Finite Group Databasebeta

← #36726598

Subgroups — #36726598

Order 22784.

2296 conjugacy classes of subgroups.

The subgroup lattice has 1574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26025796C211yesmaximal, characteristic, complemented
2#26025769C211yesmaximal, characteristic, complemented
3#26025704C211yesmaximal, characteristic, complemented
4#26025677C211yesmaximal, characteristic, complemented
5#26025579C211yesmaximal, characteristic, complemented
6#26025552C211yesmaximal, characteristic, complemented
7#26025382C211yesmaximal, characteristic, complemented
8#26025355C211yesmaximal, characteristic, complemented
9#26024810C211yesmaximal, characteristic, complemented
10#26024753C211yesmaximal, characteristic, complemented
11#26024505C211yesmaximal, characteristic, complemented
12#26024380C211yesmaximal, characteristic, complemented
13#26024082C211yesmaximal, characteristic, complemented
14#26023794C211yesmaximal, characteristic
15#26023708C211yesmaximal, characteristic, complemented
16#26023551C211yesmaximal, characteristic, complemented
17#26023537C211yesmaximal, characteristic, complemented
18#26023510C211yesmaximal, characteristic, complemented
19#26023495C211yesmaximal, characteristic, complemented
20#26022802C211yesmaximal, characteristic, complemented
21#26022793C211yesmaximal, characteristic, complemented
22#26022784C211yesmaximal, characteristic, complemented
23#26022769C211yesmaximal, characteristic, complemented
24#121×Dic89C211yesmaximal, characteristic, complemented
25#26022762C211yesmaximal, characteristic, complemented
26#26022757C211yesmaximal, characteristic, complemented
27#26022757C211yesmaximal, characteristic, complemented
28#26022692C211yesmaximal, characteristic, complemented
29C4×D4×Dic89C211yesmaximal, characteristic, complemented
30C2×#19151445C211yesmaximal, characteristic, complemented
31C89×#2444C211yesmaximal, characteristic, complemented
32C23×C4×D89C2211yescharacteristic
33C2×#15668007C2211yescharacteristic
34C2×#15667998C2211yescharacteristic
35C2×#15667995C2211yescharacteristic
36C2×#15667989C2211yescharacteristic
37C2×#15667984C2211yescharacteristic
38C2×#15667980C2211yescharacteristic
39C2×#15667980C2211yescharacteristic
40C2×#15667977C2211yescharacteristic, complemented
41C2×D4×Dic89C2211yescharacteristic
42C2×D4×Dic89C2211yescharacteristic
43C2×D4×Dic89C2211yescharacteristic
44C2×D4×Dic89C2211yescharacteristic, complemented
45C2×#15667972C2211yescharacteristic
46C2×#15667972C2211yescharacteristic
47C2×#15667972C2211yescharacteristic
48C2×#15667972C2211yescharacteristic
49C2×#15667968C2211yescharacteristic, complemented
50C22×#13083551C2211yescharacteristic
51C22×#13083551C2211yescharacteristic
52C22×C4×Dic89C2211yescharacteristic
53C22×C4×Dic89C2211yescharacteristic
54C22×C4×Dic89C2211yescharacteristic, complemented
55C89⋊#401C2211yescharacteristic, complemented
56#19151540C2211yescharacteristic, complemented
57#19151539C2211yescharacteristic, complemented
58#19151539C2211yescharacteristic, complemented
59#19151539C2211yescharacteristic, complemented
60#19151538C2211yescharacteristic, complemented
61#19151533C2211yescharacteristic
62#19151532C2211yescharacteristic, complemented
63#19151532C2211yescharacteristic, complemented
64#19151527C2211yescharacteristic
65#19151527C2211yescharacteristic
66#19151526C2211yescharacteristic, complemented
67#19151526C2211yescharacteristic, complemented
68#19151525C2211yescharacteristic
69#19151524C2211yescharacteristic
70#19151524C2211yescharacteristic
71#19151521C2211yescharacteristic, complemented
72#19151520C2211yescharacteristic
73#19151520C2211yescharacteristic
74#19151514C2211yescharacteristic
75#19151514C2211yescharacteristic
76#19151513C2211yescharacteristic
77#19151513C2211yescharacteristic
78#19151513C2211yescharacteristic
79#19151513C2211yescharacteristic
80#19151511C2211yescharacteristic
81#19151510C2211yescharacteristic, complemented
82#19151506C2211yescharacteristic
83#19151502C2211yescharacteristic, complemented
84#19151502C2211yescharacteristic, complemented
85#19151501C2211yescharacteristic, complemented
86#19151498C2211yescharacteristic
87#19151498C2211yescharacteristic
88#19151497C2211yescharacteristic, complemented
89#19151495C2211yescharacteristic, complemented
90#19151493C2211yescharacteristic, complemented
91#19151492C2211yescharacteristic, complemented
92#19151492C2211yescharacteristic, complemented
93#19151491C2211yescharacteristic, complemented
94#19151491C2211yescharacteristic, complemented
95#19151490C2211yescharacteristic
96#19151490C2211yescharacteristic
97#19151489C2211yescharacteristic
98#19151489C2211yescharacteristic
99#19151488C2211yescharacteristic
100#19151488C2211yescharacteristic
101#19151487C2211yescharacteristic
102#19151487C2211yescharacteristic
103#19151486C2211yescharacteristic, complemented
104#19151486C2211yescharacteristic, complemented
105#19151485C2211yescharacteristic, complemented
106#19151483C2211yescharacteristic, complemented
107#19151483C2211yescharacteristic, complemented
