Finite Group Databasebeta

← C2×#13119140 #16031967

Subgroups — C2×#13119140 #16031967

Order 3328.

3678 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88137C212yesmaximal
2C22×C4×C22⋊D13C211yesmaximal, characteristic
3C22×C4⋊C4×D13C211yesmaximal, characteristic, complemented
4#13119140C2116yesmaximal, direct product factor
5C2×#11718318C212yesmaximal, complemented
6C2×#11718613C212yesmaximal, complemented
7C2×#11718646C211yesmaximal, characteristic, complemented
8C2×#11718634C211yesmaximal, characteristic, complemented
9C2×#11718325C212yesmaximal, complemented
10C2×#11718873C211yesmaximal, characteristic, complemented
11C2×#11718648C211yesmaximal, characteristic, complemented
12C2×C13×#380C211yesmaximal, characteristic, complemented
13C24×C4×C13C2211yescharacteristic
14C23×C22⋊D13C2211yescharacteristic
15C23×C4×D13C2212yes—
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C22⋊Dic13C2212yes—
21C22×C22⋊Dic13C2211yescharacteristic
22C2×C4×C22⋊D13—28no—
23C2×C4×C22⋊D13C2218yes—
24C22×#6103C2212yes—
25C22×#6103C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2212yes—
29C22×#6101C2212yes—
30C22×#6101C2211yescharacteristic
31C22×#6101C2212yes—
32C22×C4×Dic13C2211yescharacteristic
33C2×C4⋊C4×D13—28no—
34C2×C4⋊C4×D13C2218yescomplemented
35C2×#88137—216no—
36C2×#88137C22116yes—
37C13×#380C2218yescomplemented
38C2×C13×#95C2212yes—
39#11718873C2218yescomplemented
40C2×#88071C2212yes—
41C2×#88071C2212yes—
42C2×#88071C2212yes—
43C2×#88071C2212yes—
44#11718648C2218yescomplemented
45#11718646C2218yescomplemented
46#11718634C2218yescomplemented
47#11718613C22116yescomplemented
48#11718325C22116yescomplemented
49#11718318C22116yescomplemented
50C25×C13C2311yescharacteristic
51C24×D13C2311yescharacteristic
52C23×C4×C13—24no—
53C23×C4×C13—24no—
54C23×C4×C13—24no—
55C23×C4×C13C2314yes—
56C23×C4×C13C2312yes—
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2312yes—
59C23×C4×C13C2311yescharacteristic
60C22×C22⋊D13—24no—
61C22×C22⋊D13—24no—
62C22×C22⋊D13D418yes—
63C22×C22⋊D13C2314yes—
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2312yes—
66C23×Dic13C2312yes—
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C22×C4×D13—24no—
70C22×C4×D13—24no—
71C22×C4×D13—28no—
72C22×C4×D13—28no—
73C22×C4×D13—28no—
74C22×C4×D13D418yes—
75C22×C4×D13C2318yes—
76C22×C4×D13C2314yes—
77C2×C13×C4⋊C4—24no—
78C2×C13×C4⋊C4—24no—
79C2×C13×C4⋊C4C2314yes—
80C2×C13×C4⋊C4C2314yes—
81C2×C13×C22⋊C4—28no—
82C2×C13×C22⋊C4C2318yes—
83C2×C22⋊Dic13—28no—
84C2×C22⋊Dic13—24no—
85C2×C22⋊Dic13C2318yes—
86C2×C22⋊Dic13C2314yes—
87C4×C22⋊D13—232no—
88C2×#6103—28no—
89C2×#6103—24no—
90C2×#6103C2318yes—
91C2×#6103C2314yes—
92C2×C4⋊Dic13—24no—
93C2×C4⋊Dic13—24no—
94C2×C4⋊Dic13—28no—
95C2×C4⋊Dic13C2318yes—
96C2×C4⋊Dic13C2314yes—
97C2×C4⋊Dic13C2314yes—
98C2×#6101—28no—
99C2×#6101—28no—
100C2×#6101—24no—
