Finite Group Databasebeta

← C2×#13113394 #15830256

Subgroups — C2×#13113394 #15830256

Order 3328.

1366 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719301C211yesmaximal, characteristic
2C2×#11718379C211yesmaximal, characteristic, complemented
3C2×#11718311C211yesmaximal, characteristic, complemented
4#13113394C218yesmaximal, direct product factor
5C2×#11718062C211yesmaximal, characteristic, complemented
6C2×#11718129C211yesmaximal, characteristic, complemented
7C2×#11718043C211yesmaximal, characteristic, complemented
8C2×C13×#327C211yesmaximal, characteristic, complemented
9C22×#6129—21no—
10C2×C13×#121C2211yescharacteristic
11C2×#88194C411yescharacteristic, complemented
12C2×#88193—21no—
13C2×D4×Dic13C411yescharacteristic, complemented
14C2×#88184C2211yescharacteristic
15C22×#6101—21no—
16C22×C4×Dic13C2211yescharacteristic
17#11719301—22no—
18#11719301—22no—
19#11719301C414yescomplemented
20#11719301C2214yes—
21C2×#88147C411yescharacteristic, complemented
22C2×#88142C411yescharacteristic, complemented
23C2×#88139—21no—
24C2×#88135—21no—
25C2×C13×C22⋊C8C2211yescharacteristic
26C2×C13×#95C2211yescharacteristic
27C2×#88071—21no—
28C2×#88071C2211yescharacteristic
29C2×C22⋊#1055C2211yescharacteristic
30C2×#88054—21no—
31C2×C8×Dic13—21no—
32#11718379—22no—
33#11718379C2214yescomplemented
34#11718311—22no—
35#11718311C2214yescomplemented
36C13×#327C2214yescomplemented
37#11718129C2214yescomplemented
38#11718062C2214yescomplemented
39#11718043C2214yescomplemented
40C22×D4×C13—21no—
41C22×D4×C13C2×C411yescharacteristic
42C23×C4×C13—21no—
43C23×C4×C13C2311yescharacteristic
44C22×C22⋊D13—21no—
45C22×C22⋊D13—21no—
46C22×C22⋊D13—21no—
47C23×Dic13—21no—
48C23×Dic13—21no—
49C23×Dic13D411yescharacteristic
50C23×Dic13D411yescharacteristic
51C2×#6129—24no—
52C2×#6129—24no—
53C2×#6129—44no—
54C2×#6129—44no—
55C22×D52C2×C411yescharacteristic
56C22×C4×D13—21no—
57C22×Dic26—21no—
58C22×C8×C13—21no—
59C13×#121—21no—
60C13×#121—21no—
61C13×#121C2×C412yes—
62C13×#121C2312yes—
63C2×C13×C4⋊C4C2×C411yescharacteristic
64C2×C13×C22⋊C4—21no—
65C2×C22⋊Dic13—21no—
66#88194—22no—
67#88194C2×C414yescomplemented
68#88193—24no—
69#88193—24no—
70D4×Dic13—22no—
71D4×Dic13C2×C414yescomplemented
72#88184—21no—
73#88184—21no—
74#88184C2×C412yes—
75#88184C2312yes—
76C2×#6103—21no—
77C2×#6103—21no—
78C2×C4⋊Dic13C2×C411yescharacteristic
79C2×#6101—21no—
80C2×#6101—24no—
81C2×#6101—44no—
82C2×C4×Dic13C2×C411yescharacteristic
83C2×C4×Dic13C2×C411yescharacteristic
84C2×C4×Dic13C2×C412yes—
85C2×C4×Dic13D412yes—
86C2×C4×Dic13D411yescharacteristic
87C2×C4×Dic13D411yescharacteristic
88C2×C4×Dic13D412yes—
89C2×C4×Dic13C2312yes—
90C22×#1055—21no—
91#88147—22no—
92#88147C2×C414yescomplemented
93#88142—22no—
94#88142C2×C414yescomplemented
95#88139—24no—
96#88139—24no—
97#88135—24no—
98#88135—24no—
99C13×C22⋊C8—21no—
100C13×C22⋊C8C2312yes—
101C13×#95—21no—
102C13×#95C2312yes—
103#88071—21no—
104#88071—24no—
105#88071C2312yes—
106C22⋊#1055—21no—
107C22⋊#1055C2312yes—
108#88054—24no—
109C8×Dic13—24no—
110C2×#1517—131nomaximal, Sylow
111C24×C13—21no—
112C24×C13C2×D411yescharacteristic
113C23×D13—21no—
114C2×D4×C13—22no—
115C2×D4×C13—22no—
116C2×D4×C13—21no—
117C2×D4×C13—42no—
118C2×D4×C13—42no—
119C2×D4×C13—42no—
120C2×D4×C13C22×C412yes—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—42no—