108#19151483C2211yescharacteristic, complemented
109#19151481C2211yescharacteristic, complemented
110#19151480C2211yescharacteristic, complemented
111#19151480C2211yescharacteristic, complemented
112#19151479C2211yescharacteristic, complemented
113#19151478C2211yescharacteristic
114#19151478C2211yescharacteristic
115#19151478C2211yescharacteristic
116#19151477C2211yescharacteristic
117#19151475C2211yescharacteristic
118#19151474C2211yescharacteristic
119#19151474C2211yescharacteristic
120#19151474C2211yescharacteristic
121#19151474C2211yescharacteristic
122#19151472C2211yescharacteristic
123#19151472C2211yescharacteristic
124#19151472C2211yescharacteristic
125#19151472C2211yescharacteristic
126#19151471C2211yescharacteristic
127#19151471C2211yescharacteristic
128#19151471C2211yescharacteristic
129#19151471C2211yescharacteristic
130#19151470C2211yescharacteristic
131#19151470C2211yescharacteristic, complemented
132#19151465C2211yescharacteristic, complemented
133#19151462C2211yescharacteristic, complemented
134#19151458C2211yescharacteristic
135#19151456C2211yescharacteristic
136#19151456C2211yescharacteristic, complemented
137#19151453C2211yescharacteristic
138#19151453C2211yescharacteristic
139C4⋊C4×Dic89C2211yescharacteristic, complemented
140C4⋊C4×Dic89C2211yescharacteristic, complemented
141C4⋊C4×Dic89C2211yescharacteristic, complemented
142C4⋊C4×Dic89C2211yescharacteristic, complemented
143C4×C4⋊Dic89C2211yescharacteristic, complemented
144#19151449C2211yescharacteristic, complemented
145#19151449C2211yescharacteristic, complemented
146#19151449C2211yescharacteristic, complemented
147C22⋊C4×Dic89C2211yescharacteristic
148C22⋊C4×Dic89C2211yescharacteristic
149C22⋊C4×Dic89C2211yescharacteristic
150C22⋊C4×Dic89C2211yescharacteristic, complemented
151C22⋊C4×Dic89C2211yescharacteristic, complemented
152C22⋊C4×Dic89C2211yescharacteristic, complemented
153C22⋊C4×Dic89C2211yescharacteristic, complemented
154C22⋊C4×Dic89C2211yescharacteristic, complemented
155C4×C22⋊Dic89C2211yescharacteristic
156C4×C22⋊Dic89C2211yescharacteristic, complemented
157#19151445C2211yescharacteristic
158#19151445C2211yescharacteristic
159#19151445C2211yescharacteristic
160#19151445C2211yescharacteristic
161#19151445C2211yescharacteristic
162#19151445C2211yescharacteristic
163#19151445C2211yescharacteristic
164#19151445C2211yescharacteristic
165#19151445C2211yescharacteristic
166#19151445C2211yescharacteristic
167#19151445C2211yescharacteristic
168#19151445C2211yescharacteristic
169#19151443C2211yescharacteristic, complemented
170C2×#15667919C2211yescharacteristic
171C42×Dic89C2211yescharacteristic, complemented
172C2×#121×C89C2211yescharacteristic
173C2×C4×D4×C89C2211yescharacteristic
174#400×C89C2211yescharacteristic, complemented
175#397×C89C2211yescharacteristic, complemented
176#397×C89C2211yescharacteristic, complemented
177#394×C89C2211yescharacteristic, complemented
178#388×C89C2211yescharacteristic, complemented
179#387×C89C2211yescharacteristic, complemented
180#386×C89C2211yescharacteristic
181#386×C89C2211yescharacteristic
182#386×C89C2211yescharacteristic
183#386×C89C2211yescharacteristic, complemented
184#385×C89C2211yescharacteristic
185#381×C89C2211yescharacteristic, complemented
186C2×#95×C89C2211yescharacteristic
187C24×D89C2311yescharacteristic
188C22×Dic178C2311yescharacteristic
189C22×C22⋊D89C2311yescharacteristic
190C22×C22⋊D89C2311yescharacteristic
191C22×C22⋊D89C2311yescharacteristic
192C22×C22⋊D89C2311yescharacteristic
193C23×Dic89C2311yescharacteristic
194C23×Dic89C2311yescharacteristic
195C23×Dic89C2311yescharacteristic
196C23×Dic89C2311yescharacteristic
197C23×Dic89C2311yescharacteristic
198C23×Dic89C2311yescharacteristic
199C22×C4×D89—24no—
200C22×C4×D89—42no—
201C22×C4×D89—42no—
202C22×C4×D89C2311yescharacteristic
203C22×C4×D89C2311yescharacteristic
204C22×C4×D89C2311yescharacteristic
205C22×C4×D89C2311yescharacteristic
206#15668007—24no—
207#15667998—24no—
208#15667995—24no—
209#15667989—24no—
210#15667984—24no—
211#15667980—24no—
212#15667980—24no—
213#15667977—42no—
214D4×Dic89—24no—
215D4×Dic89—24no—
216D4×Dic89—24no—
217D4×Dic89—42no—
218#15667972—42no—
219#15667972—42no—
220#15667972—42no—
221#15667972—42no—
222#15667968—42no—
223C2×C4⋊Dic89C2311yescharacteristic
224C2×C4⋊Dic89C2311yescharacteristic
225C2×C4⋊Dic89C2311yescharacteristic
226C2×C4⋊Dic89C2311yescharacteristic
227C2×C4⋊Dic89C2311yescharacteristic
228C2×C4⋊Dic89C2311yescharacteristic
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×C22⋊Dic89C2311yescharacteristic
244C2×C22⋊Dic89C2311yescharacteristic
245C2×C22⋊Dic89C2311yescharacteristic
246C2×C22⋊Dic89C2311yescharacteristic
247C2×C22⋊Dic89C2311yescharacteristic
248C2×C22⋊Dic89C2311yescharacteristic
249C2×C22⋊Dic89C2311yescharacteristic
250C2×C22⋊Dic89C2311yescharacteristic
251C2×C22⋊Dic89C2311yescharacteristic
252C2×C22⋊Dic89C2311yescharacteristic
253C2×C22⋊Dic89C2311yescharacteristic
254C2×C22⋊Dic89C2311yescharacteristic
255C2×C22⋊Dic89C2311yescharacteristic
