Finite Group Databasebeta

← #16797444

Subgroups — #16797444

Order 3328.

998 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719107C212yesmaximal
2#13131408C211yesmaximal, characteristic, complemented
3#13131407C211yesmaximal, characteristic, complemented
4C4×#88103C211yesmaximal, characteristic, complemented
5#13130639C212yesmaximal, complemented
6#13130617C212yesmaximal, complemented
7#13130615C212yesmaximal, complemented
8#13130600C211yesmaximal, characteristic, complemented
9#13130599C211yesmaximal, characteristic, complemented
10#13130492C211yesmaximal, characteristic, complemented
11C4×#88170C211yesmaximal, characteristic
12C2×#88240C2212yes—
13C2×#88238C2212yes—
14C2×#88170C2211yescharacteristic
15C4×#6131C2211yescharacteristic
16C4×#6129C2211yescharacteristic
17C2×#88118C2212yes—
18C2×#88116C2212yes—
19C4×#6122—21no—
20C2×#88110—21no—
21#11719107C4116yescomplemented
22C2×#88103C2212yes—
23C2×#88100C2212yes—
24C2×C8×#261C2212yes—
25#11719072—22no—
26#11719072C2212yes—
27#11719072C2212yes—
28#11719062—22no—
29#11719057C2211yescharacteristic
30C4×#6118—21no—
31C4×#6118C2211yescharacteristic
32C4×#6118C2211yescharacteristic
33#11719047—21no—
34#11719047C2211yescharacteristic
35C4×C13×SD16C411yescharacteristic, complemented
36SD16×Dic13C411yescharacteristic, complemented
37C4×#6107C411yescharacteristic, complemented
38C4×#6104C411yescharacteristic, complemented
39#11718521C2211yescharacteristic
40#11718513C411yescharacteristic, complemented
41#11718465C2211yescharacteristic
42#11718451C411yescharacteristic, complemented
43#11718433C2211yescharacteristic
44#11718417C411yescharacteristic, complemented
45C4×#6095C411yescharacteristic, complemented
46C4×C8×D13C2211yescharacteristic
47#11718268C2212yes—
48#11718247C2212yes—
49#11718247C2212yes—
50C2×#6131C2311yescharacteristic
51C2×#6129C2311yescharacteristic
52C2×#6122—22no—
53C22×#1057—22no—
54#88240—24no—
55#88240C2×C418yescomplemented
56#88238—24no—
57#88238C2×C418yescomplemented
58C2×C4×#261C2312yes—
59C2×#6118—22no—
60C2×#6118C2312yes—
61C2×#6118C2312yes—
62C2×D13⋊C8—22no—
63C2×D13⋊C8C2312yes—
64C2×C13×SD16C2×C411yescharacteristic
65C4×Q8×C13C2×C411yescharacteristic
66C4×D4×C13C2×C411yescharacteristic
67Q8×Dic13C2×C411yescharacteristic
68C2×#6107C2×C411yescharacteristic
69D4×Dic13C2×C411yescharacteristic
70C2×#6104C2×C411yescharacteristic
71C4×C22⋊D13—21no—
72C2×C4×Dic13—21no—
73#88170C2×C418yes—
74C2×#6095C2×C411yescharacteristic
75C2×C8×D13C2311yescharacteristic
76C2×C8×D13C2311yescharacteristic
77#88147—21no—
78#88147C2×C411yescharacteristic
79#88146—21no—
80#88146C2311yescharacteristic
81#88146C2311yescharacteristic
82#88141C2×C411yescharacteristic
83#88135—21no—
84#88131—21no—
85C4×D52—21no—
86C4×D52C2×C411yescharacteristic
87C42×D13—21no—
88C42×D13C2311yescharacteristic
89C4×Dic26C2×C411yescharacteristic
90#88118C2×C418yescomplemented
91#88116C2×C418yescomplemented
92(C2×#261)⋊C4—21no—
93(C2×#261)⋊C4—21no—
94#88110—22no—
95#88110—22no—
96#88110—21no—
97#88110—21no—
98#88110D411yescharacteristic
99#88110D411yescharacteristic
100#88110D412yes—
101C4×#1057—22no—
102C4×#1057—22no—
103C4×#1057—21no—
104C4×#1057—21no—
105#88103C2×C418yescomplemented
106#88100—24no—
