Finite Group Databasebeta

← C2×#41×C22⋊D13 #16769876

Subgroups — C2×#41×C22⋊D13 #16769876

Order 3328.

12314 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D13C211yesmaximal, characteristic, complemented
2#41×C22⋊D13C2132yesmaximal, direct product factor
3C2×#11719539C211yesmaximal, characteristic, complemented
4C2×Q8×C22⋊D13C211yesmaximal, characteristic, complemented
5C2×#11719522C211yesmaximal, characteristic, complemented
6C2×#11719536C211yesmaximal, characteristic, complemented
7C2×#11719529C213yesmaximal, complemented
8C2×#11719511C213yesmaximal, complemented
9C2×#11719534C213yesmaximal, complemented
10C2×D4×C22⋊D13C213yesmaximal, complemented
11C2×#11719537C213yesmaximal, complemented
12C2×#11719496C213yesmaximal, complemented
13C2×#11719533C213yesmaximal, complemented
14C2×#41×Dic13C211yesmaximal, characteristic, complemented
15C22×C4×C22⋊D13C213yesmaximal, complemented
16C23×C13×#41C211yesmaximal, characteristic, complemented
17C22×C13×#41—216no—
18C22×C13×#41C2211yescharacteristic
19C22×C13×#41C2213yescomplemented
20C22×C13×#41C2211yescharacteristic, complemented
21C22×C13×#41C2213yescomplemented
22C22×C13×#41C22116yescomplemented
23C23×Q8×C13C2211yescharacteristic, complemented
24C23×D4×C13C2213yescomplemented
25C24×C4×C13C2213yescomplemented
26C23×C22⋊D13C2213yes—
27C2×#41×D13—216no—
28C2×#41×D13C22116yescomplemented
29C22×#6131C2211yescharacteristic, complemented
30C22×Q8×D13C2211yescharacteristic, complemented
31C22×#6129C2213yescomplemented
32C22×D4×D13C2213yescomplemented
33C22×#6127C2213yescomplemented
34C23×C4×D13C2213yescomplemented
35C2×#88207C2216yescomplemented
36C22×C22⋊Dic13C2213yescomplemented
37#11719539C22116yescomplemented
38#11719537C22148yescomplemented
39#11719536C22116yescomplemented
40#11719534C22148yescomplemented
41#11719533C22148yescomplemented
42#41×Dic13C22116yescomplemented
43#11719529C22148yescomplemented
44#11719522C22116yescomplemented
45Q8×C22⋊D13C22116yescomplemented
46C2×#88201C2213yescomplemented
47C2×#88200C2213yescomplemented
48C2×#88200C2213yescomplemented
49C2×Q8×Dic13C2211yescharacteristic, complemented
50C2×Q8×Dic13C2211yescharacteristic, complemented
51C2×#88198C2213yescomplemented
52#11719511C22148yescomplemented
53C2×#88194C2213yescomplemented
54C2×#88193C2216yescomplemented
55C2×#88193C2216yescomplemented
56D4×C22⋊D13C22148yescomplemented
57C2×#88192C2213yescomplemented
58C2×#88192C2213yescomplemented
59C2×#88191C2216yescomplemented
60C2×#88190C2213yescomplemented
61C2×#88189C2216yescomplemented
62C2×D4×Dic13C2213yescomplemented
63C2×D4×Dic13C2213yescomplemented
64#11719496C22148yescomplemented
65C2×#88184C2213yescomplemented
66C2×#88184C2213yescomplemented
67C2×#88183C2216yescomplemented
68C2×C4×C22⋊D13C2211yescharacteristic
69C2×C4×C22⋊D13C2213yes—
70C2×C4×C22⋊D13C2213yescomplemented
71C2×C4×C22⋊D13C2213yescomplemented
72C2×C4×C22⋊D13C2213yescomplemented
73C2×C4×C22⋊D13C2213yescomplemented
74C2×C4×C22⋊D13C2213yescomplemented
75C2×C4×C22⋊D13C2213yescomplemented
76C2×C4×C22⋊D13C2216yescomplemented
77C2×C4×C22⋊D13C22148yescomplemented
78C22×#6103C2213yescomplemented
