Finite Group Databasebeta

← #15871121

Subgroups — #15871121

Order 3328.

730 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125179C211yesmaximal, characteristic
2#13123768C211yesmaximal, characteristic, complemented
3#13123546C211yesmaximal, characteristic
4#13115815C211yesmaximal, characteristic, complemented
5#13115666C211yesmaximal, characteristic
6#13115542C211yesmaximal, characteristic, complemented
7#13115541C211yesmaximal, characteristic, complemented
8#13115538C211yesmaximal, characteristic, complemented
9#13115537C211yesmaximal, characteristic, complemented
10#13114975C211yesmaximal, characteristic, complemented
11#13114682C211yesmaximal, characteristic, complemented
12#13114680C211yesmaximal, characteristic, complemented
13#13114678C211yesmaximal, characteristic, complemented
14#13114524C211yesmaximal, 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#11718789—22no—
30#11718780C2211yescharacteristic
31#11718779C2211yescharacteristic
32#11718779C2211yescharacteristic
33#11718774C2211yescharacteristic
34C8×C22⋊D13—22no—
35#11718762C2211yescharacteristic
36C2×#88055C2211yescharacteristic
37C2×#88055C2211yescharacteristic
38C2×C8×Dic13C2211yescharacteristic
39C2×C8×Dic13C2211yescharacteristic
40#11718663C2211yescharacteristic
41#11718660C2211yescharacteristic
42#11718593C2211yescharacteristic
43C2×#88045C2211yescharacteristic
44C2×C4×#1055C2211yescharacteristic
45#11718458C412yescomplemented
46#11718456C412yescomplemented
47#11718426C412yescomplemented
48#11718425C412yescomplemented
49#11718362—22no—
50C8×Dic26—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×Dic13C2311yescharacteristic
79C2×C4×Dic13C2311yescharacteristic
80C2×#6099C2311yescharacteristic
81C2×#6099C2311yescharacteristic
82C22×#1055C2311yescharacteristic
83C22×#1055C2311yescharacteristic
84#88155—22no—
85#88155—22no—
86C2×#6094—21no—
87C2×C8×D13—21no—
88#88144C2×C412yes—
89#88142C2×C412yes—
90#88132—22no—
91C4×Dic26—22no—
92C13×#104—22no—
93C13×#103C2×C412yes—
94C13×#102C2×C412yes—
95C13×#97—21no—
96C13×#97—22no—
97C4×C8×C13—21no—
98#88077—22no—
99#88075C2×C412yes—
100#88072C2×C412yes—
101#88071—22no—
102C22⋊#1055—22no—
103#88065—22no—
104#88061C2×C412yes—
105#88060—22no—
106#88056C2×C412yes—
107#88055—21no—
108#88055—22no—
109#88055C2×C412yes—
110#88055C2×C412yes—
111#88054—22no—
112#88054—22no—
113#88054—22no—
114C8×Dic13—21no—
115C8×Dic13—22no—
116C8×Dic13D412yes—
117C8×Dic13D412yes—
118#88050C2×C412yes—
119#88049C2×C412yes—
120#88045—22no—
121C4⋊#1055—22no—
122C4×#1055—22no—
123#21663—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×Dic13C22×C411yescharacteristic
177C4×Dic13C22×C411yescharacteristic
178C4×Dic13C2×D412yes—
179C4×Dic13#4112yes—
180#6099—21no—
181#6099—21no—
182#6099—21no—
183#6099—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055C22×C412yes—
191C2×#1055C2×D412yes—
192#6094—42no—
193C8×D13—42no—
194#3135—131no—
195#2960—131no—
196#2931—131no—
197#1995—131no—
198#1963—131no—
199#1937—131no—
200#1937—131no—
201#1937—131no—
202#1937—131no—
203#1838—131no—
204#1765—131no—
205#1765—131no—
206#1765—131no—
207#1765D1311yescharacteristic, complemented
208#1726—131no—
209C23×C13—21no—
210C23×C13C2×#4111yescharacteristic
211C22×D13—21no—
212Q8×C13—21no—
213Q8×C13—21no—
214D4×C13—21no—
215D4×C13—21no—
216D4×C13—41no—
217D4×C13—41no—
218C2×C4×C13—22no—
