Finite Group Databasebeta

← C2×#13116041 #15890393

Subgroups — C2×#13116041 #15890393

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×#88151C211yesmaximal, characteristic
2C22×#88056C211yesmaximal, characteristic, complemented
3C22×#88050C211yesmaximal, characteristic, complemented
4C22×#88060C211yesmaximal, characteristic
5C2×#11718648C211yesmaximal, characteristic
6#13116041C218yesmaximal, direct product factor
7C2×#11718121C211yesmaximal, characteristic, complemented
8C22×C13×#107C211yesmaximal, characteristic, complemented
9C23×C4×D13C2211yescharacteristic
10C23×Dic26C2211yescharacteristic
11C23×C8×C13C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×#6103—21no—
15C22×#6103—21no—
16C22×C4⋊Dic13—21no—
17C22×C4⋊Dic13C2211yescharacteristic
18C23×#1055C2211yescharacteristic
19C2×#88151—22no—
20C2×#88151—24no—
21C2×#88151—24no—
22C2×#88151C2214yes—
23C2×C13×#107—24no—
24C2×C13×#107C2214yescomplemented
25C2×#88071—21no—
26C2×#88060—24no—
27C2×#88060C2214yes—
28C2×#88056—24no—
29C2×#88056C2214yescomplemented
30#11718648—22no—
31#11718648C2214yes—
32C2×#88050—24no—
33C2×#88050C2214yescomplemented
34#11718121C2214yescomplemented
35C24×D13D411yescharacteristic
36C23×C4×C13—21no—
37C23×C4×C13—21no—
38C23×C4×C13C2311yescharacteristic
39C23×Dic13—21no—
40C23×Dic13—21no—
41C23×Dic13D411yescharacteristic
42C22×C4×D13—22no—
43C22×C4×D13—22no—
44C22×C4×D13—22no—
45C22×C4×D13—22no—
46C22×C4×D13—22no—
47C22×C4×D13—22no—
48C22×C4×D13D412yes—
49C22×C4×D13C2312yes—
50C22×Dic26—22no—
51C22×Dic26—22no—
52C22×Dic26—22no—
53C22×Dic26—22no—
54C22×Dic26—21no—
55C22×Dic26—22no—
56C22×Dic26D414yes—
57C22×Dic26C2312yes—
58C22×C8×C13—22no—
59C22×C8×C13—22no—
60C22×C8×C13D414yes—
61C22×C8×C13C2312yes—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4D414yes—
68C2×C13×C4⋊C4C2312yes—
69C2×C13×C4⋊C4C2312yes—
70C2×#6103—28no—
71C2×#6103—24no—
72C2×#6103—24no—
73C2×#6103—44no—
74C2×C4⋊Dic13—28no—
75C2×C4⋊Dic13—24no—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13C2312yes—
80C22×#1055—22no—
81C22×#1055—22no—
82C22×#1055—22no—
83C22×#1055C2312yes—
84#88151—216no—
85#88151—28no—
86#88151—28no—
87C13×#107—28no—
88#88071—24no—
89#88060—28no—
90#88056—28no—
91#88050—28no—
92C2×#2036—131nomaximal, Sylow
93C24×C13C2×D411yescharacteristic
94C23×D13—22no—
95C23×D13—22no—
96C23×D13—22no—
97C23×D13—22no—
98C23×D13—22no—
99C23×D13—22no—
100C23×D13Q1614yes—
101C23×D13C2×D412yes—
102C22×C4×C13—24no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—42no—
106C22×C4×C13—42no—
107C22×C4×C13—42no—
108C22×C4×C13—42no—
109C22×C4×C13—42no—
110C22×C4×C13C2×D412yes—
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D412yes—
113C22×C4×C13C2×D412yes—
114C22×C4×C13#4112yes—
115C22×C4×C13#4112yes—
116C22×C4×C13#4112yes—
117C22×C4×C13C2411yescharacteristic
118C22×Dic13—22no—
119C22×Dic13—24no—
120C22×Dic13—22no—
121C22×Dic13—22no—
122C22×Dic13—22no—
123C22×Dic13—22no—
124C22×Dic13—42no—
125C22×Dic13—42no—
126C22×Dic13—42no—
127C22×Dic13—42no—
128C22×Dic13—42no—
129C22×Dic13C2×D412yes—
130C2×C4×D13—24no—
131C2×C4×D13—24no—