79C2×#88180C2213yescomplemented
80C2×#88178C2213yescomplemented
81C2×#88178C2213yescomplemented
82C22×#6101C2213yescomplemented
83C22×C4×Dic13C2213yescomplemented
84C25×C13C2313yes—
85C24×D13C2313yes—
86C2×C13×#41—2128no—
87C2×C13×#41—28no—
88C2×C13×#41—224no—
89C2×C13×#41—224no—
90C2×C13×#41D4116yescomplemented
91C2×C13×#41C2318yes—
92C2×C13×#41C23124yescomplemented
93C2×C13×#41C23124yescomplemented
94C2×C13×#41C2318yescomplemented
95C22×Q8×C13—28no—
96C22×Q8×C13C2313yes—
97C22×Q8×C13C2311yescharacteristic
98C22×Q8×C13C2318yescomplemented
99C22×D4×C13—224no—
100C22×D4×C13C2316yes—
101C22×D4×C13C2313yes—
102C22×D4×C13C2313yes—
103C22×D4×C13C23124yescomplemented
104C23×C4×C13—224no—
105C23×C4×C13C2313yes—
106C23×C4×C13C2313yes—
107C23×C4×C13C2313yes—
108C23×C4×C13C2311yescharacteristic
109C23×C4×C13C2313yes—
110C23×C4×C13C2313yes—
111C23×C4×C13C23124yescomplemented
112C22×C22⋊D13—224no—
113C22×C22⋊D13C2313yes—
114C22×C22⋊D13C2313yes—
115C22×C22⋊D13C23124yes—
116C22×C22⋊D13C2313yes—
117C22×C22⋊D13C2316yes—
118C22×C22⋊D13C2316yes—
119C22×C22⋊D13C2311yescharacteristic
120C23×Dic13C2313yes—
121C23×Dic13C2313yes—
122C23×Dic13C2313yes—
123#41×D13—2128no—
124C2×#6131—28no—
125C2×#6131C2318yescomplemented
126C2×Q8×D13—28no—
127C2×Q8×D13C2318yescomplemented
128C2×#6129—224no—
129C2×#6129C23124yescomplemented
130C2×D4×D13—224no—
131C2×D4×D13C23124yescomplemented
132C2×#6127—224no—
133C2×#6127C23124yescomplemented
134C22×D52C2313yes—
135C22×C4×D13—224no—
136C22×C4×D13C2311yescharacteristic
137C22×C4×D13C2313yes—
138C22×C4×D13C2313yes—
139C22×C4×D13C2313yes—
140C22×C4×D13C23124yescomplemented
141C22×Dic26C2313yes—
142#88207C23148yescomplemented
143C2×C22⋊Dic13C2313yes—
144C2×C22⋊Dic13C2316yes—
145C2×C22⋊Dic13C2316yes—
146C2×C22⋊Dic13C2311yescharacteristic
147C2×C22⋊Dic13C2313yes—
148C2×C22⋊Dic13C2313yes—
149C2×C22⋊Dic13C23124yescomplemented
150#88201C23124yescomplemented
151#88200C23124yescomplemented
152#88200C23124yescomplemented
153Q8×Dic13C2318yescomplemented
154Q8×Dic13C2318yescomplemented
155#88198C23124yescomplemented
156#88194C23124yescomplemented
157#88193C23148yescomplemented
158#88193C23148yescomplemented
159#88192C23124yescomplemented
160#88192C23124yescomplemented
161#88191C23148yescomplemented
162#88190C23124yescomplemented
163#88189C23148yescomplemented
164D4×Dic13C23124yescomplemented
165D4×Dic13C23124yescomplemented
166#88184C23124yescomplemented
167#88184C23124yescomplemented
168#88183C23148yescomplemented
169C4×C22⋊D13C2318yes—
170C4×C22⋊D13C23124yes—
171C4×C22⋊D13C23124yescomplemented
172C4×C22⋊D13C23124yescomplemented
173C4×C22⋊D13C23124yescomplemented
174C4×C22⋊D13C23124yescomplemented
175C4×C22⋊D13C23124yescomplemented
176C4×C22⋊D13C23124yescomplemented
177C4×C22⋊D13C23148yescomplemented
178C2×#6103C2311yescharacteristic
179C2×#6103C2313yes—
180C2×#6103C2313yes—
181C2×#6103C2313yes—
182C2×#6103C2316yes—
183C2×#6103C23124yescomplemented
184#88180C23124yescomplemented
185C2×C4⋊Dic13C2313yes—
186C2×C4⋊Dic13C2313yes—
187#88178C23124yescomplemented
188#88178C23124yescomplemented
189C2×#6101C2311yescharacteristic
190C2×#6101C2313yes—
