Finite Group Databasebeta

← C2×#13116007 #15890342

Subgroups — C2×#13116007 #15890342

Order 3328.

1234 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719222C211yesmaximal, characteristic, complemented
2C2×#11718666C211yesmaximal, characteristic
3C22×#88065C211yesmaximal, characteristic
4C2×#11718667C211yesmaximal, characteristic
5#13116007C218yesmaximal, direct product factor
6C2×#11718151C211yesmaximal, characteristic, complemented
7C2×#11718124C211yesmaximal, characteristic, complemented
8C2×C13×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#6127C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C2×C13×#117C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C22×C4×Dic13C2211yescharacteristic
15C22×#6099C2211yescharacteristic
16#11719222—22no—
17#11719222—22no—
18#11719222—22no—
19#11719222C2214yescomplemented
20C2×#88144—21no—
21C2×#88142—21no—
22C2×#88132—22no—
23C2×C4×Dic26—22no—
24C2×#88065—21no—
25C2×#88065—21no—
26C2×#88065—22no—
27C2×#88065C2214yes—
28#11718667—22no—
29#11718667C2214yes—
30#11718666—22no—
31#11718666C2214yes—
32C2×#88046—22no—
33C2×#88045—22no—
34C13×H(3,ℤ/4)C2214yescomplemented
35#11718151C2214yescomplemented
36#11718124C2214yescomplemented
37C23×C4×C13C2311yescharacteristic
38C22×C22⋊D13—21no—
39C23×Dic13—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×#117—21no—
67C13×#117—21no—
68C13×#117D412yes—
69C13×#117C2312yes—
70C13×#117C2312yes—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C42×C13—21no—
76C2×C42×C13D412yes—
77C2×C22⋊Dic13D412yes—
78#88180—21no—
79#88180—21no—
80#88180D412yes—
81#88180C2312yes—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—21no—
84C2×#6101—22no—
85C2×#6101—22no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13D411yescharacteristic
91C2×C4×Dic13D411yescharacteristic
92C2×C4×Dic13D412yes—
93C2×C4×Dic13C2312yes—
94C2×#6099—21no—
95C2×#6099—21no—
96C2×#6099—21no—
97C2×#6099—21no—
98C2×#6099—21no—
99C2×#6099C2312yes—
100C22×#1055—21no—
101#88144—24no—
102#88144—24no—
103#88142—24no—
104#88142—24no—
105#88132—28no—
106#88132—28no—
107C4×Dic26—28no—
108C4×Dic26—28no—
109#88065—24no—
110#88065—24no—
111#88046—28no—
112#88045—28no—
113C2×#2031—131nomaximal, Sylow
114C24×C13C2×D411yescharacteristic
115C23×D13—21no—
116C22×C4×C13—22no—
117C22×C4×C13—41no—
118C22×C4×C13C2×D411yescharacteristic
119C22×C4×C13C2×D411yescharacteristic
120C22×C4×C13C2×D411yescharacteristic
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×Q811yescharacteristic
124C22×C4×C13C2×Q811yescharacteristic
125C22×C4×C13#4111yescharacteristic
126C22×C4×C13#4111yescharacteristic
127C22×C4×C13#4111yescharacteristic
128C22×C4×C13#4111yescharacteristic
129C22×C4×C13#4111yescharacteristic
130C22×C4×C13#4111yescharacteristic
131C22×C4×C13C2411yescharacteristic
132C2×C22⋊D13—22no—
133C2×C22⋊D13—22no—
134C2×C22⋊D13—41no—
135C2×C22⋊D13—41no—
136C2×C22⋊D13—41no—
137C2×C22⋊D13—41no—
138C22×Dic13—21no—
139C22×Dic13—22no—
140C22×Dic13—21no—
141C22×Dic13—22no—
142C22×Dic13—21no—
143C22×Dic13—22no—
144C22×Dic13—44no—
145#6127—22no—
146#6127—22no—
147#6127—22no—
148#6127—22no—
149#6127—22no—
150#6127—22no—
151#6127—22no—
152#6127—22no—
153#6127—41no—
154#6127—41no—
155#6127—41no—
156#6127—41no—
157#6127—41no—
158#6127—41no—
159#6127—41no—
160#6127—41no—
161C2×D52—21no—
162C2×D52—21no—
163C2×D52—21no—
164C2×D52—21no—
165C2×D52—21no—
166C2×D52C2×Q812yescomplemented
167C2×C4×D13—22no—
168C2×C4×D13—22no—
169C2×C4×D13—41no—
170C2×C4×D13—41no—
171C2×C4×D13—41no—
172C2×C4×D13—41no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26—21no—
176C2×Dic26—21no—
