Finite Group Databasebeta

← #15899075

Subgroups — #15899075

Order 3328.

1078 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88144C211yesmaximal, characteristic
2C2×#11718457C212yesmaximal, complemented
3C22⋊Q8×Dic13C211yesmaximal, characteristic
4#13116177C212yesmaximal, complemented
5#13115985C212yesmaximal, complemented
6#13115790C212yesmaximal, complemented
7#13115144C211yesmaximal, characteristic
8#13115029C211yesmaximal, characteristic
9#13115026C211yesmaximal, characteristic
10#13114814C211yesmaximal, characteristic
11C13×#1872C211yesmaximal, characteristic
12C2×C13×C22⋊Q8C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C2×Q8×Dic13C2211yescharacteristic
15C22×C4⋊Dic13—21no—
16C22×C4⋊Dic13C2211yescharacteristic
17C22×#6101—21no—
18C22×C4×Dic13C2211yescharacteristic
19C2×#88144—21no—
20C2×#88144—21no—
21C2×#88144—28no—
22C2×#88144C2212yes—
23C2×#88144C2212yes—
24C2×C13×#103C2212yes—
25C2×C13×C22⋊C8C2211yescharacteristic
26#11718891C2211yescharacteristic
27C2×#88075C2212yes—
28#11718873C2211yescharacteristic
29C2×C22⋊#1055C2211yescharacteristic
30C2×#88058C2212yes—
31C2×#88054C2212yes—
32#11718646C2211yescharacteristic
33#11718642—21no—
34C4⋊C4×Dic13—21no—
35C4⋊C4×Dic13C2211yescharacteristic
36C2×#88048C2212yes—
37#11718611—21no—
38C22⋊C4×Dic13—21no—
39#11718457—28no—
40C13×#340C2212yes—
41#11718143C2212yes—
42#11718142C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45C22×Q8×C13C2311yescharacteristic
46C23×C4×C13—21no—
47C23×C4×C13C2311yescharacteristic
48C23×Dic13—21no—
49C23×Dic13D411yescharacteristic
50C23×Dic13D411yescharacteristic
51C22×C8×C13C2312yes—
52C13×C22⋊Q8—22no—
53C13×C22⋊Q8Q814yes—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—24no—
57C2×C13×C4⋊C4C2312yes—
58C2×C13×C4⋊C4C2311yescharacteristic
59C2×C13×C22⋊C4—21no—
60C2×C22⋊Dic13—21no—
61Q8×Dic13—24no—
62C2×C4⋊Dic13—28no—
63C2×C4⋊Dic13—21no—
64C2×C4⋊Dic13—22no—
65C2×C4⋊Dic13—22no—
66C2×C4⋊Dic13—24no—
67C2×C4⋊Dic13—21no—
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13C2311yescharacteristic
70C2×C4⋊Dic13C2311yescharacteristic
71C2×C4⋊Dic13C2312yes—
72C2×#6101—28no—
73C2×#6101—22no—
74C2×#6101—22no—
75C2×C4×Dic13—24no—
76C2×C4×Dic13—21no—
77C2×C4×Dic13—21no—
78C2×C4×Dic13D411yescharacteristic
79C2×C4×Dic13D411yescharacteristic
80C2×C4×Dic13C2311yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C22×#1055C2312yes—
83#88144—28no—
84#88144—28no—
85#88144—24no—
86#88144—24no—
87#88144—24no—
88#88144D418yes—
89C13×#103—24no—
90C13×C22⋊C8—22no—
91#88075—24no—
92#88071—21no—
93#88071—21no—
94#88071—21no—
95#88071—21no—
96#88071—21no—
97C22⋊#1055—22no—
98#88058—24no—
99#88054—24no—
100#88048—24no—
101#24307—131nomaximal, Sylow
102C24×C13C2×D411yescharacteristic
103C2×Q8×C13—21no—
104C2×Q8×C13—22no—
105C2×Q8×C13—22no—
