Finite Group Databasebeta

← C2×#13114623 #15860564

Subgroups — C2×#13114623 #15860564

Order 3328.

2242 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88135C211yesmaximal, characteristic
2C22×#88046C212yesmaximal
3C2×C22⋊C4×Dic13C212yesmaximal, complemented
4#13114623C218yesmaximal, direct product factor
5C2×#11718118C211yesmaximal, characteristic, complemented
6C2×C13×#342C211yesmaximal, characteristic, complemented
7C23×C22⋊D13C2211yescharacteristic
8C24×Dic13C2211yescharacteristic
9C23×C4×D13C411yescharacteristic, complemented
10C22×C13×C22⋊C4C2211yescharacteristic
11C22×C13×C22⋊C4C2212yes—
12C22×C22⋊Dic13C2212yes—
13C22×#6103C411yescharacteristic, complemented
14C22×#6101C411yescharacteristic, complemented
15C22×C4×Dic13—22no—
16C22×C4×Dic13C411yescharacteristic, complemented
17C2×#88135—22no—
18C2×#88135—24no—
19C2×#88135—22no—
20C2×#88135C414yescomplemented
21C2×#88135C2214yes—
22C2×#88071—22no—
23C2×#88046C4116yescomplemented
24C2×#88046C2218yes—
25C22⋊C4×Dic13—24no—
26C22⋊C4×Dic13C2218yescomplemented
27C13×#342C2214yescomplemented
28#11718118C2214yescomplemented
29C25×C13C2311yescharacteristic
30C24×D13C2×C411yescharacteristic
31C23×C4×C13—22no—
32C23×C4×C13C2×C411yescharacteristic
33C23×C4×C13C2×C411yescharacteristic
34C22×C22⋊D13—22no—
35C22×C22⋊D13—22no—
36C22×C22⋊D13—22no—
37C22×C22⋊D13—22no—
38C22×C22⋊D13C2×C418yes—
39C22×C22⋊D13C2×C412yes—
40C22×C22⋊D13C2312yes—
41C23×Dic13—22no—
42C23×Dic13—44no—
43C23×Dic13C2×C411yescharacteristic
44C23×Dic13C2×C411yescharacteristic
45C23×Dic13C2×C412yes—
46C23×Dic13C2×C411yescharacteristic
47C23×Dic13D412yes—
48C23×Dic13D414yes—
49C23×Dic13D412yes—
50C23×Dic13C2312yes—
51C22×C4×D13—22no—
52C22×C4×D13—21no—
53C22×C4×D13—21no—
54C22×C4×D13—44no—
55C22×C4×D13C2×C414yescomplemented
56C2×C13×C22⋊C4—22no—
57C2×C13×C22⋊C4—22no—
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4—24no—
60C2×C13×C22⋊C4C2×C412yes—
61C2×C13×C22⋊C4C2×C418yescomplemented
62C2×C13×C22⋊C4C2312yes—
63C2×C13×C22⋊C4C2314yes—
64C2×C22⋊Dic13—22no—
65C2×C22⋊Dic13—24no—
66C2×C22⋊Dic13C2×C418yescomplemented
67C2×C22⋊Dic13C2314yes—
68C2×#6103—22no—
69C2×#6103—22no—
70C2×#6103C2×C414yescomplemented
71C2×#6101—22no—
72C2×#6101—22no—
73C2×#6101C2×C414yescomplemented
74C2×C4×Dic13—22no—
75C2×C4×Dic13—21no—
76C2×C4×Dic13—21no—
77C2×C4×Dic13—28no—
78C2×C4×Dic13—48no—
79C2×C4×Dic13C2×C414yescomplemented
80#88135—28no—
81#88135—28no—
82#88135—28no—
83#88135—28no—
84#88071—28no—
85#88046C2×C4132yescomplemented
86C2×C4×#99—131nomaximal, Sylow
87C24×C13—42no—
88C24×C13—42no—
89C24×C13C22×C411yescharacteristic
90C24×C13C22×C411yescharacteristic
91C24×C13C22×C414yes—
92C24×C13C2×D412yes—
93C24×C13C2×D412yes—
94C24×C13#4112yes—
95C24×C13#4112yes—
96C24×C13C2411yescharacteristic
97C23×D13—21no—
98C23×D13—21no—
99C23×D13—22no—
