Finite Group Databasebeta

← #36768522

Subgroups — #36768522

Order 22784.

1410 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26028590C211yesmaximal, characteristic, complemented
2#26028576C211yesmaximal, characteristic
3#26027812C211yesmaximal, characteristic, complemented
4#26027789C211yesmaximal, characteristic, complemented
5#26027692C211yesmaximal, characteristic, complemented
6#26027676C211yesmaximal, characteristic, complemented
7#26027662C211yesmaximal, characteristic, complemented
8#26027652C211yesmaximal, characteristic, complemented
9#26027615C211yesmaximal, characteristic, complemented
10#26027608C211yesmaximal, characteristic, complemented
11#26027506C211yesmaximal, characteristic
12#26027487C211yesmaximal, characteristic
13#26027422C211yesmaximal, characteristic, complemented
14#26027396C211yesmaximal, characteristic
15#26027330C211yesmaximal, characteristic, complemented
16#26027325C211yesmaximal, characteristic, complemented
17#26027304C211yesmaximal, characteristic
18#26026427C211yesmaximal, characteristic, complemented
19#26026409C211yesmaximal, characteristic
20#26025781C211yesmaximal, characteristic, complemented
21#26025694C211yesmaximal, characteristic, complemented
22#26025692C211yesmaximal, characteristic, complemented
23#26025566C211yesmaximal, characteristic, complemented
24#26025125C211yesmaximal, characteristic, complemented
25#26025120C211yesmaximal, characteristic, complemented
26#26025057C211yesmaximal, characteristic, complemented
27#26025034C211yesmaximal, characteristic, complemented
28#26023041C211yesmaximal, characteristic
29#26023004C211yesmaximal, characteristic, complemented
30#26022649C211yesmaximal, characteristic, complemented
31C89×#2758C211yesmaximal, characteristic, complemented
32C2×#15667997C2211yescharacteristic
33C2×#15667992C2211yescharacteristic
34C2×C42×D89C2211yescharacteristic
35C89⋊#401C2211yescharacteristic
36C89⋊#401C2211yescharacteristic
37#19151540C2211yescharacteristic
38#19151540C2211yescharacteristic
39#19151540C2211yescharacteristic
40#19151539C2211yescharacteristic
41#19151539C2211yescharacteristic
42#19151539C2211yescharacteristic
43#19151539C2211yescharacteristic
44#19151539C2211yescharacteristic
45#19151538C2211yescharacteristic
46#19151538C2211yescharacteristic
47#19151537C2211yescharacteristic
48#19151537C2211yescharacteristic
49#19151536C2211yescharacteristic
50#19151533C2211yescharacteristic
51#19151533C2211yescharacteristic
52#19151532C2211yescharacteristic
53#19151531C2211yescharacteristic
54#19151530C2211yescharacteristic
55#19151529C2211yescharacteristic
56#19151528C2211yescharacteristic
57#19151527C2211yescharacteristic
58#19151527C2211yescharacteristic
59#19151527C2211yescharacteristic
60#19151527C2211yescharacteristic
61#19151527C2211yescharacteristic
62#19151527C2211yescharacteristic
63#19151525C2211yescharacteristic
64#19151520C2211yescharacteristic
65#19151520C2211yescharacteristic
66#19151519C2211yescharacteristic
67#19151519C2211yescharacteristic
68#19151518C2211yescharacteristic
69#19151517C2211yescharacteristic
70#19151516C2211yescharacteristic
71#19151516C2211yescharacteristic
72#19151511C2211yescharacteristic
73#19151511C2211yescharacteristic
74#19151511C2211yescharacteristic
75#19151509C2211yescharacteristic
