Finite Group Databasebeta

← C2×#99×Dic13 #15860567

Subgroups — C2×#99×Dic13 #15860567

Order 3328.

2242 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×D4×Dic13C211yesmaximal, characteristic
2C22×#88074C211yesmaximal, characteristic
3C2×C22⋊C4×Dic13C212yesmaximal, complemented
4#99×Dic13C218yesmaximal, direct product factor
5C2×#11718119C212yesmaximal, complemented
6C22×C13×#99C211yesmaximal, characteristic
7C23×D4×C13C2211yescharacteristic
8C24×Dic13C411yescharacteristic, complemented
9C24×Dic13C2211yescharacteristic
10C22×C13×C22⋊C4C2212yes—
11C22×C22⋊Dic13C411yescharacteristic, complemented
12C22×C22⋊Dic13C2211yescharacteristic
13C22×C22⋊Dic13C2212yes—
14C2×D4×Dic13—22no—
15C2×D4×Dic13—24no—
16C2×D4×Dic13—22no—
17C2×D4×Dic13C414yescomplemented
18C2×D4×Dic13C2214yes—
19C22×C4⋊Dic13C411yescharacteristic, complemented
20C22×C4×Dic13—22no—
21C22×C4×Dic13C411yescharacteristic, complemented
22C2×C13×#99C418yescomplemented
23C2×C13×#99C2214yes—
24C2×#88074C418yescomplemented
25C2×#88074C2214yes—
26C2×#88071—22no—
27C22⋊C4×Dic13—24no—
28C22⋊C4×Dic13C2218yescomplemented
29#11718119C2218yescomplemented
30C25×C13C2×C411yescharacteristic
31C25×C13C2311yescharacteristic
32C22×D4×C13—22no—
33C22×D4×C13—22no—
34C22×D4×C13—24no—
35C22×D4×C13C2×C414yes—
36C22×D4×C13C2×C412yes—
37C22×D4×C13C2×C414yes—
38C22×D4×C13C2312yes—
39C23×C4×C13—22no—
40C23×C4×C13C2×C411yescharacteristic
41C23×Dic13—22no—
42C23×Dic13—22no—
43C23×Dic13—21no—
44C23×Dic13—21no—
45C23×Dic13—44no—
46C23×Dic13—44no—
47C23×Dic13C2×C411yescharacteristic
48C23×Dic13C2×C411yescharacteristic
49C23×Dic13C2×C411yescharacteristic
50C23×Dic13C2×C411yescharacteristic
51C23×Dic13C2×C412yes—
52C23×Dic13C2×C414yescomplemented
53C23×Dic13D412yes—
54C23×Dic13D414yes—
55C23×Dic13D412yes—
56C23×Dic13C2312yes—
57C2×C13×C22⋊C4—22no—
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4C2×C418yescomplemented
60C2×C13×C22⋊C4C2314yes—
61C2×C22⋊Dic13—22no—
62C2×C22⋊Dic13—22no—
63C2×C22⋊Dic13—22no—
64C2×C22⋊Dic13—24no—
65C2×C22⋊Dic13—22no—
66C2×C22⋊Dic13—22no—
67C2×C22⋊Dic13C2×C412yes—
68C2×C22⋊Dic13C2×C414yescomplemented
69C2×C22⋊Dic13C2×C418yescomplemented
70C2×C22⋊Dic13C2312yes—
71C2×C22⋊Dic13C2314yes—
72D4×Dic13—28no—
73D4×Dic13—28no—
74D4×Dic13—28no—
75D4×Dic13—28no—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13C2×C414yescomplemented
79C2×C4×Dic13—22no—
80C2×C4×Dic13—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13—28no—
83C2×C4×Dic13—48no—
84C2×C4×Dic13C2×C414yescomplemented
85C13×#99C2×C4116yescomplemented
86#88074C2×C4116yescomplemented
87#88071—28no—
88C2×C4×#99—131nomaximal, Sylow
89C24×C13—21no—
90C24×C13—21no—
91C24×C13—22no—
92C24×C13—42no—
93C24×C13—42no—
94C24×C13—42no—
95C24×C13—42no—
96C24×C13C4214yescomplemented
97C24×C13C22×C411yescharacteristic
98C24×C13C22×C412yes—
99C24×C13C22×C411yescharacteristic
100C24×C13C22×C412yes—
101C24×C13C22×C412yes—
102C24×C13C2×D412yes—
