Finite Group Databasebeta

← C4×#11718474 #15869424

Subgroups — C4×#11718474 #15869424

Order 3328.

1054 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718474C211yesmaximal, characteristic
2C2×C4×#6107C211yesmaximal, characteristic, complemented
3C2×C4×C8×D13C211yesmaximal, characteristic
4C4×#88151C211yesmaximal, characteristic
5C4×#88200C211yesmaximal, characteristic
6#13115694C211yesmaximal, characteristic, complemented
7#13115568C211yesmaximal, characteristic, complemented
8#13115514C211yesmaximal, characteristic, complemented
9#13115510C211yesmaximal, characteristic, complemented
10#13115258C211yesmaximal, characteristic
11#13115256C211yesmaximal, characteristic
12#13114864C211yesmaximal, characteristic
13C4×#88047C211yesmaximal, characteristic, complemented
14C4×#88056C211yesmaximal, characteristic, complemented
15C4×C13×#103C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C2×#88200C2211yescharacteristic
18C22×#6107C2211yescharacteristic
19C22×C8×D13C2211yescharacteristic
20C22×C8×D13C2211yescharacteristic
21C2×#88151C2211yescharacteristic
22C2×C42×D13C2211yescharacteristic
23C2×C4×Dic26C2211yescharacteristic
24C2×C13×#103C2211yescharacteristic
25C2×C13×#103C2211yescharacteristic
26C2×C4×C8×C13C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28#11718891C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88056C2211yescharacteristic
31C2×#88056C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34C4×#6107—24no—
35#11718650—21no—
36#11718648C2211yescharacteristic
37#11718648C2211yescharacteristic
38#11718646C2211yescharacteristic
39#11718639—21no—
40#11718635C2211yescharacteristic
41#11718634C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C4×#6103—21no—
47C4×#6103—21no—
48C4×C4⋊Dic13—21no—
49C4×C4⋊Dic13C2211yescharacteristic
50C4×#6101—21no—
51C2×C4×#1055C2211yescharacteristic
52#11718474C418yesdirect product factor
53C4×C8×D13—24no—
54#11718329—21no—
55#11718314—21no—
56C13×#340C2211yescharacteristic
57C13×#340C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C22×C4×D13D411yescharacteristic
64C22×C4×D13D411yescharacteristic
65C22×C4×D13C2311yescharacteristic
66C22×Dic26C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C4×Q8×C13—22no—
70C4×Q8×C13—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C42×C13—21no—
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78#88200—22no—
79#88200C2×C414yes—
80C2×#6107—22no—
81C2×#6107—22no—
82C2×#6107C2×C414yescomplemented
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13D411yescharacteristic
98C2×C4×Dic13D411yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C2×C8×D13—22no—
103C2×C8×D13—22no—
104C2×C8×D13—22no—
105C2×C8×D13—22no—
106C2×C8×D13—22no—
107C2×C8×D13C2×C414yes—
108#88151—22no—
109#88151C2×C414yes—
110C42×D13—22no—
111C42×D13—22no—
112C4×Dic26—22no—
113C4×Dic26—22no—
114C13×#103—22no—
115C13×#103C2×C414yescomplemented
116C4×C8×C13—22no—
117C13×#95—21no—
118#88075—22no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88071—21no—
128#88056—22no—
129#88056C2×C414yescomplemented
130C8×Dic13—22no—
131C8×Dic13—22no—
132#88050—22no—
133#88047—22no—
134#88047—22no—
135#88047C2×C414yescomplemented
136C4×#1055D414yes—
137C4×#467—131nomaximal, Sylow
138C23×D13C2×D411yescharacteristic
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13—21no—
143C2×Q8×C13—21no—
