Finite Group Databasebeta

← C2×#13115030 #15863631

Subgroups — C2×#13115030 #15863631

Order 3328.

1966 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D13C211yesmaximal, characteristic
2C22×#88057C211yesmaximal, characteristic, complemented
3C22×#88048C211yesmaximal, characteristic, complemented
4C22×#88060C211yesmaximal, characteristic
5C2×#11718648C211yesmaximal, characteristic
6#13115030C218yesmaximal, direct product factor
7C2×#11718121C211yesmaximal, characteristic, complemented
8C2×C13×#340C211yesmaximal, characteristic, complemented
9C23×C4×D13—21no—
10C23×C4×D13C2211yescharacteristic
11C23×C8×C13C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×#6103—21no—
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×#6101—21no—
18C23×#1055C2211yescharacteristic
19C2×C4⋊C4×D13—22no—
20C2×C4⋊C4×D13—24no—
21C2×C4⋊C4×D13—24no—
22C2×C4⋊C4×D13C2214yes—
23C2×#88071—21no—
24C2×#88060C418yescomplemented
25C2×#88060C2214yes—
26C2×#88057—24no—
27C2×#88057C2214yescomplemented
28#11718648—22no—
29#11718648C2214yes—
30C2×#88048—24no—
31C2×#88048C2214yescomplemented
32C13×#340C2214yescomplemented
33#11718121C2214yescomplemented
34C24×D13D411yescharacteristic
35C23×C4×C13—21no—
36C23×C4×C13—21no—
37C23×C4×C13C2311yescharacteristic
38C23×Dic13—21no—
39C23×Dic13—21no—
40C23×Dic13D411yescharacteristic
41C22×C4×D13—22no—
42C22×C4×D13—22no—
43C22×C4×D13—22no—
44C22×C4×D13—22no—
45C22×C4×D13—28no—
46C22×C4×D13—24no—
47C22×C4×D13—44no—
48C22×C4×D13—44no—
49C22×C4×D13C2×C414yes—
50C22×C4×D13D412yes—
51C22×C4×D13Q814yes—
52C22×C4×D13C2312yes—
53C22×C8×C13—22no—
54C22×C8×C13—22no—
55C22×C8×C13C2×C414yescomplemented
56C22×C8×C13C2312yes—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4D414yes—
63C2×C13×C4⋊C4C2312yes—
64C2×C13×C4⋊C4C2312yes—
65C2×#6103—24no—
66C2×#6103—44no—
67C2×C4⋊Dic13—22no—
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13D414yes—
73C2×C4⋊Dic13C2312yes—
74C2×C4⋊Dic13C2312yes—
75C2×#6101—28no—
76C2×#6101—24no—
77C22×#1055—22no—
78C22×#1055—22no—
79C22×#1055C2×C414yescomplemented
80C22×#1055C2312yes—
81C4⋊C4×D13—216no—
82C4⋊C4×D13—28no—
83C4⋊C4×D13—28no—
84#88071—24no—
85#88060C2×C4116yescomplemented
86#88057—28no—
87#88048—28no—
88C2×#1853—131nomaximal, Sylow
89C24×C13C2×D411yescharacteristic
90C23×D13—22no—
91C23×D13—22no—
92C23×D13—22no—
93C23×D13—22no—
94C23×D13C4⋊C414yes—
95C23×D13SD1614yes—
96C23×D13SD1614yes—
97C23×D13C2×D412yes—
98C22×C4×C13—24no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—42no—
102C22×C4×C13—42no—
103C22×C4×C13—42no—
104C22×C4×C13—42no—
105C22×C4×C13—42no—
106C22×C4×C13C22×C412yes—
107C22×C4×C13C2×D412yes—
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D412yes—
110C22×C4×C13C2×Q812yes—
111C22×C4×C13#4112yes—
112C22×C4×C13#4112yes—
113C22×C4×C13C2411yescharacteristic
114C22×Dic13—22no—
115C22×Dic13—22no—
116C22×Dic13—24no—
117C22×Dic13—22no—
118C22×Dic13—22no—
119C22×Dic13—42no—
120C22×Dic13—42no—
121C22×Dic13—42no—
122C22×Dic13—42no—
123C22×Dic13—42no—
124C22×Dic13C4⋊C414yes—
125C22×Dic13C2×D412yes—
126C2×C4×D13—28no—
127C2×C4×D13—28no—
128C2×C4×D13—24no—
129C2×C4×D13—28no—
130C2×C4×D13—28no—
131C2×C4×D13—24no—