107C8×#261C2×C418yescomplemented
108C13×#106C2×C411yescharacteristic
109C13×#103C2×C411yescharacteristic
110C13×#102C2×C411yescharacteristic
111C4×C8×C13C2×C411yescharacteristic
112#88075C2×C411yescharacteristic
113#88072C2×C411yescharacteristic
114#88061C2×C411yescharacteristic
115#88057C2×C411yescharacteristic
116#88056C2×C411yescharacteristic
117C8×Dic13C2×C411yescharacteristic
118C8×Dic13C2×C411yescharacteristic
119#88050C2×C411yescharacteristic
120#88049C2×C411yescharacteristic
121#88047C2×C411yescharacteristic
122#88047C2×C411yescharacteristic
123C4×#1055C2×C411yescharacteristic
124#20514—131nomaximal, Sylow
125C22×#261—22no—
126C2×Q8×C13C22×C411yescharacteristic
127C2×D4×C13C22×C411yescharacteristic
128C22×C4×C13—21no—
129C2×C22⋊D13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132#6131—22no—
133#6131C22×C414yes—
134#6129—22no—
135#6129C22×C414yes—
136C2×D52—21no—
137C2×D52C22×C411yescharacteristic
138C2×C4×D13—21no—
139C2×C4×D13—21no—
140C2×C4×D13—21no—
141C2×C4×D13#4111yescharacteristic
142C2×C4×D13#4111yescharacteristic
143C2×C4×D13C2411yescharacteristic
144C2×Dic26C22×C411yescharacteristic
145#6122—28no—
146C2×#1057—22no—
147C2×#1057—22no—
148C2×#1057—28no—
149C2×#1057C2×D412yes—
150C2×#1057C2×D412yes—
151C4×#261—22no—
152C4×#261C22×C414yes—
153#6118—22no—
154#6118—22no—
155#6118—28no—
156#6118C22×C414yes—
157#6118C22×C414yes—
158D13⋊C8—28no—
159D13⋊C8C22×C414yes—
160D13⋊C8#4114yes—
161C13×SD16C4214yes—
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C22×C411yescharacteristic
164C13×C4⋊C4—21no—
165C13×C4⋊C4C22×C411yescharacteristic
166C13×C4⋊C4C22×C411yescharacteristic
167C13×C22⋊C4—21no—
168C42×C13—21no—
169C42×C13C22×C411yescharacteristic
170C22⋊Dic13—21no—
171#6107C4214yes—
172#6104C4214yes—
173#6103—21no—
174#6103—21no—
175#6103—21no—
176#6103—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13C22×C411yescharacteristic
179C4⋊Dic13C22×C411yescharacteristic
180#6101—21no—
181#6101—21no—
182C4×Dic13—21no—
183C4×Dic13—21no—
184C4×Dic13—21no—
185C4×Dic13—21no—
186C4×Dic13—21no—
187C4×Dic13C22×C411yescharacteristic
188C4×Dic13C2×D411yescharacteristic
189C4×Dic13C2×D411yescharacteristic
190C2×#1055C22×C411yescharacteristic
191C2×#1055C22×C411yescharacteristic
192#6095C4214yes—
193C8×D13—22no—
194C8×D13C22×C414yes—
195C2×#443—132no—
196C4×#135—131no—
197#2875—131no—
198#2875—131no—
199C4×#108—131no—
200#1772—132no—
201#1765—132no—
202#1765—132no—
203#1759—131no—
204#1759—131no—
205#1726—131no—
206C23×C13—21no—
207C22×D13—21no—
208C22×D13C2×#4111yescharacteristic
209C2×#261—24no—
210C2×#261—42no—
211C2×#261—42no—
212Q8×C13—21no—
213Q8×C13C2×C4212yes—
214D4×C13—21no—
215D4×C13C2×C4212yes—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—81no—
220C2×C4×C13C4×D411yescharacteristic
221C2×C4×C13C4×D411yescharacteristic
222C2×C4×C13C23×C411yescharacteristic
223C22⋊D13—24no—
224C2×Dic13—21no—
225C2×Dic13—24no—
226C2×Dic13—21no—
227C2×Dic13—21no—
228C2×Dic13—81no—
229C2×Dic13C4×D411yescharacteristic
230C2×Dic13C4×D411yescharacteristic
231C2×Dic13C22×D411yescharacteristic
232D52—24no—
233D52—21no—
234D52C2×C4212yes—
235C4×D13—24no—
236C4×D13—41no—
237C4×D13—41no—
238C4×D13—81no—
239C4×D13—81no—
240C4×D13C23×C412yes—
241C4×D13C2×#4112yes—
