Finite Group Databasebeta

← #36760111

Subgroups — #36760111

Order 22784.

1574 conjugacy classes of subgroups.

The subgroup lattice has 1246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26028611C211yesmaximal, characteristic
2#26028611C211yesmaximal, characteristic
3#26028611C211yesmaximal, characteristic
4#26025656C211yesmaximal, characteristic
5#26025654C211yesmaximal, characteristic
6#26025652C211yesmaximal, characteristic
7#26025650C211yesmaximal, characteristic
8#26025647C211yesmaximal, characteristic
9#26025645C211yesmaximal, characteristic
10#26025643C211yesmaximal, characteristic
11#26025485C211yesmaximal, characteristic
12#26025483C211yesmaximal, characteristic
13#26025481C211yesmaximal, characteristic
14#26025479C211yesmaximal, characteristic
15#26025282C211yesmaximal, characteristic
16#26025282C211yesmaximal, characteristic
17#26024112C211yesmaximal, characteristic
18#26024110C211yesmaximal, characteristic
19#26024108C211yesmaximal, characteristic
20#26024106C211yesmaximal, characteristic
21#26023351C211yesmaximal, characteristic
22#26023349C211yesmaximal, characteristic
23#26023345C211yesmaximal, characteristic
24#26023343C211yesmaximal, characteristic
25#26023206C211yesmaximal, characteristic
26#26023206C211yesmaximal, characteristic
27#26022809C211yesmaximal, characteristic
28#26022809C211yesmaximal, characteristic
29C4×#15668002C211yesmaximal, characteristic
30C4×#15667977C211yesmaximal, characteristic
31C89×#2585C211yesmaximal, characteristic
32C2×#15668002C2211yescharacteristic
33C2×#15668002C2211yescharacteristic
34C2×#15668002C2211yescharacteristic
35C2×#15668002C2211yescharacteristic
36C2×#15668002C2211yescharacteristic
37C2×#15668002C2211yescharacteristic
38C2×#15668002C2211yescharacteristic
39C2×C4×Dic178C2211yescharacteristic
40C2×#15667977C2211yescharacteristic
41C2×#15667977C2211yescharacteristic
42#19151540C2211yescharacteristic
43#19151540C2211yescharacteristic
44#19151539C2211yescharacteristic
45#19151539C2211yescharacteristic
46#19151538C2211yescharacteristic
47#19151537C2211yescharacteristic
48#19151536C2211yescharacteristic
49#19151532C2211yescharacteristic
50#19151532C2211yescharacteristic
51#19151532C2211yescharacteristic
52#19151532C2211yescharacteristic
53#19151531C2211yescharacteristic
54#19151531C2211yescharacteristic
55#19151531C2211yescharacteristic
56#19151531C2211yescharacteristic
57#19151530C2211yescharacteristic
58#19151530C2211yescharacteristic
59#19151530C2211yescharacteristic
60#19151529C2211yescharacteristic
61#19151528C2211yescharacteristic
62#19151502C2211yescharacteristic
63#19151502C2211yescharacteristic
64#19151502C2211yescharacteristic
65#19151502C2211yescharacteristic
66#19151497C2211yescharacteristic
67#19151497C2211yescharacteristic
68#19151497C2211yescharacteristic
69#19151496C2211yescharacteristic
70#19151496C2211yescharacteristic
71#19151496C2211yescharacteristic
72#19151495C2211yescharacteristic
73#19151495C2211yescharacteristic
74#19151495C2211yescharacteristic
75#19151495C2211yescharacteristic
76#19151495C2211yescharacteristic
77#19151495C2211yescharacteristic
78#19151495C2211yescharacteristic
79#19151495C2211yescharacteristic
80#19151495C2211yescharacteristic
81#19151495C2211yescharacteristic
82#19151495C2211yescharacteristic
83#19151494C2211yescharacteristic
84#19151494C2211yescharacteristic
85#19151494C2211yescharacteristic
86#19151493C2211yescharacteristic
87#19151493C2211yescharacteristic
88#19151493C2211yescharacteristic
89#19151493C2211yescharacteristic
90#19151493C2211yescharacteristic
91#19151493C2211yescharacteristic
92#19151493C2211yescharacteristic
93#19151493C2211yescharacteristic
94#19151493C2211yescharacteristic
95#19151493C2211yescharacteristic
96#19151493C2211yescharacteristic
97#19151485C2211yescharacteristic
98#19151485C2211yescharacteristic
