Finite Group Databasebeta

← #36716007

Subgroups — #36716007

Order 22784.

3032 conjugacy classes of subgroups.

The subgroup lattice has 1608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19152248C211yesmaximal, characteristic
2C2×#19152077C211yesmaximal, characteristic, complemented
3C2×C4×#13083573C211yesmaximal, characteristic, complemented
4#26023307C211yesmaximal, characteristic, complemented
5#26023301C211yesmaximal, characteristic, complemented
6#26023276C211yesmaximal, characteristic, complemented
7#26023258C211yesmaximal, characteristic, complemented
8#26023245C211yesmaximal, characteristic, complemented
9#26023243C211yesmaximal, characteristic, complemented
10#26023238C211yesmaximal, characteristic, complemented
11#26023238C211yesmaximal, characteristic, complemented
12#26023179C211yesmaximal, characteristic, complemented
13#26023159C211yesmaximal, characteristic, complemented
14#26023119C211yesmaximal, characteristic, complemented
15#26023118C211yesmaximal, characteristic, complemented
16#26023078C211yesmaximal, characteristic, complemented
17#26023078C211yesmaximal, characteristic, complemented
18#26022967C211yesmaximal, characteristic, complemented
19#26022957C211yesmaximal, characteristic, complemented
20#26022954C211yesmaximal, characteristic, complemented
21#26022927C211yesmaximal, characteristic, complemented
22#26022926C211yesmaximal, characteristic, complemented
23#26022922C211yesmaximal, characteristic, complemented
24C4×#15667989C211yesmaximal, characteristic, complemented
25#26022777C211yesmaximal, characteristic, complemented
26C4×#15667994C211yesmaximal, characteristic, complemented
27#26022692C211yesmaximal, characteristic, complemented
28C2×#19151481C211yesmaximal, characteristic, complemented
29#387×D89C211yesmaximal, characteristic, complemented
30#26022611C211yesmaximal, characteristic, complemented
31C89×#2364C211yesmaximal, characteristic, complemented
32C22×#13083573C2211yescharacteristic
33C22×#13083573C2211yescharacteristic
34#19152248C4116yescomplemented
35C2×#15668011C2211yescharacteristic
36C2×#15667994C2211yescharacteristic
37C2×#15667994C2211yescharacteristic
38C2×#15667993C2211yescharacteristic
39C2×#15667993C2211yescharacteristic
40C2×#15667989C2211yescharacteristic
41C2×#15667989C2211yescharacteristic
42C2×#15667983C2211yescharacteristic
43#19152077—28no—
44C4×#13083573—28no—
45C2×C4×Dic178C2211yescharacteristic
46C2×C4×Dic178C2211yescharacteristic
47C2×#15667977C2211yescharacteristic
48C2×#15667977C2211yescharacteristic
49C2×D4×Dic89C2211yescharacteristic
50C2×D4×Dic89C2211yescharacteristic
51C2×D4×Dic89C2211yescharacteristic
52C2×C4×C22⋊D89C2211yescharacteristic
53C2×C4×C22⋊D89C2211yescharacteristic
54C2×C4×C22⋊D89C2211yescharacteristic
55C2×C4×C22⋊D89C2211yescharacteristic
56C2×C4×C22⋊D89C2211yescharacteristic
57C2×#15667972C2211yescharacteristic
58C2×#15667972C2211yescharacteristic
59C2×#15667972C2211yescharacteristic
60C2×#15667972C2211yescharacteristic
61C2×#15667970C2211yescharacteristic
62C2×#15667969C2211yescharacteristic
63C2×#15667968C2211yescharacteristic
64C2×#15667968C2211yescharacteristic
65C2×#15667968C2211yescharacteristic
66C2×#15667968C2211yescharacteristic
67C22×C4⋊Dic89C2211yescharacteristic
68C22×#13083553C2211yescharacteristic
69C22×#13083553C2211yescharacteristic
70C2×C4⋊C4×D89C2211yescharacteristic
71C2×C4⋊C4×D89C2211yescharacteristic
72C22×C4×Dic89C2211yescharacteristic
73C22×C4×Dic89C2211yescharacteristic
74C2×C42×D89C2211yescharacteristic
75#19151502C2211yescharacteristic
76#19151502C2211yescharacteristic
77#19151502C2211yescharacteristic
78#19151502C2211yescharacteristic
79#19151496C2211yescharacteristic
80#19151496C2211yescharacteristic
81#19151495C2211yescharacteristic
82#19151495C2211yescharacteristic
83#19151495C2211yescharacteristic
84#19151495C2211yescharacteristic
85#19151493C2211yescharacteristic
86#19151493C2211yescharacteristic
87#19151492C2211yescharacteristic
88#19151492C2211yescharacteristic
89#19151492C2211yescharacteristic
90#19151492C2211yescharacteristic
91#19151491C2211yescharacteristic
92#19151491C2211yescharacteristic
93#19151486C2211yescharacteristic
94#19151486C2211yescharacteristic
95#19151486C2211yescharacteristic
96#19151486C2211yescharacteristic
97#19151485C2211yescharacteristic
98#19151485C2211yescharacteristic
99#19151484C2211yescharacteristic
100#19151484C2211yescharacteristic
101#19151483C2211yescharacteristic
102#19151483C2211yescharacteristic
103#19151483C2211yescharacteristic
104#19151483C2211yescharacteristic
105#19151482C2211yescharacteristic
106#19151482C2211yescharacteristic
107#19151481C2211yescharacteristic
108#19151481C2211yescharacteristic
109#19151481C2211yescharacteristic
110#19151481C2211yescharacteristic
111#19151481C2211yescharacteristic
112#19151481C2211yescharacteristic
113#19151481C2211yescharacteristic
114#19151481C2211yescharacteristic
