Finite Group Databasebeta

← #36768585

Subgroups — #36768585

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#26028580C211yesmaximal, characteristic, complemented
2#26028577C211yesmaximal, characteristic, complemented
3#26028102C211yesmaximal, characteristic, complemented
4#26027891C211yesmaximal, characteristic, complemented
5#26027887C211yesmaximal, characteristic, complemented
6#26027877C211yesmaximal, characteristic, complemented
7#26027769C211yesmaximal, characteristic, complemented
8#26027694C211yesmaximal, characteristic, complemented
9#26027535C211yesmaximal, characteristic, complemented
10#26027498C211yesmaximal, characteristic, complemented
11#26027489C211yesmaximal, characteristic, complemented
12#26027369C211yesmaximal, characteristic, complemented
13#26027299C211yesmaximal, characteristic, complemented
14#26027287C211yesmaximal, characteristic, complemented
15#26026882C211yesmaximal, characteristic, complemented
16#26026817C211yesmaximal, characteristic, complemented
17#26026804C211yesmaximal, characteristic, complemented
18#26026650C211yesmaximal, characteristic, complemented
19#26026180C211yesmaximal, characteristic, complemented
20#26024576C211yesmaximal, characteristic, complemented
21#26024510C211yesmaximal, characteristic, complemented
22#26023993C211yesmaximal, characteristic, complemented
23#26023917C211yesmaximal, characteristic, complemented
24#26023801C211yesmaximal, characteristic, complemented
25#26023646C211yesmaximal, characteristic, complemented
26#26023625C211yesmaximal, characteristic
27#26023578C211yesmaximal, characteristic, complemented
28#26022909C211yesmaximal, characteristic, complemented
29#26022826C211yesmaximal, characteristic, complemented
30C2×#19151490C211yesmaximal, characteristic, complemented
31C89×#2643C211yesmaximal, characteristic, complemented
32C22×D4×D89C2211yescharacteristic
33C2×#15668007C2211yescharacteristic, complemented
34C2×#15667996C2211yescharacteristic
35C2×#15667996C2211yescharacteristic, complemented
36C2×#15667994C2211yescharacteristic, complemented
37C2×#15667993C2211yescharacteristic
38C2×#15667991C2211yescharacteristic, complemented
39C2×#15667990C2211yescharacteristic, complemented
40C2×#15667986C2211yescharacteristic
41C2×#15667984C2211yescharacteristic
42C2×#15667982C2211yescharacteristic
43C2×#15667982C2211yescharacteristic
44C2×#15667972C2211yescharacteristic, complemented
45C22×C4⋊Dic89C2211yescharacteristic, complemented
46C22×#13083551C2211yescharacteristic
47C22×#13083551C2211yescharacteristic
48C22×#13083551C2211yescharacteristic
49C2×C22⋊C4×D89C2211yescharacteristic
50C22×C4×Dic89C2211yescharacteristic, complemented
51#19151540C2211yescharacteristic, complemented
52#19151540C2211yescharacteristic, complemented
53#19151539C2211yescharacteristic, complemented
54#19151538C2211yescharacteristic, complemented
55#19151538C2211yescharacteristic, complemented
56#19151537C2211yescharacteristic, complemented
57#19151534C2211yescharacteristic, complemented
58#19151533C2211yescharacteristic
59#19151532C2211yescharacteristic, complemented
60#19151530C2211yescharacteristic, complemented
61#19151526C2211yescharacteristic, complemented
62#19151525C2211yescharacteristic
63#19151525C2211yescharacteristic
64#19151525C2211yescharacteristic, complemented
65#19151525C2211yescharacteristic, complemented
66#19151525C2211yescharacteristic, complemented
67#19151525C2211yescharacteristic, complemented
68#19151525C2211yescharacteristic, complemented
69#19151522C2211yescharacteristic
70#19151520C2211yescharacteristic
71#19151520C2211yescharacteristic, complemented
72#19151520C2211yescharacteristic, complemented
73#19151516C2211yescharacteristic
74#19151516C2211yescharacteristic
75#19151516C2211yescharacteristic
76#19151516C2211yescharacteristic, complemented
77#19151516C2211yescharacteristic, complemented
78#19151515C2211yescharacteristic