99#19151485C2211yescharacteristic
100#19151485C2211yescharacteristic
101#19151485C2211yescharacteristic
102#19151485C2211yescharacteristic
103#19151484C2211yescharacteristic
104#19151484C2211yescharacteristic
105#19151484C2211yescharacteristic
106#19151484C2211yescharacteristic
107#19151484C2211yescharacteristic
108#19151483C2211yescharacteristic
109#19151483C2211yescharacteristic
110#19151483C2211yescharacteristic
111#19151482C2211yescharacteristic
112#19151482C2211yescharacteristic
113#19151482C2211yescharacteristic
114#19151482C2211yescharacteristic
115#19151481C2211yescharacteristic
116#19151481C2211yescharacteristic
117#19151481C2211yescharacteristic
118#19151481C2211yescharacteristic
119#19151480C2211yescharacteristic
120#19151480C2211yescharacteristic
121#19151480C2211yescharacteristic
122#19151479C2211yescharacteristic
123#19151479C2211yescharacteristic
124#19151479C2211yescharacteristic
125#19151479C2211yescharacteristic
126#19151479C2211yescharacteristic
127#19151467C2211yescharacteristic
128#19151467C2211yescharacteristic
129#19151467C2211yescharacteristic
130#19151467C2211yescharacteristic
131#19151467C2211yescharacteristic
132#19151467C2211yescharacteristic
133#19151462C2211yescharacteristic
134#19151462C2211yescharacteristic
135#19151462C2211yescharacteristic
136#19151462C2211yescharacteristic
137#19151462C2211yescharacteristic
138#19151462C2211yescharacteristic
139#19151462C2211yescharacteristic
140C4⋊C4×Dic89C2211yescharacteristic
141C4⋊C4×Dic89C2211yescharacteristic
142C4⋊C4×Dic89C2211yescharacteristic
143C4⋊C4×Dic89C2211yescharacteristic
144C4⋊C4×Dic89C2211yescharacteristic
145C4⋊C4×Dic89C2211yescharacteristic
146C4×#13083553C2211yescharacteristic
147C4×#13083553C2211yescharacteristic
148C4×#13083553C2211yescharacteristic
149C4×#13083553C2211yescharacteristic
150C4×#13083553C2211yescharacteristic
151C4×#13083553C2211yescharacteristic
152C4×#13083553C2211yescharacteristic
153C4×#13083553C2211yescharacteristic
154C4×C4⋊Dic89C2211yescharacteristic
155#19151449C2211yescharacteristic
156#19151449C2211yescharacteristic
157#19151449C2211yescharacteristic
158#19151449C2211yescharacteristic
159#19151449C2211yescharacteristic
160#19151449C2211yescharacteristic
161#19151449C2211yescharacteristic
162#19151449C2211yescharacteristic
163#19151449C2211yescharacteristic
164#19151449C2211yescharacteristic
165#19151449C2211yescharacteristic
166#19151449C2211yescharacteristic
167#19151449C2211yescharacteristic
168#19151449C2211yescharacteristic
169C42×Dic89C2211yescharacteristic
170C42×Dic89C2211yescharacteristic
171C42×Dic89C2211yescharacteristic
172#400×C89C2211yescharacteristic
173#398×C89C2211yescharacteristic
174#398×C89C2211yescharacteristic
175#398×C89C2211yescharacteristic
176#389×C89C2211yescharacteristic
177#389×C89C2211yescharacteristic
178#389×C89C2211yescharacteristic
179#387×C89C2211yescharacteristic
180#387×C89C2211yescharacteristic
181#387×C89C2211yescharacteristic
182#387×C89C2211yescharacteristic
183#387×C89C2211yescharacteristic
184#387×C89C2211yescharacteristic
185C4×C4⋊C4×C89C2211yescharacteristic
186C4×C4⋊C4×C89C2211yescharacteristic
187C22×Dic178C2311yescharacteristic
188#15668002—24no—
189#15668002—24no—
190#15668002—24no—
191#15668002—24no—
192#15668002—24no—
193#15668002—24no—
194#15668002—24no—
195C4×Dic178—24no—
196#15667977—24no—
197#15667977Q818yes—
198C2×C4⋊Dic89C2311yescharacteristic
199C2×C4⋊Dic89C2311yescharacteristic
200C2×C4⋊Dic89C2311yescharacteristic
201C2×C4⋊Dic89C2311yescharacteristic
202C2×C4⋊Dic89C2311yescharacteristic
203C2×C4⋊Dic89C2311yescharacteristic
204C2×C4⋊Dic89C2311yescharacteristic
205C2×C4⋊Dic89C2311yescharacteristic
206C2×C4⋊Dic89C2311yescharacteristic
207C2×C4⋊Dic89C2311yescharacteristic
208C2×C4⋊Dic89C2311yescharacteristic
209C2×C4⋊Dic89C2311yescharacteristic
210C2×C4⋊Dic89C2311yescharacteristic
