Finite Group Databasebeta

← #36768591

Subgroups — #36768591

Order 22784.

1994 conjugacy classes of subgroups.

The subgroup lattice has 1600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26028581C211yesmaximal, characteristic, complemented
2#26028571C211yesmaximal, characteristic, complemented
3#26028115C211yesmaximal, characteristic, complemented
4#26027890C211yesmaximal, characteristic, complemented
5#26027878C211yesmaximal, characteristic, complemented
6#26027875C211yesmaximal, characteristic, complemented
7#26027770C211yesmaximal, characteristic, complemented
8#26027687C211yesmaximal, characteristic, complemented
9#26027522C211yesmaximal, characteristic, complemented
10#26027509C211yesmaximal, characteristic, complemented
11#26027494C211yesmaximal, characteristic, complemented
12#26027372C211yesmaximal, characteristic, complemented
13#26027298C211yesmaximal, characteristic, complemented
14#26027293C211yesmaximal, characteristic, complemented
15#26026885C211yesmaximal, characteristic, complemented
16#26026815C211yesmaximal, characteristic, complemented
17#26026808C211yesmaximal, characteristic, complemented
18#26026643C211yesmaximal, characteristic, complemented
19#26026207C211yesmaximal, characteristic, complemented
20#26026182C211yesmaximal, characteristic, complemented
21#26024582C211yesmaximal, characteristic, complemented
22#26024512C211yesmaximal, characteristic, complemented
23#26023993C211yesmaximal, characteristic, complemented
24#26023918C211yesmaximal, characteristic, complemented
25#26023799C211yesmaximal, characteristic, complemented
26#26023648C211yesmaximal, characteristic, complemented
27#26023626C211yesmaximal, characteristic
28#26022907C211yesmaximal, characteristic, complemented
29#26022830C211yesmaximal, characteristic, complemented
30C2×#19151491C211yesmaximal, characteristic, complemented
31C89×#2405C211yesmaximal, characteristic, complemented
32C2×#15668005C2211yescharacteristic, complemented
33C2×#15667995C2211yescharacteristic, complemented
34C2×#15667994C2211yescharacteristic, complemented
35C2×#15667989C2211yescharacteristic, complemented
36C2×#15667989C2211yescharacteristic, complemented
37C2×#15667984C2211yescharacteristic
38C2×#15667984C2211yescharacteristic
39C2×#15667981C2211yescharacteristic
40C2×#15667981C2211yescharacteristic
41C2×#15667972C2211yescharacteristic, complemented
42C22×C4⋊Dic89C2211yescharacteristic, complemented
43C22×C22⋊Dic89C2211yescharacteristic
44C22×C22⋊Dic89C2211yescharacteristic
45C22×C22⋊Dic89C2211yescharacteristic
46C22×C4×Dic89C2211yescharacteristic, complemented
47C89⋊#401C2211yescharacteristic, complemented
48#19151540C2211yescharacteristic, complemented
49#19151540C2211yescharacteristic, complemented
50#19151540C2211yescharacteristic, complemented
51#19151539C2211yescharacteristic, complemented
52#19151539C2211yescharacteristic, complemented
53#19151538C2211yescharacteristic, complemented
54#19151538C2211yescharacteristic, complemented
55#19151536C2211yescharacteristic, complemented
56#19151536C2211yescharacteristic, complemented
57#19151534C2211yescharacteristic
58#19151534C2211yescharacteristic, complemented
59#19151532C2211yescharacteristic, complemented
60#19151529C2211yescharacteristic, complemented
61#19151527C2211yescharacteristic, complemented
62#19151526C2211yescharacteristic
63#19151526C2211yescharacteristic
64#19151526C2211yescharacteristic, complemented
65#19151526C2211yescharacteristic, complemented
66#19151526C2211yescharacteristic, complemented
67#19151525C2211yescharacteristic, complemented
68#19151524C2211yescharacteristic, complemented
69#19151523C2211yescharacteristic, complemented
70#19151523C2211yescharacteristic, complemented
71#19151523C2211yescharacteristic, complemented
72#19151521C2211yescharacteristic
73#19151521C2211yescharacteristic
74#19151521C2211yescharacteristic, complemented
75#19151521C2211yescharacteristic, complemented
76#19151521C2211yescharacteristic, complemented
77#19151514C2211yescharacteristic, complemented
78#19151514C2211yescharacteristic, complemented
79#19151514C2211yescharacteristic, complemented
80#19151513C2211yescharacteristic
81#19151513C2211yescharacteristic
82#19151513C2211yescharacteristic, complemented
83#19151512C2211yescharacteristic
84#19151512C2211yescharacteristic
85#19151511C2211yescharacteristic, complemented
86#19151510C2211yescharacteristic
87#19151510C2211yescharacteristic, complemented
88#19151510C2211yescharacteristic, complemented
89#19151506C2211yescharacteristic
90#19151506C2211yescharacteristic
91#19151503C2211yescharacteristic, complemented
92#19151498C2211yescharacteristic
