Finite Group Databasebeta

← #15830440

Subgroups — #15830440

Order 3328.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128868C211yesmaximal, characteristic
2#13123871C211yesmaximal, characteristic, complemented
3#13113411C211yesmaximal, characteristic, complemented
4#13113403C211yesmaximal, characteristic, complemented
5#13113395C211yesmaximal, characteristic, complemented
6#13113390C211yesmaximal, characteristic, complemented
7#13113382C211yesmaximal, characteristic, complemented
8#13113377C211yesmaximal, characteristic, complemented
9#13113372C211yesmaximal, characteristic, complemented
10#13113364C211yesmaximal, characteristic, complemented
11#13113351C211yesmaximal, characteristic, complemented
12#13113338C211yesmaximal, characteristic, complemented
13#13113325C211yesmaximal, characteristic, complemented
14C2×#11718043C211yesmaximal, characteristic, complemented
15C13×#2318C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17D4×C22⋊D13—21no—
18#11719496C2211yescharacteristic
19#11719496C2211yescharacteristic
20C2×#88184C2211yescharacteristic
21C2×#88184C2211yescharacteristic
22#11719270C411yescharacteristic, complemented
23#11719270C411yescharacteristic, complemented
24#11719268C411yescharacteristic, complemented
25#11719267—21no—
26#11719265—21no—
27#11719265—21no—
28#11719258C411yescharacteristic, complemented
29#11719255C411yescharacteristic, complemented
30#11719255C411yescharacteristic, complemented
31D4×D52C411yescharacteristic, complemented
32#11719250—21no—
33#11719248C411yescharacteristic, complemented
34#11719219—21no—
35#11719195—21no—
36#11719195—21no—
37#11719184C2211yescharacteristic
38#11719182C2211yescharacteristic
39C13×#388—21no—
40C13×#387—21no—
41C13×#386—21no—
42C13×#385—21no—
43C13×#383C2211yescharacteristic, complemented
44C13×#382C2211yescharacteristic, complemented
45C13×#381C2211yescharacteristic, complemented
46C13×#380C2211yescharacteristic, complemented
47C4×C13×C22⋊C4C2211yescharacteristic, complemented
48C2×C13×#95C2211yescharacteristic, complemented
49#11718868C2211yescharacteristic, complemented
50#11718868C2211yescharacteristic, complemented
51C2×C22⋊#1055C2211yescharacteristic, complemented
52C2×C22⋊#1055C2211yescharacteristic, complemented
53#11718673—21no—
54#11718672—21no—
55#11718672—21no—
56D4×#1055—21no—
57#11718587C2211yescharacteristic, complemented
58#11718586C2211yescharacteristic, complemented
59#11718044C2211yescharacteristic, complemented
60#11718044C2211yescharacteristic, complemented
61#11718044C2211yescharacteristic, complemented
62#11718044C2211yescharacteristic, complemented
63#11718043C2211yescharacteristic
64#11718043C2211yescharacteristic
65#11718043C2211yescharacteristic
66#11718043C2211yescharacteristic
67#11718043C2211yescharacteristic, complemented
68#11718043C2211yescharacteristic, complemented
69#11718043C2211yescharacteristic, complemented
70#11718043C2211yescharacteristic, complemented
