Finite Group Databasebeta

← C2×#13116018 #15890367

Subgroups — C2×#13116018 #15890367

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88184C211yesmaximal, characteristic
2C22×#88047C211yesmaximal, characteristic, complemented
3C22×#88049C211yesmaximal, characteristic, complemented
4C22×#88049C211yesmaximal, characteristic, complemented
5C22×C22⋊#1055C211yesmaximal, characteristic, complemented
6#13116018C218yesmaximal, direct product factor
7C2×#11718121C211yesmaximal, characteristic, complemented
8C2×C13×#380C211yesmaximal, characteristic, complemented
9C24×C4×C13C2211yescharacteristic
10C23×C22⋊D13—21no—
11C23×D52C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4—21no—
15C2×#88184—22no—
16C2×#88184—24no—
17C2×#88184—24no—
18C2×#88184C2214yes—
19C22×#6103—21no—
20C22×C4⋊Dic13C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C13×#380—22no—
24C13×#380C2214yescomplemented
25C2×C13×#95—21no—
26C2×C22⋊#1055—24no—
27C2×C22⋊#1055C2214yescomplemented
28C2×#88049—24no—
29C2×#88049—24no—
30C2×#88049C2214yescomplemented
31C2×#88049C2214yescomplemented
32C2×#88047—24no—
33C2×#88047C2214yescomplemented
34#11718121C2214yescomplemented
35C25×C13D411yescharacteristic
36C24×D13—21no—
37C23×C4×C13—22no—
38C23×C4×C13—22no—
39C23×C4×C13—22no—
40C23×C4×C13—22no—
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13—21no—
44C23×C4×C13—21no—
45C23×C4×C13D412yes—
46C23×C4×C13D411yescharacteristic
47C23×C4×C13C2312yes—
48C23×C4×C13C2311yescharacteristic
49C22×C22⋊D13—28no—
50C22×C22⋊D13—24no—
51C22×C22⋊D13—44no—
52C22×C22⋊D13—44no—
53C23×Dic13—21no—
54C22×D52—22no—
55C22×D52—22no—
56C22×D52—22no—
57C22×D52—22no—
58C22×D52—22no—
59C22×D52—21no—
60C22×D52D414yes—
61C22×D52C2312yes—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2312yes—
69C2×C13×C4⋊C4C2312yes—
70C2×C13×C22⋊C4—24no—
71C2×C13×C22⋊C4—44no—
72#88184—216no—
73#88184—28no—
74#88184—28no—
75C2×#6103—28no—
76C2×#6103—24no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13D414yes—
80C2×C4⋊Dic13C2312yes—
81C22×#1055—22no—
82C22×#1055—22no—
83C22×#1055—22no—
84C22×#1055—22no—
85C22×#1055—22no—
86C22×#1055D414yescomplemented
87C22×#1055C2312yes—
88C22×#1055C2312yes—
89C13×#95—24no—
90C22⋊#1055—28no—
91#88049—28no—
92#88049—28no—
93#88047—28no—
94C2×#2033—131nomaximal, Sylow
95C24×C13—22no—
96C24×C13—22no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13D814yes—
102C24×C13C2×D412yes—
103C24×C13C2×D411yescharacteristic
104C23×D13—24no—
105C23×D13—22no—
106C23×D13—42no—
107C23×D13—42no—
108C23×D13—42no—
109C23×D13—42no—
110C23×D13—42no—
111C23×D13—42no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—24no—
116C22×C4×C13—24no—
117C22×C4×C13—24no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—44no—
127C22×C4×C13—44no—
128C22×C4×C13—44no—
129C22×C4×C13—44no—
130C22×C4×C13—42no—
131C22×C4×C13—42no—
132C22×C4×C13—42no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13C2×D412yes—
137C22×C4×C13C2×D412yes—
138C22×C4×C13C2×D412yes—
139C22×C4×C13C2×D412yes—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13#4112yes—
142C22×C4×C13#4112yes—
143C22×C4×C13#4112yes—
