Finite Group Databasebeta

← #15867764

Subgroups — #15867764

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718494C211yesmaximal, characteristic
2#13117241C211yesmaximal, characteristic
3C4×C4⋊C4×D13C211yesmaximal, characteristic
4#13115600C211yesmaximal, characteristic, complemented
5#13115599C211yesmaximal, characteristic, complemented
6#13115597C211yesmaximal, characteristic, complemented
7#13115030C212yesmaximal
8#13115027C212yesmaximal
9#106×Dic13C212yesmaximal, complemented
10#13114724C212yesmaximal, complemented
11C13×#1948C211yesmaximal, characteristic, complemented
12C2×#88146—21no—
13C2×C4⋊C4×D13C2211yescharacteristic
14C2×C4⋊C4×D13C2211yescharacteristic
15C2×C42×D13—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#11718648—21no—
25#11718648C2212yes—
26#11718638—21no—
27C4⋊C4×Dic13—21no—
28C4⋊C4×Dic13C2212yes—
29C4⋊C4×Dic13C2211yescharacteristic
30C4⋊C4×Dic13C2211yescharacteristic
31C2×#88048C2212yes—
32C2×#88048C2212yes—
33#11718596C2211yescharacteristic
34C4×C4⋊Dic13C2211yescharacteristic
35C4×#6101—21no—
36C2×C4⋊#1055C2211yescharacteristic
37#11718494C418yescomplemented
38D13×#95—21no—
39#11718310—21no—
40C13×#340C2212yes—
41#11718143C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44C22×C4×D13—21no—
45C22×C4×D13—21no—
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D411yescharacteristic
48C22×C4×D13C2311yescharacteristic
49C22×C8×C13C2312yes—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4C2312yes—
53C2×C13×C4⋊C4C2311yescharacteristic
54C2×C13×C4⋊C4C2311yescharacteristic
55C2×C42×C13—21no—
56C2×C42×C13C2311yescharacteristic
57C2×#6103—22no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13C2312yes—
61C2×C4⋊Dic13C2311yescharacteristic
62C2×C4⋊Dic13C2311yescharacteristic
63C2×#6101—21no—
64C2×#6101—21no—
65C2×C4×Dic13—21no—
66C2×C4×Dic13—21no—
67C2×C4×Dic13—21no—
68C2×C4×Dic13—22no—
69C2×C4×Dic13D411yescharacteristic
70C2×C4×Dic13D411yescharacteristic
71C2×C4×Dic13C2311yescharacteristic
72C22×#1055C2312yes—
73#88146—44no—
74C4⋊C4×D13—22no—
75C4⋊C4×D13—22no—
76C4⋊C4×D13—22no—
77C4⋊C4×D13—22no—
78C42×D13—44no—
79C42×D13C2×C414yes—
80C42×D13Q814yes—
81C13×#106—24no—
82C13×C4⋊C8C2×C414yescomplemented
83C13×#95—21no—
84#88071—21no—
85#88071—21no—
86#88071—21no—
87#88071—22no—
88#88071—22no—
89#88060C2×C418yes—
90#88057—24no—
91C8×Dic13C2×C418yescomplemented
92#88048—24no—
93#88048—24no—
94C4⋊#1055C2×C414yescomplemented
95#21359—131nomaximal, Sylow
96C23×D13C2×D411yescharacteristic
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2411yescharacteristic
103C22×Dic13—21no—
104C22×Dic13—21no—
105C22×Dic13—22no—
106C22×Dic13C2×D411yescharacteristic
107C22×Dic13C2×D411yescharacteristic
108C22×Dic13C2×D411yescharacteristic
109C2×C4×D13—21no—
110C2×C4×D13—21no—
111C2×C4×D13—21no—
112C2×C4×D13—21no—
113C2×C4×D13—24no—
114C2×C4×D13—24no—
115C2×C4×D13—41no—