93#19151498C2211yescharacteristic, complemented
94#19151498C2211yescharacteristic, complemented
95#19151498C2211yescharacteristic, complemented
96#19151494C2211yescharacteristic, complemented
97#19151493C2211yescharacteristic, complemented
98#19151493C2211yescharacteristic, complemented
99#19151492C2211yescharacteristic
100#19151492C2211yescharacteristic, complemented
101#19151492C2211yescharacteristic, complemented
102#19151492C2211yescharacteristic, complemented
103#19151492C2211yescharacteristic, complemented
104#19151492C2211yescharacteristic, complemented
105#19151491C2211yescharacteristic
106#19151491C2211yescharacteristic
107#19151491C2211yescharacteristic
108#19151491C2211yescharacteristic
109#19151491C2211yescharacteristic, complemented
110#19151491C2211yescharacteristic, complemented
111#19151491C2211yescharacteristic, complemented
112#19151491C2211yescharacteristic, complemented
113#19151491C2211yescharacteristic, complemented
114#19151491C2211yescharacteristic, complemented
115#19151488C2211yescharacteristic, complemented
116#19151488C2211yescharacteristic, complemented
117#19151486C2211yescharacteristic
118#19151486C2211yescharacteristic, complemented
119#19151486C2211yescharacteristic, complemented
120#19151486C2211yescharacteristic, complemented
121#19151486C2211yescharacteristic, complemented
122#19151486C2211yescharacteristic, complemented
123#19151486C2211yescharacteristic, complemented
124#19151485C2211yescharacteristic, complemented
125#19151483C2211yescharacteristic, complemented
126#19151481C2211yescharacteristic, complemented
127#19151479C2211yescharacteristic, complemented
128#19151479C2211yescharacteristic, complemented
129#19151479C2211yescharacteristic, complemented
130#19151479C2211yescharacteristic, complemented
131#19151478C2211yescharacteristic
132#19151478C2211yescharacteristic
133#19151478C2211yescharacteristic
134#19151478C2211yescharacteristic
135#19151478C2211yescharacteristic
136#19151478C2211yescharacteristic
137#19151478C2211yescharacteristic
138#19151478C2211yescharacteristic
139#19151478C2211yescharacteristic
140#19151478C2211yescharacteristic
141#19151477C2211yescharacteristic
142#19151477C2211yescharacteristic, complemented
143#19151475C2211yescharacteristic, complemented
144#19151475C2211yescharacteristic, complemented
145#19151475C2211yescharacteristic, complemented
146#19151474C2211yescharacteristic
147#19151474C2211yescharacteristic, complemented
148#19151474C2211yescharacteristic, complemented
149#19151473C2211yescharacteristic, complemented
150#19151473C2211yescharacteristic, complemented
151#19151472C2211yescharacteristic, complemented
152#19151471C2211yescharacteristic
153#19151471C2211yescharacteristic, complemented
154#19151470C2211yescharacteristic, complemented
155#19151470C2211yescharacteristic, complemented
156#19151470C2211yescharacteristic, complemented
157#19151463C2211yescharacteristic, complemented
158#19151461C2211yescharacteristic
159#19151461C2211yescharacteristic
160#19151461C2211yescharacteristic, complemented
161#19151456C2211yescharacteristic, complemented
162#19151456C2211yescharacteristic, complemented
163#19151456C2211yescharacteristic, complemented
164#19151456C2211yescharacteristic, complemented
165#19151455C2211yescharacteristic, complemented
166#19151454C2211yescharacteristic
167#19151454C2211yescharacteristic
168#19151454C2211yescharacteristic
169C22⋊C4×Dic89C2211yescharacteristic, complemented
170C2×#15667919C2211yescharacteristic, complemented
171C2×#15667919C2211yescharacteristic, complemented
172C23×D4×C89C2211yescharacteristic
173C2×#123×C89C2211yescharacteristic
174C2×#123×C89C2211yescharacteristic
175C22×C22⋊C4×C89C2211yescharacteristic
176#394×C89C2211yescharacteristic
177#394×C89C2211yescharacteristic
178#394×C89C2211yescharacteristic
179#394×C89C2211yescharacteristic
180#386×C89C2211yescharacteristic
181#386×C89C2211yescharacteristic
182#385×C89C2211yescharacteristic
183#385×C89C2211yescharacteristic
184#379×C89C2211yescharacteristic
185#379×C89C2211yescharacteristic
186#379×C89C2211yescharacteristic
187C22×Dic178C2311yescharacteristic
188C22×C22⋊D89C2311yescharacteristic
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×D89C2311yescharacteristic
200#15668005—42no—
201#15667995—42no—
202#15667994—42no—
203#15667989—42no—
204#15667989—42no—
205#15667984—42no—
206#15667984—42no—
207#15667981—24no—
208#15667981—42no—
209#15667972—42no—
210C2×C4⋊Dic89—42no—
211C2×C4⋊Dic89C2311yescharacteristic
212C2×C4⋊Dic89C2311yescharacteristic
213C2×C4⋊Dic89C2311yescharacteristic
214C2×C4⋊Dic89C2311yescharacteristic