76#19151509C2211yescharacteristic
77#19151505C2211yescharacteristic
78#19151504C2211yescharacteristic
79#19151503C2211yescharacteristic
80#19151503C2211yescharacteristic
81#19151502C2211yescharacteristic
82#19151502C2211yescharacteristic
83#19151502C2211yescharacteristic
84#19151502C2211yescharacteristic
85#19151500C2211yescharacteristic
86#19151497C2211yescharacteristic
87#19151495C2211yescharacteristic
88#19151495C2211yescharacteristic
89#19151495C2211yescharacteristic
90#19151495C2211yescharacteristic
91#19151494C2211yescharacteristic
92#19151490C2211yescharacteristic
93#19151490C2211yescharacteristic
94#19151490C2211yescharacteristic
95#19151490C2211yescharacteristic
96#19151490C2211yescharacteristic
97#19151490C2211yescharacteristic
98#19151490C2211yescharacteristic
99#19151490C2211yescharacteristic
100#19151489C2211yescharacteristic
101#19151489C2211yescharacteristic
102#19151489C2211yescharacteristic
103#19151488C2211yescharacteristic
104#19151488C2211yescharacteristic
105#19151488C2211yescharacteristic
106#19151487C2211yescharacteristic
107#19151487C2211yescharacteristic
108#19151487C2211yescharacteristic
109#19151487C2211yescharacteristic
110#19151485C2211yescharacteristic
111#19151485C2211yescharacteristic
112#19151485C2211yescharacteristic
113#19151485C2211yescharacteristic
114#19151484C2211yescharacteristic
115#19151484C2211yescharacteristic
116#19151484C2211yescharacteristic
117#19151484C2211yescharacteristic
118#19151483C2211yescharacteristic
119#19151483C2211yescharacteristic
120#19151483C2211yescharacteristic
121#19151483C2211yescharacteristic
122#19151482C2211yescharacteristic
123#19151482C2211yescharacteristic
124#19151482C2211yescharacteristic
125#19151481C2211yescharacteristic
126#19151481C2211yescharacteristic
127#19151481C2211yescharacteristic
128#19151480C2211yescharacteristic
129#19151480C2211yescharacteristic
130#19151480C2211yescharacteristic
131#19151480C2211yescharacteristic
132#19151480C2211yescharacteristic
133#19151480C2211yescharacteristic
134#19151479C2211yescharacteristic
135#19151479C2211yescharacteristic
136#19151476C2211yescharacteristic
137#19151476C2211yescharacteristic
138#19151476C2211yescharacteristic
139#19151472C2211yescharacteristic
140#19151469C2211yescharacteristic
141#19151469C2211yescharacteristic
142#19151469C2211yescharacteristic
143#19151469C2211yescharacteristic
144#19151469C2211yescharacteristic
145#19151469C2211yescharacteristic
146#19151466C2211yescharacteristic
147#19151465C2211yescharacteristic
148#19151465C2211yescharacteristic
149#19151463C2211yescharacteristic
150#19151462C2211yescharacteristic
151#19151462C2211yescharacteristic
152#19151460C2211yescharacteristic
153#19151460C2211yescharacteristic
154#19151460C2211yescharacteristic
155#19151460C2211yescharacteristic
156#19151460C2211yescharacteristic
157#19151460C2211yescharacteristic
158#19151457C2211yescharacteristic
159#19151457C2211yescharacteristic
160#19151455C2211yescharacteristic
161#19151455C2211yescharacteristic
162C4⋊C4×Dic89C2211yescharacteristic
163C4×#13083553C2211yescharacteristic
164C4×C4⋊Dic89C2211yescharacteristic
165#19151449C2211yescharacteristic
166#19151449C2211yescharacteristic
167#19151445C2211yescharacteristic
168#19151445C2211yescharacteristic