79#19151515C2211yescharacteristic
80#19151515C2211yescharacteristic, complemented
81#19151514C2211yescharacteristic
82#19151514C2211yescharacteristic
83#19151514C2211yescharacteristic
84#19151514C2211yescharacteristic, complemented
85#19151511C2211yescharacteristic
86#19151511C2211yescharacteristic, complemented
87#19151511C2211yescharacteristic, complemented
88#19151510C2211yescharacteristic, complemented
89#19151508C2211yescharacteristic
90#19151507C2211yescharacteristic
91#19151502C2211yescharacteristic, complemented
92#19151499C2211yescharacteristic
93#19151499C2211yescharacteristic, complemented
94#19151498C2211yescharacteristic, complemented
95#19151498C2211yescharacteristic, complemented
96#19151497C2211yescharacteristic, complemented
97#19151495C2211yescharacteristic, complemented
98#19151495C2211yescharacteristic, complemented
99#19151491C2211yescharacteristic, complemented
100#19151491C2211yescharacteristic, complemented
101#19151491C2211yescharacteristic, complemented
102#19151491C2211yescharacteristic, complemented
103#19151490C2211yescharacteristic
104#19151490C2211yescharacteristic
105#19151490C2211yescharacteristic
106#19151490C2211yescharacteristic
107#19151490C2211yescharacteristic, complemented
108#19151490C2211yescharacteristic, complemented
109#19151490C2211yescharacteristic, complemented
110#19151490C2211yescharacteristic, complemented
111#19151490C2211yescharacteristic, complemented
112#19151490C2211yescharacteristic, complemented
113#19151488C2211yescharacteristic
114#19151488C2211yescharacteristic, complemented
115#19151488C2211yescharacteristic, complemented
116#19151488C2211yescharacteristic, complemented
117#19151487C2211yescharacteristic
118#19151487C2211yescharacteristic, complemented
119#19151487C2211yescharacteristic, complemented
120#19151487C2211yescharacteristic, complemented
121#19151487C2211yescharacteristic, complemented
122#19151487C2211yescharacteristic, complemented
123#19151486C2211yescharacteristic, complemented
124#19151485C2211yescharacteristic, complemented
125#19151485C2211yescharacteristic, complemented
126#19151484C2211yescharacteristic, complemented
127#19151484C2211yescharacteristic, complemented
128#19151484C2211yescharacteristic, complemented
129#19151481C2211yescharacteristic, complemented
130#19151481C2211yescharacteristic, complemented
131#19151478C2211yescharacteristic
132#19151477C2211yescharacteristic
133#19151477C2211yescharacteristic
134#19151477C2211yescharacteristic, complemented
135#19151477C2211yescharacteristic, complemented
136#19151476C2211yescharacteristic
137#19151476C2211yescharacteristic
138#19151476C2211yescharacteristic
139#19151476C2211yescharacteristic
140#19151476C2211yescharacteristic, complemented
141#19151476C2211yescharacteristic, complemented
142#19151476C2211yescharacteristic, complemented
143#19151476C2211yescharacteristic, complemented
144#19151475C2211yescharacteristic
145#19151475C2211yescharacteristic
146#19151474C2211yescharacteristic
147#19151474C2211yescharacteristic
148#19151472C2211yescharacteristic
149#19151472C2211yescharacteristic
150#19151472C2211yescharacteristic
151#19151472C2211yescharacteristic, complemented
152#19151472C2211yescharacteristic, complemented
153#19151470C2211yescharacteristic, complemented
154#19151469C2211yescharacteristic, complemented
155#19151462C2211yescharacteristic, complemented
156#19151460C2211yescharacteristic
157#19151460C2211yescharacteristic
158#19151459C2211yescharacteristic, complemented
159#19151457C2211yescharacteristic, complemented
160#19151456C2211yescharacteristic, complemented
161#19151455C2211yescharacteristic, complemented
162#19151455C2211yescharacteristic, complemented
163#19151455C2211yescharacteristic, complemented
164#19151453C2211yescharacteristic
165#19151453C2211yescharacteristic
166#19151453C2211yescharacteristic
167#19151453C2211yescharacteristic