215C2×C4⋊Dic89C2311yescharacteristic
216C2×C4⋊Dic89C2311yescharacteristic
217C2×C4⋊Dic89C2311yescharacteristic
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×C22⋊Dic89—42no—
234C2×C22⋊Dic89—42no—
235C2×C22⋊Dic89—42no—
236C2×C22⋊Dic89C2311yescharacteristic
237C2×C22⋊Dic89C2311yescharacteristic
238C2×C22⋊Dic89C2311yescharacteristic
239C2×C22⋊Dic89C2311yescharacteristic
240C2×C22⋊Dic89C2311yescharacteristic
241C2×C22⋊Dic89C2311yescharacteristic
242C2×C22⋊Dic89C2311yescharacteristic
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×C22⋊Dic89C2311yescharacteristic
257C2×C22⋊Dic89C2311yescharacteristic
258C2×C22⋊Dic89C2311yescharacteristic
259C2×C22⋊Dic89C2311yescharacteristic
260C2×C22⋊Dic89C2311yescharacteristic
261C2×C22⋊Dic89C2311yescharacteristic
262C2×C22⋊Dic89C2311yescharacteristic
263C2×C22⋊Dic89C2311yescharacteristic
264C2×C22⋊Dic89C2311yescharacteristic
265C2×#13083551C2311yescharacteristic
266C2×#13083551C2311yescharacteristic
267C2×#13083551C2311yescharacteristic
268C2×#13083551C2311yescharacteristic
269C2×#13083551C2311yescharacteristic
270C2×#13083551C2311yescharacteristic
271C2×#13083551C2311yescharacteristic
272C2×#13083551C2311yescharacteristic
273C2×#13083551C2311yescharacteristic
274C2×C4×Dic89—42no—
275C2×C4×Dic89C2311yescharacteristic
276C2×C4×Dic89C2311yescharacteristic
277C2×C4×Dic89C2311yescharacteristic
278C2×C4×Dic89C2311yescharacteristic
279C2×C4×Dic89C2311yescharacteristic
280C2×C4×Dic89C2311yescharacteristic
281C2×C4×Dic89C2311yescharacteristic
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
317#15667919C2311yescharacteristic
318#15667919C2311yescharacteristic
319#15667919C2311yescharacteristic
320#15667919C2311yescharacteristic
321#15667919C2311yescharacteristic
322C25×C89C2311yescharacteristic
323C25×C89C2311yescharacteristic
324C22×D4×C89—24no—
325C22×D4×C89—42no—
326C22×D4×C89—42no—
327C22×D4×C89C2311yescharacteristic
328C22×D4×C89C2311yescharacteristic
329C22×D4×C89C2311yescharacteristic
330C22×D4×C89C2311yescharacteristic
331C23×C4×C89C2311yescharacteristic
332C23×C4×C89C2311yescharacteristic
333C23×C4×C89C2311yescharacteristic
334#123×C89—42no—
335#123×C89—42no—
336C2×C4⋊C4×C89C2311yescharacteristic
337C2×C4⋊C4×C89C2311yescharacteristic
338C2×C4⋊C4×C89C2311yescharacteristic
339C2×C4⋊C4×C89C2311yescharacteristic
340C2×C22⋊C4×C89—24no—
341C2×C22⋊C4×C89C2311yescharacteristic
342C2×C22⋊C4×C89C2311yescharacteristic
343C2×C22⋊C4×C89C2311yescharacteristic
344C2×C22⋊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×C22⋊C4×C89C2311yescharacteristic
357C2×C22⋊C4×C89C2311yescharacteristic
358C2×C22⋊C4×C89C2311yescharacteristic
359#95×C89C2311yescharacteristic
360#95×C89C2311yescharacteristic
361#95×C89C2311yescharacteristic
362#95×C89C2311yescharacteristic
363C23×D89C2411yescharacteristic
364C2×Dic178—41no—
365C2×Dic178—41no—
366C2×Dic178—41no—
367C2×C22⋊D89—22no—
368C2×C22⋊D89—22no—
369C2×C22⋊D89—22no—
370C2×C22⋊D89—22no—
371C2×C22⋊D89—22no—
372C2×C22⋊D89—22no—
373C2×C22⋊D89—41no—
374C2×C22⋊D89—41no—
375C2×C22⋊D89—41no—
376C2×C22⋊D89—41no—
377C2×C22⋊D89—41no—
378C2×C22⋊D89—41no—
379C2×C22⋊D89—41no—
380C2×C22⋊D89—41no—
381C2×C22⋊D89—41no—
382C22×Dic89—22no—
383C22×Dic89—22no—
384C22×Dic89—22no—
385C22×Dic89—22no—
386C22×Dic89—22no—
387C22×Dic89—41no—
388C22×Dic89—41no—
389C22×Dic89—41no—
390C22×Dic89—41no—
391C22×Dic89—41no—
392C22×Dic89—41no—
393C22×Dic89—41no—
394C22×Dic89—41no—
395C22×Dic89—41no—
396C22×Dic89—41no—
397C22×Dic89—41no—
398C22×Dic89—41no—
399C22×Dic89—41no—
400C22×Dic89C2411yescharacteristic
401C22×Dic89C2411yescharacteristic
402C22×Dic89C2411yescharacteristic
403C22×Dic89C2411yescharacteristic
404C22×Dic89C2411yescharacteristic
405C22×Dic89C2411yescharacteristic
406C22×Dic89C2411yescharacteristic
407C22×Dic89C2411yescharacteristic
408C22×Dic89C2411yescharacteristic
409C22×Dic89C2411yescharacteristic
410C22×Dic89C2411yescharacteristic
411C22×Dic89C2411yescharacteristic
412C22×Dic89C2411yescharacteristic
413C22×Dic89C2411yescharacteristic
414C22×Dic89C2411yescharacteristic
415C2×C4×D89—41no—
416C2×C4×D89—41no—
417C2×C4×D89—41no—
418C4⋊Dic89—22no—
419C4⋊Dic89—22no—
420C4⋊Dic89—41no—
421C4⋊Dic89—41no—
422C4⋊Dic89—41no—
423C4⋊Dic89—41no—
424C4⋊Dic89—41no—
425#13083553—22no—
426#13083553—22no—
427#13083553—41no—
428#13083553—41no—
429#13083553—41no—
430#13083553—41no—
431#13083553—41no—
432#13083553—41no—
433#13083553—41no—
434#13083553—41no—
435#13083553—41no—
436#13083553—41no—
437#13083553—41no—
438#13083553—41no—
439#13083553—41no—
440C22⋊Dic89—22no—
441C22⋊Dic89—22no—
442C22⋊Dic89—22no—
443C22⋊Dic89—22no—
444C22⋊Dic89—22no—
445C22⋊Dic89—22no—
446C22⋊Dic89—22no—