132C2×C4×D13—24no—
133C2×C4×D13—22no—
134C2×C4×D13—22no—
135C2×C4×D13—22no—
136C2×C4×D13—22no—
137C2×C4×D13—22no—
138C2×C4×D13—22no—
139C2×C4×D13—44no—
140C2×C4×D13—44no—
141C2×C4×D13—44no—
142C2×C4×D13—44no—
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—
156C2×C8×C13—28no—
157C2×C8×C13—22no—
158C2×C8×C13—22no—
159C2×C8×C13C2×D414yes—
160C13×C4⋊C4—24no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—42no—
165C13×C4⋊C4C2×D414yes—
166#6103—216no—
167#6103—48no—
168C4⋊Dic13—216no—
169C4⋊Dic13—22no—
170C4⋊Dic13—22no—
171C4⋊Dic13—42no—
172C2×#1055—22no—
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#1055—44no—
176C22×C22⋊Q8—131no—
177C22×#107D1311yescharacteristic, complemented
178C22×#103—131no—
179C22×#103—131no—
180C22×C22⋊C8—131no—
181C2×#380—131no—
182#2036—138no—
183C2×#340—131no—
184C23×C13#12012yes—
185C23×C13#12112yes—
186C23×C13#12312yes—
187C23×C13C2×Q1612yes—
188C23×C13#13512yes—
189C23×C13AGL(1,ℤ/8)12yes—
190C23×C13#13712yes—
191C23×C13C22×D411yescharacteristic
192C22×D13—22no—
193C22×D13—22no—
194C22×D13—22no—
195C22×D13—22no—
196C22×D13—22no—
197C22×D13—22no—
198C22×D13—28no—
199C22×D13—28no—
200C22×D13—28no—
201C22×D13—44no—
202C22×D13—44no—
203C22×D13—44no—
204C22×D13—44no—
205C22×D13C2×Q1614yes—
206C2×C4×C13—24no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—48no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—84no—
214C2×C4×C13#12012yes—
215C2×C4×C13#12114yes—
216C2×C4×C13#12114yes—
217C2×C4×C13#12112yes—
218C2×C4×C13#12314yes—
219C2×C4×C13#12312yes—
220C2×C4×C13#12414yes—
221C2×C4×C13C22×D411yescharacteristic
222C2×C4×C13C22×D411yescharacteristic
223C2×C4×C13C22×D411yescharacteristic
224C2×C4×C13C2×#4111yescharacteristic
225C2×C4×C13C2×#4111yescharacteristic
226C2×C4×C13C2×#4111yescharacteristic
227C2×Dic13—22no—
228C2×Dic13—24no—
229C2×Dic13—22no—
230C2×Dic13—22no—
231C2×Dic13—42no—
232C2×Dic13—42no—
233C2×Dic13—48no—
234C2×Dic13—44no—
235C2×Dic13—42no—
236C2×Dic13—42no—
237C2×Dic13—42no—
238C2×Dic13—84no—
239C4×D13—42no—
240C4×D13—42no—
241C4×D13—42no—
242C4×D13—42no—
243C4×D13—48no—
244Dic26—24no—
245Dic26—24no—
246Dic26—42no—
247Dic26—42no—
248Dic26—48no—
249C8×C13—24no—
250#1055—42no—
251C23×Q8—131no—
252C24×C4—131no—
253C23×C8—131no—
254C23×C8C2×D1311yescharacteristic
255C2×C22⋊Q8—134no—
256C2×C22⋊Q8—262no—
257C2×C22⋊Q8—264no—
258C2×C22⋊Q8—264no—
259C22×C4⋊C4—131no—
260C22×C4⋊C4—261no—
261C22×C4⋊C4C2×D1311yescharacteristic
262C22×C4⋊C4C2×D1311yescharacteristic
263C22×C22⋊C4—261no—
264C22×C22⋊C4—261no—
265C2×#107—24no—
266C2×#107C2×D1314yescomplemented
267C2×#103—134no—
268C2×#103—134no—
269C2×#103—264no—
270C2×#103—264no—
271C2×C22⋊C8—134no—
272C2×C22⋊C8—264no—
273#380—134no—
274#380—262no—
275C2×#95—261no—
276#340—134no—
277C22×C13#39414yes—
278C22×C13#44914yes—
279C22×C13#45114yes—
280C22×C13#46714yes—
281C22×C13#46814yes—
282C22×C13#48414yes—
283C22×C13#48514yes—
284C22×C13C2×#12011yescharacteristic
285C22×C13C2×#12111yescharacteristic
286C22×C13C2×#12311yescharacteristic
287C22×C13C22×Q1611yescharacteristic
288C22×C13C2×#13511yescharacteristic