168#19151453C2211yescharacteristic
169#19151453C2211yescharacteristic
170C22⋊C4×Dic89C2211yescharacteristic, complemented
171C2×#15667919C2211yescharacteristic, complemented
172#401×C89C2211yescharacteristic, complemented
173#400×C89C2211yescharacteristic, complemented
174#400×C89C2211yescharacteristic, complemented
175#400×C89C2211yescharacteristic, complemented
176#397×C89C2211yescharacteristic, complemented
177#397×C89C2211yescharacteristic, complemented
178#397×C89C2211yescharacteristic, complemented
179#396×C89C2211yescharacteristic, complemented
180#386×C89C2211yescharacteristic
181#386×C89C2211yescharacteristic
182#386×C89C2211yescharacteristic
183#385×C89C2211yescharacteristic, complemented
184#385×C89C2211yescharacteristic, complemented
185#385×C89C2211yescharacteristic, complemented
186C2×#95×C89C2211yescharacteristic, complemented
187C24×D89C2311yescharacteristic
188C24×D89C2311yescharacteristic
189C22×Dic178C2311yescharacteristic
190C22×D356C2311yescharacteristic
191C22×D356C2311yescharacteristic
192C22×D356C2311yescharacteristic
193C22×D356C2311yescharacteristic
194C22×C22⋊D89C2311yescharacteristic
195C22×C22⋊D89C2311yescharacteristic
196C22×C22⋊D89C2311yescharacteristic
197C22×C22⋊D89C2311yescharacteristic
198C2×D4×D89—24no—
199C2×D4×D89—42no—
200C2×D4×D89—42no—
201C23×Dic89C2311yescharacteristic
202C23×Dic89C2311yescharacteristic
203C23×Dic89C2311yescharacteristic
204C22×C4×D89C2311yescharacteristic
205C22×C4×D89C2311yescharacteristic
206C22×C4×D89C2311yescharacteristic
207C22×C4×D89C2311yescharacteristic
208#15668007—42no—
209#15667996—42no—
210#15667996—42no—
211#15667994—42no—
212#15667993—42no—
213#15667991—42no—
214#15667990—42no—
215#15667986—42no—
216#15667984—42no—
217#15667982—24no—
218#15667982—42no—
219#15667972—42no—
220C2×C4⋊Dic89—42no—
221C2×C4⋊Dic89C2311yescharacteristic
222C2×C4⋊Dic89C2311yescharacteristic
223C2×C4⋊Dic89C2311yescharacteristic
224C2×C4⋊Dic89C2311yescharacteristic
225C2×C4⋊Dic89C2311yescharacteristic
226C2×C4⋊Dic89C2311yescharacteristic
227C2×C4⋊Dic89C2311yescharacteristic
228C2×C4⋊Dic89C2311yescharacteristic
229C2×C4⋊Dic89C2311yescharacteristic
230C2×C4⋊Dic89C2311yescharacteristic
231C2×#13083553C2311yescharacteristic
232C2×#13083553C2311yescharacteristic
233C2×#13083553C2311yescharacteristic
234C2×#13083553C2311yescharacteristic
235C2×#13083553C2311yescharacteristic
236C2×#13083553C2311yescharacteristic
237C2×#13083553C2311yescharacteristic
238C2×#13083553C2311yescharacteristic
239C2×#13083553C2311yescharacteristic
240C2×#13083553C2311yescharacteristic
241C2×C22⋊Dic89C2311yescharacteristic
242C2×C22⋊Dic89C2311yescharacteristic
243C2×C22⋊Dic89C2311yescharacteristic
244C2×C22⋊Dic89C2311yescharacteristic
245C2×C22⋊Dic89C2311yescharacteristic
246C2×C22⋊Dic89C2311yescharacteristic
247C2×C22⋊Dic89C2311yescharacteristic
248C2×#13083551—24no—
249C2×#13083551—42no—
250C2×#13083551—42no—
251C2×#13083551C2311yescharacteristic
252C2×#13083551C2311yescharacteristic
253C2×#13083551C2311yescharacteristic
254C2×#13083551C2311yescharacteristic
255C2×#13083551C2311yescharacteristic
256C2×#13083551C2311yescharacteristic
257C2×#13083551C2311yescharacteristic
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×#13083551C2311yescharacteristic
279C2×#13083551C2311yescharacteristic
280C2×#13083551C2311yescharacteristic
281C2×#13083551C2311yescharacteristic
282C2×#13083551C2311yescharacteristic
283C2×#13083551C2311yescharacteristic
284C2×#13083551C2311yescharacteristic
285C2×#13083551C2311yescharacteristic
286C2×#13083551C2311yescharacteristic
287C2×#13083551C2311yescharacteristic
288C2×#13083551C2311yescharacteristic
289C2×#13083551C2311yescharacteristic
290C2×#13083551C2311yescharacteristic
291C22⋊C4×D89—42no—
292C2×C4×Dic89—42no—
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
328C22×D4×C89C2311yescharacteristic
329C23×C4×C89C2311yescharacteristic
