Finite Group Databasebeta

← #36715852

Subgroups — #36715852

Order 22784.

2546 conjugacy classes of subgroups.

The subgroup lattice has 1606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19152181C211yesmaximal, characteristic
2#26023383C211yesmaximal, characteristic, complemented
3#26023372C211yesmaximal, characteristic, complemented
4#26023368C211yesmaximal, characteristic, complemented
5#26023362C211yesmaximal, characteristic, complemented
6#26023330C211yesmaximal, characteristic, complemented
7#26023321C211yesmaximal, characteristic, complemented
8#26023299C211yesmaximal, characteristic, complemented
9#26023297C211yesmaximal, characteristic, complemented
10#26023288C211yesmaximal, characteristic, complemented
11#26023269C211yesmaximal, characteristic, complemented
12#26023258C211yesmaximal, characteristic, complemented
13#26023240C211yesmaximal, characteristic, complemented
14#26023234C211yesmaximal, characteristic, complemented
15#26023234C211yesmaximal, characteristic, complemented
16#26023229C211yesmaximal, characteristic, complemented
17#26023229C211yesmaximal, characteristic, complemented
18#26023060C211yesmaximal, characteristic, complemented
19#26023036C211yesmaximal, characteristic, complemented
20#26023021C211yesmaximal, characteristic, complemented
21#26023012C211yesmaximal, characteristic, complemented
22#26022886C211yesmaximal, characteristic, complemented
23C4×#15668007C211yesmaximal, characteristic, complemented
24C4×#15667998C211yesmaximal, characteristic, complemented
25C4×#15667997C211yesmaximal, characteristic, complemented
26C4×#15667985C211yesmaximal, characteristic, complemented
27#26022697C211yesmaximal, characteristic, complemented
28C2×#19151487C211yesmaximal, characteristic, complemented
29#26022604C211yesmaximal, characteristic, complemented
30C4×#15667972C211yesmaximal, characteristic, complemented
31C89×#2275C211yesmaximal, characteristic, complemented
32#19152181C4116yescomplemented
33C2×#15668007C2211yescharacteristic
34C2×#15668006C2211yescharacteristic
35C2×#15668000C2211yescharacteristic
36C2×#15667998C2211yescharacteristic
37C2×#15667997C2211yescharacteristic
38C2×#15667995C2211yescharacteristic
39C2×#15667989C2211yescharacteristic
40C2×#15667986C2211yescharacteristic
41C2×#15667985C2211yescharacteristic
42C2×#15667984C2211yescharacteristic
43C2×#15667982C2211yescharacteristic
44C2×#15667980C2211yescharacteristic
45C2×C4×Dic178C2211yescharacteristic, complemented
46C2×C4×D356C2211yescharacteristic
47C2×C4×D356C2211yescharacteristic
48C2×C4×C22⋊D89C2211yescharacteristic
49C2×C4×C22⋊D89C2211yescharacteristic
50C2×C4×C22⋊D89C2211yescharacteristic
51C2×C4×C22⋊D89C2211yescharacteristic, complemented
52C2×#15667972C2211yescharacteristic
53C2×#15667972C2211yescharacteristic
54C2×#15667971C2211yescharacteristic, complemented
55C22×#13083553C2211yescharacteristic
56C22×#13083551C2211yescharacteristic
57C22×#13083551C2211yescharacteristic
58C22×#13083551C2211yescharacteristic
59C2×C22⋊C4×D89C2211yescharacteristic
60C2×C22⋊C4×D89C2211yescharacteristic
61C22×C4×Dic89C2211yescharacteristic
62C2×C42×D89C2211yescharacteristic, complemented
63#19151504C2211yescharacteristic, complemented
64#19151502C2211yescharacteristic, complemented
65#19151502C2211yescharacteristic, complemented
66#19151500C2211yescharacteristic
67#19151500C2211yescharacteristic
68#19151498C2211yescharacteristic
69#19151498C2211yescharacteristic
70#19151498C2211yescharacteristic, complemented
71#19151496C2211yescharacteristic, complemented
72#19151495C2211yescharacteristic, complemented
73#19151495C2211yescharacteristic, complemented
74#19151493C2211yescharacteristic, complemented
75#19151492C2211yescharacteristic, complemented
76#19151491C2211yescharacteristic, complemented
77#19151491C2211yescharacteristic, complemented
78#19151490C2211yescharacteristic
79#19151490C2211yescharacteristic
80#19151489C2211yescharacteristic
81#19151489C2211yescharacteristic
82#19151489C2211yescharacteristic
83#19151489C2211yescharacteristic
84#19151489C2211yescharacteristic, complemented
85#19151488C2211yescharacteristic
86#19151488C2211yescharacteristic
87#19151488C2211yescharacteristic, complemented
88#19151487C2211yescharacteristic
89#19151487C2211yescharacteristic
90#19151487C2211yescharacteristic
91#19151487C2211yescharacteristic
92#19151487C2211yescharacteristic
93#19151487C2211yescharacteristic
94#19151487C2211yescharacteristic
95#19151487C2211yescharacteristic
96#19151487C2211yescharacteristic, complemented
