Finite Group Databasebeta

← C2×#13116039 #15890391

Subgroups — C2×#13116039 #15890391

Order 3328.

1662 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88178C211yesmaximal, characteristic
2C22×#88047C211yesmaximal, characteristic, complemented
3C22×#88050C211yesmaximal, characteristic, complemented
4C22×#88050C211yesmaximal, characteristic, complemented
5C22×C22⋊#1055C211yesmaximal, characteristic
6#13116039C218yesmaximal, direct product factor
7C2×#11718121C211yesmaximal, characteristic, complemented
8C2×C13×#380C211yesmaximal, characteristic
9C24×C4×C13C2211yescharacteristic
10C23×Dic26C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C22⋊C4—21no—
14C22×C22⋊Dic13—21no—
15C22×C4⋊Dic13C2211yescharacteristic
16C2×#88178—22no—
17C2×#88178—24no—
18C2×#88178—24no—
19C2×#88178C2214yes—
20C22×#6101—21no—
21C23×#1055C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C13×#380—22no—
24C13×#380C2214yes—
25C2×C13×#95—21no—
26C2×C22⋊#1055—24no—
27C2×C22⋊#1055C2214yes—
28C2×#88050—24no—
29C2×#88050—24no—
30C2×#88050C2214yescomplemented
31C2×#88050C2214yescomplemented
32C2×#88047—24no—
33C2×#88047C2214yescomplemented
34#11718121C2214yescomplemented
35C25×C13D411yescharacteristic
36C23×C4×C13—22no—
37C23×C4×C13—22no—
38C23×C4×C13—22no—
39C23×C4×C13—22no—
40C23×C4×C13—22no—
41C23×C4×C13—22no—
42C23×C4×C13—21no—
43C23×C4×C13—21no—
44C23×C4×C13D412yes—
45C23×C4×C13D411yescharacteristic
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C23×Dic13—21no—
49C23×Dic13—21no—
50C22×Dic26—22no—
51C22×Dic26—22no—
52C22×Dic26—22no—
53C22×Dic26—22no—
54C22×Dic26—22no—
55C22×Dic26—21no—
56C22×Dic26D414yes—
57C22×Dic26C2312yes—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4C2312yes—
65C2×C13×C4⋊C4C2312yes—
66C2×C13×C22⋊C4—24no—
67C2×C13×C22⋊C4—44no—
68C2×C22⋊Dic13—28no—
69C2×C22⋊Dic13—24no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13D414yes—
73C2×C4⋊Dic13C2312yes—
74#88178—216no—
75#88178—28no—
76#88178—28no—
77C2×#6101—28no—
78C2×#6101—24no—
79C22×#1055—22no—
80C22×#1055—22no—
81C22×#1055—22no—
82C22×#1055—22no—
83C22×#1055—22no—
84C22×#1055D414yes—
85C22×#1055C2312yes—
86C22×#1055C2312yes—
87C13×#95—24no—
88C22⋊#1055—28no—
89#88050—28no—
90#88050—28no—
91#88047—28no—
92C2×#2036—131nomaximal, Sylow
93C24×C13—22no—
94C24×C13—22no—
95C24×C13—22no—
96C24×C13—22no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13Q1614yes—
100C24×C13C2×D412yes—
101C24×C13C2×D411yescharacteristic
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—24no—
106C22×C4×C13—24no—
107C22×C4×C13—24no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—44no—
117C22×C4×C13—44no—
118C22×C4×C13—44no—
119C22×C4×C13—44no—
120C22×C4×C13—42no—
121C22×C4×C13—42no—
122C22×C4×C13—42no—
123C22×C4×C13—42no—
124C22×C4×C13—42no—
125C22×C4×C13—42no—
126C22×C4×C13C2×D412yes—
127C22×C4×C13C2×D412yes—
128C22×C4×C13C2×D412yes—
129C22×C4×C13C2×D412yes—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13#4112yes—