330C23×C4×C89C2311yescharacteristic
331C23×C4×C89C2311yescharacteristic
332C2×C4⋊C4×C89C2311yescharacteristic
333C2×C4⋊C4×C89C2311yescharacteristic
334C2×C4⋊C4×C89C2311yescharacteristic
335C2×C4⋊C4×C89C2311yescharacteristic
336C2×C4⋊C4×C89C2311yescharacteristic
337C2×C4⋊C4×C89C2311yescharacteristic
338C2×C22⋊C4×C89C2311yescharacteristic
339C2×C22⋊C4×C89C2311yescharacteristic
340C2×C22⋊C4×C89C2311yescharacteristic
341C2×C22⋊C4×C89C2311yescharacteristic
342C2×C22⋊C4×C89C2311yescharacteristic
343C2×C22⋊C4×C89C2311yescharacteristic
344C2×C22⋊C4×C89C2311yescharacteristic
345C2×C22⋊C4×C89C2311yescharacteristic
346C2×C22⋊C4×C89C2311yescharacteristic
347#95×C89C2311yescharacteristic
348#95×C89C2311yescharacteristic
349#95×C89C2311yescharacteristic
350#95×C89C2311yescharacteristic
351#95×C89C2311yescharacteristic
352#95×C89C2311yescharacteristic
353#95×C89C2311yescharacteristic
354#95×C89C2311yescharacteristic
355#95×C89C2311yescharacteristic
356#95×C89C2311yescharacteristic
357#95×C89C2311yescharacteristic
358#95×C89C2311yescharacteristic
359#95×C89C2311yescharacteristic
360#95×C89C2311yescharacteristic
361#95×C89C2311yescharacteristic
362#95×C89C2311yescharacteristic
363C23×D89—22no—
364C23×D89—22no—
365C23×D89—22no—
366C23×D89—41no—
367C23×D89—41no—
368C23×D89—41no—
369C23×D89—41no—
370C23×D89—41no—
371C23×D89—41no—
372C23×D89—41no—
373C23×D89—41no—
374C23×D89—41no—
375C23×D89—41no—
376C23×D89#4114yes—
377C23×D89C2411yescharacteristic
378C23×D89C2411yescharacteristic
379C23×D89C2411yescharacteristic
380C23×D89C2411yescharacteristic
381C2×Dic178—41no—
382C2×Dic178—41no—
383C2×Dic178—41no—
384C2×D356—22no—
385C2×D356—22no—
386C2×D356—22no—
387C2×D356—41no—
388C2×D356—41no—
389C2×D356—41no—
390C2×D356—41no—
391C2×D356—41no—
392C2×D356—41no—
393C2×D356—41no—
394C2×D356—41no—
395C2×D356—41no—
396C2×C22⋊D89—22no—
397C2×C22⋊D89—22no—
398C2×C22⋊D89—22no—
399C2×C22⋊D89—22no—
400C2×C22⋊D89—22no—
401C2×C22⋊D89—22no—
402C2×C22⋊D89—22no—
403C2×C22⋊D89—22no—
404C2×C22⋊D89—41no—
405C2×C22⋊D89—41no—
406C2×C22⋊D89—41no—
407C2×C22⋊D89—41no—
408D4×D89—416no—
409C22×Dic89—22no—
410C22×Dic89—22no—
411C22×Dic89—22no—
412C22×Dic89—22no—
413C22×Dic89—22no—
414C22×Dic89—22no—
415C22×Dic89—41no—
416C22×Dic89—41no—
417C22×Dic89—41no—
418C22×Dic89C2411yescharacteristic
419C22×Dic89C2411yescharacteristic
420C22×Dic89C2411yescharacteristic
421C22×Dic89C2411yescharacteristic
422C22×Dic89C2411yescharacteristic
423C22×Dic89C2411yescharacteristic
424C22×Dic89C2411yescharacteristic
425C22×Dic89C2411yescharacteristic
426C22×Dic89C2411yescharacteristic
427C22×Dic89C2411yescharacteristic
428C22×Dic89C2411yescharacteristic
429C22×Dic89C2411yescharacteristic
430C2×C4×D89—22no—
431C2×C4×D89—41no—
432C2×C4×D89—41no—
433C2×C4×D89—41no—
434C2×C4×D89—41no—
435C2×C4×D89—41no—
436C2×C4×D89—41no—
437C2×C4×D89—41no—
438C2×C4×D89—41no—
439C2×C4×D89—41no—
440C2×C4×D89—41no—
441C2×C4×D89—41no—
442C4⋊Dic89—22no—
443C4⋊Dic89—22no—
444C4⋊Dic89—41no—
445C4⋊Dic89—41no—
446C4⋊Dic89—41no—
447C4⋊Dic89—41no—
448C4⋊Dic89—41no—
449C4⋊Dic89—41no—
450C4⋊Dic89—41no—
451C4⋊Dic89—41no—
452#13083553—22no—
453#13083553—22no—
454#13083553—41no—
455#13083553—41no—
456#13083553—41no—
457#13083553—41no—
458#13083553—41no—
459#13083553—41no—
460#13083553—41no—
461#13083553—41no—
462C22⋊Dic89—22no—
463C22⋊Dic89—22no—
464C22⋊Dic89—41no—
465C22⋊Dic89—41no—
466C22⋊Dic89—41no—
467C22⋊Dic89—41no—
468C22⋊Dic89—41no—
469#13083551—22no—
470#13083551—22no—
471#13083551—22no—
472#13083551—22no—
473#13083551—22no—
474#13083551—22no—
475#13083551—22no—
476#13083551—22no—
477#13083551—22no—
478#13083551—41no—
479#13083551—41no—
480#13083551—41no—
481#13083551—41no—
482#13083551—41no—
483#13083551—41no—
484#13083551—41no—
485#13083551—41no—
486#13083551—41no—
487#13083551—41no—
488#13083551—41no—
489#13083551—41no—
490#13083551—41no—
491#13083551—41no—
492#13083551—41no—
493#13083551—41no—