211C2×#13083553C2311yescharacteristic
212C2×#13083553C2311yescharacteristic
213C2×#13083553C2311yescharacteristic
214C2×#13083553C2311yescharacteristic
215C2×#13083553C2311yescharacteristic
216C2×#13083553C2311yescharacteristic
217C2×#13083553C2311yescharacteristic
218C2×#13083553C2311yescharacteristic
219C2×#13083553C2311yescharacteristic
220C2×#13083553C2311yescharacteristic
221C2×#13083553C2311yescharacteristic
222C2×#13083553C2311yescharacteristic
223C2×#13083553C2311yescharacteristic
224C2×#13083553C2311yescharacteristic
225C2×#13083553C2311yescharacteristic
226C2×#13083553C2311yescharacteristic
227C2×#13083553C2311yescharacteristic
228C2×#13083553C2311yescharacteristic
229C2×#13083553C2311yescharacteristic
230C2×#13083553C2311yescharacteristic
231C2×#13083553C2311yescharacteristic
232C2×#13083553C2311yescharacteristic
233C2×#13083553C2311yescharacteristic
234C2×#13083553C2311yescharacteristic
235C2×#13083553C2311yescharacteristic
236C2×#13083553C2311yescharacteristic
237C2×#13083553C2311yescharacteristic
238C2×#13083553C2311yescharacteristic
239C2×#13083553C2311yescharacteristic
240C2×#13083553C2311yescharacteristic
241C2×#13083553C2311yescharacteristic
242C2×#13083553C2311yescharacteristic
243C2×#13083553C2311yescharacteristic
244C2×#13083553C2311yescharacteristic
245C2×#13083553C2311yescharacteristic
246C2×#13083553C2311yescharacteristic
247C2×#13083553C2311yescharacteristic
248C2×#13083553C2311yescharacteristic
249C2×C4×Dic89C2311yescharacteristic
250C2×C4×Dic89C2311yescharacteristic
251C2×C4×Dic89C2311yescharacteristic
252C2×C4×Dic89C2311yescharacteristic
253C2×C4×Dic89C2311yescharacteristic
254C2×C4×Dic89C2311yescharacteristic
255C2×C4×Dic89C2311yescharacteristic
256C2×C4×Dic89C2311yescharacteristic
257C2×C4×Dic89C2311yescharacteristic
258C2×C4×Dic89C2311yescharacteristic
259C2×C4×Dic89C2311yescharacteristic
260C2×C4×Dic89C2311yescharacteristic
261C2×C4×Dic89C2311yescharacteristic
262C2×C4×Dic89C2311yescharacteristic
263C2×C4×Dic89C2311yescharacteristic
264C2×C4×Dic89C2311yescharacteristic
265C2×C4×Dic89C2311yescharacteristic
266C2×C4×Dic89C2311yescharacteristic
267C2×C4×Dic89C2311yescharacteristic
268C2×C4×Dic89C2311yescharacteristic
269C2×C4×Dic89C2311yescharacteristic
270C2×C4×Dic89C2311yescharacteristic
271C2×C4×Dic89C2311yescharacteristic
272C2×C4×Dic89C2311yescharacteristic
273C2×C4×Dic89C2311yescharacteristic
274C2×C4×Dic89C2311yescharacteristic
275#15667919C2311yescharacteristic
276#15667919C2311yescharacteristic
277#15667919C2311yescharacteristic
278#15667919C2311yescharacteristic
279#15667919C2311yescharacteristic
280#15667919C2311yescharacteristic
281#15667919C2311yescharacteristic
282#15667919C2311yescharacteristic
283#15667919C2311yescharacteristic
284#15667919C2311yescharacteristic
285#15667919C2311yescharacteristic
286#15667919C2311yescharacteristic
287#15667919C2311yescharacteristic
288#15667919C2311yescharacteristic
289#15667919C2311yescharacteristic
290#15667919C2311yescharacteristic
291#15667919C2311yescharacteristic
292#15667919C2311yescharacteristic
293#15667919C2311yescharacteristic
294#15667919C2311yescharacteristic
295#15667919C2311yescharacteristic
296#15667919C2311yescharacteristic
297#15667919C2311yescharacteristic
298#15667919C2311yescharacteristic
299#15667919C2311yescharacteristic
300#15667919C2311yescharacteristic
301#15667919C2311yescharacteristic
302#15667919C2311yescharacteristic
303#15667919C2311yescharacteristic
304#15667919C2311yescharacteristic
305#15667919C2311yescharacteristic
306#15667919C2311yescharacteristic
307#15667919C2311yescharacteristic
308#15667919C2311yescharacteristic
309#15667919C2311yescharacteristic
310#15667919C2311yescharacteristic
311#15667919C2311yescharacteristic
312#15667919C2311yescharacteristic
313#15667919C2311yescharacteristic
314#15667919C2311yescharacteristic
