175C4⋊Dic13—42no—
176C4⋊Dic13C22×C412yes—
177#6101—24no—
178#6101—24no—
179#6101—24no—
180#6101—24no—
181#6101—24no—
182#6101—44no—
183#6101—44no—
184#6101—44no—
185C4×Dic13—24no—
186C4×Dic13C22⋊C414yes—
187C4×Dic13C22⋊C414yes—
188C4×Dic13C22×C412yes—
189C4×Dic13C2×D412yes—
190C2×#1055—22no—
191C2×#1055—22no—
192C2×#1055—22no—
193C2×#533—131no—
194C2×#431—131no—
195C2×#384—131no—
196#1990—132no—
197#1956—132no—
198#1872—132no—
199#1872—132no—
200#1803—131no—
201#1803—131no—
202#1803—131no—
203#1803D1311yescharacteristic, complemented
204C23×C13C22×D411yescharacteristic
205C22×D13—21no—
206C22×D13—21no—
207C22×D13—21no—
208C22×D13—21no—
209C22×D13C2×C22⋊C412yes—
210C22×D13C2×SD1612yes—
211C22×D13C2×Q1612yes—
212Q8×C13—22no—
213Q8×C13—22no—
214Q8×C13—41no—
215Q8×C13—41no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13C2×C22⋊C412yes—
228C2×C4×C13C2×C22⋊C412yes—
229C2×C4×C13C2×SD1612yes—
230C2×C4×C13C2×Q1612yes—
231C2×C4×C13C23×C411yescharacteristic
232C2×C4×C13C22×D411yescharacteristic
233C2×C4×C13H(5,𝔽2)11yescharacteristic
234C2×C4×C13H(5,𝔽2)11yescharacteristic
235C2×C4×C132−1+411yescharacteristic
236C2×C4×C132−1+411yescharacteristic
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—41no—
242C2×Dic13—41no—
243C2×Dic13—41no—
244C2×Dic13—41no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13C2×C22⋊C412yes—
249C2×Dic13C2×C22⋊C412yes—
250C2×Dic13C2×C22⋊C412yes—
251C2×Dic13C2×SD1612yes—
252C2×Dic13C2×Q1612yes—
253C2×Dic13AGL(1,ℤ/8)12yes—
254C2×Dic13#13712yes—
255C4×D13—22no—
256C4×D13—22no—
257C4×D13—22no—
258C4×D13—22no—
259C4×D13—28no—
260C4×D13—88no—
261C4×D13#103116yescomplemented
262Dic26—22no—
263Dic26—22no—
264Dic26—41no—
265Dic26—41no—
266Dic26—48no—
267C8×C13—42no—
268#1055—42no—
269#533—138no—
270#533—264no—
271C2×C4⋊Q8—131no—
272C2×C4⋊Q8—131no—
273C2×#125—261no—
274C2×C22⋊Q8—131no—
275C2×C22⋊Q8—131no—
276C2×C22⋊Q8—261no—
277C2×C4×Q8—131no—
278C2×C4×Q8—261no—
279C2×C4×Q8C2×D1311yescharacteristic
280C2×#117—261no—
281C22×C4⋊C4—132no—
282C22×C4⋊C4—261no—
283C22×C4⋊C4—261no—
284C22×C42—131no—
285#431—264no—
286C2×C4⋊C8—131no—
287C2×C4⋊C8C2×D1311yescharacteristic
288C2×#103—132no—
289C2×#103—132no—
290C2×#103—132no—
291C2×#103C2×D1312yes—
292C2×C22⋊C8—132no—
293C2×C4×C8—132no—
294#384—132no—
295#384—131no—
296#384—261no—
297#384—261no—
298#384C2×D1311yescharacteristic
299#340—132no—
300#340—132no—
301#340—132no—
302#340C2×D1312yes—
303C22×C13C22×C22⋊C411yescharacteristic
304C22×C13#53511yescharacteristic
305C22×C13#53611yescharacteristic
306C22×C13C22×SD1611yescharacteristic
307C22×C13C22×Q1611yescharacteristic
308C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
309C22×C13C2×#13711yescharacteristic
310C2×D13—22no—
311C2×D13—22no—
312C2×D13—22no—
313C2×D13—22no—
314C2×D13—22no—
315C2×D13—22no—
316C2×D13C2×#10314yes—