132C22×C4×C13#4112yes—
133C22×C4×C13#4112yes—
134C22×C4×C13C2411yescharacteristic
135C22×Dic13—24no—
136C22×Dic13—24no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—42no—
140C22×Dic13—42no—
141C22×Dic13—42no—
142C22×Dic13—42no—
143C2×Dic26—28no—
144C2×Dic26—28no—
145C2×Dic26—22no—
146C2×Dic26—22no—
147C2×Dic26—22no—
148C2×Dic26—22no—
149C2×Dic26—24no—
150C2×Dic26—22no—
151C2×Dic26—44no—
152C2×Dic26—42no—
153C2×Dic26—42no—
154C2×Dic26—44no—
155C2×Dic26C2×D414yes—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4—42no—
162C13×C22⋊C4—48no—
163C22⋊Dic13—216no—
164C4⋊Dic13—24no—
165C4⋊Dic13—22no—
166C4⋊Dic13C2×D414yes—
167#6101—216no—
168C2×#1055—28no—
169C2×#1055—22no—
170C2×#1055—22no—
171C2×#1055—22no—
172C2×#1055—22no—
173C2×#1055—22no—
174C2×#1055—44no—
175C2×#1055C2×D414yes—
176C22×C22⋊Q8—131no—
177C22×#107—131no—
178C22×#103—131no—
179C22×#103—131no—
180C22×C22⋊C8—131no—
181C2×#380D1311yescharacteristic
182#2036—138no—
183C2×#340—131no—
184C23×C13—22no—
185C23×C13—22no—
186C23×C13—22no—
187C23×C13—22no—
188C23×C13—22no—
189C23×C13—22no—
190C23×C13—28no—
191C23×C13—28no—
192C23×C13—28no—
193C23×C13—44no—
194C23×C13—44no—
195C23×C13—44no—
196C23×C13—44no—
197C23×C13#12012yes—
198C23×C13#12112yes—
199C23×C13#12312yes—
200C23×C13C2×Q1614yes—
201C23×C13C2×Q1612yes—
202C23×C13#13512yes—
203C23×C13AGL(1,ℤ/8)12yes—
204C23×C13#13712yes—
205C23×C13C22×D411yescharacteristic
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—44no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—42no—
214C2×C4×C13—48no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—84no—
222C2×C4×C13—84no—
223C2×C4×C13#12012yes—
224C2×C4×C13#12114yes—
225C2×C4×C13#12114yes—
226C2×C4×C13#12112yes—
227C2×C4×C13#12314yes—
228C2×C4×C13#12312yes—
229C2×C4×C13#12414yes—
230C2×C4×C13C22×D411yescharacteristic
231C2×C4×C13C22×D411yescharacteristic
232C2×C4×C13C22×D411yescharacteristic
233C2×C4×C13C2×#4111yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×Dic13—24no—
237C2×Dic13—24no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—48no—
243C2×Dic13—48no—
244Dic26—24no—
245Dic26—24no—
246Dic26—42no—
247Dic26—42no—
248Dic26—48no—
249#1055—24no—
250#1055—42no—
251C23×Q8—131no—
252C24×C4C2×D1311yescharacteristic
253C23×C8—131no—
254C23×C8—131no—
255C2×C22⋊Q8—134no—
256C2×C22⋊Q8—264no—
257C2×C22⋊Q8—264no—
258C2×C22⋊Q8—262no—
259C22×C4⋊C4—131no—
260C22×C4⋊C4—261no—
261C22×C4⋊C4C2×D1311yescharacteristic
262C22×C4⋊C4C2×D1311yescharacteristic
263C22×C22⋊C4—21no—
264C22×C22⋊C4—261no—
265C2×#107—134no—
266C2×#107—264no—
267C2×#103—134no—
268C2×#103—134no—
269C2×#103—264no—
270C2×#103—264no—
271C2×C22⋊C8—134no—
272C2×C22⋊C8—264no—
273#380—22no—
274#380C2×D1314yes—
275C2×#95—21no—
276#340—134no—
277C22×C13—24no—
278C22×C13—24no—
279C22×C13—24no—
280C22×C13—42no—
281C22×C13—42no—
282C22×C13—42no—
283C22×C13—42no—
284C22×C13—416no—
285C22×C13#39414yes—
286C22×C13#44914yes—