315#15667919C2311yescharacteristic
316#15667919C2311yescharacteristic
317C2×C4⋊C4×C89C2311yescharacteristic
318C2×C4⋊C4×C89C2311yescharacteristic
319C2×C4⋊C4×C89C2311yescharacteristic
320C2×C4⋊C4×C89C2311yescharacteristic
321C2×C4⋊C4×C89C2311yescharacteristic
322C2×C4⋊C4×C89C2311yescharacteristic
323C2×C4⋊C4×C89C2311yescharacteristic
324C2×C4⋊C4×C89C2311yescharacteristic
325C2×C4⋊C4×C89C2311yescharacteristic
326C2×C4⋊C4×C89C2311yescharacteristic
327C2×C4⋊C4×C89C2311yescharacteristic
328C2×C4⋊C4×C89C2311yescharacteristic
329C2×C4⋊C4×C89C2311yescharacteristic
330C2×C4⋊C4×C89C2311yescharacteristic
331C2×C42×C89C2311yescharacteristic
332C2×C42×C89C2311yescharacteristic
333C2×C42×C89C2311yescharacteristic
334C2×C42×C89C2311yescharacteristic
335C2×C42×C89C2311yescharacteristic
336#95×C89C2311yescharacteristic
337#95×C89C2311yescharacteristic
338#95×C89C2311yescharacteristic
339#95×C89C2311yescharacteristic
340#95×C89C2311yescharacteristic
341#95×C89C2311yescharacteristic
342#95×C89C2311yescharacteristic
343#95×C89C2311yescharacteristic
344#95×C89C2311yescharacteristic
345#95×C89C2311yescharacteristic
346#95×C89C2311yescharacteristic
347#95×C89C2311yescharacteristic
348#95×C89C2311yescharacteristic
349#95×C89C2311yescharacteristic
350#95×C89C2311yescharacteristic
351#95×C89C2311yescharacteristic
352C2×Dic178—22no—
353C2×Dic178—22no—
354C2×Dic178C2×Q814yes—
355C22×Dic89C2411yescharacteristic
356C22×Dic89C2411yescharacteristic
357C22×Dic89C2411yescharacteristic
358C22×Dic89C2411yescharacteristic
359C22×Dic89C2411yescharacteristic
360C22×Dic89C2411yescharacteristic
361C22×Dic89C2411yescharacteristic
362C22×Dic89C2411yescharacteristic
363C22×Dic89C2411yescharacteristic
364C22×Dic89C2411yescharacteristic
365C22×Dic89C2411yescharacteristic
366C22×Dic89C2411yescharacteristic
367C22×Dic89C2411yescharacteristic
368C22×Dic89C2411yescharacteristic
369C22×Dic89C2411yescharacteristic
370C22×Dic89C2411yescharacteristic
371C4⋊Dic89—22no—
372C4⋊Dic89—22no—
373C4⋊Dic89—22no—
374C4⋊Dic89—22no—
375C4⋊Dic89—22no—
376C4⋊Dic89—22no—
377C4⋊Dic89—22no—
378C4⋊Dic89—22no—
379C4⋊Dic89—41no—
380C4⋊Dic89—41no—
381C4⋊Dic89—41no—
382C4⋊Dic89—41no—
383C4⋊Dic89—41no—
384#13083553—22no—
385#13083553—22no—
386#13083553—22no—
387#13083553—22no—
388#13083553—22no—
389#13083553—22no—
390#13083553—22no—
391#13083553—22no—
392#13083553—22no—
393#13083553—22no—
394#13083553—22no—
395#13083553—22no—
396#13083553—22no—
397#13083553—22no—
398#13083553—22no—
399#13083553—22no—
400#13083553—22no—
401#13083553—22no—
402#13083553—22no—
403#13083553—22no—
404#13083553—22no—
405#13083553—22no—
406#13083553—22no—
407#13083553—22no—
408#13083553—22no—
409#13083553—22no—
410#13083553—22no—
411#13083553—22no—
412#13083553—41no—
413#13083553—41no—
414#13083553—41no—
415#13083553—41no—
416#13083553—41no—
417#13083553—41no—
418#13083553C2×Q814yes—
419#13083553C2×Q814yes—
420#13083553#4114yes—
421#13083553#4114yes—
422C4×Dic89—22no—
423C4×Dic89—22no—
424C4×Dic89—22no—
425C4×Dic89—22no—
426C4×Dic89—22no—
427C4×Dic89—22no—
428C4×Dic89—22no—
429C4×Dic89—22no—
430C4×Dic89—22no—
431C4×Dic89—22no—
432C4×Dic89—22no—
433C4×Dic89—22no—
434C4×Dic89—41no—
435C4×Dic89—41no—
436C4×Dic89—41no—
437C4×Dic89—41no—
438C4×Dic89—41no—
439C4×Dic89—41no—
440C4×Dic89—41no—
441C4×Dic89—41no—
442C4×Dic89—41no—
443C4×Dic89—41no—
444C4×Dic89C2×Q814yes—
445C4×Dic89C2×Q814yes—
446C4×Dic89C2×Q814yes—
447C4×Dic89#4114yes—
448C22×C4×C89C2411yescharacteristic
449C22×C4×C89C2411yescharacteristic
450C22×C4×C89C2411yescharacteristic
451C22×C4×C89C2411yescharacteristic
452C22×C4×C89C2411yescharacteristic
453C22×C4×C89C2411yescharacteristic
454C22×C4×C89C2411yescharacteristic
455C22×C4×C89C2411yescharacteristic
456C22×C4×C89C2411yescharacteristic
457C22×C4×C89C2411yescharacteristic
458C22×C4×C89C2411yescharacteristic