256C2×#13083551—24no—
257C2×#13083551—24no—
258C2×#13083551C2311yescharacteristic
259C2×#13083551C2311yescharacteristic
260C2×#13083551C2311yescharacteristic
261C2×#13083551C2311yescharacteristic
262C2×#13083551C2311yescharacteristic
263C2×#13083551C2311yescharacteristic
264C2×#13083551C2311yescharacteristic
265C2×#13083551C2311yescharacteristic
266C2×#13083551C2311yescharacteristic
267C2×#13083551C2311yescharacteristic
268C2×#13083551C2311yescharacteristic
269C2×#13083551C2311yescharacteristic
270C2×#13083551C2311yescharacteristic
271C2×#13083551C2311yescharacteristic
272C2×#13083551C2311yescharacteristic
273C2×#13083551C2311yescharacteristic
274C2×#13083551C2311yescharacteristic
275C2×#13083551C2311yescharacteristic
276C2×#13083551C2311yescharacteristic
277C2×#13083551C2311yescharacteristic
278C2×C4×Dic89—42no—
279C2×C4×Dic89—42no—
280C2×C4×Dic89—42no—
281C2×C4×Dic89C2311yescharacteristic
282C2×C4×Dic89C2311yescharacteristic
283C2×C4×Dic89C2311yescharacteristic
284C2×C4×Dic89C2311yescharacteristic
285C2×C4×Dic89C2311yescharacteristic
286C2×C4×Dic89C2311yescharacteristic
287C2×C4×Dic89C2311yescharacteristic
288C2×C4×Dic89C2311yescharacteristic
289C2×C4×Dic89C2311yescharacteristic
290C2×C4×Dic89C2311yescharacteristic
291C2×C4×Dic89C2311yescharacteristic
292C2×C4×Dic89C2311yescharacteristic
293C2×C4×Dic89C2311yescharacteristic
294C2×C4×Dic89C2311yescharacteristic
295C2×C4×Dic89C2311yescharacteristic
296C2×C4×Dic89C2311yescharacteristic
297C2×C4×Dic89C2311yescharacteristic
298C2×C4×Dic89C2311yescharacteristic
299C2×C4×Dic89C2311yescharacteristic
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
317#15667919C2311yescharacteristic
318#15667919C2311yescharacteristic
319#15667919C2311yescharacteristic
320#15667919C2311yescharacteristic
321#15667919C2311yescharacteristic
322#15667919C2311yescharacteristic
323#15667919C2311yescharacteristic
324#15667919C2311yescharacteristic
325#15667919C2311yescharacteristic
326#15667919C2311yescharacteristic
327#15667919C2311yescharacteristic
328#15667919C2311yescharacteristic
329#15667919C2311yescharacteristic
330#15667919C2311yescharacteristic
331#15667919C2311yescharacteristic
332C22×D4×C89C2311yescharacteristic
333C22×D4×C89C2311yescharacteristic
334C22×D4×C89C2311yescharacteristic
335C23×C4×C89C2311yescharacteristic
336C23×C4×C89C2311yescharacteristic
337C23×C4×C89C2311yescharacteristic
338C23×C4×C89C2311yescharacteristic
339#121×C89—24no—
340C4×D4×C89—24no—
341C2×C4⋊C4×C89C2311yescharacteristic
342C2×C4⋊C4×C89C2311yescharacteristic
343C2×C4⋊C4×C89C2311yescharacteristic
344C2×C4⋊C4×C89C2311yescharacteristic
345C2×C22⋊C4×C89C2311yescharacteristic
346C2×C22⋊C4×C89C2311yescharacteristic
347C2×C22⋊C4×C89C2311yescharacteristic
348C2×C22⋊C4×C89C2311yescharacteristic
349C2×C22⋊C4×C89C2311yescharacteristic
350C2×C22⋊C4×C89C2311yescharacteristic
351C2×C22⋊C4×C89C2311yescharacteristic
352C2×C22⋊C4×C89C2311yescharacteristic
353C2×C22⋊C4×C89C2311yescharacteristic
354C2×C22⋊C4×C89C2311yescharacteristic
355C2×C22⋊C4×C89C2311yescharacteristic
356C2×C42×C89C2311yescharacteristic
357#95×C89C2311yescharacteristic
358#95×C89C2311yescharacteristic
359#95×C89C2311yescharacteristic
360#95×C89C2311yescharacteristic
361#95×C89C2311yescharacteristic
362#95×C89C2311yescharacteristic
363#95×C89C2311yescharacteristic
364#95×C89C2311yescharacteristic
365#95×C89C2311yescharacteristic
366#95×C89C2311yescharacteristic
367#95×C89C2311yescharacteristic
368#95×C89C2311yescharacteristic
369C23×D89—22no—
370C23×D89—22no—
371C23×D89—22no—
372C23×D89—22no—
373C23×D89—22no—
374C23×D89—41no—
375C23×D89—41no—
376C23×D89C2411yescharacteristic
377C23×D89C2411yescharacteristic
378C2×Dic178—22no—
379C2×Dic178—22no—
380C2×Dic178—41no—
381C2×C22⋊D89—22no—
382C2×C22⋊D89—22no—
383C2×C22⋊D89—22no—
384C2×C22⋊D89—22no—
385C2×C22⋊D89—22no—
386C2×C22⋊D89—22no—
387C2×C22⋊D89—22no—
388C2×C22⋊D89—22no—
389C2×C22⋊D89—41no—
390C2×C22⋊D89—41no—
391C2×C22⋊D89—41no—
392C2×C22⋊D89—41no—
393C22×Dic89—22no—
394C22×Dic89—22no—
395C22×Dic89—22no—
396C22×Dic89—22no—
397C22×Dic89—22no—
398C22×Dic89—22no—
399C22×Dic89—22no—
400C22×Dic89—22no—
401C22×Dic89—22no—
402C22×Dic89—22no—
403C22×Dic89—22no—
404C22×Dic89—22no—
405C22×Dic89—22no—
406C22×Dic89—22no—
407C22×Dic89—41no—
408C22×Dic89—41no—
409C22×Dic89—41no—
410C22×Dic89#4114yes—
411C22×Dic89C2411yescharacteristic
412C22×Dic89C2411yescharacteristic
413C22×Dic89C2411yescharacteristic
414C22×Dic89C2411yescharacteristic
415C22×Dic89C2411yescharacteristic
416C22×Dic89C2411yescharacteristic
417C22×Dic89C2411yescharacteristic
418C22×Dic89C2411yescharacteristic
419C22×Dic89C2411yescharacteristic
420C22×Dic89C2411yescharacteristic
421C22×Dic89C2411yescharacteristic
422C22×Dic89C2411yescharacteristic
423C22×Dic89C2411yescharacteristic
424C22×Dic89C2411yescharacteristic
425C2×C4×D89—22no—
426C2×C4×D89—22no—
427C2×C4×D89—22no—
428C2×C4×D89—22no—
429C2×C4×D89—22no—
430C2×C4×D89—22no—
431C2×C4×D89—22no—
432C2×C4×D89—22no—
433C2×C4×D89—41no—
434C2×C4×D89—41no—
