Finite Group Databasebeta

← #15833013

Subgroups — #15833013

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124897C211yesmaximal, characteristic
2#13123944C211yesmaximal, characteristic, complemented
3#13123911C211yesmaximal, characteristic, complemented
4#13113716C211yesmaximal, characteristic, complemented
5#13113702C211yesmaximal, characteristic, complemented
6#13113681C211yesmaximal, characteristic, complemented
7#13113667C211yesmaximal, characteristic, complemented
8#13113661C211yesmaximal, characteristic, complemented
9#13113650C211yesmaximal, characteristic, complemented
10C8×#6095C211yesmaximal, characteristic, complemented
11C8×D104C211yesmaximal, characteristic, complemented
12#13113621C211yesmaximal, characteristic, complemented
13#13113271C211yesmaximal, characteristic, complemented
14#13113236C211yesmaximal, characteristic, complemented
15C13×#1454C211yesmaximal, characteristic, complemented
16#11719182C2211yescharacteristic
17C4×#6127C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C13×#431C2211yescharacteristic
21#11718587C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23#11718511C411yescharacteristic
24#11718509C411yescharacteristic
25#11718504C411yescharacteristic
26#11718503C411yescharacteristic
27#11718497—21no—
28#11718497—21no—
29#11718494—21no—
30D13×C4⋊C8—21no—
31#11718398C411yescharacteristic
32#11718398C411yescharacteristic
33#11718395C411yescharacteristic
34#11718395C411yescharacteristic
35#11718388—21no—
36#11718388—21no—
37#11718386—21no—
38#11718386—21no—
39C4×D104C2211yescharacteristic
40C4×D104C2211yescharacteristic
41C4×#6095C2211yescharacteristic
42C4×#6095C2211yescharacteristic
43#11718349C2211yescharacteristic
44#11718349C2211yescharacteristic
45C8×D52C2211yescharacteristic
46C8×D52C2211yescharacteristic
47C8×D52C2211yescharacteristic
48C8×D52C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#322C2211yescharacteristic
52C13×#322C2211yescharacteristic
53C13×#322C2211yescharacteristic
54C82×C13C2211yescharacteristic
55#11718051C2211yescharacteristic
56#11718051C2211yescharacteristic
57#11718051C2211yescharacteristic
58#11718051C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718050C2211yescharacteristic
63#11718049C2211yescharacteristic
64#11718049C2211yescharacteristic
65#11718048C2211yescharacteristic
66#11718048C2211yescharacteristic
67C2×#6127—21no—
68C2×#6127C2×C411yescharacteristic
69C2×C42×C13C2311yescharacteristic
70#88184—21no—
71#88184C2×C411yescharacteristic
72#88184C2×C411yescharacteristic
73C4×C22⋊D13—21no—
74C4×C22⋊D13—21no—
75#88180C2×C411yescharacteristic
76C22×#1055—21no—
77C2×D104C2×C411yescharacteristic
78C2×D104C2×C411yescharacteristic
79C2×#6095C2×C411yescharacteristic
80C2×#6095C2×C411yescharacteristic
81C2×#6094—21no—
82C2×#6094—21no—
83C2×C8×D13—21no—
84C2×C8×D13—21no—
85C2×C8×D13—21no—
86C2×C8×D13—21no—
87#88129—21no—
88#88128C2×C411yescharacteristic
89C4×D52—21no—
90C4×D52C2×C411yescharacteristic
91C4×D52C2311yescharacteristic
92C4×D52C2311yescharacteristic
93C4×D52C2311yescharacteristic
94#88126—21no—
95C42×D13—21no—
96#88123C2×C411yescharacteristic
97C4×Dic26C2×C411yescharacteristic
98C4×Dic26C2311yescharacteristic
99C13×C4⋊C8—21no—
100C13×C4⋊C8C2×C411yescharacteristic
101C13×C4⋊C8C2×C411yescharacteristic
102C13×C4⋊C8D411yescharacteristic