116C2×C4×D13—41no—
117C2×C4×D13—42no—
118C2×C4×D13—42no—
119C2×C4×D13—42no—
120C2×C4×D13—42no—
121C2×C4×D13C4⋊C414yes—
122C2×C4×D13C4⋊C414yes—
123C2×C4×D13SD1614yes—
124C2×C4×D13SD1614yes—
125C2×C4×D13C22×C412yes—
126C2×C4×D13C2×Q812yes—
127C2×C8×C13—22no—
128C2×C8×C13—22no—
129C2×C8×C13C22×C414yes—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4—22no—
134C13×C4⋊C4—42no—
135C13×C4⋊C4—42no—
136C13×C4⋊C4#4112yes—
137C13×C4⋊C4#4112yes—
138C42×C13—42no—
139C42×C13C22×C412yes—
140C42×C13C2×Q812yes—
141#6103—44no—
142C4⋊Dic13—21no—
143C4⋊Dic13—21no—
144C4⋊Dic13—22no—
145C4⋊Dic13—22no—
146C4⋊Dic13—42no—
147C4⋊Dic13—42no—
148C4⋊Dic13#4112yes—
149C4⋊Dic13#4112yes—
150#6101—24no—
151#6101—24no—
152C4×Dic13—42no—
153C4×Dic13—42no—
154C4×Dic13—42no—
155C4×Dic13—44no—
156C4×Dic13C4⋊C414yes—
157C4×Dic13C4⋊C414yes—
158C4×Dic13C22×C412yes—
159C4×Dic13C2×Q812yes—
160C2×#1055—22no—
161C2×#1055—22no—
162C2×#1055C22×C414yes—
163C2×#431—131no—
164#2285—131no—
165C2×C4×C4⋊C4—131no—
166#1948—131no—
167#1948—131no—
168#1948—131no—
169#1948D1311yescharacteristic, complemented
170#1853—132no—
171#1853—132no—
172C4×#106—132no—
173C4×#106—132no—
174C23×C13C22×D411yescharacteristic
175C22×D13—21no—
176C22×D13—21no—
177C22×D13—21no—
178C22×D13—21no—
179C22×D13C2×C4⋊C412yes—
180C22×D13C2×SD1612yes—
181C22×D13C2×SD1612yes—
182C2×C4×C13—21no—
183C2×C4×C13—21no—
184C2×C4×C13—22no—
185C2×C4×C13—22no—
186C2×C4×C13—41no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—42no—
191C2×C4×C13—42no—
192C2×C4×C13—42no—
193C2×C4×C13C2×C4⋊C412yes—
194C2×C4×C13C2×C4⋊C412yes—
195C2×C4×C13C2×SD1612yes—
196C2×C4×C13C2×SD1612yes—
197C2×C4×C13C23×C411yescharacteristic
198C2×C4×C13C22×Q811yescharacteristic
199C2×C4×C13C2×#4111yescharacteristic
200C2×C4×C13C2×#4111yescharacteristic
201C2×C4×C13C2×#4111yescharacteristic
202C2×C4×C13C2×#4111yescharacteristic
203C2×Dic13—21no—
204C2×Dic13—21no—
205C2×Dic13—21no—
206C2×Dic13—21no—
207C2×Dic13—22no—
208C2×Dic13—22no—
209C2×Dic13—41no—
210C2×Dic13—41no—
211C2×Dic13—41no—
212C2×Dic13—41no—
213C2×Dic13—42no—
214C2×Dic13—42no—
215C2×Dic13—42no—
216C2×Dic13C2×C4⋊C412yes—
217C2×Dic13C2×C4⋊C412yes—
218C2×Dic13C2×C4⋊C412yes—
219C2×Dic13C2×SD1612yes—
220C2×Dic13C2×SD1612yes—
221C4×D13—22no—
222C4×D13—22no—
223C4×D13—22no—
224C4×D13—22no—
225C4×D13—44no—
226C4×D13—48no—
227C4×D13—48no—
228C4×D13#106116yescomplemented
229C8×C13—24no—
230#1055—24no—
231C2×#117—261no—
232C22×C4⋊C4—131no—
233C22×C4⋊C4—131no—
234C22×C42—131no—
235C22×C42—261no—
236#431—138no—
237C2×#106—132no—
238C2×#106—132no—
239C2×#106—132no—
240C2×#106C2×D1312yes—
241C2×C4⋊C8—131no—
242C2×C4⋊C8C2×D1311yescharacteristic
243C2×C22⋊C8—132no—
244C2×C4×C8—132no—
245#384—131no—
246#384C2×D1311yescharacteristic
247#382—261no—
248#380—132no—
249#380—261no—
250C4×C4⋊C4—131no—
251C4×C4⋊C4—131no—
252C4×C4⋊C4—132no—
253C4×C4⋊C4—131no—
254C4×C4⋊C4—261no—