71#11718043C2211yescharacteristic, complemented
72#11718043C2211yescharacteristic, complemented
73#11718043C2211yescharacteristic, complemented
74#11718043C2211yescharacteristic, complemented
75C22×D4×C13D411yescharacteristic
76C23×C4×C13—21no—
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C22×C22⋊D13—21no—
80C22×C22⋊D13—21no—
81C2×D4×D13—21no—
82C2×#6127—21no—
83C2×#6127C2×C411yescharacteristic
84C2×#6127C2×C411yescharacteristic, complemented
85C22×D52C2×C411yescharacteristic
86C22×D52C2×C411yescharacteristic, complemented
87C4×D4×C13C2×C411yescharacteristic
88C4×D4×C13C2×C411yescharacteristic
89C4×D4×C13C2×C411yescharacteristic
90C4×D4×C13C2×C411yescharacteristic
91C4×D4×C13D411yescharacteristic
92C4×D4×C13D411yescharacteristic
93C4×D4×C13D411yescharacteristic
94C4×D4×C13D411yescharacteristic
95C2×C13×C4⋊C4—21no—
96C2×C13×C4⋊C4—21no—
97C2×C13×C4⋊C4D411yescharacteristic
98C2×C13×C22⋊C4—21no—
99C2×C13×C22⋊C4—21no—
100C2×C13×C22⋊C4—21no—
101C2×C13×C22⋊C4D411yescharacteristic
102C2×C13×C22⋊C4D411yescharacteristic
103C2×C42×C13—21no—
104C2×C42×C13C2311yescharacteristic
105#88207—21no—
106#88207—21no—
107#88194—21no—
108#88193—21no—
109#88193—21no—
110#88192—21no—
111#88191—21no—
112#88191—21no—
113D4×Dic13—21no—
114#88184—21no—
115#88184—21no—
116#88184—21no—
117#88184—21no—
118#88184—21no—
119#88184C2×C411yescharacteristic
120#88184C2×C411yescharacteristic
121#88184C2×C411yescharacteristic
122#88184C2×C411yescharacteristic, complemented
123#88184C2×C411yescharacteristic, complemented
124#88184C2×C411yescharacteristic, complemented
125#88184C2311yescharacteristic
126#88184C2311yescharacteristic
127#88184C2311yescharacteristic
128#88183—21no—
129#88183—21no—
130#88183—21no—
131C4×C22⋊D13—21no—
132C4×C22⋊D13—21no—
133C4×C22⋊D13—21no—
134C4×C22⋊D13—21no—
135C4×C22⋊D13—21no—
136C2×#6103—21no—
137C2×#6103—21no—
138#88180C2×C411yescharacteristic
139#88180C2×C411yescharacteristic, complemented
140C2×C4⋊Dic13C2×C411yescharacteristic
141C2×C4⋊Dic13C2×C411yescharacteristic, complemented
142#88178C2×C411yescharacteristic
143#88178C2×C411yescharacteristic, complemented
144#88178C2311yescharacteristic
145C2×#6099—21no—
146C2×#6099—21no—
147C22×#1055—21no—
148C22×#1055—21no—
149#88152—21no—
150#88152—21no—
151#88149—21no—
152#88148—21no—
153#88148—21no—
154#88147—21no—
155#88146—21no—
156#88144—21no—
157#88139—21no—
158#88139—21no—
159#88138—21no—
160#88138—21no—
161#88138—21no—
162#88138—21no—
163#88137—21no—
164#88137—21no—
165#88136—21no—
166#88136—21no—
167#88135—21no—
168#88135—21no—
169C22⋊C4×D13—21no—
170C22⋊C4×D13—21no—
171#88132—21no—
172#88132—21no—
173#88130—21no—
174#88129—21no—
175#88129C2×C411yescharacteristic, complemented
176#88128C2×C411yescharacteristic, complemented
177C4×D52—21no—
178C4×D52C2×C411yescharacteristic, complemented
179C4×D52C2×C411yescharacteristic, complemented
180C4×D52C2×C411yescharacteristic, complemented
181#88126—21no—
182#88124C2×C411yescharacteristic, complemented