103C13×C4⋊C8D411yescharacteristic
104C13×C22⋊C8—21no—
105C13×C22⋊C8C2×C411yescharacteristic
106C13×C22⋊C8C2×C411yescharacteristic
107C13×C22⋊C8D411yescharacteristic
108C13×C22⋊C8D411yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C22⋊#1055—21no—
116#88061C2×C411yescharacteristic
117#88061C2×C411yescharacteristic
118#88061C2×C411yescharacteristic
119#88061C2×C411yescharacteristic
120#88061C2×C411yescharacteristic
121#88061C2×C411yescharacteristic
122#88060—21no—
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88060—21no—
127#88060—21no—
128#88058C2×C411yescharacteristic
129#88058C2×C411yescharacteristic
130#88057C2×C411yescharacteristic
131#88057C2×C411yescharacteristic
132#88056C2×C411yescharacteristic
133#88056C2×C411yescharacteristic
134#88054—21no—
135#88054—21no—
136C8×Dic13—21no—
137C8×Dic13—21no—
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143#88043—21no—
144#17920—131nomaximal, Sylow
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C2×C22⋊D13—21no—
149C2×C22⋊D13—21no—
150C2×C22⋊D13—21no—
151#6127—22no—
152#6127—22no—
153#6127—81no—
154#6127—81no—
155C2×D52—21no—
156C2×D52—21no—
157C2×D52C22×C411yescharacteristic
158C2×D52C22×C411yescharacteristic
159C2×D52C22×C411yescharacteristic
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×Dic26—21no—
166C2×Dic26C22×C411yescharacteristic
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C2×C8×C13C2×D411yescharacteristic
176C2×C8×C13C2×D411yescharacteristic
177C42×C13C22×C411yescharacteristic
178C42×C13C2×D411yescharacteristic
179C42×C13#4111yescharacteristic
180C42×C13C2411yescharacteristic
181C22⋊Dic13—21no—
182#6103—21no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13C22×C411yescharacteristic
190C4⋊Dic13C22×C411yescharacteristic
191C4⋊Dic13C22×C411yescharacteristic
192C4⋊Dic13C22×C411yescharacteristic
193#6101—21no—
194#6101—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—81no—
203D104—22no—
204D104—22no—
205#6095—22no—
206#6095—22no—
207#6094—81no—
208#6094—81no—
209C8×D13—81no—
210C8×D13—81no—
211C8×D13—81no—
212C8×D13—81no—
213#3106—131no—
214#2988—131no—
215#2981—131no—
216#1588—131no—
217#1586—131no—
218#1583—131no—
219#1581—131no—
220#1580—131no—
221SD16⋊C8—131no—
222C8×SD16—131no—
223C8×D8—131no—
224#1573—131no—
225#1488—131no—
226#1480—131no—
227#1454D1311yescharacteristic, complemented
228C23×C13C4×D411yescharacteristic
229C22×D13—21no—
230C22×D13—21no—
231C22×D13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—41no—
237C2×C4×C13C4×D411yescharacteristic
238C2×C4×C13C4×D411yescharacteristic
239C2×C4×C13C4×D411yescharacteristic
240C2×C4×C13C23×C411yescharacteristic
241C2×C4×C13C22×D411yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C22⋊D13—24no—
244C22⋊D13—81no—
245C22⋊D13—81no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251D52—21no—
252D52—21no—
253D52—21no—
254D52—21no—
255D52—21no—
256D52—81no—
257D52—81no—
258D52#13112yes—
259C4×D13—24no—
260C4×D13—41no—
261C4×D13—41no—
262C4×D13—41no—
263C4×D13—41no—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—81no—
267Dic26—21no—
268Dic26—81no—
269Dic26#13112yes—
270C8×C13—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—21no—
275C8×C13—21no—
276C8×C13—21no—
277C8×C13—21no—
278C8×C13—41no—
279C8×C13—41no—
280#1055—41no—
281#1055—41no—