101C2×#6101C2318yes—
102C2×#6101C2318yes—
103C2×#6101C2314yes—
104C2×C4×Dic13—24no—
105C2×C4×Dic13C2314yes—
106C4⋊C4×D13—232no—
107#88137—264no—
108C13×#95C2318yes—
109#88071C2318yes—
110#88071C2318yes—
111#88071C2318yes—
112#88071C2318yes—
113C2×#2486—131nomaximal, Sylow
114C24×C13—22no—
115C24×C13—22no—
116C24×C13—22no—
117C24×C13—22no—
118C24×C13—22no—
119C24×C13—22no—
120C24×C13C2×D414yes—
121C24×C13C2412yes—
122C24×C13C2411yescharacteristic
123C23×D13—22no—
124C23×D13—22no—
125C23×D13—22no—
126C23×D13—22no—
127C23×D13C2×D414yes—
128C23×D13C2×D414yes—
129C23×D13#4114yes—
130C23×D13C2412yes—
131C22×C4×C13—22no—
132C22×C4×C13—24no—
133C22×C4×C13—24no—
134C22×C4×C13—24no—
135C22×C4×C13—24no—
136C22×C4×C13—24no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—24no—
140C22×C4×C13—28no—
141C22×C4×C13—28no—
142C22×C4×C13—28no—
143C22×C4×C13—416no—
144C22×C4×C13C2×D414yes—
145C22×C4×C13#4114yes—
146C22×C4×C13#4114yes—
147C22×C4×C13C2412yes—
148C22×C4×C13C2414yes—
149C22×C4×C13C2414yes—
150C22×C4×C13C2412yes—
151C2×C22⋊D13—232no—
152C2×C22⋊D13—28no—
153C2×C22⋊D13—28no—
154C2×C22⋊D13C2×D4116yes—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—24no—
161C22×Dic13—24no—
162C22×Dic13—24no—
163C22×Dic13—24no—
164C22×Dic13—24no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—24no—
168C22×Dic13C2×D414yes—
169C22×Dic13C2×D414yes—
170C22×Dic13C2412yes—
171C22×Dic13C2414yes—
172C22×Dic13C2414yes—
173C22×Dic13C2412yes—
174C22×Dic13C2412yes—
175C2×C4×D13—232no—
176C2×C4×D13—28no—
177C2×C4×D13—28no—
178C2×C4×D13—216no—
179C2×C4×D13—216no—
180C2×C4×D13—216no—
181C2×C4×D13—432no—
182C2×C4×D13C2×D4116yes—
183C13×C4⋊C4—28no—
184C13×C4⋊C4—28no—
185C13×C22⋊C4—216no—
186C22⋊Dic13—216no—
187C22⋊Dic13—28no—
188#6103—216no—
189#6103—28no—
190C4⋊Dic13—28no—
191C4⋊Dic13—28no—
192C4⋊Dic13—216no—
193#6101—216no—
194#6101—216no—
195#6101—28no—
196C4×Dic13—28no—
197C22×#123—132no—
198C22×C4×D4—131no—
199C23×C4⋊C4—131no—
200#2486—1316no—
201C2×#398—132no—
202C2×#397—132no—
203C2×#389—131no—
204C2×#389—131no—
205C2×#381—132no—
206C2×#380—131no—
207C2×#380—131no—
208C2×#380D1311yescharacteristic, complemented
209C23×C13—28no—
210C23×C13—28no—
211C23×C13—28no—
212C23×C13—22no—
213C23×C13—22no—
214C23×C13—22no—
215C23×C13—22no—
216C23×C13—22no—
217C23×C13—22no—
218C23×C13—44no—
219C23×C13—44no—
220C23×C13—44no—
221C23×C13—44no—
222C23×C13C22×D414yes—
223C23×C13C22×D412yes—
224C23×C13C22×D412yes—
225C23×C13C2×#4112yes—
226C23×C13C2×#4112yes—
227C23×C13C2×#4112yes—
228C23×C132−1+412yes—
229C23×C132−1+412yes—
230C23×C13C2511yescharacteristic
231C22×D13—28no—
232C22×D13—28no—
233C22×D13—28no—
234C22×D13—28no—
235C22×D13—28no—
236C22×D13—28no—
237C22×D13—22no—
238C22×D13—22no—
239C22×D13—22no—
240C22×D13—22no—
241C22×D13#121116yes—
242C22×D13C22×D414yes—
243C22×D13C22×D414yes—