144C22×C4×C13C2411yescharacteristic
145C2×C22⋊D13—216no—
146C2×C22⋊D13—48no—
147C2×C22⋊D13—432no—
148C2×C22⋊D13—48no—
149C22×Dic13—24no—
150C22×Dic13—22no—
151C22×Dic13—42no—
152C22×Dic13—42no—
153C2×D52—28no—
154C2×D52—28no—
155C2×D52—22no—
156C2×D52—22no—
157C2×D52—22no—
158C2×D52—22no—
159C2×D52—24no—
160C2×D52—22no—
161C2×D52—44no—
162C2×D52—42no—
163C2×D52—42no—
164C2×D52—44no—
165C2×D52C2×D414yes—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—42no—
171C13×C4⋊C4—42no—
172C13×C22⋊C4—48no—
173#6103—216no—
174C4⋊Dic13—24no—
175C4⋊Dic13—22no—
176C4⋊Dic13C2×D414yes—
177C2×#1055—28no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055—22no—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#1055—44no—
184C2×#1055C2×D414yescomplemented
185C22×#121—131no—
186C22×#107—131no—
187C22×#102—131no—
188C22×#102—131no—
189C22×C22⋊C8—131no—
190C2×#380D1311yescharacteristic, complemented
191#2033—138no—
192C2×#340—131no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—28no—
200C23×C13—28no—
201C23×C13—28no—
202C23×C13—44no—
203C23×C13—44no—
204C23×C13—44no—
205C23×C13—44no—
206C23×C13#12012yes—
207C23×C13#12112yes—
208C23×C13#12312yes—
209C23×C13C2×D814yes—
210C23×C13C2×D812yes—
211C23×C13#13512yes—
212C23×C13AGL(1,ℤ/8)12yes—
213C23×C13#13712yes—
214C23×C13C22×D411yescharacteristic
215C22×D13—24no—
216C22×D13—42no—
217C22×D13—42no—
218C22×D13—42no—
219C22×D13—42no—
220C22×D13—42no—
221C22×D13—42no—
222C22×D13—48no—
223C22×D13—48no—
224C22×D13—48no—
225C22×D13—84no—
226C22×D13—84no—
227C22×D13—84no—
228C22×D13—84no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—44no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—48no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—84no—
245C2×C4×C13—84no—
246C2×C4×C13#12012yes—
247C2×C4×C13#12114yes—
248C2×C4×C13#12114yes—
249C2×C4×C13#12112yes—
250C2×C4×C13#12314yes—
251C2×C4×C13#12312yes—
252C2×C4×C13#12414yes—
253C2×C4×C13C22×D411yescharacteristic
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C22⋊D13—432no—
260C2×Dic13—24no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—48no—
264D52—24no—
265D52—24no—
266D52—42no—
267D52—42no—
268D52—48no—
269#1055—24no—
270#1055—42no—
271C23×D4—131no—
272C23×D4—261no—
273C24×C4C2×D1311yescharacteristic
274C23×C8—131no—
275C23×C8—131no—
276C2×#121—134no—
277C2×#121—264no—
278C2×#121—264no—
279C2×#121—262no—
280C22×C4⋊C4—131no—
281C22×C4⋊C4C2×D1311yescharacteristic
282C22×C4⋊C4C2×D1311yescharacteristic
283C22×C22⋊C4—21no—
284C22×C22⋊C4—261no—
285C2×#107—134no—
286C2×#107—264no—
287C2×#102—134no—
288C2×#102—134no—
289C2×#102—264no—
290C2×#102—264no—
291C2×C22⋊C8—134no—
292C2×C22⋊C8—264no—
293#380—22no—
294#380C2×D1314yescomplemented
295C2×#95—21no—
296#340—134no—
297C22×C13—24no—
298C22×C13—24no—
299C22×C13—24no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—42no—
303C22×C13—42no—
304C22×C13—416no—
305C22×C13#39414yes—
306C22×C13#44714yes—
307C22×C13#45214yes—
308C22×C13#46614yes—
309C22×C13#46814yes—
310C22×C13#48014yes—
311C22×C13#48214yes—
312C22×C13C2×#12011yescharacteristic
313C22×C13C2×#12111yescharacteristic
314C22×C13C2×#12311yescharacteristic