169#19151445C2211yescharacteristic
170#19151443C2211yescharacteristic
171#19151443C2211yescharacteristic
172#400×C89C2211yescharacteristic
173#400×C89C2211yescharacteristic
174#400×C89C2211yescharacteristic
175#400×C89C2211yescharacteristic
176#400×C89C2211yescharacteristic
177#395×C89C2211yescharacteristic
178#391×C89C2211yescharacteristic
179#391×C89C2211yescharacteristic
180#389×C89C2211yescharacteristic
181#387×C89C2211yescharacteristic
182#387×C89C2211yescharacteristic
183#387×C89C2211yescharacteristic
184#387×C89C2211yescharacteristic
185#383×C89C2211yescharacteristic
186#383×C89C2211yescharacteristic
187C22×Dic178C2311yescharacteristic
188C22×Dic178C2311yescharacteristic
189C22×D356C2311yescharacteristic
190C22×C4×D89C2311yescharacteristic
191C22×C4×D89C2311yescharacteristic
192C22×C4×D89C2311yescharacteristic
193C22×C4×D89C2311yescharacteristic
194#15667997—24no—
195#15667992—24no—
196C2×C4⋊Dic89C2311yescharacteristic
197C2×C4⋊Dic89C2311yescharacteristic
198C2×C4⋊Dic89C2311yescharacteristic
199C2×C4⋊Dic89C2311yescharacteristic
200C2×C4⋊Dic89C2311yescharacteristic
201C2×C4⋊Dic89C2311yescharacteristic
202C2×C4⋊Dic89C2311yescharacteristic
203C2×C4⋊Dic89C2311yescharacteristic
204C2×C4⋊Dic89C2311yescharacteristic
205C2×#13083553C2311yescharacteristic
206C2×#13083553C2311yescharacteristic
207C2×#13083553C2311yescharacteristic
208C2×#13083553C2311yescharacteristic
209C2×#13083553C2311yescharacteristic
210C2×#13083553C2311yescharacteristic
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×#13083551C2311yescharacteristic
224C2×#13083551C2311yescharacteristic
225C2×#13083551C2311yescharacteristic
226C2×#13083551C2311yescharacteristic
227C2×#13083551C2311yescharacteristic
228C2×#13083551C2311yescharacteristic
229C2×#13083551C2311yescharacteristic
230C2×#13083551C2311yescharacteristic
231C2×#13083551C2311yescharacteristic
232C2×#13083551C2311yescharacteristic
233C2×#13083551C2311yescharacteristic
234C2×#13083551C2311yescharacteristic
235C2×#13083551C2311yescharacteristic
236C2×#13083551C2311yescharacteristic
237C2×#13083551C2311yescharacteristic
238C2×#13083551C2311yescharacteristic
239C2×#13083551C2311yescharacteristic
240C2×#13083551C2311yescharacteristic
241C2×#13083551C2311yescharacteristic
242C2×#13083551C2311yescharacteristic
243C2×#13083551C2311yescharacteristic
244C2×#13083551C2311yescharacteristic
245C2×#13083551C2311yescharacteristic
246C2×#13083551C2311yescharacteristic
247C2×C4×Dic89C2311yescharacteristic
248C2×C4×Dic89C2311yescharacteristic
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
259C42×D89—24no—
260#15667919C2311yescharacteristic
261#15667919C2311yescharacteristic
262#15667919C2311yescharacteristic
263#15667919C2311yescharacteristic
264#15667919C2311yescharacteristic
265#15667919C2311yescharacteristic
266#15667919C2311yescharacteristic
267#15667919C2311yescharacteristic
268#15667919C2311yescharacteristic
269#15667919C2311yescharacteristic
270#15667919C2311yescharacteristic
271#15667919C2311yescharacteristic
272#15667919C2311yescharacteristic
273#15667919C2311yescharacteristic
274#15667919C2311yescharacteristic
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
310C22×Q8×C89C2311yescharacteristic
311C2×C4⋊C4×C89C2311yescharacteristic
312C2×C4⋊C4×C89C2311yescharacteristic