183#88123C2×C411yescharacteristic, complemented
184C4×Dic26C2×C411yescharacteristic, complemented
185C13×#95—21no—
186C13×#95—21no—
187C13×#95—21no—
188C13×#95—21no—
189C13×#95—21no—
190C13×#95C2311yescharacteristic
191C13×#95C2311yescharacteristic
192C13×#95C2311yescharacteristic
193C13×#95C2311yescharacteristic
194C22⋊#1055—21no—
195C22⋊#1055—21no—
196C22⋊#1055—21no—
197C22⋊#1055—21no—
198C22⋊#1055C2311yescharacteristic
199C22⋊#1055C2311yescharacteristic
200C22⋊#1055C2311yescharacteristic
201C22⋊#1055C2311yescharacteristic
202C4⋊#1055—21no—
203C4⋊#1055—21no—
204#88043—21no—
205C4×#1055—21no—
206#17597—131nomaximal, Sylow
207C24×C13C2×D411yescharacteristic
208C24×C13C2×D411yescharacteristic
209C23×D13—21no—
210C23×D13—21no—
211C2×D4×C13—42no—
212C2×D4×C13C22⋊C411yescharacteristic
213C2×D4×C13C22⋊C411yescharacteristic
214C2×D4×C13C22⋊C411yescharacteristic
215C2×D4×C13C22⋊C411yescharacteristic
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—42no—
221C22×C4×C13—81no—
222C22×C4×C13—81no—
223C22×C4×C13—81no—
224C22×C4×C13—81no—
225C22×C4×C13C22×C411yescharacteristic
226C22×C4×C13C22×C411yescharacteristic
227C22×C4×C13C22×C411yescharacteristic
228C22×C4×C13C22×C411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2×D411yescharacteristic
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13C2×D411yescharacteristic
235C22×C4×C13C2×D411yescharacteristic
236C22×C4×C13C2×D411yescharacteristic
237C22×C4×C13C2411yescharacteristic
238C2×C22⋊D13—21no—
239C2×C22⋊D13—21no—
240C2×C22⋊D13—21no—
241C2×C22⋊D13—21no—
242C2×C22⋊D13—21no—
243C2×C22⋊D13—21no—
244C2×C22⋊D13—21no—
245C2×C22⋊D13—21no—
246C2×C22⋊D13—21no—
247C2×C22⋊D13—21no—
248C2×C22⋊D13—21no—
249C2×C22⋊D13—81no—
250C2×C22⋊D13—81no—
251C2×C22⋊D13—81no—
252C2×C22⋊D13—81no—
253C22×Dic13—21no—
254C22×Dic13—21no—
255D4×D13—44no—
256#6127—81no—
257#6127—81no—
258#6127—81no—
259#6127—81no—
260C2×D52—21no—
261C2×D52—21no—
262C2×D52—21no—
263C2×D52—21no—
264C2×D52—81no—
265C2×D52—81no—
266C2×D52C22×C411yescharacteristic
267C2×D52C22×C411yescharacteristic
268C2×D52C22×C411yescharacteristic
269C2×C4×D13—21no—
270C2×C4×D13—21no—
271C2×C4×D13—21no—
272C2×C4×D13—21no—
273C2×C4×D13—21no—
274C2×Dic26—21no—
275C2×Dic26C22×C411yescharacteristic
276C13×C4⋊C4—81no—
277C13×C4⋊C4—81no—
278C13×C4⋊C4C22⋊C411yescharacteristic
279C13×C4⋊C4C22⋊C411yescharacteristic
280C13×C4⋊C4C22⋊C411yescharacteristic
281C13×C4⋊C4C22⋊C411yescharacteristic
282C13×C22⋊C4—42no—
283C13×C22⋊C4—81no—
284C13×C22⋊C4—81no—
285C13×C22⋊C4C22⋊C411yescharacteristic
286C13×C22⋊C4C22⋊C411yescharacteristic
287C13×C22⋊C4C22⋊C411yescharacteristic
288C13×C22⋊C4C22⋊C411yescharacteristic
289C13×C22⋊C4C22⋊C411yescharacteristic
290C13×C22⋊C4C22⋊C411yescharacteristic
291C13×C22⋊C4C22⋊C411yescharacteristic
292C13×C22⋊C4C22⋊C411yescharacteristic
293C42×C13—81no—
294C42×C13C22×C411yescharacteristic
295C42×C13C22×C411yescharacteristic
296C42×C13C2×D411yescharacteristic
297C42×C13C2×D411yescharacteristic