103C24×C13C2×D412yes—
104C24×C13#4114yes—
105C24×C13C2411yescharacteristic
106C2×D4×C13—24no—
107C2×D4×C13—24no—
108C2×D4×C13—28no—
109C2×D4×C13—28no—
110C2×D4×C13—28no—
111C2×D4×C13—28no—
112C2×D4×C13—24no—
113C2×D4×C13—24no—
114C2×D4×C13C4218yescomplemented
115C2×D4×C13C22×C414yes—
116C2×D4×C13C22×C414yes—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—22no—
120C22×C4×C13—28no—
121C22×C4×C13—24no—
122C22×C4×C13—44no—
123C22×C4×C13—44no—
124C22×C4×C13C4214yescomplemented
125C22×C4×C13C22×C412yes—
126C22×Dic13—28no—
127C22×Dic13—24no—
128C22×Dic13—21no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—28no—
133C22×Dic13—24no—
134C22×Dic13—24no—
135C22×Dic13—24no—
136C22×Dic13—44no—
137C22×Dic13—48no—
138C22×Dic13—44no—
139C22×Dic13—42no—
140C22×Dic13—44no—
141C22×Dic13—44no—
142C22×Dic13—48no—
143C22×Dic13—48no—
144C22×Dic13—44no—
145C22×Dic13—44no—
146C22×Dic13—44no—
147C22×Dic13—42no—
148C22×Dic13—42no—
149C22×Dic13C22⋊C411yescharacteristic
150C22×Dic13C22⋊C412yes—
151C22×Dic13C22⋊C412yes—
152C22×Dic13C22⋊C414yes—
153C22×Dic13C22⋊C412yes—
154C22×Dic13C22⋊C414yes—
155C22×Dic13C22⋊C411yescharacteristic
156C22×Dic13C22×C412yes—
157C22×Dic13C22×C412yes—
158C22×Dic13C22×C412yes—
159C22×Dic13C22×C412yes—
160C22×Dic13C2×D414yes—
161C22×Dic13C2×D414yes—
162C13×C22⋊C4—28no—
163C13×C22⋊C4—24no—
164C13×C22⋊C4C22×C418yescomplemented
165C22⋊Dic13—24no—
166C22⋊Dic13—28no—
167C22⋊Dic13—24no—
168C22⋊Dic13—24no—
169C22⋊Dic13—28no—
170C22⋊Dic13C22×C418yescomplemented
171C4⋊Dic13—28no—
172C4×Dic13—24no—
173C4×Dic13—24no—
174C4×Dic13—416no—
175C22×C4×D4—131no—
176C22×#99—131no—
177C22×#99D1311yescharacteristic
178C2×C4×C22⋊C4—132no—
179C4×#99—138no—
180C2×#342—132no—
181C23×C13—24no—
182C23×C13—22no—
183C23×C13—24no—
184C23×C13—22no—
185C23×C13—22no—
186C23×C13—22no—
187C23×C13—24no—
188C23×C13—24no—
189C23×C13—41no—
190C23×C13—42no—
191C23×C13—41no—
192C23×C13—41no—
193C23×C13—44no—
194C23×C13—44no—
195C23×C13—42no—
196C23×C13—48no—
197C23×C13—41no—
198C23×C13—42no—
199C23×C13—42no—
200C23×C13—48no—
201C23×C13—42no—
202C23×C13—48no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—42no—
206C23×C13C2×C4212yes—
207C23×C13C2×C4212yes—
208C23×C13C2×C4214yescomplemented
209C23×C13C2×C22⋊C412yes—
210C23×C13C2×C22⋊C411yescharacteristic
211C23×C13C2×C22⋊C411yescharacteristic
212C23×C13#11712yes—
213C23×C13#11712yes—
214C23×C13C4×D414yes—
215C23×C13C4×D414yes—
216C23×C13C4×D414yes—
217C23×C13C4×D414yes—
218C23×C13C23×C411yescharacteristic
219C23×C13C23×C411yescharacteristic
220C23×C13C23×C411yescharacteristic
221C23×C13C22×D412yes—
222C23×C13C2×#4112yes—
223D4×C13—28no—
224D4×C13—28no—
225D4×C13—216no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—28no—
231C2×C4×C13—44no—
232C2×C4×C13—44no—
233C2×C4×C13—416no—
234C2×C4×C13C2×C4214yescomplemented
235C2×Dic13—22no—
236C2×Dic13—24no—
237C2×Dic13—28no—
238C2×Dic13—24no—
239C2×Dic13—24no—