144C2×Q8×C13C22×C412yes—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2411yescharacteristic
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13C2×D411yescharacteristic
157C22×Dic13C2×D411yescharacteristic
158C22×Dic13C2×D411yescharacteristic
159C2×C4×D13—22no—
160C2×C4×D13—22no—
161C2×C4×D13—22no—
162C2×C4×D13—22no—
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—21no—
167C2×C4×D13—22no—
168C2×C4×D13Q1614yescomplemented
169C2×C4×D13C22×C412yes—
170C2×C4×D13#4112yes—
171C2×Dic26—21no—
172C2×Dic26—21no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26—21no—
176C2×Dic26C22×C412yes—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—21no—
180C2×C8×C13—21no—
181C2×C8×C13C22×C412yes—
182C2×C8×C13#4112yes—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—42no—
189C13×C4⋊C4C22×C412yes—
190C42×C13—42no—
191C42×C13—42no—
192C42×C13C2×D412yes—
193C42×C13#4112yes—
194#6107—28no—
195#6103—24no—
196#6103—24no—
197#6103—42no—
198#6103—42no—
199C4⋊Dic13—21no—
200C4⋊Dic13—24no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—42no—
206C4⋊Dic13C22×C412yes—
207#6101—24no—
208#6101—42no—
209#6101—42no—
210C4×Dic13—22no—
211C4×Dic13—22no—
212C4×Dic13—21no—
213C4×Dic13—21no—
214C4×Dic13—42no—
215C4×Dic13—42no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055C22×C412yes—
219C2×#1055C2×D412yes—
220C2×#1055C2×D412yes—
221C2×#1055#4112yes—
222C8×D13—28no—
223C8×D13—28no—
224C2×#467—131no—
225C2×C4×Q16—131no—
226C22×C4×C8—131no—
227C4×C22⋊Q8—131no—
228C4×C22⋊Q8—131no—
229#1969—131no—
230#1942—131no—
231#1933—131no—
232#1933—131no—
233#1892—131no—
234#1892—131no—
235#1808—131no—
236C4×#107—131no—
237C4×#103—131no—
238C4×#103D1311yescharacteristic, complemented
239C23×C13C22×D411yescharacteristic
240C22×D13—21no—
241C22×D13—21no—
242C22×D13—21no—
243C22×D13—21no—
244C22×D13C4×D412yes—
245C22×D13C2×Q1612yes—
246C22×D13#13512yes—
247Q8×C13—22no—
248Q8×C13—22no—
249Q8×C13—41no—
250Q8×C13—41no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13#12112yes—
266C2×C4×C13#12112yes—
267C2×C4×C13C2×Q1612yes—
268C2×C4×C13#13512yes—
269C2×C4×C13C23×C411yescharacteristic
270C2×C4×C13C22×D411yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281C2×Dic13—22no—
282C2×Dic13—22no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13C4×D412yes—
294C2×Dic13C2×Q1612yes—
295C2×Dic13#13512yes—
296C4×D13—28no—
297C4×D13—22no—
298C4×D13—22no—
299C4×D13—22no—
300C4×D13—22no—
301C4×D13—28no—
302Dic26—22no—
303Dic26—22no—
304Dic26—41no—
305Dic26—41no—
306C8×C13—22no—
307C8×C13—22no—
308#1055—22no—
309#1055C4×D414yes—
310C22×Q16—131no—
311C23×C8—131no—
312C23×C8—131no—
313C2×C22⋊Q8—131no—
314C2×C22⋊Q8—131no—
315C2×C4×Q8—131no—
316C2×C4×Q8C2×D1311yescharacteristic
317C22×C42—131no—
318#467—138no—
319C4×Q16—264no—
320C2×#107—131no—
321C2×#107—131no—
322C2×#107—131no—
323C2×#103—131no—
324C2×#103—131no—
325C2×#103—131no—
326C2×#103—131no—
327C2×#103C2×D1311yescharacteristic
328C2×#103C2×D1311yescharacteristic
329C2×C4×C8—131no—
330C2×C4×C8—131no—
331C2×C4×C8—131no—
332C2×C4×C8—264no—
333C2×C4×C8C2×D1311yescharacteristic
334#391—131no—
335#391—131no—
336#389—131no—
337#389—131no—
338#387—261no—
339#387—261no—
340#385—261no—
341#385—261no—
342#380—131no—
343#380—131no—
344C4×C4⋊C4—131no—
345C4×C4⋊C4—261no—
346C4×C4⋊C4—261no—
347C4×C4⋊C4C2×D1311yescharacteristic
348C4×C22⋊C4—261no—
349C4×C22⋊C4—261no—