313C2×C4⋊C4×C89C2311yescharacteristic
314C2×C4⋊C4×C89C2311yescharacteristic
315C2×C4⋊C4×C89C2311yescharacteristic
316C2×C4⋊C4×C89C2311yescharacteristic
317C2×C4⋊C4×C89C2311yescharacteristic
318C2×C4⋊C4×C89C2311yescharacteristic
319C2×C4⋊C4×C89C2311yescharacteristic
320C2×C42×C89C2311yescharacteristic
321C2×C42×C89C2311yescharacteristic
322C2×C42×C89C2311yescharacteristic
323#95×C89C2311yescharacteristic
324#95×C89C2311yescharacteristic
325#95×C89C2311yescharacteristic
326#95×C89C2311yescharacteristic
327#95×C89C2311yescharacteristic
328#95×C89C2311yescharacteristic
329#95×C89C2311yescharacteristic
330#95×C89C2311yescharacteristic
331#95×C89C2311yescharacteristic
332#95×C89C2311yescharacteristic
333#95×C89C2311yescharacteristic
334#95×C89C2311yescharacteristic
335#95×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
345C23×D89C2411yescharacteristic
346C23×D89C2411yescharacteristic
347C2×Dic178—22no—
348C2×Dic178—41no—
349C2×Dic178—41no—
350C2×Dic178—41no—
351C2×Dic178—41no—
352C2×Dic178—41no—
353C2×D356—22no—
354C2×D356—41no—
355C2×D356—41no—
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
370C2×C4×D89—22no—
371C2×C4×D89—22no—
372C2×C4×D89—22no—
373C2×C4×D89—41no—
374C2×C4×D89—41no—
375C2×C4×D89—41no—
376C2×C4×D89—41no—
377C2×C4×D89—41no—
378C2×C4×D89—41no—
379C2×C4×D89—41no—
380C2×C4×D89—41no—
381C2×C4×D89#4114yes—
382C4⋊Dic89—22no—
383C4⋊Dic89—22no—
384C4⋊Dic89—41no—
385C4⋊Dic89—41no—
386C4⋊Dic89—41no—
387C4⋊Dic89—41no—
388C4⋊Dic89—41no—
389C4⋊Dic89—41no—
390C4⋊Dic89—41no—
391#13083553—22no—
392#13083553—22no—
393#13083553—22no—
394#13083553—22no—
395#13083553—41no—
396#13083553—41no—
397#13083553—41no—
398#13083553—41no—
399#13083553—41no—
400#13083553—41no—
401#13083553—41no—
402#13083553—41no—
403#13083553—41no—
404#13083553—41no—
405#13083553—41no—
406#13083553—41no—
407#13083553—41no—
408#13083553—41no—
409#13083551—22no—
410#13083551—22no—
411#13083551—22no—
412#13083551—22no—
413#13083551—22no—
414#13083551—22no—
415#13083551—41no—
416#13083551—41no—
417#13083551—41no—
418#13083551—41no—
419#13083551—41no—
420#13083551—41no—
421#13083551—41no—
422#13083551—41no—
423#13083551—41no—
424#13083551—41no—
425#13083551—41no—
426#13083551—41no—
427#13083551—41no—
428#13083551—41no—
429#13083551—41no—
430#13083551—41no—
431#13083551—41no—
432#13083551—41no—
433C4×Dic89—22no—
434C4×Dic89—22no—
435C4×Dic89—22no—
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×Dic89—41no—
445C2×Q8×C89—41no—
446C2×Q8×C89—41no—
447C2×Q8×C89—41no—
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—41no—
466C4⋊C4×C89—41no—
467C4⋊C4×C89—41no—
468C4⋊C4×C89—41no—
469C4⋊C4×C89—41no—
470C4⋊C4×C89—41no—
471C4⋊C4×C89—41no—
472C42×C89—22no—
473C42×C89—41no—
474C42×C89—41no—
475C23×C89C2511yescharacteristic
476C22×D89—21no—
477C22×D89—21no—
478C22×D89—21no—
479C22×D89—21no—
480C22×D89—21no—
481C22×D89—21no—
482C22×D89—21no—
483C22×D89—21no—
484C22×D89—21no—
485C22×D89—21no—
486C22×D89—21no—
487C22×D89—21no—
488C22×D89—21no—
489C22×D89C2×#4112yes—
490Q8×C89—82no—
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×C89—21no—
523C2×C4×C89—21no—
524C2×C4×C89—21no—
525C2×C4×C89—21no—
526C2×C4×C89—21no—
527C2×C4×C89—21no—
528C2×C4×C89—21no—
529C2×C4×C89—21no—
530C2×C4×C89—21no—
531C2×C4×C89—21no—
532C2×C4×C89—21no—
533C2×C4×C89—21no—
