Finite Group Databasebeta

← #15829932

Subgroups — #15829932

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128446C211yesmaximal, characteristic
2#13123961C211yesmaximal, characteristic, complemented
3#13113306C211yesmaximal, characteristic, complemented
4#13113302C211yesmaximal, characteristic, complemented
5#13113297C211yesmaximal, characteristic, complemented
6#13113280C211yesmaximal, characteristic, complemented
7#13113271C211yesmaximal, characteristic, complemented
8#13113262C211yesmaximal, characteristic, complemented
9#13113250C211yesmaximal, characteristic, complemented
10#13113245C211yesmaximal, characteristic, complemented
11#13113236C211yesmaximal, characteristic, complemented
12#13113228C211yesmaximal, characteristic, complemented
13#13113224C211yesmaximal, characteristic, complemented
14C2×#11718051C211yesmaximal, characteristic, complemented
15C13×#2922C211yesmaximal, characteristic, complemented
16C4×C13×#41C2211yescharacteristic
17#11719534—21no—
18#11719290C411yescharacteristic
19#11719285—21no—
20#11719284C411yescharacteristic
21#11719270C411yescharacteristic
22#11719270C411yescharacteristic
23#11719255C411yescharacteristic
24#11719255C411yescharacteristic
25D4×D52C411yescharacteristic
26#11719252—21no—
27#11719252—21no—
28C4×D4×D13—21no—
29#11719248C411yescharacteristic
30#11719235—21no—
31#11719232—21no—
32#11719232—21no—
33#11719184C2211yescharacteristic
34#11719184C2211yescharacteristic
35#11719182C2211yescharacteristic
36C4×#6127C2211yescharacteristic
37C2×C4×D52C2211yescharacteristic
38C2×C4×D52C2211yescharacteristic
39C13×#433—21no—
40C13×#433—21no—
41C13×#431C2211yescharacteristic, complemented
42C13×#431C2211yescharacteristic, complemented
43C13×#431C2211yescharacteristic, complemented
44C13×#431C2211yescharacteristic, complemented
45C13×#424—21no—
46C13×#408—21no—
47C4×C13×M16C2211yescharacteristic, complemented
48C2×C4×C8×C13C2211yescharacteristic, complemented
49#11718685—21no—
50#11718672—21no—
51#11718672—21no—
52D4×#1055—21no—
53#11718587C2211yescharacteristic, complemented
54#11718587C2211yescharacteristic, complemented
55#11718586C2211yescharacteristic, complemented
56#11718585C2211yescharacteristic, complemented
57C2×C4⋊#1055C2211yescharacteristic, complemented
58C2×C4⋊#1055C2211yescharacteristic, complemented
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718051C2211yescharacteristic
63#11718051C2211yescharacteristic, complemented
64#11718051C2211yescharacteristic, complemented
65#11718051C2211yescharacteristic, complemented
66#11718051C2211yescharacteristic, complemented
67#11718051C2211yescharacteristic, complemented
68#11718051C2211yescharacteristic, complemented
69#11718051C2211yescharacteristic, complemented
70#11718051C2211yescharacteristic, complemented
