Finite Group Databasebeta

← C2×D13×#484 #16730674

Subgroups — C2×D13×#484 #16730674

Order 3328.

2662 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C22⋊Q8C211yesmaximal, characteristic
2C22×C4⋊C4×D13C211yesmaximal, characteristic
3C2×#11718545C212yesmaximal, complemented
4C2×#11718383C211yesmaximal, characteristic, complemented
5C2×#11718631C211yesmaximal, characteristic, complemented
6C2×#11718470C212yesmaximal, complemented
7C2×#11718705C211yesmaximal, characteristic, complemented
8D13×#484C2116yesmaximal, direct product factor
9C2×D13×#107C212yesmaximal, complemented
10C2×D13×#103C212yesmaximal, complemented
11C2×D13×C22⋊C8C211yesmaximal, characteristic
12C2×C13×#484C211yesmaximal, characteristic, complemented
13C22×Q8×D13C2211yescharacteristic
14C23×C4×D13—21no—
15C23×C4×D13C2211yescharacteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C2×#88200C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C2×#88178C2211yescharacteristic
21C22×#6101—21no—
22C22×C8×D13C2212yes—
23D13×C22⋊Q8—24no—
24D13×C22⋊Q8C2218yes—
25C2×#88151C2211yescharacteristic
26C2×#88150—21no—
27C2×C4⋊C4×D13—21no—
28C2×C4⋊C4×D13—21no—
29C2×C4⋊C4×D13—24no—
30C2×C4⋊C4×D13—21no—
31C2×C4⋊C4×D13C2212yes—
32C2×C4⋊C4×D13C2218yes—
33C2×C4⋊C4×D13C2212yes—
34C2×C4⋊C4×D13C2211yescharacteristic
35C2×C22⋊C4×D13—21no—
36C2×#88132—21no—
37C13×#484C2218yescomplemented
38C2×C13×#107C2212yescomplemented
39C2×C13×#103C2212yescomplemented
40C2×C13×C22⋊C8C2211yescharacteristic
41C2×#88075C2212yescomplemented
42C2×C22⋊#1055C2211yescharacteristic
43C2×#88060C2212yes—
44C2×#88058C2212yescomplemented
45C2×#88056C2212yescomplemented
46#11718705C2218yescomplemented
47#11718631C2218yescomplemented
48C2×#88050C2212yescomplemented
49C2×#88047C2212yescomplemented
50C2×#88047C2212yescomplemented
51#11718545C22116yescomplemented
52D13×#107C22116yescomplemented
53#11718470C22116yescomplemented
54D13×#103C22116yescomplemented
55D13×C22⋊C8C2218yes—
56#11718383C2218yescomplemented
57C24×D13D411yescharacteristic
58C22×Q8×C13C2311yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C23×Dic13D411yescharacteristic
63C2×Q8×D13—22no—
64C2×Q8×D13—28no—
65C2×Q8×D13C2314yes—
66C22×C4×D13—28no—
67C22×C4×D13—21no—
68C22×C4×D13—21no—
69C22×C4×D13—28no—
70C22×C4×D13—22no—
71C22×C4×D13—22no—
72C22×C4×D13—48no—
73C22×C4×D13D411yescharacteristic
74C22×C4×D13D411yescharacteristic
75C22×C4×D13D414yes—
76C22×C4×D13C2311yescharacteristic
77C22×C4×D13C2314yes—
78C22×C4×D13C2311yescharacteristic
79C22×Dic26—21no—
80C22×Dic26C2311yescharacteristic
81C22×C8×C13C2312yes—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8C2314yes—
84C2×C13×C4⋊C4—21no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4C2312yes—
88C2×C13×C4⋊C4C2314yes—
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C22⋊C4—21no—
91C2×C22⋊Dic13—21no—
92#88200—22no—
93#88200C2314yes—
94C2×#6103—21no—
95C2×#6103—21no—
96C2×C4⋊Dic13—21no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13—21no—
99C2×C4⋊Dic13C2314yes—
100C2×C4⋊Dic13C2312yes—
