Finite Group Databasebeta

← C2×#13116009 #15890344

Subgroups — C2×#13116009 #15890344

Order 3328.

1234 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719175C211yesmaximal, characteristic, complemented
2C2×#11718800C211yesmaximal, characteristic
3C22×#88045C211yesmaximal, characteristic
4C2×#11718667C211yesmaximal, characteristic
5#13116009C218yesmaximal, direct product factor
6C2×#11718148C211yesmaximal, characteristic, complemented
7C2×#11718123C211yesmaximal, characteristic, complemented
8C2×C13×#339C211yesmaximal, characteristic, complemented
9C22×#6127C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C2×C13×#117C2211yescharacteristic
12C22×C42×C13C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C2×#88180C2211yescharacteristic
15C2×#88178—22no—
16C22×#6099C2211yescharacteristic
17#11719175—22no—
18#11719175—22no—
19#11719175—22no—
20#11719175C2214yescomplemented
21C2×#88124—21no—
22C2×#88123—21no—
23C2×C4×Dic26—22no—
24#11718800—22no—
25#11718800C2214yes—
26C2×#88065—22no—
27#11718667—22no—
28#11718667C2214yes—
29C2×#88046—22no—
30C2×#88045—21no—
31C2×#88045—21no—
32C2×#88045—22no—
33C2×#88045C2214yes—
34C13×#339C2214yescomplemented
35#11718148C2214yescomplemented
36#11718123C2214yescomplemented
37C23×C4×C13—21no—
38C23×C4×C13C2311yescharacteristic
39C22×C22⋊D13—21no—
40C2×#6127—21no—
41C2×#6127—21no—
42C2×#6127—21no—
43C2×#6127—21no—
44C2×#6127—21no—
45C2×#6127—21no—
46C2×#6127—21no—
47C2×#6127—21no—
48C2×#6127—21no—
49C2×#6127—21no—
50C2×#6127Q812yescomplemented
51C2×#6127C2312yes—
52C22×D52Q811yescharacteristic, complemented
53C22×C4×D13—21no—
54C22×Dic26—22no—
55C22×Dic26Q811yescharacteristic, complemented
56C2×C13×M16—21no—
57C2×C13×M16—21no—
58C2×C13×M16—21no—
59C2×C13×M16—21no—
60C2×C13×M16—21no—
61C2×C13×M16C2312yes—
62C22×C8×C13—21no—
63C13×#117—21no—
64C13×#117—21no—
65C13×#117—21no—
66C13×#117C2312yes—
67C2×C13×C4⋊C4—21no—
68C2×C13×C22⋊C4—21no—
69C2×C42×C13—21no—
70C2×C42×C13—21no—
71C2×C42×C13—21no—
72C2×C42×C13—21no—
73C2×C42×C13D411yescharacteristic
74C2×C42×C13D411yescharacteristic
75C2×C42×C13D412yes—
76C2×C42×C13C2312yes—
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13D412yes—
79#88180—21no—
80#88180—21no—
81#88180—21no—
82#88180—21no—
83#88180D412yes—
84#88180D412yes—
85#88180C2312yes—
86#88180C2312yes—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90#88178—28no—
91#88178—28no—
92C2×#6101—24no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13D412yes—
95C2×#6099—21no—
96C2×#6099—21no—
97C2×#6099—21no—
98C2×#6099—21no—
99C2×#6099—21no—
100C2×#6099C2312yes—
101C22×#1055—21no—
102#88124—24no—
103#88124—24no—
104#88123—24no—
105#88123—24no—
106C4×Dic26—28no—
107C4×Dic26—28no—
108#88065—28no—
109#88046—28no—
110#88045—24no—
111#88045—24no—
112C2×#2031—131nomaximal, Sylow
113C24×C13C2×D411yescharacteristic
114C23×D13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—44no—
120C22×C4×C13—41no—
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×Q811yescharacteristic
127C22×C4×C13C2×Q811yescharacteristic
128C22×C4×C13#4111yescharacteristic