298C22⋊Dic13—21no—
299C22⋊Dic13—21no—
300C22⋊Dic13—21no—
301C22⋊Dic13—21no—
302C22⋊Dic13—21no—
303#6103—21no—
304#6103—21no—
305#6103—21no—
306#6103—21no—
307#6103—21no—
308#6103—21no—
309#6103—21no—
310#6103—21no—
311#6103—21no—
312#6103—21no—
313#6103—21no—
314#6103—21no—
315#6103—21no—
316#6103—21no—
317C4⋊Dic13—21no—
318C4⋊Dic13—21no—
319C4⋊Dic13—21no—
320C4⋊Dic13C22×C411yescharacteristic
321C4⋊Dic13C22×C411yescharacteristic
322C4⋊Dic13C22×C411yescharacteristic
323C4⋊Dic13C22×C411yescharacteristic
324#6101—21no—
325#6101—21no—
326#6101—21no—
327#6101—21no—
328#6101—21no—
329#6101—21no—
330C4×Dic13—21no—
331C4×Dic13—21no—
332C4×Dic13—21no—
333#6099—81no—
334#6099—81no—
335C2×#1055—21no—
336C2×#1055—21no—
337C2×#1055—21no—
338C2×#1055—21no—
339C2×#1055—81no—
340C2×#1055—81no—
341#3519—131no—
342#2974—131no—
343#2318D1311yescharacteristic, complemented
344#1521—131no—
345#1519—131no—
346#1517—131no—
347#1516—131no—
348#1514—131no—
349#1513—131no—
350#1512—131no—
351#1510—131no—
352#1507—131no—
353#1504—131no—
354#1501—131no—
355C2×#327—131no—
356C23×C13—21no—
357C23×C13—21no—
358C23×C13—22no—
359C23×C13—21no—
360C23×C13—21no—
361C23×C13—41no—
362C23×C13—41no—
363C23×C13—41no—
364C23×C13C2×C22⋊C411yescharacteristic
365C23×C13C2×C22⋊C411yescharacteristic
366C23×C13C2×C22⋊C411yescharacteristic
367C23×C13C2×C22⋊C411yescharacteristic
368C23×C13C22×D411yescharacteristic
369C22×D13—21no—
370C22×D13—21no—
371C22×D13—21no—
372C22×D13—42no—
373C22×D13—42no—
374C22×D13—81no—
375C22×D13—81no—
376C22×D13—81no—
377C22×D13—81no—
378D4×C13—22no—
379D4×C13—22no—
380D4×C13—41no—
381D4×C13—41no—
382C2×C4×C13—21no—
383C2×C4×C13—21no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—84no—
409C2×C4×C13C2×C22⋊C411yescharacteristic
410C2×C4×C13C2×C22⋊C411yescharacteristic
411C2×C4×C13C2×C22⋊C411yescharacteristic
412C2×C4×C13C2×C22⋊C411yescharacteristic
413C2×C4×C13C2×C22⋊C411yescharacteristic
414C2×C4×C13C2×C22⋊C411yescharacteristic
415C2×C4×C13C2×C22⋊C411yescharacteristic
416C2×C4×C13C2×C22⋊C411yescharacteristic
417C2×C4×C13C23×C411yescharacteristic
418C2×C4×C13C22×D411yescharacteristic
419C22⋊D13—42no—
420C22⋊D13—41no—
421C22⋊D13—41no—
422C22⋊D13—41no—
423C22⋊D13—41no—
424C22⋊D13—41no—
425C22⋊D13—41no—
426C22⋊D13—42no—
427C22⋊D13—81no—
428C22⋊D13—81no—
429C22⋊D13—81no—
430C22⋊D13—81no—
431C22⋊D13—81no—
432C22⋊D13—81no—
433C2×Dic13—21no—
434C2×Dic13—21no—
435C2×Dic13—21no—
436C2×Dic13—21no—
437C2×Dic13—21no—
438C2×Dic13—81no—
439C2×Dic13—81no—
440D52—42no—
441D52—41no—
442D52—41no—
443D52—41no—
444D52—81no—
445D52—81no—
446D52—81no—
447C4×D13—42no—
448C4×D13—81no—
449C4×D13—81no—
450C4×D13—81no—
451C4×D13—81no—
452Dic26—41no—
453Dic26—81no—
454#1055—41no—
455#1055—41no—
456#1055—41no—
457#1055—41no—
458#555—131no—
459#554—131no—
460#553—131no—
461#553—131no—
462#553—261no—
463#550—131no—
464#546—131no—
465#546—131no—
466#546—261no—
467#546—261no—
468D42—131no—
469D42—261no—
470#540—261no—