177C2×Dic26—28no—
178C2×Dic26—21no—
179C2×Dic26—48no—
180C2×Dic26C2×Q812yescomplemented
181C13×M16—22no—
182C13×M16—22no—
183C13×M16—41no—
184C13×M16—41no—
185C2×C8×C13—22no—
186C2×C8×C13—41no—
187C2×C8×C13—41no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—41no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—41no—
196C42×C13—22no—
197C42×C13—22no—
198C42×C13—41no—
199C42×C13C2×D414yes—
200C22⋊Dic13—22no—
201C22⋊Dic13C2×D414yes—
202C4⋊Dic13—28no—
203C4⋊Dic13—22no—
204C4⋊Dic13—22no—
205#6101—28no—
206#6101—28no—
207C4×Dic13—22no—
208C4×Dic13—22no—
209C4×Dic13—21no—
210C4×Dic13—21no—
211C4×Dic13—22no—
212C4×Dic13—22no—
213C4×Dic13C2×D412yes—
214C4×Dic13C2×D412yes—
215#6099—22no—
216#6099—22no—
217#6099—41no—
218#6099—41no—
219C2×#1055—22no—
220C2×#1055—41no—
221C2×#1055—41no—
222C2×#533—131no—
223C2×#421—131no—
224C22×#104—131no—
225C2×#410—131no—
226#2031—138no—
227C2×#344—131no—
228C2×#339—131no—
229C2×H(3,ℤ/4)D1311yescharacteristic, complemented
230C23×C13—42no—
231C23×C13#12011yescharacteristic
232C23×C13#12011yescharacteristic
233C23×C13C22⋊Q811yescharacteristic
234C23×C13C22⋊Q811yescharacteristic
235C23×C13#12411yescharacteristic
236C23×C13#12411yescharacteristic
237C23×C13C22×D411yescharacteristic
238C22×D13—22no—
239C22×D13—41no—
240C22×D13—41no—
241C22×D13—82no—
242C2×C4×C13—24no—
243C2×C4×C13—44no—
244C2×C4×C13—42no—
245C2×C4×C13—82no—
246C2×C4×C13#12011yescharacteristic
247C2×C4×C13#12011yescharacteristic
248C2×C4×C13C22⋊Q811yescharacteristic
249C2×C4×C13C22⋊Q811yescharacteristic
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×C13#12411yescharacteristic
259C2×C4×C13#12411yescharacteristic
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×C13C22×D411yescharacteristic
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C22×Q811yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C22⋊D13—42no—
275C22⋊D13—42no—
276C22⋊D13—42no—
277C22⋊D13—42no—
278C2×Dic13—24no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—24no—
282C2×Dic13—22no—
283C2×Dic13—44no—
284C2×Dic13—44no—
285C2×Dic13—44no—
286C2×Dic13—42no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289D52—22no—
290D52—22no—
291D52—41no—
292D52—41no—
293C4×D13—42no—
294C4×D13—42no—
295C4×D13—42no—
296C4×D13—42no—
297Dic26—22no—
298Dic26—22no—
299Dic26—416no—
300Dic26—41no—
301Dic26—41no—
302C8×C13—42no—
303#1055—42no—
304C22×#41—131no—
305C22×M16—131no—
306C22×M16C2×D1311yescharacteristic
307#533—134no—
308#533—262no—
309#533—262no—
310#533—262no—
311C2×C4⋊Q8—261no—
312C2×#125—261no—
313C2×C22⋊Q8—262no—
314C2×C4×Q8—262no—
315C2×#117—131no—
316C2×#117C2×D1311yescharacteristic
317C2×#117C2×D1311yescharacteristic
318C22×C42—131no—
319#421—134no—
320#421—262no—
321C2×#104—134no—
322C2×#104—261no—
323C2×#104—261no—
324C2×#104—262no—
325C2×#104—262no—
326#410—134no—
327#410—262no—
328C2×#99—262no—
329#344—134no—
330#339—134no—
331H(3,ℤ/4)C2×D1314yescomplemented
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—22no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13#39311yescharacteristic
340C22×C13#39311yescharacteristic
341C22×C13#39311yescharacteristic
342C22×C13#39311yescharacteristic
343C22×C13C2×#12011yescharacteristic
344C22×C13C2×C22⋊Q811yescharacteristic
345C22×C13C2×#12411yescharacteristic
346C2×D13—42no—
347C2×D13—82no—
348C2×D13—82no—
349C2×D13—82no—
350C4×C13—44no—
351C4×C13—82no—
352C4×C13#39311yescharacteristic
353C4×C13#39311yescharacteristic
354C4×C13#39311yescharacteristic
355C4×C13#39311yescharacteristic
356C4×C13C2×C22⋊Q811yescharacteristic
357C4×C13C2×C22⋊Q811yescharacteristic
