Finite Group Databasebeta

← #15870972

Subgroups — #15870972

Order 3328.

834 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718461C211yesmaximal, characteristic
2C4×#88144C211yesmaximal, characteristic, complemented
3C4×#88201C211yesmaximal, characteristic
4#13115799C211yesmaximal, characteristic, complemented
5#13115644C211yesmaximal, characteristic
6#13115534C211yesmaximal, characteristic
7#13115531C211yesmaximal, characteristic
8#13115528C211yesmaximal, characteristic, complemented
9#13115523C211yesmaximal, characteristic, complemented
10#13114965C211yesmaximal, characteristic, complemented
11#13114666C211yesmaximal, characteristic, complemented
12#13114664C211yesmaximal, characteristic
13#13114662C211yesmaximal, characteristic
14#97×Dic13C211yesmaximal, characteristic, complemented
15C13×#1763C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C2×#88201C2211yescharacteristic
18C2×#88144C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C2×C13×#103C2211yescharacteristic
21C2×C13×#103C2211yescharacteristic
22C2×C13×#97C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24#11718891C2211yescharacteristic
25C2×#88075C2211yescharacteristic
26C2×#88075C2211yescharacteristic
27C2×#88061C2211yescharacteristic
28C2×#88061C2211yescharacteristic
29C2×#88055C2211yescharacteristic
30C2×#88055C2211yescharacteristic
31C2×C8×Dic13C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33#11718651—21no—
34#11718651—21no—
35#11718649C2211yescharacteristic
36#11718646C2211yescharacteristic
37#11718638C2211yescharacteristic
38#11718638C2211yescharacteristic
39#11718634C2211yescharacteristic
40C2×#88049C2211yescharacteristic
41C2×#88049C2211yescharacteristic
42C4×#6103—21no—
43C4×#6103—21no—
44C4×C4⋊Dic13—21no—
45C4×C4⋊Dic13C2211yescharacteristic
46C4×#6101—21no—
47C42×Dic13C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49#11718461C418yescomplemented
50#11718316—21no—
51#11718315—21no—
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×Q8×C13C2311yescharacteristic
61C22×D52C2311yescharacteristic
62C22×C4×D13—21no—
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C4×Q8×C13—22no—
66C4×Q8×C13—22no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C42×C13—21no—
72C2×C42×C13—21no—
73C2×C42×C13C2311yescharacteristic
74#88201—22no—
75#88201C2×C414yes—
76C2×#6103—21no—
77C2×#6103—21no—
78C2×#6103—21no—
79C2×#6103—21no—
80C2×#6103—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×#6101—21no—
87C2×#6101—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13D411yescharacteristic
90C2×C4×Dic13D411yescharacteristic
91C2×C4×Dic13D411yescharacteristic
92C2×C4×Dic13D411yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97#88144—22no—
98#88144C2×C414yescomplemented
99C4×D52—22no—
100C4×D52—22no—
101C13×#103—22no—
102C13×#103C2×C414yescomplemented
103C13×#97—22no—
104C13×#95—21no—
105#88075—22no—
106#88075C2×C414yescomplemented
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88061—22no—
117#88061C2×C414yes—
118#88055—22no—
119#88055—22no—
120C8×Dic13—22no—
121C8×Dic13C2×C414yescomplemented
122#88049—22no—
123#88049C2×C414yes—
124#88043—22no—
125#21648—131nomaximal, Sylow
126C23×D13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13C22×C412yes—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2411yescharacteristic
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13C2×D411yescharacteristic
144C22×Dic13C2×D411yescharacteristic
145C22×Dic13C2×D411yescharacteristic
146C22×Dic13C2×D411yescharacteristic
147C2×D52—21no—
148C2×D52—21no—
149C2×D52—21no—
150C2×D52—21no—
151C2×D52—21no—
152C2×D52C22×C412yes—
153C2×C4×D13—42no—
154C2×C4×D13—42no—
155C2×C4×D13—42no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13C22×C412yes—
161C2×C8×C13#4112yes—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—42no—
168C13×C4⋊C4C22×C412yes—
169C42×C13—42no—