115#19151480C2211yescharacteristic
116#19151480C2211yescharacteristic
117#19151479C2211yescharacteristic
118#19151479C2211yescharacteristic
119#19151478C2211yescharacteristic
120#19151478C2211yescharacteristic
121#19151478C2211yescharacteristic
122#19151478C2211yescharacteristic
123#19151474C2211yescharacteristic
124#19151474C2211yescharacteristic
125#19151474C2211yescharacteristic
126#19151474C2211yescharacteristic
127#19151473C2211yescharacteristic
128#19151473C2211yescharacteristic
129#19151472C2211yescharacteristic
130#19151472C2211yescharacteristic
131#19151471C2211yescharacteristic
132#19151471C2211yescharacteristic
133#19151471C2211yescharacteristic
134#19151471C2211yescharacteristic
135#19151470C2211yescharacteristic
136#19151470C2211yescharacteristic
137#19151462C2211yescharacteristic
138#19151460C2211yescharacteristic
139#19151460C2211yescharacteristic
140#19151459C2211yescharacteristic
141#19151459C2211yescharacteristic
142#19151458C2211yescharacteristic
143#19151457C2211yescharacteristic
144#19151456C2211yescharacteristic
145#19151456C2211yescharacteristic
146C4×#13083553C2211yescharacteristic
147C4×#13083553C2211yescharacteristic
148C4×#13083553C2211yescharacteristic
149C4×#13083553C2211yescharacteristic
150C4×C4⋊Dic89C2211yescharacteristic
151C4×C4⋊Dic89C2211yescharacteristic
152#19151449C2211yescharacteristic
153#19151449C2211yescharacteristic
154#19151449C2211yescharacteristic
155#19151449C2211yescharacteristic
156C22⋊C4×Dic89C2211yescharacteristic
157C22⋊C4×Dic89C2211yescharacteristic
158C22⋊C4×Dic89C2211yescharacteristic
159C22⋊C4×Dic89C2211yescharacteristic
160C22⋊C4×Dic89C2211yescharacteristic
161C22⋊C4×Dic89C2211yescharacteristic
162C4×#13083551C2211yescharacteristic
163C4×#13083551C2211yescharacteristic
164C4×C22⋊Dic89C2211yescharacteristic
165C4×C22⋊Dic89C2211yescharacteristic
166#19151445C2211yescharacteristic
167#19151443C2211yescharacteristic
168C2×#15667919C2211yescharacteristic
169C2×#15667919C2211yescharacteristic
170C2×#15667919C2211yescharacteristic
171#95×D89C2211yescharacteristic
172#95×D89C2211yescharacteristic
173#95×D89C2211yescharacteristic
174#95×D89C2211yescharacteristic
175C2×#121×C89C2211yescharacteristic
176C2×C4×D4×C89C2211yescharacteristic
177C2×C4×D4×C89C2211yescharacteristic
178#388×C89C2211yescharacteristic
179#388×C89C2211yescharacteristic
180#387×C89C2211yescharacteristic
181#387×C89C2211yescharacteristic
182#386×C89C2211yescharacteristic
183#386×C89C2211yescharacteristic
184#386×C89C2211yescharacteristic
185#386×C89C2211yescharacteristic
186C4×C22⋊C4×C89C2211yescharacteristic
187C4×C22⋊C4×C89C2211yescharacteristic
188C4×C22⋊C4×C89C2211yescharacteristic
189C2×#95×C89C2211yescharacteristic
190C2×#13083573—24no—
191C2×#13083573—24no—
192C2×#13083573—24no—
193C2×#13083573—24no—
194C2×#13083573C2×C418yescomplemented
195C2×#13083573C2×C418yescomplemented
196C22×Dic178C2311yescharacteristic
197C22×Dic178C2311yescharacteristic
198C22×C22⋊D89C2311yescharacteristic
199C22×C22⋊D89C2311yescharacteristic
200C22×C22⋊D89C2311yescharacteristic
201C23×Dic89C2311yescharacteristic
202C23×Dic89C2311yescharacteristic
203C23×Dic89C2311yescharacteristic
204C23×Dic89C2311yescharacteristic
205C23×Dic89C2311yescharacteristic
206C23×Dic89C2311yescharacteristic
207C23×Dic89C2311yescharacteristic
208C23×Dic89C2311yescharacteristic
209C22×C4×D89C2311yescharacteristic
210C22×C4×D89C2311yescharacteristic
211C22×C4×D89C2311yescharacteristic
212C22×C4×D89C2311yescharacteristic
213C22×C4×D89C2311yescharacteristic
214C22×C4×D89C2311yescharacteristic
215C22×C4×D89C2311yescharacteristic
216#15668011C2×C418yescomplemented
217#15667994C2×C418yescomplemented
218#15667994C2×C418yescomplemented
219#15667993C2×C418yescomplemented
220#15667993C2×C418yescomplemented
221#15667989C2×C418yescomplemented
222#15667989C2×C418yescomplemented
223#15667983C2×C418yescomplemented
224C4×Dic178—24no—
225C4×Dic178—24no—
226#15667977—24no—
227#15667977—24no—
228D4×Dic89—24no—
229D4×Dic89—24no—
230D4×Dic89C2×C418yescomplemented
231C4×C22⋊D89—24no—
232C4×C22⋊D89—24no—
233C4×C22⋊D89—24no—
234C4×C22⋊D89—24no—
235C4×C22⋊D89C2×C418yescomplemented
236#15667972—24no—
237#15667972—24no—
238#15667972—24no—
239#15667972D418yescomplemented
240#15667970—24no—
241#15667969—24no—
242#15667968—24no—
243#15667968—24no—
244#15667968—24no—
245#15667968—24no—
246C2×C4⋊Dic89C2×C418yescomplemented
247C2×C4⋊Dic89C2311yescharacteristic
248C2×C4⋊Dic89C2311yescharacteristic
249C2×C4⋊Dic89C2311yescharacteristic
250C2×C4⋊Dic89C2311yescharacteristic
251C2×C4⋊Dic89C2311yescharacteristic
252C2×C4⋊Dic89C2311yescharacteristic
253C2×C4⋊Dic89C2311yescharacteristic
254C2×C4⋊Dic89C2311yescharacteristic
255C2×#13083553—24no—
256C2×#13083553—24no—
257C2×#13083553C2311yescharacteristic
258C2×#13083553C2311yescharacteristic
259C2×#13083553C2311yescharacteristic
260C2×#13083553C2311yescharacteristic