97#19151487C2211yescharacteristic, complemented
98#19151486C2211yescharacteristic, complemented
99#19151485C2211yescharacteristic, complemented
100#19151485C2211yescharacteristic, complemented
101#19151484C2211yescharacteristic, complemented
102#19151484C2211yescharacteristic, complemented
103#19151482C2211yescharacteristic, complemented
104#19151482C2211yescharacteristic, complemented
105#19151482C2211yescharacteristic, complemented
106#19151481C2211yescharacteristic, complemented
107#19151481C2211yescharacteristic, complemented
108#19151480C2211yescharacteristic, complemented
109#19151480C2211yescharacteristic, complemented
110#19151479C2211yescharacteristic, complemented
111#19151478C2211yescharacteristic
112#19151478C2211yescharacteristic
113#19151477C2211yescharacteristic
114#19151477C2211yescharacteristic
115#19151477C2211yescharacteristic
116#19151477C2211yescharacteristic
117#19151477C2211yescharacteristic, complemented
118#19151476C2211yescharacteristic
119#19151476C2211yescharacteristic
120#19151476C2211yescharacteristic
121#19151476C2211yescharacteristic
122#19151474C2211yescharacteristic
123#19151474C2211yescharacteristic
124#19151474C2211yescharacteristic, complemented
125#19151473C2211yescharacteristic
126#19151473C2211yescharacteristic
127#19151472C2211yescharacteristic
128#19151472C2211yescharacteristic
129#19151471C2211yescharacteristic
130#19151471C2211yescharacteristic
131#19151471C2211yescharacteristic, complemented
132#19151469C2211yescharacteristic
133#19151469C2211yescharacteristic
134#19151469C2211yescharacteristic, complemented
135#19151465C2211yescharacteristic, complemented
136#19151462C2211yescharacteristic, complemented
137#19151460C2211yescharacteristic, complemented
138#19151457C2211yescharacteristic, complemented
139C4×#13083553C2211yescharacteristic, complemented
140C4×#13083553C2211yescharacteristic, complemented
141C4×#13083553C2211yescharacteristic, complemented
142C4×#13083553C2211yescharacteristic, complemented
143C4×C4⋊Dic89C2211yescharacteristic, complemented
144C4×C4⋊Dic89C2211yescharacteristic, complemented
145#19151449C2211yescharacteristic, complemented
146#19151449C2211yescharacteristic, complemented
147C22⋊C4×Dic89C2211yescharacteristic
148C22⋊C4×Dic89C2211yescharacteristic
149C22⋊C4×Dic89C2211yescharacteristic
150C22⋊C4×Dic89C2211yescharacteristic
151C4×#13083551C2211yescharacteristic
152C4×#13083551C2211yescharacteristic
153C4×#13083551C2211yescharacteristic
154C4×#13083551C2211yescharacteristic
155C4×#13083551C2211yescharacteristic
156C4×#13083551C2211yescharacteristic
157C4×#13083551C2211yescharacteristic
158C4×#13083551C2211yescharacteristic
159C4×#13083551C2211yescharacteristic, complemented
160C4×#13083551C2211yescharacteristic, complemented
161C4×C22⋊Dic89C2211yescharacteristic
162C4×C22⋊Dic89C2211yescharacteristic, complemented
163C4×C22⋊Dic89C2211yescharacteristic, complemented
164#19151445C2211yescharacteristic
165#19151445C2211yescharacteristic
166#19151445C2211yescharacteristic
167#19151445C2211yescharacteristic
168#19151445C2211yescharacteristic, complemented
169#19151445C2211yescharacteristic, complemented
170#19151444C2211yescharacteristic, complemented
171C2×#15667919C2211yescharacteristic
172C42×Dic89C2211yescharacteristic, complemented
173C2×C4×D4×C89C2211yescharacteristic
174C2×C4×D4×C89C2211yescharacteristic
175C2×C4×D4×C89C2211yescharacteristic
176C4×C4⋊C4×C89C2211yescharacteristic, complemented
177C4×C4⋊C4×C89C2211yescharacteristic, complemented
178C4×C4⋊C4×C89C2211yescharacteristic, complemented
179C4×C22⋊C4×C89C2211yescharacteristic
180C4×C22⋊C4×C89C2211yescharacteristic
181C4×C22⋊C4×C89C2211yescharacteristic
182C4×C22⋊C4×C89C2211yescharacteristic, complemented
183C4×C22⋊C4×C89C2211yescharacteristic, complemented
184C4×C22⋊C4×C89C2211yescharacteristic, complemented
185#376×C89C2211yescharacteristic, complemented
186C2×#95×C89C2211yescharacteristic
187C2×#95×C89C2211yescharacteristic, complemented
188C24×D89C2311yescharacteristic
189C22×Dic178C2311yescharacteristic
190C22×D356C2311yescharacteristic
191C22×D356C2311yescharacteristic
192C22×C22⋊D89C2311yescharacteristic
193C22×C22⋊D89C2311yescharacteristic
194C22×C22⋊D89C2311yescharacteristic
195C22×C22⋊D89C2311yescharacteristic
196C23×Dic89C2311yescharacteristic
197C23×Dic89C2311yescharacteristic
198C23×Dic89C2311yescharacteristic
199C22×C4×D89C2311yescharacteristic
200C22×C4×D89C2311yescharacteristic
201C22×C4×D89C2311yescharacteristic
