Finite Group Databasebeta

← C2×#13116006 #15890341

Subgroups — C2×#13116006 #15890341

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
2C22×#88077C211yesmaximal, characteristic
3C2×#11718901C211yesmaximal, characteristic
4#13116006C218yesmaximal, direct product factor
5C2×#11718148C211yesmaximal, characteristic, complemented
6C2×#11718147C211yesmaximal, characteristic, complemented
7C2×#11718123C211yesmaximal, characteristic, complemented
8C2×C13×#421C211yesmaximal, characteristic
9C22×C13×#41C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C2×C13×#117C2211yescharacteristic
12C2×#88180C2211yescharacteristic
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—
24C13×#421—22no—
25C13×#421C2214yes—
26C2×C13×#104—22no—
27#11718901—22no—
28#11718901C2214yes—
29C2×#88077—21no—
30C2×#88077—21no—
31C2×#88077—22no—
32C2×#88077C2214yes—
33C2×#88074—22no—
34#11718148C2214yescomplemented
35#11718147C2214yescomplemented
36#11718123C2214yescomplemented
37C2×C13×#41—21no—
38C2×C13×#41—21no—
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C2×C13×#41—21no—
42C2×C13×#41—21no—
43C2×C13×#41—21no—
44C2×C13×#41—21no—
45C2×C13×#41—21no—
46C2×C13×#41—21no—
47C2×C13×#41Q812yescomplemented
48C2×C13×#41C2312yes—
49C22×Q8×C13Q811yescharacteristic, complemented
50C22×D4×C13—21no—
51C22×D4×C13Q811yescharacteristic, complemented
52C23×C4×C13—21no—
53C23×C4×C13C2311yescharacteristic
54C23×Dic13—21no—
55C22×Dic26—22no—
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×#117D412yes—
66C13×#117C2312yes—
67C2×C13×C4⋊C4—21no—
68C2×C13×C22⋊C4—21no—
69C2×C42×C13D412yes—
70C2×C22⋊Dic13—21no—
71C2×C22⋊Dic13D412yes—
72#88180—21no—
73#88180—21no—
74#88180—21no—
75#88180—21no—
76#88180—21no—
77#88180D412yes—
78#88180C2312yes—
79#88180C2312yes—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×#6101—22no—
84C2×#6101—22no—
85C2×C4×Dic13—21no—
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—
109C13×#104—28no—
110#88077—24no—
111#88077—24no—
112#88074—28no—
113C2×#2031—131nomaximal, Sylow
114C24×C13—21no—
115C24×C13C2×D411yescharacteristic
116C13×#41—22no—
117C13×#41—22no—
118C13×#41—22no—
119C13×#41—22no—
120C13×#41—22no—
121C13×#41—22no—
122C13×#41—22no—
123C13×#41—22no—
124C13×#41—41no—
125C13×#41—41no—
126C13×#41—41no—
127C13×#41—41no—
128C13×#41—41no—
129C13×#41—41no—
130C13×#41—41no—
131C13×#41—41no—
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13C2×Q812yescomplemented
138C2×D4×C13—22no—
139C2×D4×C13—22no—
140C2×D4×C13—21no—
141C2×D4×C13—21no—
142C2×D4×C13—21no—
143C2×D4×C13—21no—
144C2×D4×C13—21no—
145C2×D4×C13—41no—
146C2×D4×C13—41no—
147C2×D4×C13—41no—
148C2×D4×C13—41no—
149C2×D4×C13C2×Q812yescomplemented
150C22×C4×C13—22no—
151C22×C4×C13—21no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—41no—
155C22×C4×C13—41no—
156C22×C4×C13—41no—
157C22×C4×C13—41no—
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×Q811yescharacteristic
164C22×C4×C13C2×Q811yescharacteristic
165C22×C4×C13#4111yescharacteristic
166C22×C4×C13#4111yescharacteristic
167C22×C4×C13#4111yescharacteristic
168C22×C4×C13#4111yescharacteristic
169C22×C4×C13#4111yescharacteristic
170C22×C4×C13#4111yescharacteristic
171C22×C4×C13C2411yescharacteristic
172C22×Dic13—21no—
173C22×Dic13—22no—
174C22×Dic13—21no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—44no—