358C4×C13C2×#12411yescharacteristic
359C4×C13C2×#12411yescharacteristic
360Dic13—24no—
361Dic13—44no—
362Dic13—42no—
363Dic13—42no—
364C2×#41—132no—
365C2×#41—132no—
366C2×#41—261no—
367C2×#41—261no—
368C2×#41—261no—
369C2×#41—261no—
370C2×#41—261no—
371C2×#41—261no—
372C2×#41—261no—
373C2×#41—261no—
374C2×#41—261no—
375C2×#41—261no—
376C22×Q8—131no—
377C22×Q8—262no—
378C22×D4—131no—
379C22×D4—261no—
380C23×C4—261no—
381C23×C4—261no—
382C23×C4C22×D1311yescharacteristic
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—132no—
389C2×M16—261no—
390C2×M16—261no—
391C2×M16—261no—
392C2×M16—261no—
393C2×M16—261no—
394C2×M16C22×D1312yes—
395C22×C8—21no—
396C22×C8—261no—
397C4⋊Q8—264no—
398C4⋊Q8—264no—
399#125—264no—
400#125—264no—
401C22⋊Q8—268no—
402C22⋊Q8—268no—
403C4×Q8—268no—
404C4×Q8—268no—
405#117—21no—
406#117—21no—
407#117—21no—
408#117—21no—
409#117—21no—
410#117—132no—
411#117—132no—
412#117—261no—
413#117—261no—
414#117D5212yes—
415#117C22×D1312yes—
416#117C22×D1312yes—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—262no—
420C2×C4⋊C4—262no—
421C2×C4⋊C4—262no—
422C2×C4⋊C4—261no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—132no—
426C2×C42—21no—
427C2×C42—131no—
428C2×C42—131no—
429C2×C42—132no—
430C2×C42—132no—
431C2×C42—261no—
432C2×C42—261no—
433C2×C42—261no—
434C2×C42—261no—
435C2×C42D5212yes—
436#104—264no—
437#104—264no—
438#104—268no—
439#99—268no—
440C2×C13—21no—
441C2×C13—21no—
442C2×C13—21no—
443C2×C13—21no—
444C2×C13—21no—
445C2×C13—21no—
446C2×C13#203112yescomplemented
447C2×C13C2×#39311yescharacteristic
448D13—82no—
449C24—261no—
450C24D4×D1311yescharacteristic
451#41—262no—
452#41—262no—
453#41—262no—
454#41—262no—
455#41—262no—
456#41—262no—
457#41—262no—
458#41—262no—
459#41—521no—
460#41—521no—
461#41—521no—
462#41—521no—
463#41—521no—
464#41—521no—
465#41—521no—
466#41—521no—
467C2×Q8—132no—
468C2×Q8—268no—
469C2×Q8—261no—
470C2×Q8—261no—
471C2×Q8—261no—
472C2×Q8—261no—
473C2×Q8—261no—
474C2×Q8—528no—
475C2×D4—132no—
476C2×D4—262no—
477C2×D4—262no—
478C2×D4—261no—
479C2×D4—261no—
480C2×D4—261no—
481C2×D4—261no—
482C2×D4—261no—
483C2×D4—521no—
484C2×D4—521no—
485C2×D4—521no—
486C2×D4—521no—
487C22×C4—22no—
488C22×C4—41no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—262no—
492C22×C4—262no—
493C22×C4—261no—
494C22×C4—262no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4—524no—
498C22×C4—521no—
499C22×C4—521no—
500C22×C4—521no—
501C22×C4—521no—
502C22×C4C2×D5211yescharacteristic
503C22×C4C2×D5211yescharacteristic
504C22×C4#612711yescharacteristic
505C22×C4#612711yescharacteristic
506C22×C4#612711yescharacteristic
507C22×C4#612711yescharacteristic
508C22×C4D4×D1311yescharacteristic
509C22×C4D4×D1311yescharacteristic
510C22×C4D4×D1311yescharacteristic
511C22×C4#612911yescharacteristic
512C22×C4#612911yescharacteristic
513C22×C4Q8×D1311yescharacteristic
514C22×C4Q8×D1311yescharacteristic
515C22×C4C23×D1311yescharacteristic
516M16—22no—
517M16—22no—
518M16—41no—
519M16—41no—
520M16—262no—
521M16—262no—
522M16—521no—
523M16—521no—
524C2×C8—22no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—262no—
528C2×C8—521no—
529C2×C8—521no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—41no—
534C4⋊C4—268no—
535C4⋊C4—268no—
536C4⋊C4—268no—
537C4⋊C4—262no—
538C4⋊C4—262no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—41no—
543C22⋊C4—134no—
544C22⋊C4—262no—
545C42—22no—
546C42—22no—
547C42—41no—
548C42—132no—
549C42—132no—
550C42—262no—
551C42—261no—
552C42—261no—
553C42—262no—
554C42—262no—
555C42—262no—
556C42C2×D5214yes—
