Finite Group Databasebeta

← #15871110

Subgroups — #15871110

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125179C211yesmaximal, characteristic
2#13123774C211yesmaximal, characteristic, complemented
3#13123552C211yesmaximal, characteristic
4#13115811C211yesmaximal, characteristic, complemented
5#13115662C211yesmaximal, characteristic
6#13115548C211yesmaximal, characteristic, complemented
7#13115544C211yesmaximal, characteristic, complemented
8#13115542C211yesmaximal, characteristic, complemented
9#13115538C211yesmaximal, characteristic, complemented
10#13114975C211yesmaximal, characteristic, complemented
11#13114680C211yesmaximal, characteristic, complemented
12#13114675C211yesmaximal, characteristic, complemented
13#13114671C211yesmaximal, characteristic, complemented
14#97×Dic13C211yesmaximal, characteristic, complemented
15C13×#1765C211yesmaximal, characteristic, complemented
16C2×C13×#131C2211yescharacteristic
17#11719537C2211yescharacteristic
18C2×#88155C2211yescharacteristic
19#11719222C2211yescharacteristic
20C2×C13×#104C2211yescharacteristic
21C13×#416C2211yescharacteristic
22C13×#405C2211yescharacteristic
23C2×C13×#97C2211yescharacteristic
24C2×#88077C2211yescharacteristic
25#11718895C2211yescharacteristic
26#11718894C2211yescharacteristic
27C2×#88065C2211yescharacteristic
28#11718790C2211yescharacteristic
29#11718788—22no—
30#11718780C2211yescharacteristic
31#11718779C2211yescharacteristic
32#11718779C2211yescharacteristic
33#11718774C2211yescharacteristic
34#11718772—22no—
35#11718762C2211yescharacteristic
36C2×#88055C2211yescharacteristic
37C2×#88055C2211yescharacteristic
38C2×C8×Dic13C2211yescharacteristic
39C2×C8×Dic13C2211yescharacteristic
40#11718663C2211yescharacteristic
41#11718660C2211yescharacteristic
42C42×Dic13C2211yescharacteristic
43C2×#88045C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45#11718458C412yescomplemented
46#11718456C412yescomplemented
47#11718426C412yescomplemented
48#11718425C412yescomplemented
49#11718362—22no—
50#11718340—22no—
51C13×#341C2211yescharacteristic
52C13×#339C2211yescharacteristic
53#11718150C2211yescharacteristic
54#11718150C2211yescharacteristic
55#11718147C2211yescharacteristic
56#11718144C2211yescharacteristic
57#11718124C2211yescharacteristic
58#11718115C2211yescharacteristic
59C2×C13×#41C2311yescharacteristic
60C2×#6127C2311yescharacteristic
61C13×#131—22no—
62C13×#131—22no—
63C2×C13×M16—21no—
64C2×C13×M16C2311yescharacteristic
65C2×C13×M16C2311yescharacteristic
66C22×C8×C13—21no—
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C13×#117C2311yescharacteristic
70C2×C42×C13C2311yescharacteristic
71#88201C2×C411yescharacteristic
72#88198C2×C411yescharacteristic
73#88194C2×C411yescharacteristic
74#88193—22no—
75#88190C2×C411yescharacteristic
76C4×C22⋊D13—22no—
77#88180C2311yescharacteristic
78C2×C4×Dic13—22no—
79C2×C4×Dic13C2311yescharacteristic
80C2×C4×Dic13C2311yescharacteristic
81C2×#6099C2311yescharacteristic
82C2×#6099C2311yescharacteristic
83C22×#1055C2311yescharacteristic
84C22×#1055C2311yescharacteristic
85#88155—22no—
86#88155—22no—