240C2×Dic13—28no—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—28no—
244C2×Dic13—44no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—44no—
248C2×Dic13—48no—
249C2×Dic13—44no—
250C2×Dic13—44no—
251C2×Dic13—416no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—48no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13#9914yesdirect product factor
260C2×Dic13C2×C22⋊C412yes—
261C2×Dic13C2×C22⋊C414yes—
262C2×Dic13C2×C22⋊C412yes—
263C23×D4C2×D1311yescharacteristic
264C24×C4—131no—
265C24×C4—131no—
266C2×C4×D4—134no—
267C2×C4×D4—134no—
268C2×C4×D4—262no—
269C2×C4×D4—262no—
270C2×C4×D4—264no—
271C22×C4⋊C4—131no—
272C22×C22⋊C4—132no—
273C22×C22⋊C4—131no—
274C22×C22⋊C4—131no—
275C22×C22⋊C4C2×D1312yes—
276C22×C42—131no—
277C22×C42—262no—
278C2×#99—138no—
279C2×#99—134no—
280C2×#99Dic1318yesdirect product factor
281C2×#99C2×D1314yes—
282C4×C22⋊C4—138no—
283C4×C22⋊C4—264no—
284C2×#95—262no—
285#342—138no—
286C22×C13—22no—
287C22×C13—21no—
288C22×C13—21no—
289C22×C13—22no—
290C22×C13—22no—
291C22×C13—21no—
292C22×C13—21no—
293C22×C13—22no—
294C22×C13—28no—
295C22×C13—28no—
296C22×C13—24no—
297C22×C13—24no—
298C22×C13—24no—
299C22×C13—42no—
300C22×C13—42no—
301C22×C13—44no—
302C22×C13—44no—
303C22×C13—41no—
304C22×C13—41no—
305C22×C13—42no—
306C22×C13—44no—
307C22×C13—44no—
308C22×C13—48no—
309C22×C13—42no—
310C22×C13—42no—
311C22×C13—48no—
312C22×C13C4×C22⋊C412yes—
313C22×C13C4×C22⋊C414yes—
314C22×C13C4×C22⋊C412yes—
315C22×C13C2×#9912yes—
316C22×C13#41012yes—
317C22×C13C22×C4211yescharacteristic
318C22×C13C22×C22⋊C411yescharacteristic
319C22×C13C2×#11711yescharacteristic
320C22×C13C2×C4×D412yes—
321C22×C13C2×C4×D412yes—
322C4×C13—24no—
323C4×C13—48no—
324Dic13—22no—
325Dic13—24no—
326Dic13—48no—
327Dic13—42no—
328Dic13—42no—
329Dic13C2×#9914yesdirect product factor
330C25C4×D1311yescharacteristic
331C25C22×D1311yescharacteristic
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4C4×D1314yes—
336C22×D4C4×D1312yes—
337C22×D4C2×Dic1314yes—
338C22×D4C22×D1312yes—
339C23×C4—22no—
340C23×C4—131no—
341C23×C4—132no—
342C23×C4—131no—
343C23×C4—132no—
344C23×C4—132no—
345C23×C4—134no—
346C23×C4—132no—
347C23×C4—131no—
348C23×C4—131no—
349C23×C4—134no—
350C23×C4—261no—
351C23×C4—262no—
352C23×C4—261no—
353C23×C4—262no—
354C23×C4—524no—
355C23×C4—524no—
356C23×C4C4×D1311yescharacteristic
357C4×D4—268no—
358C4×D4—268no—
359C4×D4—268no—
360C4×D4—268no—
361C2×C4⋊C4—134no—
362C2×C4⋊C4—262no—
363C2×C4⋊C4—262no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—138no—
367C2×C22⋊C4—134no—
368C2×C22⋊C4—132no—
369C2×C22⋊C4—134no—
370C2×C22⋊C4—132no—
371C2×C22⋊C4—262no—
372C2×C22⋊C4—262no—
373C2×C22⋊C4—262no—
374C2×C22⋊C4—262no—
375C2×C22⋊C4—262no—
376C2×C22⋊C4—264no—
377C2×C22⋊C4C2×Dic1318yescomplemented
378C2×C22⋊C4C22×D1314yes—
379C2×C42—134no—
380C2×C42—262no—
381C2×C42—261no—
382C2×C42—261no—
383C2×C42—268no—
384C2×C42—528no—
385#99—1316no—
386#99C2×Dic13116yesdirect product factor