71#11718048C2211yescharacteristic, complemented
72#11718048C2211yescharacteristic, complemented
73#11718048C2211yescharacteristic, complemented
74#11718048C2211yescharacteristic, complemented
75C2×C13×#41D411yescharacteristic
76C2×D4×D13—21no—
77C2×#6127—21no—
78C2×#6127C2×C411yescharacteristic
79C22×D52C2×C411yescharacteristic
80C22×D52C2×C411yescharacteristic
81C22×C4×D13—21no—
82C22×C4×D13—21no—
83C2×C13×M16—21no—
84C22×C8×C13—21no—
85C4×Q8×C13C2×C411yescharacteristic
86C4×Q8×C13D411yescharacteristic
87C4×D4×C13C2×C411yescharacteristic
88C4×D4×C13C2×C411yescharacteristic
89C4×D4×C13C2×C411yescharacteristic
90C4×D4×C13D411yescharacteristic
91C4×D4×C13D411yescharacteristic
92C4×D4×C13D411yescharacteristic
93C13×#117D411yescharacteristic
94C13×#117D411yescharacteristic
95C13×#117D411yescharacteristic
96C2×C42×C13C2311yescharacteristic
97C2×C42×C13C2311yescharacteristic
98C2×C42×C13C2311yescharacteristic
99#88201—21no—
100#88200—21no—
101#88193—21no—
102#88193—21no—
103#88191—21no—
104#88191—21no—
105D4×Dic13—21no—
106#88184—21no—
107#88184C2×C411yescharacteristic
108#88184C2×C411yescharacteristic
109#88184C2×C411yescharacteristic
110#88184C2×C411yescharacteristic
111#88183—21no—
112#88183—21no—
113C4×C22⋊D13—21no—
114C4×C22⋊D13—21no—
115C4×C22⋊D13—21no—
116C4×C22⋊D13—21no—
117C2×#6103—21no—
118C2×#6103—21no—
119#88180C2×C411yescharacteristic
120C2×C4⋊Dic13C2×C411yescharacteristic
121C2×C4⋊Dic13C2×C411yescharacteristic
122#88178C2×C411yescharacteristic
123#88178C2×C411yescharacteristic
124C2×#6099—21no—
125C22×#1055—21no—
126C22×#1055—21no—
127#88152—21no—
128#88152—21no—
129#88150—21no—
130#88150—21no—
131#88149—21no—
132#88148—21no—
133#88148—21no—
134#88148—21no—
135#88148—21no—
136#88147—21no—
137C4⋊C4×D13—21no—
138#88144—21no—
139#88138—21no—
140#88138—21no—
141#88137—21no—
142#88137—21no—
143#88136—21no—
144#88136—21no—
145#88135—21no—
146#88135—21no—
147C22⋊C4×D13—21no—
148C22⋊C4×D13—21no—
149#88132—21no—
150#88132—21no—
151#88130—21no—
152#88130—21no—
153#88129—21no—
154#88129C2×C411yescharacteristic
155#88129C2×C411yescharacteristic
156#88128C2×C411yescharacteristic
157C4×D52—21no—
158C4×D52—21no—
159C4×D52—21no—
160C4×D52—21no—
161C4×D52—21no—
162C4×D52C2×C411yescharacteristic
163C4×D52C2×C411yescharacteristic
164C4×D52C2×C411yescharacteristic
165C4×D52C2×C411yescharacteristic
166C4×D52C2×C411yescharacteristic
167C4×D52C2311yescharacteristic
168C4×D52C2311yescharacteristic
169C4×D52C2311yescharacteristic
170#88126—21no—
171#88126—21no—
172#88126—21no—
173C42×D13—21no—
174#88124C2×C411yescharacteristic
175#88124C2×C411yescharacteristic
176#88123C2×C411yescharacteristic
177C4×Dic26C2×C411yescharacteristic
178C4×Dic26C2311yescharacteristic
179C13×C4⋊C8—21no—
180C13×C4⋊C8—21no—
181C13×C4⋊C8—21no—