282#1055—41no—
283#1055—41no—
284#532—131no—
285C4×#41—131no—
286#482—131no—
287#482—131no—
288#477—131no—
289#476—131no—
290#460—131no—
291#459—131no—
292#449—131no—
293#449—131no—
294C8×Q8—131no—
295C8×Q8—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×D8—131no—
299C4×D8—131no—
300#436—131no—
301#436—131no—
302#435—261no—
303#435—261no—
304C8×D4—131no—
305C8×D4—131no—
306C8×D4—131no—
307C8×D4—131no—
308C8×D4—261no—
309C8×D4—261no—
310#432—131no—
311#431—261no—
312#431C2×D1311yescharacteristic
313#431C2×D1311yescharacteristic
314#431C2×D1311yescharacteristic
315C2×C4⋊C8—131no—
316C2×C4⋊C8—261no—
317#408—261no—
318#408—261no—
319#335—131no—
320#335—131no—
321#334—131no—
322#334—131no—
323Q8⋊C8—131no—
324Q8⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331#322C2×D1311yescharacteristic
332#322C2×D1311yescharacteristic
333#322C2×D1311yescharacteristic
334C82C2×D1311yescharacteristic
335C22×C13—21no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13C2×C4×D411yescharacteristic
339C2×D13—22no—
340C2×D13—41no—
341C2×D13—41no—
342C2×D13—41no—
343C2×D13—41no—
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—41no—
347C2×D13—41no—
348C4×C13—21no—
349C4×C13—21no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13C2×#13111yescharacteristic
353C4×C13C2×#13111yescharacteristic
354C4×C13#57611yescharacteristic
355C4×C13#57711yescharacteristic
356Dic13—22no—
357Dic13—41no—
358Dic13—41no—
359Dic13—41no—
360Dic13—41no—
361C2×#41—131no—
362C2×#41—261no—
363C2×SD16—131no—
364C2×SD16—131no—
365C2×D8—131no—
366C2×D8—131no—
367C2×M16—261no—
368C2×M16—261no—
369C22×C8—261no—
370C22×C8—261no—
371C22×C8—261no—
372C22×C8—261no—
373C22×C8—261no—
374C4⋊Q8—131no—
375#127—131no—
376#124—261no—
377#121—131no—
378#121—131no—
379#121—261no—
380C4×Q8—131no—
381C4×Q8—131no—
382C4×D4—131no—
383C4×D4—131no—
384C4×D4—131no—
385C4×D4—131no—
386C4×D4—261no—
387C4×D4—261no—
388C4×D4—261no—
389#117—131no—
390#117—261no—
391C2×C42—261no—
392C2×C42C22×D1311yescharacteristic
393#107—131no—
394#107—131no—
395#106—131no—
396#106—131no—
397C4⋊C8—21no—
398C4⋊C8—131no—
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—261no—
403C4⋊C8—261no—
404C4⋊C8—261no—
405C4⋊C8C4×D1311yescharacteristic
406C4⋊C8C4×D1311yescharacteristic
407C4⋊C8D5211yescharacteristic
408C4⋊C8D5211yescharacteristic
409#103—131no—
410#103—131no—
411#102—131no—
412#102—131no—
413#102—131no—
414#102—131no—
415#102—131no—
416#102—131no—
417C22⋊C8—21no—
418C22⋊C8—261no—
419C22⋊C8—261no—
420C22⋊C8—261no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8C4×D1311yescharacteristic
426C22⋊C8C4×D1311yescharacteristic
427C22⋊C8D5211yescharacteristic
428C22⋊C8D5211yescharacteristic
429#97—261no—
430C4×C8—261no—
431C4×C8—261no—
432C4×C8C22×D1311yescharacteristic
433C4×C8C22×D1311yescharacteristic
434C4×C8C22×D1311yescharacteristic
435C4×C8C22×D1311yescharacteristic
436C4×C8C22×D1311yescharacteristic
437C4×C8C22×D1311yescharacteristic
438C2×C13—41no—
439C2×C13#292911yescharacteristic
440C2×C13#294611yescharacteristic
441C2×C13#295711yescharacteristic
442D13—42no—
443D13—81no—
444D13—81no—
445#41—262no—
446#41—262no—
447#41—1041no—
448#41—1041no—
449C2×Q8—131no—
450C2×Q8—261no—
451C2×D4—131no—
452C2×D4—131no—
453C2×D4—131no—
454C2×D4—261no—
455C2×D4—261no—
456C2×D4—261no—
