Finite Group Databasebeta

← #15834030

Subgroups — #15834030

Order 3328.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124896C211yesmaximal, characteristic
2#13123582C211yesmaximal, characteristic, complemented
3#13113748C211yesmaximal, characteristic, complemented
4#13113719C211yesmaximal, characteristic, complemented
5#13113714C211yesmaximal, characteristic, complemented
6#13113698C211yesmaximal, characteristic, complemented
7#13113679C211yesmaximal, characteristic, complemented
8#13113663C211yesmaximal, characteristic, complemented
9#13113646C211yesmaximal, characteristic, complemented
10C8×#6106C211yesmaximal, characteristic, complemented
11#13113622C211yesmaximal, characteristic, complemented
12#13113304C211yesmaximal, characteristic, complemented
13#13113223C211yesmaximal, characteristic, complemented
14#13113133C211yesmaximal, characteristic, complemented
15C13×#2971C211yesmaximal, characteristic, complemented
16C4×C13×#41C2211yescharacteristic
17C2×#88161—21no—
18#11719182C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C8×Q8×C13C2211yescharacteristic
21C13×#436—21no—
22C13×#436—21no—
23C13×#436C2211yescharacteristic
24C13×#436C2211yescharacteristic
25C13×#432—21no—
26C13×#432C2211yescharacteristic
27C4×C13×M16—21no—
28C4×C13×M16C2211yescharacteristic
29#11718899C411yescharacteristic
30#11718899C411yescharacteristic
31#11718790—21no—
32#11718688C411yescharacteristic
33C4×#6106C2211yescharacteristic
34C4×#6106C2211yescharacteristic
35#11718682C411yescharacteristic
36#11718676C411yescharacteristic
37C4×#6104C2211yescharacteristic
38C4×#6104C2211yescharacteristic
39#11718669C411yescharacteristic
40#11718664C411yescharacteristic
41#11718664C411yescharacteristic
42#11718586C2211yescharacteristic
43#11718586C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45#11718367—21no—
46#11718367—21no—
47#11718349C2211yescharacteristic
48#11718349C2211yescharacteristic
49C8×D52C2211yescharacteristic
50C8×D52C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55#11718075C2211yescharacteristic
56#11718075C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41C2×C411yescharacteristic
68C2×#6127—21no—
69C2×C13×M16—21no—
70C2×C13×M16—21no—
71C2×C13×M16D411yescharacteristic
72C2×C13×M16D411yescharacteristic
73C4×Q8×C13C2×C411yescharacteristic
74C4×Q8×C13C2311yescharacteristic
75C4×D4×C13—21no—
76C4×D4×C13—21no—
77C4×D4×C13C2×C411yescharacteristic
78C4×D4×C13C2311yescharacteristic
79C13×#117—21no—
80C13×#117C2×C411yescharacteristic
81C2×C42×C13—21no—
82C2×C42×C13C2311yescharacteristic
83C2×#6106C2×C411yescharacteristic
84C2×#6106C2×C411yescharacteristic
85C2×#6104C2×C411yescharacteristic
86C2×#6104C2×C411yescharacteristic
87#88184—21no—
88#88184C2×C411yescharacteristic
89#88184C2×C411yescharacteristic
90C22×#1055—21no—
91#88161—44no—
92C2×#6094—21no—
93C2×#6094—21no—
94C2×C8×D13—21no—
95C2×C8×D13—21no—
96#88129—21no—
97#88128C2×C411yescharacteristic
98C4×D52—21no—
99C4×D52C2311yescharacteristic
100C4×D52C2311yescharacteristic
101#88123C2×C411yescharacteristic
102C13×C4⋊C8—21no—
103C13×C4⋊C8—21no—
104C13×C4⋊C8C2311yescharacteristic
105C13×C4⋊C8C2311yescharacteristic
106C13×C22⋊C8—21no—
107C13×C22⋊C8—21no—
108C13×C22⋊C8—21no—
109C13×#97—21no—
110C13×#97D411yescharacteristic
111C13×#97D411yescharacteristic
112C4×C8×C13—21no—
113C4×C8×C13—21no—
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116#88075C2×C411yescharacteristic