350#340—131no—
351#340—131no—
352#340—131no—
353#340—131no—
354#340C2×D1311yescharacteristic
355#340C2×D1311yescharacteristic
356C22×C13C2×C4×D411yescharacteristic
357C22×C13C2×#12111yescharacteristic
358C22×C13#53211yescharacteristic
359C22×C13C22×Q1611yescharacteristic
360C22×C13C2×#13511yescharacteristic
361C22×C13C2×#13511yescharacteristic
362C22×C13C2×#13511yescharacteristic
363C2×D13—22no—
364C2×D13—22no—
365C2×D13—22no—
366C2×D13—22no—
367C2×D13—22no—
368C2×D13—22no—
369C2×D13C4×Q1614yescomplemented
370C4×C13—22no—
371C4×C13—42no—
372C4×C13—42no—
373C4×C13—81no—
374C4×C13—81no—
375C4×C13#46714yescomplemented
376C4×C13C2×C4×D411yescharacteristic
377C4×C13C4×#4111yescharacteristic
378C4×C13#52511yescharacteristic
379C4×C13#52911yescharacteristic
380Dic13—22no—
381Dic13—22no—
382Dic13—22no—
383Dic13—42no—
384Dic13—42no—
385Dic13—81no—
386Dic13—81no—
387C22×Q8—131no—
388C22×Q8C22×D1311yescharacteristic
389C23×C4—131no—
390C23×C4—131no—
391C23×C4—131no—
392C2×Q16—134no—
393C2×Q16—262no—
394C2×Q16—262no—
395C22×C8—131no—
396C22×C8—131no—
397C22×C8—134no—
398C22×C8—262no—
399C22×C8—262no—
400C22×C8—262no—
401C22×C8—262no—
402C22×C8—262no—
403C22×C8C22×D1311yescharacteristic
404C22×C8C22×D1311yescharacteristic
405C22⋊Q8—134no—
406C22⋊Q8—134no—
407C22⋊Q8—262no—
408C22⋊Q8—262no—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—262no—
412C4×Q8—262no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4—261no—
420C2×C4⋊C4—261no—
421C2×C4⋊C4—261no—
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C4⋊C4C22×D1311yescharacteristic
424C2×C4⋊C4C22×D1311yescharacteristic
425C2×C22⋊C4—261no—
426C2×C22⋊C4—261no—
427C2×C22⋊C4—261no—
428C2×C22⋊C4—261no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—131no—
432C2×C42—131no—
433C2×C42—131no—
434C2×C42—262no—
435C2×C42—262no—
436C2×C42—261no—
437C2×C42—261no—
438C2×C42C22×D1311yescharacteristic
439#107—134no—
440#107—262no—
441#107—262no—
442#103—22no—
443#103—134no—
444#103—262no—
445#103—262no—
446#103—262no—
447#103C4×D1314yescomplemented
448C4×C8—22no—
449C4×C8—134no—
450C4×C8—262no—
451C4×C8—262no—
452#95—21no—
453#95—261no—
454#95—261no—
455#95—261no—
456#95—261no—
457#95—261no—
458#95—261no—
459#95—261no—
460#95—261no—
461#95—261no—
462C2×C13C4×#12111yescharacteristic
463C2×C13C2×C4×Q1611yescharacteristic
464C2×C13C4×#13511yescharacteristic
465C2×C13C2×#46711yescharacteristic
466C2×C13#305011yescharacteristic
467C2×C13#316811yescharacteristic
468C2×C13#317011yescharacteristic
469D13—24no—
470C24—131no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—132no—
477C2×Q8—261no—
478C2×Q8—261no—
479C2×Q8—261no—
480C2×Q8—261no—
481C2×Q8—261no—
482C2×Q8C2×C4×D1312yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—131no—
488C22×C4—131no—
489C22×C4—131no—
490C22×C4—134no—
491C22×C4—132no—
492C22×C4—132no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4—262no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—261no—
501C22×C4—261no—
502C22×C4—261no—
503C22×C4—261no—
504C22×C4—261no—
505C22×C4—261no—
506C22×C4D4×D1311yescharacteristic
507C22×C4D4×D1311yescharacteristic
508C22×C4C23×D1311yescharacteristic
509Q16—268no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—132no—
515C2×C8—132no—
516C2×C8—132no—
517C2×C8—132no—
518C2×C8—268no—
519C2×C8—268no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8C2×C4×D1312yes—