132C2×C4×D13—22no—
133C2×C4×D13—22no—
134C2×C4×D13—22no—
135C2×C4×D13—22no—
136C2×C4×D13—216no—
137C2×C4×D13—48no—
138C2×C4×D13—432no—
139C2×C4×D13—48no—
140C2×C4×D13C4⋊C418yes—
141C2×C4×D13C22×C414yes—
142C2×C4×D13C2×Q814yes—
143C2×C8×C13—28no—
144C2×C8×C13—22no—
145C2×C8×C13—22no—
146C2×C8×C13C22×C414yescomplemented
147C13×C4⋊C4—24no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—42no—
152C13×C4⋊C4C2×D414yes—
153#6103—48no—
154C4⋊Dic13—24no—
155C4⋊Dic13—22no—
156C4⋊Dic13—22no—
157C4⋊Dic13—22no—
158C4⋊Dic13—42no—
159C4⋊Dic13C2×D414yes—
160#6101—216no—
161C2×#1055—28no—
162C2×#1055—22no—
163C2×#1055—22no—
164C2×#1055C22×C414yescomplemented
165C23×C4⋊C4—131no—
166C22×#106—131no—
167C22×#106—131no—
168C22×C22⋊C8—131no—
169C2×#380—131no—
170#1853—138no—
171C2×#340—131no—
172C2×#340D1311yescharacteristic, complemented
173C23×C13C2×C4⋊C412yes—
174C23×C13#12012yes—
175C23×C13#12312yes—
176C23×C13C2×SD1612yes—
177C23×C13C2×SD1612yes—
178C23×C13AGL(1,ℤ/8)12yes—
179C23×C13#13712yes—
180C23×C13C22×D411yescharacteristic
181C22×D13—22no—
182C22×D13—22no—
183C22×D13—22no—
184C22×D13—22no—
185C22×D13—28no—
186C22×D13—28no—
187C22×D13—28no—
188C22×D13—28no—
189C22×D13—28no—
190C22×D13—28no—
191C22×D13#106116yescomplemented
192C22×D13C2×C4⋊C414yes—
193C22×D13C2×SD1614yes—
194C22×D13C2×SD1614yes—
195C2×C4×C13—24no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—48no—
199C2×C4×C13—42no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—84no—
203C2×C4×C13C2×C4⋊C412yes—
204C2×C4×C13C4×D414yes—
205C2×C4×C13C4×D414yes—
206C2×C4×C13#12012yes—
207C2×C4×C13C22⋊Q814yes—
208C2×C4×C13C22⋊Q814yes—
209C2×C4×C13#12312yes—
210C2×C4×C13C23×C411yescharacteristic
211C2×C4×C13C22×D411yescharacteristic
212C2×C4×C13C22×D411yescharacteristic
213C2×C4×C13C22×Q811yescharacteristic
214C2×C4×C13C2×#4111yescharacteristic
215C2×C4×C13C2×#4111yescharacteristic
216C2×Dic13—22no—
217C2×Dic13—22no—
218C2×Dic13—28no—
219C2×Dic13—24no—
220C2×Dic13—42no—
221C2×Dic13—42no—
222C2×Dic13—48no—
223C2×Dic13—42no—
224C2×Dic13—42no—
225C2×Dic13—42no—
226C2×Dic13—84no—
227C2×Dic13C2×C4⋊C414yes—
228C4×D13—24no—
229C4×D13—24no—
230C4×D13—24no—
231C4×D13—24no—
232C4×D13—216no—
233C4×D13—432no—
234C8×C13—24no—
235#1055—24no—
236C24×C4—131no—
237C24×C4—261no—
238C23×C8—131no—
239C23×C8C2×D1311yescharacteristic
240C22×C4⋊C4—131no—
241C22×C4⋊C4—131no—
242C22×C4⋊C4—134no—
243C22×C4⋊C4—264no—
244C22×C4⋊C4—262no—
245C22×C4⋊C4—261no—
246C22×C4⋊C4—264no—
247C22×C4⋊C4C2×D1311yescharacteristic
248C22×C4⋊C4C2×D1311yescharacteristic
249C22×C22⋊C4—261no—
250C2×#106—134no—
251C2×#106—134no—
252C2×#106—264no—
253C2×#106—264no—
254C2×C22⋊C8—138no—
255C2×C22⋊C8—134no—
256#380—134no—
257#380—262no—
258C2×#95—261no—
259#340—134no—
260#340C2×D1314yescomplemented
261C22×C13#38514yes—
262C22×C13C2×#10614yes—
263C22×C13#42814yes—
264C22×C13#44814yes—
265C22×C13#45014yes—
266C22×C13#48114yes—
267C22×C13#48314yes—
268C22×C13C22×C4⋊C411yescharacteristic
269C22×C13C2×#12011yescharacteristic
270C22×C13C2×#12311yescharacteristic
271C22×C13C22×SD1611yescharacteristic
272C22×C13C22×SD1611yescharacteristic
273C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C13C2×#13711yescharacteristic