117#88075C2×C411yescharacteristic
118#88072C2×C411yescharacteristic
119#88072C2×C411yescharacteristic
120C22⋊#1055—21no—
121C22⋊#1055C2×C411yescharacteristic
122C22⋊#1055C2×C411yescharacteristic
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88060—21no—
127#88049C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88049C2×C411yescharacteristic
130#88049C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88048C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134#88047C2×C411yescharacteristic
135C4⋊#1055—21no—
136C4⋊#1055—21no—
137C4⋊#1055C2×C411yescharacteristic
138C4⋊#1055C2×C411yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#18011—131nomaximal, Sylow
146C13×#41—22no—
147C13×#41—41no—
148C2×Q8×C13C22×C411yescharacteristic
149C2×D4×C13—21no—
150C2×D4×C13C22×C411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13C22×C411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13#4111yescharacteristic
157C2×C22⋊D13—21no—
158C2×C22⋊D13—21no—
159#6127—42no—
160#6127—42no—
161C2×D52—21no—
162C2×D52—21no—
163C2×D52C22×C411yescharacteristic
164C2×D52C22×C411yescharacteristic
165C2×C4×D13—21no—
166C2×C4×D13—21no—
167C2×Dic26—21no—
168C13×M16—22no—
169C13×M16—41no—
170C13×M16—42no—
171C13×M16—42no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13C2×D411yescharacteristic
175C2×C8×C13C2×D411yescharacteristic
176C2×C8×C13C2×D411yescharacteristic
177C2×C8×C13C2×D411yescharacteristic
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4C22×C411yescharacteristic
181C13×C4⋊C4C22×C411yescharacteristic
182C13×C22⋊C4—21no—
183C13×C22⋊C4—21no—
184C13×C22⋊C4—21no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13C22×C411yescharacteristic
189C42×C13C2×D411yescharacteristic
190C42×C13#4111yescharacteristic
191C42×C13C2411yescharacteristic
192#6106—22no—
193#6106—22no—
194#6104—41no—
195#6104—41no—
196#6103—21no—
197#6103—21no—
198#6103—21no—
199#6103—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13C22×C411yescharacteristic
202C4⋊Dic13C22×C411yescharacteristic
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—42no—
208C2×#1055C22×C411yescharacteristic
209C2×#1055C22×C411yescharacteristic
210C2×#1055C22×C411yescharacteristic
211C2×#1055C22×C411yescharacteristic
212#6094—42no—
213#6094—42no—
214C8×D13—42no—
215C8×D13—42no—
216#3106—131no—
217#2971D1311yescharacteristic, complemented
218#2935—131no—
219#1594—131no—
220#1589—131no—
221#1588—131no—
222#1586—131no—
223#1583—131no—
224#1581—131no—
225SD16⋊C8—131no—
226C8×SD16—131no—
227#1573—131no—
228#1496—131no—
229#1477—131no—
230#1453—131no—
231C23×C13—21no—
232C23×C13C4×D411yescharacteristic
233C22×D13—21no—
234C22×D13—21no—
235Q8×C13—21no—
236Q8×C13#13112yescomplemented
237D4×C13—21no—
238D4×C13—21no—
239D4×C13—42no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—41no—
248C2×C4×C13—42no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—81no—
252C2×C4×C13C4×D411yescharacteristic
253C2×C4×C13C4×D411yescharacteristic
254C2×C4×C13C4×D411yescharacteristic
255C2×C4×C13C23×C411yescharacteristic
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C22⋊D13—42no—
259C22⋊D13—42no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262D52—21no—
263D52—21no—
264D52—21no—
265D52—21no—
266D52—42no—
267D52—81no—
268C4×D13—41no—
269C4×D13—41no—
270C4×D13—41no—
271C4×D13—41no—
272Dic26—42no—
273C8×C13—21no—
274C8×C13—21no—
275C8×C13—21no—
276C8×C13—41no—
277C8×C13—41no—
278C8×C13AGL(1,ℤ/8)12yes—
