Finite Group Databasebeta

← C2×D13×#548 #16769849

Subgroups — C2×D13×#548 #16769849

Order 3328.

12142 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D13C211yesmaximal, characteristic, complemented
2C23×Q8×D13C211yesmaximal, characteristic, complemented
3C2×#11719281C211yesmaximal, characteristic, complemented
4C2×#11719522C211yesmaximal, characteristic, complemented
5C2×#11719338C213yesmaximal, complemented
6C2×#11719257C213yesmaximal, complemented
7C2×#11719382C213yesmaximal, complemented
8C2×#11719536C211yesmaximal, characteristic, complemented
9C2×#11719303C213yesmaximal, complemented
10D13×#548C2132yesmaximal, direct product factor
11C2×D13×#124C213yesmaximal, complemented
12C2×D13×C22⋊Q8C213yesmaximal, complemented
13C2×D13×#121C213yesmaximal, complemented
14C2×C4×Q8×D13C211yesmaximal, characteristic, complemented
15C2×C4×D4×D13C213yesmaximal, complemented
16C2×C13×#548C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic, complemented
18C23×Q8×C13C2211yescharacteristic, complemented
19C2×#41×D13—216no—
20C2×#41×D13C22116yescomplemented
21C22×#6131C2211yescharacteristic, complemented
22C22×Q8×D13—216no—
23C22×Q8×D13C2213yes—
24C22×Q8×D13C2211yescharacteristic
25C22×Q8×D13C2211yescharacteristic, complemented
26C22×Q8×D13C2213yescomplemented
27C22×Q8×D13C22116yescomplemented
28C22×#6129C2213yescomplemented
29C22×D4×D13C2213yes—
30C22×D4×D13C2213yes—
31C22×#6127C2213yescomplemented
32C23×C4×D13C2213yes—
33C23×C4×D13C2213yes—
34C23×Dic26C2213yescomplemented
35C13×#548C22116yescomplemented
36C2×C13×#124C2213yescomplemented
37C2×C13×C22⋊Q8C2213yescomplemented
38C2×C13×#121C2213yescomplemented
39C2×C4×Q8×C13C2211yescharacteristic, complemented
40C2×C4×D4×C13C2213yescomplemented
41#11719536C22116yescomplemented
42#11719522C22116yescomplemented
43C2×#88201C2213yescomplemented
44C2×#88200C2213yescomplemented
45C2×Q8×Dic13C2211yescharacteristic, complemented
46C2×#88193C2216yescomplemented
47C2×#88192C2213yescomplemented
48C2×#88190C2213yescomplemented
49C2×D4×Dic13C2213yescomplemented
50C2×#88184C2213yescomplemented
51C2×C4×C22⋊D13C2213yescomplemented
52C2×C4×C22⋊D13C2213yescomplemented
53C2×#88178C2213yescomplemented
54#11719382C22148yescomplemented
55D13×#124C22148yescomplemented
56#11719338C22148yescomplemented
57D13×C22⋊Q8C22148yescomplemented
58D13×#121C22148yescomplemented
59#11719303C22148yescomplemented
60#11719281C22116yescomplemented
61C4×Q8×D13C22116yescomplemented
62#11719257C22148yescomplemented
63C4×D4×D13C22148yescomplemented
64C2×#88151C2213yescomplemented
65C2×#88150C2216yescomplemented
66C2×#88149C2213yescomplemented
67C2×#88147C2213yescomplemented
68C2×C4⋊C4×D13C2213yes—
69C2×C4⋊C4×D13C2213yes—
70C2×#88141C2213yescomplemented
71C2×#88139C2216yescomplemented
72C2×#88139C2216yescomplemented
73C2×#88138C2216yescomplemented
74C2×#88135C2213yescomplemented
75C2×#88135C2213yescomplemented
76C2×C22⋊C4×D13C2211yescharacteristic
77C2×C22⋊C4×D13C2213yes—
78C2×C22⋊C4×D13C2216yes—