459C22×C4×C89C2411yescharacteristic
460C22×C4×C89C2411yescharacteristic
461C22×C4×C89C2411yescharacteristic
462C22×C4×C89C2411yescharacteristic
463C4⋊C4×C89—22no—
464C4⋊C4×C89—22no—
465C4⋊C4×C89—22no—
466C4⋊C4×C89—22no—
467C4⋊C4×C89—22no—
468C4⋊C4×C89—22no—
469C4⋊C4×C89—22no—
470C4⋊C4×C89—22no—
471C4⋊C4×C89—41no—
472C4⋊C4×C89—41no—
473C4⋊C4×C89—41no—
474C4⋊C4×C89—41no—
475C4⋊C4×C89—41no—
476C4⋊C4×C89C2×Q814yes—
477C42×C89—22no—
478C42×C89—41no—
479C42×C89—41no—
480C42×C89—41no—
481C42×C89—41no—
482C23×C89C2511yescharacteristic
483C2×C4×C89—21no—
484C2×C4×C89—21no—
485C2×C4×C89—21no—
486C2×C4×C89—21no—
487C2×C4×C89—21no—
488C2×C4×C89—21no—
489C2×C4×C89—21no—
490C2×C4×C89—21no—
491C2×C4×C89—21no—
492C2×C4×C89—21no—
493C2×C4×C89—21no—
494C2×C4×C89—21no—
495C2×C4×C89—21no—
496C2×C4×C89—21no—
497C2×C4×C89—21no—
498C2×C4×C89—21no—
499C2×C4×C89—21no—
500C2×C4×C89—21no—
501C2×C4×C89—21no—
502C2×C4×C89—21no—
503C2×C4×C89—21no—
504C2×C4×C89—21no—
505C2×C4×C89—21no—
506C2×C4×C89—21no—
507C2×C4×C89—21no—
508C2×C4×C89—21no—
509C2×C4×C89—21no—
510C2×C4×C89—21no—
511C2×C4×C89—21no—
512C2×C4×C89—21no—
513C2×C4×C89—21no—
514C2×C4×C89—21no—
515C2×C4×C89—21no—
516C2×C4×C89—21no—
517C2×C4×C89—21no—
518C2×C4×C89—21no—
519C2×C4×C89—21no—
520C2×C4×C89—21no—
521C2×C4×C89—21no—
522C2×C4×C89C22×Q812yes—
523C2×C4×C89C22×Q812yes—
524C2×C4×C89C22×Q812yes—
525C2×C4×C89C2×#4112yes—
526C2×C4×C89C2×#4112yes—
527C2×C4×C89C2×#4112yes—
528C2×Dic89—21no—
529C2×Dic89—21no—
530C2×Dic89—21no—
531C2×Dic89—21no—
532C2×Dic89—21no—
533C2×Dic89—21no—
534C2×Dic89—21no—
535C2×Dic89—21no—
536C2×Dic89—21no—
537C2×Dic89—21no—
538C2×Dic89—21no—
539C2×Dic89—21no—
540C2×Dic89—21no—
541C2×Dic89—21no—
542C2×Dic89—21no—
543C2×Dic89—21no—
544C2×Dic89—21no—
545C2×Dic89—21no—
546C2×Dic89—21no—
547C2×Dic89—21no—
548C2×Dic89—21no—
549C2×Dic89—21no—
550C2×Dic89—21no—
551C2×Dic89—21no—
552C2×Dic89—21no—
553C2×Dic89—21no—
554C2×Dic89—21no—
555C2×Dic89—21no—
556C2×Dic89—21no—
557C2×Dic89—21no—
558C2×Dic89—21no—
559C2×Dic89—21no—
560C2×Dic89—21no—
561C2×Dic89—21no—
562C2×Dic89—21no—
563C2×Dic89—21no—
564C2×Dic89—21no—
565C2×Dic89C22×Q812yes—
566C2×Dic89C22×Q812yes—
567C2×Dic89C22×Q812yes—
568C2×Dic89C22×Q812yes—
569C2×Dic89C2×#4112yes—
570C2×Dic89C2×#4112yes—
571C2×Dic89C2×#4112yes—
572C2×Dic89C2×#4112yes—
573C2×Dic89C2×#4112yes—
574C2×Dic89C2×#4112yes—
575C2×Dic892−1+412yes—
576Dic178—28no—
577C22×C89C23×Q811yescharacteristic
578C22×C89C22×#4111yescharacteristic
579C22×C89C22×#4111yescharacteristic
580C22×C89C22×#4111yescharacteristic
581C22×C89C2×2−1+411yescharacteristic
582C22×C89#58511yescharacteristic
583C22×C89#58511yescharacteristic
584C4×C89—22no—
585C4×C89—22no—
586C4×C89—22no—
587C4×C89—22no—
588C4×C89—22no—
589C4×C89—22no—
590C4×C89—41no—
591C4×C89—41no—
592C4×C89—41no—
593C4×C89—41no—
594C4×C89—41no—
595C4×C89—41no—
596C4×C89—41no—
597C4×C89—41no—
598C4×C89—41no—
599Dic89—22no—
600Dic89—22no—
601Dic89—22no—
602Dic89—22no—
603Dic89—22no—
604Dic89—41no—
605Dic89—41no—
606Dic89—41no—
607Dic89—41no—
608Dic89—41no—
609Dic89—41no—
610Dic89—41no—
611Dic89—41no—
612Dic89—41no—
613Dic89#53314yes—
614Dic89#55714yes—
615#36600—891nomaximal, Sylow
616C2×C89C2×#53311yescharacteristic
617C2×C89C2×#55711yescharacteristic
618C2×C89#348011yescharacteristic
619C2×C89#348011yescharacteristic
620C2×C89#350411yescharacteristic
621C2×C89#351511yescharacteristic
622C2×C89#351511yescharacteristic
623#2859—891no—
624#2859—891no—
625#2859—891no—
626#2585—891no—
627#2585—891no—
628#2585—891no—
629#2585—891no—
630#2585—891no—
631#2585—891no—
632#2585—891no—
633#2585D8911yescharacteristic
634#2570—891no—
635#2570—891no—
636#2570—891no—
637#2570—891no—
638#2552—891no—
639#2552—891no—
640#2453—891no—
641#2453—891no—
642#2453—891no—
643#2453—891no—
644#2370—891no—
645#2370—891no—
646#2370—891no—
647#2370—891no—
648#2355—891no—
649#2355—891no—