178C22×Dic13—41no—
179C2×Dic26—28no—
180C2×Dic26—48no—
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×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C42×C13—22no—
193C42×C13C2×D414yes—
194C22⋊Dic13—22no—
195C22⋊Dic13—22no—
196C22⋊Dic13—41no—
197C22⋊Dic13C2×D414yes—
198C4⋊Dic13—28no—
199C4⋊Dic13—22no—
200C4⋊Dic13—22no—
201C4⋊Dic13—22no—
202C4⋊Dic13—41no—
203#6101—28no—
204#6101—28no—
205C4×Dic13—22no—
206C4×Dic13—22no—
207C4×Dic13—21no—
208C4×Dic13—21no—
209C4×Dic13—22no—
210C4×Dic13—22no—
211C4×Dic13—22no—
212C4×Dic13—41no—
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×#421D1311yescharacteristic
224C22×#104—131no—
225C2×#410—131no—
226#2031—138no—
227C2×#344—131no—
228C2×#339—131no—
229C2×H(3,ℤ/4)—131no—
230C23×C13—22no—
231C23×C13—42no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13—82no—
235C23×C13#12011yescharacteristic
236C23×C13#12011yescharacteristic
237C23×C13C22⋊Q811yescharacteristic
238C23×C13C22⋊Q811yescharacteristic
239C23×C13#12411yescharacteristic
240C23×C13#12411yescharacteristic
241C23×C13C22×D411yescharacteristic
242Q8×C13—22no—
243Q8×C13—22no—
244Q8×C13—41no—
245Q8×C13—41no—
246D4×C13—22no—
247D4×C13—22no—
248D4×C13—42no—
249D4×C13—42no—
250D4×C13—42no—
251D4×C13—42no—
252D4×C13—41no—
253D4×C13—41no—
254C2×C4×C13—24no—
255C2×C4×C13—22no—
256C2×C4×C13—44no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13#12011yescharacteristic
264C2×C4×C13#12011yescharacteristic
265C2×C4×C13C22⋊Q811yescharacteristic
266C2×C4×C13C22⋊Q811yescharacteristic
267C2×C4×C13C22⋊Q811yescharacteristic
268C2×C4×C13C22⋊Q811yescharacteristic
269C2×C4×C13C22⋊Q811yescharacteristic
270C2×C4×C13C22⋊Q811yescharacteristic
271C2×C4×C13C22⋊Q811yescharacteristic
272C2×C4×C13C22⋊Q811yescharacteristic
273C2×C4×C13C22⋊Q811yescharacteristic
274C2×C4×C13C22⋊Q811yescharacteristic
275C2×C4×C13#12411yescharacteristic
276C2×C4×C13#12411yescharacteristic
277C2×C4×C13#12411yescharacteristic
278C2×C4×C13#12411yescharacteristic
279C2×C4×C13#12411yescharacteristic
280C2×C4×C13#12411yescharacteristic
281C2×C4×C13#12411yescharacteristic
282C2×C4×C13#12411yescharacteristic
283C2×C4×C13#12411yescharacteristic
284C2×C4×C13#12411yescharacteristic
285C2×C4×C13C22×D411yescharacteristic
286C2×C4×C13C22×D411yescharacteristic
287C2×C4×C13C22×Q811yescharacteristic
288C2×C4×C13C2×#4111yescharacteristic
289C2×C4×C13C2×#4111yescharacteristic
290C2×C4×C13C2×#4111yescharacteristic
291C2×Dic13—24no—
292C2×Dic13—22no—
293C2×Dic13—22no—
294C2×Dic13—24no—
295C2×Dic13—44no—
296C2×Dic13—44no—
297C2×Dic13—44no—
298C2×Dic13—42no—
299C2×Dic13—42no—
300C2×Dic13—82no—
301Dic26—416no—
302C8×C13—42no—
303#1055—42no—
304C22×#41C2×D1311yescharacteristic
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×#117—131no—
317C2×#117C2×D1311yescharacteristic
318C22×C42—131no—
319#421—22no—
320#421C2×D1314yes—
321C2×#104—22no—
322C2×#104—134no—
323C2×#104—261no—
324C2×#104—261no—
325C2×#104—262no—
326#410—134no—
327#410—262no—
328C2×#99—262no—
329#344—134no—
330#339—134no—
331H(3,ℤ/4)—134no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—22no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—42no—
340C22×C13—82no—
341C22×C13—82no—
342C22×C13—82no—
343C22×C13#39311yescharacteristic