124C22×C4×C13—42no—
125C22×C4×C13—42no—
126C22×C4×C13—42no—
127C22×C4×C13C22×C411yescharacteristic
128C22×C4×C13C22×C411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2411yescharacteristic
133C2×C22⋊D13—22no—
134C2×C22⋊D13—22no—
135C2×C22⋊D13—24no—
136C2×C22⋊D13—24no—
137C2×C22⋊D13—44no—
138C2×C22⋊D13—42no—
139C2×C22⋊D13—42no—
140C2×C22⋊D13—44no—
141C22×Dic13—21no—
142C22×Dic13—24no—
143C22×Dic13—22no—
144C22×Dic13—42no—
145C22×Dic13—44no—
146C22×Dic13—42no—
147C22×Dic13—42no—
148C22×Dic13—42no—
149C22×Dic13C22⋊C411yescharacteristic
150C22×Dic13C22⋊C411yescharacteristic
151C22×Dic13C22⋊C412yes—
152C22×Dic13C22⋊C411yescharacteristic
153C22×Dic13C22⋊C411yescharacteristic
154C22×Dic13C22⋊C412yes—
155C22×Dic13D814yes—
156C22×Dic13SD1614yes—
157C22×Dic13C2×D412yes—
158C22×Dic13C2×D412yes—
159#6129—416no—
160#6129—48no—
161#6129—48no—
162C2×D52—21no—
163C2×D52—42no—
164C2×D52C22×C412yes—
165C2×C4×D13—24no—
166C2×C4×D13—44no—
167C2×Dic26—24no—
168C2×Dic26—44no—
169C2×C8×C13—22no—
170C2×C8×C13—42no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4C22×C412yes—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—22no—
175C22⋊Dic13—24no—
176#6103—22no—
177#6103—22no—
178#6103—24no—
179C4⋊Dic13—21no—
180C4⋊Dic13C22×C412yes—
181#6101—24no—
182#6101—48no—
183C4×Dic13C22⋊C412yes—
184C4×Dic13C22⋊C412yes—
185C4×Dic13C22⋊C412yes—
186C4×Dic13C22⋊C412yes—
187C4×Dic13C22×C412yes—
188C4×Dic13C22×C412yes—
189C4×Dic13C2×D412yes—
190C4×Dic13C2×D412yes—
191C2×#1055—22no—
192C2×#1055—42no—
193C2×#532—131no—
194C2×#431—131no—
195C2×#382—131no—
196#1517—138no—
197C2×#327—131no—
198C2×#327—131no—
199C2×#327—131no—
200C2×#327D1311yescharacteristic, complemented
201C23×C13—22no—
202C23×C13—22no—
203C23×C13—22no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13C2×C22⋊C411yescharacteristic
208C23×C13C2×C22⋊C411yescharacteristic
209C23×C13C2×D812yes—
210C23×C13C2×SD1612yes—
211C23×C13C22×D411yescharacteristic
212C22×D13—22no—
213C22×D13—42no—
214C22×D13—42no—
215C22×D13—42no—
216D4×C13—42no—
217D4×C13—42no—
218D4×C13—42no—
219D4×C13—42no—
220D4×C13—44no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—84no—
233C2×C4×C13C2×C22⋊C411yescharacteristic
234C2×C4×C13C2×C22⋊C411yescharacteristic
235C2×C4×C13C23×C411yescharacteristic
236C2×C4×C13C22×D411yescharacteristic
237C22⋊D13—48no—
238C22⋊D13—42no—
239C22⋊D13—42no—
240C22⋊D13—44no—
241C22⋊D13—48no—
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—48no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—84no—
253C2×Dic13#10214yes—
254C2×Dic13#10214yes—
255C2×Dic13#10218yes—
256C2×Dic13C2×C22⋊C412yes—
257C2×Dic13C2×C22⋊C412yes—
258C2×Dic13C2×C22⋊C412yes—
259C2×Dic13C2×C22⋊C412yes—
260C2×Dic13C2×D814yes—
261C2×Dic13C2×SD1614yes—
262D52—42no—
263D52—42no—
264C4×D13—48no—
265Dic26—48no—
266C8×C13—42no—
267#1055—42no—
268C22×#41—261no—
269#532—134no—
270#532—134no—
271#532—262no—
272#532—262no—
273C2×C4⋊Q8—131no—
274C2×#127—131no—
275C2×#124—261no—
276C2×#121—131no—
277C2×#121—261no—
278C2×#121C2×D1311yescharacteristic
279C2×C4×D4—131no—
280C2×C4×D4—131no—
281C2×C4×D4—261no—
282C22×C4⋊C4—261no—
283C22×C42—131no—
284#431—134no—
285#431—262no—
286C2×C4⋊C8—261no—
287C2×C22⋊C8—131no—
288C2×C22⋊C8C2×D1311yescharacteristic
289C2×C4×C8—261no—
290#382—134no—