244C22×D13C2×#4114yes—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—24no—
254C2×C4×C13—48no—
255C2×C4×C13—44no—
256C2×C4×C13—48no—
257C2×C4×C13—416no—
258C2×C4×C13#123116yescomplemented
259C2×C4×C13C22×D414yes—
260C2×C4×C13C2×#4114yes—
261C2×C4×C13C2×#4114yes—
262C22⋊D13—232no—
263C2×Dic13—28no—
264C2×Dic13—28no—
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—24no—
271C2×Dic13—24no—
272C2×Dic13—24no—
273C2×Dic13—24no—
274C2×Dic13—24no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—24no—
278C2×Dic13—48no—
279C2×Dic13—44no—
280C2×Dic13—48no—
281C2×Dic13C22×D414yes—
282C2×Dic13C22×D414yes—
283C4×D13—232no—
284C4×D13—432no—
285C23×D4—131no—
286C24×C4—131no—
287C24×C4—132no—
288C24×C4C2×D1311yescharacteristic
289C2×#123—1316no—
290C2×#123—2616no—
291C2×C4×D4—138no—
292C2×C4×D4—268no—
293C22×C4⋊C4—132no—
294C22×C4⋊C4—131no—
295C22×C4⋊C4—132no—
296C22×C4⋊C4—132no—
297C22×C4⋊C4—131no—
298C22×C4⋊C4—131no—
299C22×C4⋊C4—138no—
300C22×C4⋊C4—268no—
301C22×C4⋊C4C2×D1311yescharacteristic
302C22×C4⋊C4C2×D1311yescharacteristic
303C22×C22⋊C4—131no—
304C22×C22⋊C4—132no—
305C22×C22⋊C4—131no—
306C22×C22⋊C4—132no—
307C22×C22⋊C4C2×D1312yes—
308C22×C42—131no—
309#398—1316no—
310#397—1316no—
311#389—138no—
312#389—138no—
313#381—1316no—
314#380—138no—
315#380—138no—
316#380C2×D1318yescomplemented
317C2×#95—132no—
318C2×#95—132no—
319C2×#95—132no—
320C2×#95—132no—
321C2×#95C2×D1312yes—
322C22×C13—24no—
323C22×C13—24no—
324C22×C13—24no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13—42no—
328C22×C13—42no—
329C22×C13—416no—
330C22×C13C2×#12114yes—
331C22×C13C2×#12314yes—
332C22×C13#53614yes—
333C22×C13#54714yes—
334C22×C13#54714yes—
335C22×C13#55214yes—
336C22×C13#55214yes—
337C22×C13C23×D411yescharacteristic
338C22×C13C23×D411yescharacteristic
339C22×C13C22×#4111yescharacteristic
340C22×C13C22×#4111yescharacteristic
341C22×C13C22×#4111yescharacteristic
342C22×C13C2×2−1+411yescharacteristic
343C22×C13C2×2−1+411yescharacteristic
344C2×D13—24no—
345C2×D13—24no—
346C2×D13—24no—
347C2×D13—24no—
348C2×D13—24no—
349C2×D13—24no—
350C2×D13—232no—
351C2×D13C2×#12118yes—
352C4×C13—44no—
353C4×C13—42no—
354C4×C13—44no—
355C4×C13C2×#12318yescomplemented
356Dic13—24no—
357Dic13—24no—
358Dic13—44no—
359Dic13—42no—
360Dic13—44no—
361C25—131no—
362C25C22×D1311yescharacteristic
363C22×D4—138no—
364C22×D4—134no—
365C22×D4—264no—
366C22×D4—264no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—131no—
371C23×C4—131no—
372C23×C4—138no—
373C23×C4—134no—
374C23×C4—132no—
375C23×C4—131no—
376C23×C4—132no—
377C23×C4—138no—
378C23×C4—268no—
379C23×C4—268no—
380C23×C4—268no—
381C23×C4—264no—
382C23×C4—264no—
383C23×C4C22×D1314yes—
384C23×C4C22×D1312yes—
385C23×C4C22×D1311yescharacteristic
386C23×C4C22×D1312yes—
387C23×C4C22×D1311yescharacteristic
388#123—2664no—