202C22×C4×D89C2311yescharacteristic
203C22×C4×D89C2311yescharacteristic
204C22×C4×D89C2311yescharacteristic
205C22×C4×D89C2311yescharacteristic
206#15668007C2×C418yescomplemented
207#15668006C2×C418yescomplemented
208#15668000C2×C418yescomplemented
209#15667998C2×C418yescomplemented
210#15667997C2×C418yescomplemented
211#15667995C2×C418yescomplemented
212#15667989C2×C418yescomplemented
213#15667986C2×C418yescomplemented
214#15667985C2×C418yescomplemented
215#15667984C2×C418yescomplemented
216#15667982C2×C418yescomplemented
217#15667980C2×C418yescomplemented
218C4×Dic178—42no—
219C4×D356—42no—
220C4×D356—42no—
221C4×C22⋊D89—42no—
222C4×C22⋊D89—42no—
223C4×C22⋊D89—42no—
224C4×C22⋊D89C2×C418yescomplemented
225#15667972—24no—
226#15667972—24no—
227#15667971—42no—
228C2×C4⋊Dic89C2311yescharacteristic
229C2×C4⋊Dic89C2311yescharacteristic
230C2×C4⋊Dic89C2311yescharacteristic
231C2×C4⋊Dic89C2311yescharacteristic
232C2×C4⋊Dic89C2311yescharacteristic
233C2×#13083553—42no—
234C2×#13083553C2311yescharacteristic
235C2×#13083553C2311yescharacteristic
236C2×#13083553C2311yescharacteristic
237C2×#13083553C2311yescharacteristic
238C2×#13083553C2311yescharacteristic
239C2×#13083553C2311yescharacteristic
240C2×#13083553C2311yescharacteristic
241C2×#13083553C2311yescharacteristic
242C2×#13083553C2311yescharacteristic
243C2×#13083553C2311yescharacteristic
244C2×#13083553C2311yescharacteristic
245C2×#13083553C2311yescharacteristic
246C2×#13083553C2311yescharacteristic
247C2×#13083553C2311yescharacteristic
248C2×C22⋊Dic89C2311yescharacteristic
249C2×C22⋊Dic89C2311yescharacteristic
250C2×C22⋊Dic89C2311yescharacteristic
251C2×C22⋊Dic89C2311yescharacteristic
252C2×C22⋊Dic89C2311yescharacteristic
253C2×C22⋊Dic89C2311yescharacteristic
254C2×C22⋊Dic89C2311yescharacteristic
255C2×C22⋊Dic89C2311yescharacteristic
256C2×#13083551—42no—
257C2×#13083551—42no—
258C2×#13083551C2×C418yescomplemented
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
287C22⋊C4×D89—24no—
288C22⋊C4×D89—24no—
289C2×C4×Dic89—42no—
290C2×C4×Dic89C2311yescharacteristic
291C2×C4×Dic89C2311yescharacteristic
292C2×C4×Dic89C2311yescharacteristic
293C2×C4×Dic89C2311yescharacteristic
294C2×C4×Dic89C2311yescharacteristic
295C2×C4×Dic89C2311yescharacteristic
296C2×C4×Dic89C2311yescharacteristic
297C2×C4×Dic89C2311yescharacteristic
298C2×C4×Dic89C2311yescharacteristic
299C2×C4×Dic89C2311yescharacteristic
300C2×C4×Dic89C2311yescharacteristic
301C2×C4×Dic89C2311yescharacteristic
302C2×C4×Dic89C2311yescharacteristic
303C2×C4×Dic89C2311yescharacteristic
304C2×C4×Dic89C2311yescharacteristic
305C2×C4×Dic89C2311yescharacteristic
306C2×C4×Dic89C2311yescharacteristic
307C42×D89—42no—
308#15667919C2311yescharacteristic
309#15667919C2311yescharacteristic
310#15667919C2311yescharacteristic
311#15667919C2311yescharacteristic
312#15667919C2311yescharacteristic
313#15667919C2311yescharacteristic
314#15667919C2311yescharacteristic
315#15667919C2311yescharacteristic
316#15667919C2311yescharacteristic
317#15667919C2311yescharacteristic
318#15667919C2311yescharacteristic
319#15667919C2311yescharacteristic
320#15667919C2311yescharacteristic
321#15667919C2311yescharacteristic
322#15667919C2311yescharacteristic
323#15667919C2311yescharacteristic
324#15667919C2311yescharacteristic
325#15667919C2311yescharacteristic
326#15667919C2311yescharacteristic
327#15667919C2311yescharacteristic
328#15667919C2311yescharacteristic
329#15667919C2311yescharacteristic
330#15667919C2311yescharacteristic
331#15667919C2311yescharacteristic
332#15667919C2311yescharacteristic
333#15667919C2311yescharacteristic
334#15667919C2311yescharacteristic
335#15667919C2311yescharacteristic
336#15667919C2311yescharacteristic
337#15667919C2311yescharacteristic
338C22×D4×C89C2311yescharacteristic
339C23×C4×C89C2311yescharacteristic
340C23×C4×C89C2311yescharacteristic
341C23×C4×C89C2311yescharacteristic
342C23×C4×C89C2311yescharacteristic
343C23×C4×C89C2311yescharacteristic
344C23×C4×C89C2311yescharacteristic
345C4×D4×C89—24no—
346C4×D4×C89—24no—
347C4×D4×C89C2×C418yescomplemented
348C2×C4⋊C4×C89C2311yescharacteristic
349C2×C4⋊C4×C89C2311yescharacteristic
350C2×C4⋊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×C42×C89C2311yescharacteristic
358C2×C42×C89C2311yescharacteristic
359C2×C42×C89C2311yescharacteristic
360C2×C42×C89C2311yescharacteristic
361C2×C42×C89C2311yescharacteristic
362C2×C42×C89C2311yescharacteristic
363C2×C42×C89C2311yescharacteristic
364C2×C42×C89C2311yescharacteristic
365C2×C42×C89C2311yescharacteristic