471#538—261no—
472#538—261no—
473#532—131no—
474#529—131no—
475#525—131no—
476#525—131no—
477C2×#121—131no—
478C2×#121—131no—
479#518—261no—
480C2×C4×D4C2×D1311yescharacteristic
481#436—261no—
482#435—261no—
483#435—261no—
484C8×D4—261no—
485#432—131no—
486#431—131no—
487#407—131no—
488#407—131no—
489C2×C22⋊C8—131no—
490C2×C22⋊C8—131no—
491#388—21no—
492#387—21no—
493#386—21no—
494#385—21no—
495#383C2×D1311yescharacteristic, complemented
496#382C2×D1311yescharacteristic, complemented
497#381C2×D1311yescharacteristic, complemented
498#380C2×D1311yescharacteristic, complemented
499C4×C22⋊C4C2×D1311yescharacteristic, complemented
500C2×#95C2×D1311yescharacteristic, complemented
501#328—131no—
502#328—131no—
503#328—131no—
504#328—131no—
505#327—131no—
506#327—131no—
507#327—131no—
508#327—131no—
509#327—131no—
510#327—131no—
511#327—131no—
512#327—131no—
513#327—131no—
514#327—131no—
515#327—131no—
516#327—131no—
517C22×C13—21no—
518C22×C13—21no—
519C22×C13—21no—
520C22×C13—21no—
521C22×C13—21no—
522C22×C13—21no—
523C22×C13—21no—
524C22×C13—21no—
525C22×C13—21no—
526C22×C13—21no—
527C22×C13—21no—
528C22×C13—21no—
529C22×C13—21no—
530C22×C13—42no—
531C22×C13—42no—
532C22×C13—81no—
533C22×C13—81no—
534C22×C13#42112yes—
535C22×C13C22×C22⋊C411yescharacteristic
536C22×C13#57611yescharacteristic
537C22×C13#57711yescharacteristic
538C2×D13—41no—
539C2×D13—41no—
540C2×D13—41no—
541C2×D13—41no—
542C2×D13—41no—
543C2×D13—41no—
544C2×D13—41no—
545C2×D13—41no—
546C2×D13—41no—
547C2×D13—162no—
548C2×D13—162no—
549C4×C13—21no—
550C4×C13—21no—
551C4×C13—21no—
552C4×C13—21no—
553C4×C13—21no—
554C4×C13—21no—
555C4×C13—21no—
556C4×C13—21no—
557C4×C13—21no—
558C4×C13—21no—
559C4×C13—81no—
560C4×C13—81no—
561C4×C13—81no—
562C4×C13—81no—
563Dic13—41no—
564Dic13—41no—
565Dic13—41no—
566Dic13—41no—
567Dic13—41no—
568C2×#41—131no—
569C2×#41—131no—
570C2×#41—261no—
571C22×D4—131no—
572C22×D4—131no—
573C22×D4—261no—
574C22×D4—261no—
575C22×D4—261no—
576C22×D4C22⋊D1311yescharacteristic
577C23×C4—21no—
578C23×C4C22×D1311yescharacteristic
579C23×C4C22×D1311yescharacteristic
580C2×M16—261no—
581C2×M16—261no—
582C22×C8—261no—
583C22×C8—261no—
584C4⋊Q8—131no—
585#127—131no—
586#127—261no—
587#126—261no—
588#126—261no—
589#126—261no—
590#125—131no—
591#125—261no—
592#124—131no—
593#124—261no—
594#124—261no—
595#124—261no—
596#123—261no—
597#123—261no—
598#123—261no—
599#123—261no—
600#123—261no—
601#123—261no—
602#123—261no—
603C22⋊Q8—131no—
604C22⋊Q8—131no—
605C22⋊Q8—131no—
606C22⋊Q8—261no—
607C22⋊Q8—261no—
608#121—131no—
609#121—131no—
610#121—131no—
611#121—131no—
612#121—131no—
613#121—131no—
614#121—131no—
615#121—131no—
616#121—131no—
617#121—261no—
618#121—261no—
619#121—261no—
620#121—261no—
621#121—261no—
622#121—261no—
623#121—261no—
624#121—261no—
625#121—261no—
626#121—261no—
627#121—261no—
628#121—261no—
629#121—261no—
630#120—261no—
631#120—261no—
632#120—261no—
633#120—261no—
634#120—261no—
635#120—261no—