101C2×C4⋊Dic13C2311yescharacteristic
102#88178—22no—
103#88178C2314yes—
104C2×#6101—21no—
105C2×#6101—21no—
106C2×#6101—21no—
107C2×#6101—28no—
108C2×#6101—22no—
109C2×#6101—22no—
110C22×#1055C2312yes—
111C2×C8×D13—28no—
112C2×C8×D13C2318yes—
113#88151—22no—
114#88151C2314yes—
115#88150—28no—
116C4⋊C4×D13—28no—
117C4⋊C4×D13—28no—
118C4⋊C4×D13—24no—
119C4⋊C4×D13—24no—
120C4⋊C4×D13—28no—
121C4⋊C4×D13—22no—
122C4⋊C4×D13C2318yes—
123C4⋊C4×D13C2318yes—
124C4⋊C4×D13C2314yes—
125C22⋊C4×D13—28no—
126#88132—28no—
127C13×#107C2318yescomplemented
128C13×#103C2318yescomplemented
129C13×C22⋊C8C2314yes—
130#88075C2318yescomplemented
131C22⋊#1055C2314yes—
132#88060C2318yes—
133#88058C2318yescomplemented
134#88056C2318yescomplemented
135#88050C2318yescomplemented
136#88047C2318yescomplemented
137#88047C2318yescomplemented
138C22×#484—131nomaximal, Sylow
139C24×C13C2×D411yescharacteristic
140C23×D13—24no—
141C23×D13—24no—
142C23×D13Q1618yes—
143C23×D13C2×D414yes—
144C23×D13C2×D411yescharacteristic
145C23×D13C2×D411yescharacteristic
146C2×Q8×C13—21no—
147C2×Q8×C13—24no—
148C2×Q8×C13C2412yes—
149C22×C4×C13—24no—
150C22×C4×C13—24no—
151C22×C4×C13—22no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—44no—
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2412yes—
158C22×C4×C13C2411yescharacteristic
159C22×Dic13—24no—
160C22×Dic13—21no—
161C22×Dic13—24no—
162C22×Dic13—22no—
163C22×Dic13—21no—
164C22×Dic13—44no—
165C22×Dic13C2×D414yes—
166C22×Dic13C2×D411yescharacteristic
167C22×Dic13C2×D411yescharacteristic
168Q8×D13—216no—
169Q8×D13—48no—
170C2×C4×D13—24no—
171C2×C4×D13—24no—
172C2×C4×D13—24no—
173C2×C4×D13—216no—
174C2×C4×D13—216no—
175C2×C4×D13—24no—
176C2×C4×D13—24no—
177C2×C4×D13—28no—
178C2×C4×D13—28no—
179C2×C4×D13—48no—
180C2×C4×D13—432no—
181C2×C4×D13—44no—
182C2×C4×D13—44no—
183C2×C4×D13—48no—
184C2×C4×D13C2×D414yes—
185C2×C4×D13C2×D414yes—
186C2×C4×D13C2×D412yes—
187C2×C4×D13C2×D412yes—
188C2×C4×D13#4118yes—
189C2×C4×D13C2412yes—
190C2×C4×D13C2412yes—
191C2×Dic26—24no—
192C2×Dic26—21no—
193C2×Dic26—24no—
194C2×Dic26—44no—
195C2×Dic26C2412yes—
196C2×C8×C13—24no—
197C2×C8×C13C2414yes—
198C13×C4⋊C4—24no—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—24no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4C2414yes—
203C13×C4⋊C4C2412yes—
204C13×C22⋊C4—24no—
205C22⋊Dic13—24no—
206#6103—24no—
207#6103—24no—
208C4⋊Dic13—24no—
209C4⋊Dic13—22no—
210C4⋊Dic13—21no—
211C4⋊Dic13—24no—
212C4⋊Dic13C2414yes—
213C4⋊Dic13C2412yes—
214#6101—24no—
215#6101—24no—
216#6101—24no—
217#6101—28no—
218#6101—28no—
219C2×#1055—24no—
220C2×#1055C2414yes—
221C8×D13—216no—
222C22×C22⋊Q8—131no—
223C23×C4⋊C4—131no—
224C2×#484—1316no—
225C2×#484—132no—
226C2×#484—132no—
227C2×#484—131no—
228C2×#484—131no—
229C2×#484—131no—
230C2×#484D1311yescharacteristic, direct product factor
231C22×#107—132no—
232C22×#103—132no—
233C22×C22⋊C8—131no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13C2×Q1614yes—
237C23×C13C22×D412yes—
238C23×C13C22×D411yescharacteristic
239C22×D13—22no—
240C22×D13—22no—