534C2×C4×C89—21no—
535C2×C4×C89C2×#4112yes—
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×Dic89—21no—
566C2×Dic89—21no—
567C2×Dic89—21no—
568C2×Dic89—21no—
569C2×Dic89—21no—
570C2×Dic89—21no—
571C2×Dic89—21no—
572C2×Dic89—21no—
573C2×Dic89—21no—
574C2×Dic89—21no—
575C2×Dic89—21no—
576C2×Dic89C2×#4112yes—
577C2×Dic892−1+412yes—
578D356—82no—
579C4×D89—44no—
580C4×D89—44no—
581C4×D89—44no—
582C4×D89—82no—
583Dic178—82no—
584Dic178—82no—
585C22×C89C22×#4111yescharacteristic
586C22×C89C2×2−1+411yescharacteristic
587C22×C89#58511yescharacteristic
588C22×C89#58511yescharacteristic
589C22×C89#58511yescharacteristic
590C22×C89#58511yescharacteristic
591C22×C89#58511yescharacteristic
592C2×D89—22no—
593C2×D89—22no—
594C2×D89—22no—
595C2×D89—41no—
596C2×D89—41no—
597C2×D89—41no—
598C2×D89—41no—
599C2×D89—41no—
600C2×D89—41no—
601C2×D89—41no—
602C2×D89—41no—
603C2×D89—41no—
604C2×D89—41no—
605C2×D89—41no—
606C4×C89—22no—
607C4×C89—41no—
608C4×C89—41no—
609C4×C89—41no—
610C4×C89—41no—
611C4×C89—41no—
612C4×C89—41no—
613C4×C89—41no—
614C4×C89—41no—
615C4×C89—41no—
616C4×C89—41no—
617C4×C89—41no—
618C4×C89—41no—
619C4×C89—41no—
620C4×C89—41no—
621Dic89—22no—
622Dic89—22no—
623Dic89—41no—
624Dic89—41no—
625Dic89—41no—
626Dic89—41no—
627Dic89—41no—
628Dic89—41no—
629Dic89—41no—
630Dic89—41no—
631Dic89—41no—
632Dic89—41no—
633Dic89—41no—
634Dic89—41no—
635#36984—891nomaximal, Sylow
636C2×C89#345511yescharacteristic
637C2×C89#349111yescharacteristic
638C2×C89#349511yescharacteristic
639C2×C89#355711yescharacteristic
640C2×C89#356511yescharacteristic
641C2×C89#356611yescharacteristic
642C2×C89#356811yescharacteristic
643D89—42no—
644D89—81no—
645#2855—891no—
646#2853—891no—
647#2774—891no—
648#2773—891no—
649#2765—891no—
650#2764—891no—
651#2763—891no—
652#2762—891no—
653#2759—891no—
654#2758—891no—
655#2758D8911yescharacteristic, complemented
656#2751—891no—
657#2750—891no—
658#2745—891no—
659#2743—891no—
660#2739—891no—
661#2738—891no—
662#2737—891no—
663#2665—891no—
664#2663—891no—
665#2596—891no—
666#2588—891no—
667#2588—891no—
668#2577—891no—
669#2533—891no—
670#2532—891no—
671#2528—891no—
672#2527—891no—
673#2335—891no—
674#2332—891no—
675#2283—891no—
676C89#3698411yescharacteristic, complemented, Sylow
677C2×#123—891no—
678C2×C22⋊Q8—891no—
679C22×C42—891no—
680#401—891no—
681#401—891no—
682#400—891no—
683#400—891no—
684#400—891no—
685#400—891no—
686#400—891no—
687#400—891no—
688#400—891no—
689#400—891no—
690#400—891no—
691#400—891no—
692#400—891no—
693#400—891no—
694#400—891no—
695#400C2×D8911yescharacteristic
696#400C2×D8911yescharacteristic
697#400C2×D8911yescharacteristic
698#400C2×D8911yescharacteristic
699#400C2×D8911yescharacteristic
700#399—891no—
701#399—891no—
702#398—891no—
703#398—891no—
704#398—891no—
705#398—891no—
706#398—891no—
707#397—891no—
708#397—891no—
709#397—891no—
710#397—891no—
711#397—891no—
712#397—891no—
713#397—891no—
714#396—891no—
715#396—891no—
716#395—891no—
717#395—891no—
718#395—891no—
719#395—891no—
720#395C2×D8911yescharacteristic
721#394—891no—
722#394—891no—
723#393—891no—
724#393—891no—
725#393—891no—
726#393—891no—
727#393—891no—
728#391—891no—
729#391—891no—
730#391—891no—
731#391—891no—
732#391—891no—
733#391—891no—
734#391—891no—
735#391—891no—