494#13083551—41no—
495#13083551—41no—
496#13083551—41no—
497#13083551—41no—
498#13083551—41no—
499#13083551—41no—
500#13083551—41no—
501#13083551—41no—
502#13083551—41no—
503#13083551—41no—
504#13083551—41no—
505#13083551—41no—
506#13083551—41no—
507#13083551—41no—
508#13083551—41no—
509C4×Dic89—41no—
510C4×Dic89—41no—
511C4×Dic89—41no—
512C4×Dic89—41no—
513C4×Dic89—41no—
514C4×Dic89—41no—
515C4×Dic89—41no—
516C24×C89C2411yescharacteristic
517C24×C89C2411yescharacteristic
518C2×D4×C89—22no—
519C2×D4×C89—22no—
520C2×D4×C89—22no—
521C22×C4×C89—22no—
522C22×C4×C89—22no—
523C22×C4×C89—22no—
524C22×C4×C89—41no—
525C22×C4×C89—41no—
526C22×C4×C89—41no—
527C22×C4×C89—41no—
528C22×C4×C89—41no—
529C22×C4×C89—41no—
530C22×C4×C89C2411yescharacteristic
531C22×C4×C89C2411yescharacteristic
532C22×C4×C89C2411yescharacteristic
533C22×C4×C89C2411yescharacteristic
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
543C4⋊C4×C89—41no—
544C4⋊C4×C89—41no—
545C4⋊C4×C89—41no—
546C4⋊C4×C89—41no—
547C4⋊C4×C89—41no—
548C4⋊C4×C89—41no—
549C22⋊C4×C89—22no—
550C22⋊C4×C89—22no—
551C22⋊C4×C89—22no—
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×C89C2×#4112yes—
570C23×C89H(5,𝔽2)12yes—
571C23×C89H(5,𝔽2)12yes—
572C23×C89C2511yescharacteristic
573C22×D89—21no—
574C22×D89—21no—
575C22×D89—21no—
576C22×D89—21no—
577C22×D89—21no—
578C22×D89—21no—
579C22×D89—21no—
580C22×D89—21no—
581C22×D89—21no—
582C22×D89—21no—
583C22×D89—21no—
584C22×D89—21no—
585C22×D89—28no—
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—21no—
598C22×D89—21no—
599C22×D89—21no—
600C22×D89—44no—
601C22×D89—44no—
602C22×D89—44no—
603C22×D89—82no—
604C22×D89—82no—
605C22×D89—82no—
606C22×D89—82no—
607C22×D89—82no—
608C22×D89—82no—
609C22×D89—82no—
610C22×D89—82no—
611C22×D89—82no—
612C22×D89—82no—
613C22×D89C2×#4112yes—
614C22×D89C2×#4112yes—
615D4×C89—44no—
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—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—21no—
650C2×C4×C89—21no—
651C2×C4×C89—21no—
652C2×C4×C89—21no—
653C2×C4×C89—21no—
654C2×C4×C89—21no—
655C2×C4×C89—44no—
656C2×C4×C89—44no—
657C2×C4×C89—82no—
658C22⋊D89—44no—
659C22⋊D89—44no—
660C22⋊D89—44no—
661C22⋊D89—82no—
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—44no—
698C2×Dic89—44no—
699C2×Dic89—82no—
700C2×Dic89H(5,𝔽2)12yes—
701D356—44no—
702D356—82no—
703D356—82no—
704D356—82no—
705C4×D89—44no—
706C4×D89—82no—
707C4×D89—82no—
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—41no—
717C22×C89—41no—
718C22×C89—41no—
719C22×C89—41no—
720C22×C89—41no—
721C22×C89—41no—
722C22×C89—41no—
723C22×C89#53814yes—
724C22×C89C22×#4111yescharacteristic
725C22×C89C2×H(5,𝔽2)11yescharacteristic
726C22×C89C2×H(5,𝔽2)11yescharacteristic
727C22×C89C2×H(5,𝔽2)11yescharacteristic
728C22×C89#58511yescharacteristic
729C22×C89#58511yescharacteristic
730C22×C89#58511yescharacteristic
731C2×D89—22no—
732C2×D89—22no—
733C2×D89—22no—
734C2×D89—22no—
735C2×D89—22no—
736C2×D89—22no—
737C2×D89—41no—
738C2×D89—41no—
739C2×D89—41no—
740C2×D89—41no—
741C2×D89—41no—
742C2×D89—41no—
743C2×D89—41no—
744C2×D89—41no—
745C2×D89—41no—
746C2×D89—41no—
747C2×D89—41no—
748C2×D89—41no—
749C2×D89—41no—
750C2×D89—41no—
751C2×D89—41no—
752C2×D89—41no—
753C2×D89—41no—
754C2×D89—41no—
755C2×D89—41no—
756C2×D89—41no—
757C2×D89—41no—
758C2×D89—41no—
759C2×D89—88no—
760C2×D89—88no—
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—
771C4×C89—41no—
772C4×C89—41no—
773C4×C89—41no—
774Dic89—22no—
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—81no—
789C2×C89C2×#53811yescharacteristic
790C2×C89#349111yescharacteristic
791C2×C89#350511yescharacteristic
792C2×C89#353311yescharacteristic
793C2×C89#353411yescharacteristic
794C2×C89#355811yescharacteristic
795C2×C89#356011yescharacteristic
796D89—42no—
797D89—42no—
798D89—81no—
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#2643D8911yescharacteristic, complemented