435C2×C4×D89—41no—
436C2×C4×D89—41no—
437C2×C4×D89—416no—
438C4⋊Dic89—22no—
439C4⋊Dic89—22no—
440C4⋊Dic89—22no—
441C4⋊Dic89—22no—
442C4⋊Dic89—22no—
443C4⋊Dic89—41no—
444#13083553—22no—
445#13083553—22no—
446#13083553—22no—
447#13083553—22no—
448#13083553—22no—
449#13083553—22no—
450#13083553—41no—
451#13083553—41no—
452#13083553—41no—
453#13083553—41no—
454#13083553—41no—
455#13083553—41no—
456#13083553—41no—
457#13083553—41no—
458C22⋊Dic89—22no—
459C22⋊Dic89—22no—
460C22⋊Dic89—22no—
461C22⋊Dic89—22no—
462C22⋊Dic89—22no—
463C22⋊Dic89—22no—
464C22⋊Dic89—22no—
465C22⋊Dic89—22no—
466C22⋊Dic89—22no—
467C22⋊Dic89—41no—
468C22⋊Dic89—41no—
469C22⋊Dic89—41no—
470C22⋊Dic89#4114yes—
471#13083551—22no—
472#13083551—22no—
473#13083551—22no—
474#13083551—22no—
475#13083551—22no—
476#13083551—22no—
477#13083551—22no—
478#13083551—22no—
479#13083551—22no—
480#13083551—22no—
481#13083551—22no—
482#13083551—22no—
483#13083551—22no—
484#13083551—22no—
485#13083551—41no—
486#13083551—41no—
487#13083551—41no—
488#13083551—41no—
489#13083551#4114yes—
490#13083551#4114yes—
491C4×Dic89—22no—
492C4×Dic89—22no—
493C4×Dic89—22no—
494C4×Dic89—22no—
495C4×Dic89—22no—
496C4×Dic89—22no—
497C4×Dic89—22no—
498C4×Dic89—22no—
499C4×Dic89—22no—
500C4×Dic89—22no—
501C4×Dic89—22no—
502C4×Dic89—22no—
503C4×Dic89—22no—
504C4×Dic89—41no—
505C4×Dic89—41no—
506C4×Dic89—41no—
507C4×Dic89—41no—
508C4×Dic89—41no—
509C4×Dic89—41no—
510C24×C89C2411yescharacteristic
511C24×C89C2411yescharacteristic
512C24×C89C2411yescharacteristic
513C2×D4×C89—22no—
514C2×D4×C89—22no—
515C2×D4×C89—22no—
516C2×D4×C89—22no—
517C2×D4×C89—22no—
518C2×D4×C89—22no—
519C2×D4×C89—22no—
520C2×D4×C89—41no—
521C2×D4×C89#4114yes—
522C22×C4×C89—22no—
523C22×C4×C89—22no—
524C22×C4×C89—22no—
525C22×C4×C89—22no—
526C22×C4×C89—22no—
527C22×C4×C89—22no—
528C22×C4×C89—22no—
529C22×C4×C89—41no—
530C22×C4×C89—41no—
531C22×C4×C89—41no—
532C22×C4×C89—41no—
533C22×C4×C89—41no—
534C22×C4×C89C2411yescharacteristic
535C22×C4×C89C2411yescharacteristic
536C22×C4×C89C2411yescharacteristic
537C22×C4×C89C2411yescharacteristic
538C22×C4×C89C2411yescharacteristic
539C22×C4×C89C2411yescharacteristic
540C22×C4×C89C2411yescharacteristic
541C22×C4×C89C2411yescharacteristic
542C22×C4×C89C2411yescharacteristic
543C22×C4×C89C2411yescharacteristic
544C22×C4×C89C2411yescharacteristic
545C22×C4×C89C2411yescharacteristic
546C4⋊C4×C89—22no—
547C4⋊C4×C89—22no—
548C4⋊C4×C89—22no—
549C4⋊C4×C89—41no—
550C22⋊C4×C89—22no—
551C22⋊C4×C89—22no—
552C22⋊C4×C89—22no—
553C22⋊C4×C89—22no—
554C22⋊C4×C89—22no—
555C22⋊C4×C89—22no—
556C22⋊C4×C89—41no—
557C22⋊C4×C89—41no—
558C22⋊C4×C89—41no—
559C22⋊C4×C89—41no—
560C22⋊C4×C89—41no—
561C42×C89—22no—
562C23×C89—21no—
563C23×C89—21no—
564C23×C89—21no—
565C23×C89—21no—
566C23×C89—21no—
567C23×C89—21no—
568C23×C89—21no—
569C23×C89—21no—
570C23×C89—21no—
571C23×C89—21no—
572C23×C89—21no—
573C23×C89—21no—
574C23×C89—21no—
575C23×C89—21no—
576C23×C89—21no—
577C23×C89—21no—
578C23×C89—21no—
579C23×C89C2×#4112yes—
580C23×C89C2×#4112yes—
581C23×C89C2×#4112yes—
582C23×C89C2×#4112yes—
583C23×C89C2511yescharacteristic
584C22×D89—28no—
585C22×D89—21no—
586C22×D89—21no—
587C22×D89—21no—
588C22×D89—21no—
589C22×D89—21no—
590C22×D89—21no—
591C22×D89—21no—
592C22×D89—21no—
593C22×D89—21no—
594C22×D89—21no—
595C22×D89—21no—
596C22×D89—21no—
597C22×D89—44no—
598C22×D89—44no—
599C22×D89—44no—
600C22×D89—44no—
601C22×D89—44no—
602C22×D89—44no—
603C22×D89C2×#4112yes—
604C22×D89C2×#4112yes—
605D4×C89—28no—
606D4×C89—44no—
607D4×C89—44no—
608C2×C4×C89—21no—
609C2×C4×C89—21no—
610C2×C4×C89—21no—
611C2×C4×C89—21no—
612C2×C4×C89—21no—
613C2×C4×C89—21no—
614C2×C4×C89—21no—
615C2×C4×C89—21no—
616C2×C4×C89—21no—
617C2×C4×C89—21no—
618C2×C4×C89—21no—
619C2×C4×C89—21no—
620C2×C4×C89—21no—
621C2×C4×C89—21no—
622C2×C4×C89—21no—
623C2×C4×C89—21no—
624C2×C4×C89—21no—
625C2×C4×C89—21no—
626C2×C4×C89—21no—
627C2×C4×C89—21no—
628C2×C4×C89—21no—
629C2×C4×C89—21no—
630C2×C4×C89—21no—
631C2×C4×C89—21no—
632C2×C4×C89—21no—
633C2×C4×C89—21no—
634C2×C4×C89—21no—
635C2×C4×C89—21no—
636C2×C4×C89—21no—
637C2×C4×C89—21no—
638C2×C4×C89—21no—
639C2×C4×C89—21no—
640C2×C4×C89—21no—
641C2×C4×C89—44no—
642C2×C4×C89—44no—
643C2×C4×C89—44no—
644C2×C4×C89—44no—
645C2×C4×C89C2×#4112yes—
646C2×C4×C89C2×#4112yes—
647C2×C4×C89C2×#4112yes—
648C22⋊D89—44no—
649C22⋊D89—44no—
650C22⋊D89—44no—
651C22⋊D89—44no—
652C2×Dic89—21no—
653C2×Dic89—21no—
654C2×Dic89—21no—
655C2×Dic89—21no—
656C2×Dic89—21no—
657C2×Dic89—21no—
658C2×Dic89—21no—
659C2×Dic89—21no—
660C2×Dic89—21no—
661C2×Dic89—21no—
662C2×Dic89—28no—
663C2×Dic89—21no—
664C2×Dic89—21no—
665C2×Dic89—21no—
666C2×Dic89—21no—
667C2×Dic89—21no—
668C2×Dic89—21no—
669C2×Dic89—21no—
670C2×Dic89—21no—
671C2×Dic89—21no—
672C2×Dic89—21no—
673C2×Dic89—21no—
674C2×Dic89—21no—
675C2×Dic89—21no—
676C2×Dic89—21no—
677C2×Dic89—21no—
678C2×Dic89—21no—
679C2×Dic89—21no—
680C2×Dic89—21no—
681C2×Dic89—21no—
682C2×Dic89—21no—
683C2×Dic89—21no—
684C2×Dic89—21no—
685C2×Dic89—21no—
686C2×Dic89—21no—
687C2×Dic89—44no—