261C2×#13083553C2311yescharacteristic
262C2×#13083553C2311yescharacteristic
263C2×#13083553C2311yescharacteristic
264C2×#13083553C2311yescharacteristic
265C2×#13083553C2311yescharacteristic
266C2×#13083553C2311yescharacteristic
267C2×#13083553C2311yescharacteristic
268C2×#13083553C2311yescharacteristic
269C2×#13083553C2311yescharacteristic
270C2×#13083553C2311yescharacteristic
271C2×#13083553C2311yescharacteristic
272C2×#13083553C2311yescharacteristic
273C2×#13083553C2311yescharacteristic
274C2×#13083553C2311yescharacteristic
275C2×#13083553C2311yescharacteristic
276C2×#13083553C2311yescharacteristic
277C2×#13083553C2311yescharacteristic
278C4⋊C4×D89—24no—
279C4⋊C4×D89C2×C418yescomplemented
280C2×C22⋊Dic89C2311yescharacteristic
281C2×C22⋊Dic89C2311yescharacteristic
282C2×C22⋊Dic89C2311yescharacteristic
283C2×C22⋊Dic89C2311yescharacteristic
284C2×C22⋊Dic89C2311yescharacteristic
285C2×C22⋊Dic89C2311yescharacteristic
286C2×C22⋊Dic89C2311yescharacteristic
287C2×C22⋊Dic89C2311yescharacteristic
288C2×C22⋊Dic89C2311yescharacteristic
289C2×C22⋊Dic89C2311yescharacteristic
290C2×C22⋊Dic89C2311yescharacteristic
291C2×C22⋊Dic89C2311yescharacteristic
292C2×C22⋊Dic89C2311yescharacteristic
293C2×#13083551C2311yescharacteristic
294C2×#13083551C2311yescharacteristic
295C2×#13083551C2311yescharacteristic
296C2×#13083551C2311yescharacteristic
297C2×#13083551C2311yescharacteristic
298C2×C4×Dic89—24no—
299C2×C4×Dic89—24no—
300C2×C4×Dic89C2311yescharacteristic
301C2×C4×Dic89C2311yescharacteristic
302C2×C4×Dic89C2311yescharacteristic
303C2×C4×Dic89C2311yescharacteristic
304C2×C4×Dic89C2311yescharacteristic
305C2×C4×Dic89C2311yescharacteristic
306C2×C4×Dic89C2311yescharacteristic
307C2×C4×Dic89C2311yescharacteristic
308C2×C4×Dic89C2311yescharacteristic
309C2×C4×Dic89C2311yescharacteristic
310C2×C4×Dic89C2311yescharacteristic
311C2×C4×Dic89C2311yescharacteristic
312C2×C4×Dic89C2311yescharacteristic
313C2×C4×Dic89C2311yescharacteristic
314C2×C4×Dic89C2311yescharacteristic
315C2×C4×Dic89C2311yescharacteristic
316C2×C4×Dic89C2311yescharacteristic
317C2×C4×Dic89C2311yescharacteristic
318C2×C4×Dic89C2311yescharacteristic
319C42×D89—24no—
320#15667919C2311yescharacteristic
321#15667919C2311yescharacteristic
322#15667919C2311yescharacteristic
323#15667919C2311yescharacteristic
324#15667919C2311yescharacteristic
325#15667919C2311yescharacteristic
326#15667919C2311yescharacteristic
327#15667919C2311yescharacteristic
328#15667919C2311yescharacteristic
329#15667919C2311yescharacteristic
330#15667919C2311yescharacteristic
331#15667919C2311yescharacteristic
332#15667919C2311yescharacteristic
333#15667919C2311yescharacteristic
334#15667919C2311yescharacteristic
335#15667919C2311yescharacteristic
336#15667919C2311yescharacteristic
337#15667919C2311yescharacteristic
338#15667919C2311yescharacteristic
339#15667919C2311yescharacteristic
340#15667919C2311yescharacteristic
341#15667919C2311yescharacteristic
342#15667919C2311yescharacteristic
343#15667919C2311yescharacteristic
344#15667919C2311yescharacteristic
345#15667919C2311yescharacteristic
346#15667919C2311yescharacteristic
347#15667919C2311yescharacteristic
348#15667919C2311yescharacteristic
349#15667919C2311yescharacteristic
350#15667919C2311yescharacteristic
351#15667919C2311yescharacteristic
352#15667919C2311yescharacteristic
353#15667919C2311yescharacteristic
354C22×D4×C89C2311yescharacteristic
355C22×D4×C89C2311yescharacteristic
356C22×D4×C89C2311yescharacteristic
357C23×C4×C89C2311yescharacteristic
358C23×C4×C89C2311yescharacteristic
359C23×C4×C89C2311yescharacteristic
360C23×C4×C89C2311yescharacteristic
361C23×C4×C89C2311yescharacteristic
362#121×C89C2×C418yescomplemented
363C4×D4×C89—24no—
364C4×D4×C89—24no—
365C2×C4⋊C4×C89C2311yescharacteristic
366C2×C4⋊C4×C89C2311yescharacteristic
367C2×C4⋊C4×C89C2311yescharacteristic
368C2×C22⋊C4×C89C2311yescharacteristic
369C2×C22⋊C4×C89C2311yescharacteristic
370C2×C22⋊C4×C89C2311yescharacteristic
371C2×C22⋊C4×C89C2311yescharacteristic
372C2×C22⋊C4×C89C2311yescharacteristic
373C2×C22⋊C4×C89C2311yescharacteristic
374C2×C22⋊C4×C89C2311yescharacteristic
375C2×C22⋊C4×C89C2311yescharacteristic
376C2×C22⋊C4×C89C2311yescharacteristic
377C2×C22⋊C4×C89C2311yescharacteristic
378C2×C42×C89C2311yescharacteristic
379C2×C42×C89C2311yescharacteristic
380C2×C42×C89C2311yescharacteristic
381C2×C42×C89C2311yescharacteristic
382#95×C89C2311yescharacteristic
383#95×C89C2311yescharacteristic
384#95×C89C2311yescharacteristic
385#95×C89C2311yescharacteristic
386#95×C89C2311yescharacteristic
387#95×C89C2311yescharacteristic
388#95×C89C2311yescharacteristic
389#95×C89C2311yescharacteristic
390#95×C89C2311yescharacteristic
391#95×C89C2311yescharacteristic
392C23×D89C2411yescharacteristic
393#13083573—232no—
394#13083573—232no—
395C2×Dic178—22no—
396C2×Dic178—22no—
397C2×Dic178—22no—
398C2×Dic178—22no—