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#2405—891no—
828#2321—891no—
829#2308—891no—
830C2×#388—891no—
831C89#3698611yescharacteristic, complemented, Sylow
832C23×D4—891no—
833C2×#126—891no—
834C2×#123—891no—
835C2×#123—891no—
836C2×#123—891no—
837C2×#123—891no—
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⋊C4—891no—
850C22×C42—891no—
851#401C2×D8911yescharacteristic, complemented
852#400—891no—
853#400—891no—
854#400—891no—
855#400—891no—
856#400—891no—
857#400—891no—
858#400C2×D8911yescharacteristic, complemented
859#400C2×D8911yescharacteristic, complemented
860#400C2×D8911yescharacteristic, complemented
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#397C2×D8911yescharacteristic, complemented
874#397C2×D8911yescharacteristic, complemented
875#397C2×D8911yescharacteristic, complemented
876#396—891no—
877#396—891no—
878#396—891no—
879#396—891no—
880#396C2×D8911yescharacteristic, complemented
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#394—891no—
890#394—891no—
891#394—891no—
892#394—891no—
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#386C2×D8911yescharacteristic
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#385C2×D8911yescharacteristic, complemented
967#385C2×D8911yescharacteristic, complemented
968#385C2×D8911yescharacteristic, complemented
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#379—891no—
982#379—891no—
983#379—891no—
984C4×C22⋊C4—891no—
985C2×#95—891no—
986C2×#95C2×D8911yescharacteristic, complemented
987C25—891no—
988C25—891no—
989C22×Q8—891no—
990C22×D4—891no—
991C22×D4—891no—
992C22×D4—891no—
993C22×D4—891no—
994C22×D4—891no—
995C22×D4—891no—
996C22×D4—891no—
997C22×D4—891no—
998C22×D4—3562no—
999C22×D4—3562no—
1000C22×D4—1784no—
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—3562no—
1014#123—3562no—
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—3562no—
1045C2×C4⋊C4C22×D8911yescharacteristic
1046C2×C4⋊C4C22×D8911yescharacteristic
1047C2×C4⋊C4C22×D8911yescharacteristic
1048C2×C4⋊C4C22×D8911yescharacteristic
1049C2×C4⋊C4C22×D8911yescharacteristic
1050C2×C4⋊C4C22×D8911yescharacteristic
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—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—891no—
1091C2×C22⋊C4—891no—
1092C2×C22⋊C4—891no—
1093C2×C22⋊C4—891no—
1094C2×C22⋊C4—891no—
1095C2×C22⋊C4—891no—
1096C2×C22⋊C4—891no—
1097C2×C22⋊C4—891no—
1098C2×C22⋊C4—3562no—
1099C2×C22⋊C4—3562no—
1100C2×C22⋊C4—3562no—
1101C2×C22⋊C4—1784no—
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#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
1156#95C22×D8911yescharacteristic
1157#95C22×D8911yescharacteristic
1158#95C22×D8911yescharacteristic
1159#95C22×D8911yescharacteristic
1160#95C22×D8911yescharacteristic
1161#95C22×D8911yescharacteristic
1162#95C22×D8911yescharacteristic
1163C24—894no—
1164C24—891no—
1165C24—891no—
1166C24—891no—
1167C24—891no—
1168C24—3561no—
1169C24—3561no—
1170C24—3561no—
1171C24—3561no—
1172C24—3561no—
1173C24—3561no—
1174C24—3561no—
1175C24—3561no—
1176C24—3561no—
1177C24—3561no—
1178C24—1782no—
1179C24—1782no—
1180C24—1782no—
1181C24C23×D8911yescharacteristic
1182C24C23×D8911yescharacteristic
1183C2×Q8—3561no—
1184C2×Q8—3561no—
1185C2×Q8—3561no—
1186C2×D4—22no—
1187C2×D4—22no—
1188C2×D4—22no—
1189C2×D4—3561no—
1190C2×D4—3561no—
1191C2×D4—3561no—
1192C2×D4—3561no—
1193C2×D4—3561no—
1194C2×D4—3561no—
1195C2×D4—3561no—
1196C2×D4—3561no—
1197C2×D4—3561no—
1198C2×D4—35616no—
1199C2×D4—3561no—
1200C2×D4—3561no—
1201C2×D4—3561no—
1202C2×D4—3561no—
1203C2×D4—1782no—
1204C2×D4—1782no—
1205C2×D4—1782no—
1206C2×D4—1782no—
1207C2×D4—1782no—
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—41no—
1218C22×C4—41no—
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—3561no—
1236C22×C4—3561no—
1237C22×C4—3561no—
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—1782no—