79C2×#88132C2216yescomplemented
80C2×#88129C2213yescomplemented
81C2×C4×D52C2213yescomplemented
82C2×C42×D13C2213yes—
83C2×C4×Dic26C2213yescomplemented
84C24×D13C2313yes—
85C24×D13C2311yescharacteristic
86C2×C13×#41—28no—
87C2×C13×#41C2318yescomplemented
88C22×Q8×C13—28no—
89C22×Q8×C13C2313yes—
90C22×Q8×C13C2311yescharacteristic
91C22×Q8×C13C2318yescomplemented
92C22×D4×C13C2313yes—
93C22×D4×C13C2313yes—
94C23×C4×C13C2313yes—
95C23×C4×C13C2313yes—
96C22×C22⋊D13C2313yes—
97C22×C22⋊D13C2313yes—
98C22×C22⋊D13C2316yes—
99C23×Dic13C2313yes—
100C23×Dic13C2313yes—
101#41×D13—2128no—
102C2×#6131—28no—
103C2×#6131C2318yescomplemented
104C2×Q8×D13—28no—
105C2×Q8×D13—2128no—
106C2×Q8×D13—224no—
107C2×Q8×D13—224no—
108C2×Q8×D13D4116yescomplemented
109C2×Q8×D13C23124yes—
110C2×Q8×D13C2318yes—
111C2×Q8×D13C2318yescomplemented
112C2×Q8×D13C23124yescomplemented
113C2×#6129—224no—
114C2×#6129C23124yescomplemented
115C2×D4×D13—224no—
116C2×D4×D13—224no—
117C2×D4×D13C23124yes—
118C2×D4×D13C23124yes—
119C2×#6127—224no—
120C2×#6127C23124yescomplemented
121C22×D52C2313yes—
122C22×D52C2313yes—
123C22×C4×D13—224no—
124C22×C4×D13—224no—
125C22×C4×D13C2311yescharacteristic
126C22×C4×D13C2313yes—
127C22×C4×D13C2313yes—
128C22×C4×D13C2313yes—
129C22×C4×D13C2313yes—
130C22×C4×D13C2311yescharacteristic
131C22×C4×D13C2313yes—
132C22×C4×D13C2313yes—
133C22×C4×D13C23124yes—
134C22×C4×D13C23124yes—
135C22×C4×D13C2313yes—
136C22×Dic26—224no—
137C22×Dic26C2313yes—
138C22×Dic26C2316yes—
139C22×Dic26C2313yes—
140C22×Dic26C23124yescomplemented
141C13×#124C23124yescomplemented
142C13×C22⋊Q8C23124yescomplemented
143C13×#121C23124yescomplemented
144C4×Q8×C13C2318yescomplemented
145C4×D4×C13C23124yescomplemented
146C2×C13×C4⋊C4C2313yes—
147C2×C13×C4⋊C4C2313yes—
148C2×C13×C22⋊C4C2316yes—
149C2×C13×C22⋊C4C2311yescharacteristic
150C2×C13×C22⋊C4C2313yes—
151C2×C42×C13C2313yes—
152C2×C22⋊Dic13C2316yes—
153C2×C22⋊Dic13C2313yes—
154C2×C22⋊Dic13C2311yescharacteristic
155#88201C23124yescomplemented
156#88200C23124yescomplemented
157Q8×Dic13C2318yescomplemented
158#88193C23148yescomplemented
159#88192C23124yescomplemented
160#88190C23124yescomplemented
161D4×Dic13C23124yescomplemented
162#88184C23124yescomplemented
163C4×C22⋊D13C23124yescomplemented
164C4×C22⋊D13C23124yescomplemented
165C2×#6103C2311yescharacteristic
166C2×#6103C2313yes—
167C2×#6103C2316yes—
168C2×#6103C2316yes—
169C2×#6103C2313yes—
170C2×#6103C2311yescharacteristic
171C2×C4⋊Dic13C2313yes—
172C2×C4⋊Dic13C2313yes—
173#88178C23124yescomplemented
174C2×#6101C2316yes—
175C2×#6101C2313yes—
176C2×#6101C2313yes—
177C2×C4×Dic13C2313yes—
178C2×C4×Dic13C2313yes—
179C2×C4×Dic13C2313yes—
180#88151C23124yescomplemented
181#88150C23148yescomplemented
182#88149C23124yescomplemented
183#88147C23124yescomplemented
184C4⋊C4×D13C23124yes—
185C4⋊C4×D13C23124yes—
186#88141C23124yescomplemented
187#88139C23148yescomplemented
188#88139C23148yescomplemented
189#88138C23148yescomplemented