366#95×C89C2311yescharacteristic
367#95×C89C2311yescharacteristic
368#95×C89C2311yescharacteristic
369#95×C89C2311yescharacteristic
370#95×C89C2311yescharacteristic
371#95×C89C2311yescharacteristic
372#95×C89C2311yescharacteristic
373#95×C89C2311yescharacteristic
374#95×C89C2311yescharacteristic
375#95×C89C2311yescharacteristic
376C23×D89—22no—
377C23×D89—22no—
378C23×D89—41no—
379C23×D89—41no—
380C23×D89—41no—
381C23×D89—41no—
382C23×D89C22×C414yes—
383C23×D89C2411yescharacteristic
384C23×D89C2411yescharacteristic
385C23×D89C2411yescharacteristic
386C2×Dic178—41no—
387C2×Dic178—41no—
388C2×Dic178C22×C414yes—
389C2×D356—41no—
390C2×D356—41no—
391C2×D356—41no—
392C2×D356—41no—
393C2×D356C22×C414yes—
394C2×D356C22×C414yes—
395C2×C22⋊D89—22no—
396C2×C22⋊D89—22no—
397C2×C22⋊D89—41no—
398C2×C22⋊D89—41no—
399C2×C22⋊D89—41no—
400C2×C22⋊D89—41no—
401C2×C22⋊D89—41no—
402C2×C22⋊D89—41no—
403C2×C22⋊D89C22×C414yes—
404C2×C22⋊D89C22×C414yes—
405C2×C22⋊D89C22×C414yes—
406C2×C22⋊D89C22×C414yes—
407C22×Dic89—22no—
408C22×Dic89—22no—
409C22×Dic89—22no—
410C22×Dic89—22no—
411C22×Dic89—41no—
412C22×Dic89—41no—
413C22×Dic89—41no—
414C22×Dic89—41no—
415C22×Dic89C22×C414yes—
416C22×Dic89C2411yescharacteristic
417C22×Dic89C2411yescharacteristic
418C22×Dic89C2411yescharacteristic
419C22×Dic89C2411yescharacteristic
420C22×Dic89C2411yescharacteristic
421C22×Dic89C2411yescharacteristic
422C22×Dic89C2411yescharacteristic
423C22×Dic89C2411yescharacteristic
424C22×Dic89C2411yescharacteristic
425C22×Dic89C2411yescharacteristic
426C22×Dic89C2411yescharacteristic
427C22×Dic89C2411yescharacteristic
428C22×Dic89C2411yescharacteristic
429C2×C4×D89—22no—
430C2×C4×D89—22no—
431C2×C4×D89—22no—
432C2×C4×D89—22no—
433C2×C4×D89—22no—
434C2×C4×D89—22no—
435C2×C4×D89—22no—
436C2×C4×D89—22no—
437C2×C4×D89—41no—
438C2×C4×D89—41no—
439C2×C4×D89—41no—
440C2×C4×D89—41no—
441C2×C4×D89—41no—
442C2×C4×D89—41no—
443C2×C4×D89—41no—
444C2×C4×D89—41no—
445C2×C4×D89—41no—
446C2×C4×D89—41no—
447C2×C4×D89—41no—
448C2×C4×D89—41no—
449C2×C4×D89C22×C414yes—
450C4⋊Dic89—22no—
451C4⋊Dic89—22no—
452C4⋊Dic89—41no—
453C4⋊Dic89—41no—
454C4⋊Dic89C22×C414yes—
455#13083553—22no—
456#13083553—22no—
457#13083553—22no—
458#13083553—22no—
459#13083553—41no—
460#13083553—41no—
461#13083553—41no—
462#13083553—41no—
463#13083553—41no—
464#13083553—41no—
465#13083553C22×C414yes—
466#13083553C22×C414yes—
467#13083553C22×C414yes—
468#13083553C22×C414yes—
469C22⋊Dic89—22no—
470C22⋊Dic89—22no—
471C22⋊Dic89—22no—
472C22⋊Dic89—22no—
473C22⋊Dic89—41no—
474C22⋊Dic89—41no—
475C22⋊Dic89C22×C414yes—
476C22⋊Dic89C22×C414yes—
477#13083551—22no—
478#13083551—22no—
479#13083551—22no—
480#13083551—22no—
481#13083551—22no—
482#13083551—22no—
483#13083551—22no—
484#13083551—22no—
485#13083551—22no—
486#13083551—22no—
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#13083551C22×C414yes—
496#13083551C22×C414yes—
497#13083551C22×C414yes—
498#13083551C22×C414yes—
499#13083551C22×C414yes—
500#13083551C22×C414yes—
501#13083551C22×C414yes—
502#13083551C22×C414yes—
503#13083551C22×C414yes—
504#13083551C22×C414yes—
505C4×Dic89—22no—
506C4×Dic89—22no—
507C4×Dic89—22no—
508C4×Dic89—22no—
509C4×Dic89—22no—
510C4×Dic89—22no—
511C4×Dic89—41no—
512C4×Dic89—41no—
513C4×Dic89—41no—
514C4×Dic89—41no—
515C4×Dic89—41no—
516C4×Dic89—41no—
517C4×Dic89—41no—
518C4×Dic89—41no—
519C4×Dic89—41no—
520C4×Dic89—41no—
521C4×Dic89C22×C414yes—
522C24×C89C2411yescharacteristic
523C24×C89C2411yescharacteristic
524C2×D4×C89—22no—
525C2×D4×C89—22no—
526C2×D4×C89C22×C414yes—
527C22×C4×C89—22no—
528C22×C4×C89—22no—
529C22×C4×C89—22no—
530C22×C4×C89—22no—
531C22×C4×C89—41no—
532C22×C4×C89—41no—
533C22×C4×C89—41no—
534C22×C4×C89—41no—
535C22×C4×C89—41no—
536C22×C4×C89—41no—
537C22×C4×C89—41no—
538C22×C4×C89—41no—
539C22×C4×C89—41no—
540C22×C4×C89—41no—
541C22×C4×C89—41no—
542C22×C4×C89—41no—
543C22×C4×C89C22×C414yes—
544C22×C4×C89C22×C414yes—
545C22×C4×C89C2411yescharacteristic
546C22×C4×C89C2411yescharacteristic
547C22×C4×C89C2411yescharacteristic
548C22×C4×C89C2411yescharacteristic
549C22×C4×C89C2411yescharacteristic
550C22×C4×C89C2411yescharacteristic
551C22×C4×C89C2411yescharacteristic
552C22×C4×C89C2411yescharacteristic
553C22×C4×C89C2411yescharacteristic
554C22×C4×C89C2411yescharacteristic
555C22×C4×C89C2411yescharacteristic
556C22×C4×C89C2411yescharacteristic
557C22×C4×C89C2411yescharacteristic
558C4⋊C4×C89—22no—
559C4⋊C4×C89—22no—
560C4⋊C4×C89C22×C414yes—
561C22⋊C4×C89—22no—
562C22⋊C4×C89—22no—