182C13×C4⋊C8—21no—
183C13×C22⋊C8—21no—
184C13×C22⋊C8—21no—
185C13×C22⋊C8—21no—
186C13×C22⋊C8—21no—
187C13×#97—21no—
188C4×C8×C13—21no—
189C4×C8×C13C2311yescharacteristic
190C4×C8×C13C2311yescharacteristic
191C4×C8×C13C2311yescharacteristic
192C4×C8×C13C2311yescharacteristic
193C22⋊#1055—21no—
194C22⋊#1055—21no—
195C22⋊#1055—21no—
196C4⋊#1055—21no—
197C4⋊#1055—21no—
198C4⋊#1055—21no—
199C4⋊#1055C2311yescharacteristic
200C4⋊#1055C2311yescharacteristic
201C4⋊#1055C2311yescharacteristic
202C4⋊#1055C2311yescharacteristic
203#88043—21no—
204#88043—21no—
205C4×#1055—21no—
206#17521—131nomaximal, Sylow
207C23×D13—21no—
208C23×D13—21no—
209C13×#41—42no—
210C2×Q8×C13C22⋊C411yescharacteristic
211C2×D4×C13C22⋊C411yescharacteristic
212C2×D4×C13C22⋊C411yescharacteristic
213C2×D4×C13C22⋊C411yescharacteristic
214C22×C4×C13C22×C411yescharacteristic
215C22×C4×C13C22×C411yescharacteristic
216C22×C4×C13C22×C411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D411yescharacteristic
219C22×C4×C13C2×D411yescharacteristic
220C22×C4×C13C2×D411yescharacteristic
221C22×C4×C13C2×D411yescharacteristic
222C22×C4×C13C2×D411yescharacteristic
223C2×C22⋊D13—21no—
224C2×C22⋊D13—21no—
225C2×C22⋊D13—21no—
226C2×C22⋊D13—21no—
227C2×C22⋊D13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230D4×D13—44no—
231#6127—22no—
232#6127—41no—
233#6127—81no—
234#6127—81no—
235C2×D52—22no—
236C2×D52—22no—
237C2×D52—21no—
238C2×D52—21no—
239C2×D52—21no—
240C2×D52—21no—
241C2×D52—41no—
242C2×D52—41no—
243C2×D52C22×C411yescharacteristic
244C2×D52C22×C411yescharacteristic
245C2×D52C22×C411yescharacteristic
246C2×C4×D13—21no—
247C2×C4×D13—21no—
248C2×C4×D13—21no—
249C2×C4×D13—21no—
250C2×C4×D13—21no—
251C2×C4×D13—21no—
252C2×C4×D13—21no—
253C2×C4×D13—21no—
254C2×C4×D13—21no—
255C2×C4×D13—81no—
256C2×C4×D13—81no—
257C2×C4×D13—81no—
258C2×C4×D13—81no—
259C2×Dic26—21no—
260C2×Dic26C22×C411yescharacteristic
261C13×M16—42no—
262C2×C8×C13—21no—
263C2×C8×C13—21no—
264C2×C8×C13—21no—
265C2×C8×C13—21no—
266C2×C8×C13—42no—
267C13×C4⋊C4C22⋊C411yescharacteristic
268C13×C4⋊C4C22⋊C411yescharacteristic
269C13×C4⋊C4C22⋊C411yescharacteristic
270C13×C4⋊C4C22⋊C411yescharacteristic
271C13×C4⋊C4C22⋊C411yescharacteristic
272C13×C4⋊C4C22⋊C411yescharacteristic
273C13×C22⋊C4C22⋊C411yescharacteristic
274C13×C22⋊C4C22⋊C411yescharacteristic
275C13×C22⋊C4C22⋊C411yescharacteristic
276C13×C22⋊C4C22⋊C411yescharacteristic
277C13×C22⋊C4C22⋊C411yescharacteristic
278C13×C22⋊C4C22⋊C411yescharacteristic
279C42×C13C22×C411yescharacteristic
280C42×C13C22×C411yescharacteristic
281C42×C13C22×C411yescharacteristic
282C42×C13C2×D411yescharacteristic
283C42×C13C2×D411yescharacteristic
284C42×C13C2×D411yescharacteristic
285C42×C13C2×D411yescharacteristic
286C42×C13C2×D411yescharacteristic