129C22×C4×C13#4111yescharacteristic
130C22×C4×C13#4111yescharacteristic
131C22×C4×C13#4111yescharacteristic
132C22×C4×C13#4111yescharacteristic
133C22×C4×C13#4111yescharacteristic
134C22×C4×C13C2411yescharacteristic
135C2×C22⋊D13—22no—
136C2×C22⋊D13—22no—
137C2×C22⋊D13—41no—
138C2×C22⋊D13—41no—
139C2×C22⋊D13—41no—
140C2×C22⋊D13—41no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—21no—
144#6127—22no—
145#6127—22no—
146#6127—22no—
147#6127—22no—
148#6127—22no—
149#6127—22no—
150#6127—22no—
151#6127—22no—
152#6127—41no—
153#6127—41no—
154#6127—41no—
155#6127—41no—
156#6127—41no—
157#6127—41no—
158#6127—41no—
159#6127—41no—
160C2×D52—21no—
161C2×D52—21no—
162C2×D52—21no—
163C2×D52—21no—
164C2×D52—21no—
165C2×D52C2×Q812yescomplemented
166C2×C4×D13—22no—
167C2×C4×D13—22no—
168C2×C4×D13—41no—
169C2×C4×D13—41no—
170C2×C4×D13—41no—
171C2×C4×D13—41no—
172C2×Dic26—21no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26—21no—
176C2×Dic26—28no—
177C2×Dic26—21no—
178C2×Dic26—48no—
179C2×Dic26C2×Q812yescomplemented
180C13×M16—22no—
181C13×M16—22no—
182C13×M16—41no—
183C13×M16—41no—
184C2×C8×C13—22no—
185C2×C8×C13—41no—
186C2×C8×C13—41no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—41no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—41no—
191C42×C13—22no—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—22no—
195C42×C13—22no—
196C42×C13—41no—
197C42×C13C2×D412yes—
198C42×C13C2×D412yes—
199C22⋊Dic13—22no—
200C22⋊Dic13—22no—
201C22⋊Dic13—22no—
202C22⋊Dic13C2×D414yes—
203C4⋊Dic13—28no—
204C4⋊Dic13—22no—
205C4⋊Dic13—22no—
206C4⋊Dic13—22no—
207C4⋊Dic13—22no—
208#6101—216no—
209C4×Dic13—22no—
210C4×Dic13—22no—
211C4×Dic13—22no—
212C4×Dic13C2×D414yes—
213#6099—22no—
214#6099—22no—
215#6099—41no—
216#6099—41no—
217C2×#1055—22no—
218C2×#1055—41no—
219C2×#1055—41no—
220C2×#533—131no—
221C2×#421—131no—
222C22×#104—131no—
223C2×#410—131no—
224#2031—138no—
225C2×#344—131no—
226C2×#339D1311yescharacteristic, complemented
227C2×H(3,ℤ/4)—131no—
228C23×C13—42no—
229C23×C13#12011yescharacteristic
230C23×C13#12011yescharacteristic
231C23×C13C22⋊Q811yescharacteristic
232C23×C13C22⋊Q811yescharacteristic
233C23×C13#12411yescharacteristic
234C23×C13#12411yescharacteristic
235C23×C13C22×D411yescharacteristic
236C22×D13—22no—
237C22×D13—41no—
238C22×D13—41no—
239C22×D13—82no—
240C2×C4×C13—24no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—44no—
244C2×C4×C13—44no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—82no—
248C2×C4×C13#12011yescharacteristic
249C2×C4×C13#12011yescharacteristic
250C2×C4×C13C22⋊Q811yescharacteristic
251C2×C4×C13C22⋊Q811yescharacteristic
252C2×C4×C13C22⋊Q811yescharacteristic
253C2×C4×C13C22⋊Q811yescharacteristic
254C2×C4×C13C22⋊Q811yescharacteristic
255C2×C4×C13C22⋊Q811yescharacteristic
256C2×C4×C13C22⋊Q811yescharacteristic
257C2×C4×C13C22⋊Q811yescharacteristic
258C2×C4×C13C22⋊Q811yescharacteristic
259C2×C4×C13C22⋊Q811yescharacteristic
260C2×C4×C13#12411yescharacteristic
261C2×C4×C13#12411yescharacteristic
262C2×C4×C13#12411yescharacteristic
