Finite Group Databasebeta

← C2×#13116050 #15890509

Subgroups — C2×#13116050 #15890509

Order 3328.

1434 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718656C211yesmaximal, characteristic, complemented
2C22×#88077C211yesmaximal, characteristic
3C2×#11718893C211yesmaximal, characteristic
4C22×#88076C211yesmaximal, characteristic, complemented
5C2×#11718891C211yesmaximal, characteristic, complemented
6#13116050C218yesmaximal, direct product factor
7C2×#11718124C211yesmaximal, characteristic, complemented
8C2×C13×#536C211yesmaximal, characteristic
9C22×C13×#41C2211yescharacteristic
10C23×Q8×C13C2211yescharacteristic
11C13×#536—22no—
12C13×#536—22no—
13C13×#536—22no—
14C13×#536C2214yes—
15C2×C13×C4⋊Q8—21no—
16C2×C13×#124—21no—
17C2×C13×#123—22no—
18C2×C13×C22⋊Q8—21no—
19C2×C13×C22⋊Q8—21no—
20C2×C13×#117C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23C22×#6099C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C2×#88077—24no—
26C2×#88077C2214yes—
27#11718893—22no—
28#11718893C2214yes—
29#11718891—22no—
30#11718891C2214yescomplemented
31C2×#88076—24no—
32C2×#88076C2214yescomplemented
33C2×#88075—21no—
34C2×#88072—21no—
35C2×#88071—22no—
36#11718656—22no—
37#11718656C2214yescomplemented
38C2×#88048—21no—
39C2×#88047—21no—
40#11718124C2214yescomplemented
41C2×C13×#41—21no—
42C2×C13×#41—21no—
43C2×C13×#41—22no—
44C2×C13×#41—22no—
45C2×C13×#41—22no—
46C2×C13×#41—22no—
47C2×C13×#41D412yes—
48C2×C13×#41C2312yes—
49C22×Q8×C13—21no—
50C22×Q8×C13—21no—
51C22×Q8×C13—21no—
52C22×Q8×C13—21no—
53C22×Q8×C13—22no—
54C22×Q8×C13—22no—
55C22×Q8×C13—22no—
56C22×Q8×C13—22no—
57C22×Q8×C13D411yescharacteristic
58C22×Q8×C13D412yes—
59C22×Q8×C13C2312yes—
60C22×D4×C13—21no—
61C22×D4×C13D411yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13D412yes—
64C23×C4×C13C2311yescharacteristic
65C23×Dic13—21no—
66C23×Dic13—21no—
67C13×C4⋊Q8—24no—
68C13×C4⋊Q8—24no—
69C13×#124—24no—
70C13×#124—24no—
71C13×#123—28no—
72C13×#123—28no—
73C13×C22⋊Q8—24no—
74C13×C22⋊Q8—24no—
75C13×C22⋊Q8—24no—
76C13×C22⋊Q8—24no—
77C13×#117—21no—
78C13×#117—21no—
79C13×#117D412yes—
80C13×#117C2312yes—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4D411yescharacteristic
84C2×C13×C4⋊C4D411yescharacteristic
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—21no—
88C2×C42×C13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13C2312yes—
95C2×C4×Dic13—22no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13C2312yes—
99C2×#6099—21no—
100C2×#6099—22no—
101C2×#6099—21no—
102C2×#6099—22no—
103C2×#6099—22no—
104C2×#6099D414yes—
105C2×#6099C2312yes—
106C2×#6099C2312yes—
107C22×#1055—21no—
108C22×#1055—21no—
109#88077—28no—
110#88076—28no—
111#88075—24no—
112#88072—24no—
113#88071—28no—
114#88048—24no—
115#88047—24no—
116C2×#2038—131nomaximal, Sylow
117C24×C13—21no—
118C24×C13C2×D411yescharacteristic
119C13×#41—24no—
120C13×#41—24no—
121C13×#41—22no—
122C13×#41—22no—
123C13×#41—22no—
124C13×#41—22no—
125C13×#41—42no—
126C13×#41—42no—
127C13×#41—42no—
128C13×#41—42no—
129C2×Q8×C13—22no—
130C2×Q8×C13—22no—
131C2×Q8×C13—21no—
132C2×Q8×C13—24no—
133C2×Q8×C13—24no—
134C2×Q8×C13—22no—
135C2×Q8×C13—22no—
136C2×Q8×C13—22no—
137C2×Q8×C13—22no—
138C2×Q8×C13—22no—
139C2×Q8×C13—22no—
140C2×Q8×C13—22no—
141C2×Q8×C13—22no—
142C2×Q8×C13—42no—