287C42×C13C2×D411yescharacteristic
288C42×C13C2411yescharacteristic
289C22⋊Dic13—21no—
290C22⋊Dic13—21no—
291C22⋊Dic13—21no—
292#6103—21no—
293#6103—21no—
294#6103—21no—
295#6103—21no—
296#6103—21no—
297#6103—21no—
298#6103—21no—
299#6103—21no—
300#6103—21no—
301#6103—21no—
302#6103—21no—
303#6103—21no—
304#6103—21no—
305#6103—21no—
306#6103—21no—
307#6103—21no—
308C4⋊Dic13—21no—
309C4⋊Dic13—21no—
310C4⋊Dic13—21no—
311C4⋊Dic13C22×C411yescharacteristic
312C4⋊Dic13C22×C411yescharacteristic
313C4⋊Dic13C22×C411yescharacteristic
314C4⋊Dic13C22×C411yescharacteristic
315#6101—21no—
316#6101—21no—
317#6101—21no—
318#6101—21no—
319#6101—21no—
320#6101—21no—
321#6101—21no—
322#6101—21no—
323C4×Dic13—21no—
324C4×Dic13—21no—
325C4×Dic13—21no—
326#6099—81no—
327C2×#1055—21no—
328C2×#1055—21no—
329C2×#1055—21no—
330C2×#1055—21no—
331C2×#1055—81no—
332C2×#1055—81no—
333#3481—131no—
334#2990—131no—
335#2922D1311yescharacteristic, complemented
336#1496—131no—
337#1495—131no—
338#1494—131no—
339#1490—131no—
340#1488—131no—
341#1486—131no—
342#1483—131no—
343#1482—131no—
344#1480—131no—
345#1478—131no—
346#1477—131no—
347C2×D4⋊C8—131no—
348C23×C13C2×C22⋊C411yescharacteristic
349C23×C13C2×C22⋊C411yescharacteristic
350C23×C13C2×C22⋊C411yescharacteristic
351C22×D13—21no—
352C22×D13—21no—
353C22×D13—21no—
354C22×D13—42no—
355C22×D13—42no—
356C22×D13—42no—
357C22×D13—42no—
358C22×D13—81no—
359C22×D13—81no—
360Q8×C13—41no—
361D4×C13—22no—
362D4×C13—22no—
363D4×C13—41no—
364C2×C4×C13—22no—
365C2×C4×C13—21no—
366C2×C4×C13—21no—
367C2×C4×C13—21no—
368C2×C4×C13—21no—
369C2×C4×C13—21no—
370C2×C4×C13—21no—
371C2×C4×C13—21no—
372C2×C4×C13—21no—
373C2×C4×C13—21no—
374C2×C4×C13—21no—
375C2×C4×C13—21no—
376C2×C4×C13—21no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13C2×C22⋊C411yescharacteristic
380C2×C4×C13C2×C22⋊C411yescharacteristic
381C2×C4×C13C2×C22⋊C411yescharacteristic
382C2×C4×C13C2×C22⋊C411yescharacteristic
383C2×C4×C13C2×C22⋊C411yescharacteristic
384C2×C4×C13C2×C22⋊C411yescharacteristic
385C2×C4×C13C2×C22⋊C411yescharacteristic
386C2×C4×C13C2×C22⋊C411yescharacteristic
387C2×C4×C13C2×C22⋊C411yescharacteristic
388C2×C4×C13C23×C411yescharacteristic
389C2×C4×C13C22×D411yescharacteristic
390C2×C4×C13C22×D411yescharacteristic
391C22⋊D13—42no—
392C22⋊D13—42no—
393C22⋊D13—42no—
394C22⋊D13—81no—
395C22⋊D13—81no—
396C2×Dic13—21no—
397C2×Dic13—21no—
398C2×Dic13—21no—
399C2×Dic13—21no—
400C2×Dic13—21no—
401C2×Dic13—81no—
402C2×Dic13—81no—
403D52—21no—
404D52—21no—
405D52—21no—
406D52—21no—
407D52—21no—
408D52—42no—
409D52—42no—
410D52—42no—
411D52—81no—
412D52#13112yes—
413C4×D13—42no—
414C4×D13—42no—
415C4×D13—41no—
416C4×D13—41no—
417C4×D13—41no—
418C4×D13—41no—
419C4×D13—41no—
420C4×D13—41no—
421C4×D13—81no—
422C4×D13—81no—
423C4×D13—81no—
424C4×D13—81no—