190#88135C23124yescomplemented
191#88135C23124yescomplemented
192C22⋊C4×D13C2318yes—
193C22⋊C4×D13C23124yes—
194C22⋊C4×D13C23148yes—
195#88132C23148yescomplemented
196#88129C23124yescomplemented
197C4×D52C23124yescomplemented
198C42×D13C23124yes—
199C4×Dic26C23124yescomplemented
200C22×#548—131nomaximal, Sylow
201C24×C13C2413yes—
202C24×C13C2411yescharacteristic
203C23×D13—24no—
204C23×D13—24no—
205C23×D13—212no—
206C23×D13—212no—
207C23×D13—212no—
208C23×D13#4118yescomplemented
209C23×D13C24112yes—
210C23×D13C2413yes—
211C23×D13C2414yes—
212C23×D13C2411yescharacteristic
213C23×D13C2411yescharacteristic
214C13×#41—232no—
215C2×Q8×C13—232no—
216C2×Q8×C13—212no—
217C2×Q8×C13C2×D418yescomplemented
218C2×Q8×C13C24112yes—
219C2×Q8×C13C2414yes—
220C2×D4×C13—212no—
221C2×D4×C13—212no—
222C2×D4×C13C24112yes—
223C2×D4×C13C24112yes—
224C22×C4×C13—212no—
225C22×C4×C13—212no—
226C22×C4×C13C2411yescharacteristic
227C22×C4×C13C2413yes—
228C22×C4×C13C2411yescharacteristic
229C22×C4×C13C2413yes—
230C22×C4×C13C24112yes—
231C22×C4×C13C24112yes—
232C22×C4×C13C2413yes—
233C2×C22⋊D13—212no—
234C2×C22⋊D13—212no—
235C2×C22⋊D13—224no—
236C2×C22⋊D13C24112yes—
237C2×C22⋊D13C24112yes—
238C2×C22⋊D13C24124yes—
239C22×Dic13—212no—
240C22×Dic13—212no—
241C22×Dic13C24112yes—
242C22×Dic13C24112yes—
243C22×Dic13C2411yescharacteristic
244C22×Dic13C2413yes—
245C22×Dic13C2411yescharacteristic
246C22×Dic13C2413yes—
247C22×Dic13C2413yes—
248#6131—232no—
249Q8×D13—232no—
250Q8×D13—296no—
251Q8×D13—296no—
252Q8×D13C2×D4164yescomplemented
253#6129—296no—
254D4×D13—296no—
255D4×D13—296no—
256#6127—296no—
257C2×D52—212no—
258C2×D52—212no—
259C2×D52C24112yes—
260C2×D52C24112yes—
261C2×C4×D13—24no—
262C2×C4×D13—212no—
263C2×C4×D13—212no—
264C2×C4×D13—24no—
265C2×C4×D13—212no—
266C2×C4×D13—212no—
267C2×C4×D13—212no—
268C2×C4×D13—212no—
269C2×C4×D13—296no—
270C2×C4×D13—296no—
271C2×C4×D13C2×D4124yes—
272C2×C4×D13C2414yes—
273C2×C4×D13C24112yes—
274C2×C4×D13C24112yes—
275C2×C4×D13C24112yes—
276C2×C4×D13C24112yes—
277C2×C4×D13C2414yes—
278C2×C4×D13C24112yes—
279C2×C4×D13C24112yes—
280C2×C4×D13C24112yes—
281C2×Dic26—212no—
282C2×Dic26—224no—
283C2×Dic26—296no—
284C2×Dic26C2×D4124yescomplemented
285C2×Dic26C24112yes—
286C2×Dic26C24124yes—
287C2×Dic26C24112yes—
288C13×C4⋊C4C24112yes—
289C13×C4⋊C4C24112yes—
290C13×C22⋊C4C24124yes—
291C13×C22⋊C4C2414yes—
292C13×C22⋊C4C24112yes—
293C42×C13C24112yes—
294C22⋊Dic13C24124yes—
295C22⋊Dic13C24112yes—
296C22⋊Dic13C2414yes—
297#6103C2414yes—
298#6103C24112yes—
299#6103C24124yes—
300#6103C24124yes—
301#6103C24112yes—
302#6103C2414yes—
303C4⋊Dic13C24112yes—
304C4⋊Dic13C24112yes—
305#6101C24124yes—
306#6101C24112yes—
307#6101C24112yes—
308C4×Dic13C24112yes—
309C4×Dic13C24112yes—
310C4×Dic13C24112yes—
311C23×#41—131no—
312C24×Q8—131no—
313C2×#548—131no—
314C2×#548—131no—
315C2×#548—1332no—
316C2×#548—133no—
317C2×#548—133no—
318C2×#548—133no—
319C2×#548—131no—
320C2×#548—133no—