219C2×C4×C13—21no—
220C2×C4×C13—22no—
221C2×C4×C13—42no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13C23×C411yescharacteristic
225C2×C4×C13C22×D411yescharacteristic
226C2×C4×C13C2×#4111yescharacteristic
227C2×C4×C13C2×#4111yescharacteristic
228C2×C4×C13C2×#4111yescharacteristic
229C2×C4×C13C2×#4111yescharacteristic
230C22⋊D13—44no—
231C22⋊D13—41no—
232C22⋊D13—41no—
233C2×Dic13—22no—
234C2×Dic13—21no—
235C2×Dic13—22no—
236C2×Dic13—42no—
237C2×Dic13—42no—
238C2×Dic13C4×D412yes—
239C2×Dic13C4×D412yes—
240D52—21no—
241D52—21no—
242C4×D13—41no—
243C4×D13—41no—
244Dic26—21no—
245Dic26—21no—
246Dic26—44no—
247C8×C13—22no—
248C8×C13—41no—
249C8×C13—41no—
250C8×C13#12412yes—
251C8×C13#12412yes—
252#1055—22no—
253#1055—22no—
254#1055—41no—
255#1055—41no—
256C2×#131—131no—
257C2×#131C2×D1311yescharacteristic
258#533—131no—
259#532—131no—
260#491—132no—
261#490—132no—
262#489—132no—
263#489—132no—
264#446—262no—
265C8×Q8—262no—
266#436—262no—
267C8×D4—262no—
268#424—131no—
269#424—131no—
270#423—131no—
271#423—131no—
272C2×#104—131no—
273C2×#104—131no—
274C2×#104—131no—
275C2×#104C2×D1311yescharacteristic
276#416—131no—
277#416—131no—
278#416—131no—
279#416C2×D1311yescharacteristic
280#408—131no—
281#408—131no—
282#405—131no—
283#405C2×D1311yescharacteristic
284C2×#97—131no—
285C2×#97—131no—
286C2×#97C2×D1311yescharacteristic
287C2×C4×C8—131no—
288C2×C4×C8—131no—
289C2×C4×C8—131no—
290#376—131no—
291#341—131no—
292#341—131no—
293#341—131no—
294#341C2×D1311yescharacteristic
295#339—131no—
296#339—131no—
297#339—131no—
298#339C2×D1311yescharacteristic
299C22×C13—22no—
300C22×C13—42no—
301C22×C13—41no—
302C22×C13C2×C4×D411yescharacteristic
303C22×C13#52911yescharacteristic
304C22×C13#52911yescharacteristic
305C2×D13—42no—
306C2×D13—41no—
307C4×C13—42no—
308C4×C13—42no—
309C4×C13—41no—
310C4×C13C4×#4111yescharacteristic
311C4×C13C4×#4111yescharacteristic
312C4×C13C2×#12411yescharacteristic
313C4×C13#53211yescharacteristic
314Dic13—22no—
315Dic13—22no—
316Dic13—42no—
317Dic13—42no—
318Dic13—41no—
319C2×#41—131no—
320C2×#41C22×D1311yescharacteristic
321#131—22no—
322#131—22no—
323#131—262no—
324#131—262no—
325C2×M16—21no—
326C2×M16—131no—
327C2×M16—131no—
328C2×M16—261no—
329C2×M16C22×D1311yescharacteristic
330C2×M16C22×D1311yescharacteristic
331C22×C8—21no—
332C22×C8—131no—
333C22×C8—131no—
334C22×C8—261no—
335C22×C8C22×D1311yescharacteristic
336C22×C8C22×D1311yescharacteristic
337C4⋊Q8—132no—
338C4⋊Q8—131no—
339#127—131no—
340#125—132no—
341#124—131no—
342#124—131no—
343C22⋊Q8—262no—
344#121—262no—
345C4×Q8—262no—
346C4×D4—262no—
347#117—131no—
348#117C22×D1311yescharacteristic
349C2×C42—131no—
350C2×C42—131no—
351C2×C42C22×D1311yescharacteristic
352C4⋊C8—262no—
353C4⋊C8—262no—
354C4⋊C8—262no—
355C4⋊C8—262no—
356#104—22no—
357#104—262no—
358#104—262no—
359#104—262no—
360#103—132no—
361#103—132no—
362#103—132no—
363#103C4×D1312yes—
364#102—132no—
365#102—132no—
366#102—132no—
367#102C4×D1312yes—
368C22⋊C8—262no—
369C22⋊C8—262no—
370#97—21no—
371#97—22no—
372#97—132no—
373#97—132no—
374#97—262no—
375#97—261no—
376C4×C8—21no—
377C4×C8—132no—
378C4×C8—132no—
379C4×C8—262no—
380C4×C8—261no—
381C4×C8—262no—
382#95—262no—
383C2×C13—21no—
384C2×C13—21no—
385C2×C13—81no—
386C2×C13C4×#12411yescharacteristic
387C2×C13#295512yes—
388D13—81no—