291#382—262no—
292C2×#95—131no—
293C2×#95—261no—
294C2×#95C2×D1311yescharacteristic
295#327—134no—
296#327—134no—
297#327—134no—
298#327C2×D1314yescomplemented
299C22×C13—21no—
300C22×C13—21no—
301C22×C13—21no—
302C22×C13—21no—
303C22×C13—24no—
304C22×C13—24no—
305C22×C13—42no—
306C22×C13—42no—
307C22×C13—42no—
308C22×C13—84no—
309C22×C13#41012yes—
310C22×C13C2×#10212yes—
311C22×C13C2×#10212yes—
312C22×C13#42112yes—
313C22×C13C22×C22⋊C411yescharacteristic
314C22×C13C22×D811yescharacteristic
315C22×C13C22×SD1611yescharacteristic
316C2×D13—42no—
317C2×D13—42no—
318C2×D13—42no—
319C2×D13—84no—
320C4×C13—21no—
321C4×C13—21no—
322C4×C13—21no—
323C4×C13—21no—
324C4×C13—42no—
325C4×C13—82no—
326Dic13—22no—
327Dic13—22no—
328Dic13—42no—
329Dic13—82no—
330Dic13C2×#10214yes—
331Dic13C2×#10214yes—
332C2×#41—264no—
333C2×#41—264no—
334C2×#41—524no—
335C2×#41—524no—
336C22×Q8—261no—
337C22×D4—21no—
338C22×D4—131no—
339C22×D4—261no—
340C22×D4—261no—
341C22×D4—261no—
342C22×D4C4×D1311yescharacteristic
343C23×C4—21no—
344C23×C4—131no—
345C23×C4—131no—
346C23×C4—261no—
347C23×C4—261no—
348C23×C4—261no—
349C23×C4C22×D1311yescharacteristic
350C22×C8—21no—
351C22×C8—261no—
352C4⋊Q8—134no—
353C4⋊Q8—262no—
354#127—134no—
355#127—262no—
356#124—264no—
357#124—264no—
358#121—21no—
359#121—21no—
360#121—132no—
361#121—132no—
362#121—264no—
363#121—264no—
364#121—261no—
365#121—261no—
366#121C4×D1312yes—
367#121C22×D1312yes—
368C4×D4—134no—
369C4×D4—134no—
370C4×D4—264no—
371C4×D4—264no—
372C4×D4—262no—
373C4×D4—262no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—264no—
377C2×C4⋊C4—524no—
378C2×C4⋊C4C4×D1311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—261no—
381C2×C22⋊C4—261no—
382C2×C22⋊C4—261no—
383C2×C42—131no—
384C2×C42—131no—
385C2×C42—132no—
386C2×C42—131no—
387C2×C42—131no—
388C2×C42—132no—
389C2×C42—132no—
390C2×C42—132no—
391C4⋊C8—264no—
392C22⋊C8—21no—
393C22⋊C8—132no—
394C22⋊C8—261no—
395C22⋊C8C22×D1312yes—
396C4×C8—264no—
397#95—21no—
398#95—132no—
399#95—264no—
400#95—261no—
401#95C22×D1312yes—
402C2×C13—21no—
403C2×C13—21no—
404C2×C13—22no—
405C2×C13—82no—
406C2×C13#151714yescomplemented
407C2×C13C2×#41011yescharacteristic
408C2×C13C22×#10211yescharacteristic
409C2×C13C2×#42111yescharacteristic
410D13—82no—
411C24—21no—
412C24—261no—
413C24D4×D1311yescharacteristic
414#41—5216no—
415#41—528no—
416#41—528no—
417C2×Q8—264no—
418C2×Q8—524no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—132no—
426C2×D4—264no—
427C2×D4—264no—
428C2×D4—262no—
429C2×D4—262no—
430C2×D4—261no—
431C2×D4—522no—
432C2×D4—524no—
433C2×D4—524no—
434C2×D4—522no—
435C2×D4—522no—
436C2×D4C2×C4×D1312yes—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—132no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—134no—
447C22×C4—134no—
448C22×C4—132no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—132no—
452C22×C4—132no—
453C22×C4—264no—
454C22×C4—264no—
455C22×C4—261no—
456C22×C4—262no—
457C22×C4—524no—
458C22×C4—524no—
459C22×C4—522no—
460C22×C4—522no—
461C22×C4—522no—
462C22×C4—522no—
463C22×C4C2×C4×D1311yescharacteristic
464C22×C4C2×C4×D1311yescharacteristic
465C22×C4D4×D1311yescharacteristic
466C22×C4D4×D1311yescharacteristic
467C22×C4D4×D1311yescharacteristic
468C22×C4C23×D1311yescharacteristic
469C2×C8—22no—
470C2×C8—42no—