255C4×C4⋊C4—261no—
256C4×C4⋊C4—261no—
257C4×C4⋊C4C2×D1311yescharacteristic
258C2×#95—261no—
259#340—132no—
260#340—132no—
261#340—132no—
262#340C2×D1312yes—
263C22×C13C22×C4⋊C411yescharacteristic
264C22×C13#52511yescharacteristic
265C22×C13#52511yescharacteristic
266C22×C13C22×SD1611yescharacteristic
267C22×C13C22×SD1611yescharacteristic
268C22×C13#57511yescharacteristic
269C22×C13#57511yescharacteristic
270C2×D13—22no—
271C2×D13—22no—
272C2×D13—22no—
273C2×D13—22no—
274C2×D13—22no—
275C2×D13—22no—
276C2×D13C2×#10614yes—
277C4×C13—22no—
278C4×C13—42no—
279C4×C13—42no—
280C4×C13—82no—
281C4×C13C2×#10614yes—
282C4×C13C4×#4111yescharacteristic
283C4×C13C4×#4111yescharacteristic
284C4×C13#53311yescharacteristic
285C4×C13#53311yescharacteristic
286Dic13—22no—
287Dic13—22no—
288Dic13—42no—
289Dic13—42no—
290Dic13—82no—
291Dic13C2×#10614yes—
292C23×C4—131no—
293C23×C4—131no—
294C23×C4—131no—
295C23×C4—261no—
296C23×C4—261no—
297C22×C8—132no—
298C22×C8C22×D1312yes—
299#117—524no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—131no—
303C2×C4⋊C4—131no—
304C2×C4⋊C4—132no—
305C2×C4⋊C4—262no—
306C2×C4⋊C4—262no—
307C2×C4⋊C4—261no—
308C2×C4⋊C4—261no—
309C2×C4⋊C4—262no—
310C2×C4⋊C4—262no—
311C2×C4⋊C4—261no—
312C2×C4⋊C4—261no—
313C2×C4⋊C4C22×D1312yes—
314C2×C4⋊C4C22×D1311yescharacteristic
315C2×C4⋊C4C22×D1311yescharacteristic
316C2×C22⋊C4—262no—
317C2×C42—21no—
318C2×C42—131no—
319C2×C42—131no—
320C2×C42—131no—
321C2×C42—134no—
322C2×C42—134no—
323C2×C42—262no—
324C2×C42—261no—
325C2×C42—261no—
326C2×C42—261no—
327C2×C42—524no—
328C2×C42C22×D1311yescharacteristic
329#106—24no—
330#106—264no—
331#106—264no—
332#106—264no—
333C4⋊C8—134no—
334C4⋊C8C4×D1314yescomplemented
335C22⋊C8—138no—
336C4×C8—138no—
337#95—21no—
338#95—261no—
339#95—261no—
340#95—262no—
341#95—262no—
342#95—261no—
343C2×C13#229611yescharacteristic
344C2×C13C22×#10611yescharacteristic
345C2×C13#291111yescharacteristic
346C2×C13#310111yescharacteristic
347C2×C13#310111yescharacteristic
348C2×C13#310311yescharacteristic
349C2×C13#310311yescharacteristic
350D13—24no—
351C24—131no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—131no—
356C22×C4—134no—
357C22×C4—134no—
358C22×C4—134no—
359C22×C4—131no—
360C22×C4—131no—
361C22×C4—132no—
362C22×C4—132no—
363C22×C4—134no—
364C22×C4—264no—
365C22×C4—264no—
366C22×C4—261no—
367C22×C4—261no—
368C22×C4—261no—
369C22×C4—261no—
370C22×C4—261no—
371C22×C4—261no—
372C22×C4—262no—
373C22×C4—521no—
374C22×C4—521no—
375C22×C4—522no—
376C22×C4—522no—
377C22×C4—522no—
378C22×C4—522no—
379C22×C4D4×D1311yescharacteristic
380C22×C4D4×D1311yescharacteristic
381C22×C4C23×D1311yescharacteristic
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—134no—
385C2×C8—262no—
386C2×C8—262no—
387C2×C8C2×C4×D1314yes—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—42no—
393C4⋊C4—42no—
394C4⋊C4—132no—
395C4⋊C4—132no—