389#41—21no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41—261no—
394#41—261no—
395#41—261no—
396#41—261no—
397C2×Q8—131no—
398C2×Q8—262no—
399C2×Q8C2×C4×D1311yescharacteristic
400C2×D4—21no—
401C2×D4—131no—
402C2×D4—262no—
403C2×D4—261no—
404C2×D4C2×C4×D1311yescharacteristic
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—132no—
408C22×C4—261no—
409C22×C4—261no—
410C22×C4C23×D1311yescharacteristic
411M16—21no—
412M16—21no—
413M16—21no—
414M16—21no—
415M16—42no—
416M16—261no—
417M16—261no—
418M16—261no—
419M16—261no—
420M16—522no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—42no—
426C2×C8—132no—
427C2×C8—132no—
428C2×C8—261no—
429C2×C8—261no—
430C2×C8—261no—
431C2×C8—261no—
432C2×C8—261no—
433C2×C8—261no—
434C2×C8—522no—
435C2×C8C2×C4×D1312yes—
436C2×C8#612712yes—
437C2×C8D4×D1311yescharacteristic
438C2×C8D4×D1311yescharacteristic
439C2×C8#612912yes—
440C4⋊C4—132no—
441C4⋊C4—262no—
442C4⋊C4—262no—
443C4⋊C4—262no—
444C4⋊C4—262no—
445C4⋊C4C2×C4×D1312yes—
446C22⋊C4—21no—
447C22⋊C4—262no—
448C22⋊C4—262no—
449C22⋊C4—261no—
450C42—21no—
451C42—21no—
452C42—131no—
453C42—131no—
454C42—132no—
455C42—132no—
456C42—261no—
457C42—261no—
458C42#612712yes—
459C13#2166311yescharacteristic, complemented, Sylow
460C23—21no—
461C23—261no—
462C23#41×D1311yescharacteristic
463Q8—21no—
464Q8—21no—
465Q8—261no—
466Q8—261no—
467Q8—524no—
468D4—21no—
469D4—21no—
470D4—41no—
471D4—41no—
472D4—261no—
473D4—261no—
474D4—524no—
475D4—521no—
476D4—521no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—132no—
484C2×C4—132no—
485C2×C4—262no—
486C2×C4—262no—
487C2×C4—261no—
488C2×C4—522no—
489C2×C4—522no—
490C2×C4—521no—
491C2×C4—521no—
492C2×C4C22×C4×D1311yescharacteristic
493C2×C4C2×#612711yescharacteristic
494C2×C4C2×#612711yescharacteristic
495C2×C4C2×D4×D1311yescharacteristic
496C2×C4C2×#612911yescharacteristic
497C2×C4#41×D1311yescharacteristic
498C8—22no—
499C8—41no—
500C8—41no—
501C8—262no—
502C8—262no—
503C8—521no—
504C8—521no—
505C8#8813912yes—
506C8#8813912yes—
507C22—22no—
508C22—42no—
509C22—41no—
510C22—522no—
511C22—521no—
512C22#1171923311yescharacteristic
513C22#1171924311yescharacteristic
514C22C4×D4×D1311yescharacteristic
515C4—42no—
516C4—42no—
517C4—41no—
518C4—262no—
519C4—262no—
520C4—522no—
521C4—522no—
522C4—521no—
523C4C4×#612711yescharacteristic
524C4C2×#8813911yescharacteristic
525C4C4×#612911yescharacteristic
526C4#1171925311yescharacteristic
527C2—21no—
528C2—21no—
529C2—81no—
530C2—1041no—
531C2C4×#8813911yescharacteristic
532C2#1312373612yes—
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#21663
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. #13123768C2semidirect
4. #13115815C2semidirect
6. #13115542C2semidirect
7. #13115541C2semidirect
8. #13115538C2semidirect
9. #13115537C2semidirect
10. #13114975C2semidirect
11. #13114682C2semidirect
12. #13114680C2semidirect
13. #13114678C2semidirect
14. #13114524C2semidirect
15. C13×#1765C2semidirect
45. #11718458C4semidirect
46. #11718456C4semidirect
47. #11718426C4semidirect
48. #11718425C4semidirect
207. #1765D13semidirect
459. C13#21663semidirect

Maximal subgroups

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

subgroupindex
#131251792
#131237682
#131235462
#131158152
#131156662
#131155422
#131155412
#131155382
#131155372
#131149752
#131146822
#131146802
#131146782
#131145242
C13×#17652
#2166313