287C22×C13#45114yes—
288C22×C13#46714yes—
289C22×C13#46814yes—
290C22×C13#48414yes—
291C22×C13#48514yes—
292C22×C13C2×#12011yescharacteristic
293C22×C13C2×#12111yescharacteristic
294C22×C13C2×#12311yescharacteristic
295C22×C13C22×Q1611yescharacteristic
296C22×C13C2×#13511yescharacteristic
297C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C13C2×#13711yescharacteristic
299C4×C13—42no—
300C4×C13—82no—
301C4×C13—82no—
302C4×C13#39414yes—
303C4×C13C2×#12111yescharacteristic
304C4×C13C2×#12111yescharacteristic
305C4×C13C2×#12311yescharacteristic
306C4×C13C2×#12411yescharacteristic
307Dic13—44no—
308Dic13—44no—
309C25C22⋊D1311yescharacteristic
310C22×Q8—134no—
311C22×Q8—132no—
312C22×Q8—262no—
313C22×Q8—261no—
314C22×Q8—262no—
315C22×Q8—262no—
316C22×Q8—262no—
317C22×Q8—262no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4—261no—
327C23×C4—261no—
328C23×C4C22⋊D1312yes—
329C23×C4C22⋊D1311yescharacteristic
330C23×C4C22×D1312yes—
331C23×C4C22×D1311yescharacteristic
332C22×C8—134no—
333C22×C8—132no—
334C22×C8—132no—
335C22×C8—262no—
336C22×C8—262no—
337C22×C8—262no—
338C22×C8—262no—
339C22×C8—262no—
340C22⋊Q8—268no—
341C22⋊Q8—268no—
342C22⋊Q8—2616no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—134no—
350C2×C4⋊C4—132no—
351C2×C4⋊C4—268no—
352C2×C4⋊C4—262no—
353C2×C4⋊C4—261no—
354C2×C4⋊C4—264no—
355C2×C4⋊C4C22×D1312yes—
356C2×C4⋊C4C22×D1312yes—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—268no—
360C2×C22⋊C4—264no—
361#107—268no—
362#103—268no—
363#103—268no—
364C22⋊C8—268no—
365#95—24no—
366C2×C13—44no—
367C2×C13#203618yescomplemented
368C2×C13C2×#39411yescharacteristic
369C2×C13C2×#45111yescharacteristic
370C2×C13C2×#44911yescharacteristic
371C2×C13C2×#46711yescharacteristic
372C2×C13C2×#46811yescharacteristic
373C2×C13C2×#48511yescharacteristic
374C2×C13C2×#48411yescharacteristic
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24#610714yes—
382C24C2×C22⋊D1312yes—
383C24C2×C22⋊D1311yescharacteristic
384C2×Q8—134no—
385C2×Q8—264no—
386C2×Q8—262no—
387C2×Q8—268no—
388C2×Q8—268no—
389C2×Q8—262no—
390C2×Q8—262no—
391C2×Q8—262no—
392C2×Q8—262no—
393C2×Q8—524no—
394C2×Q8—524no—
395C2×Q8—522no—
396C2×Q8—522no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4—44no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—264no—
422C22×C4—264no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—522no—
426C22×C4—522no—
427C22×C4—522no—
428C22×C4—522no—
429C22×C4#612712yes—
430C22×C4#612712yes—
431C22×C4D4×D1312yes—
432C22×C4D4×D1312yes—
433C22×C4D4×D1312yes—
434C22×C4#612912yes—
435C22×C4C2×C22⋊D1312yes—
436C22×C4C2×C22⋊D1311yescharacteristic
437C22×C4C23×D1311yescharacteristic
438C2×C8—134no—
439C2×C8—268no—
440C2×C8—262no—
441C2×C8—262no—
442C2×C8—262no—
443C2×C8—262no—
444C2×C8—262no—
445C2×C8—524no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—42no—
451C4⋊C4—42no—
452C4⋊C4—134no—
453C4⋊C4—2616no—
454C4⋊C4—264no—
455C4⋊C4—262no—
