Finite Group Databasebeta

← #15841499

Subgroups — #15841499

Order 3328.

1170 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125980C211yesmaximal, characteristic, complemented
2#13124844C211yesmaximal, characteristic, complemented
3#13124633C211yesmaximal, characteristic, complemented
4#13114120C214yesmaximal, complemented
5#13113987C214yesmaximal, complemented
6#13113508C211yesmaximal, characteristic, complemented
7#13113261C211yesmaximal, characteristic, complemented
8#13113227C211yesmaximal, characteristic, complemented
9C2×C13×#547C211yesmaximal, characteristic
10C22×C13×#41—21no—
11C13×#547—22no—
12C13×#547—22no—
13C13×#547—22no—
14C13×#547C2214yes—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#123—22no—
17C2×C13×C22⋊Q8—21no—
18C2×C13×#121—21no—
19C2×C4×D4×C13C2211yescharacteristic
20C2×C4×D4×C13C2211yescharacteristic
21C22×C13×C4⋊C4—21no—
22#11719175C2211yescharacteristic
23#11718879—21no—
24#11718876—21no—
25#11718755—22no—
26#11718754C2212yescomplemented
27#11718740C2212yescomplemented
28#11718680C2212yescomplemented
29C4×#6105—22no—
30#11718670—22no—
31#11718669C2212yescomplemented
32#11718669C2212yescomplemented
33#11718668C2212yescomplemented
34#11718632—22no—
35#11718632—21no—
36#11718625—21no—
37#11718586C2211yescharacteristic
38#11718586C2211yescharacteristic
39#11718585C2211yescharacteristic
40#11718139C2214yescomplemented
41D4⋊#1055C2214yescomplemented
42D4⋊#1055C2214yescomplemented
43C2×C13×#41—24no—
44C2×C13×#41—24no—
45C2×C13×#41—44no—
46C2×C13×#41—44no—
47C22×Q8×C13—21no—
48C22×D4×C13—22no—
49C22×D4×C13D411yescharacteristic
50C22×D4×C13D411yescharacteristic
51C23×C4×C13—22no—
52C23×C4×C13—21no—
53C23×C4×C13—21no—
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8D412yes—
57C13×C4⋊Q8C2312yes—
58C13×#123—28no—
59C13×#123—28no—
60C13×C22⋊Q8—24no—
61C13×C22⋊Q8—24no—
62C13×#121—24no—
63C13×#121—24no—
64C4×D4×C13—21no—
65C4×D4×C13—21no—
66C4×D4×C13—21no—
67C4×D4×C13—21no—
68C4×D4×C13D412yes—
69C4×D4×C13D412yes—
70C4×D4×C13C2312yes—
71C4×D4×C13C2312yes—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—24no—
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4D412yes—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C42×C13C2311yescharacteristic
83C2×#6105—22no—
84#88180—21no—
85#88178—21no—
86#88178—21no—
87C2×#6099—21no—
88#88124—21no—
89#88123C2311yescharacteristic
90#88123C2311yescharacteristic
91C4×Dic26—21no—
92C4×Dic26—21no—
93#88072—22no—
94#88072—22no—
95#88072—22no—
96C22⋊#1055—21no—
97C22⋊#1055—21no—
98#88050—22no—
99#88050—24no—
100#88048—22no—
101#88048—22no—
102#88048—24no—
103#88047—22no—
104C4⋊#1055—21no—
105C4⋊#1055—21no—
106C4⋊#1055C2312yes—
107C4⋊#1055C2312yes—
108C4×#1055—21no—
109C4×#1055C2312yes—
110#18757—131nomaximal, Sylow
111C24×C13—21no—
112C24×C13—21no—
113C13×#41—48no—
114C13×#41—416no—
115C13×#41—48no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13—42no—
119C2×Q8×C13—42no—
120C2×D4×C13—28no—
121C2×D4×C13—21no—
122C2×D4×C13—21no—
123C2×D4×C13—22no—
124C2×D4×C13—42no—
125C2×D4×C13—48no—
126C2×D4×C13SD1614yescomplemented
127C2×D4×C13C2×D412yes—
128C2×D4×C13C2×D412yes—
129C22×C4×C13—28no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—44no—
138C22×C4×C13—48no—
139C22×C4×C13—42no—
140C22×C4×C13—42no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C2×Dic26—21no—
145C2×Dic26—21no—
146C13×C4⋊C4—28no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4C2×D412yes—
153C13×C4⋊C4C2×D412yes—
154C13×C4⋊C4C2×D414yes—
155C13×C22⋊C4—28no—
156C13×C22⋊C4—22no—
157C13×C22⋊C4—22no—
158C13×C22⋊C4—22no—
159C13×C22⋊C4—22no—
160C42×C13C2×D411yescharacteristic