263C2×C4×C13#12411yescharacteristic
264C2×C4×C13#12411yescharacteristic
265C2×C4×C13#12411yescharacteristic
266C2×C4×C13#12411yescharacteristic
267C2×C4×C13#12411yescharacteristic
268C2×C4×C13#12411yescharacteristic
269C2×C4×C13#12411yescharacteristic
270C2×C4×C13C22×D411yescharacteristic
271C2×C4×C13C22×D411yescharacteristic
272C2×C4×C13C22×Q811yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C22⋊D13—42no—
277C22⋊D13—42no—
278C22⋊D13—42no—
279C22⋊D13—42no—
280C2×Dic13—24no—
281C2×Dic13—24no—
282C2×Dic13—22no—
283C2×Dic13—44no—
284C2×Dic13—44no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287D52—22no—
288D52—22no—
289D52—41no—
290D52—41no—
291C4×D13—42no—
292C4×D13—42no—
293C4×D13—42no—
294C4×D13—42no—
295Dic26—22no—
296Dic26—22no—
297Dic26—416no—
298Dic26—41no—
299Dic26—41no—
300C8×C13—42no—
301#1055—42no—
302C22×#41—131no—
303C22×M16—131no—
304C22×M16C2×D1311yescharacteristic
305#533—134no—
306#533—262no—
307#533—262no—
308#533—262no—
309C2×C4⋊Q8—261no—
310C2×#125—261no—
311C2×C22⋊Q8—262no—
312C2×C4×Q8—262no—
313C2×#117—131no—
314C2×#117—131no—
315C2×#117C2×D1311yescharacteristic
316C22×C42C2×D1311yescharacteristic
317#421—134no—
318#421—262no—
319C2×#104—134no—
320C2×#104—262no—
321C2×#104—261no—
322C2×#104—261no—
323C2×#104—262no—
324#410—134no—
325#410—262no—
326C2×#99—262no—
327#344—134no—
328#339C2×D1314yescomplemented
329H(3,ℤ/4)—134no—
330C22×C13—22no—
331C22×C13—22no—
332C22×C13—22no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13#39311yescharacteristic
338C22×C13#39311yescharacteristic
339C22×C13#39311yescharacteristic
340C22×C13#39311yescharacteristic
341C22×C13C2×#12011yescharacteristic
342C22×C13C2×C22⋊Q811yescharacteristic
343C22×C13C2×#12411yescharacteristic
344C2×D13—42no—
345C2×D13—82no—
346C2×D13—82no—
347C2×D13—82no—
348C4×C13—24no—
349C4×C13—42no—
350C4×C13—82no—
351C4×C13#39311yescharacteristic
352C4×C13#39311yescharacteristic
353C4×C13#39311yescharacteristic
354C4×C13#39311yescharacteristic
355C4×C13C2×C22⋊Q811yescharacteristic
356C4×C13C2×C22⋊Q811yescharacteristic
357C4×C13C2×#12411yescharacteristic
358C4×C13C2×#12411yescharacteristic
359Dic13—44no—
360Dic13—44no—
361Dic13—42no—
362C2×#41—132no—
363C2×#41—132no—
364C2×#41—261no—
365C2×#41—261no—
366C2×#41—261no—
367C2×#41—261no—
368C2×#41—261no—
369C2×#41—261no—
370C2×#41—261no—
371C2×#41—261no—
372C2×#41—261no—
373C2×#41—261no—
374C22×Q8—131no—
375C22×Q8—262no—
376C22×D4—131no—
377C22×D4—261no—
378C23×C4—21no—
379C23×C4—261no—
380C23×C4C22×D1311yescharacteristic
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—132no—
387C2×M16—261no—
388C2×M16—261no—
389C2×M16—261no—
390C2×M16—261no—
391C2×M16—261no—
392C2×M16C22×D1312yes—
393C22×C8—21no—
394C22×C8—261no—
395C4⋊Q8—264no—
396C4⋊Q8—264no—
397#125—264no—
398#125—264no—
399C22⋊Q8—268no—
400C22⋊Q8—268no—
401C4×Q8—268no—
402C4×Q8—268no—
403#117—21no—
404#117—21no—
405#117—21no—
406#117—132no—
407#117—132no—
408#117—132no—
409#117—132no—
410#117—261no—
411#117—261no—
412#117—261no—
413#117—261no—