1250C22×C4—1782no—
1251C22×C4—1782no—
1252C22×C4—1782no—
1253C22×C4—1782no—
1254C22×C4—1782no—
1255C22×C4—1782no—
1256C22×C4C23×D8911yescharacteristic
1257C22×C4C23×D8911yescharacteristic
1258C22×C4C23×D8911yescharacteristic
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—41no—
1274C4⋊C4—41no—
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—41no—
1299C22⋊C4—41no—
1300C22⋊C4—41no—
1301C22⋊C4—41no—
1302C22⋊C4—41no—
1303C22⋊C4—41no—
1304C22⋊C4—3561no—
1305C22⋊C4—3561no—
1306C22⋊C4—3561no—
1307C22⋊C4—3561no—
1308C22⋊C4—3561no—
1309C22⋊C4—3561no—
1310C22⋊C4—3561no—
1311C22⋊C4—3561no—
1312C22⋊C4—3561no—
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—1782no—
1341C22⋊C4—1782no—
1342C22⋊C4—1782no—
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—892no—
1370C23—892no—
1371C23—3564no—
1372C23—3564no—
1373C23—3564no—
1374C23—1781no—
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—1781no—
1388C23—1781no—
1389C23—1781no—
1390C23—1781no—
1391C23—1781no—
1392C23—1781no—
1393C23—1781no—
1394C23—1781no—
1395C23—1781no—
1396C23—1781no—
1397C23—1781no—
1398C23—1781no—
1399C23—1781no—
1400C23—1788no—
1401C23—7122no—
1402C23—7122no—
1403C23—7122no—
1404C23—7122no—
1405C23—7122no—
1406C23—7122no—
1407C23—7122no—
1408C23—7122no—
1409C23—7122no—
1410C23—7122no—
1411C23#41×D8912yes—
1412C23#1566805812yes—
1413C23#1566805812yes—
1414C23C24×D8911yescharacteristic
1415Q8—7122no—
1416D4—44no—
1417D4—3564no—
1418D4—3564no—
1419D4—3564no—
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—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—44no—
1465C2×C4—44no—
1466C2×C4—82no—
1467C2×C4—892no—
1468C2×C4—3564no—
1469C2×C4—3564no—
1470C2×C4—3564no—
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—1781no—
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—41no—
1517C22—41no—
1518C22—41no—
1519C22—41no—
1520C22—41no—
1521C22—41no—
1522C22—41no—
1523C22—3561no—
1524C22—3561no—
1525C22—3561no—
1526C22—3561no—
1527C22—3561no—
1528C22—3561no—
1529C22—3561no—
1530C22—3561no—
1531C22—3561no—
1532C22—3561no—
1533C22—3561no—
1534C22—3561no—
1535C22—3561no—
1536C22—3561no—
1537C22—3561no—
1538C22—3561no—
1539C22—3561no—
1540C22—3561no—
1541C22—3561no—
1542C22—3561no—
1543C22—3561no—
1544C22—3561no—
1545C22—1782no—
1546C22—1782no—
1547C22—1782no—
1548C22—1782no—
1549C22—1782no—
1550C22—1782no—
1551C22—7128no—
1552C22—7128no—
1553C22#1915218714yes—
1554C22C2×#41×D8911yescharacteristic
1555C22H(5,𝔽2)×D8911yescharacteristic
1556C22C2×#1566805811yescharacteristic
1557C22C2×#1566805811yescharacteristic
1558C22#1915243311yescharacteristic
1559C22#1915243311yescharacteristic
1560C22#1915243511yescharacteristic
1561C4—41no—
1562C4—41no—
1563C4—41no—
1564C4—41no—
1565C4—41no—
1566C4—41no—
1567C4—41no—
1568C4—41no—
1569C4—41no—
1570C4—41no—
1571C4—41no—
1572C4—41no—
1573C4—41no—
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—81no—
1588C2—3562no—
1589C2—3562no—
1590C2—7121no—
1591C2—7121no—
1592C2C2×#1915218711yescharacteristic
1593C2#2603394611yescharacteristic
1594C2#2603409011yescharacteristic
1595C2#2603442011yescharacteristic
1596C2#2603444011yescharacteristic
1597C2#2603477311yescharacteristic
1598C2#2603480911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutator, socle, cosocleC23×C89C25
FittingC89×#2643C2
prime radical#26023625C2
hypercenter#2643D89
hypocenterC89#36986
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2643

Complements

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

NH ≅ G/Ntype
1. #26028580C2semidirect
2. #26028577C2semidirect
3. #26028102C2semidirect
4. #26027891C2semidirect
5. #26027887C2semidirect
6. #26027877C2semidirect
7. #26027769C2semidirect
8. #26027694C2semidirect
9. #26027535C2semidirect
10. #26027498C2semidirect
11. #26027489C2semidirect
12. #26027369C2semidirect
13. #26027299C2semidirect
14. #26027287C2semidirect
15. #26026882C2semidirect