161C42×C13C2×D411yescharacteristic
162C42×C13C2×D411yescharacteristic
163C42×C13C2411yescharacteristic
164C22⋊Dic13—41no—
165#6105—44no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170#6101—41no—
171#6101—41no—
172C4×Dic13—41no—
173#6099—42no—
174C2×#1055—22no—
175C2×#1055—22no—
176C2×#1055—22no—
177C2×#547D1311yescharacteristic
178#3229—131no—
179#3101—131no—
180#3077—131no—
181#1654—134no—
182#1635—134no—
183#1546—131no—
184#1486—131no—
185#1478—131no—
186C23×C13—22no—
187C23×C13—24no—
188C23×C13—22no—
189C23×C13—42no—
190C23×C13—42no—
191C23×C13—42no—
192C23×C13—42no—
193C23×C13—42no—
194C23×C13#12011yescharacteristic
195Q8×C13—42no—
196Q8×C13—42no—
197Q8×C13—44no—
198D4×C13—22no—
199D4×C13—22no—
200D4×C13—22no—
201D4×C13—24no—
202D4×C13—42no—
203D4×C13—416no—
204D4×C13C2×SD1614yes—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—24no—
209C2×C4×C13—41no—
210C2×C4×C13—44no—
211C2×C4×C13—42no—
212C2×C4×C13—416no—
213C2×C4×C13—42no—
214C2×C4×C13—44no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—44no—
218C2×C4×C13—44no—
219C2×C4×C13#12011yescharacteristic
220C2×C4×C13#12011yescharacteristic
221C2×C4×C13#12011yescharacteristic
222C2×C4×C13C2×SD1612yes—
223C2×C4×C13AGL(1,ℤ/8)12yes—
224C2×C4×C13C22×D411yescharacteristic
225C2×C4×C13C22×D411yescharacteristic
226C2×C4×C13C22×D411yescharacteristic
227C2×Dic13—41no—
228C2×Dic13—41no—
229Dic26—42no—
230Dic26—42no—
231#1055—42no—
232#1055—42no—
233#1055—42no—
234C22×#41—21no—
235#547—22no—
236#547—22no—
237#547—22no—
238#547C2×D1314yes—
239#533—131no—
240C2×C4⋊Q8C2×D1311yescharacteristic
241C2×#123—22no—
242C2×C22⋊Q8—21no—
243C2×#121—21no—
244C2×C4×D4C2×D1311yescharacteristic
245C2×C4×D4C2×D1311yescharacteristic
246C22×C4⋊C4—21no—
247#498—132no—
248#487—132no—
249#483—261no—
250#483—262no—
251#478—262no—
252#476—132no—
253#476—132no—
254#475—262no—
255#474—132no—
256#461—132no—
257#450—261no—
258C4×SD16—262no—
259#431—131no—
260#431—131no—
261#428—261no—
262#423—131no—
263#418—261no—
264#332—134no—
265D4⋊C8—134no—
266D4⋊C8—134no—
267C22×C13—21no—
268C22×C13—21no—
269C22×C13—24no—
270C22×C13—48no—
271C22×C13—42no—
272C22×C13—42no—
273C22×C13—42no—
274C22×C13—42no—
275C22×C13—42no—
276C22×C13—84no—
277C22×C13#45012yes—
278C22×C13C2×#12011yescharacteristic
279C4×C13—21no—
280C4×C13—21no—
281C4×C13—21no—
282C4×C13—42no—
283C4×C13—44no—
284C4×C13—42no—
285C4×C13#45012yes—
286C4×C13C22×SD1611yescharacteristic
287C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C13#57512yes—
289Dic13—81no—
290Dic13—81no—
291C2×#41—24no—
292C2×#41—24no—
293C2×#41—44no—
294C2×#41—44no—
295C22×Q8—21no—
296C22×D4—22no—
297C22×D4C22⋊D1311yescharacteristic
298C22×D4C22⋊D1311yescharacteristic
299C23×C4—22no—
300C23×C4—21no—
301C23×C4—21no—
302C2×SD16—262no—
303C2×M16—261no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—131no—
307C4⋊Q8—131no—
308C4⋊Q8C22⋊D1312yes—
309C4⋊Q8C22×D1312yes—
310#125—261no—
311#123—28no—
312#123—28no—
313C22⋊Q8—24no—
314C22⋊Q8—24no—
315C22⋊Q8—261no—
316C22⋊Q8—261no—
317#121—24no—
318#121—24no—
319C4×Q8—261no—
320C4×Q8—261no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4C22⋊D1312yes—
326C4×D4C22⋊D1312yes—
327C4×D4C22×D1312yes—
328C4×D4C22×D1312yes—
329#117—261no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4C22⋊D1311yescharacteristic
335C2×C4⋊C4C22⋊D1311yescharacteristic
336C2×C4⋊C4C22⋊D1312yes—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C42C22×D1311yescharacteristic
341#107—262no—
342#106—262no—
343#106—262no—
344#106—264no—
345C4⋊C8—132no—
346C4⋊C8—132no—
347C4⋊C8—261no—
348C4⋊C8—261no—
349#103—262no—
350#103—264no—
351#102—262no—
352#102—262no—
353#102—262no—