396C4⋊C4—264no—
397C4⋊C4—264no—
398C4⋊C4—261no—
399C4⋊C4—261no—
400C4⋊C4—262no—
401C4⋊C4—262no—
402C4⋊C4—522no—
403C4⋊C4—522no—
404C4⋊C4#612912yes—
405C4⋊C4#613112yes—
406C22⋊C4—524no—
407C42—42no—
408C42—134no—
409C42—134no—
410C42—132no—
411C42—132no—
412C42—522no—
413C42—522no—
414C42—524no—
415C42—522no—
416C42C2×C4×D1312yes—
417C42Q8×D1312yes—
418C13#2135911yescharacteristic, complemented, Sylow
419C23—132no—
420C23—132no—
421C23—132no—
422C23—261no—
423C23—261no—
424C23—261no—
425C23—261no—
426C23C2×D4×D1311yescharacteristic
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—132no—
439C2×C4—132no—
440C2×C4—132no—
441C2×C4—1316no—
442C2×C4—132no—
443C2×C4—132no—
444C2×C4—261no—
445C2×C4—261no—
446C2×C4—261no—
447C2×C4—261no—
448C2×C4—262no—
449C2×C4—262no—
450C2×C4—262no—
451C2×C4—262no—
452C2×C4—262no—
453C2×C4—262no—
454C2×C4—524no—
455C2×C4—528no—
456C2×C4—528no—
457C2×C4—521no—
458C2×C4—521no—
459C2×C4—521no—
460C2×C4—521no—
461C2×C4—522no—
462C2×C4—522no—
463C2×C4—522no—
464C2×C4C4⋊C4×D1312yes—
465C2×C4C4⋊C4×D1312yes—
466C2×C4SD16×D1312yes—
467C2×C4SD16×D1312yes—
468C2×C4C22×C4×D1311yescharacteristic
469C2×C4C2×#612911yescharacteristic
470C2×C4C2×Q8×D1311yescharacteristic
471C2×C4C2×#613111yescharacteristic
472C2×C4#41×D1311yescharacteristic
473C2×C4#41×D1311yescharacteristic
474C8—24no—
475C8—264no—
476C22—134no—
477C22—262no—
478C22—262no—
479C22—262no—
480C22—262no—
481C22—262no—
482C22—262no—
483C22C2×C4⋊C4×D1311yescharacteristic
484C22#1171931111yescharacteristic
485C22#1171933211yescharacteristic
486C22C2×SD16×D1311yescharacteristic
487C22C2×SD16×D1311yescharacteristic
488C22#1171947811yescharacteristic
489C22#1171948211yescharacteristic
490C4—22no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—134no—
495C4—262no—
496C4—262no—
497C4—522no—
498C4—522no—
499C4—1042no—
500C4D13×#10614yes—
501C4C4×#612911yescharacteristic
502C4C4×#613111yescharacteristic
503C4#1171939311yescharacteristic
504C4#1171943311yescharacteristic
505C2—264no—
506C2#1311731711yescharacteristic
507C2C2×D13×#10611yescharacteristic
508C2#1312342311yescharacteristic
509C2#1312484311yescharacteristic
510C2#1312484611yescharacteristic
511C2#1312486611yescharacteristic
512C2#1312486911yescharacteristic
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#21359
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. #106×Dic13C2semidirect
10. #13114724C2semidirect
11. C13×#1948C2semidirect
37. #11718494C4semidirect
82. C13×C4⋊C8C2×C4semidirect
91. C8×Dic13C2×C4semidirect
94. C4⋊#1055C2×C4semidirect
169. #1948D13semidirect
228. C4×D13#106semidirect
334. C4⋊C8C4×D13semidirect
418. C13#21359semidirect

Maximal subgroups

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

subgroupindex
C2×#117184942
#131172412
C4×C4⋊C4×D132
#131156002
#131155992
#131155972
#131150302
#131150272
#106×Dic132
#131147242
C13×#19482
#2135913