636C4×Q8—131no—
637C4×D4—131no—
638C4×D4—131no—
639C4×D4—131no—
640C4×D4—261no—
641C4×D4—261no—
642C4×D4—261no—
643C4×D4—261no—
644C4×D4—261no—
645C4×D4—261no—
646C4×D4—261no—
647C4×D4—261no—
648C4×D4—261no—
649C4×D4—261no—
650C4×D4C4×D1311yescharacteristic
651C4×D4C4×D1311yescharacteristic
652C4×D4C4×D1311yescharacteristic
653C4×D4C4×D1311yescharacteristic
654C4×D4D5211yescharacteristic
655C4×D4D5211yescharacteristic
656C4×D4D5211yescharacteristic
657C4×D4D5211yescharacteristic
658#117—131no—
659#117—131no—
660#117—261no—
661#117—261no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—131no—
665C2×C4⋊C4—131no—
666C2×C4⋊C4C22⋊D1311yescharacteristic
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—261no—
671C2×C22⋊C4—261no—
672C2×C22⋊C4—261no—
673C2×C22⋊C4—261no—
674C2×C22⋊C4C22⋊D1311yescharacteristic
675C2×C22⋊C4C22⋊D1311yescharacteristic
676C2×C42—21no—
677C2×C42C22×D1311yescharacteristic
678C4⋊C8—261no—
679C4⋊C8—261no—
680C22⋊C8—131no—
681C22⋊C8—131no—
682C22⋊C8—131no—
683C22⋊C8—131no—
684C22⋊C8—261no—
685C22⋊C8—261no—
686C22⋊C8—261no—
687C22⋊C8—261no—
688#97—261no—
689C4×C8—261no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95C22×D1311yescharacteristic
696#95C22×D1311yescharacteristic
697#95C22×D1311yescharacteristic
698#95C22×D1311yescharacteristic
699C2×C13—21no—
700C2×C13—21no—
701C2×C13—22no—
702C2×C13—41no—
703C2×C13—41no—
704C2×C13—41no—
705C2×C13#288311yescharacteristic
706C2×C13#289711yescharacteristic
707C2×C13C2×#42111yescharacteristic
708D13—81no—
709D13—81no—
710D13—81no—
711C24—261no—
712C24—261no—
713C24C2×C22⋊D1311yescharacteristic
714C24C2×C22⋊D1311yescharacteristic
715#41—1041no—
716#41—1041no—
717#41—1041no—
718#41—1041no—
719C2×Q8—131no—
720C2×Q8—261no—
721C2×D4—42no—
722C2×D4—131no—
723C2×D4—131no—
724C2×D4—131no—
725C2×D4—261no—
726C2×D4—261no—
727C2×D4—261no—
728C2×D4—261no—
729C2×D4—261no—
730C2×D4—261no—
731C2×D4—261no—
732C2×D4—261no—
733C2×D4—261no—
734C2×D4—261no—
735C2×D4—261no—
736C2×D4—261no—
737C2×D4—261no—
738C2×D4—261no—
739C2×D4—261no—
740C2×D4—524no—
741C2×D4—1041no—
742C2×D4—1041no—
743C2×D4—1041no—
744C2×D4—1041no—
745C2×D4—1041no—
746C2×D4—1041no—
747C2×D4#610311yescharacteristic
748C2×D4#610311yescharacteristic
749C2×D4#610311yescharacteristic
750C2×D4#610311yescharacteristic
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—81no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4—81no—
760C22×C4—261no—
761C22×C4—261no—
762C22×C4—261no—
763C22×C4—261no—
764C22×C4—261no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4C2×C4×D1311yescharacteristic
768C22×C4C2×C4×D1311yescharacteristic
769C22×C4C2×C4×D1311yescharacteristic
770C22×C4C2×C4×D1311yescharacteristic
771C22×C4C2×D5211yescharacteristic
772C22×C4C2×D5211yescharacteristic
773C22×C4C2×D5211yescharacteristic
774C22×C4C2×D5211yescharacteristic
775C22×C4C2×C22⋊D1311yescharacteristic
776C22×C4C2×C22⋊D1311yescharacteristic
777C22×C4C2×C22⋊D1311yescharacteristic