736#391C2×D8911yescharacteristic
737#391C2×D8911yescharacteristic
738#390—891no—
739#389—891no—
740#389—891no—
741#389—891no—
742#389—891no—
743#389—891no—
744#389—891no—
745#389C2×D8911yescharacteristic
746#388—891no—
747#388—891no—
748#388—891no—
749#388—891no—
750#388—891no—
751#388—891no—
752#388—891no—
753#388—891no—
754#388—891no—
755#388—891no—
756#388—891no—
757#388—891no—
758#388—891no—
759#388—891no—
760#388—891no—
761#388—891no—
762#388—891no—
763#388—891no—
764#387—891no—
765#387—891no—
766#387—891no—
767#387—891no—
768#387—891no—
769#387—891no—
770#387—891no—
771#387—891no—
772#387—891no—
773#387—891no—
774#387—891no—
775#387—891no—
776#387—891no—
777#387—891no—
778#387—891no—
779#387—891no—
780#387—891no—
781#387—891no—
782#387—891no—
783#387—891no—
784#387—891no—
785#387—891no—
786#387—891no—
787#387—891no—
788#387—891no—
789#387—891no—
790#387C2×D8911yescharacteristic
791#387C2×D8911yescharacteristic
792#387C2×D8911yescharacteristic
793#387C2×D8911yescharacteristic
794#386—891no—
795#386—891no—
796#386—891no—
797#385—891no—
798#385—891no—
799#385—891no—
800#385—891no—
801#385—891no—
802#385—891no—
803#385—891no—
804#383—891no—
805#383—891no—
806#383—891no—
807#383C2×D8911yescharacteristic
808#383C2×D8911yescharacteristic
809#382—891no—
810#382—891no—
811#382—891no—
812#381—891no—
813#381—891no—
814#381—891no—
815#381—891no—
816#381—891no—
817#381—891no—
818#380—891no—
819#380—891no—
820#380—891no—
821#380—891no—
822C4×C4⋊C4—891no—
823C4×C4⋊C4—891no—
824C4×C4⋊C4—891no—
825C4×C4⋊C4—891no—
826C4×C4⋊C4—891no—
827C4×C22⋊C4—891no—
828C4×C22⋊C4—891no—
829C4×C22⋊C4—891no—
830#376—891no—
831#376—891no—
832C22×Q8—891no—
833C22×Q8—891no—
834C22×Q8C22×D8911yescharacteristic
835C22×D4—891no—
836C23×C4—891no—
837C23×C4—891no—
838C23×C4—891no—
839C23×C4—891no—
840#123—1784no—
841C22⋊Q8—1784no—
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⋊C4C22×D8911yescharacteristic
870C2×C4⋊C4C22×D8911yescharacteristic
871C2×C4⋊C4C22×D8911yescharacteristic
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×C22⋊C4—891no—
879C2×C22⋊C4—891no—
880C2×C22⋊C4—891no—
881C2×C22⋊C4—891no—
882C2×C22⋊C4—891no—
883C2×C22⋊C4—891no—
884C2×C22⋊C4—891no—
885C2×C22⋊C4—891no—
886C2×C22⋊C4—891no—
887C2×C22⋊C4—891no—
888C2×C22⋊C4—891no—
889C2×C22⋊C4—891no—
890C2×C22⋊C4—891no—
891C2×C22⋊C4—891no—
892C2×C22⋊C4—891no—
893C2×C22⋊C4—891no—
894C2×C22⋊C4—891no—
895C2×C22⋊C4—891no—
896C2×C22⋊C4—891no—
897C2×C22⋊C4—891no—
898C2×C22⋊C4—891no—
899C2×C22⋊C4—891no—
900C2×C22⋊C4—891no—
901C2×C22⋊C4—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×C42—891no—
913C2×C42—891no—
914C2×C42—1784no—
915C2×C42C22×D8911yescharacteristic
916C2×C42C22×D8911yescharacteristic
917C2×C42C22×D8911yescharacteristic
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#95—891no—
960#95—891no—
961#95—891no—
962#95—891no—
963#95—891no—
964#95—891no—
965#95—891no—
966#95—891no—
967#95—891no—
968#95C22×D8911yescharacteristic
969#95C22×D8911yescharacteristic
970#95C22×D8911yescharacteristic
971#95C22×D8911yescharacteristic
972#95C22×D8911yescharacteristic
973#95C22×D8911yescharacteristic
974#95C22×D8911yescharacteristic
975#95C22×D8911yescharacteristic
976#95C22×D8911yescharacteristic
977#95C22×D8911yescharacteristic
978#95C22×D8911yescharacteristic