425Dic26—21no—
426Dic26—21no—
427Dic26—81no—
428C8×C13—41no—
429C8×C13—41no—
430C8×C13—41no—
431C8×C13—41no—
432#1055—41no—
433#1055—41no—
434#1055—41no—
435#1055—41no—
436#559—131no—
437#554—131no—
438#554—131no—
439#553—131no—
440#553—131no—
441#553—261no—
442#551—261no—
443#551—261no—
444#546—131no—
445#546—131no—
446#546—261no—
447D42—131no—
448#532—131no—
449#529—131no—
450#529—131no—
451#529—261no—
452#525—261no—
453#525—261no—
454C4×#41—131no—
455C4×#41C2×D1311yescharacteristic
456C2×C4×D4—131no—
457C2×C4×D4—131no—
458C2×C4×D4—261no—
459#446—261no—
460#435—261no—
461#435—261no—
462C8×D4—261no—
463#433—21no—
464#433—21no—
465#432—131no—
466#432—131no—
467#431—131no—
468#431C2×D1311yescharacteristic, complemented
469#431C2×D1311yescharacteristic, complemented
470#431C2×D1311yescharacteristic, complemented
471#431C2×D1311yescharacteristic, complemented
472#424—21no—
473#423—131no—
474C2×C4⋊C8—131no—
475C2×C4⋊C8—131no—
476#408—21no—
477C4×M16C2×D1311yescharacteristic, complemented
478C2×C4×C8C2×D1311yescharacteristic, complemented
479Q8⋊C8—131no—
480Q8⋊C8—131no—
481Q8⋊C8—131no—
482Q8⋊C8—131no—
483D4⋊C8—131no—
484D4⋊C8—131no—
485D4⋊C8—131no—
486D4⋊C8—131no—
487D4⋊C8—131no—
488D4⋊C8—131no—
489D4⋊C8—131no—
490D4⋊C8—131no—
491D4⋊C8—131no—
492D4⋊C8—131no—
493D4⋊C8—131no—
494D4⋊C8—131no—
495C22×C13—21no—
496C22×C13—21no—
497C22×C13—21no—
498C22×C13—21no—
499C22×C13—21no—
500C22×C13—21no—
501C22×C13—21no—
502C22×C13—21no—
503C22×C13#42112yes—
504C22×C13C22×C22⋊C411yescharacteristic
505C2×D13—22no—
506C2×D13—41no—
507C2×D13—41no—
508C2×D13—41no—
509C2×D13—41no—
510C2×D13—41no—
511C2×D13—41no—
512C2×D13—41no—
513C2×D13—41no—
514C2×D13—84no—
515C2×D13—84no—
516C4×C13—21no—
517C4×C13—21no—
518C4×C13—21no—
519C4×C13—21no—
520C4×C13—21no—
521C4×C13—21no—
522C4×C13—21no—
523C4×C13—21no—
524C4×C13—21no—
525C4×C13—21no—
526C4×C13C2×#13111yescharacteristic
527C4×C13#56811yescharacteristic
528C4×C13#57611yescharacteristic
529C4×C13#57711yescharacteristic
530Dic13—41no—
531Dic13—41no—
532Dic13—41no—
533Dic13—41no—
534Dic13—41no—
535C2×#41—131no—
536C2×#41—261no—
537C2×#41C22⋊D1311yescharacteristic
538C22×D4—131no—
539C22×D4—131no—
540C22×D4—261no—
541C23×C4—261no—
542C23×C4—261no—
543C2×M16—21no—
544C2×M16—261no—
545C22×C8—21no—
546C22×C8—261no—
547C22×C8—261no—
548C4⋊Q8—131no—
549#127—131no—
550#126—261no—
551#126—261no—
552#126—261no—
553#126—261no—
554#125—131no—
555#125—131no—
556#125—261no—
557#124—131no—
558#124—131no—
559#124—261no—
560#124—261no—
561#123—261no—
562#123—261no—
563#123—261no—
564#123—261no—
565#123—261no—
566#123—261no—
567#123—261no—
568#123—261no—
569C22⋊Q8—131no—
570C22⋊Q8—131no—
571C22⋊Q8—261no—
572C22⋊Q8—261no—
573C22⋊Q8—261no—
574C22⋊Q8—261no—
575C22⋊Q8—261no—
576#121—131no—
577#121—131no—
