Finite Group Databasebeta

← #15873433

Subgroups — #15873433

Order 3328.

966 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
1C2×#11718494C211yesmaximal, characteristic
2#13117240C211yesmaximal, characteristic
3D13×#384C211yesmaximal, characteristic
4#13115600C211yesmaximal, characteristic, complemented
5#13115599C211yesmaximal, characteristic, complemented
6#13115597C211yesmaximal, characteristic, complemented
7#13115030C212yesmaximal
8#13115027C212yesmaximal
9#13114991C212yesmaximal, complemented
10#13114962C212yesmaximal, complemented
11C13×#1948C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×D13—21no—
13C2×C4⋊C4×D13—21no—
14C2×C4⋊C4×D13C2212yes—
15C2×#88126—21no—
16C2×C42×D13C2211yescharacteristic
17C2×C13×#106C2212yes—
18C2×C13×C4⋊C8C2211yescharacteristic
19C13×#384C2211yescharacteristic
20C4×C13×C4⋊C4C2211yescharacteristic
21C2×#88060C2212yes—
22C2×#88057C2212yes—
23C2×C8×Dic13C2212yes—
24#11718648C2211yescharacteristic
25#11718648C2211yescharacteristic
26#11718637—21no—
27#11718637—21no—
28#11718637C2212yes—
29#11718637C2211yescharacteristic
30#11718637C2211yescharacteristic
31C2×#88048C2212yes—
32C2×#88048C2212yes—
33#11718596C2211yescharacteristic
34C4×C4⋊Dic13C2211yescharacteristic
35C4×#6101—21no—
36C2×C4⋊#1055C2211yescharacteristic
37#11718494C418yescomplemented
38#11718328—21no—
39#11718311—21no—
40C13×#340C2212yes—
41#11718143C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44C22×C4×D13—22no—
45C22×C4×D13D411yescharacteristic
46C22×C4×D13D411yescharacteristic
47C22×C4×D13C2311yescharacteristic
48C22×C8×C13C2312yes—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4C2311yescharacteristic
52C2×C13×C4⋊C4C2311yescharacteristic
53C2×C13×C4⋊C4C2312yes—
54C2×C42×C13—21no—
55C2×C42×C13C2311yescharacteristic
56C2×#6103—21no—
57C2×#6103—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13C2312yes—
61C2×C4⋊Dic13C2311yescharacteristic
62C2×C4⋊Dic13C2311yescharacteristic
63C2×#6101—21no—
64C2×#6101—21no—
65C2×#6101—22no—
66C2×#6101—22no—
67C2×#6101—22no—
68C2×#6101—21no—
69C2×#6101—21no—
70C2×C4×Dic13—21no—
71C2×C4×Dic13D411yescharacteristic
72C2×C4×Dic13D411yescharacteristic
73C2×C4×Dic13C2311yescharacteristic
74C22×#1055C2312yes—
75C4⋊C4×D13—42no—
76C4⋊C4×D13—42no—
77C4⋊C4×D13—44no—
78C4⋊C4×D13—44no—
79#88126—44no—
80C42×D13C2×C414yes—
81C42×D13Q814yes—
82C13×#106—42no—
83C13×C4⋊C8C2×C414yescomplemented
84C13×#95—21no—
85#88071—21no—
86#88071—21no—
87#88071—21no—
88#88060C2×C418yes—
89#88057—42no—
90C8×Dic13C2×C418yescomplemented
91#88048—42no—
92#88048—42no—
93C4⋊#1055C2×C414yescomplemented
94#21981—131nomaximal, Sylow
95C23×D13C2×D411yescharacteristic
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—22no—
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2411yescharacteristic
102C22×Dic13—21no—
103C22×Dic13—21no—
104C22×Dic13—22no—
105C22×Dic13C2×D411yescharacteristic
106C22×Dic13C2×D411yescharacteristic