447C22⋊Dic89—22no—
448C22⋊Dic89—41no—
449C22⋊Dic89—41no—
450C22⋊Dic89—41no—
451C22⋊Dic89—41no—
452C22⋊Dic89—41no—
453C22⋊Dic89—41no—
454C22⋊Dic89—41no—
455C22⋊Dic89—41no—
456C22⋊Dic89—41no—
457C22⋊Dic89—41no—
458C22⋊Dic89—41no—
459C22⋊Dic89—41no—
460C22⋊Dic89—41no—
461C22⋊Dic89—41no—
462C22⋊Dic89—41no—
463C22⋊Dic89—41no—
464C22⋊Dic89—41no—
465C22⋊Dic89—41no—
466C22⋊Dic89—41no—
467C22⋊Dic89—41no—
468C22⋊Dic89—41no—
469#13083551—41no—
470#13083551—41no—
471#13083551—41no—
472#13083551—41no—
473#13083551—41no—
474#13083551—41no—
475#13083551—41no—
476#13083551—41no—
477#13083551—41no—
478C4×Dic89—41no—
479C4×Dic89—41no—
480C4×Dic89—41no—
481C4×Dic89—41no—
482C4×Dic89—41no—
483C4×Dic89—41no—
484C4×Dic89—41no—
485C24×C89—22no—
486C24×C89—22no—
487C24×C89—22no—
488C24×C89—41no—
489C24×C89—41no—
490C24×C89—41no—
491C24×C89—41no—
492C24×C89—41no—
493C24×C89—41no—
494C24×C89—41no—
495C24×C89—41no—
496C24×C89—41no—
497C24×C89—41no—
498C24×C89#4114yes—
499C24×C89C2411yescharacteristic
500C24×C89C2411yescharacteristic
501C24×C89C2411yescharacteristic
502C24×C89C2411yescharacteristic
503C24×C89C2411yescharacteristic
504C2×D4×C89—22no—
505C2×D4×C89—22no—
506C2×D4×C89—22no—
507C2×D4×C89—22no—
508C2×D4×C89—22no—
509C2×D4×C89—22no—
510C2×D4×C89—22no—
511C2×D4×C89—22no—
512C2×D4×C89—41no—
513C2×D4×C89—41no—
514C2×D4×C89—41no—
515C2×D4×C89—41no—
516C2×D4×C89—416no—
517C22×C4×C89—22no—
518C22×C4×C89—22no—
519C22×C4×C89—22no—
520C22×C4×C89—22no—
521C22×C4×C89—22no—
522C22×C4×C89—41no—
523C22×C4×C89—41no—
524C22×C4×C89—41no—
525C22×C4×C89—41no—
526C22×C4×C89C2411yescharacteristic
527C22×C4×C89C2411yescharacteristic
528C22×C4×C89C2411yescharacteristic
529C22×C4×C89C2411yescharacteristic
530C22×C4×C89C2411yescharacteristic
531C22×C4×C89C2411yescharacteristic
532C22×C4×C89C2411yescharacteristic
533C22×C4×C89C2411yescharacteristic
534C22×C4×C89C2411yescharacteristic
535C22×C4×C89C2411yescharacteristic
536C4⋊C4×C89—41no—
537C4⋊C4×C89—41no—
538C4⋊C4×C89—41no—
539C4⋊C4×C89—41no—
540C22⋊C4×C89—22no—
541C22⋊C4×C89—22no—
542C22⋊C4×C89—22no—
543C22⋊C4×C89—22no—
544C22⋊C4×C89—22no—
545C22⋊C4×C89—22no—
546C22⋊C4×C89—41no—
547C22⋊C4×C89—41no—
548C22⋊C4×C89—41no—
549C22⋊C4×C89—41no—
550C22⋊C4×C89—41no—
551C22⋊C4×C89—41no—
552C22⋊C4×C89—41no—
553C22⋊C4×C89—41no—
554C22⋊C4×C89—41no—
555C22⋊C4×C89—41no—
556C22⋊C4×C89—41no—
557C22⋊C4×C89—41no—
558C23×C89—21no—
559C23×C89—21no—
560C23×C89—21no—
561C23×C89—21no—
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—28no—
575C23×C89—21no—
576C23×C89—21no—
577C23×C89—21no—
578C23×C89—21no—
579C23×C89—21no—
580C23×C89—21no—
581C23×C89—21no—
582C23×C89—21no—
583C23×C89—21no—
584C23×C89—21no—
585C23×C89—21no—
586C23×C89—21no—
587C23×C89—21no—
588C23×C89—21no—
589C23×C89—44no—
590C23×C89—44no—
591C23×C89—44no—
592C23×C89—82no—
593C23×C89—82no—
594C23×C89—82no—
595C23×C89—82no—
596C23×C89—82no—
597C23×C89—82no—
598C23×C89—82no—
599C23×C89—82no—
600C23×C89—82no—
601C23×C89—82no—
602C23×C89C2×#4112yes—
603C23×C89C2×#4112yes—
604C23×C89C2×#4112yes—
605C23×C89H(5,𝔽2)12yes—
606C23×C89H(5,𝔽2)12yes—
607C23×C89C2511yescharacteristic
608C22×D89—21no—
609C22×D89—21no—
610C22×D89—21no—
611C22×D89—21no—
612C22×D89—21no—
613C22×D89—21no—
614C22×D89—21no—
615D4×C89—44no—
616D4×C89—44no—
617D4×C89—44no—
618D4×C89—44no—
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—21no—
642C2×C4×C89—21no—
643C2×C4×C89—21no—
644C2×C4×C89—21no—
645C2×C4×C89—21no—
646C2×C4×C89—21no—
647C2×C4×C89—21no—
648C2×C4×C89—21no—
649C2×C4×C89—44no—
650C2×C4×C89—44no—
651C2×C4×C89—44no—
652C22⋊D89—44no—
653C22⋊D89—82no—
654C22⋊D89—82no—
655C22⋊D89—82no—
656C22⋊D89—82no—
657C2×Dic89—21no—
658C2×Dic89—21no—
659C2×Dic89—21no—
660C2×Dic89—21no—
661C2×Dic89—21no—
662C2×Dic89—21no—
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—21no—
688C2×Dic89—21no—
689C2×Dic89—21no—
690C2×Dic89—21no—
691C2×Dic89—21no—
692C2×Dic89—21no—
693C2×Dic89—21no—
694C2×Dic89—21no—
695C2×Dic89—21no—
696C2×Dic89—21no—
697C2×Dic89—21no—
698C2×Dic89—21no—
699C2×Dic89—21no—
700C2×Dic89—21no—
701C2×Dic89—44no—
702C2×Dic89—44no—
703C2×Dic89—82no—
704C2×Dic89—82no—
705C2×Dic89—82no—
706C2×Dic89—82no—
707C2×Dic89H(5,𝔽2)12yes—
708C4×D89—82no—
709Dic178—82no—
710C22×C89—22no—
711C22×C89—22no—
712C22×C89—22no—
713C22×C89—22no—
714C22×C89—22no—
715C22×C89—22no—
716C22×C89—22no—
717C22×C89—22no—
718C22×C89—22no—
719C22×C89—22no—
720C22×C89—22no—
721C22×C89—22no—
722C22×C89—41no—
723C22×C89—41no—
724C22×C89—41no—
725C22×C89—41no—
726C22×C89—41no—
727C22×C89—41no—
728C22×C89—41no—
729C22×C89—41no—
730C22×C89—41no—
731C22×C89—41no—
732C22×C89—41no—
733C22×C89—41no—