191C2×#6101C2313yes—
192C2×#6101C2313yes—
193C2×#6101C2316yes—
194C2×#6101C23124yescomplemented
195C2×C4×Dic13C2311yescharacteristic
196C2×C4×Dic13C2313yes—
197C2×C4×Dic13C2313yes—
198C2×C4×Dic13C2313yes—
199C2×C4×Dic13C23124yescomplemented
200C2×D4×#41—131nomaximal, Sylow
201C24×C13—212no—
202C24×C13—212no—
203C24×C13—46no—
204C24×C13C2413yes—
205C24×C13C24112yes—
206C24×C13C2413yes—
207C24×C13C2411yescharacteristic
208C23×D13—212no—
209C23×D13—212no—
210C23×D13—46no—
211C23×D13C2413yes—
212C23×D13C24112yes—
213C23×D13C2411yescharacteristic
214C13×#41—232no—
215C13×#41—296no—
216C13×#41—296no—
217C13×#41C2×D4164yescomplemented
218C2×Q8×C13—232no—
219C2×Q8×C13—212no—
220C2×Q8×C13C2×D418yescomplemented
221C2×Q8×C13C24112yes—
222C2×Q8×C13C2414yes—
223C2×D4×C13—224no—
224C2×D4×C13—296no—
225C2×D4×C13—212no—
226C2×D4×C13C2×D4124yescomplemented
227C2×D4×C13C24124yes—
228C2×D4×C13C24112yes—
229C2×D4×C13C24112yes—
230C22×C4×C13—212no—
231C22×C4×C13—24no—
232C22×C4×C13—212no—
233C22×C4×C13—212no—
234C22×C4×C13—212no—
235C22×C4×C13—296no—
236C22×C4×C13C2×D4124yescomplemented
237C22×C4×C13C2411yescharacteristic
238C22×C4×C13C2413yes—
239C22×C4×C13C24112yes—
240C22×C4×C13C24112yes—
241C22×C4×C13C24112yes—
242C22×C4×C13C2414yes—
243C22×C4×C13C24112yes—
244C22×C4×C13C2413yes—
245C22×C4×C13C24112yes—
246C22×C4×C13C2411yescharacteristic
247C2×C22⋊D13—224no—
248C2×C22⋊D13—212no—
249C2×C22⋊D13—212no—
250C2×C22⋊D13—296no—
251C2×C22⋊D13—212no—
252C2×C22⋊D13—412no—
253C2×C22⋊D13#4118yesdirect product factor
254C2×C22⋊D13C24112yes—
255C2×C22⋊D13C24112yes—
256C2×C22⋊D13C24112yes—
257C2×C22⋊D13C24124yes—
258C2×C22⋊D13C24124yes—
259C2×C22⋊D13C2414yes—
260C22×Dic13—212no—
261C22×Dic13—212no—
262C22×Dic13—46no—
263C22×Dic13C2411yescharacteristic
264C22×Dic13C2413yes—
265C22×Dic13C2413yes—
266C22×Dic13C24112yes—
267C22×Dic13C2413yes—
268C22×Dic13C2411yescharacteristic
269C22×Dic13C24112yes—
270C22×Dic13C24112yes—
271C22×Dic13C2411yescharacteristic
272#6131—232no—
273Q8×D13—232no—
274#6129—296no—
275D4×D13—296no—
276#6127—296no—
277C2×D52—212no—
278C2×D52C24112yes—
279C2×C4×D13—24no—
280C2×C4×D13—212no—
281C2×C4×D13—212no—
282C2×C4×D13—212no—
283C2×C4×D13—296no—
284C2×C4×D13C2414yes—
285C2×C4×D13C24112yes—
286C2×C4×D13C24112yes—
287C2×C4×D13C24112yes—
288C2×Dic26—212no—
289C2×Dic26C24112yes—
290C22⋊Dic13C24112yes—
291C22⋊Dic13C24124yes—
292C22⋊Dic13C24124yes—
293C22⋊Dic13C2414yes—
294C22⋊Dic13C24112yes—
295C22⋊Dic13C24112yes—
296#6103C2414yes—
297#6103C24112yes—
298#6103C24112yes—
299#6103C24112yes—
300#6103C24124yes—
301C4⋊Dic13C24112yes—
302C4⋊Dic13C24112yes—
303#6101C2414yes—
304#6101C24112yes—
305#6101C24112yes—
306#6101C24112yes—
307#6101C24124yes—
308C4×Dic13C2414yes—
309C4×Dic13C24112yes—
310C4×Dic13C24112yes—
311C4×Dic13C24112yes—
312C23×#41—131no—
313C23×#41D1311yescharacteristic, complemented
314D4×#41—1332no—
315C2×#550—131no—
316C2×D4×Q8—131no—
317C2×#548—131no—
318C2×#548—131no—
319C2×#547—133no—
320C2×#546—133no—
321C2×#546—133no—
322C2×D42—133no—
323C2×#532—133no—
324C2×#525—133no—
325C2×#525—133no—
326C2×C4×#41—131no—
327C22×C4×D4—133no—
328C23×C13—22no—