578#121—131no—
579#121—131no—
580#121—261no—
581#121—261no—
582#121—261no—
583#121—261no—
584#121—261no—
585#121—261no—
586#120—261no—
587#120—261no—
588#120—261no—
589#120—261no—
590C4×Q8—131no—
591C4×Q8—131no—
592C4×Q8C4×D1311yescharacteristic
593C4×Q8D5211yescharacteristic
594C4×D4—131no—
595C4×D4—131no—
596C4×D4—131no—
597C4×D4—131no—
598C4×D4—131no—
599C4×D4—131no—
600C4×D4—131no—
601C4×D4—131no—
602C4×D4—261no—
603C4×D4—261no—
604C4×D4—261no—
605C4×D4—261no—
606C4×D4—261no—
607C4×D4—261no—
608C4×D4—261no—
609C4×D4—261no—
610C4×D4—261no—
611C4×D4—261no—
612C4×D4—261no—
613C4×D4—261no—
614C4×D4—261no—
615C4×D4C4×D1311yescharacteristic
616C4×D4C4×D1311yescharacteristic
617C4×D4C4×D1311yescharacteristic
618C4×D4D5211yescharacteristic
619C4×D4D5211yescharacteristic
620C4×D4D5211yescharacteristic
621#117—131no—
622#117—261no—
623#117—261no—
624#117—261no—
625#117C22⋊D1311yescharacteristic
626#117C22⋊D1311yescharacteristic
627#117C22⋊D1311yescharacteristic
628C2×C4⋊C4—131no—
629C2×C4⋊C4—131no—
630C2×C4⋊C4—261no—
631C2×C22⋊C4—261no—
632C2×C22⋊C4—261no—
633C2×C22⋊C4—261no—
634C2×C22⋊C4—261no—
635C2×C42—261no—
636C2×C42C22×D1311yescharacteristic
637C2×C42C22×D1311yescharacteristic
638C2×C42C22×D1311yescharacteristic
639C4⋊C8—21no—
640C4⋊C8—21no—
641C4⋊C8—21no—
642C4⋊C8—21no—
643C4⋊C8—131no—
644C4⋊C8—131no—
645C4⋊C8—131no—
646C4⋊C8—131no—
647C4⋊C8—261no—
648C4⋊C8—261no—
649C4⋊C8—261no—
650C22⋊C8—21no—
651C22⋊C8—21no—
652C22⋊C8—21no—
653C22⋊C8—21no—
654C22⋊C8—261no—
655C22⋊C8—261no—
656C22⋊C8—261no—
657#97—21no—
658#97—261no—
659#97—261no—
660C4×C8—21no—
661C4×C8—261no—
662C4×C8C22×D1311yescharacteristic
663C4×C8C22×D1311yescharacteristic
664C4×C8C22×D1311yescharacteristic
665C4×C8C22×D1311yescharacteristic
666C2×C13—22no—
667C2×C13—41no—
668C2×C13—41no—
669C2×C13#288011yescharacteristic
670C2×C13#289711yescharacteristic
671C2×C13C2×#42111yescharacteristic
672D13—42no—
673D13—81no—
674D13—81no—
675C24—261no—
676C24—261no—
677#41—42no—
678#41—262no—
679#41—521no—
680#41—1041no—
681#41—1041no—
682C2×Q8—131no—
683C2×Q8—261no—
684C2×Q8#610311yescharacteristic
685C2×D4—131no—
686C2×D4—131no—
687C2×D4—131no—
688C2×D4—262no—
689C2×D4—262no—
690C2×D4—261no—
691C2×D4—261no—
692C2×D4—261no—
693C2×D4—261no—
694C2×D4—261no—
695C2×D4—261no—
696C2×D4—261no—
697C2×D4—261no—
698C2×D4—261no—
699C2×D4—521no—
700C2×D4—521no—
701C2×D4—524no—
702C2×D4#610311yescharacteristic
703C2×D4#610311yescharacteristic
704C2×D4#610311yescharacteristic
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—1041no—
717C22×C4—1041no—
718C22×C4—1041no—
719C22×C4—1041no—
720C22×C4C2×C4×D1311yescharacteristic
721C22×C4C2×C4×D1311yescharacteristic
722C22×C4C2×C4×D1311yescharacteristic
723C22×C4C2×D5211yescharacteristic
724C22×C4C2×D5211yescharacteristic