734C22×C89—41no—
735C22×C89—41no—
736C22×C89—41no—
737C22×C89—41no—
738C22×C89—41no—
739C22×C89—41no—
740C22×C89—41no—
741C22×C89—41no—
742C22×C89—41no—
743C22×C89—41no—
744C22×C89—88no—
745C22×C89—88no—
746C22×C89#53814yes—
747C22×C89C22×#4111yescharacteristic
748C22×C89C2×H(5,𝔽2)11yescharacteristic
749C22×C89C2×H(5,𝔽2)11yescharacteristic
750C22×C89C2×H(5,𝔽2)11yescharacteristic
751C22×C89#58511yescharacteristic
752C22×C89#58511yescharacteristic
753C22×C89#58511yescharacteristic
754C2×D89—41no—
755C2×D89—41no—
756C2×D89—41no—
757C2×D89—41no—
758C2×D89—41no—
759C2×D89—41no—
760C2×D89—41no—
761C4×C89—41no—
762C4×C89—41no—
763C4×C89—41no—
764C4×C89—41no—
765C4×C89—41no—
766C4×C89—41no—
767C4×C89—41no—
768C4×C89—41no—
769C4×C89—41no—
770C4×C89—41no—
771Dic89—22no—
772Dic89—41no—
773Dic89—41no—
774Dic89—41no—
775Dic89—41no—
776Dic89—41no—
777Dic89—41no—
778Dic89—41no—
779Dic89—41no—
780Dic89—41no—
781Dic89—41no—
782Dic89—41no—
783Dic89—41no—
784Dic89—41no—
785Dic89—41no—
786#36986—891nomaximal, Sylow
787C2×C89—24no—
788C2×C89—42no—
789C2×C89—42no—
790C2×C89—81no—
791C2×C89—81no—
792C2×C89C2×#53811yescharacteristic
793C2×C89#349111yescharacteristic
794C2×C89#350511yescharacteristic
795C2×C89#353311yescharacteristic
796C2×C89#353411yescharacteristic
797C2×C89#355811yescharacteristic
798C2×C89#356011yescharacteristic
799D89—81no—
800#2854—891no—
801#2853—891no—
802#2797—891no—
803#2779—891no—
804#2779—891no—
805#2778—891no—
806#2771—891no—
807#2765—891no—
808#2753—891no—
809#2751—891no—
810#2750—891no—
811#2741—891no—
812#2736—891no—
813#2735—891no—
814#2702—891no—
815#2697—891no—
816#2696—891no—
817#2685—891no—
818#2643—891no—
819#2639—891no—
820#2488—891no—
821#2481—891no—
822#2443—891no—
823#2437—891no—
824#2425—891no—
825#2412—891no—
826#2410—891no—
827#2405D8911yescharacteristic, complemented
828#2321—891no—
829#2308—891no—
830C2×#388—891no—
831C89#3698611yescharacteristic, complemented, Sylow
832C23×D4C2×D8911yescharacteristic
833C2×#126—891no—
834C2×#123—891no—
835C2×#123—891no—
836C2×#123C2×D8911yescharacteristic
837C2×#123C2×D8911yescharacteristic
838C2×C22⋊Q8—891no—
839C2×C22⋊Q8—891no—
840C2×#121—891no—
841C2×#121—891no—
842C2×#120—891no—
843C2×#120—891no—
844C2×C4×D4—891no—
845C22×C4⋊C4—891no—
846C22×C22⋊C4—891no—
847C22×C22⋊C4—891no—
848C22×C22⋊C4—891no—
849C22×C22⋊C4C2×D8911yescharacteristic
850C22×C42—891no—
851#401—891no—
852#400—891no—
853#400—891no—
854#400—891no—
855#400—891no—
856#400—891no—
857#400—891no—
858#400—891no—
859#400—891no—
860#400—891no—
861#399—891no—
862#399—891no—
863#398—891no—
864#398—891no—
865#397—891no—
866#397—891no—
867#397—891no—
868#397—891no—
869#397—891no—
870#397—891no—
871#397—891no—
872#397—891no—
873#397—891no—
874#397—891no—
875#397—891no—
876#396—891no—
877#396—891no—
878#396—891no—
879#396—891no—
880#396—891no—
881#394—891no—
882#394—891no—
883#394—891no—
884#394—891no—
885#394—891no—
886#394—891no—
887#394—891no—
888#394—891no—
889#394C2×D8911yescharacteristic
890#394C2×D8911yescharacteristic
891#394C2×D8911yescharacteristic
892#394C2×D8911yescharacteristic
893#393—891no—
894#393—891no—
895#393—891no—
896#393—891no—
897#392—891no—
898#392—891no—
899#391—891no—
900#390—891no—
901#390—891no—
902#390—891no—
903#390—891no—
904#389—891no—
905#389—891no—
906#389—891no—
907#388—891no—
908#388—891no—
909#388—891no—
910#388—891no—
911#388—891no—
912#388—891no—
913#388—891no—
914#388—891no—
915#388—891no—
916#388—891no—
917#388—891no—
918#388—891no—
919#388—891no—
920#388—891no—
921#388—891no—
922#388—891no—
923#388—891no—
924#388—891no—
925#388—891no—
926#388—891no—
927#388—891no—
928#388—891no—
929#388—891no—
930#388—891no—
931#388—891no—
932#387—891no—
933#387—891no—
934#387—891no—
935#387—891no—
936#387—891no—
937#387—891no—
938#387—891no—
939#386—891no—
940#386—891no—
941#386—891no—
942#386—891no—
943#386—891no—
944#386—891no—
945#386—891no—
946#386—891no—
947#386—891no—
948#386—891no—
949#386—891no—
950#386—891no—
951#386—891no—
952#386—891no—
953#386—891no—
954#386—891no—
955#386—891no—
956#386—891no—
957#386C2×D8911yescharacteristic
958#386C2×D8911yescharacteristic
959#385—891no—
960#385—891no—
961#385—891no—
962#385—891no—
963#385—891no—
964#385—891no—
965#385—891no—
966#385—891no—
967#385C2×D8911yescharacteristic
968#385C2×D8911yescharacteristic
969#382—891no—
970#381—891no—
971#381—891no—
972#381—891no—
973#380—891no—
974#380—891no—
975#380—891no—
976#380—891no—
977#380—891no—
978#379—891no—
979#379—891no—
980#379—891no—
981#379C2×D8911yescharacteristic
982#379C2×D8911yescharacteristic
983#379C2×D8911yescharacteristic
984C4×C22⋊C4—891no—
985C2×#95—891no—
986C2×#95—891no—