100C23×D13—42no—
101C23×D13—42no—
102C23×D13C4214yescomplemented
103C23×D13C22×C412yes—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—28no—
109C22×C4×C13—24no—
110C22×C4×C13—44no—
111C22×C4×C13—44no—
112C22×C4×C13—42no—
113C22×C4×C13—42no—
114C22×C4×C13C22×C412yes—
115C22×C4×C13C22×C412yes—
116C2×C22⋊D13—24no—
117C2×C22⋊D13—24no—
118C2×C22⋊D13—28no—
119C2×C22⋊D13—28no—
120C2×C22⋊D13—28no—
121C2×C22⋊D13—28no—
122C2×C22⋊D13—24no—
123C2×C22⋊D13—22no—
124C2×C22⋊D13—22no—
125C2×C22⋊D13C4218yescomplemented
126C2×C22⋊D13C22×C418yes—
127C22×Dic13—21no—
128C22×Dic13—21no—
129C22×Dic13—22no—
130C22×Dic13—28no—
131C22×Dic13—24no—
132C22×Dic13—28no—
133C22×Dic13—24no—
134C22×Dic13—44no—
135C22×Dic13—48no—
136C22×Dic13—44no—
137C22×Dic13—42no—
138C22×Dic13—44no—
139C22×Dic13—44no—
140C22×Dic13—44no—
141C22×Dic13C4214yescomplemented
142C22×Dic13C22⋊C414yes—
143C22×Dic13C22⋊C411yescharacteristic
144C22×Dic13C22⋊C412yes—
145C22×Dic13C22⋊C412yes—
146C22×Dic13C22⋊C414yes—
147C22×Dic13C22⋊C412yes—
148C22×Dic13C22⋊C411yescharacteristic
149C22×Dic13C22×C412yes—
150C22×Dic13C22×C412yes—
151C22×Dic13C22×C412yes—
152C22×Dic13C2×D414yes—
153C22×Dic13C2×D414yes—
154C2×C4×D13—24no—
155C2×C4×D13—24no—
156C2×C4×D13—44no—
157C2×C4×D13—48no—
158C2×C4×D13—44no—
159C2×C4×D13—48no—
160C13×C22⋊C4—24no—
161C13×C22⋊C4—28no—
162C13×C22⋊C4—24no—
163C13×C22⋊C4—24no—
164C13×C22⋊C4C22×C418yescomplemented
165C22⋊Dic13—28no—
166C22⋊Dic13—24no—
167C22⋊Dic13C22×C418yescomplemented
168#6103—28no—
169#6101—28no—
170C4×Dic13—24no—
171C4×Dic13—24no—
172C4×Dic13—416no—
173C22×C4×D4—131no—
174C22×#99—132no—
175C2×C4×C22⋊C4—132no—
176C4×#99—138no—
177C2×#342—131no—
178C2×#342D1311yescharacteristic, complemented
179C23×C13—24no—
180C23×C13—22no—
181C23×C13—24no—
182C23×C13—22no—
183C23×C13—41no—
184C23×C13—42no—
185C23×C13—41no—
186C23×C13—41no—
187C23×C13—48no—
188C23×C13—42no—
189C23×C13—44no—
190C23×C13—44no—
191C23×C13—41no—
192C23×C13C2×C4212yes—
193C23×C13C2×C4212yes—
194C23×C13C2×C22⋊C412yes—
195C23×C13C2×C22⋊C411yescharacteristic
196C23×C13C2×C22⋊C411yescharacteristic
197C23×C13#11712yes—
198C23×C13#11712yes—
199C23×C13C4×D414yes—
200C23×C13C4×D414yes—
201C23×C13C4×D414yes—
202C23×C13C4×D414yes—
203C23×C13C23×C411yescharacteristic
204C23×C13C23×C412yes—
205C23×C13C22×D412yes—
206C23×C13C2×#4111yescharacteristic
207C23×C13C2×#4111yescharacteristic
208C22×D13—22no—
209C22×D13—22no—
210C22×D13—24no—
211C22×D13—24no—
212C22×D13—42no—
213C22×D13—42no—
214C22×D13—48no—
215C22×D13—42no—
216C22×D13—42no—
217C22×D13—42no—
218C22×D13—48no—
219C22×D13—42no—
220C22×D13C2×C4214yescomplemented
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—28no—
224C2×C4×C13—44no—
225C2×C4×C13—42no—
226C2×C4×C13—44no—
227C2×C4×C13—416no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C22⋊D13—28no—
234C22⋊D13—28no—