241C22×D13—28no—
242C22×D13—28no—
243C22×D13—232no—
244C22×D13#12314yes—
245C22×D13C2×Q1614yes—
246C22×D13C2×Q16116yes—
247C22×D13C2×Q1614yes—
248C22×D13AGL(1,ℤ/8)14yes—
249C22×D13C22×D412yes—
250C22×D13C22×D412yes—
251Q8×C13—24no—
252Q8×C13—42no—
253C2×C4×C13—22no—
254C2×C4×C13—24no—
255C2×C4×C13—24no—
256C2×C4×C13—24no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—48no—
260C2×C4×C13—42no—
261C2×C4×C13—44no—
262C2×C4×C13—42no—
263C2×C4×C13C22×D412yes—
264C2×C4×C13C22×D411yescharacteristic
265C2×C4×C13C2×#4114yes—
266C2×C4×C13C2511yescharacteristic
267C2×Dic13—22no—
268C2×Dic13—28no—
269C2×Dic13—22no—
270C2×Dic13—24no—
271C2×Dic13—22no—
272C2×Dic13—48no—
273C2×Dic13—42no—
274C2×Dic13—44no—
275C2×Dic13—42no—
276C2×Dic13#12314yes—
277C2×Dic13C22×D412yes—
278C2×Dic13C22×D412yes—
279C4×D13—28no—
280C4×D13—24no—
281C4×D13—24no—
282C4×D13—28no—
283C4×D13—416no—
284C4×D13—48no—
285C4×D13—48no—
286C4×D13—416no—
287C4×D13#12318yes—
288C4×D13C2×#4118yes—
289Dic26—24no—
290Dic26—42no—
291Dic26—48no—
292C8×C13—24no—
293#1055—24no—
294C23×Q8—131no—
295C24×C4—131no—
296C24×C4—261no—
297C23×C8—132no—
298C2×C22⋊Q8—131no—
299C2×C22⋊Q8—131no—
300C2×C22⋊Q8—138no—
301C2×C22⋊Q8—131no—
302C2×C22⋊Q8—261no—
303C2×C22⋊Q8—261no—
304C2×C22⋊Q8—264no—
305C2×C22⋊Q8C2×D1311yescharacteristic
306C22×C4⋊C4—131no—
307C22×C4⋊C4—132no—
308C22×C4⋊C4—138no—
309C22×C4⋊C4—132no—
310C22×C4⋊C4—131no—
311C22×C4⋊C4—261no—
312C22×C4⋊C4—264no—
313C22×C4⋊C4—261no—
314C22×C4⋊C4—261no—
315C22×C4⋊C4—261no—
316C22×C4⋊C4C2×D1311yescharacteristic
317C22×C22⋊C4—261no—
318#484—138no—
319#484—138no—
320#484—1316no—
321#484—1316no—
322#484—138no—
323#484C2×D1318yesdirect product factor
324C2×#107—132no—
325C2×#107—132no—
326C2×#107—132no—
327C2×#107—1316no—
328C2×#107C2×D1312yescomplemented
329C2×#103—132no—
330C2×#103—132no—
331C2×#103—132no—
332C2×#103—1316no—
333C2×#103C2×D1312yescomplemented
334C2×C22⋊C8—131no—
335C2×C22⋊C8—132no—
336C2×C22⋊C8—138no—
337C2×C22⋊C8C2×D1311yescharacteristic
338C22×C13—28no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13C2×#12312yes—
342C22×C13C22×Q1614yes—
343C22×C13C22×Q1612yes—
344C22×C13C2×AGL(1,ℤ/8)12yes—
345C22×C13C23×D411yescharacteristic
346C2×D13—28no—
347C2×D13—22no—
348C2×D13—22no—
349C2×D13—232no—
350C2×D13#484116yesdirect product factor
351C2×D13C2×#12314yes—
352C2×D13C22×Q1614yes—
353C2×D13C22×Q1614yes—
354C2×D13C2×AGL(1,ℤ/8)14yes—
355C4×C13—22no—
356C4×C13—42no—
357C4×C13—44no—
358C4×C13—42no—
359C4×C13C2×#12312yes—
360C4×C13C22×#4112yes—
361Dic13—22no—
362Dic13—42no—
363Dic13—44no—
364Dic13—42no—
365Dic13C2×#12314yes—
366C25—131no—
367C22×Q8—134no—
368C22×Q8—131no—
369C22×Q8—261no—
370C22×Q8—262no—
371C22×Q8—268no—
372C22×Q8C22×D1311yescharacteristic
373C23×C4—21no—
374C23×C4—131no—
375C23×C4—131no—
376C23×C4—131no—
377C23×C4—131no—
378C23×C4—134no—
379C23×C4—134no—
380C23×C4—131no—
381C23×C4—268no—
382C23×C4—261no—
383C23×C4—261no—
384C23×C4—268no—
385C23×C4—262no—
386C23×C4—262no—
387C23×C4—261no—
388C23×C4—528no—
389C23×C4C22×D1311yescharacteristic