688C2×Dic89—44no—
689C2×Dic89—44no—
690C2×Dic89—44no—
691C2×Dic89—44no—
692C2×Dic89C2×#4112yes—
693C2×Dic89C2×#4112yes—
694C2×Dic89C2×#4112yes—
695C2×Dic89C2×#4112yes—
696C2×Dic89C2×#4112yes—
697C2×Dic89C2×#4112yes—
698C2×Dic89H(5,𝔽2)12yes—
699C2×Dic89H(5,𝔽2)12yes—
700C4×D89—44no—
701C4×D89—44no—
702C4×D89—44no—
703C4×D89—44no—
704Dic178—44no—
705C22×C89—22no—
706C22×C89—22no—
707C22×C89—22no—
708C22×C89—22no—
709C22×C89—22no—
710C22×C89—22no—
711C22×C89—22no—
712C22×C89—22no—
713C22×C89—22no—
714C22×C89—41no—
715C22×C89—41no—
716C22×C89—41no—
717C22×C89—41no—
718C22×C89—41no—
719C22×C89—41no—
720C22×C89—41no—
721C22×C89—41no—
722C22×C89—41no—
723C22×C89—41no—
724C22×C89—41no—
725C22×C89#52914yes—
726C22×C89C22×#4111yescharacteristic
727C22×C89C22×#4111yescharacteristic
728C22×C89C22×#4111yescharacteristic
729C22×C89C22×#4111yescharacteristic
730C22×C89C22×#4111yescharacteristic
731C22×C89C2×H(5,𝔽2)11yescharacteristic
732C22×C89C2×H(5,𝔽2)11yescharacteristic
733C2×D89—22no—
734C2×D89—22no—
735C2×D89—22no—
736C2×D89—22no—
737C2×D89—22no—
738C2×D89—22no—
739C2×D89—416no—
740C2×D89—41no—
741C2×D89—41no—
742C2×D89—41no—
743C2×D89—41no—
744C2×D89—41no—
745C2×D89—41no—
746C2×D89—41no—
747C2×D89—41no—
748C4×C89—22no—
749C4×C89—22no—
750C4×C89—22no—
751C4×C89—41no—
752C4×C89—41no—
753C4×C89—41no—
754C4×C89—41no—
755C4×C89—41no—
756C4×C89—41no—
757C4×C89—41no—
758C4×C89—41no—
759C4×C89—41no—
760Dic89—22no—
761Dic89—22no—
762Dic89—22no—
763Dic89—22no—
764Dic89—22no—
765Dic89—41no—
766Dic89—41no—
767Dic89—41no—
768Dic89—41no—
769Dic89—41no—
770Dic89—41no—
771Dic89—41no—
772Dic89—41no—
773Dic89#53814yes—
774#34959—891nomaximal, Sylow
775C2×C89—24no—
776C2×C89—42no—
777C2×C89—81no—
778C2×C89C2×#52911yescharacteristic
779C2×C89#344411yescharacteristic
780C2×C89C2×#53811yescharacteristic
781C2×C89#348111yescharacteristic
782C2×C89#348111yescharacteristic
783C2×C89#348111yescharacteristic
784C2×C89#348111yescharacteristic
785D89—42no—
786D89—42no—
787#2597—891no—
788#2595—891no—
789#2589—891no—
790#2587—891no—
791#2578—891no—
792#2576—891no—
793#2559—891no—
794#2557—891no—
795#2510—891no—
796#2505—891no—
797#2480—891no—
798#2472—891no—
799#2450—891no—
800#2444D8911yescharacteristic, complemented
801#2424—891no—
802#2418—891no—
803#2401—891no—
804#2398—891no—
805#2395—891no—
806#2392—891no—
807C4×#126—891no—
808C4×#124—891no—
809C4×C22⋊Q8—891no—
810C4×#123—891no—
811C4×#121—891no—
812C4×#121—891no—
813C4×#120—891no—
814C4×#120—891no—
815#2290—891no—
816C42×D4—891no—
817C2×C4×C22⋊C4—891no—
818C89#3495911yescharacteristic, complemented, Sylow
819C24×C4—891no—
820C2×#126—891no—
821C2×#124—891no—
822C2×#123—891no—
823C2×C22⋊Q8—891no—
824C2×#121—891no—
825C2×#121C2×D8911yescharacteristic
826C2×#120—891no—
827C2×#120—891no—
828C2×C4×Q8—891no—
829C2×C4×D4—891no—
830C2×C4×D4—891no—
831C2×C4×D4—891no—
832C2×C4×D4—891no—
833C2×C4×D4—891no—
834C2×C4×D4—891no—
835C2×C4×D4—891no—
836C2×C4×D4—891no—
837C2×C4×D4C2×D8911yescharacteristic
838C2×#117—891no—
839C22×C22⋊C4—891no—
840C22×C22⋊C4—891no—
841C22×C42—891no—
842C22×C42—891no—
843C22×C42—891no—
844#401—891no—
845#400—891no—
846#400—891no—
847#400—891no—
848#400—891no—
849#400—891no—
850#400C2×D8911yescharacteristic, complemented
851#399—891no—
852#398—891no—
853#398—891no—
854#397—891no—
855#397—891no—
856#397—891no—
857#397—891no—
858#397—891no—
859#397—891no—
860#397—891no—
861#397C2×D8911yescharacteristic, complemented
862#397C2×D8911yescharacteristic, complemented
863#396—891no—
864#396—891no—
865#396—891no—
866#394—891no—
867#394—891no—
868#394—891no—
869#394—891no—
870#394—891no—
871#394—891no—
872#394C2×D8911yescharacteristic, complemented
873#393—891no—
874#393—891no—
875#392—891no—
876#391—891no—
877#391—891no—
878#390—891no—
879#390—891no—
880#390—891no—
881#389—891no—
882#389—891no—
883#389—891no—
884#388—891no—
885#388—891no—
886#388—891no—
887#388—891no—
888#388—891no—
889#388—891no—
890#388—891no—
891#388—891no—
892#388—891no—
893#388—891no—
894#388—891no—
895#388—891no—
896#388—891no—
897#388—891no—
898#388C2×D8911yescharacteristic, complemented
899#387—891no—
900#387—891no—
901#387—891no—
902#387—891no—
903#387—891no—
904#387—891no—
905#387—891no—
906#387—891no—
907#387C2×D8911yescharacteristic, complemented
908#386—891no—
909#386—891no—
910#386—891no—
911#386—891no—
912#386—891no—
913#386—891no—
914#386—891no—
915#386—891no—
916#386—891no—
917#386C2×D8911yescharacteristic
918#386C2×D8911yescharacteristic
919#386C2×D8911yescharacteristic
920#386C2×D8911yescharacteristic, complemented
921#385—891no—
922#385—891no—
923#385—891no—
924#385—891no—
925#385—891no—
926#385—891no—
927#385—891no—
928#385—891no—
929#385—891no—
930#385—891no—
931#385C2×D8911yescharacteristic
932#383—891no—
933#382—891no—
934#381C2×D8911yescharacteristic, complemented
935#380—891no—
936#380—891no—
937#380—891no—
938#379—891no—
939#379—891no—
940C4×C4⋊C4—891no—
941C4×C4⋊C4—891no—
942C4×C4⋊C4—891no—
943C4×C4⋊C4—891no—
944C4×C4⋊C4—891no—
945C4×C4⋊C4—891no—
946C4×C4⋊C4—891no—