16. #26026817C2semidirect
17. #26026804C2semidirect
18. #26026650C2semidirect
19. #26026180C2semidirect
20. #26024576C2semidirect
21. #26024510C2semidirect
22. #26023993C2semidirect
23. #26023917C2semidirect
24. #26023801C2semidirect
25. #26023646C2semidirect
27. #26023578C2semidirect
28. #26022909C2semidirect
29. #26022826C2semidirect
30. C2×#19151490C2semidirect
31. C89×#2643C2semidirect
33. C2×#15668007C22semidirect
35. C2×#15667996C22semidirect
36. C2×#15667994C22semidirect
38. C2×#15667991C22semidirect
39. C2×#15667990C22semidirect
44. C2×#15667972C22semidirect
45. C22×C4⋊Dic89C22semidirect
50. C22×C4×Dic89C22semidirect
51. #19151540C22semidirect
52. #19151540C22semidirect
53. #19151539C22semidirect
54. #19151538C22semidirect
55. #19151538C22semidirect
56. #19151537C22semidirect
57. #19151534C22semidirect
59. #19151532C22semidirect
60. #19151530C22semidirect
61. #19151526C22semidirect
64. #19151525C22semidirect
65. #19151525C22semidirect
66. #19151525C22semidirect
67. #19151525C22semidirect
68. #19151525C22semidirect
71. #19151520C22semidirect
72. #19151520C22semidirect
76. #19151516C22semidirect
77. #19151516C22semidirect
80. #19151515C22semidirect
84. #19151514C22semidirect
86. #19151511C22semidirect
87. #19151511C22semidirect
88. #19151510C22semidirect
91. #19151502C22semidirect
93. #19151499C22semidirect
94. #19151498C22semidirect
95. #19151498C22semidirect
96. #19151497C22semidirect
97. #19151495C22semidirect
98. #19151495C22semidirect
99. #19151491C22semidirect
100. #19151491C22semidirect
101. #19151491C22semidirect
102. #19151491C22semidirect
107. #19151490C22semidirect
108. #19151490C22semidirect
109. #19151490C22semidirect
110. #19151490C22semidirect
111. #19151490C22semidirect
112. #19151490C22semidirect
114. #19151488C22semidirect
115. #19151488C22semidirect
116. #19151488C22semidirect
118. #19151487C22semidirect
119. #19151487C22semidirect
120. #19151487C22semidirect
121. #19151487C22semidirect
122. #19151487C22semidirect
123. #19151486C22semidirect
124. #19151485C22semidirect
125. #19151485C22semidirect
126. #19151484C22semidirect
127. #19151484C22semidirect
128. #19151484C22semidirect
129. #19151481C22semidirect
130. #19151481C22semidirect
134. #19151477C22semidirect
135. #19151477C22semidirect
140. #19151476C22semidirect
141. #19151476C22semidirect
142. #19151476C22semidirect
143. #19151476C22semidirect
151. #19151472C22semidirect
152. #19151472C22semidirect
153. #19151470C22semidirect
154. #19151469C22semidirect
155. #19151462C22semidirect
158. #19151459C22semidirect
159. #19151457C22semidirect
160. #19151456C22semidirect
161. #19151455C22semidirect
162. #19151455C22semidirect
163. #19151455C22semidirect
170. C22⋊C4×Dic89C22semidirect
171. C2×#15667919C22semidirect
172. #401×C89C22semidirect
173. #400×C89C22semidirect
174. #400×C89C22semidirect
175. #400×C89C22semidirect
176. #397×C89C22semidirect
177. #397×C89C22semidirect
178. #397×C89C22semidirect
179. #396×C89C22semidirect
183. #385×C89C22semidirect
184. #385×C89C22semidirect
185. #385×C89C22semidirect
186. C2×#95×C89C22semidirect
818. #2643D89semidirect
831. C89#36986semidirect
851. #401C2×D89semidirect
858. #400C2×D89semidirect
859. #400C2×D89semidirect
860. #400C2×D89semidirect
873. #397C2×D89semidirect
874. #397C2×D89semidirect
875. #397C2×D89semidirect
880. #396C2×D89semidirect
966. #385C2×D89semidirect
967. #385C2×D89semidirect
968. #385C2×D89semidirect
986. C2×#95C2×D89semidirect

Maximal subgroups

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

subgroupindex
#260285802
#260285772
#260281022
#260278912
#260278872
#260278772
#260277692
#260276942
#260275352
#260274982
#260274892
#260273692
#260272992
#260272872
#260268822
#260268172
#260268042
#260266502
#260261802
#260245762
#260245102
#260239932
#260239172
#260238012
#260236462
#260236252
#260235782
#260229092
#260228262
C2×#191514902
C89×#26432
#3698689