289C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C13C2×#13711yescharacteristic
291C2×D13—24no—
292C2×D13—24no—
293C2×D13—24no—
294C2×D13—42no—
295C2×D13—42no—
296C2×D13—42no—
297C2×D13—42no—
298C2×D13—416no—
299C4×C13—44no—
300C4×C13—82no—
301C4×C13#39414yes—
302C4×C13C2×#12111yescharacteristic
303C4×C13C2×#12111yescharacteristic
304C4×C13C2×#12311yescharacteristic
305C4×C13C2×#12411yescharacteristic
306Dic13—44no—
307Dic13—42no—
308Dic13—82no—
309C25—131no—
310C22×Q8—134no—
311C22×Q8—132no—
312C22×Q8—261no—
313C22×Q8—262no—
314C22×Q8—262no—
315C22×Q8—262no—
316C22×Q8—262no—
317C22×Q8—262no—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—131no—
321C23×C4—132no—
322C23×C4—132no—
323C23×C4—261no—
324C23×C4—262no—
325C23×C4—262no—
326C23×C4—262no—
327C23×C4—262no—
328C23×C4—262no—
329C23×C4—262no—
330C23×C4—261no—
331C23×C4C22×D1311yescharacteristic
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—132no—
335C22×C8—262no—
336C22×C8—262no—
337C22×C8—262no—
338C22×C8D5214yes—
339C22×C8C22×D1312yes—
340C22⋊Q8—268no—
341C22⋊Q8—2616no—
342C22⋊Q8—268no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—132no—
349C2×C4⋊C4—264no—
350C2×C4⋊C4—268no—
351C2×C4⋊C4—262no—
352C2×C4⋊C4—262no—
353C2×C4⋊C4—261no—
354C2×C4⋊C4C22⋊D1314yes—
355C2×C4⋊C4C22×D1312yes—
356C2×C4⋊C4C22×D1312yes—
357C2×C22⋊C4—264no—
358C2×C22⋊C4—268no—
359C2×C22⋊C4—264no—
360C2×C22⋊C4—524no—
361#107—28no—
362#103—268no—
363#103—268no—
364C22⋊C8—268no—
365#95—264no—
366C2×C13#203618yescomplemented
367C2×C13C2×#39411yescharacteristic
368C2×C13C2×#45111yescharacteristic
369C2×C13C2×#44911yescharacteristic
370C2×C13C2×#46711yescharacteristic
371C2×C13C2×#46811yescharacteristic
372C2×C13C2×#48511yescharacteristic
373C2×C13C2×#48411yescharacteristic
374D13—44no—
375C24—134no—
376C24—132no—
377C24—262no—
378C24—262no—
379C24—262no—
380C24—262no—
381C24—262no—
382C24—262no—
383C24D4×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—522no—
394C2×Q8—522no—
395C2×Q8—524no—
396C2×Q8—524no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—132no—
406C22×C4—262no—
407C22×C4—262no—
408C22×C4—264no—
409C22×C4—262no—
410C22×C4—262no—
411C22×C4—264no—
412C22×C4—264no—
413C22×C4—264no—
414C22×C4—262no—
415C22×C4—262no—
416C22×C4—262no—
417C22×C4—262no—
418C22×C4—262no—
419C22×C4—262no—
420C22×C4—262no—
421C22×C4—522no—
422C22×C4—522no—
423C22×C4—524no—
424C22×C4—524no—
425C22×C4—524no—
426C22×C4—524no—
427C22×C4—522no—
428C22×C4—522no—
429C22×C4—522no—
430C22×C4C2×D5212yes—
431C22×C4#612712yes—
432C22×C4D4×D1311yescharacteristic
433C22×C4D4×D1312yes—
434C22×C4#613112yes—
435C22×C4#613112yes—
436C22×C4C2×C22⋊D1312yes—
437C22×C4C23×D1311yescharacteristic
438C2×C8—28no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—262no—
442C2×C8—262no—
443C2×C8—262no—
444C2×C8—524no—
445C2×C8C2×D5214yes—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—42no—
451C4⋊C4—2616no—
452C4⋊C4—262no—
453C4⋊C4—262no—
454C4⋊C4—522no—
455C4⋊C4C2×C22⋊D1314yes—
456C22⋊C4—2616no—
457C22⋊C4—528no—
458C13C2×#203611yescharacteristic, complemented, Sylow