329C23×C13—26no—
330C23×C13—26no—
331C23×C13—22no—
332C23×C13—224no—
333C23×C13—26no—
334C23×C13—26no—
335C23×C13—224no—
336C23×C13—26no—
337C23×C13—412no—
338C23×C13—448no—
339C23×C13C22×D4112yes—
340C23×C13C2×#4114yescomplemented
341C23×C13C2516yes—
342C23×C13C2516yes—
343C23×C13C2512yes—
344C23×C13C2511yescharacteristic
345C22×D13—22no—
346C22×D13—22no—
347C22×D13—26no—
348C22×D13—224no—
349C22×D13—26no—
350C22×D13—26no—
351C22×D13—224no—
352C22×D13—412no—
353C22×D13—448no—
354C22×D13C2×#4114yescomplemented
355C22×D13C2516yes—
356C22×D13C2512yes—
357Q8×C13—224no—
358Q8×C13C22×D4116yescomplemented
359D4×C13—248no—
360D4×C13—224no—
361D4×C13C22×D4148yescomplemented
362C2×C4×C13—22no—
363C2×C4×C13—26no—
364C2×C4×C13—224no—
365C2×C4×C13—28no—
366C2×C4×C13—224no—
367C2×C4×C13—224no—
368C2×C4×C13—224no—
369C2×C4×C13C22×D4112yes—
370C2×C4×C13C22×D414yes—
371C2×C4×C13C22×D4148yescomplemented
372C2×C4×C13C2512yes—
373C2×C4×C13C2516yes—
374C2×C4×C13C2512yes—
375C2×C4×C13C2516yes—
376C22⋊D13—248no—
377C22⋊D13—224no—
378C22⋊D13—224no—
379C22⋊D13—224no—
380C22⋊D13—424no—
381C22⋊D13C2×#41116yesdirect product factor
382C2×Dic13—26no—
383C2×Dic13—22no—
384C2×Dic13—224no—
385C2×Dic13—26no—
386C2×Dic13—22no—
387C2×Dic13—26no—
388C2×Dic13—224no—
389C2×Dic13—412no—
390C2×Dic13C2×#4114yescomplemented
391C2×Dic13C2512yes—
392C2×Dic13C2516yes—
393C2×Dic13C2516yes—
394C2×Dic13C2516yes—
395C2×Dic13C2512yes—
396C2×Dic13C2512yes—
397D52—224no—
398C4×D13—28no—
399C4×D13—224no—
400C4×D13—224no—
401C4×D13—224no—
402Dic26—224no—
403C22×#41—216no—
404C22×#41—1316no—
405C22×#41—131no—
406C22×#41—133no—
407C22×#41—133no—
408C22×#41—2616no—
409C22×#41C2×D1311yescharacteristic
410C22×#41C2×D1313yescomplemented
411C22×#41C2×D1313yescomplemented
412C22×#41C2×D1311yescharacteristic, complemented
413C22×#41C2×D13116yescomplemented
414C23×Q8—131no—
415C23×Q8C2×D1311yescharacteristic, complemented
416C23×D4—133no—
417C23×D4—133no—
418C23×D4C2×D1313yescomplemented
419C24×C4—133no—
420C24×C4C2×D1313yescomplemented
421#550—1316no—
422D4×Q8—1316no—
423#548—1316no—
424#548—1316no—
425#547—1348no—
426#546—1348no—
427#546—1348no—
428D42—1348no—
429#532—1348no—
430C2×C4⋊Q8—133no—
431C2×#127—133no—
432C2×#124—133no—
433C2×#124—133no—
434#525—1348no—
435#525—1348no—
436C2×#123—136no—
437C2×#123—136no—
438C2×C22⋊Q8—133no—
439C2×C22⋊Q8—133no—
440C2×C22⋊Q8—133no—
441C2×C22⋊Q8—133no—
442C2×#121—133no—
443C2×#121—133no—
444C2×#121—136no—
445C2×#121—136no—
446C2×#121—133no—
447C2×#121—133no—
448C2×#120—136no—
449C2×#120—136no—
450C4×#41—1316no—
451C2×C4×Q8—131no—
452C2×C4×Q8—131no—
453C2×C4×D4—133no—
454C2×C4×D4—133no—
455C2×C4×D4—131no—
456C2×C4×D4—133no—
457C2×C4×D4—133no—
458C2×C4×D4—133no—
459C2×C4×D4—133no—
460C2×C4×D4—133no—
461C2×C4×D4—133no—
462C2×C4×D4—133no—
463C2×C4×D4—136no—
464C2×C4×D4—1348no—
465C2×#117—133no—
466C22×C4⋊C4—133no—
467C22×C22⋊C4—133no—
468C22×C22⋊C4—133no—
469C22×C42—133no—
470C22×C13—22no—
471C22×C13—26no—
472C22×C13—26no—
473C22×C13—22no—
474C22×C13—224no—
475C22×C13—28no—
476C22×C13—26no—
477C22×C13—26no—
478C22×C13—26no—
479C22×C13—448no—
480C22×C13—412no—