979#95C22×D8911yescharacteristic
980#95C22×D8911yescharacteristic
981#95C22×D8911yescharacteristic
982#95C22×D8911yescharacteristic
983#95C22×D8911yescharacteristic
984#95C22×D8911yescharacteristic
985#95C22×D8911yescharacteristic
986#95C22×D8911yescharacteristic
987#95C22×D8911yescharacteristic
988#95C22×D8911yescharacteristic
989#95C22×D8911yescharacteristic
990C24—891no—
991C24—891no—
992C2×Q8—41no—
993C2×Q8—41no—
994C2×Q8—41no—
995C2×Q8—3561no—
996C2×Q8—3561no—
997C2×Q8—3561no—
998C2×Q8—3561no—
999C2×Q8—3561no—
1000C2×Q8—1782no—
1001C2×D4—3561no—
1002C2×D4—3561no—
1003C2×D4—1782no—
1004C22×C4—891no—
1005C22×C4—891no—
1006C22×C4—894no—
1007C22×C4—891no—
1008C22×C4—891no—
1009C22×C4—891no—
1010C22×C4—891no—
1011C22×C4—891no—
1012C22×C4—891no—
1013C22×C4—891no—
1014C22×C4—891no—
1015C22×C4—891no—
1016C22×C4—891no—
1017C22×C4—891no—
1018C22×C4—891no—
1019C22×C4—3561no—
1020C22×C4—3561no—
1021C22×C4—3561no—
1022C22×C4—3561no—
1023C22×C4—3561no—
1024C22×C4—3561no—
1025C22×C4—3561no—
1026C22×C4—3561no—
1027C22×C4—1782no—
1028C22×C4—1782no—
1029C22×C4—1782no—
1030C22×C4C23×D8911yescharacteristic
1031C22×C4C23×D8911yescharacteristic
1032C22×C4C23×D8911yescharacteristic
1033C22×C4C23×D8911yescharacteristic
1034C22×C4C23×D8911yescharacteristic
1035C22×C4C23×D8911yescharacteristic
1036C22×C4C23×D8911yescharacteristic
1037C22×C4C23×D8911yescharacteristic
1038C22×C4C23×D8911yescharacteristic
1039C22×C4C23×D8911yescharacteristic
1040C22×C4C23×D8911yescharacteristic
1041C22×C4C23×D8911yescharacteristic
1042C22×C4C23×D8911yescharacteristic
1043C22×C4C23×D8911yescharacteristic
1044C22×C4C23×D8911yescharacteristic
1045C4⋊C4—22no—
1046C4⋊C4—22no—
1047C4⋊C4—41no—
1048C4⋊C4—41no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—3561no—
1055C4⋊C4—3561no—
1056C4⋊C4—3561no—
1057C4⋊C4—3561no—
1058C4⋊C4—3561no—
1059C4⋊C4—3561no—
1060C4⋊C4—3561no—
1061C4⋊C4—3561no—
1062C4⋊C4—3561no—
1063C4⋊C4—3561no—
1064C4⋊C4—3561no—
1065C4⋊C4—3561no—
1066C4⋊C4—3561no—
1067C4⋊C4—3561no—
1068C4⋊C4—3561no—
1069C4⋊C4—3561no—
1070C4⋊C4—3561no—
1071C4⋊C4—3561no—
1072C4⋊C4—3561no—
1073C4⋊C4—3561no—
1074C4⋊C4—3561no—
1075C4⋊C4—1782no—
1076C4⋊C4—1782no—
1077C4⋊C4—1782no—
1078C4⋊C4—1782no—
1079C4⋊C4—1782no—
1080C4⋊C4—1782no—
1081C22⋊C4—3561no—
1082C22⋊C4—3561no—
1083C22⋊C4—3561no—
1084C22⋊C4—3561no—
1085C22⋊C4—3561no—
1086C22⋊C4—3561no—
1087C22⋊C4—3561no—
1088C22⋊C4—3561no—
1089C22⋊C4—3561no—
1090C22⋊C4—3561no—
1091C22⋊C4—3561no—
1092C22⋊C4—3561no—
1093C22⋊C4—3561no—
1094C22⋊C4—3561no—
1095C22⋊C4—3561no—
1096C22⋊C4—3561no—
1097C22⋊C4—3561no—
1098C22⋊C4—3561no—
1099C22⋊C4—1782no—
1100C22⋊C4—1782no—
1101C22⋊C4—1782no—
1102C22⋊C4—1782no—
1103C22⋊C4—1782no—
1104C22⋊C4—1782no—
1105C42—22no—
1106C42—41no—
1107C42—41no—
1108C42—3561no—
1109C42—3561no—
1110C42—3561no—
1111C42—3561no—
1112C42—3561no—
1113C42—3561no—
1114C42—3561no—
1115C42—3561no—
1116C42—3561no—
1117C42—1782no—
1118C42—1782no—
1119C42—1782no—
1120C23—892no—
1121C23—1781no—
1122C23—1781no—
1123C23—1781no—
1124C23—1781no—
1125C23—1781no—
1126C23—1781no—
1127C23—1781no—
1128C23—1781no—
1129C23—1781no—
1130C23—1781no—
1131C23—1781no—
1132C23—1781no—
1133C23—1781no—
1134C23C24×D8911yescharacteristic
1135Q8—82no—
1136Q8—7122no—
1137Q8—7122no—
1138D4—7122no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—892no—