344C22×C13#39311yescharacteristic
345C22×C13#39311yescharacteristic
346C22×C13#39311yescharacteristic
347C22×C13C2×#12011yescharacteristic
348C22×C13C2×C22⋊Q811yescharacteristic
349C22×C13C2×#12411yescharacteristic
350C4×C13—44no—
351C4×C13—42no—
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—82no—
364C2×#41—21no—
365C2×#41—21no—
366C2×#41—21no—
367C2×#41—21no—
368C2×#41—21no—
369C2×#41—21no—
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41Dic2612yescomplemented
375C2×#41C22×D1312yes—
376C22×Q8—262no—
377C22×Q8Dic2611yescharacteristic, complemented
378C22×D4—21no—
379C22×D4Dic2611yescharacteristic, complemented
380C23×C4—21no—
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—132no—
408#117—132no—
409#117—132no—
410#117—261no—
411#117—261no—
412#117—261no—
413#117—261no—
414#117—261no—
415#117C22⋊D1312yes—
416#117C22×D1312yes—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—262no—
419C2×C4⋊C4—262no—
420C2×C4⋊C4—262no—
421C2×C4⋊C4—261no—
422C2×C4⋊C4—261no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—132no—
425C2×C22⋊C4—261no—
426C2×C42—131no—
427C2×C42—131no—
428C2×C42—132no—
429C2×C42—132no—
430C2×C42—261no—
431C2×C42—261no—
432C2×C42—261no—
433C2×C42—261no—
434C2×C42—261no—
435C2×C42C22⋊D1312yes—
436#104—28no—
437#104—264no—
438#104—264no—
439#99—268no—
440C2×C13—21no—
441C2×C13—21no—
442C2×C13—21no—
443C2×C13—21no—
444C2×C13—21no—
445C2×C13—21no—
446C2×C13—82no—
447C2×C13#203112yescomplemented
448C2×C13C2×#39311yescharacteristic
449C24—21no—
450C24D4×D1311yescharacteristic
451#41—22no—
452#41—22no—
453#41—22no—
454#41—22no—
455#41—22no—
456#41—22no—
457#41—22no—
458#41—22no—
459#41—41no—
460#41—41no—
461#41—41no—
462#41—41no—
463#41—41no—
464#41—41no—
465#41—41no—
466#41—41no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—268no—
473C2×Q8—528no—
474C2×Q8C2×Dic2612yescomplemented
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4C2×Dic2612yescomplemented
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—261no—
496C22×C4—261no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—524no—
501C22×C4—521no—
502C22×C4C2×Dic2611yescharacteristic
503C22×C4C2×Dic2611yescharacteristic
504C22×C4#612711yescharacteristic
505C22×C4#612711yescharacteristic
506C22×C4D4×D1311yescharacteristic
507C22×C4D4×D1311yescharacteristic
508C22×C4D4×D1311yescharacteristic
509C22×C4#612911yescharacteristic
510C22×C4#612911yescharacteristic
511C22×C4#612911yescharacteristic
512C22×C4#612911yescharacteristic
513C22×C4C2×C22⋊D1311yescharacteristic
514C22×C4C2×C22⋊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—268no—
533C4⋊C4—268no—
534C4⋊C4—268no—
535C4⋊C4—262no—
536C4⋊C4—262no—
537C4⋊C4—262no—
538C4⋊C4—521no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—134no—
542C22⋊C4—262no—
543C22⋊C4—262no—
544C22⋊C4—521no—
545C42—22no—
546C42—132no—
547C42—132no—
548C42—262no—
549C42—261no—
550C42—261no—
551C42—262no—
552C42—262no—
553C42—262no—
554C42—262no—
555C42—521no—
556C42C2×C22⋊D1314yes—
557C13C2×#203111yescharacteristic, complemented, Sylow
558C23—22no—
559C23—42no—
560C23—41no—
561C23—41no—
562C23—82no—
563C23#8813211yescharacteristic
564C23#8813211yescharacteristic
565C23#8813911yescharacteristic
566C23#8813911yescharacteristic
567C23#8819111yescharacteristic
568C23#8819111yescharacteristic