107C22×Dic13C2×D411yescharacteristic
108C2×C4×D13—21no—
109C2×C4×D13—21no—
110C2×C4×D13—21no—
111C2×C4×D13—21no—
112C2×C4×D13—22no—
113C2×C4×D13—22no—
114C2×C4×D13—44no—
115C2×C4×D13—44no—
116C2×C4×D13—44no—
117C2×C4×D13C4⋊C414yes—
118C2×C4×D13C4⋊C414yes—
119C2×C4×D13SD1614yes—
120C2×C4×D13SD1614yes—
121C2×C4×D13C22×C412yes—
122C2×C4×D13C2×Q812yes—
123C2×C8×C13—22no—
124C2×C8×C13—22no—
125C2×C8×C13C22×C414yes—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4—22no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—42no—
133C13×C4⋊C4—42no—
134C42×C13—42no—
135C42×C13C22×C412yes—
136C42×C13C2×Q812yes—
137#6103—42no—
138#6103—42no—
139C4⋊Dic13—22no—
140C4⋊Dic13—22no—
141C4⋊Dic13—21no—
142C4⋊Dic13—21no—
143C4⋊Dic13—21no—
144C4⋊Dic13—21no—
145C4⋊Dic13—42no—
146C4⋊Dic13—42no—
147#6101—44no—
148#6101—42no—
149#6101—42no—
150#6101—44no—
151#6101—44no—
152#6101—42no—
153#6101—42no—
154C4×Dic13—42no—
155C4×Dic13C4⋊C414yes—
156C4×Dic13C4⋊C414yes—
157C4×Dic13C22×C412yes—
158C4×Dic13C2×Q812yes—
159C2×#1055—22no—
160C2×#1055—22no—
161C2×#1055C22×C414yes—
162C2×#431—131no—
163#2285—131no—
164C2×#384—131no—
165#1948—131no—
166#1948—131no—
167#1948—131no—
168#1948D1311yescharacteristic, complemented
169#1853—132no—
170#1853—132no—
171#1844—132no—
172#1834—132no—
173C23×C13C22×D411yescharacteristic
174C22×D13—21no—
175C22×D13—21no—
176C22×D13—21no—
177C22×D13—21no—
178C22×D13C2×C4⋊C412yes—
179C22×D13C2×SD1612yes—
180C22×D13C2×SD1612yes—
181C2×C4×C13—21no—
182C2×C4×C13—21no—
183C2×C4×C13—42no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—42no—
189C2×C4×C13—42no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13C2×C4⋊C412yes—
193C2×C4×C13C2×C4⋊C412yes—
194C2×C4×C13C2×SD1612yes—
195C2×C4×C13C2×SD1612yes—
196C2×C4×C13C23×C411yescharacteristic
197C2×C4×C13C22×Q811yescharacteristic
198C2×C4×C13H(5,𝔽2)11yescharacteristic
199C2×C4×C13H(5,𝔽2)11yescharacteristic
200C2×C4×C132−1+411yescharacteristic
201C2×C4×C132−1+411yescharacteristic
202C2×Dic13—21no—
203C2×Dic13—21no—
204C2×Dic13—42no—
205C2×Dic13—41no—
206C2×Dic13—41no—
207C2×Dic13—41no—
208C2×Dic13—41no—
209C2×Dic13—42no—
210C2×Dic13—42no—
211C2×Dic13—41no—
212C2×Dic13—41no—
213C2×Dic13C2×C4⋊C412yes—
214C2×Dic13C2×C4⋊C412yes—
215C2×Dic13C2×C4⋊C412yes—
216C2×Dic13C2×SD1612yes—
217C2×Dic13C2×SD1612yes—
218C2×Dic13AGL(1,ℤ/8)12yes—
219C2×Dic13#13712yes—
220C4×D13—22no—
221C4×D13—22no—
222C4×D13—22no—
223C4×D13—22no—
224C4×D13—28no—
225C4×D13—88no—
226C4×D13#106116yescomplemented
227C8×C13—24no—
228#1055—24no—
229C2×#117—261no—
230C22×C4⋊C4—132no—
231C22×C4⋊C4—261no—
232C22×C4⋊C4—261no—
233C22×C42—131no—
234#431—138no—
235C2×#106—132no—
236C2×#106—132no—
237C2×#106—132no—
238C2×#106C2×D1312yes—
239C2×C4⋊C8—131no—
240C2×C4⋊C8C2×D1311yescharacteristic
241C2×C22⋊C8—132no—
242C2×C4×C8—132no—
243#384—131no—
244#384—132no—
245#384—131no—
246#384—131no—
247#384—261no—
248#384—261no—
249#384C2×D1311yescharacteristic
250#382—261no—