399C2×Dic178C22×C414yes—
400C2×Dic178C22×C414yes—
401C2×C22⋊D89—22no—
402C2×C22⋊D89—22no—
403C2×C22⋊D89—22no—
404C2×C22⋊D89—22no—
405C2×C22⋊D89C22×C414yes—
406C2×C22⋊D89C22×C414yes—
407C2×C22⋊D89C22×C414yes—
408C2×C22⋊D89C2×D414yes—
409C2×C22⋊D89#4114yes—
410C22×Dic89—22no—
411C22×Dic89—22no—
412C22×Dic89—22no—
413C22×Dic89—22no—
414C22×Dic89—22no—
415C22×Dic89—22no—
416C22×Dic89—22no—
417C22×Dic89—22no—
418C22×Dic89—22no—
419C22×Dic89—22no—
420C22×Dic89—22no—
421C22×Dic89—41no—
422C22×Dic89—41no—
423C22×Dic89—41no—
424C22×Dic89—41no—
425C22×Dic89—41no—
426C22×Dic89—41no—
427C22×Dic89—41no—
428C22×Dic89—41no—
429C22×Dic89C22×C414yes—
430C22×Dic89C22×C414yes—
431C22×Dic89C22×C414yes—
432C22×Dic89C22×C414yes—
433C22×Dic89C2×D414yes—
434C22×Dic89C2411yescharacteristic
435C22×Dic89C2411yescharacteristic
436C22×Dic89C2411yescharacteristic
437C22×Dic89C2411yescharacteristic
438C22×Dic89C2411yescharacteristic
439C22×Dic89C2411yescharacteristic
440C22×Dic89C2411yescharacteristic
441C22×Dic89C2411yescharacteristic
442C22×Dic89C2411yescharacteristic
443C22×Dic89C2411yescharacteristic
444C22×Dic89C2411yescharacteristic
445C22×Dic89C2411yescharacteristic
446C22×Dic89C2411yescharacteristic
447C22×Dic89C2411yescharacteristic
448C22×Dic89C2411yescharacteristic
449C2×C4×D89—22no—
450C2×C4×D89—22no—
451C2×C4×D89—22no—
452C2×C4×D89—22no—
453C2×C4×D89—22no—
454C2×C4×D89—22no—
455C2×C4×D89—22no—
456C2×C4×D89—22no—
457C2×C4×D89—41no—
458C2×C4×D89—41no—
459C2×C4×D89—41no—
460C2×C4×D89—41no—
461C2×C4×D89—41no—
462C2×C4×D89—41no—
463C2×C4×D89—41no—
464C2×C4×D89—41no—
465C2×C4×D89—41no—
466C2×C4×D89C22×C414yes—
467C2×C4×D89C22×C414yes—
468C2×C4×D89C22×C414yes—
469C2×C4×D89C2×D414yes—
470C4⋊Dic89—22no—
471C4⋊Dic89—22no—
472C4⋊Dic89—41no—
473C4⋊Dic89—41no—
474C4⋊Dic89C22×C414yes—
475C4⋊Dic89C22×C414yes—
476C4⋊Dic89C22×C414yes—
477C4⋊Dic89C22×C414yes—
478#13083553—22no—
479#13083553—22no—
480#13083553—22no—
481#13083553—22no—
482#13083553—22no—
483#13083553—22no—
484#13083553—22no—
485#13083553—22no—
486#13083553—22no—
487#13083553—22no—
488#13083553—22no—
489#13083553—22no—
490#13083553—41no—
491#13083553—41no—
492#13083553—41no—
493#13083553C22×C414yes—
494#13083553C22×C414yes—
495#13083553C22×C414yes—
496#13083553C22×C414yes—
497#13083553C22×C414yes—
498#13083553C2×D414yes—
499C22⋊Dic89—22no—
500C22⋊Dic89—22no—
501C22⋊Dic89—22no—
502C22⋊Dic89—22no—
503C22⋊Dic89—41no—
504C22⋊Dic89—41no—
505C22⋊Dic89—41no—
506C22⋊Dic89—41no—
507C22⋊Dic89C22×C414yes—
508C22⋊Dic89C22×C414yes—
509C22⋊Dic89C22×C414yes—
510C22⋊Dic89C22×C414yes—
511C22⋊Dic89C22×C414yes—
512#13083551—22no—
513#13083551—22no—
514#13083551—22no—
515#13083551C22×C414yes—
516#13083551C2×D414yes—
517C4×Dic89—22no—
518C4×Dic89—22no—
519C4×Dic89—22no—
520C4×Dic89—22no—
521C4×Dic89—22no—
522C4×Dic89—22no—
523C4×Dic89—22no—
524C4×Dic89—22no—
525C4×Dic89—22no—
526C4×Dic89—22no—
527C4×Dic89—22no—
528C4×Dic89—22no—
529C4×Dic89—22no—
530C4×Dic89—41no—
531C4×Dic89—41no—
532C4×Dic89—41no—
533C4×Dic89—41no—
534C4×Dic89C22×C414yes—
535C4×Dic89C2×D414yes—
536C24×C89C2411yescharacteristic
537C24×C89C2411yescharacteristic
538C24×C89C2411yescharacteristic
539C2×D4×C89—22no—
540C2×D4×C89—22no—
541C2×D4×C89—22no—
542C2×D4×C89—22no—
543C2×D4×C89—41no—
544C2×D4×C89—41no—
545C2×D4×C89C22×C414yes—
546C2×D4×C89C22×C414yes—
547C2×D4×C89C22×C414yes—
548C22×C4×C89—22no—
549C22×C4×C89—22no—
550C22×C4×C89—22no—
551C22×C4×C89—22no—
552C22×C4×C89—22no—
553C22×C4×C89—22no—
554C22×C4×C89—41no—
555C22×C4×C89—41no—
556C22×C4×C89—41no—
557C22×C4×C89—41no—
558C22×C4×C89—41no—
559C22×C4×C89—41no—
560C22×C4×C89—41no—
561C22×C4×C89—41no—
562C22×C4×C89C22×C414yes—
563C22×C4×C89C2411yescharacteristic
564C22×C4×C89C2411yescharacteristic
565C22×C4×C89C2411yescharacteristic
566C22×C4×C89C2411yescharacteristic
567C22×C4×C89C2411yescharacteristic
568C22×C4×C89C2411yescharacteristic
569C22×C4×C89C2411yescharacteristic
570C22×C4×C89C2411yescharacteristic
571C22×C4×C89C2411yescharacteristic
572C22×C4×C89C2411yescharacteristic
573C22×C4×C89C2411yescharacteristic
574C22×C4×C89C2411yescharacteristic
575C4⋊C4×C89—22no—
576C4⋊C4×C89—22no—
577C4⋊C4×C89C22×C414yes—
578C22⋊C4×C89—22no—
579C22⋊C4×C89—22no—
580C22⋊C4×C89—22no—
581C22⋊C4×C89—22no—
582C22⋊C4×C89—41no—
583C22⋊C4×C89—41no—
584C22⋊C4×C89—41no—
585C22⋊C4×C89C22×C414yes—
586C22⋊C4×C89C22×C414yes—
587C22⋊C4×C89C2×D414yes—
588C42×C89—22no—
589C42×C89—22no—
590C42×C89—41no—
591C42×C89—41no—
592C23×C89—21no—
593C23×C89—21no—
594C23×C89—21no—
595C23×C89—21no—
596C23×C89—21no—
597C23×C89—21no—
598C23×C89—21no—
599C23×C89—21no—
600C23×C89—21no—
601C23×C89—21no—
602C23×C89—21no—
603C23×C89—21no—
604C23×C89—21no—
605C23×C89—21no—
606C23×C89—21no—
607C23×C89—21no—
608C23×C89C23×C412yes—
609C23×C89C23×C412yes—
610C23×C89C23×C412yes—
611C23×C89C22×D412yes—
612C23×C89C2×#4112yes—
613C23×C89C2511yescharacteristic
614C22×D89—21no—
615C22×D89—21no—