321C2×#548D1311yescharacteristic, direct product factor
322C22×#124—133no—
323C22×C22⋊Q8—133no—
324C22×#121—133no—
325C22×C4×Q8—131no—
326C22×C4×D4—133no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—26no—
330C23×C13—26no—
331C23×C13—26no—
332C23×C13C2×#4114yescomplemented
333C23×C13C2516yes—
334C23×C13C2512yes—
335C23×C13C2511yescharacteristic
336C22×D13—22no—
337C22×D13—22no—
338C22×D13—232no—
339C22×D13—28no—
340C22×D13—28no—
341C22×D13—26no—
342C22×D13—26no—
343C22×D13—26no—
344C22×D13—224no—
345C22×D13—224no—
346C22×D13—224no—
347C22×D13—448no—
348C22×D13C22×D414yes—
349C22×D13C2×#4114yes—
350C22×D13C2×#41116yescomplemented
351C22×D13C2×#4114yescomplemented
352C22×D132−1+414yes—
353C22×D13C2516yes—
354C22×D13C2512yes—
355C22×D13C2512yes—
356Q8×C13—224no—
357Q8×C13C22×D4116yescomplemented
358D4×C13—224no—
359D4×C13—224no—
360C2×C4×C13—26no—
361C2×C4×C13—22no—
362C2×C4×C13—26no—
363C2×C4×C13—22no—
364C2×C4×C13—224no—
365C2×C4×C13—224no—
366C2×C4×C13C22×D4112yes—
367C2×C4×C13C2512yes—
368C2×C4×C13C2516yes—
369C2×C4×C13C2512yes—
370C2×C4×C13C2516yes—
371C2×C4×C13C2516yes—
372C22⋊D13—224no—
373C22⋊D13—224no—
374C22⋊D13—248no—
375C2×Dic13—26no—
376C2×Dic13—22no—
377C2×Dic13—26no—
378C2×Dic13—22no—
379C2×Dic13—224no—
380C2×Dic13—224no—
381C2×Dic13C22×D4112yes—
382C2×Dic13C2512yes—
383C2×Dic13C2516yes—
384C2×Dic13C2512yes—
385C2×Dic13C2516yes—
386C2×Dic13C2516yes—
387D52—224no—
388D52—224no—
389C4×D13—28no—
390C4×D13—224no—
391C4×D13—224no—
392C4×D13—28no—
393C4×D13—224no—
394C4×D13—224no—
395C4×D13—224no—
396C4×D13—224no—
397C4×D13C22×D4148yes—
398Dic26—224no—
399Dic26—248no—
400Dic26C22×D4148yescomplemented
401C22×#41—1316no—
402C22×#41—131no—
403C22×#41—133no—
404C22×#41—133no—
405C22×#41—2616no—
406C22×#41C2×D1311yescharacteristic, complemented
407C23×Q8—131no—
408C23×Q8—133no—
409C23×Q8—133no—
410C23×Q8—131no—
411C23×Q8—1316no—
412C23×Q8—133no—
413C23×Q8—2616no—
414C23×Q8C2×D1311yescharacteristic, complemented
415C23×D4—133no—
416C23×D4—133no—
417C24×C4—133no—
418C24×C4—133no—
419#548—1316no—
420#548—1316no—
421#548—1348no—
422#548—1348no—
423#548—1348no—
424#548—1316no—
425#548—1348no—
426#548C2×D13116yesdirect product factor
427C2×#124—133no—
428C2×#124—133no—
429C2×#124—1348no—
430C2×#124—136no—
431C2×#124—136no—
432C2×#124—133no—
433C2×#124C2×D1313yescomplemented
434C2×C22⋊Q8—133no—
435C2×C22⋊Q8—133no—
436C2×C22⋊Q8—1348no—
437C2×C22⋊Q8—136no—
438C2×C22⋊Q8—133no—
439C2×C22⋊Q8—136no—
440C2×C22⋊Q8C2×D1313yescomplemented
441C2×#121—133no—
442C2×#121—136no—
443C2×#121—133no—
444C2×#121—1348no—
445C2×#121—133no—
446C2×#121—136no—
447C2×#121C2×D1313yescomplemented
448C2×C4×Q8—131no—
449C2×C4×Q8—1316no—
450C2×C4×Q8—133no—
451C2×C4×Q8—133no—
452C2×C4×Q8C2×D1311yescharacteristic, complemented
453C2×C4×D4—133no—
454C2×C4×D4—133no—
455C2×C4×D4—133no—
456C2×C4×D4—1348no—
457C2×C4×D4—133no—
458C2×C4×D4—133no—
459C2×C4×D4—133no—
460C2×C4×D4—133no—
461C2×C4×D4C2×D1313yescomplemented
462C22×C4⋊C4—133no—