481C22×C13C23×D4112yes—
482C22×C13C23×D412yes—
483C22×C13C22×#4112yes—
484C22×C13C22×#4114yescomplemented
485C22×C13#58512yes—
486C22×C13C2611yescharacteristic
487C2×D13—22no—
488C2×D13—22no—
489C2×D13—28no—
490C2×D13—26no—
491C2×D13—26no—
492C2×D13—26no—
493C2×D13—448no—
494C2×D13—412no—
495C2×D13C22×#4114yescomplemented
496C4×C13—22no—
497C4×C13—26no—
498C4×C13C23×D4112yes—
499C4×C13C23×D414yes—
500Dic13—26no—
501Dic13—22no—
502Dic13—26no—
503Dic13—22no—
504Dic13—26no—
505Dic13C22×#4114yescomplemented
506C25—133no—
507C25C22×D1313yes—
508C2×#41—2128no—
509C2×#41—28no—
510C2×#41—224no—
511C2×#41—224no—
512C2×#41—138no—
513C2×#41—1324no—
514C2×#41—1324no—
515C2×#41—26128no—
516C2×#41—268no—
517C2×#41—2624no—
518C2×#41—2624no—
519C2×#41C22⋊D13116yesdirect product factor
520C2×#41C22×D1318yes—
521C2×#41C22×D13124yescomplemented
522C2×#41C22×D13124yescomplemented
523C2×#41C22×D1318yescomplemented
524C22×Q8—28no—
525C22×Q8—138no—
526C22×Q8—133no—
527C22×Q8—268no—
528C22×Q8C22×D1313yes—
529C22×Q8C22×D1311yescharacteristic
530C22×Q8C22×D1318yescomplemented
531C22×D4—224no—
532C22×D4—131no—
533C22×D4—133no—
534C22×D4—133no—
535C22×D4—133no—
536C22×D4—1324no—
537C22×D4—136no—
538C22×D4—136no—
539C22×D4—1324no—
540C22×D4—133no—
541C22×D4—2624no—
542C22×D4—2624no—
543C22×D4C22×D1316yes—
544C22×D4C22×D1313yes—
545C22×D4C22×D1313yes—
546C22×D4C22×D13124yescomplemented
547C23×C4—224no—
548C23×C4—133no—
549C23×C4—133no—
550C23×C4—133no—
551C23×C4—133no—
552C23×C4—133no—
553C23×C4—1324no—
554C23×C4—131no—
555C23×C4—133no—
556C23×C4—2624no—
557C23×C4C22×D1313yes—
558C23×C4C22×D1313yes—
559C23×C4C22×D1313yes—
560C23×C4C22×D1311yescharacteristic
561C23×C4C22×D1313yes—
562C23×C4C22×D1313yes—
563C23×C4C22×D13124yescomplemented
564C4⋊Q8—1324no—
565#127—1324no—
566#124—1324no—
567#124—1324no—
568#123—1348no—
569#123—1348no—
570C22⋊Q8—1324no—
571C22⋊Q8—1324no—
572C22⋊Q8—1324no—
573C22⋊Q8—1324no—
574#121—1324no—
575#121—1324no—
576#121—1348no—
577#121—1348no—
578#121—1324no—
579#121—1324no—
580#120—1348no—
581#120—1348no—
582C4×Q8—138no—
583C4×Q8—138no—
584C4×D4—1324no—
585C4×D4—1324no—
586C4×D4—138no—
587C4×D4—1324no—
588C4×D4—1324no—
589C4×D4—1324no—
590C4×D4—1324no—
591C4×D4—1324no—
592C4×D4—1324no—
593C4×D4—1324no—
594C4×D4—1348no—
595#117—1324no—
596C2×C4⋊C4—131no—
597C2×C4⋊C4—133no—
598C2×C4⋊C4—133no—
599C2×C4⋊C4—133no—
600C2×C4⋊C4—1324no—
601C2×C4⋊C4—133no—
602C2×C4⋊C4—133no—
603C2×C4⋊C4—136no—
604C2×C22⋊C4—131no—
605C2×C22⋊C4—133no—
606C2×C22⋊C4—133no—
607C2×C22⋊C4—133no—
608C2×C22⋊C4—1324no—
609C2×C22⋊C4—136no—
610C2×C22⋊C4—136no—
611C2×C22⋊C4—131no—
612C2×C22⋊C4—133no—
613C2×C22⋊C4—133no—
614C2×C22⋊C4—133no—
615C2×C22⋊C4—1324no—
616C2×C22⋊C4—136no—
617C2×C42—133no—
618C2×C42—133no—
619C2×C42—1324no—
620C2×C42—133no—
621C2×C42—131no—
622C2×C13—212no—
623C2×C13—24no—
624C2×C13—46no—
625C2×C13D4×#4114yescomplemented
626C2×C13C24×D411yescharacteristic
627C2×C13C23×#4111yescharacteristic
628C2×C13C2×#58511yescharacteristic
629D13—24no—
630D13—46no—
631C24—212no—
632C24—212no—
633C24—46no—
634C24—131no—
635C24—133no—
636C24—1312no—
637C24—2612no—