170C42×C13—42no—
171C42×C13#4112yes—
172C42×C13#4112yes—
173#6103—24no—
174#6103—24no—
175#6103—42no—
176#6103—42no—
177#6103—42no—
178C4⋊Dic13—21no—
179C4⋊Dic13—24no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—42no—
185C4⋊Dic13C22×C412yes—
186#6101—24no—
187#6101—42no—
188C4×Dic13—21no—
189C4×Dic13—21no—
190C4×Dic13—41no—
191C4×Dic13—41no—
192C4×Dic13—41no—
193C4×Dic13—41no—
194C4×Dic13—42no—
195C4×Dic13C22×C412yes—
196C4×Dic13#4112yes—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055C22×C412yes—
202C2×#1055#4112yes—
203C2×#488—131no—
204C4×#125—131no—
205C4×#124—131no—
206#1991—131no—
207#1958—131no—
208#1936—131no—
209#1936—131no—
210#1935—131no—
211#1935—131no—
212#1835—131no—
213#1763—131no—
214#1763D1311yescharacteristic, complemented
215#1762—131no—
216#1762—131no—
217C4×#97—131no—
218C23×C13C22×D411yescharacteristic
219C22×D13—22no—
220C22×D13—41no—
221C22×D13—41no—
222C22×D13—41no—
223C22×D13—41no—
224C22×D13—41no—
225C22×D13—41no—
226Q8×C13—22no—
227Q8×C13—22no—
228Q8×C13—41no—
229Q8×C13—41no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13#12412yes—
247C2×C4×C13#12412yes—
248C2×C4×C13C23×C411yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—22no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13C4×D412yes—
274C2×Dic13C4×D412yes—
275D52—22no—
276D52—22no—
277D52—41no—
278D52—41no—
279C4×D13—84no—
280C8×C13—22no—
281C8×C13—22no—
282#1055—22no—
283#1055—22no—
284C2×#125—131no—
285C2×#124—131no—
286C2×C4×Q8C2×D1311yescharacteristic
287C2×C4×D4—131no—
288#488—138no—
289C2×#103—131no—
290C2×#103—131no—
291C2×#103C2×D1311yescharacteristic
292C2×#103C2×D1311yescharacteristic
293C2×#102—131no—
294C2×#102—131no—
295C2×#102—131no—
296C2×#102—131no—
297C2×#97—131no—
298C2×#97—131no—
299C2×#97—131no—
300C2×#97C2×D1311yescharacteristic
301C2×C4×C8—131no—
302C2×C4×C8—131no—
303#391—131no—
304#390—131no—
305#389—131no—
306#389—131no—
307#388—261no—
308#388—261no—
309#387—261no—
310#387—261no—
311#382—131no—
312#382—131no—
313C4×C4⋊C4—131no—
314C4×C4⋊C4—261no—
315C4×C4⋊C4—261no—
316C4×C4⋊C4C2×D1311yescharacteristic
317C4×C22⋊C4—261no—
318C4×C22⋊C4—261no—
319C43—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340C2×D1311yescharacteristic
327#340C2×D1311yescharacteristic
328C22×C13C2×C4×D411yescharacteristic
329C22×C13C2×#12411yescharacteristic
330C22×C13#53211yescharacteristic
331C22×C13#57511yescharacteristic
332C22×C13#57511yescharacteristic
333C22×C13#57511yescharacteristic
334C22×C13#57511yescharacteristic
335C2×D13—42no—
336C2×D13—42no—
337C2×D13—42no—
338C2×D13—81no—
339C2×D13—81no—
340C2×D13—81no—
341C2×D13—81no—
342C4×C13—22no—
343C4×C13—22no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13—81no—
347C4×C13—81no—
348C4×C13C4×#4111yescharacteristic
349C4×C13C4×#4111yescharacteristic
350C4×C13#52911yescharacteristic
351C4×C13#52911yescharacteristic
352Dic13—22no—
353Dic13—22no—
354Dic13—41no—
355Dic13—41no—
356Dic13—42no—
357Dic13—81no—
358Dic13—81no—
359C22×Q8C22×D1311yescharacteristic
360C22×D4—131no—
361C23×C4—261no—
362C22×C8—131no—
363C22×C8—131no—
364C22×C8C22×D1311yescharacteristic
365C22×C8C22×D1311yescharacteristic
366#125—134no—
367#125—262no—
368#124—134no—
369#124—262no—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×D4—262no—
373C4×D4—262no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C22⋊C4—261no—
388C2×C22⋊C4—261no—
389C2×C22⋊C4—261no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—131no—
393C2×C42—131no—
394C2×C42—131no—
395C2×C42—131no—
396C2×C42—131no—
397C2×C42—131no—
398C2×C42—261no—
399C2×C42C22×D1311yescharacteristic
400#103—22no—
401#103—134no—
402#103—262no—
403#103C4×D1314yescomplemented
404#102—134no—
405#102—134no—
406#102—262no—
407#102—262no—
408#97—22no—
409#97—262no—
410#97—262no—
411#97—262no—
412C4×C8—134no—
413C4×C8—262no—