279#1055—21no—
280#1055—21no—
281#1055—21no—
282#1055—21no—
283#1055—41no—
284#1055—41no—
285#1055—41no—
286#1055—41no—
287C2×#131—261no—
288#532—131no—
289C4×#41C2×D1311yescharacteristic
290#482—131no—
291#482—131no—
292#477—131no—
293#476—131no—
294#460—131no—
295#459—131no—
296#449—131no—
297#449—131no—
298C8×Q8C2×D1311yescharacteristic
299C8×Q8C2×D1311yescharacteristic
300C4×SD16—131no—
301C4×SD16—131no—
302C4×D8—131no—
303C4×D8—131no—
304#436—21no—
305#436—21no—
306#436—131no—
307#436—131no—
308#436C2×D1311yescharacteristic
309#436C2×D1311yescharacteristic
310#435—261no—
311#435—261no—
312C8×D4—131no—
313C8×D4—131no—
314#432—21no—
315#432C2×D1311yescharacteristic
316#431—131no—
317#431—131no—
318C2×C4⋊C8—131no—
319#408—261no—
320C4×M16—21no—
321C4×M16C2×D1311yescharacteristic
322#335—131no—
323#335—131no—
324#334—131no—
325#334—131no—
326Q8⋊C8—131no—
327Q8⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8—131no—
332D4⋊C8—131no—
333D4⋊C8—131no—
334#322—131no—
335#322—131no—
336#322—131no—
337C82—131no—
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—21no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13C2×C4×D411yescharacteristic
345C2×D13—41no—
346C2×D13—41no—
347C2×D13—41no—
348C2×D13—41no—
349C2×D13—41no—
350C2×D13—41no—
351C4×C13—21no—
352C4×C13—22no—
353C4×C13—21no—
354C4×C13—21no—
355C4×C13—21no—
356C4×C13—41no—
357C4×C13—41no—
358C4×C13C2×#13111yescharacteristic
359C4×C13#56811yescharacteristic
360C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
361C4×C13#57511yescharacteristic
362Dic13—41no—
363Dic13—41no—
364C2×#41—261no—
365C2×#41C4×D1311yescharacteristic
366C2×SD16—131no—
367C2×SD16—131no—
368C2×D8—131no—
369C2×D8—131no—
370#131—524no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—261no—
374C2×M16—261no—
375C2×M16C22⋊D1311yescharacteristic
376C2×M16C22⋊D1311yescharacteristic
377C22×C8—261no—
378C22×C8—261no—
379C22×C8—261no—
380C4⋊Q8—131no—
381#127—131no—
382#124—261no—
383#121—131no—
384#121—131no—
385#121—261no—
386C4×Q8C4×D1311yescharacteristic
387C4×Q8C22×D1311yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—131no—
391C4×D4—131no—
392C4×D4—261no—
393C4×D4C4×D1311yescharacteristic
394C4×D4C22×D1311yescharacteristic
395#117—21no—
396#117C4×D1311yescharacteristic
397C2×C42—21no—
398C2×C42C22×D1311yescharacteristic
399#107—131no—
400#107—131no—
401#106—131no—
402#106—131no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—131no—
406C4⋊C8—131no—
407C4⋊C8—131no—
408C4⋊C8—131no—
409C4⋊C8—261no—
410C4⋊C8—261no—
411C4⋊C8C22×D1311yescharacteristic
412C4⋊C8C22×D1311yescharacteristic
413#103—131no—
414#103—131no—
415#102—131no—
416#102—131no—
417#102—131no—
418#102—131no—
419#102—131no—
420#102—131no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—131no—
425C22⋊C8—131no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8—261no—
429C22⋊C8—261no—
430C22⋊C8—261no—
431#97—21no—
432#97C22⋊D1311yescharacteristic
433#97C22⋊D1311yescharacteristic
434C4×C8—21no—
435C4×C8—21no—
436C4×C8—131no—
437C4×C8—131no—
438C4×C8—131no—
439C4×C8—131no—
440C4×C8C22×D1311yescharacteristic
441C4×C8C22×D1311yescharacteristic
442C2×C13—41no—
443C2×C13—81no—
444C2×C13#293311yescharacteristic
445C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
446C2×C13#295711yescharacteristic
447D13—81no—
448D13—81no—
449#41—22no—
450#41—41no—
451#41—522no—
452#41—522no—
453C2×Q8—261no—
454C2×Q8C2×C4×D1311yescharacteristic