987C25C22×D8911yescharacteristic
988C25C22×D8911yescharacteristic
989C22×Q8—891no—
990C22×D4—24no—
991C22×D4—42no—
992C22×D4—42no—
993C22×D4—891no—
994C22×D4—891no—
995C22×D4—891no—
996C22×D4—891no—
997C22×D4—891no—
998C22×D4C22×D8911yescharacteristic
999C22×D4C22×D8911yescharacteristic
1000C22×D4C22×D8911yescharacteristic
1001C22×D4C22×D8911yescharacteristic
1002C23×C4—891no—
1003C23×C4—891no—
1004C23×C4—891no—
1005C23×C4—891no—
1006C23×C4—891no—
1007C23×C4—891no—
1008C23×C4—891no—
1009C23×C4C22×D8911yescharacteristic
1010C23×C4C22×D8911yescharacteristic
1011C23×C4C22×D8911yescharacteristic
1012#126—3562no—
1013#123—42no—
1014#123—42no—
1015#123—3562no—
1016#123—3562no—
1017C22⋊Q8—3562no—
1018C22⋊Q8—3562no—
1019#121—3562no—
1020#121—3562no—
1021#120—3562no—
1022#120—1784no—
1023C4×D4—3562no—
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⋊C4—891no—
1040C2×C4⋊C4—891no—
1041C2×C4⋊C4—891no—
1042C2×C4⋊C4—891no—
1043C2×C4⋊C4—891no—
1044C2×C4⋊C4—891no—
1045C2×C4⋊C4—891no—
1046C2×C4⋊C4—3562no—
1047C2×C4⋊C4C22×D8911yescharacteristic
1048C2×C4⋊C4C22×D8911yescharacteristic
1049C2×C4⋊C4C22×D8911yescharacteristic
1050C2×C4⋊C4C22×D8911yescharacteristic
1051C2×C22⋊C4—24no—
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—891no—
1077C2×C22⋊C4—891no—
1078C2×C22⋊C4—891no—
1079C2×C22⋊C4—891no—
1080C2×C22⋊C4—891no—
1081C2×C22⋊C4—891no—
1082C2×C22⋊C4—891no—
1083C2×C22⋊C4—891no—
1084C2×C22⋊C4—891no—
1085C2×C22⋊C4—891no—
1086C2×C22⋊C4—891no—
1087C2×C22⋊C4—891no—
1088C2×C22⋊C4—891no—
1089C2×C22⋊C4—891no—
1090C2×C22⋊C4—3562no—
1091C2×C22⋊C4—3562no—
1092C2×C22⋊C4—3562no—
1093C2×C22⋊C4C22×D8911yescharacteristic
1094C2×C22⋊C4C22×D8911yescharacteristic
1095C2×C22⋊C4C22×D8911yescharacteristic
1096C2×C22⋊C4C22×D8911yescharacteristic
1097C2×C22⋊C4C22×D8911yescharacteristic
1098C2×C22⋊C4C22×D8911yescharacteristic
1099C2×C22⋊C4C22×D8911yescharacteristic
1100C2×C22⋊C4C22×D8911yescharacteristic
1101C2×C22⋊C4C22×D8911yescharacteristic
1102C2×C22⋊C4C22×D8911yescharacteristic
1103C2×C22⋊C4C22×D8911yescharacteristic
1104C2×C22⋊C4C22×D8911yescharacteristic
1105C2×C22⋊C4C22×D8911yescharacteristic
1106C2×C22⋊C4C22×D8911yescharacteristic
1107C2×C22⋊C4C22×D8911yescharacteristic
1108C2×C22⋊C4C22×D8911yescharacteristic
1109C2×C22⋊C4C22×D8911yescharacteristic
1110C2×C22⋊C4C22×D8911yescharacteristic
1111C2×C42—891no—
1112C2×C42—891no—
1113C2×C42—891no—
1114C2×C42—891no—
1115C2×C42—891no—
1116C2×C42—891no—
1117C2×C42—891no—
1118C2×C42—3562no—
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#95—891no—
1145#95—891no—
1146#95—891no—
1147#95—891no—
1148#95—891no—
1149#95—891no—
1150#95—891no—
1151#95—891no—
1152#95—891no—
1153#95—891no—
1154#95—891no—
1155#95—891no—
1156#95—891no—
1157#95—891no—
1158#95—891no—
1159#95C22×D8911yescharacteristic
1160#95C22×D8911yescharacteristic
1161#95C22×D8911yescharacteristic
1162#95C22×D8911yescharacteristic
1163C24—22no—
1164C24—22no—
1165C24—22no—
1166C24—41no—
1167C24—41no—
1168C24—41no—
1169C24—41no—
1170C24—41no—
1171C24—41no—
1172C24—41no—
1173C24—41no—
1174C24—41no—
1175C24—41no—
1176C24—891no—
1177C24#1308357314yes—
1178C24C23×D8911yescharacteristic
1179C24C23×D8911yescharacteristic
1180C24C23×D8911yescharacteristic
1181C24C23×D8911yescharacteristic
1182C24C23×D8911yescharacteristic
1183C2×Q8—3561no—
1184C2×Q8—3561no—
1185C2×Q8—3561no—
1186C2×D4—22no—
1187C2×D4—22no—
1188C2×D4—22no—
1189C2×D4—22no—
1190C2×D4—22no—
1191C2×D4—22no—
1192C2×D4—22no—
1193C2×D4—22no—
1194C2×D4—41no—
1195C2×D4—41no—
1196C2×D4—41no—
1197C2×D4—41no—
1198C2×D4—416no—
1199C2×D4—3561no—
1200C2×D4—3561no—
1201C2×D4—3561no—
1202C2×D4—3561no—
1203C2×D4—3561no—
1204C2×D4—3561no—
1205C2×D4—3561no—
1206C2×D4—3561no—
1207C2×D4—3561no—
1208C2×D4—1782no—
1209C2×D4—1782no—
1210C2×D4—1782no—
1211C2×D4—1782no—
1212C2×D4—1782no—
1213C2×D4—1782no—
1214C22×C4—22no—
1215C22×C4—22no—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—891no—
1224C22×C4—891no—
1225C22×C4—891no—
1226C22×C4—891no—
1227C22×C4—891no—
1228C22×C4—891no—
1229C22×C4—891no—
1230C22×C4—891no—
1231C22×C4—891no—
1232C22×C4—891no—
1233C22×C4—891no—
1234C22×C4—891no—
1235C22×C4—891no—
1236C22×C4—891no—
1237C22×C4—891no—
1238C22×C4—3561no—
1239C22×C4—3561no—
1240C22×C4—3561no—
1241C22×C4—3561no—
1242C22×C4—3561no—
1243C22×C4—3561no—
1244C22×C4—3561no—
1245C22×C4—3561no—
1246C22×C4—3561no—
1247C22×C4—3561no—
1248C22×C4—3561no—
1249C22×C4—3561no—
1250C22×C4—3561no—
1251C22×C4—3561no—
1252C22×C4—3561no—
1253C22×C4—3561no—
1254C22×C4—1782no—
1255C22×C4—1782no—
1256C22×C4—1782no—
1257C22×C4—1782no—
1258C22×C4—1782no—
1259C22×C4C23×D8911yescharacteristic
1260C22×C4C23×D8911yescharacteristic