778C22×C4C2×C22⋊D1311yescharacteristic
779C22×C4C23×D1311yescharacteristic
780M16—1041no—
781M16—1041no—
782C2×C8—261no—
783C2×C8—261no—
784C2×C8—261no—
785C2×C8—261no—
786C2×C8—1041no—
787C2×C8—1041no—
788C4⋊C4—81no—
789C4⋊C4—81no—
790C4⋊C4—131no—
791C4⋊C4—131no—
792C4⋊C4—131no—
793C4⋊C4—131no—
794C4⋊C4—261no—
795C4⋊C4—261no—
796C4⋊C4—261no—
797C4⋊C4—261no—
798C4⋊C4—261no—
799C4⋊C4—261no—
800C4⋊C4—261no—
801C4⋊C4—261no—
802C4⋊C4—261no—
803C4⋊C4#610311yescharacteristic
804C4⋊C4#610311yescharacteristic
805C4⋊C4#610311yescharacteristic
806C4⋊C4#610311yescharacteristic
807C22⋊C4—42no—
808C22⋊C4—81no—
809C22⋊C4—81no—
810C22⋊C4—261no—
811C22⋊C4—261no—
812C22⋊C4—261no—
813C22⋊C4—261no—
814C22⋊C4—261no—
815C22⋊C4—261no—
816C22⋊C4—261no—
817C22⋊C4—261no—
818C22⋊C4—261no—
819C22⋊C4—261no—
820C22⋊C4—261no—
821C22⋊C4—261no—
822C22⋊C4—261no—
823C22⋊C4—261no—
824C22⋊C4—261no—
825C22⋊C4—261no—
826C22⋊C4—261no—
827C22⋊C4—261no—
828C22⋊C4—261no—
829C22⋊C4#610311yescharacteristic
830C22⋊C4#610311yescharacteristic
831C22⋊C4#610311yescharacteristic
832C22⋊C4#610311yescharacteristic
833C22⋊C4#610311yescharacteristic
834C22⋊C4#610311yescharacteristic
835C22⋊C4#610311yescharacteristic
836C22⋊C4#610311yescharacteristic
837C42—81no—
838C42—261no—
839C42—261no—
840C42—261no—
841C42C2×C4×D1311yescharacteristic
842C42C2×C4×D1311yescharacteristic
843C42C2×D5211yescharacteristic
844C42C2×D5211yescharacteristic
845C13#1759711yescharacteristic, complemented, Sylow
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—261no—
855C23—261no—
856C23—261no—
857C23—522no—
858C23—522no—
859C23—1041no—
860C23—1041no—
861C23—1041no—
862C23—1041no—
863C23C2×#610311yescharacteristic
864C23C2×#610311yescharacteristic
865C23C2×#610311yescharacteristic
866C23C2×#610311yescharacteristic
867C23C22×C22⋊D1311yescharacteristic
868Q8—521no—
869Q8—1041no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—521no—
875D4—521no—
876D4—521no—
877D4—522no—
878D4—522no—
879D4—522no—
880D4—521no—
881D4—521no—
882D4—521no—
883D4—521no—
884D4—521no—
885D4—521no—
886D4—1041no—
887D4—1041no—
888D4—1041no—
889D4—1041no—
890D4—1041no—
891D4—1041no—
892D4—1041no—
893D4—1041no—
894D4—1041no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—84no—
922C2×C4—261no—
923C2×C4—261no—
924C2×C4—261no—
925C2×C4—261no—
926C2×C4—261no—
927C2×C4—522no—
928C2×C4—1041no—
929C2×C4—1041no—
930C2×C4—1041no—
931C2×C4—1041no—
932C2×C4—1041no—
933C2×C4—1041no—
934C2×C4C2×#610311yescharacteristic
935C2×C4C2×#610311yescharacteristic
936C2×C4C2×#610311yescharacteristic
937C2×C4C2×#610311yescharacteristic
938C2×C4C2×#610311yescharacteristic
939C2×C4C2×#610311yescharacteristic
940C2×C4C2×#610311yescharacteristic
941C2×C4C2×#610311yescharacteristic
942C2×C4C22×C4×D1311yescharacteristic
943C2×C4C22×D5211yescharacteristic
944C8—521no—
945C8—521no—
946C8—521no—
947C8—521no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—81no—
964C22—81no—
965C22—521no—
966C22—521no—