557C13C2×#203111yescharacteristic, complemented, Sylow
558C23—42no—
559C23—262no—
560C23—521no—
561C23—521no—
562C23—1042no—
563C23#8813611yescharacteristic
564C23#8813611yescharacteristic
565C23#8813911yescharacteristic
566C23#8813911yescharacteristic
567C23#8815011yescharacteristic
568C23#8815011yescharacteristic
569C23C2×D4×D1311yescharacteristic
570Q8—262no—
571Q8—262no—
572Q8—5216no—
573Q8—521no—
574Q8—521no—
575D4—262no—
576D4—262no—
577D4—522no—
578D4—522no—
579D4—522no—
580D4—522no—
581D4—521no—
582D4—521no—
583C2×C4—24no—
584C2×C4—44no—
585C2×C4—42no—
586C2×C4—82no—
587C2×C4—264no—
588C2×C4—262no—
589C2×C4—262no—
590C2×C4—264no—
591C2×C4—262no—
592C2×C4—524no—
593C2×C4—524no—
594C2×C4—522no—
595C2×C4—524no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—522no—
599C2×C4—522no—
600C2×C4—522no—
601C2×C4—522no—
602C2×C4#8812911yescharacteristic
603C2×C4#8812911yescharacteristic
604C2×C4#8812911yescharacteristic
605C2×C4#8812911yescharacteristic
606C2×C4#8813611yescharacteristic
607C2×C4#8813611yescharacteristic
608C2×C4#8813911yescharacteristic
609C2×C4#8813911yescharacteristic
610C2×C4#8813911yescharacteristic
611C2×C4#8813911yescharacteristic
612C2×C4#8813911yescharacteristic
613C2×C4#8813911yescharacteristic
614C2×C4#8815011yescharacteristic
615C2×C4#8815011yescharacteristic
616C2×C4#8815011yescharacteristic
617C2×C4#8815011yescharacteristic
618C2×C4#8815011yescharacteristic
619C2×C4#8815011yescharacteristic
620C2×C4#8815111yescharacteristic
621C2×C4#8815111yescharacteristic
622C2×C4#8815111yescharacteristic
623C2×C4#8815111yescharacteristic
624C2×C4C22×D5211yescharacteristic
625C2×C4C2×#612711yescharacteristic
626C2×C4C2×#612711yescharacteristic
627C2×C4C2×D4×D1311yescharacteristic
628C2×C4C2×#612911yescharacteristic
629C2×C4C2×Q8×D1311yescharacteristic
630C8—42no—
631C8—522no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—522no—
640C22—1042no—
641C22—1042no—
642C22—1042no—
643C22#1171833411yescharacteristic
644C22#1171833411yescharacteristic
645C22#1171833411yescharacteristic
646C22#1171833411yescharacteristic
647C22C2×#8813611yescharacteristic
648C22C2×#8813911yescharacteristic
649C22C2×#8815011yescharacteristic
650C4—44no—
651C4—82no—
652C4—264no—
653C4—522no—
654C4—524no—
655C4—522no—
656C4#1171833411yescharacteristic
657C4#1171833411yescharacteristic
658C4#1171833411yescharacteristic
659C4#1171833411yescharacteristic
660C4C2×#8812911yescharacteristic
661C4C2×#8813911yescharacteristic
662C4C2×#8815011yescharacteristic
663C4C2×#8815111yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—1042no—
671C2#1311600712yesdirect product factor
672C2C2×#1171833411yescharacteristic
subgroupG/H
centerC2×C4#88129
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×H(3,ℤ/4)C2
socleC22×C13#393
prime radicalC22×#6127C22
hypercenterC2×H(3,ℤ/4)D13
hypocenterC13C2×#2031
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. C2×#11719222C2semidirect
5. #13116007C2direct (N × H)
6. C2×#11718151C2semidirect
7. C2×#11718124C2semidirect
8. C2×C13×H(3,ℤ/4)C2semidirect
19. #11719222C22semidirect
34. C13×H(3,ℤ/4)C22semidirect
35. #11718151C22semidirect
36. #11718124C22semidirect
50. C2×#6127Q8semidirect
52. C22×D52Q8semidirect
55. C22×Dic26Q8semidirect
166. C2×D52C2×Q8semidirect
180. C2×Dic26C2×Q8semidirect
229. C2×H(3,ℤ/4)D13semidirect
331. H(3,ℤ/4)C2×D13semidirect
446. C2×C13#2031semidirect
557. C13C2×#2031semidirect
671. C2#13116007direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192222
C2×#117186662
C22×#880652
C2×#117186672
#131160072
C2×#117181512
C2×#117181242
C2×C13×H(3,ℤ/4)2
C2×#203113