354C22⋊C8—261no—
355C22⋊C8—261no—
356C4×C8—132no—
357C4×C8—261no—
358C2×C13—22no—
359C2×C13—44no—
360C2×C13—82no—
361C2×C13C2×#45011yescharacteristic
362C2×C13#300511yescharacteristic
363C2×C13#302011yescharacteristic
364C24—21no—
365C24—21no—
366#41—48no—
367#41—416no—
368#41—48no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—42no—
372C2×Q8—42no—
373C2×Q8—261no—
374C2×Q8—261no—
375C2×D4—28no—
376C2×D4—22no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—42no—
380C2×D4—48no—
381C2×D4#610514yescomplemented
382C2×D4C2×C22⋊D1312yes—
383C2×D4C2×C22⋊D1312yes—
384C22×C4—28no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—44no—
393C22×C4—48no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4C2×C22⋊D1311yescharacteristic
397C22×C4C2×C22⋊D1311yescharacteristic
398C22×C4C2×C22⋊D1311yescharacteristic
399SD16—524no—
400M16—522no—
401C2×C8—262no—
402C2×C8—262no—
403C2×C8—262no—
404C4⋊C4—28no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—261no—
411C4⋊C4—261no—
412C4⋊C4—261no—
413C4⋊C4—261no—
414C4⋊C4—521no—
415C4⋊C4—521no—
416C4⋊C4C2×C22⋊D1312yes—
417C4⋊C4C2×C22⋊D1314yes—
418C4⋊C4C2×C22⋊D1312yes—
419C22⋊C4—28no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—521no—
425C42—521no—
426C42C2×C22⋊D1311yescharacteristic
427C42C2×C22⋊D1311yescharacteristic
428C42C2×C22⋊D1311yescharacteristic
429C42C23×D1311yescharacteristic
430C13#1875711yescharacteristic, complemented, Sylow
431C23—22no—
432C23—24no—
433C23—22no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23#8820711yescharacteristic
440Q8—42no—
441Q8—42no—
442Q8—44no—
443Q8—522no—
444Q8—522no—
445D4—22no—
446D4—22no—
447D4—22no—
448D4—24no—
449D4—42no—
450D4—416no—
451D4C2×#610514yes—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—41no—
457C2×C4—44no—
458C2×C4—42no—
459C2×C4—416no—
460C2×C4—42no—
461C2×C4—44no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—521no—
467C2×C4—521no—
468C2×C4#8818612yes—
469C2×C4C2×#610512yes—
470C2×C4#8820711yescharacteristic
471C2×C4#8820711yescharacteristic
472C2×C4#8820711yescharacteristic
473C2×C4C22×C22⋊D1311yescharacteristic
474C2×C4C22×C22⋊D1311yescharacteristic
475C2×C4C22×C22⋊D1311yescharacteristic
476C8—522no—
477C8—522no—
478C8—522no—
479C22—21no—
480C22—21no—
481C22—24no—
482C22—48no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—84no—
489C22#1171887912yes—
490C22C2×#8820711yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—42no—
495C4—44no—
496C4—42no—
497C4—1041no—
498C4—1041no—
499C4#1171887912yes—
500C4C2×#8818611yescharacteristic
501C4C22×#610511yescharacteristic
502C4#1171952712yes—
503C2—22no—
504C2—44no—
505C2—82no—
506C2C2×#1171887911yescharacteristic
507C2#1312407811yescharacteristic
508C2#1312420011yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC2×C13×#547C2
socleC22×C13C2×#120
hypercenterC2×#547D13
hypocenterC13#18757
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13125980C2semidirect
2. #13124844C2semidirect
3. #13124633C2semidirect
4. #13114120C2semidirect
5. #13113987C2semidirect
6. #13113508C2semidirect
7. #13113261C2semidirect
8. #13113227C2semidirect
26. #11718754C22semidirect
27. #11718740C22semidirect
28. #11718680C22semidirect
31. #11718669C22semidirect
32. #11718669C22semidirect
33. #11718668C22semidirect
40. #11718139C22semidirect
41. D4⋊#1055C22semidirect
42. D4⋊#1055C22semidirect
126. C2×D4×C13SD16semidirect
381. C2×D4#6105semidirect
430. C13#18757semidirect

Maximal subgroups

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

subgroupindex
#131259802
#131248442
#131246332
#131141202
#131139872
#131135082
#131132612
#131132272
C2×C13×#5472
#1875713