650C4×#125—891no—
651C4×#125—891no—
652C4×#125—891no—
653C42×Q8—891no—
654C89#3660011yescharacteristic, complemented, Sylow
655C2×#125—891no—
656C2×#125—891no—
657C2×#125—891no—
658C2×#125—891no—
659C2×#125—891no—
660C2×#125—891no—
661C2×#125—891no—
662C2×C4×Q8—891no—
663C2×C4×Q8—891no—
664C2×C4×Q8—891no—
665#400—891no—
666#400—891no—
667#400—891no—
668#400—891no—
669#400—891no—
670#400—891no—
671#400—891no—
672#400C2×D8911yescharacteristic
673#398—891no—
674#398—891no—
675#398—891no—
676#398—891no—
677#398—891no—
678#398—891no—
679#398—891no—
680#398—891no—
681#398—891no—
682#398—891no—
683#398—891no—
684#398—891no—
685#398—891no—
686#398C2×D8911yescharacteristic
687#398C2×D8911yescharacteristic
688#398C2×D8911yescharacteristic
689#391—891no—
690#391—891no—
691#391—891no—
692#391—891no—
693#389—891no—
694#389—891no—
695#389—891no—
696#389—891no—
697#389—891no—
698#389—891no—
699#389—891no—
700#389—891no—
701#389—891no—
702#389—891no—
703#389—891no—
704#389—891no—
705#389—891no—
706#389—891no—
707#389—891no—
708#389—891no—
709#389—891no—
710#389—891no—
711#389—891no—
712#389—891no—
713#389—891no—
714#389—891no—
715#389—891no—
716#389—891no—
717#389—891no—
718#389—891no—
719#389—891no—
720#389—891no—
721#389—891no—
722#389—891no—
723#389—891no—
724#389C2×D8911yescharacteristic
725#389C2×D8911yescharacteristic
726#389C2×D8911yescharacteristic
727#387—891no—
728#387—891no—
729#387—891no—
730#387—891no—
731#387—891no—
732#387—891no—
733#387—891no—
734#387—891no—
735#387—891no—
736#387—891no—
737#387—891no—
738#387—891no—
739#387—891no—
740#387—891no—
741#387—891no—
742#387—891no—
743#387—891no—
744#387—891no—
745#387—891no—
746#387—891no—
747#387—891no—
748#387—891no—
749#387—891no—
750#387—891no—
751#387—891no—
752#387—891no—
753#387—891no—
754#387—891no—
755#387—891no—
756#387—891no—
757#387C2×D8911yescharacteristic
758#387C2×D8911yescharacteristic
759#387C2×D8911yescharacteristic
760#387C2×D8911yescharacteristic
761#387C2×D8911yescharacteristic
762#387C2×D8911yescharacteristic
763#384—891no—
764#384—891no—
765#384—891no—
766#384—891no—
767#384—891no—
768#384—891no—
769#382—891no—
770#382—891no—
771#382—891no—
772#382—891no—
773#382—891no—
774#382—891no—
775#382—891no—
776C4×C4⋊C4—891no—
777C4×C4⋊C4—891no—
778C4×C4⋊C4—891no—
779C4×C4⋊C4—891no—
780C4×C4⋊C4—891no—
781C4×C4⋊C4—891no—
782C4×C4⋊C4—891no—
783C4×C4⋊C4—891no—
784C4×C4⋊C4—891no—
785C4×C4⋊C4—891no—
786C4×C4⋊C4—891no—
787C4×C4⋊C4—891no—
788C4×C4⋊C4—891no—
789C4×C4⋊C4—891no—
790C4×C4⋊C4—891no—
791C4×C4⋊C4—891no—
792C4×C4⋊C4—891no—
793C4×C4⋊C4—891no—
794C4×C4⋊C4—891no—
795C4×C4⋊C4—891no—
796C4×C4⋊C4—891no—
797C4×C4⋊C4—891no—
798C4×C4⋊C4—891no—
799C4×C4⋊C4—891no—
800C4×C4⋊C4—891no—
801C4×C4⋊C4—891no—
802C4×C4⋊C4—891no—
803C4×C4⋊C4—891no—
804C4×C4⋊C4—891no—
805C4×C4⋊C4C2×D8911yescharacteristic
806C4×C4⋊C4C2×D8911yescharacteristic
807C43—891no—
808C43—891no—
809C43—891no—
810C22×Q8—891no—
811#125—1784no—
812#125—1784no—
813#125—1784no—
814#125—1784no—
815#125—1784no—
816#125—1784no—
817#125—1784no—
818C4×Q8—898no—
819C4×Q8—1784no—
820C4×Q8—1784no—
821C2×C4⋊C4—891no—
822C2×C4⋊C4—891no—
823C2×C4⋊C4—891no—
824C2×C4⋊C4—891no—
825C2×C4⋊C4—891no—
826C2×C4⋊C4—891no—
827C2×C4⋊C4—891no—
828C2×C4⋊C4—891no—
829C2×C4⋊C4—891no—
830C2×C4⋊C4—891no—
831C2×C4⋊C4—891no—
832C2×C4⋊C4—891no—
833C2×C4⋊C4—891no—
834C2×C4⋊C4—891no—
835C2×C4⋊C4—891no—
836C2×C4⋊C4—891no—
837C2×C4⋊C4—891no—
838C2×C4⋊C4—891no—
839C2×C4⋊C4—891no—
840C2×C4⋊C4—891no—
841C2×C4⋊C4—891no—
842C2×C4⋊C4—891no—
843C2×C4⋊C4—891no—
844C2×C4⋊C4—891no—
845C2×C4⋊C4—891no—
846C2×C4⋊C4—891no—
847C2×C4⋊C4—891no—
848C2×C4⋊C4—891no—
849C2×C4⋊C4—891no—
850C2×C4⋊C4—891no—
851C2×C4⋊C4—891no—
852C2×C4⋊C4—891no—
853C2×C4⋊C4—891no—
854C2×C4⋊C4—891no—
855C2×C4⋊C4—891no—
856C2×C4⋊C4—891no—
857C2×C4⋊C4—891no—
858C2×C4⋊C4—891no—
859C2×C4⋊C4—891no—