463C22×C4⋊C4—133no—
464C22×C22⋊C4—131no—
465C22×C22⋊C4—133no—
466C22×C22⋊C4—136no—
467C22×C42—133no—
468C22×C13—22no—
469C22×C13—22no—
470C22×C13—28no—
471C22×C13—26no—
472C22×C13—26no—
473C22×C13—26no—
474C22×C13—412no—
475C22×C13C23×D412yes—
476C22×C13C22×#4112yes—
477C22×C13C22×#4114yescomplemented
478C22×C13C2×2−1+412yes—
479C22×C13C2611yescharacteristic
480C2×D13—22no—
481C2×D13—22no—
482C2×D13—28no—
483C2×D13—232no—
484C2×D13—26no—
485C2×D13—26no—
486C2×D13—26no—
487C2×D13—412no—
488C2×D13—448no—
489C2×D13#548116yesdirect product factor
490C2×D13C23×D414yes—
491C2×D13C22×#4114yes—
492C2×D13C22×#4114yescomplemented
493C2×D13C2×2−1+414yes—
494C4×C13—26no—
495C4×C13—22no—
496C4×C13—26no—
497C4×C13—22no—
498C4×C13C23×D4112yes—
499Dic13—26no—
500Dic13—22no—
501Dic13—26no—
502Dic13—22no—
503Dic13C23×D4112yes—
504C25—131no—
505C25—133no—
506C2×#41—28no—
507C2×#41—138no—
508C2×#41—1324no—
509C2×#41—1324no—
510C2×#41—2624no—
511C2×#41—2624no—
512C2×#41—26128no—
513C2×#41—268no—
514C2×#41C22×D1318yescomplemented
515C22×Q8—28no—
516C22×Q8—1316no—
517C22×Q8—138no—
518C22×Q8—1324no—
519C22×Q8—1324no—
520C22×Q8—138no—
521C22×Q8—133no—
522C22×Q8—136no—
523C22×Q8—133no—
524C22×Q8—1324no—
525C22×Q8—2624no—
526C22×Q8—2624no—
527C22×Q8—26128no—
528C22×Q8—2624no—
529C22×Q8—268no—
530C22×Q8C22×D1313yes—
531C22×Q8C22×D1311yescharacteristic
532C22×Q8C22×D1318yescomplemented
533C22×D4—133no—
534C22×D4—133no—
535C22×D4—136no—
536C22×D4—1324no—
537C22×D4—1324no—
538C22×D4—133no—
539C22×D4—133no—
540C22×D4—2624no—
541C22×D4—2624no—
542C22×D4C22×D1313yes—
543C22×D4C22×D1313yes—
544C23×C4—133no—
545C23×C4—133no—
546C23×C4—133no—
547C23×C4—131no—
548C23×C4—133no—
549C23×C4—133no—
550C23×C4—131no—
551C23×C4—133no—
552C23×C4—1324no—
553C23×C4—133no—
554C23×C4—133no—
555C23×C4—1324no—
556C23×C4—133no—
557C23×C4—2624no—
558C23×C4—2624no—
559C23×C4C22×D1313yes—
560C23×C4C22×D1313yes—
561#124—1324no—
562#124—1324no—
563#124—1348no—
564#124—1348no—
565#124—1324no—
566#124C22×D13124yescomplemented
567C22⋊Q8—1324no—
568C22⋊Q8—1324no—
569C22⋊Q8—1348no—
570C22⋊Q8—1324no—
571C22⋊Q8—1348no—
572C22⋊Q8C22×D13124yescomplemented
573#121—1324no—
574#121—1348no—
575#121—1324no—
576#121—1324no—
577#121—1348no—
578#121C22×D13124yescomplemented
579C4×Q8—138no—
580C4×Q8—1324no—
581C4×Q8—1324no—
582C4×Q8C22×D1318yescomplemented
583C4×D4—1324no—
584C4×D4—1324no—
585C4×D4—1324no—
586C4×D4—1324no—
587C4×D4—1324no—
588C4×D4—1324no—
589C4×D4—1324no—
590C4×D4C22×D13124yescomplemented
591C2×C4⋊C4—133no—
592C2×C4⋊C4—133no—
593C2×C4⋊C4—133no—
594C2×C4⋊C4—136no—
595C2×C4⋊C4—133no—
596C2×C4⋊C4—1324no—
597C2×C4⋊C4—1324no—
598C2×C4⋊C4C22×D1313yes—
599C2×C4⋊C4C22×D1313yes—
600C2×C22⋊C4—131no—
601C2×C22⋊C4—133no—
602C2×C22⋊C4—136no—
603C2×C22⋊C4—131no—
604C2×C22⋊C4—131no—
605C2×C22⋊C4—133no—
606C2×C22⋊C4—133no—
607C2×C22⋊C4—136no—
608C2×C22⋊C4—136no—
609C2×C22⋊C4—138no—
610C2×C22⋊C4—1324no—
611C2×C22⋊C4—1348no—
612C2×C22⋊C4C22×D1311yescharacteristic