523C2×C8#612712yes—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—42no—
530C4⋊C4—132no—
531C4⋊C4—264no—
532C4⋊C4—264no—
533C4⋊C4—261no—
534C4⋊C4—261no—
535C4⋊C4—261no—
536C4⋊C4—261no—
537C4⋊C4—261no—
538C4⋊C4—522no—
539C4⋊C4—522no—
540C4⋊C4—522no—
541C4⋊C4C2×C4×D1312yes—
542C22⋊C4—264no—
543C22⋊C4—264no—
544C22⋊C4—522no—
545C22⋊C4—522no—
546C42—42no—
547C42—42no—
548C42—262no—
549C42—262no—
550C42—261no—
551C42—261no—
552C42—522no—
553C42—522no—
554C42#612712yes—
555C42D4×D1312yes—
556C13C4×#46711yescharacteristic, complemented, Sylow
557C23—132no—
558C23—132no—
559C23—132no—
560C23—261no—
561C23—261no—
562C23—261no—
563C23—261no—
564C23C2×D4×D1311yescharacteristic
565Q8—22no—
566Q8—22no—
567Q8—41no—
568Q8—41no—
569Q8—262no—
570Q8—262no—
571Q8—521no—
572Q8—521no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—132no—
588C2×C4—132no—
589C2×C4—132no—
590C2×C4—268no—
591C2×C4—261no—
592C2×C4—261no—
593C2×C4—261no—
594C2×C4—261no—
595C2×C4—261no—
596C2×C4—261no—
597C2×C4—262no—
598C2×C4—262no—
599C2×C4—268no—
600C2×C4—262no—
601C2×C4—262no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4#8813812yes—
615C2×C4#8813812yes—
616C2×C4#8817012yes—
617C2×C4Q16×D1312yes—
618C2×C4C22×C4×D1311yescharacteristic
619C2×C4C2×#612711yescharacteristic
620C2×C4C2×#612711yescharacteristic
621C2×C4C2×D4×D1311yescharacteristic
622C2×C4#41×D1311yescharacteristic
623C2×C4#41×D1311yescharacteristic
624C8—22no—
625C8—22no—
626C8—134no—
627C8—262no—
628C22—134no—
629C22—262no—
630C22—262no—
631C22—262no—
632C22—262no—
633C22—262no—
634C22—262no—
635C22C2×#8813811yescharacteristic
636C22C4×D4×D1311yescharacteristic
637C22#1171925311yescharacteristic
638C22C2×#8817011yescharacteristic
639C22C2×Q16×D1311yescharacteristic
640C22D13×#13511yescharacteristic
641C22D13×#13511yescharacteristic
642C4—22no—
643C4—42no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4—262no—
648C4—262no—
649C4—262no—
650C4—522no—
651C4—522no—
652C4—1041no—
653C4—1041no—
654C4#1171847414yesdirect product factor
655C4C4×#612711yescharacteristic
656C4#1171923311yescharacteristic
657C4C4×D4×D1311yescharacteristic
658C4#1171925211yescharacteristic
659C2—264no—
660C2C4×#8813811yescharacteristic
661C2C4×Q16×D1311yescharacteristic
662C2C4×#8817011yescharacteristic
663C2C2×#1171847411yescharacteristic
664C2#1312441611yescharacteristic
665C2#1312540211yescharacteristic
666C2#1312541911yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#103C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenterC4×#103D13
hypocenterC13C4×#467
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6107C2semidirect
6. #13115694C2semidirect
7. #13115568C2semidirect
8. #13115514C2semidirect
9. #13115510C2semidirect
13. C4×#88047C2semidirect
14. C4×#88056C2semidirect
15. C4×C13×#103C2semidirect
52. #11718474C4direct (N × H)
82. C2×#6107C2×C4semidirect
115. C13×#103C2×C4semidirect
129. #88056C2×C4semidirect
135. #88047C2×C4semidirect
168. C2×C4×D13Q16semidirect
238. C4×#103D13semidirect
369. C2×D13C4×Q16semidirect
375. C4×C13#467semidirect
447. #103C4×D13semidirect
556. C13C4×#467semidirect
654. C4#11718474direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117184742
C2×C4×#61072
C2×C4×C8×D132
C4×#881512
C4×#882002
#131156942
#131155682
#131155142
#131155102
#131152582
#131152562
#131148642
C4×#880472
C4×#880562
C4×C13×#1032
C4×#46713