242Dic26—21no—
243Dic26C2×C4212yes—
244#1057—24no—
245#1057—24no—
246#1057C4×D414yes—
247#1057C4×D414yes—
248C8×C13—21no—
249C8×C13C2×C4212yes—
250#1055—21no—
251#1055C2×C4212yes—
252C2×#135—131no—
253C2×#131—132no—
254C2×#131—132no—
255C4×#41—131no—
256C4×#41—131no—
257#443—1316no—
258C4×Q16—131no—
259C4×Q16—131no—
260C4×SD16—131no—
261C4×SD16—131no—
262C4×SD16—131no—
263C4×SD16#26111yescharacteristic, complemented
264C4×D8—131no—
265C4×D8—131no—
266C2×#108—132no—
267#427—131no—
268C2×#104—132no—
269C2×#104—132no—
270#416—131no—
271#416—131no—
272#405—132no—
273#405—132no—
274#405—262no—
275#405—262no—
276C4×M16—131no—
277C4×M16—131no—
278C4×M16—261no—
279C4×M16—261no—
280C2×#97—131no—
281C2×#97—132no—
282C2×#97—261no—
283C2×#97—261no—
284C2×C4×C8—132no—
285C2×C4×C8—131no—
286#376—131no—
287#341—132no—
288#339—132no—
289#339—132no—
290C22×C13—22no—
291C22×C13—41no—
292C22×C13—41no—
293C22×C13C2×C4×D411yescharacteristic
294C2×D13—21no—
295C2×D13—21no—
296C2×D13—22no—
297C2×D13—41no—
298C2×D13—41no—
299C2×D13C4×#4112yes—
300#261—44no—
301C4×C13—21no—
302C4×C13—21no—
303C4×C13—22no—
304C4×C13—41no—
305C4×C13—41no—
306C4×C13C22×C4211yescharacteristic
307C4×C13C4×#4111yescharacteristic
308Dic13—21no—
309Dic13—21no—
310Dic13—22no—
311Dic13—41no—
312Dic13—41no—
313Dic13C2×C4×D412yes—
314C2×#41—131no—
315C2×#41—131no—
316#135—138no—
317C2×Q16—131no—
318C2×SD16—131no—
319C2×SD16C2×#26111yescharacteristic
320C2×D8—131no—
321#131—138no—
322#131—138no—
323#131—264no—
324#131—264no—
325C2×M16—132no—
326C2×M16—132no—
327C2×M16—262no—
328C2×M16—262no—
329C22×C8—132no—
330C22×C8—131no—
331C22×C8—131no—
332C22×C8—262no—
333C22×C8—262no—
334C4×Q8—131no—
335C4×Q8—131no—
336C4×Q8—131no—
337C4×Q8C2×#26111yescharacteristic
338C4×D4—131no—
339C4×D4—131no—
340C4×D4—131no—
341C4×D4—261no—
342C4×D4—261no—
343C4×D4—261no—
344C4×D4—261no—
345C4×D4C2×#26111yescharacteristic
346#117—131no—
347#117—131no—
348#117—261no—
349#117—261no—
350C2×C42—131no—
351C2×C42—132no—
352C2×C42—261no—
353C2×C42—261no—
354#108—138no—
355#107—131no—
356#107—131no—
357#106—131no—
358#106C2×#26111yescharacteristic
359#104—138no—
360#104—138no—
361#103—131no—
362#103—131no—
363#103—131no—
364#103C2×#26111yescharacteristic
365#102—131no—
366#102—131no—
367#102—131no—
368#102C2×#26111yescharacteristic
369#97—131no—
370#97—131no—
371#97—132no—
372#97—261no—
373#97—261no—
374#97—264no—
375#97—262no—
376#97—262no—
377C4×C8—138no—
378C4×C8—131no—
379C4×C8—131no—
380C4×C8—131no—
381C4×C8—261no—
382C4×C8—261no—
383C4×C8—262no—
384C4×C8—262no—
385C4×C8C2×#26111yescharacteristic
386#95—261no—
387#95—261no—
388C2×C13—42no—
389C2×C13C42×D411yescharacteristic
390C2×C13#295711yescharacteristic
391C2×C13#295711yescharacteristic
392D13—22no—
393D13—42no—
394#41—134no—
395#41—134no—
396#41—262no—
397#41—262no—
398C2×Q8—131no—
399C2×Q8C22×#26111yescharacteristic
400C2×D4—131no—
401C2×D4—261no—
402C2×D4—261no—
403C2×D4C22×#26111yescharacteristic
404C22×C4—21no—
405C22×C4—131no—
406C22×C4—131no—
407C22×C4—131no—
408C22×C4—261no—
409C22×C4—261no—
410C22×C4—261no—
411C22×C4—261no—
412C22×C4—262no—
413C22×C4—261no—
414Q16—134no—
415SD16—134no—
416SD16C4×#26114yes—
417D8—134no—
418M16—134no—
419M16—134no—
420M16—268no—