317C4×C13—22no—
318C4×C13—42no—
319C4×C13—42no—
320C4×C13—82no—
321C4×C13C2×#10314yes—
322C4×C13#52011yescharacteristic
323C4×C13#52011yescharacteristic
324C4×C13#53711yescharacteristic
325C4×C13#53711yescharacteristic
326Dic13—22no—
327Dic13—42no—
328Dic13—42no—
329Dic13—82no—
330Dic13C2×#10314yes—
331Dic13#41714yes—
332C22×Q8—131no—
333C22×Q8—261no—
334C22×Q8C22×D1311yescharacteristic
335C23×C4—131no—
336C23×C4—131no—
337C23×C4—131no—
338C23×C4—262no—
339C22×C8—132no—
340C22×C8C22×D1312yes—
341C4⋊Q8—134no—
342C4⋊Q8—134no—
343C4⋊Q8—262no—
344C4⋊Q8—262no—
345#125—268no—
346C22⋊Q8—134no—
347C22⋊Q8—134no—
348C22⋊Q8—262no—
349C22⋊Q8—268no—
350C22⋊Q8—262no—
351C4×Q8—22no—
352C4×Q8—134no—
353C4×Q8—268no—
354C4×Q8—262no—
355C4×Q8C4×D1314yescomplemented
356#117—268no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—132no—
362C2×C4⋊C4—261no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—262no—
370C2×C4⋊C4—262no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—522no—
374C2×C4⋊C4—522no—
375C2×C4⋊C4—524no—
376C2×C4⋊C4—524no—
377C2×C4⋊C4C22×D1312yes—
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C22⋊C4—261no—
380C2×C22⋊C4—261no—
381C2×C42—21no—
382C2×C42—131no—
383C2×C42—131no—
384C2×C42—131no—
385C2×C42—134no—
386C2×C42—134no—
387C2×C42—261no—
388C2×C42C22×D1311yescharacteristic
389C4⋊C8—22no—
390C4⋊C8—262no—
391#103—42no—
392#103—522no—
393#103—522no—
394#103—522no—
395C22⋊C8—264no—
396C4×C8—264no—
397C2×C13#231111yescharacteristic
398C2×C13C22×#10311yescharacteristic
399C2×C13C2×#41711yescharacteristic
400C2×C13#320811yescharacteristic
401C2×C13#320911yescharacteristic
402C2×C13#322911yescharacteristic
403C2×C13#323011yescharacteristic
404D13—24no—
405C24—131no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—132no—
412C2×Q8—264no—
413C2×Q8—261no—
414C2×Q8—261no—
415C2×Q8—261no—
416C2×Q8—261no—
417C2×Q8—261no—
418C2×Q8—522no—
419C2×Q8—522no—
420C2×Q8C2×C4×D1312yes—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—134no—
427C22×C4—134no—
428C22×C4—134no—
429C22×C4—131no—
430C22×C4—134no—
431C22×C4—132no—
432C22×C4—132no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—262no—
442C22×C4—524no—
443C22×C4—524no—
444C22×C4—524no—
445C22×C4D4×D1311yescharacteristic
446C22×C4D4×D1311yescharacteristic
447C22×C4C23×D1311yescharacteristic
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—262no—
452C2×C8—262no—
453C2×C8—262no—
454C4⋊C4—24no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—132no—
461C4⋊C4—264no—
462C4⋊C4—264no—
463C4⋊C4—264no—
464C4⋊C4—264no—
465C4⋊C4—264no—
466C4⋊C4—264no—
467C4⋊C4—261no—
468C4⋊C4—262no—
469C4⋊C4—262no—
470C4⋊C4—522no—
471C4⋊C4—524no—
472C4⋊C4—524no—
473C4⋊C4—524no—
474C4⋊C4—522no—
475C4⋊C4C2×C4×D1312yes—
476C22⋊C4—264no—
477C22⋊C4—264no—
478C42—24no—
479C42—134no—
480C42—134no—