390C22×C8—132no—
391C22×C8—138no—
392C22×C8—268no—
393C22×C8C22×D1312yes—
394C22⋊Q8—22no—
395C22⋊Q8—134no—
396C22⋊Q8—134no—
397C22⋊Q8—134no—
398C22⋊Q8—268no—
399C22⋊Q8—268no—
400C22⋊Q8—262no—
401C22⋊Q8—262no—
402C22⋊Q8—262no—
403C22⋊Q8C22×D1314yes—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—132no—
408C2×C4⋊C4—134no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—138no—
411C2×C4⋊C4—138no—
412C2×C4⋊C4—134no—
413C2×C4⋊C4—264no—
414C2×C4⋊C4—268no—
415C2×C4⋊C4—268no—
416C2×C4⋊C4—264no—
417C2×C4⋊C4—262no—
418C2×C4⋊C4—268no—
419C2×C4⋊C4—268no—
420C2×C4⋊C4—262no—
421C2×C4⋊C4—262no—
422C2×C4⋊C4—261no—
423C2×C4⋊C4—261no—
424C2×C4⋊C4—261no—
425C2×C4⋊C4—262no—
426C2×C4⋊C4—261no—
427C2×C4⋊C4—261no—
428C2×C4⋊C4C22×D1312yes—
429C2×C4⋊C4C22×D1314yes—
430C2×C4⋊C4C22×D1311yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—268no—
433C2×C22⋊C4—261no—
434C2×C22⋊C4—261no—
435C2×C22⋊C4—261no—
436#107—138no—
437#107—138no—
438#107—138no—
439#107C22×D1318yescomplemented
440#103—138no—
441#103—138no—
442#103—138no—
443#103C22×D1318yescomplemented
444C22⋊C8—134no—
445C22⋊C8—138no—
446C22⋊C8C22×D1314yes—
447C2×C13—24no—
448C2×C13C2×#48414yescomplemented
449C2×C13C22×#12311yescharacteristic
450C2×C13C23×Q1611yescharacteristic
451C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
452D13—24no—
453D13C2×#48418yesdirect product factor
454C24—131no—
455C24—138no—
456C24—134no—
457C24—131no—
458C24—264no—
459C24—264no—
460C24D4×D1311yescharacteristic
461C2×Q8—21no—
462C2×Q8—24no—
463C2×Q8—132no—
464C2×Q8—264no—
465C2×Q8—2616no—
466C2×Q8—261no—
467C2×Q8—264no—
468C2×Q8—524no—
469C2×Q8—528no—
470C2×Q8C23×D1312yes—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—44no—
477C22×C4—131no—
478C22×C4—132no—
479C22×C4—138no—
480C22×C4—132no—
481C22×C4—134no—
482C22×C4—131no—
483C22×C4—134no—
484C22×C4—134no—
485C22×C4—132no—
486C22×C4—132no—
487C22×C4—264no—
488C22×C4—2616no—
489C22×C4—2616no—
490C22×C4—264no—
491C22×C4—264no—
492C22×C4—264no—
493C22×C4—268no—
494C22×C4—268no—
495C22×C4—264no—
496C22×C4—264no—
497C22×C4—264no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—262no—
501C22×C4—528no—
502C22×C4—524no—
503C22×C4—524no—
504C22×C4—5232no—
505C22×C4—528no—
506C22×C4—524no—
507C22×C4D4×D1312yes—
508C22×C4D4×D1311yescharacteristic
509C22×C4C23×D1312yes—
510C22×C4C23×D1311yescharacteristic
511C2×C8—24no—
512C2×C8—134no—
513C2×C8—2616no—
514C2×C8—264no—
515C2×C8C23×D1314yes—
516C4⋊C4—24no—
517C4⋊C4—22no—
518C4⋊C4—24no—
519C4⋊C4—21no—
520C4⋊C4—134no—
521C4⋊C4—132no—
522C4⋊C4—268no—
523C4⋊C4—268no—
524C4⋊C4—264no—
525C4⋊C4—264no—
526C4⋊C4—264no—
527C4⋊C4—264no—
528C4⋊C4—262no—
529C4⋊C4—261no—
530C4⋊C4—264no—
531C4⋊C4C23×D1314yes—
532C4⋊C4C23×D1312yes—
533C22⋊C4—24no—
534C22⋊C4—264no—
535C22⋊C4—264no—
536C22⋊C4—264no—
537C13C22×#48411yescharacteristic, complemented, Sylow
538C23—22no—
539C23—22no—
540C23—134no—
541C23—134no—
542C23—134no—
543C23—132no—
544C23—1316no—
545C23—134no—
546C23—132no—
547C23—268no—
548C23—268no—
549C23—2632no—