421M16—268no—
422M16—262no—
423M16—262no—
424C2×C8—134no—
425C2×C8—132no—
426C2×C8—132no—
427C2×C8—134no—
428C2×C8—131no—
429C2×C8—134no—
430C2×C8—131no—
431C2×C8—262no—
432C2×C8—268no—
433C2×C8—268no—
434C2×C8—262no—
435C2×C8—262no—
436C2×C8C22×#26111yescharacteristic
437C2×C8C22×#26111yescharacteristic
438C4⋊C4—21no—
439C4⋊C4—131no—
440C4⋊C4—131no—
441C4⋊C4—261no—
442C4⋊C4—261no—
443C4⋊C4—261no—
444C4⋊C4C22×#26111yescharacteristic
445C4⋊C4C22×#26111yescharacteristic
446C22⋊C4—21no—
447C22⋊C4—261no—
448C22⋊C4—261no—
449C22⋊C4—261no—
450C22⋊C4—261no—
451C22⋊C4—261no—
452C42—21no—
453C42—131no—
454C42—131no—
455C42—131no—
456C42—134no—
457C42—261no—
458C42—261no—
459C42—261no—
460C42—261no—
461C42—262no—
462C42—261no—
463C42C22×#26111yescharacteristic
464C13#2051411yescharacteristic, complemented, Sylow
465C23—21no—
466C23—131no—
467C23—261no—
468Q8—21no—
469Q8—132no—
470Q8—261no—
471Q8C2×C4×#26112yes—
472D4—21no—
473D4—132no—
474D4—264no—
475D4—264no—
476D4—261no—
477D4C2×C4×#26112yes—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—81no—
482C2×C4—131no—
483C2×C4—132no—
484C2×C4—132no—
485C2×C4—131no—
486C2×C4—131no—
487C2×C4—264no—
488C2×C4—264no—
489C2×C4—261no—
490C2×C4—264no—
491C2×C4—261no—
492C2×C4—261no—
493C2×C4—521no—
494C2×C4—521no—
495C2×C4—522no—
496C2×C4—522no—
497C2×C4—1041no—
498C2×C4—1041no—
499C2×C4—1041no—
500C2×C4D4×#26111yescharacteristic
501C2×C4D4×#26111yescharacteristic
502C2×C4C23×#26111yescharacteristic
503C8—21no—
504C8—134no—
505C8—134no—
506C8—132no—
507C8—264no—
508C8—264no—
509C8—261no—
510C8C2×C4×#26112yes—
511C22—22no—
512C22—41no—
513C22—41no—
514C22—132no—
515C22—261no—
516C22—261no—
517C22—262no—
518C22—521no—
519C22—521no—
520C22C2×D4×#26111yescharacteristic
521C4—22no—
522C4—21no—
523C4—21no—
524C4—41no—
525C4—41no—
526C4—132no—
527C4—262no—
528C4—261no—
529C4—261no—
530C4—524no—
531C4—521no—
532C4—521no—
533C4C22×C4×#26111yescharacteristic
534C4#41×#26111yescharacteristic
535C2—42no—
536C2—262no—
537C2—522no—
538C2C4×D4×#26111yescharacteristic
539C2#1313161411yescharacteristic
540C2#1313161511yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC4×C13×SD16C4
socleC22×C13C2×C4×D4
prime radicalC2×#88170C22
cosocleC2×C4×D13C24
hypercenterC4×SD16#261
hypocenterC13#20514
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #13131408C2semidirect
3. #13131407C2semidirect
4. C4×#88103C2semidirect
5. #13130639C2semidirect
6. #13130617C2semidirect
7. #13130615C2semidirect
8. #13130600C2semidirect
9. #13130599C2semidirect
10. #13130492C2semidirect
21. #11719107C4semidirect
35. C4×C13×SD16C4semidirect
36. SD16×Dic13C4semidirect
37. C4×#6107C4semidirect
38. C4×#6104C4semidirect
40. #11718513C4semidirect
42. #11718451C4semidirect
44. #11718417C4semidirect
45. C4×#6095C4semidirect
55. #88240C2×C4semidirect
57. #88238C2×C4semidirect
90. #88118C2×C4semidirect
91. #88116C2×C4semidirect
105. #88103C2×C4semidirect
107. C8×#261C2×C4semidirect
263. C4×SD16#261semidirect
464. C13#20514semidirect

Maximal subgroups

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

subgroupindex
C2×#117191072
#131314082
#131314072
C4×#881032
#131306392
#131306172
#131306152
#131306002
#131305992
#131304922
C4×#881702
#2051413