251#380—131no—
252#380—131no—
253#380—261no—
254C4×C4⋊C4—131no—
255C4×C4⋊C4—261no—
256C4×C4⋊C4C2×D1311yescharacteristic
257#340—132no—
258#340—132no—
259#340—132no—
260#340C2×D1312yes—
261C22×C13C22×C4⋊C411yescharacteristic
262C22×C13#53511yescharacteristic
263C22×C13#53611yescharacteristic
264C22×C13C22×SD1611yescharacteristic
265C22×C13C22×SD1611yescharacteristic
266C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C13C2×#13711yescharacteristic
268C2×D13—22no—
269C2×D13—22no—
270C2×D13—22no—
271C2×D13—22no—
272C2×D13—22no—
273C2×D13—22no—
274C2×D13C2×#10614yes—
275C4×C13—22no—
276C4×C13—81no—
277C4×C13—82no—
278C4×C13—81no—
279C4×C13C2×#10614yes—
280C4×C13#52011yescharacteristic
281C4×C13#52011yescharacteristic
282C4×C13#54411yescharacteristic
283C4×C13#54411yescharacteristic
284Dic13—22no—
285Dic13—81no—
286Dic13—82no—
287Dic13—81no—
288Dic13C2×#10614yes—
289Dic13#42814yes—
290C23×C4—131no—
291C23×C4—131no—
292C23×C4—131no—
293C23×C4—262no—
294C22×C8—132no—
295C22×C8C22×D1312yes—
296#117—524no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—132no—
300C2×C4⋊C4—131no—
301C2×C4⋊C4—131no—
302C2×C4⋊C4—262no—
303C2×C4⋊C4—262no—
304C2×C4⋊C4—262no—
305C2×C4⋊C4—261no—
306C2×C4⋊C4—261no—
307C2×C4⋊C4—261no—
308C2×C4⋊C4—261no—
309C2×C4⋊C4—261no—
310C2×C4⋊C4—261no—
311C2×C4⋊C4—522no—
312C2×C4⋊C4—522no—
313C2×C4⋊C4—524no—
314C2×C4⋊C4—524no—
315C2×C4⋊C4C22×D1312yes—
316C2×C4⋊C4C22×D1311yescharacteristic
317C2×C4⋊C4C22×D1311yescharacteristic
318C2×C22⋊C4—261no—
319C2×C22⋊C4—261no—
320C2×C42—21no—
321C2×C42—131no—
322C2×C42—131no—
323C2×C42—131no—
324C2×C42—134no—
325C2×C42—134no—
326C2×C42—261no—
327C2×C42C22×D1311yescharacteristic
328#106—42no—
329#106—522no—
330#106—522no—
331#106—522no—
332C4⋊C8—134no—
333C4⋊C8C4×D1314yescomplemented
334C22⋊C8—138no—
335C4×C8—138no—
336#95—21no—
337#95—261no—
338#95—261no—
339#95—261no—
340C2×C13#231711yescharacteristic
341C2×C13C22×#10611yescharacteristic
342C2×C13C2×#42811yescharacteristic
343C2×C13#320611yescharacteristic
344C2×C13#320811yescharacteristic
345C2×C13#322711yescharacteristic
346C2×C13#322911yescharacteristic
347D13—24no—
348C24—131no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—131no—
353C22×C4—131no—
354C22×C4—134no—
355C22×C4—134no—
356C22×C4—134no—
357C22×C4—131no—
358C22×C4—134no—
359C22×C4—132no—
360C22×C4—132no—
361C22×C4—262no—
362C22×C4—262no—
363C22×C4—261no—
364C22×C4—261no—
365C22×C4—261no—
366C22×C4—261no—
367C22×C4—261no—
368C22×C4—261no—
369C22×C4—262no—
370C22×C4—524no—
371C22×C4—524no—
372C22×C4—524no—
373C22×C4D4×D1311yescharacteristic
374C22×C4D4×D1311yescharacteristic
375C22×C4C23×D1311yescharacteristic
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—134no—
379C2×C8—262no—
380C2×C8—262no—
381C2×C8C2×C4×D1314yes—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4—261no—
391C4⋊C4—262no—
392C4⋊C4—261no—
393C4⋊C4—261no—
394C4⋊C4—262no—
395C4⋊C4—261no—
396C4⋊C4—522no—