389C4×D4—2632no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—138no—
393C2×C4⋊C4—134no—
394C2×C4⋊C4—134no—
395C2×C4⋊C4—138no—
396C2×C4⋊C4—138no—
397C2×C4⋊C4—134no—
398C2×C4⋊C4—2632no—
399C2×C4⋊C4—268no—
400C2×C4⋊C4—264no—
401C2×C4⋊C4—268no—
402C2×C4⋊C4—268no—
403C2×C4⋊C4—264no—
404C2×C4⋊C4—264no—
405C2×C4⋊C4C22×D1314yes—
406C2×C4⋊C4C22×D1314yes—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—134no—
409C2×C22⋊C4—138no—
410C2×C22⋊C4—134no—
411C2×C22⋊C4—138no—
412C2×C22⋊C4—264no—
413C2×C22⋊C4—268no—
414C2×C22⋊C4—264no—
415C2×C22⋊C4—268no—
416C2×C22⋊C4C22×D1318yes—
417C2×C42—134no—
418C2×C42—264no—
419#95—138no—
420#95—138no—
421#95—138no—
422#95—138no—
423#95C22×D1318yes—
424C2×C13—44no—
425C2×C13#248618yescomplemented
426C2×C13C22×#12111yescharacteristic
427C2×C13C22×#12311yescharacteristic
428C2×C13C2×#53611yescharacteristic
429C2×C13C2×#54711yescharacteristic
430C2×C13C2×#54711yescharacteristic
431C2×C13C2×#55211yescharacteristic
432C2×C13C2×#55211yescharacteristic
433D13—28no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—134no—
441C24—134no—
442C24—134no—
443C24—132no—
444C24—262no—
445C24—262no—
446C24—262no—
447C24—262no—
448C24D4×D1314yes—
449C24C23×D1312yes—
450C24C23×D1311yescharacteristic
451C2×D4—1316no—
452C2×D4—268no—
453C2×D4—2632no—
454C2×D4—268no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—416no—
468C22×C4—134no—
469C22×C4—134no—
470C22×C4—132no—
471C22×C4—132no—
472C22×C4—1316no—
473C22×C4—132no—
474C22×C4—134no—
475C22×C4—134no—
476C22×C4—2616no—
477C22×C4—2616no—
478C22×C4—2616no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—2632no—
484C22×C4—268no—
485C22×C4—268no—
486C22×C4—264no—
487C22×C4—262no—
488C22×C4—264no—
489C22×C4—264no—
490C22×C4—264no—
491C22×C4—264no—
492C22×C4—262no—
493C22×C4—264no—
494C22×C4—262no—
495C22×C4—5232no—
496C22×C4#612714yes—
497C22×C4D4×D1314yes—
498C22×C4#612914yes—
499C22×C4C23×D1312yes—
500C22×C4C23×D1314yes—
501C22×C4C23×D1314yes—
502C22×C4C23×D1312yes—
503C4⋊C4—28no—
504C4⋊C4—28no—
505C4⋊C4—2616no—
506C4⋊C4—268no—
507C4⋊C4—2616no—
508C4⋊C4—2616no—
509C4⋊C4—268no—
510C4⋊C4—268no—
511C22⋊C4—216no—
512C22⋊C4—268no—
513C22⋊C4—2616no—
514C22⋊C4—268no—
515C22⋊C4—2616no—
516C42—268no—
517C13C2×#248611yescharacteristic, complemented, Sylow
518C23—28no—
519C23—28no—
520C23—28no—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—22no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—44no—
531C23—1316no—
532C23—134no—
533C23—134no—
534C23—134no—
535C23—268no—
536C23—268no—
537C23—268no—
538C23—268no—
539C23—268no—
540C23—268no—
541C23—262no—
542C23—262no—
543C23—262no—
544C23—262no—
545C23C2×#612712yes—
546C23C2×D4×D1314yes—
547C23C2×D4×D1312yes—
548C23C2×D4×D1312yes—
549C23C2×#612912yes—
550C23#8825412yes—
551C23#41×D1312yes—
552C23#8825712yes—
553C23C24×D1311yescharacteristic