457C2×D4—261no—
458C2×D4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4C2×C4×D1311yescharacteristic
465C22×C4C2×D5211yescharacteristic
466C22×C4#612711yescharacteristic
467SD16—262no—
468SD16—262no—
469D8—262no—
470D8—262no—
471M16—1041no—
472M16—1041no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—1041no—
480C2×C8—1041no—
481C2×C8—1041no—
482C2×C8—1041no—
483C2×C8—1041no—
484C2×C8C2×C4×D1311yescharacteristic
485C2×C8C2×C4×D1311yescharacteristic
486C2×C8C2×C4×D1311yescharacteristic
487C2×C8C2×C4×D1311yescharacteristic
488C2×C8C2×D5211yescharacteristic
489C2×C8C2×D5211yescharacteristic
490C2×C8C2×D5211yescharacteristic
491C2×C8C2×D5211yescharacteristic
492C4⋊C4—131no—
493C4⋊C4—131no—
494C4⋊C4—131no—
495C4⋊C4—131no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C22⋊C4—261no—
500C22⋊C4—261no—
501C22⋊C4—261no—
502C22⋊C4—261no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C42—261no—
507C42—261no—
508C42—261no—
509C42C2×C4×D1311yescharacteristic
510C42C2×D5211yescharacteristic
511C42#612711yescharacteristic
512C42C23×D1311yescharacteristic
513C13#1792011yescharacteristic, complemented, Sylow
514C23—261no—
515C23—261no—
516C23—261no—
517C23C4×D5211yescharacteristic
518Q8—132no—
519Q8—261no—
520Q8—1041no—
521D4—132no—
522D4—264no—
523D4—261no—
524D4—261no—
525D4—261no—
526D4—261no—
527D4—261no—
528D4—1041no—
529D4—1041no—
530D4—1041no—
531D4—1041no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—264no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—1041no—
550C2×C4C4×D5211yescharacteristic
551C2×C4C4×D5211yescharacteristic
552C2×C4C4×D5211yescharacteristic
553C2×C4C22×C4×D1311yescharacteristic
554C2×C4C22×D5211yescharacteristic
555C2×C4C2×#612711yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—41no—
565C8—41no—
566C8—521no—
567C8—521no—
568C8—521no—
569C8—521no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—262no—
574C22—521no—
575C22—521no—
576C22—521no—
577C22—521no—
578C22—521no—
579C22—521no—
580C22—521no—
581C22—521no—
582C22C2×C4×D5211yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—262no—
588C4—521no—
589C4—521no—
590C4—521no—
591C4—521no—
592C4D13×#13111yescharacteristic
593C4D13×#13111yescharacteristic
594C4#1171945611yescharacteristic
595C4#1171945711yescharacteristic
596C2—41no—
597C2—522no—
598C2—1041no—
599C2—1041no—
600C2#1312353211yescharacteristic
601C2#1312367011yescharacteristic
602C2#1312375411yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1454C2
socleC22×C13C2×C4×D4
prime radical#13124897C2
cosocleC42×C13C24
hypercenter#1454D13
hypocenterC13#17920
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #13123944C2semidirect
3. #13123911C2semidirect
4. #13113716C2semidirect
5. #13113702C2semidirect
6. #13113681C2semidirect
7. #13113667C2semidirect
8. #13113661C2semidirect
9. #13113650C2semidirect
10. C8×#6095C2semidirect
11. C8×D104C2semidirect
12. #13113621C2semidirect
13. #13113271C2semidirect
14. #13113236C2semidirect
15. C13×#1454C2semidirect
227. #1454D13semidirect
513. C13#17920semidirect

Maximal subgroups

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

subgroupindex
#131248972
#131239442
#131239112
#131137162
#131137022
#131136812
#131136672
#131136612
#131136502
C8×#60952
C8×D1042
#131136212
#131132712
#131132362
C13×#14542
#1792013