87C2×#6094—21no—
88C2×C8×D13—21no—
89#88144C2×C412yes—
90#88142C2×C412yes—
91#88132—22no—
92C4×Dic26—22no—
93C13×#104—22no—
94C13×#103C2×C412yes—
95C13×#102C2×C412yes—
96C13×#97—21no—
97C13×#97—22no—
98C4×C8×C13—21no—
99#88077—22no—
100#88075C2×C412yes—
101#88072C2×C412yes—
102C22⋊#1055—22no—
103#88065—22no—
104#88061C2×C412yes—
105#88060—22no—
106#88056C2×C412yes—
107#88055—21no—
108#88055C2×C412yes—
109#88055C2×C412yes—
110#88055D412yes—
111#88055D412yes—
112#88054—22no—
113#88054—22no—
114#88054—22no—
115C8×Dic13—21no—
116C8×Dic13—22no—
117C8×Dic13—22no—
118#88050C2×C412yes—
119#88049C2×C412yes—
120#88045—22no—
121C4⋊#1055—22no—
122#88043—22no—
123#21662—131nomaximal, Sylow
124C13×#41—21no—
125C13×#41—21no—
126C13×#41—21no—
127C13×#41—21no—
128C2×Q8×C13C22×C411yescharacteristic
129C2×D4×C13—21no—
130C2×D4×C13C22×C411yescharacteristic
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13C2411yescharacteristic
134C2×C22⋊D13—21no—
135C2×C22⋊D13—22no—
136C22×Dic13—21no—
137C22×Dic13#4112yes—
138#6127—21no—
139#6127—21no—
140#6127—21no—
141#6127—21no—
142C2×D52C22×C411yescharacteristic
143C2×C4×D13—21no—
144C2×Dic26—22no—
145C2×Dic26C22×C411yescharacteristic
146C13×M16—21no—
147C13×M16—21no—
148C13×M16—21no—
149C13×M16—21no—
150C13×M16—42no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—42no—
156C2×C8×C13C22×C412yes—
157C2×C8×C13C2×D411yescharacteristic
158C2×C8×C13C2×D411yescharacteristic
159C2×C8×C13#4112yes—
160C2×C8×C13#4112yes—
161C13×C4⋊C4C22×C412yes—
162C13×C22⋊C4—21no—
163C42×C13—21no—
164C42×C13—21no—
165C42×C13#4112yes—
166C22⋊Dic13—21no—
167C22⋊Dic13—22no—
168#6103—22no—
169C4⋊Dic13—22no—
170C4⋊Dic13C22×C412yes—
171#6101—22no—
172#6101—22no—
173#6101—22no—
174C4×Dic13—21no—
175C4×Dic13—21no—
176C4×Dic13—44no—
177C4×Dic13C22×C411yescharacteristic
178C4×Dic13C22×C411yescharacteristic
179C4×Dic13C2×D412yes—
180C4×Dic13#4112yes—
181#6099—21no—
182#6099—21no—
183#6099—21no—
184#6099—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055C22×C412yes—
192C2×#1055C2×D412yes—
193#6094—42no—
194C8×D13—42no—
195#3135—131no—
196#2961—131no—
197#2932—131no—
198#1994—131no—
199#1962—131no—
200#1938—131no—
201#1938—131no—
202#1937—131no—
203#1937—131no—
204#1838—131no—
205#1765—131no—
206#1765D1311yescharacteristic, complemented
207#1764—131no—
208#1764—131no—
209C4×#97—131no—
210C23×C13—21no—
211C23×C13C2×#4111yescharacteristic
212C22×D13—21no—
213Q8×C13—21no—
214Q8×C13—21no—
215D4×C13—21no—
216D4×C13—21no—
217D4×C13—41no—
218D4×C13—41no—
219C2×C4×C13—22no—
220C2×C4×C13—21no—
221C2×C4×C13—22no—
222C2×C4×C13—42no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13C23×C411yescharacteristic
226C2×C4×C13C22×D411yescharacteristic
227C2×C4×C13C2×#4111yescharacteristic
228C2×C4×C13C2×#4111yescharacteristic
229C2×C4×C13C2×#4111yescharacteristic
230C2×C4×C13C2×#4111yescharacteristic
231C22⋊D13—41no—
232C22⋊D13—41no—
233C22⋊D13—82no—
234C2×Dic13—24no—
235C2×Dic13—22no—
236C2×Dic13—22no—
237C2×Dic13—21no—
238C2×Dic13—42no—
239C2×Dic13C4×D412yes—
240C2×Dic13C4×D412yes—
241D52—21no—
242D52—21no—
243C4×D13—41no—
244C4×D13—41no—