315C22×C13C22×D811yescharacteristic
316C22×C13C2×#13511yescharacteristic
317C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C13C2×#13711yescharacteristic
319C2×D13—44no—
320C2×D13—44no—
321C2×D13—44no—
322C2×D13—82no—
323C2×D13—82no—
324C2×D13—82no—
325C2×D13—82no—
326C2×D13—816no—
327C4×C13—42no—
328C4×C13—82no—
329C4×C13—82no—
330C4×C13#39414yes—
331C4×C13C2×#12111yescharacteristic
332C4×C13C2×#12111yescharacteristic
333C4×C13C2×#12311yescharacteristic
334C4×C13C2×#12411yescharacteristic
335Dic13—44no—
336C25—261no—
337C25C22⋊D1311yescharacteristic
338C22×D4—134no—
339C22×D4—132no—
340C22×D4—268no—
341C22×D4—264no—
342C22×D4—262no—
343C22×D4—262no—
344C22×D4—262no—
345C22×D4—262no—
346C22×D4—262no—
347C22×D4—261no—
348C22×D4—524no—
349C22×D4—524no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—261no—
359C23×C4C22⋊D1312yes—
360C23×C4C22⋊D1311yescharacteristic
361C23×C4C22×D1312yes—
362C23×C4C22×D1311yescharacteristic
363C22×C8—134no—
364C22×C8—132no—
365C22×C8—132no—
366C22×C8—262no—
367C22×C8—262no—
368C22×C8—262no—
369C22×C8—262no—
370C22×C8—262no—
371#121—268no—
372#121—268no—
373#121—2616no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—134no—
381C2×C4⋊C4—132no—
382C2×C4⋊C4—262no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4C22×D1312yes—
385C2×C4⋊C4C22×D1312yes—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—268no—
389C2×C22⋊C4—264no—
390#107—268no—
391#102—268no—
392#102—268no—
393C22⋊C8—268no—
394#95—24no—
395C2×C13—44no—
396C2×C13#203318yescomplemented
397C2×C13C2×#39411yescharacteristic
398C2×C13C2×#44711yescharacteristic
399C2×C13C2×#45211yescharacteristic
400C2×C13C2×#46611yescharacteristic
401C2×C13C2×#46811yescharacteristic
402C2×C13C2×#48011yescharacteristic
403C2×C13C2×#48211yescharacteristic
404D13—84no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—264no—
412C24—262no—
413C24—522no—
414C24—522no—
415C24—522no—
416C24—522no—
417C24—522no—
418C24—522no—
419C24#610414yes—
420C24C2×C22⋊D1312yes—
421C24C2×C22⋊D1311yescharacteristic
422C2×D4—134no—
423C2×D4—2616no—
424C2×D4—268no—
425C2×D4—268no—
426C2×D4—264no—
427C2×D4—262no—
428C2×D4—262no—
429C2×D4—262no—
430C2×D4—262no—
431C2×D4—262no—
432C2×D4—5232no—
433C2×D4—528no—
434C2×D4—528no—
435C2×D4—524no—
436C2×D4—524no—
437C2×D4—522no—
438C2×D4—522no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—264no—
464C22×C4—262no—
465C22×C4—522no—
466C22×C4—522no—
467C22×C4#612712yes—
468C22×C4#612712yes—
469C22×C4D4×D1312yes—
470C22×C4D4×D1312yes—
471C22×C4D4×D1312yes—
472C22×C4#612912yes—
473C22×C4C2×C22⋊D1312yes—
474C22×C4C2×C22⋊D1311yescharacteristic
475C22×C4C23×D1311yescharacteristic
476C2×C8—134no—
477C2×C8—268no—
478C2×C8—262no—
479C2×C8—262no—
480C2×C8—262no—
481C2×C8—262no—
482C2×C8—262no—
483C2×C8—524no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—134no—
491C4⋊C4—264no—
492C4⋊C4—262no—
493C22⋊C4—48no—
494C22⋊C4—2616no—
495C13C2×#203311yescharacteristic, complemented, Sylow
496C23—28no—
497C23—28no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—28no—
505C23—44no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—264no—