106C2×Q8×C13C2×Q812yes—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—24no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—42no—
114C22×C4×C13—42no—
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×Q812yes—
117C22×C4×C13#4112yes—
118C22×C4×C13C2411yescharacteristic
119C22×Dic13—24no—
120C22×Dic13—22no—
121C22×Dic13—22no—
122C22×Dic13—22no—
123C22×Dic13—22no—
124C22×Dic13—22no—
125C22×Dic13—21no—
126C22×Dic13—21no—
127C22×Dic13—41no—
128C22×Dic13—41no—
129C22×Dic13—42no—
130C22×Dic13—42no—
131C22×Dic13C2×D411yescharacteristic
132C22×Dic13C2×D411yescharacteristic
133C22×Dic13C2×D411yescharacteristic
134C22×Dic13C2×D411yescharacteristic
135C2×C8×C13—22no—
136C2×C8×C13—22no—
137C2×C8×C13—22no—
138C13×C4⋊C4—24no—
139C13×C4⋊C4—24no—
140C13×C4⋊C4—22no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4C2×D414yes—
143C13×C4⋊C4C2×Q812yes—
144C13×C22⋊C4—24no—
145C22⋊Dic13—42no—
146C4⋊Dic13—28no—
147C4⋊Dic13—24no—
148C4⋊Dic13—22no—
149C4⋊Dic13—28no—
150C4⋊Dic13—22no—
151C4⋊Dic13—22no—
152C4⋊Dic13—42no—
153C4⋊Dic13—42no—
154C4⋊Dic13C2×D414yes—
155#6101—28no—
156#6101—28no—
157C4×Dic13—22no—
158C4×Dic13—22no—
159C4×Dic13—22no—
160C4×Dic13—42no—
161C4×Dic13—42no—
162C4×Dic13C2×D414yes—
163C2×#1055—22no—
164C2×#1055—22no—
165C2×#1055—22no—
166C22×#125—131no—
167C2×#479—132no—
168C4×C22⋊Q8—131no—
169#2059—132no—
170#2026—132no—
171#1989—132no—
172#1872—131no—
173#1872D1311yescharacteristic
174#1853—131no—
175#1852—131no—
176#1797—131no—
177C23×C13—21no—
178C23×C13—21no—
179C23×C13—21no—
180C23×C13—21no—
181C23×C13C22⋊Q812yes—
182C23×C13#13512yes—
183C23×C13#13712yes—
184C23×C13C22×D411yescharacteristic
185Q8×C13—24no—
186Q8×C13—42no—
187C2×C4×C13—21no—
188C2×C4×C13—21no—
189C2×C4×C13—24no—
190C2×C4×C13—24no—
191C2×C4×C13—24no—
192C2×C4×C13—22no—
193C2×C4×C13—22no—
194C2×C4×C13—48no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—42no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—42no—
201C2×C4×C13C22⋊Q812yes—
202C2×C4×C13C22×D412yes—
203C2×C4×C13C22×Q811yescharacteristic
204C2×C4×C13C2×#4111yescharacteristic
205C2×C4×C132−1+412yes—
206C2×Dic13—21no—
207C2×Dic13—21no—
208C2×Dic13—21no—
209C2×Dic13—21no—
210C2×Dic13—21no—
211C2×Dic13—21no—
212C2×Dic13—24no—
213C2×Dic13—21no—
214C2×Dic13—21no—
215C2×Dic13—21no—
216C2×Dic13—21no—
217C2×Dic13—44no—
218C2×Dic13—44no—
219C2×Dic13—48no—
220C2×Dic13—42no—
221C2×Dic13—42no—
222C2×Dic13—41no—
223C2×Dic13—41no—
224C2×Dic13—41no—
225C2×Dic13—41no—
226C2×Dic13—41no—
227C2×Dic13—41no—
228C2×Dic13#12012yes—
229C2×Dic13#12012yes—
230C8×C13—42no—
231#1055—42no—
232C2×#125—132no—
233C2×#125—132no—
234C2×#125—261no—
235C2×#125—261no—
236C2×#125—268no—
237C2×C22⋊Q8C2×D1311yescharacteristic
238C2×C4×Q8—131no—
239C22×C4⋊C4—131no—
240C22×C4⋊C4—261no—
241C22×C4⋊C4—261no—