235C22⋊D13—216no—
236C2×Dic13—22no—
237C2×Dic13—22no—
238C2×Dic13—24no—
239C2×Dic13—24no—
240C2×Dic13—22no—
241C2×Dic13—24no—
242C2×Dic13—28no—
243C2×Dic13—24no—
244C2×Dic13—24no—
245C2×Dic13—28no—
246C2×Dic13—28no—
247C2×Dic13—44no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—44no—
251C2×Dic13—44no—
252C2×Dic13—44no—
253C2×Dic13—416no—
254C2×Dic13#9914yescomplemented
255C2×Dic13C2×C4214yescomplemented
256C2×Dic13C2×C22⋊C412yes—
257C2×Dic13C2×C22⋊C414yes—
258C2×Dic13C2×C22⋊C412yes—
259C4×D13—48no—
260C4×D13—48no—
261C23×D4—131no—
262C24×C4—131no—
263C24×C4—131no—
264C2×C4×D4—134no—
265C2×C4×D4—134no—
266C2×C4×D4—262no—
267C2×C4×D4—262no—
268C2×C4×D4—264no—
269C22×C4⋊C4—131no—
270C22×C22⋊C4—132no—
271C22×C22⋊C4—131no—
272C22×C22⋊C4C2×D1311yescharacteristic
273C22×C22⋊C4C2×D1312yes—
274C22×C42—131no—
275C22×C42—262no—
276C2×#99—1316no—
277C2×#99—138no—
278C4×C22⋊C4—138no—
279C4×C22⋊C4—264no—
280C2×#95—262no—
281#342—134no—
282#342C2×D1314yescomplemented
283C22×C13—22no—
284C22×C13—21no—
285C22×C13—21no—
286C22×C13—22no—
287C22×C13—22no—
288C22×C13—21no—
289C22×C13—21no—
290C22×C13—22no—
291C22×C13—28no—
292C22×C13—28no—
293C22×C13—24no—
294C22×C13—24no—
295C22×C13—42no—
296C22×C13—42no—
297C22×C13—44no—
298C22×C13—44no—
299C22×C13—42no—
300C22×C13—41no—
301C22×C13—41no—
302C22×C13C4×C22⋊C412yes—
303C22×C13C4×C22⋊C414yes—
304C22×C13C4×C22⋊C412yes—
305C22×C13C2×#9912yes—
306C22×C13#41012yes—
307C22×C13C22×C4211yescharacteristic
308C22×C13C22×C22⋊C411yescharacteristic
309C22×C13C2×#11711yescharacteristic
310C22×C13C2×C4×D412yes—
311C22×C13C2×C4×D412yes—
312C2×D13—24no—
313C2×D13—44no—
314C2×D13—48no—
315C2×D13—42no—
316C2×D13—42no—
317C2×D13—48no—
318C2×D13—44no—
319C4×C13—48no—
320C4×C13—42no—
321C4×C13—42no—
322Dic13—22no—
323Dic13—24no—
324Dic13—24no—
325Dic13—48no—
326Dic13C2×#9914yescomplemented
327C25—131no—
328C25C22×D1311yescharacteristic
329C22×D4—132no—
330C22×D4—138no—
331C22×D4—132no—
332C22×D4—262no—
333C22×D4—262no—
334C22×D4—262no—
335C22×D4—262no—
336C23×C4—22no—
337C23×C4—131no—
338C23×C4—131no—
339C23×C4—132no—
340C23×C4—131no—
341C23×C4—132no—
342C23×C4—132no—
343C23×C4—134no—
344C23×C4—132no—
345C23×C4—134no—
346C23×C4—262no—
347C23×C4—261no—
348C23×C4—261no—
349C23×C4—262no—
350C23×C4—524no—
351C23×C4—524no—
352C23×C4C4×D1311yescharacteristic
353C23×C4C4×D1311yescharacteristic
354C4×D4—268no—
355C4×D4—268no—
356C4×D4—268no—
357C4×D4—268no—
358C2×C4⋊C4—134no—
359C2×C4⋊C4—262no—
360C2×C4⋊C4—262no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—138no—
366C2×C22⋊C4—134no—
367C2×C22⋊C4—134no—
368C2×C22⋊C4—262no—
369C2×C22⋊C4—262no—
370C2×C22⋊C4—262no—
371C2×C22⋊C4—264no—
372C2×C22⋊C4C4×D1312yes—
373C2×C22⋊C4C4×D1318yescomplemented
374C2×C22⋊C4C22×D1312yes—
375C2×C22⋊C4C22×D1314yes—
376C2×C42—134no—
377C2×C42—262no—