414#117C22×D1312yes—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—264no—
417C2×C4⋊C4—262no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4—261no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—132no—
422C2×C22⋊C4—261no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—132no—
428C2×C42—261no—
429C2×C42D5211yescharacteristic
430C2×C42D5211yescharacteristic
431C2×C42D5212yes—
432C2×C42C22×D1312yes—
433#104—268no—
434#104—264no—
435#104—264no—
436#99—268no—
437C2×C13—21no—
438C2×C13—21no—
439C2×C13—21no—
440C2×C13—21no—
441C2×C13—21no—
442C2×C13—21no—
443C2×C13#203112yescomplemented
444C2×C13C2×#39311yescharacteristic
445D13—82no—
446C24—261no—
447C24D4×D1311yescharacteristic
448#41—262no—
449#41—262no—
450#41—262no—
451#41—262no—
452#41—262no—
453#41—262no—
454#41—262no—
455#41—262no—
456#41—521no—
457#41—521no—
458#41—521no—
459#41—521no—
460#41—521no—
461#41—521no—
462#41—521no—
463#41—521no—
464C2×Q8—132no—
465C2×Q8—268no—
466C2×Q8—261no—
467C2×Q8—261no—
468C2×Q8—261no—
469C2×Q8—261no—
470C2×Q8—261no—
471C2×Q8—528no—
472C2×D4—132no—
473C2×D4—262no—
474C2×D4—262no—
475C2×D4—261no—
476C2×D4—261no—
477C2×D4—261no—
478C2×D4—261no—
479C2×D4—261no—
480C2×D4—521no—
481C2×D4—521no—
482C2×D4—521no—
483C2×D4—521no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—44no—
489C22×C4—41no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—261no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4—521no—
496C22×C4—521no—
497C22×C4—521no—
498C22×C4—521no—
499C22×C4C2×D5211yescharacteristic
500C22×C4C2×D5211yescharacteristic
501C22×C4#612711yescharacteristic
502C22×C4#612711yescharacteristic
503C22×C4#612711yescharacteristic
504C22×C4#612711yescharacteristic
505C22×C4D4×D1311yescharacteristic
506C22×C4D4×D1311yescharacteristic
507C22×C4D4×D1311yescharacteristic
508C22×C4#612911yescharacteristic
509C22×C4#612911yescharacteristic
510C22×C4Q8×D1311yescharacteristic
511C22×C4Q8×D1311yescharacteristic
512C22×C4C23×D1311yescharacteristic
513M16—22no—
514M16—22no—
515M16—41no—
516M16—41no—
517M16—262no—
518M16—262no—
519M16—521no—
520M16—521no—
521C2×C8—22no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—262no—
525C2×C8—521no—
526C2×C8—521no—
527C4⋊C4—22no—
528C4⋊C4—41no—
529C4⋊C4—2616no—
530C4⋊C4—268no—
531C4⋊C4—262no—
532C4⋊C4—262no—
533C4⋊C4—262no—
534C4⋊C4—262no—
535C22⋊C4—22no—
536C22⋊C4—41no—
537C22⋊C4—134no—
538C22⋊C4—262no—
539C22⋊C4—262no—
540C22⋊C4—262no—
541C42—22no—
542C42—21no—
543C42—21no—
544C42—22no—
545C42—22no—
546C42—41no—
547C42—134no—
548C42—262no—
549C42—262no—
550C42—262no—
551C42C2×D5212yes—
552C42C2×D5212yes—
553C13C2×#203111yescharacteristic, complemented, Sylow
554C23—42no—
555C23—262no—
556C23—521no—
557C23—521no—
558C23—1042no—
559C23#8813611yescharacteristic
560C23#8813611yescharacteristic
561C23#8813911yescharacteristic
562C23#8813911yescharacteristic
563C23#8815011yescharacteristic
564C23#8815011yescharacteristic
565C23C2×D4×D1311yescharacteristic
566Q8—262no—
567Q8—262no—
568Q8—5216no—
569Q8—521no—
570Q8—521no—
571D4—262no—
572D4—262no—
573D4—522no—
574D4—522no—
575D4—522no—