143C2×Q8×C13—42no—
144C2×Q8×C13—42no—
145C2×Q8×C13—42no—
146C2×Q8×C13—42no—
147C2×Q8×C13—42no—
148C2×Q8×C13—42no—
149C2×Q8×C13—42no—
150C2×Q8×C13C2×D412yes—
151C2×D4×C13—22no—
152C2×D4×C13—22no—
153C2×D4×C13—21no—
154C2×D4×C13—22no—
155C2×D4×C13—22no—
156C2×D4×C13—42no—
157C2×D4×C13—42no—
158C2×D4×C13C2×D412yes—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—22no—
162C22×C4×C13—21no—
163C22×C4×C13—22no—
164C22×C4×C13—24no—
165C22×C4×C13—24no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—42no—
169C22×C4×C13—42no—
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2×D414yes—
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13#4112yes—
178C22×C4×C13#4112yes—
179C22×C4×C13#4112yes—
180C22×C4×C13C2411yescharacteristic
181C22×Dic13—24no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—42no—
185C22×Dic13—42no—
186C22×Dic13—44no—
187C22×Dic13—41no—
188C22×Dic13—41no—
189C13×C4⋊C4—28no—
190C13×C4⋊C4—28no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4C2×D412yes—
194C13×C4⋊C4C2×D412yes—
195C13×C22⋊C4—28no—
196C13×C22⋊C4—28no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C42×C13—22no—
200C42×C13—22no—
201C4⋊Dic13—22no—
202C4⋊Dic13—22no—
203C4⋊Dic13—41no—
204C4⋊Dic13—41no—
205C4×Dic13—22no—
206C4×Dic13—22no—
207C4×Dic13—42no—
208#6099—24no—
209#6099—22no—
210#6099—22no—
211#6099—22no—
212#6099—42no—
213#6099C2×D414yes—
214C2×#1055—24no—
215C2×#1055—22no—
216C2×#1055—22no—
217C2×#1055—42no—
218C2×#536D1311yescharacteristic
219C2×#428—131no—
220C22×#104—131no—
221C2×#417—131no—
222C22×#101—131no—
223C2×#391—131no—
224#2038—138no—
225C2×#339—131no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—42no—
230C23×C13—42no—
231C23×C13—42no—
232C23×C13#12011yescharacteristic
233C23×C13#12011yescharacteristic
234C23×C13#12112yes—
235C23×C13#12312yes—
236C23×C13C22×D411yescharacteristic
237Q8×C13—22no—
238Q8×C13—22no—
239Q8×C13—42no—
240Q8×C13—42no—
241Q8×C13—42no—
242Q8×C13—42no—
243Q8×C13—44no—
244Q8×C13—44no—
245Q8×C13—42no—
246D4×C13—22no—
247D4×C13—22no—
248D4×C13—42no—
249D4×C13—42no—
250D4×C13—44no—
251D4×C13—42no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—24no—
255C2×C4×C13—22no—
256C2×C4×C13—24no—
257C2×C4×C13—24no—
258C2×C4×C13—44no—
259C2×C4×C13—44no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—44no—
266C2×C4×C13#12011yescharacteristic
267C2×C4×C13#12011yescharacteristic
268C2×C4×C13#12112yes—
269C2×C4×C13#12112yes—
270C2×C4×C13#12112yes—
271C2×C4×C13#12112yes—
272C2×C4×C13#12112yes—
273C2×C4×C13#12312yes—
274C2×C4×C13#12312yes—
275C2×C4×C13#12312yes—
276C2×C4×C13#12412yes—
277C2×C4×C13#12412yes—
278C2×C4×C13C22×D411yescharacteristic
279C2×C4×C13C22×D411yescharacteristic
280C2×C4×C13C22×D411yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13C2×#4111yescharacteristic
284C2×Dic13—24no—
285C2×Dic13—42no—
286C2×Dic13—48no—
287C2×Dic13—42no—
288C2×Dic13—44no—
289C2×Dic13—42no—
290C2×Dic13—82no—
291C2×Dic13—82no—
292#1055—24no—
293#1055—42no—
294C22×#41C2×D1311yescharacteristic
295C23×Q8C2×D1311yescharacteristic
296C22×M16—131no—
297C22×M16—131no—
298#536—22no—
299#536—22no—
300#536—22no—
301#536C2×D1314yes—
302C2×C4⋊Q8—21no—
303C2×#124—21no—
304C2×#123—22no—
305C2×C22⋊Q8—21no—
306C2×C22⋊Q8—21no—
307C2×#117C2×D1311yescharacteristic
308C22×C4⋊C4—131no—