242C22×C4⋊C4C2×D1311yescharacteristic
243C22×C42—131no—
244#479—268no—
245C2×#107—132no—
246C2×#106—132no—
247C2×C4⋊C8—132no—
248C2×#103—132no—
249C2×#103C2×D1312yes—
250C2×C22⋊C8—131no—
251C2×C22⋊C8C2×D1311yescharacteristic
252#391—131no—
253#389—131no—
254#387—261no—
255#385—261no—
256#380—131no—
257C4×C4⋊C4—131no—
258C4×C4⋊C4—261no—
259C4×C22⋊C4—261no—
260#340—132no—
261#340—132no—
262#340—132no—
263#340C2×D1312yes—
264#336—132no—
265C22×C13—22no—
266C22×C13—22no—
267C22×C13—22no—
268C22×C13—22no—
269C22×C13—22no—
270C22×C13—22no—
271C22×C13#47914yescomplemented
272C22×C13C2×#12011yescharacteristic
273C22×C13C2×C22⋊Q811yescharacteristic
274C22×C13#53611yescharacteristic
275C22×C13C2×#13511yescharacteristic
276C22×C13C2×#13711yescharacteristic
277C22×C13#57511yescharacteristic
278C22×C13#57511yescharacteristic
279C4×C13—22no—
280C4×C13—42no—
281C4×C13—42no—
282C4×C13—44no—
283C4×C13#54812yes—
284C4×C13D4×Q812yes—
285Dic13—22no—
286Dic13—22no—
287Dic13—41no—
288Dic13—44no—
289Dic13—41no—
290Dic13—81no—
291Dic13—81no—
292C22×Q8C22×D1311yescharacteristic
293C23×C4—21no—
294C23×C4—131no—
295C23×C4—131no—
296C23×C4—261no—
297C23×C4C22×D1311yescharacteristic
298C22×C8—132no—
299C22×C8C22×D1312yes—
300#125—138no—
301#125—264no—
302#125—264no—
303#125—268no—
304#125—268no—
305#125—264no—
306C22⋊Q8—22no—
307C22⋊Q8Dic2614yes—
308C4×Q8—264no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—132no—
313C2×C4⋊C4—131no—
314C2×C4⋊C4—131no—
315C2×C4⋊C4—264no—
316C2×C4⋊C4—262no—
317C2×C4⋊C4—262no—
318C2×C4⋊C4—262no—
319C2×C4⋊C4—262no—
320C2×C4⋊C4—268no—
321C2×C4⋊C4—268no—
322C2×C4⋊C4—261no—
323C2×C4⋊C4—261no—
324C2×C4⋊C4—261no—
325C2×C4⋊C4C22×D1311yescharacteristic
326C2×C4⋊C4C22×D1312yes—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—261no—
329C2×C42—131no—
330C2×C42—131no—
331C2×C42—131no—
332C2×C42—131no—
333C2×C42—264no—
334C2×C42—261no—
335C2×C42—261no—
336#107—264no—
337#106—264no—
338C4⋊C8—264no—
339#103—24no—
340#103—264no—
341C22⋊C8—22no—
342C22⋊C8—262no—
343#95—261no—
344#95—261no—
345#95—261no—
346#95—261no—
347#95—261no—
348C2×C13—24no—
349C2×C13#240911yescharacteristic
350C2×C13#300211yescharacteristic
351C2×C13#300711yescharacteristic
352C2×C13C2×#47911yescharacteristic
353C2×C13#308011yescharacteristic
354C2×C13#323211yescharacteristic
355C2×C13#323611yescharacteristic
356C24D4×D1311yescharacteristic
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8C2×Dic2612yes—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—131no—
370C22×C4—131no—
371C22×C4—131no—
372C22×C4—131no—
373C22×C4—262no—
374C22×C4—262no—
375C22×C4—264no—
376C22×C4—262no—
377C22×C4—262no—
378C22×C4—262no—
379C22×C4—261no—
380C22×C4—261no—
381C22×C4—521no—
382C22×C4—521no—
383C22×C4—522no—
384C22×C4—522no—
385C22×C4C2×Dic2612yes—