378C2×C42—261no—
379C2×C42—261no—
380C2×C42—268no—
381C2×C42—528no—
382#99—1332no—
383#95—268no—
384C2×C13—22no—
385C2×C13—22no—
386C2×C13—21no—
387C2×C13—22no—
388C2×C13—21no—
389C2×C13—24no—
390C2×C13C4×#9914yescomplemented
391C2×C13C2×C4×C22⋊C411yescharacteristic
392C2×C13C22×#9911yescharacteristic
393C2×C13C2×#41011yescharacteristic
394D13—44no—
395C24—42no—
396C24—42no—
397C24—134no—
398C24—132no—
399C24—261no—
400C24—261no—
401C24—262no—
402C24—522no—
403C24—522no—
404C24C2×C4×D1311yescharacteristic
405C24C2×C4×D1311yescharacteristic
406C24C2×C4×D1314yes—
407C24D4×D1312yes—
408C24D4×D1312yes—
409C24#612912yes—
410C24#613112yes—
411C24C23×D1311yescharacteristic
412C2×D4—138no—
413C2×D4—138no—
414C2×D4—264no—
415C2×D4—268no—
416C2×D4—268no—
417C2×D4—264no—
418C2×D4—268no—
419C2×D4—268no—
420C2×D4—264no—
421C2×D4—262no—
422C2×D4—262no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—28no—
428C22×C4—24no—
429C22×C4—44no—
430C22×C4—44no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—131no—
434C22×C4—134no—
435C22×C4—132no—
436C22×C4—134no—
437C22×C4—131no—
438C22×C4—132no—
439C22×C4—132no—
440C22×C4—132no—
441C22×C4—134no—
442C22×C4—132no—
443C22×C4—134no—
444C22×C4—132no—
445C22×C4—134no—
446C22×C4—264no—
447C22×C4—264no—
448C22×C4—268no—
449C22×C4—264no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—262no—
453C22×C4—268no—
454C22×C4—264no—
455C22×C4—524no—
456C22×C4—528no—
457C22×C4—524no—
458C22×C4—528no—
459C22×C4—524no—
460C22×C4—528no—
461C22×C4—524no—
462C22×C4—522no—
463C22×C4—524no—
464C22×C4—524no—
465C22×C4—524no—
466C22×C4C2×C4×D1312yes—
467C22×C4C2×C4×D1312yes—
468C4⋊C4—268no—
469C22⋊C4—24no—
470C22⋊C4—28no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—138no—
474C22⋊C4—268no—
475C22⋊C4—268no—
476C22⋊C4—264no—
477C22⋊C4C2×C4×D1318yescomplemented
478C42—264no—
479C42—264no—
480C42—5216no—
481C13C2×C4×#9911yescharacteristic, complemented, Sylow
482C23—24no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—41no—
487C23—42no—
488C23—41no—
489C23—41no—
490C23—48no—
491C23—42no—
492C23—44no—
493C23—44no—
494C23—41no—
495C23—134no—
496C23—262no—
497C23—262no—
498C23—264no—
499C23—264no—
500C23—522no—
501C23—522no—
502C23—528no—
503C23—522no—
504C23—522no—
505C23—528no—
506C23—522no—
507C23—522no—
508C23C42×D1312yes—
509C23C42×D1312yes—
510C23C22⋊C4×D1312yes—
511C23C22⋊C4×D1311yescharacteristic
512C23C22⋊C4×D1311yescharacteristic
513C23#8813514yes—
514C23#8813514yes—
515C23#8814612yes—
516C23#8814612yes—
517C23#8814714yes—
518C23#8814714yes—
519C23C22×C4×D1311yescharacteristic
520C23C22×C4×D1312yes—
521C23C2×D4×D1312yes—
522C23C2×#612911yescharacteristic
523C23C2×#613111yescharacteristic
524D4—268no—
525D4—268no—