725C22×C4C2×D5211yescharacteristic
726C22×C4C2×C22⋊D1311yescharacteristic
727C22×C4C2×C22⋊D1311yescharacteristic
728C22×C4C2×C22⋊D1311yescharacteristic
729M16—42no—
730M16—1041no—
731C2×C8—21no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—42no—
736C2×C8—261no—
737C2×C8—261no—
738C2×C8—261no—
739C2×C8—261no—
740C2×C8—1041no—
741C2×C8—1041no—
742C4⋊C4—131no—
743C4⋊C4—131no—
744C4⋊C4—131no—
745C4⋊C4—131no—
746C4⋊C4—261no—
747C4⋊C4—261no—
748C4⋊C4—261no—
749C4⋊C4—261no—
750C4⋊C4—261no—
751C4⋊C4—261no—
752C4⋊C4—261no—
753C4⋊C4—261no—
754C4⋊C4—261no—
755C4⋊C4—261no—
756C4⋊C4—261no—
757C4⋊C4#610311yescharacteristic
758C4⋊C4#610311yescharacteristic
759C4⋊C4#610311yescharacteristic
760C4⋊C4#610311yescharacteristic
761C4⋊C4#610311yescharacteristic
762C4⋊C4#610311yescharacteristic
763C22⋊C4—261no—
764C22⋊C4—261no—
765C22⋊C4—261no—
766C22⋊C4—261no—
767C22⋊C4—261no—
768C22⋊C4—261no—
769C22⋊C4—261no—
770C22⋊C4—261no—
771C22⋊C4—261no—
772C22⋊C4—261no—
773C22⋊C4—261no—
774C22⋊C4—261no—
775C22⋊C4—261no—
776C22⋊C4—261no—
777C22⋊C4—261no—
778C22⋊C4—261no—
779C22⋊C4—261no—
780C22⋊C4—261no—
781C22⋊C4—261no—
782C22⋊C4#610311yescharacteristic
783C22⋊C4#610311yescharacteristic
784C22⋊C4#610311yescharacteristic
785C22⋊C4#610311yescharacteristic
786C22⋊C4#610311yescharacteristic
787C22⋊C4#610311yescharacteristic
788C42—261no—
789C42—261no—
790C42—261no—
791C42C2×C4×D1311yescharacteristic
792C42C2×C4×D1311yescharacteristic
793C42C2×C4×D1311yescharacteristic
794C42C2×D5211yescharacteristic
795C42C2×D5211yescharacteristic
796C42C2×D5211yescharacteristic
797C42C2×C22⋊D1311yescharacteristic
798C42C2×C22⋊D1311yescharacteristic
799C42C2×C22⋊D1311yescharacteristic
800C42C23×D1311yescharacteristic
801C13#1752111yescharacteristic, complemented, Sylow
802C23—261no—
803C23—261no—
804C23—261no—
805C23—522no—
806C23—522no—
807C23—522no—
808C23—522no—
809C23—1041no—
810C23—1041no—
811C23C2×#610311yescharacteristic
812C23C2×#610311yescharacteristic
813C23C2×#610311yescharacteristic
814Q8—41no—
815Q8—261no—
816Q8—261no—
817Q8—1041no—
818D4—22no—
819D4—22no—
820D4—41no—
821D4—132no—
822D4—261no—
823D4—261no—
824D4—261no—
825D4—261no—
826D4—261no—
827D4—522no—
828D4—522no—
829D4—522no—
830D4—522no—
831D4—522no—
832D4—522no—
833D4—1041no—
834D4—1041no—
835D4—1041no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—261no—
852C2×C4—261no—
853C2×C4—261no—
854C2×C4—261no—
855C2×C4—261no—
856C2×C4—522no—
857C2×C4—522no—
858C2×C4—521no—
859C2×C4—521no—
860C2×C4—521no—
861C2×C4—521no—
862C2×C4—521no—
863C2×C4—521no—
864C2×C4—1041no—
865C2×C4—1041no—
866C2×C4—1041no—
867C2×C4—1041no—
868C2×C4—1041no—
869C2×C4—1041no—
870C2×C4C2×#610311yescharacteristic
871C2×C4C2×#610311yescharacteristic
872C2×C4C2×#610311yescharacteristic
873C2×C4C2×#610311yescharacteristic