638C24—2612no—
639C24—526no—
640C24C23×D1313yes—
641C24C23×D13112yes—
642C24C23×D1311yescharacteristic
643C24C23×D1313yes—
644#41—232no—
645#41—296no—
646#41—296no—
647#41—2632no—
648#41—2696no—
649#41—2696no—
650#41C2×C22⋊D13164yesdirect product factor
651C2×Q8—232no—
652C2×Q8—212no—
653C2×Q8—1312no—
654C2×Q8—2632no—
655C2×Q8—2612no—
656C2×Q8C2×C22⋊D1318yescomplemented
657C2×Q8C23×D13112yes—
658C2×Q8C23×D1314yes—
659C2×D4—224no—
660C2×D4—296no—
661C2×D4—212no—
662C2×D4—138no—
663C2×D4—134no—
664C2×D4—1312no—
665C2×D4—1312no—
666C2×D4—1312no—
667C2×D4—1324no—
668C2×D4—1324no—
669C2×D4—1312no—
670C2×D4—2612no—
671C2×D4—2696no—
672C2×D4—2612no—
673C2×D4—2612no—
674C2×D4—2624no—
675C2×D4—2696no—
676C2×D4—2612no—
677C2×D4—5212no—
678C2×D4C2×C22⋊D13124yescomplemented
679C2×D4C23×D13124yes—
680C2×D4C23×D13112yes—
681C2×D4C23×D13112yes—
682C22×C4—212no—
683C22×C4—24no—
684C22×C4—212no—
685C22×C4—212no—
686C22×C4—212no—
687C22×C4—296no—
688C22×C4—131no—
689C22×C4—131no—
690C22×C4—133no—
691C22×C4—133no—
692C22×C4—1312no—
693C22×C4—131no—
694C22×C4—133no—
695C22×C4—1312no—
696C22×C4—1312no—
697C22×C4—134no—
698C22×C4—1312no—
699C22×C4—1312no—
700C22×C4—1312no—
701C22×C4—2612no—
702C22×C4—2612no—
703C22×C4—264no—
704C22×C4—2612no—
705C22×C4—2612no—
706C22×C4—2612no—
707C22×C4—2696no—
708C22×C4—526no—
709C22×C4C2×C22⋊D13124yescomplemented
710C22×C4C23×D1311yescharacteristic
711C22×C4C23×D1313yes—
712C22×C4C23×D13112yes—
713C22×C4C23×D1314yes—
714C22×C4C23×D13112yes—
715C22×C4C23×D13112yes—
716C22×C4C23×D13112yes—
717C22×C4C23×D1313yes—
718C22×C4C23×D13112yes—
719C22×C4C23×D1311yescharacteristic
720C4⋊C4—134no—
721C4⋊C4—1312no—
722C4⋊C4—1312no—
723C4⋊C4—1312no—
724C4⋊C4—1312no—
725C4⋊C4—1312no—
726C4⋊C4—1324no—
727C22⋊C4—134no—
728C22⋊C4—1312no—
729C22⋊C4—1312no—
730C22⋊C4—1312no—
731C22⋊C4—1324no—
732C22⋊C4—1324no—
733C22⋊C4—134no—
734C22⋊C4—1312no—
735C22⋊C4—1312no—
736C22⋊C4—1312no—
737C22⋊C4—1324no—
738C42—134no—
739C42—1312no—
740C42—1312no—
741C42—1312no—
742C13C2×D4×#4111yescharacteristic, complemented, Sylow
743C23—26no—
744C23—26no—
745C23—22no—
746C23—22no—
747C23—26no—
748C23—224no—
749C23—26no—
750C23—224no—
751C23—26no—
752C23—412no—
753C23—448no—
754C23—134no—
755C23—132no—
756C23—136no—
757C23—2624no—
758C23—262no—
759C23—262no—
760C23—266no—
761C23—266no—
762C23—2624no—
763C23—266no—
764C23—5212no—
765C23—5248no—
766C23#41×D1314yescomplemented
767C23C22×C22⋊D13112yes—
768C23C24×D1316yes—
769C23C24×D1312yes—
770C23C24×D1316yes—
771C23C24×D1311yescharacteristic
772Q8—224no—
773Q8—2624no—
774Q8C22×C22⋊D13116yescomplemented
775D4—248no—
776D4—224no—
777D4—1316no—
778D4—2624no—
779D4—2624no—
780D4—2624no—
781D4—2648no—
782D4—2624no—
783D4—5224no—
784D4C22×C22⋊D13148yescomplemented
785C2×C4—22no—
786C2×C4—26no—
787C2×C4—224no—
788C2×C4—28no—
789C2×C4—224no—
790C2×C4—224no—
791C2×C4—224no—
792C2×C4—134no—
793C2×C4—132no—
794C2×C4—132no—
795C2×C4—136no—
796C2×C4—136no—
797C2×C4—132no—
798C2×C4—136no—
799C2×C4—2624no—
800C2×C4—266no—
801C2×C4—262no—
802C2×C4—266no—
803C2×C4—262no—
804C2×C4—266no—
805C2×C4—2624no—
806C2×C4—268no—
807C2×C4—2624no—