563C22⋊C4×C89C22×C414yes—
564C22⋊C4×C89C22×C414yes—
565C22⋊C4×C89#4114yes—
566C22⋊C4×C89#4114yes—
567C42×C89—22no—
568C42×C89—22no—
569C42×C89—41no—
570C42×C89—41no—
571C42×C89—41no—
572C42×C89—41no—
573C42×C89—41no—
574C42×C89—41no—
575C42×C89C22×C414yes—
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×C89C23×C412yes—
587C23×C89C23×C412yes—
588C23×C89C2×#4112yes—
589C23×C89C2×#4112yes—
590C23×C89C2511yescharacteristic
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—21no—
601C22×D89—21no—
602C22×D89—21no—
603C22×D89—21no—
604C22×D89—21no—
605C22×D89—21no—
606C22×D89—21no—
607C22×D89—21no—
608C22×D89—21no—
609C22×D89—28no—
610C22×D89—44no—
611C22×D89—44no—
612C22×D89—82no—
613C22×D89—82no—
614C22×D89—82no—
615C22×D89—82no—
616C22×D89C23×C412yes—
617C22×D89C23×C412yes—
618C22×D89C23×C412yes—
619D4×C89—28no—
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—44no—
651C2×C4×C89—44no—
652C2×C4×C89—82no—
653C2×C4×C89—82no—
654C2×C4×C89—82no—
655C2×C4×C89—82no—
656C2×C4×C89C23×C412yes—
657C2×C4×C89C23×C412yes—
658C2×C4×C89C23×C412yes—
659C2×C4×C89C23×C412yes—
660C2×C4×C89C23×C412yes—
661C2×C4×C89C2×#4112yes—
662C2×C4×C89C2×#4112yes—
663C2×C4×C89C2×#4112yes—
664C2×C4×C89C2×#4112yes—
665C22⋊D89—28no—
666C22⋊D89—44no—
667C22⋊D89—44no—
668C22⋊D89—44no—
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—44no—
704C2×Dic89C23×C412yes—
705C2×Dic89C23×C412yes—
706C2×Dic89C23×C412yes—
707C2×Dic89C23×C412yes—
708C2×Dic89C23×C412yes—
709C2×Dic89H(5,𝔽2)12yes—
710C2×Dic89H(5,𝔽2)12yes—
711D356—44no—
712D356—44no—
713C4×D89—44no—
714C4×D89—44no—
715C4×D89—44no—
716C4×D89—82no—
717C4×D89—82no—
718C4×D89—82no—
719C4×D89—82no—
720Dic178—44no—
721C22×C89—22no—
722C22×C89—22no—
723C22×C89—22no—
724C22×C89—22no—
725C22×C89—22no—
726C22×C89—22no—
727C22×C89—22no—
728C22×C89—22no—
729C22×C89—22no—
730C22×C89—41no—
731C22×C89—41no—
732C22×C89—41no—
733C22×C89—41no—
734C22×C89C4×#4114yes—
735C22×C89C24×C411yescharacteristic
736C22×C89C22×#4111yescharacteristic
737C22×C89C22×#4111yescharacteristic
738C22×C89C2×H(5,𝔽2)11yescharacteristic
739C22×C89C2×H(5,𝔽2)11yescharacteristic
740C22×C89#58511yescharacteristic
741C22×C89#58511yescharacteristic
742C2×D89—22no—
743C2×D89—22no—
744C2×D89—22no—
745C2×D89—22no—
746C2×D89—22no—
747C2×D89—22no—
748C2×D89—22no—
749C2×D89—22no—
750C2×D89—22no—
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—41no—
760C2×D89—41no—
761C2×D89—41no—
762C2×D89—41no—
763C2×D89—88no—
764C4×C89—22no—
765C4×C89—22no—
766C4×C89—22no—
767C4×C89—22no—
768C4×C89—22no—
769C4×C89—22no—
770C4×C89—22no—
771C4×C89—22no—
772C4×C89—22no—
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—41no—
785Dic89—41no—
786Dic89—41no—
787Dic89—41no—
788Dic89—41no—
789Dic89—41no—
790#34283—891nomaximal, Sylow
791C2×C89—24no—
792C2×C89—42no—
793C2×C89C2×C4×#4111yescharacteristic
794C2×C89C4×H(5,𝔽2)11yescharacteristic
795C2×C89C4×H(5,𝔽2)11yescharacteristic
796C2×C89#351311yescharacteristic
797C2×C89#351411yescharacteristic
798C2×C89#351911yescharacteristic
799C2×C89#352111yescharacteristic
800D89—42no—
801D89—42no—
802D89—42no—
803C2×#538—891no—
804#2374—891no—
805#2373—891no—
806#2373—891no—
807#2372—891no—
808#2368—891no—
809#2367—891no—
810#2364—891no—
811#2364—891no—
812#2363—891no—
813#2361—891no—
814#2360—891no—
815#2359—891no—
816#2358—891no—
817#2358—891no—
818#2358—891no—
819#2358—891no—
820#2337—891no—
821#2335—891no—
822#2334—891no—
823#2333—891no—
824#2318—891no—
825C4×#126—891no—
826C4×#124—891no—
827C4×#123—891no—
828C4×#121—891no—
829#2290—891no—
830C2×#388—891no—
831#2275D8911yescharacteristic, complemented
832#2273—891no—
833C42×D4—891no—
834C89#3428311yescharacteristic, complemented, Sylow
835#538—8916no—
836C2×#126—891no—
837C2×#126—891no—
838C2×#124—891no—
839C2×#124—891no—
840C2×#123—891no—
841C2×#123—891no—
842C2×C22⋊Q8—891no—
843C2×#121—891no—
844C2×#121—891no—
845C2×#121—891no—
846C2×#120—891no—
847C2×#120—891no—
848C2×C4×Q8—891no—
849C2×C4×D4—891no—
850C2×C4×D4—891no—
851C2×C4×D4—891no—
852C2×C4×D4—891no—
853C2×C4×D4—891no—
854C2×C4×D4—891no—
855C2×C4×D4—891no—
856C2×C4×D4—891no—
857C2×C4×D4C2×D8911yescharacteristic
858C2×C4×D4C2×D8911yescharacteristic
859C2×C4×D4C2×D8911yescharacteristic
860C2×#117—891no—
861C22×C4⋊C4—891no—
862C22×C22⋊C4—891no—
863C22×C22⋊C4—891no—
864C22×C22⋊C4—891no—
865C22×C22⋊C4—891no—
866C22×C22⋊C4—891no—
867C22×C42—891no—
868C22×C42—891no—
869#391—891no—
870#391—891no—
871#391—891no—
872#390—891no—
873#390—891no—
874#390—891no—
875#390—891no—