947C4×C4⋊C4—891no—
948C4×C22⋊C4—891no—
949C4×C22⋊C4—891no—
950C4×C22⋊C4—891no—
951C4×C22⋊C4—891no—
952C4×C22⋊C4—891no—
953C4×C22⋊C4—891no—
954C4×C22⋊C4—891no—
955C4×C22⋊C4—891no—
956C4×C22⋊C4—891no—
957C4×C22⋊C4—891no—
958C4×C22⋊C4—891no—
959C4×C22⋊C4—891no—
960C4×C22⋊C4—891no—
961C4×C22⋊C4—891no—
962C4×C22⋊C4—891no—
963C4×C22⋊C4—891no—
964C4×C22⋊C4—891no—
965C4×C22⋊C4—891no—
966C4×C22⋊C4—891no—
967C4×C22⋊C4—891no—
968C4×C22⋊C4—891no—
969C4×C22⋊C4—891no—
970#376—891no—
971C2×#95—891no—
972C2×#95C2×D8911yescharacteristic
973C43—891no—
974C25—891no—
975C22×Q8—891no—
976C22×D4—891no—
977C22×D4—891no—
978C22×D4—891no—
979C22×D4—891no—
980C22×D4C22×D8911yescharacteristic
981C22×D4C22×D8911yescharacteristic
982C22×D4C22×D8911yescharacteristic
983C23×C4—891no—
984C23×C4—891no—
985C23×C4—891no—
986C23×C4—891no—
987C23×C4—891no—
988C23×C4—891no—
989C23×C4—891no—
990C23×C4—891no—
991C23×C4—891no—
992C23×C4—891no—
993C23×C4—3562no—
994C23×C4—3562no—
995C23×C4—1784no—
996C23×C4C22×D8911yescharacteristic
997C23×C4C22×D8911yescharacteristic
998C23×C4C22×D8911yescharacteristic
999C23×C4C22×D8911yescharacteristic
1000#126—1784no—
1001#124—1784no—
1002#123—1784no—
1003C22⋊Q8—1784no—
1004#121—24no—
1005#121—1784no—
1006#120—1784no—
1007#120—1784no—
1008C4×Q8—3562no—
1009C4×D4—24no—
1010C4×D4—3562no—
1011C4×D4—3562no—
1012C4×D4—3562no—
1013C4×D4—3562no—
1014C4×D4—3562no—
1015C4×D4—1784no—
1016C4×D4—1784no—
1017C4×D4—1784no—
1018#117—3562no—
1019C2×C4⋊C4—891no—
1020C2×C4⋊C4—891no—
1021C2×C4⋊C4—891no—
1022C2×C4⋊C4—891no—
1023C2×C4⋊C4—891no—
1024C2×C4⋊C4—891no—
1025C2×C4⋊C4—891no—
1026C2×C4⋊C4—891no—
1027C2×C4⋊C4—891no—
1028C2×C4⋊C4—891no—
1029C2×C4⋊C4—891no—
1030C2×C4⋊C4—891no—
1031C2×C4⋊C4—891no—
1032C2×C4⋊C4—891no—
1033C2×C4⋊C4—891no—
1034C2×C4⋊C4—891no—
1035C2×C4⋊C4—891no—
1036C2×C4⋊C4—891no—
1037C2×C4⋊C4—891no—
1038C2×C4⋊C4—891no—
1039C2×C4⋊C4C22×D8911yescharacteristic
1040C2×C4⋊C4C22×D8911yescharacteristic
1041C2×C4⋊C4C22×D8911yescharacteristic
1042C2×C4⋊C4C22×D8911yescharacteristic
1043C2×C22⋊C4—891no—
1044C2×C22⋊C4—891no—
1045C2×C22⋊C4—891no—
1046C2×C22⋊C4—891no—
1047C2×C22⋊C4—891no—
1048C2×C22⋊C4—891no—
1049C2×C22⋊C4—891no—
1050C2×C22⋊C4—891no—
1051C2×C22⋊C4—891no—
1052C2×C22⋊C4—891no—
1053C2×C22⋊C4—891no—
1054C2×C22⋊C4—891no—
1055C2×C22⋊C4—891no—
1056C2×C22⋊C4—891no—
1057C2×C22⋊C4—891no—
1058C2×C22⋊C4—891no—
1059C2×C22⋊C4—891no—
1060C2×C22⋊C4—891no—
1061C2×C22⋊C4—891no—
1062C2×C22⋊C4—891no—
1063C2×C22⋊C4—891no—
1064C2×C22⋊C4—891no—
1065C2×C22⋊C4—891no—
1066C2×C22⋊C4—891no—
1067C2×C22⋊C4—891no—
1068C2×C22⋊C4—891no—
1069C2×C22⋊C4—891no—
1070C2×C22⋊C4—891no—
1071C2×C22⋊C4—891no—
1072C2×C22⋊C4—891no—
1073C2×C22⋊C4—891no—
1074C2×C22⋊C4—891no—
1075C2×C22⋊C4—891no—
1076C2×C22⋊C4—1784no—
1077C2×C22⋊C4—1784no—
1078C2×C22⋊C4C22×D8911yescharacteristic
1079C2×C22⋊C4C22×D8911yescharacteristic
1080C2×C22⋊C4C22×D8911yescharacteristic
1081C2×C22⋊C4C22×D8911yescharacteristic
1082C2×C22⋊C4C22×D8911yescharacteristic
1083C2×C22⋊C4C22×D8911yescharacteristic
1084C2×C22⋊C4C22×D8911yescharacteristic
1085C2×C22⋊C4C22×D8911yescharacteristic
1086C2×C22⋊C4C22×D8911yescharacteristic
1087C2×C22⋊C4C22×D8911yescharacteristic
1088C2×C22⋊C4C22×D8911yescharacteristic
1089C2×C42—891no—
1090C2×C42—891no—
1091C2×C42—891no—
1092C2×C42—891no—
1093C2×C42—891no—
1094C2×C42—891no—
1095C2×C42—891no—
1096C2×C42—891no—
1097C2×C42—891no—
1098C2×C42—891no—
1099C2×C42—891no—
1100C2×C42—891no—
1101C2×C42—891no—
1102C2×C42—891no—
1103C2×C42—891no—
1104C2×C42—891no—
1105C2×C42—891no—
1106C2×C42—891no—
1107C2×C42—891no—
1108C2×C42—3562no—
1109C2×C42—3562no—
1110C2×C42—3562no—
1111C2×C42C22×D8911yescharacteristic
1112#95—891no—
1113#95—891no—
1114#95—891no—
1115#95—891no—
1116#95—891no—
1117#95—891no—
1118#95—891no—
1119#95—891no—
1120#95—891no—
1121#95—891no—
1122#95—891no—
1123#95—891no—
1124#95—891no—
1125#95—891no—
1126#95—891no—
1127#95—891no—
1128#95—891no—
1129#95—891no—
1130#95—891no—
1131#95—891no—
1132#95—891no—
1133#95—891no—
1134#95—891no—
1135#95—891no—
1136#95—891no—
1137#95—891no—
1138#95—891no—
1139#95—891no—
1140#95—891no—
1141#95—891no—
1142#95—891no—
1143#95—891no—
1144#95C22×D8911yescharacteristic
1145#95C22×D8911yescharacteristic
1146#95C22×D8911yescharacteristic
1147#95C22×D8911yescharacteristic
1148#95C22×D8911yescharacteristic
1149#95C22×D8911yescharacteristic
1150#95C22×D8911yescharacteristic
1151#95C22×D8911yescharacteristic
1152#95C22×D8911yescharacteristic
1153#95C22×D8911yescharacteristic
1154#95C22×D8911yescharacteristic
1155#95C22×D8911yescharacteristic
1156C24—891no—
1157C24—891no—
1158C24—3561no—
1159C24—3561no—
1160C24—1782no—
1161C24—1782no—
1162C24—1782no—
1163C24—1782no—
1164C24—1782no—
1165C24C23×D8911yescharacteristic
1166C24C23×D8911yescharacteristic
1167C24C23×D8911yescharacteristic
1168C2×Q8—3561no—
1169C2×Q8—1782no—
1170C2×Q8—1782no—
1171C2×D4—22no—
1172C2×D4—22no—
1173C2×D4—22no—
1174C2×D4—22no—
1175C2×D4—22no—
1176C2×D4—22no—
1177C2×D4—22no—
1178C2×D4—41no—
1179C2×D4—3561no—
1180C2×D4—3561no—
1181C2×D4—3561no—