397C4⋊C4—524no—
398C4⋊C4—524no—
399C4⋊C4—522no—
400C4⋊C4—522no—
401C4⋊C4—522no—
402C4⋊C4—522no—
403C4⋊C4—524no—
404C4⋊C4—522no—
405C22⋊C4—522no—
406C22⋊C4—522no—
407C42—42no—
408C42—134no—
409C42—134no—
410C42—132no—
411C42—132no—
412C42—522no—
413C42C2×C4×D1312yes—
414C42Q8×D1312yes—
415C13#2198111yescharacteristic, complemented, Sylow
416C23—132no—
417C23—132no—
418C23—132no—
419C23—261no—
420C23—261no—
421C23—261no—
422C23—261no—
423C23C2×D4×D1311yescharacteristic
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—132no—
436C2×C4—132no—
437C2×C4—132no—
438C2×C4—132no—
439C2×C4—132no—
440C2×C4—132no—
441C2×C4—1316no—
442C2×C4—132no—
443C2×C4—268no—
444C2×C4—261no—
445C2×C4—261no—
446C2×C4—262no—
447C2×C4—262no—
448C2×C4—262no—
449C2×C4—262no—
450C2×C4—521no—
451C2×C4—521no—
452C2×C4—522no—
453C2×C4—522no—
454C2×C4—521no—
455C2×C4—521no—
456C2×C4—522no—
457C2×C4—521no—
458C2×C4—521no—
459C2×C4—1048no—
460C2×C4C4⋊C4×D1312yes—
461C2×C4C4⋊C4×D1312yes—
462C2×C4SD16×D1312yes—
463C2×C4SD16×D1312yes—
464C2×C4C22×C4×D1311yescharacteristic
465C2×C4#8825111yescharacteristic
466C2×C4C2×Q8×D1311yescharacteristic
467C2×C4#8825411yescharacteristic
468C2×C4#8825611yescharacteristic
469C2×C4#8825711yescharacteristic
470C8—24no—
471C8—264no—
472C22—134no—
473C22—262no—
474C22—262no—
475C22—262no—
476C22—262no—
477C22—262no—
478C22—262no—
479C22C2×C4⋊C4×D1311yescharacteristic
480C22#1171931211yescharacteristic
481C22#1171933311yescharacteristic
482C22C2×SD16×D1311yescharacteristic
483C22C2×SD16×D1311yescharacteristic
484C22D13×AGL(1,ℤ/8)11yescharacteristic
485C22D13×#13711yescharacteristic
486C4—22no—
487C4—81no—
488C4—81no—
489C4—82no—
490C4—134no—
491C4—134no—
492C4—262no—
493C4—1041no—
494C4—1041no—
495C4—1042no—
496C4D13×#10614yes—
497C4#1171925111yescharacteristic
498C4#1171927911yescharacteristic
499C4#1171939411yescharacteristic
500C4#1171943411yescharacteristic
501C2—264no—
502C2#1311745811yescharacteristic
503C2C2×D13×#10611yescharacteristic
504C2D13×#42811yescharacteristic
505C2#1312576011yescharacteristic
506C2#1312577611yescharacteristic
507C2#1312596311yescharacteristic
508C2#1312597911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1948C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1948D13
hypocenterC13#21981
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
4. #13115600C2semidirect
5. #13115599C2semidirect
6. #13115597C2semidirect
9. #13114991C2semidirect
10. #13114962C2semidirect
11. C13×#1948C2semidirect
37. #11718494C4semidirect
83. C13×C4⋊C8C2×C4semidirect
90. C8×Dic13C2×C4semidirect
93. C4⋊#1055C2×C4semidirect
168. #1948D13semidirect
226. C4×D13#106semidirect
333. C4⋊C8C4×D13semidirect
415. C13#21981semidirect

Maximal subgroups

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

subgroupindex
C2×#117184942
#131172402
D13×#3842
#131156002
#131155992
#131155972
#131150302
#131150272
#131149912
#131149622
C13×#19482
#2198113