616C22×D89—21no—
617C22×D89—21no—
618C22×D89C23×C412yes—
619C22×D89C22×D412yes—
620C22×D89C2×#4112yes—
621D4×C89—28no—
622D4×C89—28no—
623D4×C89—44no—
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—44no—
654C2×C4×C89—44no—
655C2×C4×C89—44no—
656C2×C4×C89—82no—
657C2×C4×C89—82no—
658C2×C4×C89C23×C412yes—
659C2×C4×C89C23×C412yes—
660C2×C4×C89C23×C412yes—
661C2×C4×C89C23×C412yes—
662C2×C4×C89C22×D412yes—
663C2×C4×C89C22×D412yes—
664C2×C4×C892−1+412yes—
665C22⋊D89—28no—
666C22⋊D89—28no—
667C22⋊D89C4×D4116yes—
668C2×Dic89—28no—
669C2×Dic89—28no—
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—28no—
687C2×Dic89—28no—
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—21no—
702C2×Dic89—21no—
703C2×Dic89—21no—
704C2×Dic89—21no—
705C2×Dic89—21no—
706C2×Dic89—44no—
707C2×Dic89—44no—
708C2×Dic89—82no—
709C2×Dic89—82no—
710C2×Dic89C23×C412yes—
711C2×Dic89C23×C412yes—
712C2×Dic89C23×C412yes—
713C2×Dic89C23×C412yes—
714C2×Dic89C23×C412yes—
715C2×Dic89C23×C412yes—
716C2×Dic89C23×C412yes—
717C2×Dic89C22×D412yes—
718C2×Dic89C22×D412yes—
719C2×Dic89C22×D412yes—
720C2×Dic89C2×#4112yes—
721C4×D89—28no—
722C4×D89—28no—
723C4×D89—44no—
724C4×D89—44no—
725C4×D89—44no—
726C4×D89—82no—
727C4×D89—82no—
728Dic178—28no—
729Dic178—28no—
730C22×C89—22no—
731C22×C89—22no—
732C22×C89—22no—
733C22×C89—22no—
734C22×C89—22no—
735C22×C89—22no—
736C22×C89—22no—
737C22×C89—22no—
738C22×C89—22no—
739C22×C89—22no—
740C22×C89—22no—
741C22×C89—22no—
742C22×C89—41no—
743C22×C89—41no—
744C22×C89—41no—
745C22×C89—41no—
746C22×C89—41no—
747C22×C89—41no—
748C22×C89—41no—
749C22×C89—41no—
750C22×C89C2×C4×D414yes—
751C22×C89C24×C411yescharacteristic
752C22×C89C23×D411yescharacteristic
753C22×C89C22×#4111yescharacteristic
754C22×C89C2×2−1+411yescharacteristic
755C22×C89#58511yescharacteristic
756C22×C89#58511yescharacteristic
757C22×C89#58511yescharacteristic
758C2×D89—22no—
759C2×D89—22no—
760C2×D89—22no—
761C2×D89—22no—
762C2×D89—22no—
763C2×D89—22no—
764C2×D89C2×C4×D414yes—
765C4×C89—22no—
766C4×C89—22no—
767C4×C89—22no—
768C4×C89—22no—
769C4×C89—22no—
770C4×C89—22no—
771C4×C89—22no—
772C4×C89—41no—
773C4×C89—41no—
774C4×C89—41no—
775C4×C89—41no—
776C4×C89—41no—
777Dic89—22no—
778Dic89—22no—
779Dic89—22no—
780Dic89—22no—
781Dic89—22no—
782Dic89—22no—
783Dic89—22no—
784Dic89—22no—
785Dic89—41no—
786Dic89—41no—
787Dic89—41no—
788Dic89—41no—
789Dic89—41no—
790Dic89—41no—
791Dic89C2×C4×D414yes—
792#34289—891nomaximal, Sylow
793C2×C89—24no—
794C2×C89—42no—
795C2×C89—42no—
796C2×C89C22×C4×D411yescharacteristic
797C2×C89#342811yescharacteristic
798C2×C89C4×2−1+411yescharacteristic
799C2×C89#348511yescharacteristic
800C2×C89#348911yescharacteristic
801C2×C89#351511yescharacteristic
802C2×C89#352111yescharacteristic
803D89—24no—
804C2×#547—891no—
805C2×#520—891no—
806C2×C4×#41—891no—
807#2365—891no—
808#2364—891no—
809#2364D8911yescharacteristic, complemented
810#2362—891no—
811#2360—891no—
812#2359—891no—
813#2359—891no—
814#2359—891no—
815#2359—891no—
816#2352—891no—
817#2349—891no—
818#2344—891no—
819#2344—891no—
820#2339—891no—
821#2339—891no—
822#2327—891no—
823#2325—891no—
824#2325—891no—
825#2323—891no—
826#2322—891no—
827#2322—891no—
828C4×C22⋊Q8—891no—
829C4×#123—891no—
830C4×#123—891no—
831#2290—891no—
832C2×#387—891no—
833C2×#387—891no—
834#2275—891no—
835C89#3428911yescharacteristic, complemented, Sylow
836C22×#41—891no—
837C22×#41—891no—
838#547—8916no—
839C2×C4⋊Q8—891no—
840C2×#123—891no—
841C2×#123—891no—
842C2×#123—891no—
843C2×#123—891no—
844C2×C22⋊Q8—891no—
845C2×C22⋊Q8—891no—
846C2×#121—891no—
847C2×#121C2×D8911yescharacteristic
848#520—1788no—
849C4×#41—1788no—
850C2×C4×Q8—891no—
851C2×C4×Q8—891no—
852C2×C4×Q8—891no—
853C2×C4×Q8—891no—
854C2×C4×D4—891no—
855C2×C4×D4—891no—
856C2×C4×D4—891no—
857C2×C4×D4—891no—
858C2×C4×D4—891no—
859C2×C4×D4—891no—
860C2×C4×D4—891no—
861C2×C4×D4—891no—
862C2×C4×D4—891no—
863C2×C4×D4—891no—
864C2×C4×D4—891no—
865C2×C4×D4—891no—
866C2×C4×D4C2×D8911yescharacteristic
867C2×C4×D4C2×D8911yescharacteristic
868C2×#117—891no—
869C2×#117—891no—
870C2×#117—891no—
871C2×#117—891no—
872C2×#117—891no—
873C2×#117—891no—
874C22×C4⋊C4—891no—
875C22×C4⋊C4—891no—
876C22×C4⋊C4—891no—
877C22×C4⋊C4—891no—
878C22×C4⋊C4—891no—
879C22×C42—891no—
880C22×C42—891no—
881C22×C42—891no—
882#391—891no—
883#391—891no—
884#391—891no—
885#391—891no—
886#389—891no—
887#389—891no—
888#389—891no—
889#389—891no—
890#389—891no—
891#389—891no—
892#389—891no—
893#389—891no—
894#388—891no—
895#388—891no—
896#388—891no—
897#388—891no—
898#388—891no—
899#388—891no—
900#388—891no—
901#388—891no—
902#388—891no—
903#388—891no—
904#388C2×D8911yescharacteristic
905#388C2×D8911yescharacteristic
906#387—891no—
907#387—891no—
908#387—891no—
909#387—891no—
910#387—891no—
911#387—891no—
912#387—891no—
913#387—891no—
914#387—891no—
915#387—891no—
916#387—891no—
917#387—891no—
918#387—891no—