387#95—268no—
388C2×C13—22no—
389C2×C13—22no—
390C2×C13—21no—
391C2×C13—22no—
392C2×C13—21no—
393C2×C13—24no—
394C2×C13—44no—
395C2×C13C4×#9914yescomplemented
396C2×C13C2×C4×C22⋊C411yescharacteristic
397C2×C13C22×#9911yescharacteristic
398C2×C13C2×#41011yescharacteristic
399C24—22no—
400C24—21no—
401C24—21no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24C4×Dic1314yescomplemented
407C24C2×C4×D1311yescharacteristic
408C24C2×C4×D1312yes—
409C24C2×C4×D1311yescharacteristic
410C24C2×C4×D1312yes—
411C24D4×D1312yes—
412C24D4×D1312yes—
413C24#612914yes—
414C24C22×Dic1312yes—
415C24C23×D1311yescharacteristic
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4—28no—
422C2×D4—24no—
423C2×D4—24no—
424C2×D4C4×Dic1318yescomplemented
425C2×D4C2×C4×D1314yes—
426C2×D4C22×Dic1314yes—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—28no—
431C22×C4—24no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—131no—
435C22×C4—132no—
436C22×C4—134no—
437C22×C4—131no—
438C22×C4—132no—
439C22×C4—132no—
440C22×C4—134no—
441C22×C4—132no—
442C22×C4—134no—
443C22×C4—132no—
444C22×C4—134no—
445C22×C4—132no—
446C22×C4—132no—
447C22×C4—268no—
448C22×C4—264no—
449C22×C4—264no—
450C22×C4—264no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—268no—
456C22×C4—264no—
457C22×C4—524no—
458C22×C4—524no—
459C22×C4—528no—
460C22×C4—524no—
461C22×C4—522no—
462C22×C4—524no—
463C22×C4—528no—
464C22×C4—524no—
465C22×C4—528no—
466C22×C4—524no—
467C22×C4—524no—
468C22×C4—522no—
469C22×C4—522no—
470C22×C4C4×Dic1314yescomplemented
471C22×C4C2×C4×D1312yes—
472C4⋊C4—268no—
473C22⋊C4—28no—
474C22⋊C4—24no—
475C22⋊C4—138no—
476C22⋊C4—268no—
477C22⋊C4—264no—
478C22⋊C4—268no—
479C22⋊C4—264no—
480C22⋊C4—264no—
481C22⋊C4C22×Dic1318yescomplemented
482C42—264no—
483C42—264no—
484C42—5216no—
485C13C2×C4×#9911yescharacteristic, complemented, Sylow
486C23—24no—
487C23—22no—
488C23—24no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—24no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—44no—
498C23—41no—
499C23—42no—
500C23—48no—
501C23—44no—
502C23—41no—
503C23—42no—
504C23—48no—
505C23—42no—
506C23—42no—
507C23—48no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23#8813112yes—
512C23#8813112yes—
513C23C22⋊C4×D1312yes—
514C23C22⋊C4×D1311yescharacteristic
515C23C22⋊C4×D1311yescharacteristic
516C23#8813514yes—
517C23#8813514yes—
518C23C2×C4×Dic1312yes—
519C23C2×C4×Dic1312yes—
520C23C2×C4×Dic1314yescomplemented
521C23D4×Dic1314yes—
522C23D4×Dic1314yes—
523C23C22×C4×D1311yescharacteristic
524C23C22×C4×D1311yescharacteristic
525C23C2×D4×D1312yes—
526C23C2×#612912yes—
527C23C23×Dic1311yescharacteristic
528D4—28no—
529D4—28no—
530D4—216no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—28no—
536C2×C4—44no—
537C2×C4—416no—
538C2×C4—44no—
539C2×C4—134no—
540C2×C4—132no—
541C2×C4—132no—
542C2×C4—134no—
543C2×C4—268no—
544C2×C4—268no—
545C2×C4—264no—
546C2×C4—264no—