510C23—528no—
511C23—528no—
512C23—522no—
513C23—522no—
514C23—522no—
515C23—522no—
516C23—522no—
517C23—522no—
518C23—528no—
519C23—1044no—
520C23—1044no—
521C23—1044no—
522C23—1044no—
523C23#8818312yes—
524C23C2×#610414yes—
525C23C2×#610412yes—
526C23#8819112yes—
527C23#8819312yes—
528C23#8819612yes—
529C23#8820312yes—
530C23#8820412yes—
531C23C22×C22⋊D1311yescharacteristic
532D4—264no—
533D4—264no—
534D4—5232no—
535D4—522no—
536D4—522no—
537D4—528no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—48no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—84no—
554C2×C4—84no—
555C2×C4—264no—
556C2×C4—528no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4#8813714yes—
560C2×C4#8813814yes—
561C2×C4#8813814yes—
562C2×C4#8813914yes—
563C2×C4#8818312yes—
564C2×C4#8819112yes—
565C2×C4#8819312yes—
566C2×C4C2×#612711yescharacteristic
567C2×C4C2×#612711yescharacteristic
568C2×C4C2×D4×D1311yescharacteristic
569C2×C4C2×D4×D1311yescharacteristic
570C2×C4C2×D4×D1311yescharacteristic
571C2×C4C2×#612911yescharacteristic
572C8—264no—
573C8—522no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—416no—
581C22—42no—
582C22—524no—
583C22—524no—
584C22—524no—
585C22—1042no—
586C22—1042no—
587C22—1042no—
588C22—1042no—
589C22—10416no—
590C22#1171862014yes—
591C22#1171862814yes—
592C22#1171866414yes—
593C22#1171869714yes—
594C22#1171869914yes—
595C22#1171870814yes—
596C22#1171871014yes—
597C22C2×#8818311yescharacteristic
598C22C22×#610411yescharacteristic
599C22C2×#8819111yescharacteristic
600C22C2×#8819311yescharacteristic
601C22C2×#8819611yescharacteristic
602C22C2×#8820311yescharacteristic
603C22C2×#8820411yescharacteristic
604C4—42no—
605C4—82no—
606C4—82no—
607C4—524no—
608C4#1171862014yes—
609C4C2×#8813711yescharacteristic
610C4C2×#8813811yescharacteristic
611C4C2×#8813811yescharacteristic
612C4C2×#8813911yescharacteristic
613C2—44no—
614C2—1044no—
615C2#1311601818yesdirect product factor
616C2C2×#1171862011yescharacteristic
617C2C2×#1171869711yescharacteristic
618C2C2×#1171870811yescharacteristic
619C2C2×#1171869911yescharacteristic
620C2C2×#1171871011yescharacteristic
621C2C2×#1171862811yescharacteristic
622C2C2×#1171866411yescharacteristic
subgroupG/H
centerC24C2×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#380C2
socleC24×C13C2×D4
prime radicalC22×#88184C2
hypercenterC2×#380D13
hypocenterC13C2×#2033
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#88047C2semidirect
3. C22×#88049C2semidirect
4. C22×#88049C2semidirect
5. C22×C22⋊#1055C2semidirect
6. #13116018C2direct (N × H)
7. C2×#11718121C2semidirect
8. C2×C13×#380C2semidirect
24. C13×#380C22semidirect
27. C2×C22⋊#1055C22semidirect
30. C2×#88049C22semidirect
31. C2×#88049C22semidirect
33. C2×#88047C22semidirect
34. #11718121C22semidirect
86. C22×#1055D4semidirect
184. C2×#1055C2×D4semidirect
190. C2×#380D13semidirect
294. #380C2×D13semidirect
396. C2×C13#2033semidirect
495. C13C2×#2033semidirect
615. C2#13116018direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881842
C22×#880472
C22×#880492
C22×C22⋊#10552
#131160182
C2×#117181212
C2×C13×#3802
C2×#203313