1182C2×D4—3561no—
1183C2×D4—1782no—
1184C2×D4—1782no—
1185C2×D4—1782no—
1186C2×D4—1782no—
1187C2×D4—1782no—
1188C2×D4—1782no—
1189C2×D4—1782no—
1190C2×D4—1782no—
1191C2×D4#1308357314yes—
1192C22×C4—22no—
1193C22×C4—22no—
1194C22×C4—22no—
1195C22×C4—22no—
1196C22×C4—22no—
1197C22×C4—22no—
1198C22×C4—22no—
1199C22×C4—41no—
1200C22×C4—41no—
1201C22×C4—41no—
1202C22×C4—41no—
1203C22×C4—41no—
1204C22×C4—891no—
1205C22×C4—894no—
1206C22×C4—891no—
1207C22×C4—891no—
1208C22×C4—891no—
1209C22×C4—891no—
1210C22×C4—891no—
1211C22×C4—891no—
1212C22×C4—891no—
1213C22×C4—891no—
1214C22×C4—891no—
1215C22×C4—891no—
1216C22×C4—891no—
1217C22×C4—891no—
1218C22×C4—891no—
1219C22×C4—3561no—
1220C22×C4—3561no—
1221C22×C4—3561no—
1222C22×C4—3561no—
1223C22×C4—35616no—
1224C22×C4—3561no—
1225C22×C4—3561no—
1226C22×C4—3561no—
1227C22×C4—1782no—
1228C22×C4—1782no—
1229C22×C4—1782no—
1230C22×C4—1782no—
1231C22×C4—1782no—
1232C22×C4—1782no—
1233C22×C4—1782no—
1234C22×C4—1782no—
1235C22×C4—1782no—
1236C22×C4—1782no—
1237C22×C4—1782no—
1238C22×C4—1782no—
1239C22×C4—1782no—
1240C22×C4—1782no—
1241C22×C4—1782no—
1242C22×C4—1782no—
1243C22×C4—1782no—
1244C22×C4—1782no—
1245C22×C4—1782no—
1246C22×C4—1782no—
1247C22×C4—1782no—
1248C22×C4—1782no—
1249C22×C4C23×D8911yescharacteristic
1250C22×C4C23×D8911yescharacteristic
1251C22×C4C23×D8911yescharacteristic
1252C22×C4C23×D8911yescharacteristic
1253C22×C4C23×D8911yescharacteristic
1254C22×C4C23×D8911yescharacteristic
1255C22×C4C23×D8911yescharacteristic
1256C22×C4C23×D8911yescharacteristic
1257C22×C4C23×D8911yescharacteristic
1258C22×C4C23×D8911yescharacteristic
1259C22×C4C23×D8911yescharacteristic
1260C22×C4C23×D8911yescharacteristic
1261C4⋊C4—22no—
1262C4⋊C4—22no—
1263C4⋊C4—22no—
1264C4⋊C4—41no—
1265C4⋊C4—3561no—
1266C4⋊C4—3561no—
1267C4⋊C4—3561no—
1268C4⋊C4—3561no—
1269C4⋊C4—3561no—
1270C4⋊C4—3561no—
1271C4⋊C4—3561no—
1272C4⋊C4—3561no—
1273C4⋊C4—3561no—
1274C4⋊C4—1782no—
1275C4⋊C4—1782no—
1276C4⋊C4—1782no—
1277C4⋊C4—1782no—
1278C4⋊C4—1782no—
1279C4⋊C4—1782no—
1280C4⋊C4—1782no—
1281C4⋊C4—1782no—
1282C4⋊C4—1782no—
1283C4⋊C4—1782no—
1284C4⋊C4—1782no—
1285C22⋊C4—22no—
1286C22⋊C4—22no—
1287C22⋊C4—22no—
1288C22⋊C4—22no—
1289C22⋊C4—22no—
1290C22⋊C4—22no—
1291C22⋊C4—41no—
1292C22⋊C4—41no—
1293C22⋊C4—41no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
1296C22⋊C4—894no—
1297C22⋊C4—894no—
1298C22⋊C4—894no—
1299C22⋊C4—3561no—
1300C22⋊C4—3561no—
1301C22⋊C4—3561no—
1302C22⋊C4—3561no—
1303C22⋊C4—3561no—
1304C22⋊C4—3561no—
1305C22⋊C4—3561no—
1306C22⋊C4—1782no—
1307C22⋊C4—1782no—
1308C22⋊C4—1782no—
1309C22⋊C4—1782no—
1310C22⋊C4—1782no—
1311C22⋊C4—1782no—
1312C22⋊C4—1782no—
1313C22⋊C4—1782no—
1314C22⋊C4—1782no—
1315C22⋊C4—1782no—
1316C22⋊C4—1782no—
1317C22⋊C4—1782no—
1318C22⋊C4—1782no—
1319C22⋊C4—1782no—
1320C22⋊C4—1782no—
1321C22⋊C4—1782no—
1322C22⋊C4—1782no—
1323C22⋊C4—1782no—
1324C22⋊C4—1782no—
1325C22⋊C4—1782no—
1326C22⋊C4—1782no—
1327C22⋊C4—1782no—
1328C22⋊C4—1782no—
1329C42—22no—
1330C42—3561no—
1331C42—3561no—
1332C42—3561no—
1333C42—3561no—
1334C42—3561no—
1335C42—3561no—
1336C42—1782no—
1337C42—1782no—
1338C42—1782no—
1339C42—1782no—
1340C42—1782no—
1341C42—1782no—
1342C42—1782no—
1343C42—1782no—
1344C42—1782no—
1345C42—1782no—
1346C42—1782no—
1347C42—1782no—
1348C42—1782no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—892no—
1367C23—892no—
1368C23—3564no—
1369C23—3564no—
1370C23—3564no—
1371C23—3564no—
1372C23—3564no—
1373C23—3564no—
1374C23—1788no—
1375C23—1781no—
1376C23—1781no—
1377C23—1781no—
1378C23—1781no—
1379C23—1781no—
1380C23—1781no—
1381C23—1781no—
1382C23—1781no—
1383C23—1781no—
1384C23—1781no—
1385C23—1781no—
1386C23—1781no—
1387C23#41×D8912yes—
1388C23#41×D8912yes—
1389C23C2×#1308357312yes—
1390C23C2×#1308357312yes—
1391C23C24×D8911yescharacteristic
1392Q8—3564no—
1393D4—28no—
1394D4—44no—
1395D4—44no—
1396D4—3564no—
1397D4—3564no—
1398D4—3564no—
1399D4—3564no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—44no—
1434C2×C4—44no—
1435C2×C4—44no—
1436C2×C4—44no—
1437C2×C4—892no—
1438C2×C4—892no—
1439C2×C4—892no—
1440C2×C4—892no—
1441C2×C4—892no—
1442C2×C4—892no—
1443C2×C4—892no—
1444C2×C4—892no—
1445C2×C4—3564no—
1446C2×C4—3564no—
1447C2×C4—3564no—
1448C2×C4—3564no—
1449C2×C4—3564no—
1450C2×C4—3564no—
1451C2×C4—3564no—
1452C2×C4—3564no—
1453C2×C4—3564no—
1454C2×C4—1788no—
1455C2×C4—1781no—
1456C2×C4—1781no—
1457C2×C4—1781no—
1458C2×C4—1781no—
1459C2×C4—1781no—
1460C2×C4—1781no—
1461C2×C4—1781no—
1462C2×C4—1781no—
1463C2×C4—1781no—
1464C2×C4—1781no—
1465C2×C4—1781no—
1466C2×C4—1781no—
1467C2×C4—1781no—
1468C2×C4—1781no—
1469C2×C4—1781no—
1470C2×C4—1781no—
1471C2×C4—1781no—
1472C2×C4—1781no—
1473C2×C4—1781no—
1474C2×C4—1781no—
1475C2×C4—1781no—
1476C2×C4—1781no—
1477C2×C4—1781no—
1478C2×C4—1781no—
1479C2×C4—1781no—
1480C2×C4—1781no—
1481C2×C4—1781no—
1482C2×C4—1781no—
1483C2×C4—1781no—
1484C2×C4—1781no—
1485C2×C4—1781no—
1486C2×C4—1781no—
1487C2×C4—1781no—
1488C2×C4—1781no—
1489C2×C4#41×D8912yes—
1490C2×C4#41×D8912yes—
1491C2×C4C2×#1308357312yes—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—22no—