547C2×C4—264no—
548C2×C4—262no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—268no—
552C2×C4—528no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—524no—
556C2×C4—524no—
557C2×C4—528no—
558C2×C4—524no—
559C2×C4—5216no—
560C2×C4—524no—
561C2×C4—522no—
562C2×C4—522no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4C2×C4×Dic1314yescomplemented
568C22—28no—
569C22—28no—
570C22—24no—
571C22—24no—
572C22—22no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—22no—
577C22—21no—
578C22—21no—
579C22—22no—
580C22—24no—
581C22—42no—
582C22—44no—
583C22—42no—
584C22—44no—
585C22—41no—
586C22—42no—
587C22—41no—
588C22—44no—
589C22—44no—
590C22—48no—
591C22—48no—
592C22—42no—
593C22—42no—
594C22#1171840112yes—
595C22D13×#9912yes—
596C22C22⋊C4×Dic1312yes—
597C22C22⋊C4×Dic1314yes—
598C22C22⋊C4×Dic1312yes—
599C22C2×#8813111yescharacteristic
600C22C2×C22⋊C4×D1311yescharacteristic
601C22C2×#8813512yes—
602C22C22×C4×Dic1311yescharacteristic
603C22C2×D4×Dic1312yes—
604C4—24no—
605C4—48no—
606C4—134no—
607C4—264no—
608C4—262no—
609C4—528no—
610C4—522no—
611C4—522no—
612C2—22no—
613C2—22no—
614C2—21no—
615C2—21no—
616C2—22no—
617C2—24no—
618C2—44no—
619C2#99×Dic1314yesdirect product factor
620C2C2×C22⋊C4×Dic1311yescharacteristic
621C2C2×D13×#9911yescharacteristic
622C2C2×#1171840111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C13C22×C42
FrattiniC24C23×D13
FittingC22×C13×#99C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D4×C13C22
cosocleC24×C13C24
hypercenterC22×#99D13
hypocenterC13C2×C4×#99
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic13C2semidirect
4. #99×Dic13C2direct (N × H)
5. C2×#11718119C2semidirect
8. C24×Dic13C4semidirect
11. C22×C22⋊Dic13C4semidirect
17. C2×D4×Dic13C4semidirect
19. C22×C4⋊Dic13C4semidirect
21. C22×C4×Dic13C4semidirect
22. C2×C13×#99C4semidirect
24. C2×#88074C4semidirect
28. C22⋊C4×Dic13C22semidirect
29. #11718119C22semidirect
52. C23×Dic13C2×C4semidirect
59. C2×C13×C22⋊C4C2×C4semidirect
68. C2×C22⋊Dic13C2×C4semidirect
69. C2×C22⋊Dic13C2×C4semidirect
78. C2×C4⋊Dic13C2×C4semidirect
84. C2×C4×Dic13C2×C4semidirect
85. C13×#99C2×C4semidirect
86. #88074C2×C4semidirect
96. C24×C13C42semidirect
114. C2×D4×C13C42semidirect
124. C22×C4×C13C42semidirect
164. C13×C22⋊C4C22×C4semidirect
170. C22⋊Dic13C22×C4semidirect
208. C23×C13C2×C42semidirect
234. C2×C4×C13C2×C42semidirect
259. C2×Dic13#99direct (N × H)
280. C2×#99Dic13direct (N × H)
329. Dic13C2×#99direct (N × H)
377. C2×C22⋊C4C2×Dic13semidirect
386. #99C2×Dic13direct (N × H)
395. C2×C13C4×#99semidirect
406. C24C4×Dic13semidirect
424. C2×D4C4×Dic13semidirect
470. C22×C4C4×Dic13semidirect
481. C22⋊C4C22×Dic13semidirect
485. C13C2×C4×#99semidirect
520. C23C2×C4×Dic13semidirect
567. C2×C4C2×C4×Dic13semidirect
619. C2#99×Dic13direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic132
C22×#880742
C2×C22⋊C4×Dic132
#99×Dic132
C2×#117181192
C22×C13×#992
C2×C4×#9913