554D4—2632no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—44no—
565C2×C4—48no—
566C2×C4—48no—
567C2×C4—416no—
568C2×C4—134no—
569C2×C4—134no—
570C2×C4—268no—
571C2×C4—268no—
572C2×C4—262no—
573C2×C4—262no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—2632no—
577C2×C4—264no—
578C2×C4—262no—
579C2×C4—264no—
580C2×C4—264no—
581C2×C4—264no—
582C2×C4—264no—
583C2×C4—262no—
584C2×C4—264no—
585C2×C4—262no—
586C2×C4—5232no—
587C2×C4—528no—
588C2×C4—528no—
589C2×C4—524no—
590C2×C4#88137116yescomplemented
591C2×C4C2×#612714yes—
592C2×C4C2×D4×D1314yes—
593C2×C4C2×#612914yes—
594C22—24no—
595C22—24no—
596C22—24no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—416no—
601C22—42no—
602C22—138no—
603C22—264no—
604C22—264no—
605C22—264no—
606C22—264no—
607C22—264no—
608C22—2632no—
609C22—264no—
610C22C2×#8813714yes—
611C22#1171921214yes—
612C22#1171923414yes—
613C22D13×#12114yes—
614C22#1171931614yes—
615C22#1171933314yes—
616C22#1171934414yes—
617C22C22×#612711yescharacteristic
618C22C22×D4×D1311yescharacteristic
619C22C22×D4×D1311yescharacteristic
620C22C22×#612911yescharacteristic
621C22C2×#8825411yescharacteristic
622C22C2×#41×D1311yescharacteristic
623C22C2×#8825711yescharacteristic
624C4—44no—
625C4—44no—
626C4—42no—
627C4—264no—
628C4—264no—
629C4—524no—
630C4—524no—
631C4—522no—
632C4C2×#8813718yescomplemented
633C2—44no—
634C2—268no—
635C2#1311914018yesdirect product factor
636C2C2×D13×#12111yescharacteristic
637C2C22×#8813711yescharacteristic
638C2C2×#1171933311yescharacteristic
639C2C2×#1171931611yescharacteristic
640C2C2×#1171921211yescharacteristic
641C2C2×#1171934411yescharacteristic
642C2C2×#1171923411yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#380C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×#380D13
hypocenterC13C2×#2486
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D13C2semidirect
4. #13119140C2direct (N × H)
5. C2×#11718318C2semidirect
6. C2×#11718613C2semidirect
7. C2×#11718646C2semidirect
8. C2×#11718634C2semidirect
9. C2×#11718325C2semidirect
10. C2×#11718873C2semidirect
11. C2×#11718648C2semidirect
12. C2×C13×#380C2semidirect
34. C2×C4⋊C4×D13C22semidirect
37. C13×#380C22semidirect
39. #11718873C22semidirect
44. #11718648C22semidirect
45. #11718646C22semidirect
46. #11718634C22semidirect
47. #11718613C22semidirect
48. #11718325C22semidirect
49. #11718318C22semidirect
208. C2×#380D13semidirect
258. C2×C4×C13#123semidirect
316. #380C2×D13semidirect
355. C4×C13C2×#123semidirect
425. C2×C13#2486semidirect
517. C13C2×#2486semidirect
590. C2×C4#88137semidirect
632. C4C2×#88137semidirect
635. C2#13119140direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881372
C22×C4×C22⋊D132
C22×C4⋊C4×D132
#131191402
C2×#117183182
C2×#117186132
C2×#117186462
C2×#117186342
C2×#117183252
C2×#117188732
C2×#117186482
C2×C13×#3802
C2×#248613