919#387—891no—
920#387—891no—
921#387—891no—
922#387—891no—
923#387—891no—
924#387—891no—
925#387—891no—
926#387—891no—
927#387—891no—
928#387C2×D8911yescharacteristic
929#387C2×D8911yescharacteristic
930#386—891no—
931#386—891no—
932#386—891no—
933#386—891no—
934#386—891no—
935#386—891no—
936#386—891no—
937#386—891no—
938#386C2×D8911yescharacteristic
939#386C2×D8911yescharacteristic
940#386C2×D8911yescharacteristic
941#386C2×D8911yescharacteristic
942#385—891no—
943#385—891no—
944#385—891no—
945#385—891no—
946#385—891no—
947#385—891no—
948#385—891no—
949#385—891no—
950#385—891no—
951#385—891no—
952#382—891no—
953#381—891no—
954#381—891no—
955#381—891no—
956#381—891no—
957#380—891no—
958#380—891no—
959#380—891no—
960#380—891no—
961C4×C4⋊C4—891no—
962C4×C4⋊C4—891no—
963C4×C4⋊C4—891no—
964C4×C4⋊C4—891no—
965C4×C4⋊C4—891no—
966C4×C4⋊C4—891no—
967C4×C4⋊C4—891no—
968C4×C4⋊C4—891no—
969C4×C4⋊C4—891no—
970C4×C4⋊C4—891no—
971C4×C22⋊C4—891no—
972C4×C22⋊C4—891no—
973C4×C22⋊C4—891no—
974C4×C22⋊C4—891no—
975C4×C22⋊C4—891no—
976C4×C22⋊C4—891no—
977C4×C22⋊C4—891no—
978C4×C22⋊C4—891no—
979C4×C22⋊C4—891no—
980C4×C22⋊C4—891no—
981C4×C22⋊C4—891no—
982C4×C22⋊C4C2×D8911yescharacteristic
983C4×C22⋊C4C2×D8911yescharacteristic
984C4×C22⋊C4C2×D8911yescharacteristic
985#376—891no—
986C2×#95—891no—
987C2×#95—891no—
988C2×#95—891no—
989C2×#95—891no—
990C2×#95—891no—
991C2×#95—891no—
992C2×#95—891no—
993C2×#95C2×D8911yescharacteristic
994C2×#41—898no—
995C2×#41—898no—
996C2×#41—1784no—
997C2×#41—1784no—
998C2×#41—1784no—
999C2×#41—1784no—
1000C22×Q8—891no—
1001C22×Q8—891no—
1002C22×D4—891no—
1003C22×D4—891no—
1004C22×D4—891no—
1005C22×D4C22×D8911yescharacteristic
1006C22×D4C22×D8911yescharacteristic
1007C22×D4C22×D8911yescharacteristic
1008C23×C4—891no—
1009C23×C4—891no—
1010C23×C4—891no—
1011C23×C4—891no—
1012C23×C4—891no—
1013C23×C4—891no—
1014C23×C4—891no—
1015C23×C4—891no—
1016C23×C4—891no—
1017C23×C4—891no—
1018C23×C4—891no—
1019C23×C4—891no—
1020C23×C4—891no—
1021C23×C4—891no—
1022C23×C4—891no—
1023C23×C4C22×D8911yescharacteristic
1024C23×C4C22×D8911yescharacteristic
1025C23×C4C22×D8911yescharacteristic
1026C23×C4C22×D8911yescharacteristic
1027C23×C4C22×D8911yescharacteristic
1028C4⋊Q8—898no—
1029#123—898no—
1030#123—898no—
1031#123—898no—
1032#123—898no—
1033C22⋊Q8—898no—
1034C22⋊Q8—898no—
1035#121—898no—
1036#121C4×D8918yescomplemented
1037C4×Q8—1784no—
1038C4×Q8—1784no—
1039C4×Q8—1784no—
1040C4×Q8—1784no—
1041C4×D4—24no—
1042C4×D4—24no—
1043C4×D4—898no—
1044C4×D4—898no—
1045C4×D4—898no—
1046C4×D4—1784no—
1047C4×D4—1784no—
1048C4×D4—1784no—
1049C4×D4—1784no—
1050C4×D4—1784no—
1051C4×D4—1784no—
1052C4×D4—1784no—
1053C4×D4—1784no—
1054C4×D4—1784no—
1055#117—1784no—
1056#117—1784no—
1057#117—1784no—
1058#117—1784no—
1059#117—1784no—
1060#117—1784no—
1061C2×C4⋊C4—898no—
1062C2×C4⋊C4—891no—
1063C2×C4⋊C4—891no—
1064C2×C4⋊C4—891no—
1065C2×C4⋊C4—891no—
1066C2×C4⋊C4—891no—
1067C2×C4⋊C4—891no—
1068C2×C4⋊C4—891no—
1069C2×C4⋊C4—891no—
1070C2×C4⋊C4—891no—
1071C2×C4⋊C4—891no—
1072C2×C4⋊C4—898no—
1073C2×C4⋊C4—891no—
1074C2×C4⋊C4—891no—
1075C2×C4⋊C4—891no—
1076C2×C4⋊C4—891no—
1077C2×C4⋊C4—891no—
1078C2×C4⋊C4—891no—
1079C2×C4⋊C4—891no—
1080C2×C4⋊C4—891no—
1081C2×C4⋊C4—891no—
1082C2×C4⋊C4—891no—
1083C2×C4⋊C4—891no—
1084C2×C4⋊C4—891no—
1085C2×C4⋊C4—891no—
1086C2×C4⋊C4—891no—
1087C2×C4⋊C4—891no—
1088C2×C4⋊C4—891no—
1089C2×C4⋊C4—891no—
1090C2×C4⋊C4—891no—
1091C2×C4⋊C4—891no—
1092C2×C4⋊C4—1784no—
1093C2×C4⋊C4—1784no—
1094C2×C4⋊C4—1784no—
1095C2×C4⋊C4C22×D8911yescharacteristic
1096C2×C4⋊C4C22×D8911yescharacteristic
1097C2×C4⋊C4C22×D8911yescharacteristic
1098C2×C22⋊C4—891no—
1099C2×C22⋊C4—891no—
1100C2×C22⋊C4—891no—
1101C2×C22⋊C4—891no—
1102C2×C22⋊C4—891no—
1103C2×C22⋊C4—891no—
1104C2×C22⋊C4—891no—
1105C2×C22⋊C4—891no—
1106C2×C22⋊C4—891no—
1107C2×C22⋊C4—891no—
1108C2×C22⋊C4—891no—
1109C2×C22⋊C4—891no—
1110C2×C22⋊C4—891no—
1111C2×C22⋊C4—891no—
1112C2×C22⋊C4—891no—
1113C2×C22⋊C4—891no—
1114C2×C22⋊C4—891no—
1115C2×C22⋊C4—891no—
1116C2×C22⋊C4C22×D8911yescharacteristic
1117C2×C22⋊C4C22×D8911yescharacteristic
1118C2×C22⋊C4C22×D8911yescharacteristic
1119C2×C22⋊C4C22×D8911yescharacteristic
1120C2×C22⋊C4C22×D8911yescharacteristic
1121C2×C22⋊C4C22×D8911yescharacteristic
1122C2×C22⋊C4C22×D8911yescharacteristic
1123C2×C22⋊C4C22×D8911yescharacteristic
1124C2×C22⋊C4C22×D8911yescharacteristic
1125C2×C22⋊C4C22×D8911yescharacteristic
1126C2×C42—891no—
1127C2×C42—891no—
1128C2×C42—891no—
1129C2×C42—891no—
1130C2×C42—891no—
1131C2×C42—891no—
1132C2×C42—891no—
1133C2×C42—891no—
1134C2×C42—891no—
1135C2×C42—891no—
1136C2×C42—891no—
1137C2×C42—891no—
1138C2×C42—891no—
1139C2×C42—891no—
1140C2×C42—891no—
1141C2×C42—891no—
1142C2×C42—891no—
1143C2×C42—891no—
1144C2×C42—891no—
1145C2×C42—1784no—
1146C2×C42—1784no—
1147C2×C42—1784no—
1148C2×C42C22×D8911yescharacteristic
1149C2×C42C22×D8911yescharacteristic