1184C2×C4—892no—
1185C2×C4—3564no—
1186C2×C4—3564no—
1187C2×C4—3564no—
1188C2×C4—1781no—
1189C2×C4—1781no—
1190C2×C4—1781no—
1191C2×C4—1781no—
1192C2×C4—1781no—
1193C2×C4—1781no—
1194C2×C4—1781no—
1195C2×C4—1781no—
1196C2×C4—1781no—
1197C2×C4—1781no—
1198C2×C4—1781no—
1199C2×C4—1781no—
1200C2×C4—1781no—
1201C2×C4—1781no—
1202C2×C4—1781no—
1203C2×C4—1781no—
1204C2×C4—1781no—
1205C2×C4—1781no—
1206C2×C4—1781no—
1207C2×C4—1781no—
1208C2×C4—1781no—
1209C2×C4—1781no—
1210C2×C4—1781no—
1211C2×C4—1781no—
1212C2×C4—1781no—
1213C2×C4—1781no—
1214C2×C4—1781no—
1215C2×C4—1781no—
1216C2×C4—1781no—
1217C2×C4—1781no—
1218C2×C4—1781no—
1219C2×C4—1781no—
1220C2×C4—1781no—
1221C2×C4—1781no—
1222C2×C4—1781no—
1223C2×C4—1781no—
1224C2×C4—1781no—
1225C2×C4—1781no—
1226C2×C4—1781no—
1227C2×C4—1781no—
1228C2×C4—7122no—
1229C2×C4#41×D8912yes—
1230C22—3561no—
1231C22—3561no—
1232C22—3561no—
1233C22—3561no—
1234C22—3561no—
1235C22—3561no—
1236C22—3561no—
1237C22—3561no—
1238C22—3561no—
1239C22—3561no—
1240C22—3561no—
1241C22—1782no—
1242C22—1782no—
1243C22—1782no—
1244C22C2×#41×D8911yescharacteristic
1245C222−1+4×D8911yescharacteristic
1246C22#1915243311yescharacteristic
1247C22#1915243411yescharacteristic
1248C22#1915243411yescharacteristic
1249C22#1915243511yescharacteristic
1250C22#1915243511yescharacteristic
1251C4—22no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—3561no—
1267C4—3561no—
1268C4—3561no—
1269C4—3561no—
1270C4—3561no—
1271C4—3561no—
1272C4—3561no—
1273C4—3561no—
1274C4—3561no—
1275C4—3561no—
1276C4—3561no—
1277C4—3561no—
1278C4—1782no—
1279C4—1782no—
1280C2—3562no—
1281C2—7121no—
1282C2#2603363911yescharacteristic
1283C2#2603394711yescharacteristic
1284C2#2603399711yescharacteristic
1285C2#2603475211yescharacteristic
1286C2#2603489211yescharacteristic
1287C2#2603493511yescharacteristic
1288C2#2603494311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutator, socle, cosocleC23×C89C25
FittingC89×#2758C2
prime radicalC22×D356C23
hypercenter#2758D89
hypocenterC89#36984
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2758

Complements

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

NH ≅ G/Ntype
1. #26028590C2semidirect
3. #26027812C2semidirect
4. #26027789C2semidirect
5. #26027692C2semidirect
6. #26027676C2semidirect
7. #26027662C2semidirect
8. #26027652C2semidirect
9. #26027615C2semidirect
10. #26027608C2semidirect
13. #26027422C2semidirect
15. #26027330C2semidirect
16. #26027325C2semidirect
18. #26026427C2semidirect
20. #26025781C2semidirect
21. #26025694C2semidirect
22. #26025692C2semidirect
23. #26025566C2semidirect
24. #26025125C2semidirect
25. #26025120C2semidirect
26. #26025057C2semidirect
27. #26025034C2semidirect
29. #26023004C2semidirect
30. #26022649C2semidirect
31. C89×#2758C2semidirect
655. #2758D89semidirect
676. C89#36984semidirect

Maximal subgroups

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

subgroupindex
#260285902
#260285762
#260278122
#260277892
#260276922
#260276762
#260276622
#260276522
#260276152
#260276082
#260275062
#260274872
#260274222
#260273962
#260273302
#260273252
#260273042
#260264272
#260264092
#260257812
#260256942
#260256922
#260255662
#260251252
#260251202
#260250572
#260250342
#260230412
#260230042
#260226492
C89×#27582
#3698489