808C2×C4—2624no—
809C2×C4—2624no—
810C2×C4—5212no—
811C2×C4C22×C22⋊D1314yes—
812C2×C4C22×C22⋊D13112yes—
813C2×C4C22×C22⋊D13148yescomplemented
814C2×C4C24×D1312yes—
815C2×C4C24×D1316yes—
816C2×C4C24×D1312yes—
817C2×C4C24×D1316yes—
818C22—28no—
819C22—224no—
820C22—22no—
821C22—26no—
822C22—26no—
823C22—22no—
824C22—26no—
825C22—26no—
826C22—26no—
827C22—448no—
828C22—412no—
829C22—134no—
830C22—268no—
831C22—262no—
832C22—262no—
833C22—266no—
834C22—266no—
835C22—266no—
836C22—5248no—
837C22—5212no—
838C22C2×#41×D1312yes—
839C22C2×#41×D1314yescomplemented
840C22#1171964812yes—
841C22C23×C22⋊D13112yes—
842C22C23×C22⋊D1312yes—
843C22C25×D1311yescharacteristic
844C4—22no—
845C4—26no—
846C4—134no—
847C4—262no—
848C4—266no—
849C4—266no—
850C4—262no—
851C4—266no—
852C4C23×C22⋊D1314yes—
853C4C23×C22⋊D13112yes—
854C2—24no—
855C2—212no—
856C2—46no—
857C2—264no—
858C2—526no—
859C2#41×C22⋊D1314yesdirect product factor
860C2C24×C22⋊D1311yescharacteristic
861C2C22×#41×D1311yescharacteristic
862C2C2×#1171964811yescharacteristic
subgroupG/H
centerC22×C4C23×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC23×C13×#41C2
socleC23×C13C25
hypercenterC23×#41D13
hypocenterC13C2×D4×#41
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C22×#41×D13C2semidirect
2. #41×C22⋊D13C2direct (N × H)
3. C2×#11719539C2semidirect
4. C2×Q8×C22⋊D13C2semidirect
5. C2×#11719522C2semidirect
6. C2×#11719536C2semidirect
7. C2×#11719529C2semidirect
8. C2×#11719511C2semidirect
9. C2×#11719534C2semidirect
10. C2×D4×C22⋊D13C2semidirect
11. C2×#11719537C2semidirect
12. C2×#11719496C2semidirect
13. C2×#11719533C2semidirect
14. C2×#41×Dic13C2semidirect
15. C22×C4×C22⋊D13C2semidirect
16. C23×C13×#41C2semidirect
19. C22×C13×#41C22semidirect
20. C22×C13×#41C22semidirect
21. C22×C13×#41C22semidirect
22. C22×C13×#41C22semidirect
23. C23×Q8×C13C22semidirect
24. C23×D4×C13C22semidirect
25. C24×C4×C13C22semidirect
28. C2×#41×D13C22semidirect
29. C22×#6131C22semidirect
30. C22×Q8×D13C22semidirect
31. C22×#6129C22semidirect
32. C22×D4×D13C22semidirect
33. C22×#6127C22semidirect
34. C23×C4×D13C22semidirect
35. C2×#88207C22semidirect
36. C22×C22⋊Dic13C22semidirect
37. #11719539C22semidirect
38. #11719537C22semidirect
39. #11719536C22semidirect
40. #11719534C22semidirect
41. #11719533C22semidirect
42. #41×Dic13C22semidirect
43. #11719529C22semidirect
44. #11719522C22semidirect
45. Q8×C22⋊D13C22semidirect
46. C2×#88201C22semidirect
47. C2×#88200C22semidirect
48. C2×#88200C22semidirect
49. C2×Q8×Dic13C22semidirect
50. C2×Q8×Dic13C22semidirect
51. C2×#88198C22semidirect
52. #11719511C22semidirect
53. C2×#88194C22semidirect
54. C2×#88193C22semidirect
55. C2×#88193C22semidirect
56. D4×C22⋊D13C22semidirect
57. C2×#88192C22semidirect
58. C2×#88192C22semidirect
59. C2×#88191C22semidirect
60. C2×#88190C22semidirect
61. C2×#88189C22semidirect
62. C2×D4×Dic13C22semidirect
63. C2×D4×Dic13C22semidirect
64. #11719496C22semidirect
65. C2×#88184C22semidirect
66. C2×#88184C22semidirect
67. C2×#88183C22semidirect
70. C2×C4×C22⋊D13C22semidirect
71. C2×C4×C22⋊D13C22semidirect
72. C2×C4×C22⋊D13C22semidirect