860C2×C4⋊C4—891no—
861C2×C4⋊C4—891no—
862C2×C4⋊C4—891no—
863C2×C4⋊C4—891no—
864C2×C4⋊C4—891no—
865C2×C4⋊C4—891no—
866C2×C4⋊C4—891no—
867C2×C4⋊C4—891no—
868C2×C4⋊C4—891no—
869C2×C4⋊C4—891no—
870C2×C4⋊C4—891no—
871C2×C4⋊C4—891no—
872C2×C4⋊C4C22×D8911yescharacteristic
873C2×C4⋊C4C22×D8911yescharacteristic
874C2×C4⋊C4C22×D8911yescharacteristic
875C2×C4⋊C4C22×D8911yescharacteristic
876C2×C4⋊C4C22×D8911yescharacteristic
877C2×C4⋊C4C22×D8911yescharacteristic
878C2×C4⋊C4C22×D8911yescharacteristic
879C2×C4⋊C4C22×D8911yescharacteristic
880C2×C4⋊C4C22×D8911yescharacteristic
881C2×C4⋊C4C22×D8911yescharacteristic
882C2×C4⋊C4C22×D8911yescharacteristic
883C2×C4⋊C4C22×D8911yescharacteristic
884C2×C4⋊C4C22×D8911yescharacteristic
885C2×C4⋊C4C22×D8911yescharacteristic
886C2×C42—891no—
887C2×C42—891no—
888C2×C42—891no—
889C2×C42—891no—
890C2×C42—891no—
891C2×C42—891no—
892C2×C42—891no—
893C2×C42—891no—
894C2×C42—891no—
895C2×C42—891no—
896C2×C42—891no—
897C2×C42—891no—
898C2×C42—891no—
899C2×C42—891no—
900C2×C42—891no—
901C2×C42—891no—
902C2×C42—891no—
903C2×C42—891no—
904C2×C42—891no—
905C2×C42—891no—
906C2×C42—891no—
907C2×C42—891no—
908C2×C42—891no—
909C2×C42—891no—
910C2×C42—891no—
911C2×C42—891no—
912C2×C42C22×D8911yescharacteristic
913C2×C42C22×D8911yescharacteristic
914C2×C42C22×D8911yescharacteristic
915C2×C42C22×D8911yescharacteristic
916C2×C42C22×D8911yescharacteristic
917#95—891no—
918#95—891no—
919#95—891no—
920#95—891no—
921#95—891no—
922#95—891no—
923#95—891no—
924#95—891no—
925#95—891no—
926#95—891no—
927#95—891no—
928#95—891no—
929#95—891no—
930#95—891no—
931#95—891no—
932#95—891no—
933#95—891no—
934#95—891no—
935#95—891no—
936#95—891no—
937#95—891no—
938#95—891no—
939#95—891no—
940#95—891no—
941#95—891no—
942#95—891no—
943#95—891no—
944#95—891no—
945#95—891no—
946#95—891no—
947#95—891no—
948#95—891no—
949#95—891no—
950#95—891no—
951#95—891no—
952#95—891no—
953#95—891no—
954#95—891no—
955#95—891no—
956#95—891no—
957#95—891no—
958#95—891no—
959#95C22×D8911yescharacteristic
960#95C22×D8911yescharacteristic
961#95C22×D8911yescharacteristic
962#95C22×D8911yescharacteristic
963#95C22×D8911yescharacteristic
964#95C22×D8911yescharacteristic
965#95C22×D8911yescharacteristic
966#95C22×D8911yescharacteristic
967#95C22×D8911yescharacteristic
968#95C22×D8911yescharacteristic
969#95C22×D8911yescharacteristic
970#95C22×D8911yescharacteristic
971#95C22×D8911yescharacteristic
972#95C22×D8911yescharacteristic
973#95C22×D8911yescharacteristic
974#95C22×D8911yescharacteristic
975C2×Q8—894no—
976C2×Q8—1782no—
977C2×Q8—1782no—
978C22×C4—891no—
979C22×C4—891no—
980C22×C4—891no—
981C22×C4—891no—
982C22×C4—891no—
983C22×C4—891no—
984C22×C4—891no—
985C22×C4—891no—
986C22×C4—891no—
987C22×C4—891no—
988C22×C4—891no—
989C22×C4—891no—
990C22×C4—891no—
991C22×C4—891no—
992C22×C4—891no—
993C22×C4—891no—
994C22×C4C23×D8911yescharacteristic
995C22×C4C23×D8911yescharacteristic
996C22×C4C23×D8911yescharacteristic
997C22×C4C23×D8911yescharacteristic
998C22×C4C23×D8911yescharacteristic
999C22×C4C23×D8911yescharacteristic
1000C22×C4C23×D8911yescharacteristic
1001C22×C4C23×D8911yescharacteristic
1002C22×C4C23×D8911yescharacteristic
1003C22×C4C23×D8911yescharacteristic
1004C22×C4C23×D8911yescharacteristic
1005C22×C4C23×D8911yescharacteristic
1006C22×C4C23×D8911yescharacteristic
1007C22×C4C23×D8911yescharacteristic
1008C22×C4C23×D8911yescharacteristic
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
1015C4⋊C4—22no—
1016C4⋊C4—22no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—894no—
1023C4⋊C4—894no—
1024C4⋊C4—894no—
1025C4⋊C4—894no—
1026C4⋊C4—3561no—
1027C4⋊C4—3561no—
1028C4⋊C4—3561no—
1029C4⋊C4—3561no—
1030C4⋊C4—3561no—
1031C4⋊C4—3561no—
1032C4⋊C4—3561no—
1033C4⋊C4—3561no—
1034C4⋊C4—3561no—
1035C4⋊C4—3561no—
1036C4⋊C4—3561no—
1037C4⋊C4—1782no—
1038C4⋊C4—1782no—
1039C4⋊C4—1782no—