245Dic26—21no—
246Dic26—21no—
247Dic26—82no—
248C8×C13—22no—
249C8×C13—41no—
250C8×C13—41no—
251C8×C13#12412yes—
252C8×C13#12412yes—
253#1055—22no—
254#1055—22no—
255#1055—41no—
256#1055—41no—
257C2×#131—131no—
258C2×#131C2×D1311yescharacteristic
259#533—131no—
260#532—131no—
261#491—132no—
262#490—132no—
263#489—132no—
264#489—132no—
265#446—262no—
266#446—262no—
267#435—262no—
268#435—262no—
269#424—131no—
270#424—131no—
271#423—131no—
272#423—131no—
273C2×#104—131no—
274C2×#104—131no—
275C2×#104—131no—
276C2×#104C2×D1311yescharacteristic
277#416—131no—
278#416—131no—
279#416—131no—
280#416C2×D1311yescharacteristic
281#408—131no—
282#408—131no—
283#405—131no—
284#405C2×D1311yescharacteristic
285C2×#97—131no—
286C2×#97—131no—
287C2×#97—131no—
288C2×#97C2×D1311yescharacteristic
289C2×C4×C8—131no—
290C2×C4×C8—131no—
291C43—131no—
292#341—131no—
293#341—131no—
294#341—131no—
295#341C2×D1311yescharacteristic
296#339—131no—
297#339—131no—
298#339—131no—
299#339C2×D1311yescharacteristic
300C22×C13—22no—
301C22×C13—42no—
302C22×C13—41no—
303C22×C13C2×C4×D411yescharacteristic
304C22×C13#52911yescharacteristic
305C22×C13#52911yescharacteristic
306C2×D13—42no—
307C2×D13—41no—
308C4×C13—42no—
309C4×C13—42no—
310C4×C13—41no—
311C4×C13C4×#4111yescharacteristic
312C4×C13C4×#4111yescharacteristic
313C4×C13C2×#12411yescharacteristic
314C4×C13#53211yescharacteristic
315Dic13—24no—
316Dic13—22no—
317Dic13—22no—
318Dic13—42no—
319Dic13—41no—
320C2×#41—131no—
321C2×#41C22×D1311yescharacteristic
322#131—22no—
323#131—22no—
324#131—262no—
325#131—262no—
326C2×M16—21no—
327C2×M16—131no—
328C2×M16—131no—
329C2×M16—261no—
330C2×M16C22×D1311yescharacteristic
331C2×M16C22×D1311yescharacteristic
332C22×C8—21no—
333C22×C8—131no—
334C22×C8—131no—
335C22×C8—261no—
336C22×C8C22×D1311yescharacteristic
337C22×C8C22×D1311yescharacteristic
338C4⋊Q8—132no—
339C4⋊Q8—131no—
340#127—131no—
341#125—132no—
342#124—131no—
343#124—131no—
344C22⋊Q8—262no—
345#121—262no—
346C4×Q8—262no—
347C4×D4—262no—
348#117—131no—
349#117C22×D1311yescharacteristic
350C2×C42—131no—
351C2×C42—131no—
352C2×C42—262no—
353C2×C42C22×D1311yescharacteristic
354C4⋊C8—262no—
355C4⋊C8—262no—
356C4⋊C8—262no—
357C4⋊C8—262no—
358#104—22no—
359#104—262no—
360#104—262no—
361#104—262no—
362#103—132no—
363#103—132no—
364#103—132no—
365#103C4×D1312yes—
366#102—132no—
367#102—132no—
368#102—132no—
369#102C4×D1312yes—
370C22⋊C8—262no—
371C22⋊C8—262no—
372#97—21no—
373#97—22no—
374#97—132no—
375#97—132no—
376#97—132no—
377#97—132no—
378#97—261no—
379#97—262no—
380C4×C8—21no—
381C4×C8—262no—
382C4×C8—262no—
383C4×C8—261no—
384C2×C13—21no—
385C2×C13—21no—
386C2×C13—81no—
387C2×C13C4×#12411yescharacteristic
388C2×C13#295612yes—
389D13—81no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—261no—
395#41—261no—
396#41—261no—
397#41—261no—
398C2×Q8—131no—
399C2×Q8—262no—
400C2×Q8C2×C4×D1311yescharacteristic
401C2×D4—21no—
402C2×D4—131no—
403C2×D4—262no—
404C2×D4—261no—
405C2×D4C2×C4×D1311yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—132no—
409C22×C4—261no—
410C22×C4—261no—
411C22×C4C23×D1311yescharacteristic