481C42—132no—
482C42—132no—
483C42—264no—
484C42C2×C4×D1312yes—
485C42D4×D1312yes—
486C13#2186011yescharacteristic, complemented, Sylow
487C23—132no—
488C23—132no—
489C23—132no—
490C23—261no—
491C23—261no—
492C23—261no—
493C23—261no—
494C23C2×D4×D1311yescharacteristic
495Q8—22no—
496Q8—22no—
497Q8—41no—
498Q8—41no—
499Q8—262no—
500Q8—262no—
501Q8—528no—
502Q8—521no—
503Q8—521no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—132no—
516C2×C4—132no—
517C2×C4—132no—
518C2×C4—132no—
519C2×C4—132no—
520C2×C4—132no—
521C2×C4—1316no—
522C2×C4—132no—
523C2×C4—268no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—262no—
527C2×C4—262no—
528C2×C4—262no—
529C2×C4—262no—
530C2×C4—262no—
531C2×C4—262no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—1048no—
540C2×C4C22⋊C4×D1312yes—
541C2×C4C22⋊C4×D1312yes—
542C2×C4SD16×D1312yes—
543C2×C4Q16×D1312yes—
544C2×C4C22×C4×D1311yescharacteristic
545C2×C4C2×D4×D1311yescharacteristic
546C2×C4#8825111yescharacteristic
547C2×C4#8825411yescharacteristic
548C2×C4#8825611yescharacteristic
549C2×C4#8825711yescharacteristic
550C8—42no—
551C8—522no—
552C22—134no—
553C22—262no—
554C22—262no—
555C22—262no—
556C22—262no—
557C22—262no—
558C22—262no—
559C22C2×C22⋊C4×D1311yescharacteristic
560C22#1171931211yescharacteristic
561C22#1171933311yescharacteristic
562C22C2×SD16×D1311yescharacteristic
563C22C2×Q16×D1311yescharacteristic
564C22D13×AGL(1,ℤ/8)11yescharacteristic
565C22D13×#13711yescharacteristic
566C4—22no—
567C4—42no—
568C4—42no—
569C4—82no—
570C4—134no—
571C4—134no—
572C4—262no—
573C4—522no—
574C4—522no—
575C4—1042no—
576C4D13×#10314yes—
577C4#1171920911yescharacteristic
578C4#1171922811yescharacteristic
579C4#1171931311yescharacteristic
580C4#1171933411yescharacteristic
581C2—264no—
582C2#1311742511yescharacteristic
583C2C2×D13×#10311yescharacteristic
584C2D13×#41711yescharacteristic
585C2#1312577611yescharacteristic
586C2#1312578311yescharacteristic
587C2#1312597911yescharacteristic
588C2#1312598611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1803C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1803D13
hypocenterC13#21860
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
4. #13115795C2semidirect
5. #13115636C2semidirect
8. #13114842C2semidirect
9. #13114841C2semidirect
10. #13114838C2semidirect
11. C13×#1803C2semidirect
16. #11719283C4semidirect
55. C4×Q8×C13C2×C4semidirect
66. #88198C2×C4semidirect
96. #88142C2×C4semidirect
102. C4×Dic26C2×C4semidirect
203. #1803D13semidirect
261. C4×D13#103semidirect
355. C4×Q8C4×D13semidirect
486. C13#21860semidirect

Maximal subgroups

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

subgroupindex
C2×#117192832
C2×#117184942
D13×#3842
#131157952
#131156362
#131151422
#131151402
#131148422
#131148412
#131148382
C13×#18032
#2186013