526D4—2616no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—28no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—416no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—134no—
540C2×C4—132no—
541C2×C4—134no—
542C2×C4—132no—
543C2×C4—134no—
544C2×C4—268no—
545C2×C4—268no—
546C2×C4—264no—
547C2×C4—264no—
548C2×C4—264no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—262no—
552C2×C4—264no—
553C2×C4—264no—
554C2×C4—268no—
555C2×C4—528no—
556C2×C4—528no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4—524no—
560C2×C4—524no—
561C2×C4—524no—
562C2×C4—524no—
563C2×C4—5216no—
564C22—22no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—28no—
573C22—28no—
574C22—24no—
575C22—24no—
576C22—42no—
577C22—44no—
578C22—42no—
579C22—44no—
580C22—42no—
581C22—41no—
582C22—41no—
583C22—264no—
584C22—524no—
585C22—524no—
586C22—528no—
587C22—522no—
588C22—522no—
589C22—528no—
590C22#1171832712yes—
591C22#1171832714yes—
592C22#1171832712yes—
593C22#1171840112yes—
594C22D13×#9912yes—
595C22C2×C42×D1311yescharacteristic
596C22C2×C22⋊C4×D1311yescharacteristic
597C22C2×#8813512yes—
598C22C2×#8814611yescharacteristic
599C22C2×#8814712yes—
600C4—48no—
601C4—42no—
602C4—42no—
603C4—134no—
604C4—264no—
605C4—262no—
606C4—264no—
607C4—528no—
608C2—22no—
609C2—22no—
610C2—21no—
611C2—21no—
612C2—22no—
613C2—24no—
614C2—524no—
615C2#1311462314yesdirect product factor
616C2C2×#1171832711yescharacteristic
617C2C2×D13×#9911yescharacteristic
618C2C2×#1171840111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C13C22×C42
FrattiniC24C23×D13
FittingC2×C13×#342C2
socleC23×C13C2×C22⋊C4
prime radicalC23×C22⋊D13C22
cosocleC24×C13C24
hypercenterC2×#342D13
hypocenterC13C2×C4×#99
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic13C2semidirect
4. #13114623C2direct (N × H)
5. C2×#11718118C2semidirect
6. C2×C13×#342C2semidirect
9. C23×C4×D13C4semidirect
13. C22×#6103C4semidirect
14. C22×#6101C4semidirect
16. C22×C4×Dic13C4semidirect
20. C2×#88135C4semidirect
23. C2×#88046C4semidirect
26. C22⋊C4×Dic13C22semidirect
27. C13×#342C22semidirect
28. #11718118C22semidirect
55. C22×C4×D13C2×C4semidirect
61. C2×C13×C22⋊C4C2×C4semidirect
66. C2×C22⋊Dic13C2×C4semidirect
70. C2×#6103C2×C4semidirect
73. C2×#6101C2×C4semidirect
79. C2×C4×Dic13C2×C4semidirect
85. #88046C2×C4semidirect
102. C23×D13C42semidirect
125. C2×C22⋊D13C42semidirect
141. C22×Dic13C42semidirect
164. C13×C22⋊C4C22×C4semidirect
167. C22⋊Dic13C22×C4semidirect
178. C2×#342D13semidirect
220. C22×D13C2×C42semidirect
254. C2×Dic13#99semidirect
255. C2×Dic13C2×C42semidirect
282. #342C2×D13semidirect
326. Dic13C2×#99semidirect
373. C2×C22⋊C4C4×D13semidirect
390. C2×C13C4×#99semidirect
477. C22⋊C4C2×C4×D13semidirect
481. C13C2×C4×#99semidirect
615. C2#13114623direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881352
C22×#880462
C2×C22⋊C4×Dic132
#131146232
C2×#117181182
C2×C13×#3422
C2×C4×#9913