412M16—21no—
413M16—21no—
414M16—21no—
415M16—21no—
416M16—42no—
417M16—261no—
418M16—261no—
419M16—261no—
420M16—261no—
421M16—522no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—42no—
427C2×C8—132no—
428C2×C8—132no—
429C2×C8—261no—
430C2×C8—261no—
431C2×C8—261no—
432C2×C8—261no—
433C2×C8—261no—
434C2×C8—261no—
435C2×C8—522no—
436C2×C8C2×C4×D1312yes—
437C2×C8#612712yes—
438C2×C8D4×D1311yescharacteristic
439C2×C8D4×D1311yescharacteristic
440C2×C8#612912yes—
441C4⋊C4—132no—
442C4⋊C4—262no—
443C4⋊C4—262no—
444C4⋊C4—262no—
445C4⋊C4—262no—
446C4⋊C4C2×C4×D1312yes—
447C22⋊C4—21no—
448C22⋊C4—262no—
449C22⋊C4—262no—
450C22⋊C4—261no—
451C42—21no—
452C42—21no—
453C42—131no—
454C42—131no—
455C42—132no—
456C42—132no—
457C42—261no—
458C42—261no—
459C42—524no—
460C42#612712yes—
461C13#2166211yescharacteristic, complemented, Sylow
462C23—21no—
463C23—261no—
464C23#41×D1311yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—261no—
468Q8—261no—
469Q8—1042no—
470D4—21no—
471D4—21no—
472D4—41no—
473D4—41no—
474D4—261no—
475D4—261no—
476D4—521no—
477D4—521no—
478D4—1042no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—132no—
486C2×C4—132no—
487C2×C4—264no—
488C2×C4—262no—
489C2×C4—262no—
490C2×C4—261no—
491C2×C4—522no—
492C2×C4—521no—
493C2×C4—521no—
494C2×C4C22×C4×D1311yescharacteristic
495C2×C4C2×#612711yescharacteristic
496C2×C4C2×#612711yescharacteristic
497C2×C4C2×D4×D1311yescharacteristic
498C2×C4C2×#612911yescharacteristic
499C2×C4#41×D1311yescharacteristic
500C8—22no—
501C8—41no—
502C8—41no—
503C8—262no—
504C8—262no—
505C8—521no—
506C8—521no—
507C8#8813912yes—
508C8#8813912yes—
509C22—22no—
510C22—42no—
511C22—41no—
512C22—522no—
513C22—521no—
514C22#1171923311yescharacteristic
515C22#1171924311yescharacteristic
516C22C4×D4×D1311yescharacteristic
517C4—42no—
518C4—42no—
519C4—41no—
520C4—264no—
521C4—262no—
522C4—262no—
523C4—522no—
524C4—521no—
525C4C4×#612711yescharacteristic
526C4C2×#8813911yescharacteristic
527C4C4×#612911yescharacteristic
528C4#1171925311yescharacteristic
529C2—21no—
530C2—21no—
531C2—81no—
532C2—1041no—
533C2C4×#8813911yescharacteristic
534C2#1312374412yes—
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1765C2
socleC22×C13C2×C4×D4
prime radical#11719537C22
cosocleC22×C4×C13C24
hypercenter#1765D13
hypocenterC13#21662
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
2. #13123774C2semidirect
4. #13115811C2semidirect
6. #13115548C2semidirect
7. #13115544C2semidirect
8. #13115542C2semidirect
9. #13115538C2semidirect
10. #13114975C2semidirect
11. #13114680C2semidirect
12. #13114675C2semidirect
13. #13114671C2semidirect
14. #97×Dic13C2semidirect
15. C13×#1765C2semidirect
45. #11718458C4semidirect
46. #11718456C4semidirect
47. #11718426C4semidirect
48. #11718425C4semidirect
206. #1765D13semidirect
461. C13#21662semidirect

Maximal subgroups

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

subgroupindex
#131251792
#131237742
#131235522
#131158112
#131156622
#131155482
#131155442
#131155422
#131155382
#131149752
#131146802
#131146752
#131146712
#97×Dic132
C13×#17652
#2166213