386C22×C4D4×D1311yescharacteristic
387C22×C4#612912yes—
388C22×C4C23×D1311yescharacteristic
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—262no—
393C2×C8—262no—
394C2×C8—262no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—134no—
400C4⋊C4—268no—
401C4⋊C4—268no—
402C4⋊C4—268no—
403C4⋊C4—264no—
404C4⋊C4—268no—
405C4⋊C4—262no—
406C4⋊C4—262no—
407C4⋊C4—262no—
408C4⋊C4—522no—
409C4⋊C4—522no—
410C4⋊C4C2×Dic2612yes—
411C4⋊C4D4×D1314yes—
412C22⋊C4—24no—
413C22⋊C4—522no—
414C42—134no—
415C42—262no—
416C42—262no—
417C42—262no—
418C42—522no—
419C42—522no—
420C13#2430711yescharacteristic, complemented, Sylow
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23#8813212yes—
426C23#8816912yes—
427C23#8817312yes—
428C23C2×D4×D1311yescharacteristic
429Q8—24no—
430Q8—42no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—48no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—132no—
446C2×C4—132no—
447C2×C4—261no—
448C2×C4—261no—
449C2×C4—261no—
450C2×C4—261no—
451C2×C4—261no—
452C2×C4—261no—
453C2×C4—261no—
454C2×C4—261no—
455C2×C4—261no—
456C2×C4—261no—
457C2×C4—264no—
458C2×C4—524no—
459C2×C4—524no—
460C2×C4—528no—
461C2×C4—522no—
462C2×C4—522no—
463C2×C4—521no—
464C2×C4—521no—
465C2×C4—521no—
466C2×C4—521no—
467C2×C4—521no—
468C2×C4—521no—
469C2×C4#8813212yes—
470C2×C4C22×Dic2611yescharacteristic
471C2×C4C2×D4×D1312yes—
472C2×C4C2×#612911yescharacteristic
473C2×C4#8825712yes—
474C8—42no—
475C8—522no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22#1171845714yescomplemented
483C22C2×#8813211yescharacteristic
484C22D13×#12011yescharacteristic
485C22#1171935311yescharacteristic
486C22C2×#8816911yescharacteristic
487C22C2×#8817311yescharacteristic
488C22#1171947811yescharacteristic
489C22#1171948211yescharacteristic
490C4—22no—
491C4—42no—
492C4—42no—
493C4—44no—
494C4—262no—
495C4—262no—
496C4—521no—
497C4—524no—
498C4—521no—
499C4—1041no—
500C4—1041no—
501C4D4×Dic2612yes—
502C4#1171930312yes—
503C2—24no—
504C2#1311819811yescharacteristic
505C2#1312405911yescharacteristic
506C2#1312409111yescharacteristic
507C2C2×#1171845711yescharacteristic
508C2#1312465611yescharacteristic
509C2#1312600911yescharacteristic
510C2#1312603911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1872C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1872D13
hypocenterC13#24307
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#11718457C2semidirect
4. #13116177C2semidirect
5. #13115985C2semidirect
6. #13115790C2semidirect
271. C22×C13#479semidirect
420. C13#24307semidirect
482. C22#11718457semidirect

Maximal subgroups

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

subgroupindex
C22×#881442
C2×#117184572
C22⋊Q8×Dic132
#131161772
#131159852
#131157902
#131151442
#131150292
#131150262
#131148142
C13×#18722
#2430713