1150C2×C42C22×D8911yescharacteristic
1151C2×C42C22×D8911yescharacteristic
1152#95—891no—
1153#95—891no—
1154#95—891no—
1155#95—891no—
1156#95—891no—
1157#95—891no—
1158#95—891no—
1159#95—891no—
1160#95—891no—
1161#95—891no—
1162#95—891no—
1163#95—891no—
1164#95—891no—
1165#95—891no—
1166#95—891no—
1167#95—891no—
1168#95—891no—
1169#95—891no—
1170#95—891no—
1171#95—891no—
1172#95—891no—
1173#95—891no—
1174#95—891no—
1175#95—891no—
1176#95—891no—
1177#95—891no—
1178#95—891no—
1179#95—891no—
1180#95—891no—
1181#95—891no—
1182#95—891no—
1183#95—891no—
1184#95—891no—
1185#95—891no—
1186#95C22×D8911yescharacteristic
1187#95C22×D8911yescharacteristic
1188#95C22×D8911yescharacteristic
1189#95C22×D8911yescharacteristic
1190#95C22×D8911yescharacteristic
1191#95C22×D8911yescharacteristic
1192#95C22×D8911yescharacteristic
1193#95C22×D8911yescharacteristic
1194#95C22×D8911yescharacteristic
1195#95C22×D8911yescharacteristic
1196C24—891no—
1197C24C23×D8911yescharacteristic
1198C24C23×D8911yescharacteristic
1199C24C23×D8911yescharacteristic
1200#41—17832no—
1201#41—17832no—
1202C2×Q8—894no—
1203C2×Q8—894no—
1204C2×Q8—1782no—
1205C2×Q8—1782no—
1206C2×Q8—1782no—
1207C2×Q8—1782no—
1208C2×D4—22no—
1209C2×D4—22no—
1210C2×D4—22no—
1211C2×D4—22no—
1212C2×D4—41no—
1213C2×D4—41no—
1214C2×D4—894no—
1215C2×D4—894no—
1216C2×D4—894no—
1217C2×D4—894no—
1218C2×D4—894no—
1219C2×D4—1782no—
1220C2×D4—1782no—
1221C2×D4—1782no—
1222C2×D4—1782no—
1223C2×D4C2×C4×D8914yes—
1224C2×D4C2×C4×D8914yes—
1225C2×D4C2×C4×D8914yes—
1226C22×C4—22no—
1227C22×C4—22no—
1228C22×C4—22no—
1229C22×C4—22no—
1230C22×C4—22no—
1231C22×C4—22no—
1232C22×C4—41no—
1233C22×C4—41no—
1234C22×C4—41no—
1235C22×C4—41no—
1236C22×C4—41no—
1237C22×C4—41no—
1238C22×C4—41no—
1239C22×C4—41no—
1240C22×C4—891no—
1241C22×C4—894no—
1242C22×C4—894no—
1243C22×C4—894no—
1244C22×C4—894no—
1245C22×C4—894no—
1246C22×C4—891no—
1247C22×C4—891no—
1248C22×C4—891no—
1249C22×C4—891no—
1250C22×C4—891no—
1251C22×C4—891no—
1252C22×C4—891no—
1253C22×C4—891no—
1254C22×C4—894no—
1255C22×C4—894no—
1256C22×C4—894no—
1257C22×C4—894no—
1258C22×C4—891no—
1259C22×C4—891no—
1260C22×C4—891no—
1261C22×C4—891no—
1262C22×C4—891no—
1263C22×C4—891no—
1264C22×C4—3561no—
1265C22×C4—3561no—
1266C22×C4—3561no—
1267C22×C4—3561no—
1268C22×C4—3561no—
1269C22×C4—3561no—
1270C22×C4—3561no—
1271C22×C4—3561no—
1272C22×C4—3561no—
1273C22×C4—3561no—
1274C22×C4—3561no—
1275C22×C4—3561no—
1276C22×C4—3561no—
1277C22×C4—3561no—
1278C22×C4—3561no—
1279C22×C4—3561no—
1280C22×C4—3561no—
1281C22×C4—1782no—
1282C22×C4—1782no—
1283C22×C4—1782no—
1284C22×C4—1782no—
1285C22×C4—1782no—
1286C22×C4—1782no—
1287C22×C4—1782no—
1288C22×C4—1782no—
1289C22×C4—1782no—
1290C22×C4—1782no—
1291C22×C4—1782no—
1292C22×C4—1782no—
1293C22×C4—1782no—
1294C22×C4—1782no—
1295C22×C4—1782no—
1296C22×C4—1782no—
1297C22×C4—1782no—
1298C22×C4—1782no—
1299C22×C4—1782no—
1300C22×C4C2×C4×D8914yes—
1301C22×C4C23×D8911yescharacteristic
1302C22×C4C23×D8911yescharacteristic
1303C22×C4C23×D8911yescharacteristic
1304C22×C4C23×D8911yescharacteristic
1305C22×C4C23×D8911yescharacteristic
1306C22×C4C23×D8911yescharacteristic
1307C22×C4C23×D8911yescharacteristic
1308C22×C4C23×D8911yescharacteristic
1309C22×C4C23×D8911yescharacteristic
1310C22×C4C23×D8911yescharacteristic
1311C22×C4C23×D8911yescharacteristic
1312C22×C4C23×D8911yescharacteristic
1313C4⋊C4—22no—
1314C4⋊C4—22no—
1315C4⋊C4—894no—
1316C4⋊C4—894no—
1317C4⋊C4—894no—
1318C4⋊C4—894no—
1319C4⋊C4—894no—
1320C4⋊C4—894no—
1321C4⋊C4—894no—
1322C4⋊C4—894no—
1323C4⋊C4—894no—
1324C4⋊C4—894no—
1325C4⋊C4—3561no—
1326C4⋊C4—3561no—
1327C4⋊C4—3561no—
1328C4⋊C4—3561no—
1329C4⋊C4—3561no—
1330C4⋊C4—1782no—
1331C4⋊C4—1782no—
1332C4⋊C4—1782no—
1333C4⋊C4—1782no—
1334C4⋊C4—1782no—
1335C4⋊C4—1782no—
1336C4⋊C4—1782no—
1337C4⋊C4—1782no—
1338C4⋊C4—1782no—
1339C4⋊C4—1782no—
1340C4⋊C4—1782no—
1341C4⋊C4—1782no—
1342C4⋊C4—1782no—
1343C4⋊C4—1782no—
1344C4⋊C4C2×C4×D8914yes—
1345C22⋊C4—22no—
1346C22⋊C4—22no—
1347C22⋊C4—22no—
1348C22⋊C4—22no—
1349C22⋊C4—41no—
1350C22⋊C4—41no—
1351C22⋊C4—41no—
1352C22⋊C4—894no—
1353C22⋊C4—894no—
1354C22⋊C4—894no—
1355C22⋊C4—894no—
1356C22⋊C4—894no—
1357C22⋊C4—894no—
1358C22⋊C4—894no—
1359C22⋊C4—3561no—
1360C22⋊C4—3561no—
1361C22⋊C4—3561no—
1362C22⋊C4—3561no—
1363C22⋊C4—1782no—
1364C22⋊C4—1782no—
1365C22⋊C4—1782no—
1366C22⋊C4—1782no—
1367C22⋊C4—1782no—
1368C22⋊C4—1782no—
1369C22⋊C4—1782no—
1370C22⋊C4C2×C4×D8914yes—
1371C22⋊C4C2×C4×D8914yes—
1372C22⋊C4D4×D8914yes—
1373C42—22no—
1374C42—22no—
1375C42—41no—
1376C42—41no—
1377C42—894no—
1378C42—894no—
1379C42—3561no—
1380C42—3561no—
1381C42—3561no—
1382C42—3561no—
1383C42—1782no—
1384C42—1782no—
1385C42—1782no—
1386C42—1782no—
1387C42—1782no—
1388C42—1782no—
1389C42—1782no—
1390C42—1782no—
1391C42—1782no—
1392C42—1782no—
1393C42—1782no—
1394C42—1782no—
1395C42—1782no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—21no—