613C2×C22⋊C4C22×D1313yes—
614C2×C22⋊C4C22×D1316yes—
615C2×C42—133no—
616C2×C42—133no—
617C2×C42—133no—
618C2×C42—1324no—
619C2×C42C22×D1313yes—
620C2×C13—24no—
621C2×C13—46no—
622C2×C13C2×#54814yescomplemented
623C2×C13C24×D411yescharacteristic
624C2×C13C23×#4111yescharacteristic
625C2×C13C22×2−1+411yescharacteristic
626D13—24no—
627D13—46no—
628D13C2×#54818yesdirect product factor
629C24—131no—
630C24—138no—
631C24—134no—
632C24—131no—
633C24—1312no—
634C24—133no—
635C24—264no—
636C24—264no—
637C24—2612no—
638C24—2612no—
639C24—2612no—
640C24C23×D1313yes—
641C24C23×D1311yescharacteristic
642#41—232no—
643#41—2696no—
644#41—2696no—
645#41—2632no—
646C2×Q8—232no—
647C2×Q8—212no—
648C2×Q8—1364no—
649C2×Q8—1324no—
650C2×Q8—1312no—
651C2×Q8—1324no—
652C2×Q8—1312no—
653C2×Q8—2624no—
654C2×Q8—2696no—
655C2×Q8—2696no—
656C2×Q8—2696no—
657C2×Q8—2632no—
658C2×Q8—2612no—
659C2×Q8D4×D1318yescomplemented
660C2×Q8C23×D13112yes—
661C2×Q8C23×D1314yes—
662C2×D4—212no—
663C2×D4—212no—
664C2×D4—1312no—
665C2×D4—1312no—
666C2×D4—1324no—
667C2×D4—1312no—
668C2×D4—1312no—
669C2×D4—2612no—
670C2×D4—2696no—
671C2×D4—2624no—
672C2×D4—2696no—
673C2×D4—2612no—
674C2×D4—2612no—
675C2×D4—2612no—
676C2×D4C23×D13112yes—
677C2×D4C23×D13112yes—
678C22×C4—212no—
679C22×C4—212no—
680C22×C4—133no—
681C22×C4—1324no—
682C22×C4—1312no—
683C22×C4—1312no—
684C22×C4—1312no—
685C22×C4—131no—
686C22×C4—133no—
687C22×C4—133no—
688C22×C4—131no—
689C22×C4—134no—
690C22×C4—1312no—
691C22×C4—1312no—
692C22×C4—134no—
693C22×C4—1312no—
694C22×C4—1312no—
695C22×C4—1312no—
696C22×C4—1312no—
697C22×C4—2612no—
698C22×C4—2696no—
699C22×C4—2612no—
700C22×C4—2696no—
701C22×C4—264no—
702C22×C4—2612no—
703C22×C4—2612no—
704C22×C4—264no—
705C22×C4—2612no—
706C22×C4—2612no—
707C22×C4—2612no—
708C22×C4—2612no—
709C22×C4C23×D13112yes—
710C22×C4C23×D13112yes—
711C22×C4C23×D1311yescharacteristic
712C22×C4C23×D1313yes—
713C22×C4C23×D1313yes—
714C22×C4C23×D1311yescharacteristic
715C22×C4C23×D1313yes—
716C4⋊C4—1312no—
717C4⋊C4—1312no—
718C4⋊C4—1312no—
719C4⋊C4—1324no—
720C4⋊C4—1312no—
721C4⋊C4C23×D13112yes—
722C4⋊C4C23×D13112yes—
723C22⋊C4—134no—
724C22⋊C4—1312no—
725C22⋊C4—1324no—
726C22⋊C4—134no—
727C22⋊C4—134no—
728C22⋊C4—1312no—
729C22⋊C4—1312no—
730C22⋊C4—1324no—
731C22⋊C4—1324no—
732C22⋊C4C23×D1314yes—
733C22⋊C4C23×D13112yes—
734C22⋊C4C23×D13124yes—
735C42—1312no—
736C42—1312no—
737C42—1312no—
738C42C23×D13112yes—
739C13C22×#54811yescharacteristic, complemented, Sylow
740C23—22no—
741C23—22no—
742C23—26no—
743C23—26no—
744C23—26no—
745C23—134no—
746C23—134no—
747C23—134no—
748C23—132no—
749C23—134no—
750C23—1316no—
751C23—132no—
752C23—136no—
753C23—268no—
754C23—2632no—
755C23—268no—
756C23—2624no—
757C23—2624no—
758C23—2624no—
759C23—262no—
760C23—262no—
761C23—266no—
762C23—266no—
763C23—266no—
764C23—5248no—
765C23#41×D1314yescomplemented
766C23C24×D1316yes—
767C23C24×D1312yes—
768C23C24×D1311yescharacteristic
769Q8—224no—
770Q8—1348no—