874C2×C4C2×#610311yescharacteristic
875C2×C4C2×#610311yescharacteristic
876C2×C4C2×#610311yescharacteristic
877C2×C4C2×#610311yescharacteristic
878C2×C4C2×#610311yescharacteristic
879C2×C4C22×C4×D1311yescharacteristic
880C2×C4C22×D5211yescharacteristic
881C2×C4C22×C22⋊D1311yescharacteristic
882C8—41no—
883C8—41no—
884C8—41no—
885C8—41no—
886C8—521no—
887C8—521no—
888C8—521no—
889C8—521no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—262no—
899C22—521no—
900C22—521no—
901C22—521no—
902C22—521no—
903C22—521no—
904C22—521no—
905C22—521no—
906C22—521no—
907C22—1044no—
908C22—1044no—
909C22#1171866612yes—
910C22C22×#610311yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—521no—
922C4—521no—
923C4—521no—
924C4—521no—
925C4—521no—
926C4D13×#13111yescharacteristic
927C4#1171945511yescharacteristic
928C4#1171945611yescharacteristic
929C4#1171945711yescharacteristic
930C2—22no—
931C2—41no—
932C2—41no—
933C2—522no—
934C2—1041no—
935C2—1041no—
936C2#1312328311yescharacteristic
937C2#1312336311yescharacteristic
938C2C2×#1171866611yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2922C2
socleC22×C13C22×C22⋊C4
prime radical#13128446C2
cosocleC42×C13C24
hypercenter#2922D13
hypocenterC13#17521
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #13123961C2semidirect
3. #13113306C2semidirect
4. #13113302C2semidirect
5. #13113297C2semidirect
6. #13113280C2semidirect
7. #13113271C2semidirect
8. #13113262C2semidirect
9. #13113250C2semidirect
10. #13113245C2semidirect
11. #13113236C2semidirect
12. #13113228C2semidirect
13. #13113224C2semidirect
14. C2×#11718051C2semidirect
15. C13×#2922C2semidirect
41. C13×#431C22semidirect
42. C13×#431C22semidirect
43. C13×#431C22semidirect
44. C13×#431C22semidirect
47. C4×C13×M16C22semidirect
48. C2×C4×C8×C13C22semidirect
53. #11718587C22semidirect
54. #11718587C22semidirect
55. #11718586C22semidirect
56. #11718585C22semidirect
57. C2×C4⋊#1055C22semidirect
58. C2×C4⋊#1055C22semidirect
63. #11718051C22semidirect
64. #11718051C22semidirect
65. #11718051C22semidirect
66. #11718051C22semidirect
67. #11718051C22semidirect
68. #11718051C22semidirect
69. #11718051C22semidirect
70. #11718051C22semidirect
71. #11718048C22semidirect
72. #11718048C22semidirect
73. #11718048C22semidirect
74. #11718048C22semidirect
335. #2922D13semidirect
468. #431C2×D13semidirect
469. #431C2×D13semidirect
470. #431C2×D13semidirect
471. #431C2×D13semidirect
477. C4×M16C2×D13semidirect
478. C2×C4×C8C2×D13semidirect
801. C13#17521semidirect

Maximal subgroups

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

subgroupindex
#131284462
#131239612
#131133062
#131133022
#131132972
#131132802
#131132712
#131132622
#131132502
#131132452
#131132362
#131132282
#131132242
C2×#117180512
C13×#29222
#1752113