876#390—891no—
877#389—891no—
878#389—891no—
879#389—891no—
880#389—891no—
881#388—891no—
882#388—891no—
883#388—891no—
884#388—891no—
885#388—891no—
886#388—891no—
887#388—891no—
888#388—891no—
889#388—891no—
890#388—891no—
891#388—891no—
892#388—891no—
893#388—891no—
894#388—891no—
895#388—891no—
896#388—891no—
897#388—891no—
898#388—891no—
899#388—891no—
900#388—891no—
901#388—891no—
902#388—891no—
903#388—891no—
904#388—891no—
905#387—891no—
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#386—891no—
918#386—891no—
919#386—891no—
920#386—891no—
921#386—891no—
922#386—891no—
923#386—891no—
924#386—891no—
925#386—891no—
926#386—891no—
927#386—891no—
928#386—891no—
929#386—891no—
930#386—891no—
931#385—891no—
932#385—891no—
933#385—891no—
934#385—891no—
935#385—891no—
936#385—891no—
937#385—891no—
938#385—891no—
939#385—891no—
940#385—891no—
941#383—891no—
942#382—891no—
943#381—891no—
944#380—891no—
945C4×C4⋊C4—891no—
946C4×C4⋊C4—891no—
947C4×C4⋊C4—891no—
948C4×C4⋊C4—891no—
949C4×C4⋊C4—891no—
950C4×C4⋊C4—891no—
951C4×C4⋊C4—891no—
952C4×C4⋊C4—891no—
953C4×C4⋊C4C2×D8911yescharacteristic, complemented
954C4×C4⋊C4C2×D8911yescharacteristic, complemented
955C4×C4⋊C4C2×D8911yescharacteristic, complemented
956C4×C22⋊C4—891no—
957C4×C22⋊C4—891no—
958C4×C22⋊C4—891no—
959C4×C22⋊C4—891no—
960C4×C22⋊C4—891no—
961C4×C22⋊C4—891no—
962C4×C22⋊C4—891no—
963C4×C22⋊C4—891no—
964C4×C22⋊C4—891no—
965C4×C22⋊C4—891no—
966C4×C22⋊C4—891no—
967C4×C22⋊C4—891no—
968C4×C22⋊C4—891no—
969C4×C22⋊C4—891no—
970C4×C22⋊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⋊C4C2×D8911yescharacteristic
980C4×C22⋊C4C2×D8911yescharacteristic
981C4×C22⋊C4C2×D8911yescharacteristic
982C4×C22⋊C4C2×D8911yescharacteristic, complemented
983C4×C22⋊C4C2×D8911yescharacteristic, complemented
984C4×C22⋊C4C2×D8911yescharacteristic, complemented
985#376—891no—
986#376C2×D8911yescharacteristic, complemented
987C2×#95—891no—
988C2×#95C2×D8911yescharacteristic
989C2×#95C2×D8911yescharacteristic, complemented
990C43—891no—
991C25—891no—
992C22×Q8—891no—
993C22×D4—891no—
994C22×D4—891no—
995C22×D4—891no—
996C22×D4—891no—
997C22×D4—891no—
998C22×D4—891no—
999C22×D4C22×D8911yescharacteristic
1000C23×C4—891no—
1001C23×C4—891no—
1002C23×C4—891no—
1003C23×C4—891no—
1004C23×C4—891no—
1005C23×C4—891no—
1006C23×C4—891no—
1007C23×C4—891no—
1008C23×C4—891no—
1009C23×C4—891no—
1010C23×C4C22×D8911yescharacteristic
1011C23×C4C22×D8911yescharacteristic
1012C23×C4C22×D8911yescharacteristic
1013C23×C4C22×D8911yescharacteristic
1014C23×C4C22×D8911yescharacteristic
1015C23×C4C22×D8911yescharacteristic
1016#126—898no—
1017#126—898no—
1018#124—898no—
1019#124—898no—
1020#123—898no—
1021#123—898no—
1022C22⋊Q8—898no—
1023#121—898no—
1024#121—898no—
1025#121—898no—
1026#120—898no—
1027#120—898no—
1028C4×Q8—3562no—
1029C4×D4—24no—
1030C4×D4—24no—
1031C4×D4—898no—
1032C4×D4—3562no—
1033C4×D4—3562no—
1034C4×D4—3562no—
1035C4×D4—3562no—
1036C4×D4—3562no—
1037C4×D4—1784no—
1038C4×D4—1784no—
1039C4×D4C4×D8918yescomplemented
1040#117—3562no—
1041C2×C4⋊C4—891no—
1042C2×C4⋊C4—891no—
1043C2×C4⋊C4—891no—
1044C2×C4⋊C4—891no—
1045C2×C4⋊C4—891no—
1046C2×C4⋊C4—891no—
1047C2×C4⋊C4—891no—
1048C2×C4⋊C4—891no—
1049C2×C4⋊C4—891no—
1050C2×C4⋊C4—891no—
1051C2×C4⋊C4—891no—
1052C2×C4⋊C4—891no—
1053C2×C4⋊C4—891no—
1054C2×C4⋊C4—891no—
1055C2×C4⋊C4—891no—
1056C2×C4⋊C4—891no—
1057C2×C4⋊C4—891no—
1058C2×C4⋊C4—891no—
1059C2×C4⋊C4—891no—
1060C2×C4⋊C4—3562no—
1061C2×C4⋊C4C22×D8911yescharacteristic
1062C2×C4⋊C4C22×D8911yescharacteristic
1063C2×C4⋊C4C22×D8911yescharacteristic
1064C2×C22⋊C4—891no—
1065C2×C22⋊C4—891no—
1066C2×C22⋊C4—898no—
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—891no—
1099C2×C22⋊C4—891no—
1100C2×C22⋊C4—891no—
1101C2×C22⋊C4—3562no—
1102C2×C22⋊C4—3562no—
1103C2×C22⋊C4—1784no—
1104C2×C22⋊C4—1784no—
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—891no—
1119C2×C42—891no—
1120C2×C42—891no—
1121C2×C42—891no—
1122C2×C42—891no—
1123C2×C42—891no—
1124C2×C42—891no—
1125C2×C42—891no—
1126C2×C42—891no—
1127C2×C42—891no—
1128C2×C42—3562no—
1129C2×C42—3562no—
1130C2×C42C22×D8911yescharacteristic
1131C2×C42C22×D8911yescharacteristic
1132C2×C42C22×D8911yescharacteristic
1133C2×C42C22×D8911yescharacteristic
1134C2×C42C22×D8911yescharacteristic
1135C2×C42C22×D8911yescharacteristic
1136C2×C42C22×D8911yescharacteristic
1137C2×C42C22×D8911yescharacteristic
1138C2×C42C22×D8911yescharacteristic
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#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#95C22×D8911yescharacteristic