771Q8—2648no—
772Q8—2624no—
773Q8C2×D4×D13116yescomplemented
774D4—224no—
775D4—224no—
776D4—2624no—
777D4—2648no—
778D4—2624no—
779D4—2624no—
780D4—2624no—
781C2×C4—22no—
782C2×C4—26no—
783C2×C4—26no—
784C2×C4—22no—
785C2×C4—224no—
786C2×C4—224no—
787C2×C4—1312no—
788C2×C4—136no—
789C2×C4—1348no—
790C2×C4—132no—
791C2×C4—136no—
792C2×C4—136no—
793C2×C4—132no—
794C2×C4—2624no—
795C2×C4—2624no—
796C2×C4—268no—
797C2×C4—268no—
798C2×C4—2624no—
799C2×C4—2624no—
800C2×C4—2624no—
801C2×C4—2624no—
802C2×C4—262no—
803C2×C4—266no—
804C2×C4—266no—
805C2×C4—262no—
806C2×C4—2624no—
807C2×C4—2624no—
808C2×C4C2×D4×D13112yes—
809C2×C4C24×D1312yes—
810C2×C4C24×D1316yes—
811C2×C4C24×D1316yes—
812C2×C4C24×D1312yes—
813C2×C4C24×D1316yes—
814C22—28no—
815C22—22no—
816C22—22no—
817C22—26no—
818C22—26no—
819C22—26no—
820C22—412no—
821C22—1316no—
822C22—134no—
823C22—134no—
824C22—134no—
825C22—134no—
826C22—2632no—
827C22—268no—
828C22—262no—
829C22—262no—
830C22—266no—
831C22—266no—
832C22—266no—
833C22—5248no—
834C22—5212no—
835C22C22×D4×D1312yes—
836C22C2×#41×D1312yes—
837C22C2×#41×D1314yescomplemented
838C22D13×2−1+412yes—
839C22C25×D1311yescharacteristic
840C4—22no—
841C4—26no—
842C4—26no—
843C4—22no—
844C4—1312no—
845C4—262no—
846C4—266no—
847C4—266no—
848C4—262no—
849C4C22×D4×D13112yes—
850C2—24no—
851C2—46no—
852C2—138no—
853C2—264no—
854C2—526no—
855C2D13×#54814yesdirect product factor
856C2C23×D4×D1311yescharacteristic
857C2C22×#41×D1311yescharacteristic
858C2C2×D13×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#548C2
socleC23×C13C25
hypercenterC2×#548D13
hypocenterC13C22×#548
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#41×D13C2semidirect
2. C23×Q8×D13C2semidirect
3. C2×#11719281C2semidirect
4. C2×#11719522C2semidirect
5. C2×#11719338C2semidirect
6. C2×#11719257C2semidirect
7. C2×#11719382C2semidirect
8. C2×#11719536C2semidirect
9. C2×#11719303C2semidirect
10. D13×#548C2direct (N × H)
11. C2×D13×#124C2semidirect
12. C2×D13×C22⋊Q8C2semidirect
13. C2×D13×#121C2semidirect
14. C2×C4×Q8×D13C2semidirect
15. C2×C4×D4×D13C2semidirect
16. C2×C13×#548C2semidirect
17. C22×C13×#41C22semidirect
18. C23×Q8×C13C22semidirect
20. C2×#41×D13C22semidirect
21. C22×#6131C22semidirect
25. C22×Q8×D13C22semidirect
26. C22×Q8×D13C22semidirect
27. C22×Q8×D13C22semidirect
28. C22×#6129C22semidirect
31. C22×#6127C22semidirect
34. C23×Dic26C22semidirect
35. C13×#548C22semidirect
36. C2×C13×#124C22semidirect
37. C2×C13×C22⋊Q8C22semidirect
38. C2×C13×#121C22semidirect
39. C2×C4×Q8×C13C22semidirect
40. C2×C4×D4×C13C22semidirect
41. #11719536C22semidirect
42. #11719522C22semidirect
43. C2×#88201C22semidirect
44. C2×#88200C22semidirect
45. C2×Q8×Dic13C22semidirect
46. C2×#88193C22semidirect
47. C2×#88192C22semidirect
48. C2×#88190C22semidirect
49. C2×D4×Dic13C22semidirect
50. C2×#88184C22semidirect
51. C2×C4×C22⋊D13C22semidirect
52. C2×C4×C22⋊D13C22semidirect
53. C2×#88178C22semidirect
54. #11719382C22semidirect