275C2×D13—24no—
276C2×D13—24no—
277C2×D13—232no—
278C2×D13—24no—
279C2×D13—24no—
280C2×D13—24no—
281C2×D13—24no—
282C2×D13C2×#10618yescomplemented
283C4×C13—44no—
284C4×C13—82no—
285C4×C13#38514yes—
286C4×C13C2×C4×D411yescharacteristic
287C4×C13C2×C4×D411yescharacteristic
288C4×C13C2×C22⋊Q811yescharacteristic
289C4×C13C2×C22⋊Q811yescharacteristic
290Dic13—24no—
291Dic13—44no—
292Dic13—82no—
293C25—131no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—131no—
297C23×C4—134no—
298C23×C4—132no—
299C23×C4—134no—
300C23×C4—132no—
301C23×C4—264no—
302C23×C4—268no—
303C23×C4—262no—
304C23×C4—262no—
305C23×C4—262no—
306C23×C4—262no—
307C23×C4—261no—
308C23×C4—261no—
309C23×C4—524no—
310C23×C4—524no—
311C23×C4C22×D1311yescharacteristic
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—134no—
315C22×C8—132no—
316C22×C8—262no—
317C22×C8—262no—
318C22×C8C4×D1314yescomplemented
319C22×C8C22×D1312yes—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—134no—
326C2×C4⋊C4—132no—
327C2×C4⋊C4—132no—
328C2×C4⋊C4—268no—
329C2×C4⋊C4—2616no—
330C2×C4⋊C4—264no—
331C2×C4⋊C4—268no—
332C2×C4⋊C4—262no—
333C2×C4⋊C4—261no—
334C2×C4⋊C4—268no—
335C2×C4⋊C4—262no—
336C2×C4⋊C4—262no—
337C2×C4⋊C4—261no—
338C2×C4⋊C4D5214yes—
339C2×C4⋊C4C22×D1312yes—
340C2×C4⋊C4C22×D1312yes—
341C2×C22⋊C4—264no—
342C2×C22⋊C4—524no—
343#106—268no—
344#106—268no—
345C22⋊C8—1316no—
346#95—264no—
347C2×C13#185318yescomplemented
348C2×C13C2×#38511yescharacteristic
349C2×C13C22×#10611yescharacteristic
350C2×C13C2×#42811yescharacteristic
351C2×C13C2×#45011yescharacteristic
352C2×C13C2×#44811yescharacteristic
353C2×C13C2×#48311yescharacteristic
354C2×C13C2×#48111yescharacteristic
355D13—28no—
356C24—134no—
357C24—134no—
358C24—134no—
359C24—132no—
360C24—262no—
361C24—262no—
362C24—262no—
363C24—262no—
364C24D4×D1311yescharacteristic
365C22×C4—24no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—134no—
374C22×C4—132no—
375C22×C4—138no—
376C22×C4—134no—
377C22×C4—134no—
378C22×C4—2616no—
379C22×C4—262no—
380C22×C4—262no—
381C22×C4—268no—
382C22×C4—268no—
383C22×C4—264no—
384C22×C4—264no—
385C22×C4—268no—
386C22×C4—268no—
387C22×C4—262no—
388C22×C4—262no—
389C22×C4—262no—
390C22×C4—262no—
391C22×C4—264no—
392C22×C4—262no—
393C22×C4—262no—
394C22×C4—528no—
395C22×C4—528no—
396C22×C4—5232no—
397C22×C4—522no—
398C22×C4—522no—
399C22×C4—522no—
400C22×C4—522no—
401C22×C4—522no—
402C22×C4C2×C4×D1312yes—
403C22×C4C2×D5212yes—
404C22×C4#612712yes—
405C22×C4D4×D1312yes—
406C22×C4D4×D1311yescharacteristic
407C22×C4#612912yes—
408C22×C4Q8×D1312yes—
409C22×C4C23×D1311yescharacteristic
410C2×C8—28no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—134no—
414C2×C8—268no—
415C2×C8—262no—
416C2×C8—262no—
417C2×C8C2×C4×D1314yescomplemented
418C4⋊C4—24no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—42no—
423C4⋊C4—134no—
424C4⋊C4—2616no—
425C4⋊C4—264no—
426C4⋊C4—262no—
427C4⋊C4—262no—
428C4⋊C4—262no—
429C4⋊C4—522no—
430C4⋊C4C2×D5214yes—
431C22⋊C4—528no—
432C13C2×#185311yescharacteristic, complemented, Sylow
433C23—134no—
434C23—134no—
435C23—134no—
436C23—1316no—
437C23—262no—
438C23—262no—