1261C22×C4C23×D8911yescharacteristic
1262C22×C4C23×D8911yescharacteristic
1263C22×C4C23×D8911yescharacteristic
1264C22×C4C23×D8911yescharacteristic
1265C22×C4C23×D8911yescharacteristic
1266C22×C4C23×D8911yescharacteristic
1267C22×C4C23×D8911yescharacteristic
1268C22×C4C23×D8911yescharacteristic
1269C4⋊C4—41no—
1270C4⋊C4—41no—
1271C4⋊C4—41no—
1272C4⋊C4—41no—
1273C4⋊C4—3561no—
1274C4⋊C4—3561no—
1275C4⋊C4—3561no—
1276C4⋊C4—3561no—
1277C4⋊C4—3561no—
1278C4⋊C4—3561no—
1279C4⋊C4—3561no—
1280C4⋊C4—3561no—
1281C4⋊C4—3561no—
1282C4⋊C4—3561no—
1283C4⋊C4—3561no—
1284C4⋊C4—3561no—
1285C4⋊C4—3561no—
1286C4⋊C4—3561no—
1287C4⋊C4—3561no—
1288C4⋊C4—3561no—
1289C4⋊C4—3561no—
1290C4⋊C4—3561no—
1291C4⋊C4—1782no—
1292C4⋊C4—1782no—
1293C4⋊C4—1782no—
1294C4⋊C4—1782no—
1295C22⋊C4—22no—
1296C22⋊C4—22no—
1297C22⋊C4—22no—
1298C22⋊C4—22no—
1299C22⋊C4—22no—
1300C22⋊C4—22no—
1301C22⋊C4—41no—
1302C22⋊C4—41no—
1303C22⋊C4—41no—
1304C22⋊C4—41no—
1305C22⋊C4—41no—
1306C22⋊C4—41no—
1307C22⋊C4—41no—
1308C22⋊C4—41no—
1309C22⋊C4—41no—
1310C22⋊C4—41no—
1311C22⋊C4—41no—
1312C22⋊C4—41no—
1313C22⋊C4—3561no—
1314C22⋊C4—3561no—
1315C22⋊C4—3561no—
1316C22⋊C4—3561no—
1317C22⋊C4—3561no—
1318C22⋊C4—3561no—
1319C22⋊C4—3561no—
1320C22⋊C4—3561no—
1321C22⋊C4—3561no—
1322C22⋊C4—3561no—
1323C22⋊C4—3561no—
1324C22⋊C4—3561no—
1325C22⋊C4—3561no—
1326C22⋊C4—3561no—
1327C22⋊C4—3561no—
1328C22⋊C4—3561no—
1329C22⋊C4—3561no—
1330C22⋊C4—3561no—
1331C22⋊C4—3561no—
1332C22⋊C4—3561no—
1333C22⋊C4—3561no—
1334C22⋊C4—3561no—
1335C22⋊C4—3561no—
1336C22⋊C4—3561no—
1337C22⋊C4—3561no—
1338C22⋊C4—3561no—
1339C22⋊C4—3561no—
1340C22⋊C4—3561no—
1341C22⋊C4—3561no—
1342C22⋊C4—3561no—
1343C22⋊C4—1782no—
1344C22⋊C4—1782no—
1345C22⋊C4—1782no—
1346C22⋊C4—1782no—
1347C22⋊C4—1782no—
1348C22⋊C4—1782no—
1349C22⋊C4—1782no—
1350C22⋊C4—1782no—
1351C42—3561no—
1352C42—3561no—
1353C42—3561no—
1354C42—3561no—
1355C42—3561no—
1356C42—3561no—
1357C42—3561no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—21no—
1371C23—21no—
1372C23—21no—
1373C23—21no—
1374C23—28no—
1375C23—21no—
1376C23—21no—
1377C23—21no—
1378C23—21no—
1379C23—21no—
1380C23—21no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—44no—
1390C23—44no—
1391C23—44no—
1392C23—82no—
1393C23—82no—
1394C23—82no—
1395C23—82no—
1396C23—82no—
1397C23—82no—
1398C23—82no—
1399C23—82no—
1400C23—82no—
1401C23—82no—
1402C23—1781no—
1403C23—1781no—
1404C23—1781no—
1405C23—1781no—
1406C23—1781no—
1407C23—1781no—
1408C23—1781no—
1409C23C2×#1308357312yes—
1410C23C2×#1308357312yes—
1411C23C2×#1308357312yes—
1412C23#1566805712yes—
1413C23#1566805712yes—
1414C23C24×D8911yescharacteristic
1415Q8—7122no—
1416D4—44no—
1417D4—44no—
1418D4—44no—
1419D4—44no—
1420D4—3564no—
1421D4—7122no—
1422D4—7122no—
1423D4—7122no—
1424D4—7122no—
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—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—44no—
1456C2×C4—44no—
1457C2×C4—44no—
1458C2×C4—892no—
1459C2×C4—3564no—
1460C2×C4—3564no—
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—1781no—
1490C2×C4—1781no—
1491C2×C4—1781no—
1492C2×C4—1781no—
1493C2×C4—1781no—
1494C2×C4—1781no—
1495C2×C4—1781no—
1496C2×C4—1781no—
1497C2×C4—1781no—
1498C2×C4—1781no—
1499C2×C4—1781no—
1500C2×C4—1781no—
1501C2×C4—1781no—
1502C2×C4—1781no—
1503C2×C4—1781no—
1504C2×C4—1781no—
1505C2×C4—7122no—
1506C2×C4—7122no—
1507C2×C4—7122no—
1508C2×C4—7122no—
1509C2×C4—7122no—
1510C22—22no—
1511C22—22no—
1512C22—22no—
1513C22—22no—
1514C22—22no—
1515C22—22no—
1516C22—22no—
1517C22—22no—
1518C22—22no—
1519C22—22no—
1520C22—22no—
1521C22—22no—
1522C22—41no—
1523C22—41no—
1524C22—41no—
1525C22—41no—
1526C22—41no—
1527C22—41no—
1528C22—41no—
1529C22—41no—
1530C22—41no—
1531C22—41no—
1532C22—41no—
1533C22—41no—
1534C22—41no—
1535C22—41no—
1536C22—41no—
1537C22—41no—
1538C22—41no—
1539C22—41no—
1540C22—41no—
1541C22—41no—
1542C22—41no—
1543C22—41no—
1544C22—88no—
1545C22—88no—
1546C22—3561no—
1547C22—3561no—
1548C22—3561no—
1549C22—3561no—
1550C22—3561no—
1551C22—3561no—
1552C22—3561no—
1553C22#1915218314yes—
1554C22C22×#1308357311yescharacteristic
1555C22H(5,𝔽2)×D8911yescharacteristic
1556C22C2×#1566805711yescharacteristic
1557C22C2×#1566805711yescharacteristic
1558C22#1915243311yescharacteristic
1559C22#1915243411yescharacteristic
1560C22#1915243411yescharacteristic
1561C4—41no—
1562C4—41no—
1563C4—41no—
1564C4—41no—
1565C4—41no—
1566C4—41no—
1567C4—41no—
1568C4—41no—
1569C4—41no—
1570C4—41no—
1571C4—3561no—
1572C4—3561no—
1573C4—3561no—
1574C4—3561no—
1575C4—3561no—
1576C4—3561no—
1577C4—3561no—
1578C4—3561no—
1579C4—3561no—
1580C4—3561no—
1581C4—3561no—
1582C4—3561no—
1583C4—3561no—