55. D13×#124C22semidirect
56. #11719338C22semidirect
57. D13×C22⋊Q8C22semidirect
58. D13×#121C22semidirect
59. #11719303C22semidirect
60. #11719281C22semidirect
61. C4×Q8×D13C22semidirect
62. #11719257C22semidirect
63. C4×D4×D13C22semidirect
64. C2×#88151C22semidirect
65. C2×#88150C22semidirect
66. C2×#88149C22semidirect
67. C2×#88147C22semidirect
70. C2×#88141C22semidirect
71. C2×#88139C22semidirect
72. C2×#88139C22semidirect
73. C2×#88138C22semidirect
74. C2×#88135C22semidirect
75. C2×#88135C22semidirect
79. C2×#88132C22semidirect
80. C2×#88129C22semidirect
81. C2×C4×D52C22semidirect
83. C2×C4×Dic26C22semidirect
87. C2×C13×#41C23semidirect
91. C22×Q8×C13C23semidirect
103. C2×#6131C23semidirect
108. C2×Q8×D13D4semidirect
111. C2×Q8×D13C23semidirect
112. C2×Q8×D13C23semidirect
114. C2×#6129C23semidirect
120. C2×#6127C23semidirect
140. C22×Dic26C23semidirect
141. C13×#124C23semidirect
142. C13×C22⋊Q8C23semidirect
143. C13×#121C23semidirect
144. C4×Q8×C13C23semidirect
145. C4×D4×C13C23semidirect
155. #88201C23semidirect
156. #88200C23semidirect
157. Q8×Dic13C23semidirect
158. #88193C23semidirect
159. #88192C23semidirect
160. #88190C23semidirect
161. D4×Dic13C23semidirect
162. #88184C23semidirect
163. C4×C22⋊D13C23semidirect
164. C4×C22⋊D13C23semidirect
173. #88178C23semidirect
180. #88151C23semidirect
181. #88150C23semidirect
182. #88149C23semidirect
183. #88147C23semidirect
186. #88141C23semidirect
187. #88139C23semidirect
188. #88139C23semidirect
189. #88138C23semidirect
190. #88135C23semidirect
191. #88135C23semidirect
195. #88132C23semidirect
196. #88129C23semidirect
197. C4×D52C23semidirect
199. C4×Dic26C23semidirect
208. C23×D13#41semidirect
217. C2×Q8×C13C2×D4semidirect
252. Q8×D13C2×D4semidirect
284. C2×Dic26C2×D4semidirect
321. C2×#548D13direct (N × H)
332. C23×C13C2×#41semidirect
350. C22×D13C2×#41semidirect
351. C22×D13C2×#41semidirect
357. Q8×C13C22×D4semidirect
400. Dic26C22×D4semidirect
406. C22×#41C2×D13semidirect
414. C23×Q8C2×D13semidirect
426. #548C2×D13direct (N × H)
433. C2×#124C2×D13semidirect
440. C2×C22⋊Q8C2×D13semidirect
447. C2×#121C2×D13semidirect
452. C2×C4×Q8C2×D13semidirect
461. C2×C4×D4C2×D13semidirect
477. C22×C13C22×#41semidirect
489. C2×D13#548direct (N × H)
492. C2×D13C22×#41semidirect
514. C2×#41C22×D13semidirect
532. C22×Q8C22×D13semidirect
566. #124C22×D13semidirect
572. C22⋊Q8C22×D13semidirect
578. #121C22×D13semidirect
582. C4×Q8C22×D13semidirect
590. C4×D4C22×D13semidirect
622. C2×C13C2×#548semidirect
628. D13C2×#548direct (N × H)
659. C2×Q8D4×D13semidirect
739. C13C22×#548semidirect
765. C23#41×D13semidirect
773. Q8C2×D4×D13semidirect
837. C22C2×#41×D13semidirect
855. C2D13×#548direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D132
C23×Q8×D132
C2×#117192812
C2×#117195222
C2×#117193382
C2×#117192572
C2×#117193822
C2×#117195362
C2×#117193032
D13×#5482
C2×D13×#1242
C2×D13×C22⋊Q82
C2×D13×#1212
C2×C4×Q8×D132
C2×C4×D4×D132
C2×C13×#5482
C22×#54813