471C2×C8—262no—
472C2×C8—522no—
473C4⋊C4—21no—
474C4⋊C4—132no—
475C4⋊C4—264no—
476C4⋊C4—261no—
477C4⋊C4—528no—
478C4⋊C4C2×C4×D1312yes—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—264no—
482C22⋊C4—264no—
483C22⋊C4—262no—
484C22⋊C4—262no—
485C42—132no—
486C42—132no—
487C42—132no—
488C42—132no—
489C42—132no—
490C42—132no—
491C42—132no—
492C42—132no—
493C13C2×#151711yescharacteristic, complemented, Sylow
494C23—22no—
495C23—22no—
496C23—22no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—262no—
501C23—522no—
502C23—522no—
503C23—522no—
504C23C22⋊C4×D1311yescharacteristic
505C23C22⋊C4×D1311yescharacteristic
506C23D8×D1312yes—
507C23SD16×D1312yes—
508C23C2×D4×D1311yescharacteristic
509Q8—528no—
510D4—42no—
511D4—42no—
512D4—44no—
513D4—42no—
514D4—42no—
515D4—522no—
516D4—522no—
517D4—528no—
518D4—528no—
519D4—524no—
520D4—522no—
521D4—522no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—84no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—134no—
537C2×C4—134no—
538C2×C4—138no—
539C2×C4—134no—
540C2×C4—134no—
541C2×C4—132no—
542C2×C4—132no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—528no—
547C2×C4—528no—
548C2×C4—522no—
549C2×C4—522no—
550C2×C4—522no—
551C2×C4—522no—
552C2×C4—522no—
553C2×C4—522no—
554C2×C4—1044no—
555C2×C4C22⋊C4×D1311yescharacteristic
556C2×C4C22⋊C4×D1311yescharacteristic
557C2×C4C22×C4×D1311yescharacteristic
558C2×C4C2×D4×D1311yescharacteristic
559C8—42no—
560C8—522no—
561C22—21no—
562C22—21no—
563C22—24no—
564C22—24no—
565C22—21no—
566C22—21no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—84no—
571C22—522no—
572C22—522no—
573C22—522no—
574C22—1044no—
575C22#1171840112yes—
576C22D13×#10212yes—
577C22D13×#10212yes—
578C22#1171848212yes—
579C22C2×C22⋊C4×D1311yescharacteristic
580C22C2×D8×D1311yescharacteristic
581C22C2×SD16×D1311yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—82no—
588C4—134no—
589C4—134no—
590C4—262no—
591C4—262no—
592C4—522no—
593C4—1042no—
594C2—21no—
595C2—22no—
596C2—21no—
597C2—82no—
598C2—1042no—
599C2#1311339414yesdirect product factor
600C2C2×#1171840111yescharacteristic
601C2C2×D13×#10211yescharacteristic
602C2C2×#1171848211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#327C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#11719301C2
cosocleC22×C4×C13C24
hypercenterC2×#327D13
hypocenterC13C2×#1517
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#11718379C2semidirect
3. C2×#11718311C2semidirect
4. #13113394C2direct (N × H)
5. C2×#11718062C2semidirect
6. C2×#11718129C2semidirect
7. C2×#11718043C2semidirect
8. C2×C13×#327C2semidirect
11. C2×#88194C4semidirect
13. C2×D4×Dic13C4semidirect
19. #11719301C4semidirect
21. C2×#88147C4semidirect
22. C2×#88142C4semidirect
33. #11718379C22semidirect
35. #11718311C22semidirect
36. C13×#327C22semidirect
37. #11718129C22semidirect
38. #11718062C22semidirect
39. #11718043C22semidirect
67. #88194C2×C4semidirect
71. D4×Dic13C2×C4semidirect
92. #88147C2×C4semidirect
94. #88142C2×C4semidirect
200. C2×#327D13semidirect
298. #327C2×D13semidirect
406. C2×C13#1517semidirect
493. C13C2×#1517semidirect
599. C2#13113394direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193012
C2×#117183792
C2×#117183112
#131133942
C2×#117180622
C2×#117181292
C2×#117180432
C2×C13×#3272
C2×#151713