1584C4—3561no—
1585C4—1782no—
1586C2—24no—
1587C2—42no—
1588C2—42no—
1589C2—81no—
1590C2—81no—
1591C2—7121no—
1592C2C2×#1915218311yescharacteristic
1593C2#2603394811yescharacteristic
1594C2#2603408911yescharacteristic
1595C2#2603441111yescharacteristic
1596C2#2603443411yescharacteristic
1597C2#2603476211yescharacteristic
1598C2#2603479211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutator, socle, cosocleC23×C89C25
FittingC89×#2405C2
prime radical#26023626C2
hypercenter#2405D89
hypocenterC89#36986
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2405

Complements

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

NH ≅ G/Ntype
1. #26028581C2semidirect
2. #26028571C2semidirect
3. #26028115C2semidirect
4. #26027890C2semidirect
5. #26027878C2semidirect
6. #26027875C2semidirect
7. #26027770C2semidirect
8. #26027687C2semidirect
9. #26027522C2semidirect
10. #26027509C2semidirect
11. #26027494C2semidirect
12. #26027372C2semidirect
13. #26027298C2semidirect
14. #26027293C2semidirect
15. #26026885C2semidirect
16. #26026815C2semidirect
17. #26026808C2semidirect
18. #26026643C2semidirect
19. #26026207C2semidirect
20. #26026182C2semidirect
21. #26024582C2semidirect
22. #26024512C2semidirect
23. #26023993C2semidirect
24. #26023918C2semidirect
25. #26023799C2semidirect
26. #26023648C2semidirect
28. #26022907C2semidirect
29. #26022830C2semidirect
30. C2×#19151491C2semidirect
31. C89×#2405C2semidirect
32. C2×#15668005C22semidirect
33. C2×#15667995C22semidirect
34. C2×#15667994C22semidirect
35. C2×#15667989C22semidirect
36. C2×#15667989C22semidirect
41. C2×#15667972C22semidirect
42. C22×C4⋊Dic89C22semidirect
46. C22×C4×Dic89C22semidirect
47. C89⋊#401C22semidirect
48. #19151540C22semidirect
49. #19151540C22semidirect
50. #19151540C22semidirect
51. #19151539C22semidirect
52. #19151539C22semidirect
53. #19151538C22semidirect
54. #19151538C22semidirect
55. #19151536C22semidirect
56. #19151536C22semidirect
58. #19151534C22semidirect
59. #19151532C22semidirect
60. #19151529C22semidirect
61. #19151527C22semidirect
64. #19151526C22semidirect
65. #19151526C22semidirect
66. #19151526C22semidirect
67. #19151525C22semidirect
68. #19151524C22semidirect
69. #19151523C22semidirect
70. #19151523C22semidirect
71. #19151523C22semidirect
74. #19151521C22semidirect
75. #19151521C22semidirect
76. #19151521C22semidirect
77. #19151514C22semidirect
78. #19151514C22semidirect
79. #19151514C22semidirect
82. #19151513C22semidirect
85. #19151511C22semidirect
87. #19151510C22semidirect
88. #19151510C22semidirect
91. #19151503C22semidirect
93. #19151498C22semidirect
94. #19151498C22semidirect
95. #19151498C22semidirect
96. #19151494C22semidirect
97. #19151493C22semidirect
98. #19151493C22semidirect
100. #19151492C22semidirect
101. #19151492C22semidirect
102. #19151492C22semidirect
103. #19151492C22semidirect
104. #19151492C22semidirect
109. #19151491C22semidirect
110. #19151491C22semidirect
111. #19151491C22semidirect
112. #19151491C22semidirect
113. #19151491C22semidirect
114. #19151491C22semidirect
115. #19151488C22semidirect
116. #19151488C22semidirect
118. #19151486C22semidirect
119. #19151486C22semidirect
120. #19151486C22semidirect
121. #19151486C22semidirect
122. #19151486C22semidirect
123. #19151486C22semidirect
124. #19151485C22semidirect
125. #19151483C22semidirect
126. #19151481C22semidirect
127. #19151479C22semidirect
128. #19151479C22semidirect
129. #19151479C22semidirect
130. #19151479C22semidirect
142. #19151477C22semidirect
143. #19151475C22semidirect
144. #19151475C22semidirect
145. #19151475C22semidirect
147. #19151474C22semidirect
148. #19151474C22semidirect
149. #19151473C22semidirect
150. #19151473C22semidirect
151. #19151472C22semidirect
153. #19151471C22semidirect
154. #19151470C22semidirect
155. #19151470C22semidirect
156. #19151470C22semidirect
157. #19151463C22semidirect
160. #19151461C22semidirect
161. #19151456C22semidirect
162. #19151456C22semidirect
163. #19151456C22semidirect
164. #19151456C22semidirect
165. #19151455C22semidirect
169. C22⋊C4×Dic89C22semidirect
170. C2×#15667919C22semidirect
171. C2×#15667919C22semidirect
827. #2405D89semidirect
831. C89#36986semidirect

Maximal subgroups

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

subgroupindex
#260285812
#260285712
#260281152
#260278902
#260278782
#260278752
#260277702
#260276872
#260275222
#260275092
#260274942
#260273722
#260272982
#260272932
#260268852
#260268152
#260268082
#260266432
#260262072
#260261822
#260245822
#260245122
#260239932
#260239182
#260237992
#260236482
#260236262
#260229072
#260228302
C2×#191514912
C89×#24052
#3698689