569C23C2×D4×D1311yescharacteristic
570Q8—22no—
571Q8—22no—
572Q8—41no—
573Q8—41no—
574Q8—5216no—
575D4—22no—
576D4—22no—
577D4—42no—
578D4—42no—
579D4—42no—
580D4—42no—
581D4—41no—
582D4—41no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—44no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—264no—
593C2×C4—262no—
594C2×C4—262no—
595C2×C4—264no—
596C2×C4—524no—
597C2×C4—524no—
598C2×C4—522no—
599C2×C4—524no—
600C2×C4—522no—
601C2×C4—1042no—
602C2×C4#8813211yescharacteristic
603C2×C4#8813211yescharacteristic
604C2×C4#8813211yescharacteristic
605C2×C4#8813211yescharacteristic
606C2×C4#8813211yescharacteristic
607C2×C4#8813211yescharacteristic
608C2×C4#8813911yescharacteristic
609C2×C4#8813911yescharacteristic
610C2×C4#8813911yescharacteristic
611C2×C4#8813911yescharacteristic
612C2×C4#8813911yescharacteristic
613C2×C4#8813911yescharacteristic
614C2×C4#8817811yescharacteristic
615C2×C4#8817811yescharacteristic
616C2×C4#8817811yescharacteristic
617C2×C4#8817811yescharacteristic
618C2×C4#8819011yescharacteristic
619C2×C4#8819011yescharacteristic
620C2×C4#8819011yescharacteristic
621C2×C4#8819011yescharacteristic
622C2×C4#8819111yescharacteristic
623C2×C4#8819111yescharacteristic
624C2×C4C22×Dic2611yescharacteristic
625C2×C4C2×#612711yescharacteristic
626C2×C4C2×D4×D1311yescharacteristic
627C2×C4C2×#612911yescharacteristic
628C2×C4C2×#612911yescharacteristic
629C2×C4C22×C22⋊D1311yescharacteristic
630C8—42no—
631C8—522no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—42no—
640C22—82no—
641C22—82no—
642C22—82no—
643C22#1171860811yescharacteristic
644C22#1171860811yescharacteristic
645C22#1171860811yescharacteristic
646C22#1171860811yescharacteristic
647C22C2×#8813211yescharacteristic
648C22C2×#8813911yescharacteristic
649C22C2×#8819111yescharacteristic
650C4—44no—
651C4—42no—
652C4—264no—
653C4—522no—
654C4—524no—
655C4—1042no—
656C4#1171860811yescharacteristic
657C4#1171860811yescharacteristic
658C4#1171860811yescharacteristic
659C4#1171860811yescharacteristic
660C4C2×#8813211yescharacteristic
661C4C2×#8813911yescharacteristic
662C4C2×#8817811yescharacteristic
663C4C2×#8819011yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—82no—
671C2#1311600612yesdirect product factor
672C2C2×#1171860811yescharacteristic
subgroupG/H
centerC2×C4#88190
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#421C2
socleC22×C13#393
prime radicalC22×C13×#41C22
hypercenterC2×#421D13
hypocenterC13C2×#2031
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×#11719222C2semidirect
4. #13116006C2direct (N × H)
5. C2×#11718148C2semidirect
6. C2×#11718147C2semidirect
7. C2×#11718123C2semidirect
19. #11719222C22semidirect
34. #11718148C22semidirect
35. #11718147C22semidirect
36. #11718123C22semidirect
47. C2×C13×#41Q8semidirect
49. C22×Q8×C13Q8semidirect
51. C22×D4×C13Q8semidirect
137. C2×Q8×C13C2×Q8semidirect
149. C2×D4×C13C2×Q8semidirect
374. C2×#41Dic26semidirect
377. C22×Q8Dic26semidirect
379. C22×D4Dic26semidirect
447. C2×C13#2031semidirect
474. C2×Q8C2×Dic26semidirect
486. C2×D4C2×Dic26semidirect
557. C13C2×#2031semidirect
671. C2#13116006direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192222
C22×#880772
C2×#117189012
#131160062
C2×#117181482
C2×#117181472
C2×#117181232
C2×C13×#4212
C2×#203113