1408C23—21no—
1409C23—21no—
1410C23—21no—
1411C23—21no—
1412C23—892no—
1413C23—892no—
1414C23—892no—
1415C23—1781no—
1416C23—1781no—
1417C23—1781no—
1418C23—1781no—
1419C23C22×C4×D8912yes—
1420C23C22×C4×D8912yes—
1421C23C22×C4×D8912yes—
1422C23C2×D4×D8912yes—
1423C23#41×D8912yes—
1424C23C24×D8911yescharacteristic
1425Q8—1788no—
1426Q8—1788no—
1427D4—28no—
1428D4—28no—
1429D4—44no—
1430D4—8916no—
1431D4—1788no—
1432D4—1788no—
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—44no—
1463C2×C4—44no—
1464C2×C4—44no—
1465C2×C4—82no—
1466C2×C4—82no—
1467C2×C4—892no—
1468C2×C4—892no—
1469C2×C4—892no—
1470C2×C4—892no—
1471C2×C4—892no—
1472C2×C4—892no—
1473C2×C4—892no—
1474C2×C4—892no—
1475C2×C4—892no—
1476C2×C4—892no—
1477C2×C4—892no—
1478C2×C4—3564no—
1479C2×C4—3564no—
1480C2×C4—3564no—
1481C2×C4—3564no—
1482C2×C4—3564no—
1483C2×C4—1788no—
1484C2×C4—1788no—
1485C2×C4—1788no—
1486C2×C4—1788no—
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—1781no—
1507C2×C4—1781no—
1508C2×C4—1781no—
1509C2×C4—1781no—
1510C2×C4—1781no—
1511C2×C4—1781no—
1512C2×C4—1781no—
1513C2×C4—1781no—
1514C2×C4—1781no—
1515C2×C4—1781no—
1516C2×C4—1781no—
1517C2×C4—1781no—
1518C2×C4—1781no—
1519C2×C4—1781no—
1520C2×C4—1781no—
1521C2×C4—1788no—
1522C2×C4—1788no—
1523C2×C4—7122no—
1524C2×C4—7122no—
1525C2×C4—7122no—
1526C2×C4—7122no—
1527C2×C4C22×C4×D8912yes—
1528C2×C4C22×C4×D8912yes—
1529C2×C4C22×C4×D8912yes—
1530C2×C4C22×C4×D8912yes—
1531C2×C4C2×D4×D8912yes—
1532C2×C4C2×D4×D8912yes—
1533C2×C4#1566805912yes—
1534C22—22no—
1535C22—22no—
1536C22—22no—
1537C22—22no—
1538C22—22no—
1539C22—22no—
1540C22—22no—
1541C22—22no—
1542C22—22no—
1543C22—22no—
1544C22—22no—
1545C22—22no—
1546C22—41no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—894no—
1555C22—1782no—
1556C22—1782no—
1557C22—1782no—
1558C22—1782no—
1559C22—1782no—
1560C22—1782no—
1561C22C4×D4×D8914yes—
1562C22C23×C4×D8911yescharacteristic
1563C22C22×D4×D8911yescharacteristic
1564C22C2×#41×D8911yescharacteristic
1565C22C2×#1566805911yescharacteristic
1566C22#1915243311yescharacteristic
1567C22#1915243311yescharacteristic
1568C22#1915243411yescharacteristic
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—22no—
1573C4—22no—
1574C4—22no—
1575C4—22no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—41no—
1581C4—894no—
1582C4—3561no—
1583C4—3561no—
1584C4—3561no—
1585C4—3561no—
1586C4—3561no—
1587C4—3561no—
1588C4—1782no—
1589C4—1782no—
1590C4—1782no—
1591C4—1782no—
1592C4—1782no—
1593C4—1782no—
1594C4—1782no—
1595C4—1782no—
1596C2—24no—
1597C2—42no—
1598C2—42no—
1599C2—1784no—
1600C2C2×C4×D4×D8911yescharacteristic
1601C2#2603345011yescharacteristic
1602C2C4×#1566805911yescharacteristic
1603C2#2603388911yescharacteristic
1604C2#2603392311yescharacteristic
1605C2#2603422311yescharacteristic
1606C2#2603431111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC89×#2364C2
socle, cosocleC23×C89C25
prime radicalC2×#19152248C2
hypercenter#2364D89
hypocenterC89#34289
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2364

Complements

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

NH ≅ G/Ntype
2. C2×#19152077C2semidirect
3. C2×C4×#13083573C2semidirect
4. #26023307C2semidirect
5. #26023301C2semidirect
6. #26023276C2semidirect
7. #26023258C2semidirect
8. #26023245C2semidirect
9. #26023243C2semidirect
10. #26023238C2semidirect
11. #26023238C2semidirect
12. #26023179C2semidirect
13. #26023159C2semidirect
14. #26023119C2semidirect
15. #26023118C2semidirect
16. #26023078C2semidirect
17. #26023078C2semidirect
18. #26022967C2semidirect
19. #26022957C2semidirect
20. #26022954C2semidirect
21. #26022927C2semidirect
22. #26022926C2semidirect
23. #26022922C2semidirect
24. C4×#15667989C2semidirect
25. #26022777C2semidirect
26. C4×#15667994C2semidirect
27. #26022692C2semidirect
28. C2×#19151481C2semidirect
29. #387×D89C2semidirect
30. #26022611C2semidirect
31. C89×#2364C2semidirect
34. #19152248C4semidirect
194. C2×#13083573C2×C4semidirect
195. C2×#13083573C2×C4semidirect
216. #15668011C2×C4semidirect
217. #15667994C2×C4semidirect
218. #15667994C2×C4semidirect
219. #15667993C2×C4semidirect
220. #15667993C2×C4semidirect
221. #15667989C2×C4semidirect
222. #15667989C2×C4semidirect
223. #15667983C2×C4semidirect
230. D4×Dic89C2×C4semidirect
235. C4×C22⋊D89C2×C4semidirect
239. #15667972D4semidirect
246. C2×C4⋊Dic89C2×C4semidirect
279. C4⋊C4×D89C2×C4semidirect
362. #121×C89C2×C4semidirect
809. #2364D89semidirect
835. C89#34289semidirect
1036. #121C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#191522482
C2×#191520772
C2×C4×#130835732
#260233072
#260233012
#260232762
#260232582
#260232452
#260232432
#260232382
#260231792
#260231592
#260231192
#260231182
#260230782
#260229672
#260229572
#260229542
#260229272
#260229262
#260229222
C4×#156679892
#260227772
C4×#156679942
#260226922
C2×#191514812
#387×D892
#260226112
C89×#23642
#3428989