967C22—521no—
968C22—521no—
969C22—521no—
970C22—521no—
971C22—521no—
972C22—521no—
973C22—521no—
974C22—2082no—
975C22—2082no—
976C22#1171866612yes—
977C22C22×#610311yescharacteristic
978C22#1171954011yescharacteristic
979C22#1171954211yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—81no—
991C4—81no—
992C4—81no—
993C4—81no—
994C4—521no—
995C4—521no—
996C4—521no—
997C4—521no—
998C4—521no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—1041no—
1006C2—1041no—
1007C2—1041no—
1008C2#1312329611yescharacteristic
1009C2#1312335911yescharacteristic
1010C2C2×#1171866611yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2318C2
socleC22×C13C22×C22⋊C4
prime radical#13128868C2
cosocleC22×C4×C13C24
hypercenter#2318D13
hypocenterC13#17597
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #13123871C2semidirect
3. #13113411C2semidirect
4. #13113403C2semidirect
5. #13113395C2semidirect
6. #13113390C2semidirect
7. #13113382C2semidirect
8. #13113377C2semidirect
9. #13113372C2semidirect
10. #13113364C2semidirect
11. #13113351C2semidirect
12. #13113338C2semidirect
13. #13113325C2semidirect
14. C2×#11718043C2semidirect
15. C13×#2318C2semidirect
22. #11719270C4semidirect
23. #11719270C4semidirect
24. #11719268C4semidirect
28. #11719258C4semidirect
29. #11719255C4semidirect
30. #11719255C4semidirect
31. D4×D52C4semidirect
33. #11719248C4semidirect
43. C13×#383C22semidirect
44. C13×#382C22semidirect
45. C13×#381C22semidirect
46. C13×#380C22semidirect
47. C4×C13×C22⋊C4C22semidirect
48. C2×C13×#95C22semidirect
49. #11718868C22semidirect
50. #11718868C22semidirect
51. C2×C22⋊#1055C22semidirect
52. C2×C22⋊#1055C22semidirect
57. #11718587C22semidirect
58. #11718586C22semidirect
59. #11718044C22semidirect
60. #11718044C22semidirect
61. #11718044C22semidirect
62. #11718044C22semidirect
67. #11718043C22semidirect
68. #11718043C22semidirect
69. #11718043C22semidirect
70. #11718043C22semidirect
71. #11718043C22semidirect
72. #11718043C22semidirect
73. #11718043C22semidirect
74. #11718043C22semidirect
84. C2×#6127C2×C4semidirect
86. C22×D52C2×C4semidirect
122. #88184C2×C4semidirect
123. #88184C2×C4semidirect
124. #88184C2×C4semidirect
139. #88180C2×C4semidirect
141. C2×C4⋊Dic13C2×C4semidirect
143. #88178C2×C4semidirect
175. #88129C2×C4semidirect
176. #88128C2×C4semidirect
178. C4×D52C2×C4semidirect
179. C4×D52C2×C4semidirect
180. C4×D52C2×C4semidirect
182. #88124C2×C4semidirect
183. #88123C2×C4semidirect
184. C4×Dic26C2×C4semidirect
343. #2318D13semidirect
495. #383C2×D13semidirect
496. #382C2×D13semidirect
497. #381C2×D13semidirect
498. #380C2×D13semidirect
499. C4×C22⋊C4C2×D13semidirect
500. C2×#95C2×D13semidirect
845. C13#17597semidirect

Maximal subgroups

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

subgroupindex
#131288682
#131238712
#131134112
#131134032
#131133952
#131133902
#131133822
#131133772
#131133722
#131133642
#131133512
#131133382
#131133252
C2×#117180432
C13×#23182
#1759713