73. C2×C4×C22⋊D13C22semidirect
74. C2×C4×C22⋊D13C22semidirect
75. C2×C4×C22⋊D13C22semidirect
76. C2×C4×C22⋊D13C22semidirect
77. C2×C4×C22⋊D13C22semidirect
78. C22×#6103C22semidirect
79. C2×#88180C22semidirect
80. C2×#88178C22semidirect
81. C2×#88178C22semidirect
82. C22×#6101C22semidirect
83. C22×C4×Dic13C22semidirect
90. C2×C13×#41D4semidirect
92. C2×C13×#41C23semidirect
93. C2×C13×#41C23semidirect
94. C2×C13×#41C23semidirect
98. C22×Q8×C13C23semidirect
103. C22×D4×C13C23semidirect
111. C23×C4×C13C23semidirect
125. C2×#6131C23semidirect
127. C2×Q8×D13C23semidirect
129. C2×#6129C23semidirect
131. C2×D4×D13C23semidirect
133. C2×#6127C23semidirect
140. C22×C4×D13C23semidirect
142. #88207C23semidirect
149. C2×C22⋊Dic13C23semidirect
150. #88201C23semidirect
151. #88200C23semidirect
152. #88200C23semidirect
153. Q8×Dic13C23semidirect
154. Q8×Dic13C23semidirect
155. #88198C23semidirect
156. #88194C23semidirect
157. #88193C23semidirect
158. #88193C23semidirect
159. #88192C23semidirect
160. #88192C23semidirect
161. #88191C23semidirect
162. #88190C23semidirect
163. #88189C23semidirect
164. D4×Dic13C23semidirect
165. D4×Dic13C23semidirect
166. #88184C23semidirect
167. #88184C23semidirect
168. #88183C23semidirect
171. C4×C22⋊D13C23semidirect
172. C4×C22⋊D13C23semidirect
173. C4×C22⋊D13C23semidirect
174. C4×C22⋊D13C23semidirect
175. C4×C22⋊D13C23semidirect
176. C4×C22⋊D13C23semidirect
177. C4×C22⋊D13C23semidirect
183. C2×#6103C23semidirect
184. #88180C23semidirect
187. #88178C23semidirect
188. #88178C23semidirect
194. C2×#6101C23semidirect
199. C2×C4×Dic13C23semidirect
217. C13×#41C2×D4semidirect
220. C2×Q8×C13C2×D4semidirect
226. C2×D4×C13C2×D4semidirect
236. C22×C4×C13C2×D4semidirect
253. C2×C22⋊D13#41direct (N × H)
313. C23×#41D13semidirect
340. C23×C13C2×#41semidirect
354. C22×D13C2×#41semidirect
358. Q8×C13C22×D4semidirect
361. D4×C13C22×D4semidirect
371. C2×C4×C13C22×D4semidirect
381. C22⋊D13C2×#41direct (N × H)
390. C2×Dic13C2×#41semidirect
410. C22×#41C2×D13semidirect
411. C22×#41C2×D13semidirect
412. C22×#41C2×D13semidirect
413. C22×#41C2×D13semidirect
415. C23×Q8C2×D13semidirect
418. C23×D4C2×D13semidirect
420. C24×C4C2×D13semidirect
484. C22×C13C22×#41semidirect
495. C2×D13C22×#41semidirect
505. Dic13C22×#41semidirect
519. C2×#41C22⋊D13direct (N × H)
521. C2×#41C22×D13semidirect
522. C2×#41C22×D13semidirect
523. C2×#41C22×D13semidirect
530. C22×Q8C22×D13semidirect
546. C22×D4C22×D13semidirect
563. C23×C4C22×D13semidirect
625. C2×C13D4×#41semidirect
650. #41C2×C22⋊D13direct (N × H)
656. C2×Q8C2×C22⋊D13semidirect
678. C2×D4C2×C22⋊D13semidirect
709. C22×C4C2×C22⋊D13semidirect
742. C13C2×D4×#41semidirect
766. C23#41×D13semidirect
774. Q8C22×C22⋊D13semidirect
784. D4C22×C22⋊D13semidirect
813. C2×C4C22×C22⋊D13semidirect
839. C22C2×#41×D13semidirect
859. C2#41×C22⋊D13direct (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
#41×C22⋊D132
C2×#117195392
C2×Q8×C22⋊D132
C2×#117195222
C2×#117195362
C2×#117195292
C2×#117195112
C2×#117195342
C2×D4×C22⋊D132
C2×#117195372
C2×#117194962
C2×#117195332
C2×#41×Dic132
C22×C4×C22⋊D132
C23×C13×#412
C2×D4×#4113