1499C22—22no—
1500C22—22no—
1501C22—41no—
1502C22—41no—
1503C22—41no—
1504C22—41no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—41no—
1510C22—41no—
1511C22—41no—
1512C22—35616no—
1513C22—3561no—
1514C22—3561no—
1515C22—3561no—
1516C22—3561no—
1517C22—3561no—
1518C22—3561no—
1519C22—3561no—
1520C22—3561no—
1521C22—1782no—
1522C22—1782no—
1523C22—1782no—
1524C22—1782no—
1525C22—1782no—
1526C22—1782no—
1527C22#1915212514yes—
1528C22C2×#41×D8911yescharacteristic
1529C22C2×#41×D8911yescharacteristic
1530C22C2×#41×D8911yescharacteristic
1531C22C2×#41×D8911yescharacteristic
1532C22C22×#1308357311yescharacteristic
1533C22H(5,𝔽2)×D8911yescharacteristic
1534C22H(5,𝔽2)×D8911yescharacteristic
1535C4—22no—
1536C4—22no—
1537C4—22no—
1538C4—41no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—41no—
1543C4—41no—
1544C4—41no—
1545C4—41no—
1546C4—41no—
1547C4—894no—
1548C4—3561no—
1549C4—3561no—
1550C4—3561no—
1551C4—3561no—
1552C4—3561no—
1553C4—3561no—
1554C4—3561no—
1555C4—3561no—
1556C4—1782no—
1557C4—1782no—
1558C4—1782no—
1559C4—1782no—
1560C4—1782no—
1561C2—24no—
1562C2—42no—
1563C2—81no—
1564C2—3562no—
1565C2—3562no—
1566C2C2×#1915212511yescharacteristic
1567C2#2603354611yescharacteristic
1568C2#538×D8911yescharacteristic
1569C2#2603385711yescharacteristic
1570C2#2603385711yescharacteristic
1571C2#2603385911yescharacteristic
1572C2#2603385911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutator, socle, cosocleC23×C89C25
FittingC89×#2444C2
prime radical#26023794C2
hypercenter#2444D89
hypocenterC89#34959
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2444

Complements

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

NH ≅ G/Ntype
1. #26025796C2semidirect
2. #26025769C2semidirect
3. #26025704C2semidirect
4. #26025677C2semidirect
5. #26025579C2semidirect
6. #26025552C2semidirect
7. #26025382C2semidirect
8. #26025355C2semidirect
9. #26024810C2semidirect
10. #26024753C2semidirect
11. #26024505C2semidirect
12. #26024380C2semidirect
13. #26024082C2semidirect
15. #26023708C2semidirect
16. #26023551C2semidirect
17. #26023537C2semidirect
18. #26023510C2semidirect
19. #26023495C2semidirect
20. #26022802C2semidirect
21. #26022793C2semidirect
22. #26022784C2semidirect
23. #26022769C2semidirect
24. #121×Dic89C2semidirect
25. #26022762C2semidirect
26. #26022757C2semidirect
27. #26022757C2semidirect
28. #26022692C2semidirect
29. C4×D4×Dic89C2semidirect
30. C2×#19151445C2semidirect
31. C89×#2444C2semidirect
40. C2×#15667977C22semidirect
44. C2×D4×Dic89C22semidirect
49. C2×#15667968C22semidirect
54. C22×C4×Dic89C22semidirect
55. C89⋊#401C22semidirect
56. #19151540C22semidirect
57. #19151539C22semidirect
58. #19151539C22semidirect
59. #19151539C22semidirect
60. #19151538C22semidirect
62. #19151532C22semidirect
63. #19151532C22semidirect
66. #19151526C22semidirect
67. #19151526C22semidirect
71. #19151521C22semidirect
81. #19151510C22semidirect
83. #19151502C22semidirect
84. #19151502C22semidirect
85. #19151501C22semidirect
88. #19151497C22semidirect
89. #19151495C22semidirect
90. #19151493C22semidirect
91. #19151492C22semidirect
92. #19151492C22semidirect
93. #19151491C22semidirect
94. #19151491C22semidirect
103. #19151486C22semidirect
104. #19151486C22semidirect
105. #19151485C22semidirect
106. #19151483C22semidirect
107. #19151483C22semidirect
108. #19151483C22semidirect
109. #19151481C22semidirect
110. #19151480C22semidirect
111. #19151480C22semidirect
112. #19151479C22semidirect
131. #19151470C22semidirect
132. #19151465C22semidirect
133. #19151462C22semidirect
136. #19151456C22semidirect
139. C4⋊C4×Dic89C22semidirect
140. C4⋊C4×Dic89C22semidirect
141. C4⋊C4×Dic89C22semidirect
142. C4⋊C4×Dic89C22semidirect
143. C4×C4⋊Dic89C22semidirect
144. #19151449C22semidirect
145. #19151449C22semidirect
146. #19151449C22semidirect
150. C22⋊C4×Dic89C22semidirect
151. C22⋊C4×Dic89C22semidirect
152. C22⋊C4×Dic89C22semidirect
153. C22⋊C4×Dic89C22semidirect
154. C22⋊C4×Dic89C22semidirect
156. C4×C22⋊Dic89C22semidirect
169. #19151443C22semidirect
171. C42×Dic89C22semidirect
174. #400×C89C22semidirect
175. #397×C89C22semidirect
176. #397×C89C22semidirect
177. #394×C89C22semidirect
178. #388×C89C22semidirect
179. #387×C89C22semidirect
183. #386×C89C22semidirect
185. #381×C89C22semidirect
800. #2444D89semidirect
818. C89#34959semidirect
850. #400C2×D89semidirect
861. #397C2×D89semidirect
862. #397C2×D89semidirect
872. #394C2×D89semidirect
898. #388C2×D89semidirect
907. #387C2×D89semidirect
920. #386C2×D89semidirect
934. #381C2×D89semidirect

Maximal subgroups

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

subgroupindex
#260257962
#260257692
#260257042
#260256772
#260255792
#260255522
#260253822
#260253552
#260248102
#260247532
#260245052
#260243802
#260240822
#260237942
#260237082
#260235512
#260235372
#260235102
#260234952
#260228022
#260227932
#260227842
#260227692
#121×Dic892
#260227622
#260227572
#260226922
C4×D4×Dic892
C2×#191514452
C89×#24442
#3495989