309C22×C42—131no—
310#428—134no—
311#428—262no—
312C2×#107—261no—
313C2×#106—261no—
314C2×#104—134no—
315C2×#104—264no—
316#417—134no—
317#417—262no—
318C2×#103—261no—
319C2×#102—261no—
320C2×#101—134no—
321C2×#101—264no—
322#391—134no—
323#391—262no—
324C2×#95—262no—
325#339—134no—
326C22×C13—21no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13—21no—
330C22×C13—24no—
331C22×C13—24no—
332C22×C13—42no—
333C22×C13—42no—
334C22×C13—42no—
335C22×C13—84no—
336C22×C13#39412yes—
337C22×C13#39412yes—
338C22×C13#45412yes—
339C22×C13#45612yes—
340C22×C13C2×#12011yescharacteristic
341C22×C13C2×#12111yescharacteristic
342C22×C13C2×#12311yescharacteristic
343C4×C13—44no—
344C4×C13—42no—
345C4×C13—42no—
346C4×C13—42no—
347C4×C13#39412yes—
348C4×C13#39412yes—
349C4×C13C2×#12111yescharacteristic
350C4×C13C2×#12111yescharacteristic
351C4×C13C2×#12311yescharacteristic
352C4×C13C2×#12411yescharacteristic
353Dic13—44no—
354Dic13—82no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—22no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41C22⋊D1312yes—
362C2×#41C22×D1312yes—
363C22×Q8—22no—
364C22×Q8—22no—
365C22×Q8—22no—
366C22×Q8—22no—
367C22×Q8—21no—
368C22×Q8—21no—
369C22×Q8—21no—
370C22×Q8—21no—
371C22×Q8C22⋊D1311yescharacteristic
372C22×Q8C22⋊D1312yes—
373C22×Q8C22×D1312yes—
374C22×D4—21no—
375C22×D4C22⋊D1311yescharacteristic
376C23×C4—21no—
377C23×C4—261no—
378C23×C4—261no—
379C23×C4C22⋊D1312yes—
380C23×C4C22×D1311yescharacteristic
381C2×M16—134no—
382C2×M16—132no—
383C2×M16—132no—
384C2×M16—262no—
385C2×M16—261no—
386C2×M16—261no—
387C2×M16—262no—
388C2×M16—262no—
389C22×C8—261no—
390C22×C8—261no—
391C4⋊Q8—24no—
392C4⋊Q8—24no—
393#124—24no—
394#124—24no—
395#123—28no—
396#123—28no—
397C22⋊Q8—24no—
398C22⋊Q8—24no—
399C22⋊Q8—24no—
400C22⋊Q8—24no—
401#117—21no—
402#117—21no—
403#117C22⋊D1312yes—
404#117C22×D1312yes—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—132no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4C22⋊D1311yescharacteristic
414C2×C4⋊C4C22⋊D1311yescharacteristic
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—21no—
418C2×C42—21no—
419C2×C42—132no—
420C2×C42—262no—
421C2×C42—262no—
422C2×C42—261no—
423#107—264no—
424#106—264no—
425#104—268no—
426#103—264no—
427#102—264no—
428#101—268no—
429#95—268no—
430C2×C13—21no—
431C2×C13—21no—
432C2×C13—22no—
433C2×C13—82no—
434C2×C13#203814yescomplemented
435C2×C13C2×#39411yescharacteristic
436C2×C13C2×#45411yescharacteristic
437C2×C13C2×#45611yescharacteristic
438C24—21no—
439C24C2×C22⋊D1311yescharacteristic
440#41—24no—
441#41—24no—
442#41—22no—
443#41—22no—
444#41—22no—
445#41—22no—
446#41—42no—
447#41—42no—
448#41—42no—
449#41—42no—
450C2×Q8—24no—
451C2×Q8—24no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—21no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8C2×C22⋊D1312yes—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4C2×C22⋊D1312yes—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—264no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—522no—
495C22×C4—522no—
496C22×C4—524no—
497C22×C4—521no—
498C22×C4—521no—
499C22×C4D4×D1312yes—
500C22×C4#612912yes—
501C22×C4#612912yes—
502C22×C4#612912yes—
503C22×C4C2×C22⋊D1314yes—
504C22×C4C2×C22⋊D1311yescharacteristic
505C22×C4C2×C22⋊D1311yescharacteristic