414#95—21no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424C2×C13C4×#12411yescharacteristic
425C2×C13#294311yescharacteristic
426C2×C13#294311yescharacteristic
427C2×C13#314011yescharacteristic
428C2×C13#314211yescharacteristic
429C2×C13#318311yescharacteristic
430C2×C13#318311yescharacteristic
431D13—82no—
432C24—261no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×C4×D1312yes—
439C2×D4—132no—
440C2×D4—261no—
441C2×D4—261no—
442C2×D4—261no—
443C2×D4—261no—
444C2×D4—261no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—131no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—522no—
457C22×C4—522no—
458C22×C4—522no—
459C22×C4D4×D1311yescharacteristic
460C22×C4D4×D1311yescharacteristic
461C22×C4C23×D1311yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—132no—
467C2×C8—132no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8C2×C4×D1312yes—
473C2×C8#612712yes—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—42no—
480C4⋊C4—132no—
481C4⋊C4—264no—
482C4⋊C4—264no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—522no—
489C4⋊C4—522no—
490C4⋊C4C2×C4×D1312yes—
491C22⋊C4—264no—
492C22⋊C4—264no—
493C22⋊C4—522no—
494C22⋊C4—522no—
495C22⋊C4—522no—
496C42—42no—
497C42—42no—
498C42—132no—
499C42—132no—
500C42—261no—
501C42—261no—
502C42—521no—
503C42—521no—
504C42—521no—
505C42—521no—
506C42—522no—
507C42#612712yes—
508C42#612912yes—
509C13#2164811yescharacteristic, complemented, Sylow
510C23—262no—
511C23—521no—
512C23—521no—
513C23—521no—
514C23—521no—
515C23—521no—
516C23—521no—
517C23C2×D4×D1311yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—262no—
523D4—262no—
524D4—521no—
525D4—521no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—132no—
543C2×C4—132no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—262no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—1044no—
564C2×C4#8813912yes—
565C2×C4#8813912yes—
566C2×C4C22×C4×D1311yescharacteristic
567C2×C4C2×#612711yescharacteristic
568C2×C4C2×#612711yescharacteristic
569C2×C4C2×#612911yescharacteristic
570C2×C4#41×D1311yescharacteristic
571C2×C4#41×D1311yescharacteristic
572C8—22no—
573C8—22no—
574C8—262no—
575C8—262no—
576C22—522no—
577C22—522no—
578C22—522no—
579C22—1041no—
580C22—1041no—
581C22—1041no—
582C22—1041no—
583C22C2×#8813911yescharacteristic
584C22C4×D4×D1311yescharacteristic
585C22#1171925311yescharacteristic
586C22#1171947811yescharacteristic
587C22#1171948211yescharacteristic
588C22#1171948211yescharacteristic
589C22#1171948211yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—262no—
597C4—262no—
598C4—522no—
599C4—521no—
600C4—521no—
601C4—1041no—
602C4—1041no—
603C4C4×#612711yescharacteristic
604C4#1171923311yescharacteristic
605C4C4×#612911yescharacteristic
606C4#1171924311yescharacteristic
607C2—1042no—
608C2C4×#8813911yescharacteristic
609C2#1312363111yescharacteristic
610C2#1312363511yescharacteristic
611C2#1312522411yescharacteristic
612C2#1312523411yescharacteristic
613C2#1312556111yescharacteristic
614C2#1312556811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1763C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1763D13
hypocenterC13#21648
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. C4×#88144C2semidirect
4. #13115799C2semidirect
8. #13115528C2semidirect
9. #13115523C2semidirect
10. #13114965C2semidirect
11. #13114666C2semidirect
14. #97×Dic13C2semidirect
15. C13×#1763C2semidirect
49. #11718461C4semidirect
98. #88144C2×C4semidirect
102. C13×#103C2×C4semidirect
106. #88075C2×C4semidirect
121. C8×Dic13C2×C4semidirect
214. #1763D13semidirect
403. #103C4×D13semidirect
509. C13#21648semidirect

Maximal subgroups

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

subgroupindex
C2×#117184612
C4×#881442
C4×#882012
#131157992
#131156442
#131155342
#131155312
#131155282
#131155232
#131149652
#131146662
#131146642
#131146622
#97×Dic132
C13×#17632
#2164813