439C23—262no—
440C23—268no—
441C23—268no—
442C23—262no—
443C23—268no—
444C23—268no—
445C23—268no—
446C23—268no—
447C23#8813612yes—
448C23#8813712yes—
449C23C4⋊C4×D1312yes—
450C23#8816512yes—
451C23SD16×D1312yes—
452C23SD16×D1312yes—
453C23#8817212yes—
454C23C2×D4×D1311yescharacteristic
455C2×C4—24no—
456C2×C4—42no—
457C2×C4—48no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—84no—
463C2×C4—134no—
464C2×C4—262no—
465C2×C4—262no—
466C2×C4—268no—
467C2×C4—264no—
468C2×C4—264no—
469C2×C4—264no—
470C2×C4—264no—
471C2×C4—2616no—
472C2×C4—264no—
473C2×C4—5232no—
474C2×C4—522no—
475C2×C4—528no—
476C2×C4—522no—
477C2×C4—522no—
478C2×C4—522no—
479C2×C4—522no—
480C2×C4—1044no—
481C2×C4C4×D5214yes—
482C2×C4#8813514yes—
483C2×C4#8813612yes—
484C2×C4#8813712yes—
485C2×C4C4⋊C4×D1312yes—
486C2×C4#8815014yes—
487C2×C4#8815114yes—
488C2×C4C22×C4×D1311yescharacteristic
489C2×C4C22×D5211yescharacteristic
490C2×C4C2×#612711yescharacteristic
491C2×C4C2×D4×D1311yescharacteristic
492C2×C4C2×#612911yescharacteristic
493C2×C4C2×Q8×D1311yescharacteristic
494C8—24no—
495C8—264no—
496C22—138no—
497C22—264no—
498C22—264no—
499C22—264no—
500C22—264no—
501C22—2632no—
502C22—264no—
503C22—264no—
504C22#1171832914yes—
505C22#1171843714yes—
506C22#1171843814yes—
507C22#1171846614yes—
508C22#1171846714yes—
509C22D13×#10614yes—
510C22#1171854214yes—
511C22C2×#8813611yescharacteristic
512C22C2×#8813711yescharacteristic
513C22C2×C4⋊C4×D1311yescharacteristic
514C22C2×#8816511yescharacteristic
515C22C2×SD16×D1311yescharacteristic
516C22C2×SD16×D1311yescharacteristic
517C22C2×#8817211yescharacteristic
518C4—44no—
519C4—82no—
520C4—264no—
521C4—524no—
522C4—1042no—
523C4#1171832914yes—
524C4C2×C4×D5211yescharacteristic
525C4C2×#8813511yescharacteristic
526C4C2×#8815011yescharacteristic
527C4C2×#8815111yescharacteristic
528C2—268no—
529C2#1311503018yesdirect product factor
530C2C2×#1171832911yescharacteristic
531C2C2×D13×#10611yescharacteristic
532C2C2×#1171854211yescharacteristic
533C2C2×#1171843711yescharacteristic
534C2C2×#1171846711yescharacteristic
535C2C2×#1171846611yescharacteristic
536C2C2×#1171843811yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#340C2
socleC24×C13C2×D4
prime radicalC24×D13D4
cosocleC22×C4×C13C24
hypercenterC2×#340D13
hypocenterC13C2×#1853
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#88057C2semidirect
3. C22×#88048C2semidirect
6. #13115030C2direct (N × H)
7. C2×#11718121C2semidirect
8. C2×C13×#340C2semidirect
24. C2×#88060C4semidirect
27. C2×#88057C22semidirect
31. C2×#88048C22semidirect
32. C13×#340C22semidirect
33. #11718121C22semidirect
55. C22×C8×C13C2×C4semidirect
79. C22×#1055C2×C4semidirect
85. #88060C2×C4semidirect
146. C2×C8×C13C22×C4semidirect
164. C2×#1055C22×C4semidirect
172. C2×#340D13semidirect
191. C22×D13#106semidirect
260. #340C2×D13semidirect
282. C2×D13C2×#106semidirect
318. C22×C8C4×D13semidirect
347. C2×C13#1853semidirect
417. C2×C8C2×C4×D13semidirect
432. C13C2×#1853semidirect
529. C2#13115030direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D132
C22×#880572
C22×#880482
C22×#880602
C2×#117186482
#131150302
C2×#117181212
C2×C13×#3402
C2×#185313