456C22⋊C4—48no—
457C22⋊C4—2616no—
458C13C2×#203611yescharacteristic, complemented, Sylow
459C23—28no—
460C23—28no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—28no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23#8818312yes—
473C23#8818612yes—
474C23#8819112yes—
475C23#8819312yes—
476C23C2×#610714yes—
477C23C2×#610712yes—
478C23#8820412yes—
479C23#8820512yes—
480C23C22×C22⋊D1311yescharacteristic
481Q8—264no—
482Q8—264no—
483Q8—522no—
484Q8—522no—
485Q8—528no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—44no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—48no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—84no—
502C2×C4—84no—
503C2×C4—264no—
504C2×C4—264no—
505C2×C4—528no—
506C2×C4—522no—
507C2×C4—522no—
508C2×C4—522no—
509C2×C4—522no—
510C2×C4—528no—
511C2×C4#8813714yes—
512C2×C4#8813814yes—
513C2×C4#8813814yes—
514C2×C4#8813914yes—
515C2×C4#8818312yes—
516C2×C4#8819112yes—
517C2×C4#8819312yes—
518C2×C4C2×#612711yescharacteristic
519C2×C4C2×#612711yescharacteristic
520C2×C4C2×D4×D1311yescharacteristic
521C2×C4C2×D4×D1311yescharacteristic
522C2×C4C2×D4×D1311yescharacteristic
523C2×C4C2×#612911yescharacteristic
524C8—264no—
525C8—522no—
526C22—24no—
527C22—24no—
528C22—24no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—416no—
533C22—42no—
534C22#1171862014yes—
535C22#1171863114yes—
536C22#1171865714yes—
537C22#1171869814yes—
538C22#1171870314yes—
539C22#1171871114yes—
540C22#1171871214yes—
541C22C2×#8818311yescharacteristic
542C22C2×#8818611yescharacteristic
543C22C2×#8819111yescharacteristic
544C22C2×#8819311yescharacteristic
545C22C22×#610711yescharacteristic
546C22C2×#8820411yescharacteristic
547C22C2×#8820511yescharacteristic
548C4—42no—
549C4—82no—
550C4—82no—
551C4—524no—
552C4—524no—
553C4#1171862014yes—
554C4C2×#8813711yescharacteristic
555C4C2×#8813811yescharacteristic
556C4C2×#8813811yescharacteristic
557C4C2×#8813911yescharacteristic
558C2—44no—
559C2#1311603918yesdirect product factor
560C2C2×#1171862011yescharacteristic
561C2C2×#1171871111yescharacteristic
562C2C2×#1171869811yescharacteristic
563C2C2×#1171871211yescharacteristic
564C2C2×#1171870311yescharacteristic
565C2C2×#1171865711yescharacteristic
566C2C2×#1171863111yescharacteristic
subgroupG/H
centerC24C2×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#380C2
socleC24×C13C2×D4
prime radicalC25×C13D4
hypercenterC2×#380D13
hypocenterC13C2×#2036
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#88047C2semidirect
3. C22×#88050C2semidirect
4. C22×#88050C2semidirect
6. #13116039C2direct (N × H)
7. C2×#11718121C2semidirect
30. C2×#88050C22semidirect
31. C2×#88050C22semidirect
33. C2×#88047C22semidirect
34. #11718121C22semidirect
367. C2×C13#2036semidirect
458. C13C2×#2036semidirect
559. C2#13116039direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881782
C22×#880472
C22×#880502
C22×C22⋊#10552
#131160392
C2×#117181212
C2×C13×#3802
C2×#203613