576D4—522no—
577D4—521no—
578D4—521no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—82no—
587C2×C4—264no—
588C2×C4—264no—
589C2×C4—262no—
590C2×C4—524no—
591C2×C4—524no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—522no—
595C2×C4—522no—
596C2×C4—522no—
597C2×C4—522no—
598C2×C4#8812911yescharacteristic
599C2×C4#8812911yescharacteristic
600C2×C4#8812911yescharacteristic
601C2×C4#8812911yescharacteristic
602C2×C4#8813611yescharacteristic
603C2×C4#8813611yescharacteristic
604C2×C4#8813911yescharacteristic
605C2×C4#8813911yescharacteristic
606C2×C4#8813911yescharacteristic
607C2×C4#8813911yescharacteristic
608C2×C4#8813911yescharacteristic
609C2×C4#8813911yescharacteristic
610C2×C4#8815011yescharacteristic
611C2×C4#8815011yescharacteristic
612C2×C4#8815011yescharacteristic
613C2×C4#8815011yescharacteristic
614C2×C4#8815011yescharacteristic
615C2×C4#8815011yescharacteristic
616C2×C4#8815111yescharacteristic
617C2×C4#8815111yescharacteristic
618C2×C4#8815111yescharacteristic
619C2×C4#8815111yescharacteristic
620C2×C4C22×D5211yescharacteristic
621C2×C4C2×#612711yescharacteristic
622C2×C4C2×#612711yescharacteristic
623C2×C4C2×D4×D1311yescharacteristic
624C2×C4C2×#612911yescharacteristic
625C2×C4C2×Q8×D1311yescharacteristic
626C8—42no—
627C8—522no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—522no—
636C22—1042no—
637C22—1042no—
638C22—1042no—
639C22#1171833411yescharacteristic
640C22#1171833411yescharacteristic
641C22#1171833411yescharacteristic
642C22#1171833411yescharacteristic
643C22C2×#8813611yescharacteristic
644C22C2×#8813911yescharacteristic
645C22C2×#8815011yescharacteristic
646C4—24no—
647C4—42no—
648C4—82no—
649C4—524no—
650C4—524no—
651C4—522no—
652C4#1171833411yescharacteristic
653C4#1171833411yescharacteristic
654C4#1171833411yescharacteristic
655C4#1171833411yescharacteristic
656C4C2×#8812911yescharacteristic
657C4C2×#8813911yescharacteristic
658C4C2×#8815011yescharacteristic
659C4C2×#8815111yescharacteristic
660C2—21no—
661C2—21no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—1042no—
667C2#1311600912yesdirect product factor
668C2C2×#1171833411yescharacteristic
subgroupG/H
centerC2×C4#88139
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#339C2
socleC22×C13#393
prime radicalC22×#6127C22
hypercenterC2×#339D13
hypocenterC13C2×#2031
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C2×#11719175C2semidirect
5. #13116009C2direct (N × H)
6. C2×#11718148C2semidirect
7. C2×#11718123C2semidirect
8. C2×C13×#339C2semidirect
20. #11719175C22semidirect
34. C13×#339C22semidirect
35. #11718148C22semidirect
36. #11718123C22semidirect
50. C2×#6127Q8semidirect
52. C22×D52Q8semidirect
55. C22×Dic26Q8semidirect
165. C2×D52C2×Q8semidirect
179. C2×Dic26C2×Q8semidirect
226. C2×#339D13semidirect
328. #339C2×D13semidirect
443. C2×C13#2031semidirect
553. C13C2×#2031semidirect
667. C2#13116009direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191752
C2×#117188002
C22×#880452
C2×#117186672
#131160092
C2×#117181482
C2×#117181232
C2×C13×#3392
C2×#203113