459C23—134no—
460C23—262no—
461C23—262no—
462C23—262no—
463C23—262no—
464C23—262no—
465C23—262no—
466C23—268no—
467C23—268no—
468C23—268no—
469C23—524no—
470C23—524no—
471C23—524no—
472C23—524no—
473C23#8814812yes—
474C23#8814912yes—
475C23#8816512yes—
476C23#8816612yes—
477C23Q16×D1312yes—
478C23#8817212yes—
479C23#8819112yes—
480C23C2×D4×D1311yescharacteristic
481Q8—264no—
482Q8—264no—
483Q8—522no—
484Q8—522no—
485Q8—528no—
486C2×C4—24no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—48no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—84no—
494C2×C4—262no—
495C2×C4—262no—
496C2×C4—264no—
497C2×C4—262no—
498C2×C4—522no—
499C2×C4—522no—
500C2×C4—524no—
501C2×C4—528no—
502C2×C4—522no—
503C2×C4—522no—
504C2×C4—522no—
505C2×C4—522no—
506C2×C4—528no—
507C2×C4—522no—
508C2×C4—522no—
509C2×C4—522no—
510C2×C4—1044no—
511C2×C4#8814814yes—
512C2×C4#8814812yes—
513C2×C4#8814914yes—
514C2×C4#8814912yes—
515C2×C4#8818414yes—
516C2×C4#8819112yes—
517C2×C4#8820114yes—
518C2×C4C22×D5211yescharacteristic
519C2×C4C2×#612711yescharacteristic
520C2×C4C2×D4×D1311yescharacteristic
521C2×C4C2×#613111yescharacteristic
522C2×C4C2×#613111yescharacteristic
523C2×C4C22×C22⋊D1311yescharacteristic
524C8—24no—
525C8—522no—
526C22—264no—
527C22—264no—
528C22—264no—
529C22—522no—
530C22—522no—
531C22—522no—
532C22—5216no—
533C22—522no—
534C22#1171854514yes—
535C22#1171854714yes—
536C22#1171854814yes—
537C22#1171854914yes—
538C22#1171865214yes—
539C22#1171881914yes—
540C22#1171884714yes—
541C22C2×#8814811yescharacteristic
542C22C2×#8814911yescharacteristic
543C22C2×#8816511yescharacteristic
544C22C2×#8816611yescharacteristic
545C22C2×Q16×D1311yescharacteristic
546C22C2×#8817211yescharacteristic
547C22C2×#8819111yescharacteristic
548C4—44no—
549C4—82no—
550C4—522no—
551C4—524no—
552C4—1042no—
553C4#1171865214yes—
554C4C2×#8814811yescharacteristic
555C4C2×#8814911yescharacteristic
556C4C2×#8818411yescharacteristic
557C4C2×#8820111yescharacteristic
558C2—524no—
559C2#1311604118yesdirect product factor
560C2C2×#1171865211yescharacteristic
561C2C2×#1171884711yescharacteristic
562C2C2×#1171881911yescharacteristic
563C2C2×#1171854811yescharacteristic
564C2C2×#1171854711yescharacteristic
565C2C2×#1171854911yescharacteristic
566C2C2×#1171854511yescharacteristic
subgroupG/H
centerC24D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×#107C2
socleC24×C13C2×D4
prime radicalC24×D13D4
hypercenterC22×#107D13
hypocenterC13C2×#2036
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. C22×#88056C2semidirect
3. C22×#88050C2semidirect
6. #13116041C2direct (N × H)
7. C2×#11718121C2semidirect
8. C22×C13×#107C2semidirect
24. C2×C13×#107C22semidirect
29. C2×#88056C22semidirect
33. C2×#88050C22semidirect
34. #11718121C22semidirect
177. C22×#107D13semidirect
266. C2×#107C2×D13semidirect
366. C2×C13#2036semidirect
458. C13C2×#2036semidirect
559. C2#13116041direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881512
C22×#880562
C22×#880502
C22×#880602
C2×#117186482
#131160412
C2×#117181212
C22×C13×#1072
C2×#203613