1040C4⋊C4—1782no—
1041C4⋊C4—1782no—
1042C4⋊C4—1782no—
1043C4⋊C4—1782no—
1044C4⋊C4—1782no—
1045C4⋊C4—1782no—
1046C4⋊C4—1782no—
1047C4⋊C4—1782no—
1048C4⋊C4—1782no—
1049C4⋊C4—1782no—
1050C4⋊C4—1782no—
1051C4⋊C4—1782no—
1052C4⋊C4—1782no—
1053C4⋊C4—1782no—
1054C4⋊C4—1782no—
1055C4⋊C4—1782no—
1056C4⋊C4—1782no—
1057C4⋊C4—1782no—
1058C4⋊C4—1782no—
1059C4⋊C4—1782no—
1060C4⋊C4—1782no—
1061C4⋊C4—1782no—
1062C4⋊C4—1782no—
1063C4⋊C4—1782no—
1064C4⋊C4—1782no—
1065C4⋊C4—1782no—
1066C4⋊C4—1782no—
1067C4⋊C4—1782no—
1068C4⋊C4—1782no—
1069C4⋊C4—1782no—
1070C4⋊C4—1782no—
1071C4⋊C4—1782no—
1072C4⋊C4—1782no—
1073C4⋊C4Q8×D8914yes—
1074C42—22no—
1075C42—41no—
1076C42—41no—
1077C42—41no—
1078C42—41no—
1079C42—894no—
1080C42—894no—
1081C42—894no—
1082C42—894no—
1083C42—3561no—
1084C42—3561no—
1085C42—3561no—
1086C42—3561no—
1087C42—3561no—
1088C42—3561no—
1089C42—3561no—
1090C42—3561no—
1091C42—3561no—
1092C42—3561no—
1093C42—1782no—
1094C42—1782no—
1095C42—1782no—
1096C42—1782no—
1097C42—1782no—
1098C42—1782no—
1099C42—1782no—
1100C42—1782no—
1101C42—1782no—
1102C42—1782no—
1103C42—1782no—
1104C42—1782no—
1105C23C24×D8911yescharacteristic
1106Q8—1788no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—892no—
1147C2×C4—892no—
1148C2×C4—892no—
1149C2×C4—892no—
1150C2×C4—892no—
1151C2×C4—892no—
1152C2×C4—892no—
1153C2×C4—892no—
1154C2×C4—892no—
1155C2×C4—892no—
1156C2×C4—892no—
1157C2×C4—1781no—
1158C2×C4—1781no—
1159C2×C4—1781no—
1160C2×C4—1781no—
1161C2×C4—1781no—
1162C2×C4—1781no—
1163C2×C4—1781no—
1164C2×C4—1781no—
1165C2×C4—1781no—
1166C2×C4—1781no—
1167C2×C4—1781no—
1168C2×C4—1781no—
1169C2×C4—1781no—
1170C2×C4—1781no—
1171C2×C4—1781no—
1172C2×C4—1781no—
1173C2×C4—1781no—
1174C2×C4—1781no—
1175C2×C4—1781no—
1176C2×C4—1781no—
1177C2×C4—1781no—
1178C2×C4—1781no—
1179C2×C4—1781no—
1180C2×C4—1781no—
1181C2×C4—1781no—
1182C2×C4—1781no—
1183C2×C4—1781no—
1184C2×C4—1781no—
1185C2×C4—1781no—
1186C2×C4—1781no—
1187C2×C4—1781no—
1188C2×C4—1781no—
1189C2×C4—1781no—
1190C2×C4—1781no—
1191C2×C4—1781no—
1192C2×C4—1781no—
1193C2×C4—1781no—
1194C2×C4C2×Q8×D8912yes—
1195C2×C4C2×Q8×D8912yes—
1196C2×C4C2×Q8×D8912yes—
1197C2×C4#41×D8912yes—
1198C2×C4#41×D8912yes—
1199C2×C4#41×D8912yes—
1200C22C22×Q8×D8911yescharacteristic
1201C22C2×#41×D8911yescharacteristic
1202C22C2×#41×D8911yescharacteristic
1203C22C2×#41×D8911yescharacteristic
1204C222−1+4×D8911yescharacteristic
1205C22#1915243311yescharacteristic
1206C22#1915243411yescharacteristic
1207C4—22no—
1208C4—22no—
1209C4—22no—
1210C4—22no—
1211C4—22no—
1212C4—22no—
1213C4—41no—
1214C4—41no—
1215C4—41no—
1216C4—41no—
1217C4—41no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—894no—
1223C4—894no—
1224C4—3561no—
1225C4—3561no—
1226C4—3561no—
1227C4—3561no—
1228C4—3561no—
1229C4—3561no—
1230C4—3561no—
1231C4—3561no—
1232C4—3561no—
1233C4—1782no—
1234C4—1782no—
1235C4—1782no—
1236C4—1782no—
1237C4—1782no—
1238C2#533×D8911yescharacteristic
1239C2#557×D8911yescharacteristic
1240C2#2603384311yescharacteristic
1241C2#2603384611yescharacteristic
1242C2#2603407211yescharacteristic
1243C2#2603421911yescharacteristic
1244C2#2603422211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutator, socle, prime radical, cosocleC23×C89C25
FittingC89×#2585C2
hypercenter#2585D89
hypocenterC89#36600
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2585

Complements

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

NH ≅ G/Ntype
654. C89#36600semidirect

Maximal subgroups

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

subgroupindex
#260286112
#260256562
#260256542
#260256522
#260256502
#260256472
#260256452
#260256432
#260254852
#260254832
#260254812
#260254792
#260252822
#260241122
#260241102
#260241082
#260241062
#260233512
#260233492
#260233452
#260233432
#260232062
#260228092
C4×#156680022
C4×#156679772
C89×#25852
#3660089