550C23—262no—
551C23—262no—
552C23Q16×D1314yes—
553C23C2×D4×D1312yes—
554C23C2×D4×D1311yescharacteristic
555Q8—24no—
556Q8—42no—
557Q8—264no—
558Q8—528no—
559Q8—522no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—48no—
567C2×C4—44no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—134no—
571C2×C4—132no—
572C2×C4—138no—
573C2×C4—138no—
574C2×C4—132no—
575C2×C4—268no—
576C2×C4—268no—
577C2×C4—268no—
578C2×C4—262no—
579C2×C4—264no—
580C2×C4—264no—
581C2×C4—262no—
582C2×C4—262no—
583C2×C4—264no—
584C2×C4—528no—
585C2×C4—5216no—
586C2×C4—528no—
587C2×C4—5216no—
588C2×C4—528no—
589C2×C4—522no—
590C2×C4—524no—
591C2×C4—522no—
592C2×C4C2×D4×D1312yes—
593C2×C4C2×D4×D1311yescharacteristic
594C2×C4#41×D1314yes—
595C2×C4C24×D1311yescharacteristic
596C8—24no—
597C8—264no—
598C22—22no—
599C22—28no—
600C22—22no—
601C22—134no—
602C22—134no—
603C22—1316no—
604C22—134no—
605C22—134no—
606C22—2632no—
607C22—262no—
608C22—268no—
609C22—262no—
610C22D13×#12312yes—
611C22C2×Q16×D1314yes—
612C22C2×Q16×D1312yes—
613C22D13×AGL(1,ℤ/8)12yes—
614C22C22×D4×D1311yescharacteristic
615C4—22no—
616C4—44no—
617C4—42no—
618C4—42no—
619C4—134no—
620C4—262no—
621C4—522no—
622C4—524no—
623C4—522no—
624C4D13×#12312yes—
625C4C2×#41×D1312yes—
626C2—24no—
627C2—138no—
628C2—264no—
629C2D13×#48414yesdirect product factor
630C2C2×D13×#12311yescharacteristic
631C2C22×Q16×D1311yescharacteristic
632C2C2×D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#484C2
socleC23×C13C22×D4
prime radicalC24×D13D4
hypercenterC2×#484D13
hypocenterC13C22×#484
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. C2×#11718545C2semidirect
4. C2×#11718383C2semidirect
5. C2×#11718631C2semidirect
6. C2×#11718470C2semidirect
7. C2×#11718705C2semidirect
8. D13×#484C2direct (N × H)
9. C2×D13×#107C2semidirect
10. C2×D13×#103C2semidirect
12. C2×C13×#484C2semidirect
37. C13×#484C22semidirect
38. C2×C13×#107C22semidirect
39. C2×C13×#103C22semidirect
41. C2×#88075C22semidirect
44. C2×#88058C22semidirect
45. C2×#88056C22semidirect
46. #11718705C22semidirect
47. #11718631C22semidirect
48. C2×#88050C22semidirect
49. C2×#88047C22semidirect
50. C2×#88047C22semidirect
51. #11718545C22semidirect
52. D13×#107C22semidirect
53. #11718470C22semidirect
54. D13×#103C22semidirect
56. #11718383C22semidirect
127. C13×#107C23semidirect
128. C13×#103C23semidirect
130. #88075C23semidirect
133. #88058C23semidirect
134. #88056C23semidirect
135. #88050C23semidirect
136. #88047C23semidirect
137. #88047C23semidirect
230. C2×#484D13direct (N × H)
323. #484C2×D13direct (N × H)
328. C2×#107C2×D13semidirect
333. C2×#103C2×D13semidirect
350. C2×D13#484direct (N × H)
439. #107C22×D13semidirect
443. #103C22×D13semidirect
448. C2×C13C2×#484semidirect
453. D13C2×#484direct (N × H)
537. C13C22×#484semidirect
629. C2D13×#484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D13×C22⋊Q82
C22×C4⋊C4×D132
C2×#117185452
C2×#117183832
C2×#117186312
C2×#117184702
C2×#117187052
D13×#4842
C2×D13×#1072
C2×D13×#1032
C2×D13×C22⋊C82
C2×C13×#4842
C22×#48413