455C2×D4—21no—
456C2×D4—131no—
457C2×D4—131no—
458C2×D4—261no—
459C2×D4—261no—
460C2×D4—261no—
461C2×D4—261no—
462C2×D4C2×C4×D1311yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4C2×C4×D1311yescharacteristic
469C22×C4#612711yescharacteristic
470C22×C4C2×C22⋊D1311yescharacteristic
471SD16—262no—
472SD16—262no—
473D8—521no—
474D8—521no—
475M16—22no—
476M16—41no—
477M16—42no—
478M16—42no—
479M16—522no—
480M16—522no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—131no—
484C2×C8—131no—
485C2×C8—131no—
486C2×C8—131no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—522no—
492C2×C8—522no—
493C2×C8—522no—
494C2×C8C2×C22⋊D1311yescharacteristic
495C2×C8C2×C22⋊D1311yescharacteristic
496C2×C8C2×C22⋊D1311yescharacteristic
497C2×C8C2×C22⋊D1311yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—131no—
501C4⋊C4—131no—
502C4⋊C4—261no—
503C4⋊C4C2×C4×D1311yescharacteristic
504C4⋊C4C2×C4×D1311yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—261no—
509C22⋊C4—261no—
510C22⋊C4—261no—
511C22⋊C4—261no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42C2×C4×D1311yescharacteristic
516C42#612711yescharacteristic
517C42C2×C22⋊D1311yescharacteristic
518C42C23×D1311yescharacteristic
519C13#1801111yescharacteristic, complemented, Sylow
520C23—21no—
521C23—261no—
522C23—261no—
523C23C4×C22⋊D1311yescharacteristic
524Q8—21no—
525Q8—522no—
526Q8#8816112yescomplemented
527D4—21no—
528D4—21no—
529D4—42no—
530D4—261no—
531D4—261no—
532D4—261no—
533D4—261no—
534D4—522no—
535D4—522no—
536D4—522no—
537D4—1041no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4C4×C22⋊D1311yescharacteristic
557C2×C4C4×C22⋊D1311yescharacteristic
558C2×C4C4×C22⋊D1311yescharacteristic
559C2×C4C22×C4×D1311yescharacteristic
560C2×C4C2×#612711yescharacteristic
561C2×C4C22×C22⋊D1311yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—41no—
566C8—41no—
567C8—261no—
568C8—261no—
569C8—261no—
570C8—261no—
571C8—521no—
572C8—521no—
573C8—521no—
574C8—521no—
575C8#8820312yes—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—521no—
583C22—521no—
584C22—521no—
585C22—521no—
586C22—521no—
587C22—521no—
588C22C2×C4×C22⋊D1311yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—521no—
597C4—521no—
598C4C2×#8816111yescharacteristic
599C4#1171945011yescharacteristic
600C4C2×#8820311yescharacteristic
601C4#1171952711yescharacteristic
602C2—41no—
603C2—81no—
604C2—1041no—
605C2—1041no—
606C2#1312356111yescharacteristic
607C2C4×#8820311yescharacteristic
608C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2971C2
socleC22×C13C2×C4×D4
prime radical#13124896C2
cosocleC42×C13C24
hypercenter#2971D13
hypocenterC13#18011
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. #13123582C2semidirect
3. #13113748C2semidirect
4. #13113719C2semidirect
5. #13113714C2semidirect
6. #13113698C2semidirect
7. #13113679C2semidirect
8. #13113663C2semidirect
9. #13113646C2semidirect
10. C8×#6106C2semidirect
11. #13113622C2semidirect
12. #13113304C2semidirect
13. #13113223C2semidirect
14. #13113133C2semidirect
15. C13×#2971C2semidirect
217. #2971D13semidirect
236. Q8×C13#131semidirect
519. C13#18011semidirect
526. Q8#88161semidirect

Maximal subgroups

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

subgroupindex
#131248962
#131235822
#131137482
#131137192
#131137142
#131136982
#131136792
#131136632
#131136462
C8×#61062
#131136222
#131133042
#131132232
#131131332
C13×#29712
#1801113