1170#95C22×D8911yescharacteristic
1171#95C22×D8911yescharacteristic
1172#95C22×D8911yescharacteristic
1173#95C22×D8911yescharacteristic
1174#95C22×D8911yescharacteristic
1175#95C22×D8911yescharacteristic
1176#95C22×D8911yescharacteristic
1177#95C22×D8911yescharacteristic
1178#95C22×D8911yescharacteristic
1179C24—894no—
1180C24—891no—
1181C24—891no—
1182C24—891no—
1183C24—3561no—
1184C24—3561no—
1185C24—3561no—
1186C24—3561no—
1187C24—1782no—
1188C24—1782no—
1189C24C23×D8911yescharacteristic
1190C24C23×D8911yescharacteristic
1191C2×Q8—894no—
1192C2×Q8—3561no—
1193C2×Q8—3561no—
1194C2×D4—22no—
1195C2×D4—22no—
1196C2×D4—894no—
1197C2×D4—894no—
1198C2×D4—894no—
1199C2×D4—894no—
1200C2×D4—894no—
1201C2×D4—894no—
1202C2×D4—3561no—
1203C2×D4—3561no—
1204C2×D4—3561no—
1205C2×D4—3561no—
1206C2×D4—3561no—
1207C2×D4—3561no—
1208C2×D4—3561no—
1209C2×D4—3561no—
1210C2×D4—3561no—
1211C2×D4—3561no—
1212C2×D4—1782no—
1213C2×D4—1782no—
1214C2×D4C2×C4×D8914yes—
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—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—41no—
1227C22×C4—41no—
1228C22×C4—41no—
1229C22×C4—41no—
1230C22×C4—41no—
1231C22×C4—894no—
1232C22×C4—891no—
1233C22×C4—891no—
1234C22×C4—891no—
1235C22×C4—891no—
1236C22×C4—891no—
1237C22×C4—891no—
1238C22×C4—891no—
1239C22×C4—894no—
1240C22×C4—891no—
1241C22×C4—891no—
1242C22×C4—891no—
1243C22×C4—891no—
1244C22×C4—891no—
1245C22×C4—891no—
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—3561no—
1255C22×C4—3561no—
1256C22×C4—3561no—
1257C22×C4—3561no—
1258C22×C4—3561no—
1259C22×C4—3561no—
1260C22×C4—3561no—
1261C22×C4—3561no—
1262C22×C4—1782no—
1263C22×C4—1782no—
1264C22×C4—1782no—
1265C22×C4—1782no—
1266C22×C4—1782no—
1267C22×C4—1782no—
1268C22×C4—1782no—
1269C22×C4—1782no—
1270C22×C4—1782no—
1271C22×C4—1782no—
1272C22×C4—1782no—
1273C22×C4—1782no—
1274C22×C4C2×C4×D8914yes—
1275C22×C4C2×C4×D8914yes—
1276C22×C4C23×D8911yescharacteristic
1277C22×C4C23×D8911yescharacteristic
1278C22×C4C23×D8911yescharacteristic
1279C22×C4C23×D8911yescharacteristic
1280C22×C4C23×D8911yescharacteristic
1281C22×C4C23×D8911yescharacteristic
1282C22×C4C23×D8911yescharacteristic
1283C22×C4C23×D8911yescharacteristic
1284C22×C4C23×D8911yescharacteristic
1285C22×C4C23×D8911yescharacteristic
1286C22×C4C23×D8911yescharacteristic
1287C22×C4C23×D8911yescharacteristic
1288C22×C4C23×D8911yescharacteristic
1289C4⋊C4—22no—
1290C4⋊C4—22no—
1291C4⋊C4—894no—
1292C4⋊C4—894no—
1293C4⋊C4—894no—
1294C4⋊C4—894no—
1295C4⋊C4—894no—
1296C4⋊C4—3561no—
1297C4⋊C4—3561no—
1298C4⋊C4—3561no—
1299C4⋊C4—3561no—
1300C4⋊C4—3561no—
1301C4⋊C4—3561no—
1302C4⋊C4—3561no—
1303C4⋊C4—3561no—
1304C4⋊C4—1782no—
1305C4⋊C4—1782no—
1306C4⋊C4—1782no—
1307C4⋊C4—1782no—
1308C4⋊C4—1782no—
1309C4⋊C4—1782no—
1310C4⋊C4C2×C4×D8914yes—
1311C22⋊C4—22no—
1312C22⋊C4—22no—
1313C22⋊C4—894no—
1314C22⋊C4—894no—
1315C22⋊C4—894no—
1316C22⋊C4—894no—
1317C22⋊C4—894no—
1318C22⋊C4—894no—
1319C22⋊C4—894no—
1320C22⋊C4—894no—
1321C22⋊C4—894no—
1322C22⋊C4—894no—
1323C22⋊C4—894no—
1324C22⋊C4—894no—
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—1782no—
1336C22⋊C4—1782no—
1337C22⋊C4—1782no—
1338C22⋊C4—1782no—
1339C22⋊C4—1782no—
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⋊C4C2×C4×D8914yes—
1350C22⋊C4C2×C4×D8914yes—
1351C22⋊C4#1308357414yes—
1352C22⋊C4#1308357414yes—
1353C42—22no—
1354C42—22no—
1355C42—41no—
1356C42—41no—
1357C42—41no—
1358C42—41no—
1359C42—41no—
1360C42—41no—
1361C42—894no—
1362C42—3561no—
1363C42—3561no—
1364C42—3561no—
1365C42—3561no—
1366C42—3561no—
1367C42—3561no—
1368C42—3561no—
1369C42—3561no—
1370C42—3561no—
1371C42—3561no—
1372C42—1782no—
1373C42—1782no—
1374C42—1782no—
1375C42—1782no—
1376C42—1782no—
1377C42—1782no—
1378C42C2×C4×D8914yes—
1379C23—21no—
1380C23—21no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—892no—
1390C23—892no—
1391C23—892no—
1392C23—3564no—
1393C23—3564no—
1394C23—1781no—
1395C23—1781no—
1396C23—1781no—
1397C23—1781no—
1398C23—1781no—
1399C23—1781no—
1400C23—1781no—
1401C23—1781no—
1402C23—1781no—
1403C23—1781no—
1404C23—1781no—
1405C23—1781no—
1406C23—1781no—
1407C23—1781no—
1408C23—1781no—
1409C23—1781no—
1410C23—1781no—
1411C23—1781no—
1412C23—1788no—
1413C23—7122no—
1414C23—7122no—
1415C23—7122no—
1416C23—7122no—
1417C23C22×C4×D8912yes—
1418C23C22×C4×D8912yes—
1419C23C2×#1308357412yes—
1420C23C2×#1308357412yes—
1421C23C24×D8911yescharacteristic
1422Q8—3564no—
1423D4—28no—
1424D4—3564no—
1425D4—3564no—