506C22×C4C2×C22⋊D1311yescharacteristic
507C22×C4C2×C22⋊D1311yescharacteristic
508C22×C4C2×C22⋊D1311yescharacteristic
509C22×C4C23×D1311yescharacteristic
510M16—134no—
511M16—264no—
512M16—262no—
513M16—262no—
514M16—262no—
515M16—522no—
516C2×C8—264no—
517C2×C8—262no—
518C2×C8—262no—
519C2×C8—522no—
520C4⋊C4—28no—
521C4⋊C4—28no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—262no—
525C4⋊C4—262no—
526C4⋊C4—521no—
527C4⋊C4—521no—
528C4⋊C4C2×C22⋊D1312yes—
529C4⋊C4C2×C22⋊D1312yes—
530C22⋊C4—28no—
531C22⋊C4—28no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C42—22no—
535C42—22no—
536C42—262no—
537C42—262no—
538C42—522no—
539C13C2×#203811yescharacteristic, complemented, Sylow
540C23—22no—
541C23—22no—
542C23—22no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23#8818912yes—
547C23#8819312yes—
548C23#8820711yescharacteristic
549C23#8820711yescharacteristic
550C23C22×C22⋊D1311yescharacteristic
551Q8—22no—
552Q8—22no—
553Q8—42no—
554Q8—42no—
555Q8—42no—
556Q8—42no—
557Q8—44no—
558Q8—44no—
559Q8—42no—
560D4—22no—
561D4—22no—
562D4—42no—
563D4—42no—
564D4—44no—
565D4—42no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—44no—
580C2×C4—264no—
581C2×C4—522no—
582C2×C4—528no—
583C2×C4—522no—
584C2×C4—524no—
585C2×C4—522no—
586C2×C4—1042no—
587C2×C4—1042no—
588C2×C4#8818912yes—
589C2×C4#8818912yes—
590C2×C4#8818912yes—
591C2×C4#8819012yes—
592C2×C4#8819012yes—
593C2×C4#8819212yes—
594C2×C4#8819212yes—
595C2×C4#8819312yes—
596C2×C4#8819312yes—
597C2×C4#8819312yes—
598C2×C4#8820711yescharacteristic
599C2×C4#8820711yescharacteristic
600C2×C4C2×D4×D1311yescharacteristic
601C2×C4C2×#612911yescharacteristic
602C2×C4C2×#612911yescharacteristic
603C2×C4C2×#612911yescharacteristic
604C2×C4C22×C22⋊D1311yescharacteristic
605C2×C4C22×C22⋊D1311yescharacteristic
606C8—264no—
607C8—522no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—24no—
613C22—24no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—84no—
618C22#1171888312yes—
619C22#1171888312yes—
620C22#1171890612yes—
621C22#1171890712yes—
622C22C2×#8818911yescharacteristic
623C22C2×#8819311yescharacteristic
624C22C2×#8820711yescharacteristic
625C4—42no—
626C4—42no—
627C4—44no—
628C4—42no—
629C4—524no—
630C4—1042no—
631C4#1171888312yes—
632C4#1171888312yes—
633C4C2×#8818911yescharacteristic
634C4C2×#8819011yescharacteristic
635C4C2×#8819211yescharacteristic
636C4C2×#8819311yescharacteristic
637C2—21no—
638C2—21no—
639C2—22no—
640C2—82no—
641C2#1311605014yesdirect product factor
642C2C2×#1171888311yescharacteristic
643C2C2×#1171890611yescharacteristic
644C2C2×#1171890711yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#536C2
socleC23×C13#120
prime radicalC22×C13×#41C22
hypercenterC2×#536D13
hypocenterC13C2×#2038
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#11718656C2semidirect
4. C22×#88076C2semidirect
5. C2×#11718891C2semidirect
6. #13116050C2direct (N × H)
7. C2×#11718124C2semidirect
30. #11718891C22semidirect
32. C2×#88076C22semidirect
37. #11718656C22semidirect
40. #11718124C22semidirect
434. C2×C13#2038semidirect
539. C13C2×#2038semidirect
641. C2#13116050direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117186562
C22×#880772
C2×#117188932
C22×#880762
C2×#117188912
#131160502
C2×#117181242
C2×C13×#5362
C2×#203813