1426D4—3564no—
1427D4—3564no—
1428D4—3564no—
1429D4—1788no—
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—44no—
1461C2×C4—44no—
1462C2×C4—82no—
1463C2×C4—82no—
1464C2×C4—82no—
1465C2×C4—82no—
1466C2×C4—892no—
1467C2×C4—892no—
1468C2×C4—892no—
1469C2×C4—892no—
1470C2×C4—892no—
1471C2×C4—892no—
1472C2×C4—892no—
1473C2×C4—3564no—
1474C2×C4—3564no—
1475C2×C4—3564no—
1476C2×C4—3564no—
1477C2×C4—3564no—
1478C2×C4—3564no—
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—1781no—
1507C2×C4—1781no—
1508C2×C4—1781no—
1509C2×C4—1781no—
1510C2×C4—1781no—
1511C2×C4—7122no—
1512C2×C4—7122no—
1513C2×C4—7122no—
1514C2×C4—7122no—
1515C2×C4C22×C4×D8912yes—
1516C2×C4C22×C4×D8912yes—
1517C2×C4C22×C4×D8912yes—
1518C2×C4C22×C4×D8912yes—
1519C2×C4C22×C4×D8912yes—
1520C2×C4C2×#1308357412yes—
1521C2×C4C2×#1308357412yes—
1522C2×C4C2×#1308357412yes—
1523C2×C4C2×#1308357412yes—
1524C22—22no—
1525C22—22no—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—22no—
1533C22—41no—
1534C22—41no—
1535C22—41no—
1536C22—41no—
1537C22—3561no—
1538C22—3561no—
1539C22—3561no—
1540C22—3561no—
1541C22—3561no—
1542C22—3561no—
1543C22—3561no—
1544C22—3561no—
1545C22—3561no—
1546C22—3561no—
1547C22—3561no—
1548C22—3561no—
1549C22—1782no—
1550C22—1782no—
1551C22—1782no—
1552C22—1782no—
1553C22—1782no—
1554C22—1782no—
1555C22—1782no—
1556C22—1782no—
1557C22—1782no—
1558C22—7128no—
1559C22C4×#1308357414yes—
1560C22C23×C4×D8911yescharacteristic
1561C22C22×#1308357411yescharacteristic
1562C22C22×#1308357411yescharacteristic
1563C22H(5,𝔽2)×D8911yescharacteristic
1564C22H(5,𝔽2)×D8911yescharacteristic
1565C22#1915243311yescharacteristic
1566C22#1915243511yescharacteristic
1567C4—22no—
1568C4—22no—
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—22no—
1573C4—22no—
1574C4—22no—
1575C4—22no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—3561no—
1581C4—3561no—
1582C4—3561no—
1583C4—3561no—
1584C4—3561no—
1585C4—3561no—
1586C4—1782no—
1587C4—1782no—
1588C4—1782no—
1589C4—1782no—
1590C4—1782no—
1591C4—1782no—
1592C4—1782no—
1593C2—24no—
1594C2—42no—
1595C2—3562no—
1596C2—3562no—
1597C2—3562no—
1598C2C2×C4×#1308357411yescharacteristic
1599C2#2603345611yescharacteristic
1600C2#2603345811yescharacteristic
1601C2#2603419411yescharacteristic
1602C2#2603420311yescharacteristic
1603C2#2603427411yescharacteristic
1604C2#2603432211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC89×#2275C2
socle, cosocleC23×C89C25
prime radicalC2×#19152181C2
hypercenter#2275D89
hypocenterC89#34283
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2275

Complements

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

NH ≅ G/Ntype
2. #26023383C2semidirect
3. #26023372C2semidirect
4. #26023368C2semidirect
5. #26023362C2semidirect
6. #26023330C2semidirect
7. #26023321C2semidirect
8. #26023299C2semidirect
9. #26023297C2semidirect
10. #26023288C2semidirect
11. #26023269C2semidirect
12. #26023258C2semidirect
13. #26023240C2semidirect
14. #26023234C2semidirect
15. #26023234C2semidirect
16. #26023229C2semidirect
17. #26023229C2semidirect
18. #26023060C2semidirect
19. #26023036C2semidirect
20. #26023021C2semidirect
21. #26023012C2semidirect
22. #26022886C2semidirect
23. C4×#15668007C2semidirect
24. C4×#15667998C2semidirect
25. C4×#15667997C2semidirect
26. C4×#15667985C2semidirect
27. #26022697C2semidirect
28. C2×#19151487C2semidirect
29. #26022604C2semidirect
30. C4×#15667972C2semidirect
31. C89×#2275C2semidirect
32. #19152181C4semidirect
45. C2×C4×Dic178C22semidirect
51. C2×C4×C22⋊D89C22semidirect
54. C2×#15667971C22semidirect
62. C2×C42×D89C22semidirect
63. #19151504C22semidirect
64. #19151502C22semidirect
65. #19151502C22semidirect
70. #19151498C22semidirect
71. #19151496C22semidirect
72. #19151495C22semidirect
73. #19151495C22semidirect
74. #19151493C22semidirect
75. #19151492C22semidirect
76. #19151491C22semidirect
77. #19151491C22semidirect
84. #19151489C22semidirect
87. #19151488C22semidirect
96. #19151487C22semidirect
97. #19151487C22semidirect
98. #19151486C22semidirect
99. #19151485C22semidirect
100. #19151485C22semidirect
101. #19151484C22semidirect
102. #19151484C22semidirect
103. #19151482C22semidirect
104. #19151482C22semidirect
105. #19151482C22semidirect
106. #19151481C22semidirect
107. #19151481C22semidirect
108. #19151480C22semidirect
109. #19151480C22semidirect
110. #19151479C22semidirect
117. #19151477C22semidirect
124. #19151474C22semidirect
131. #19151471C22semidirect
134. #19151469C22semidirect
135. #19151465C22semidirect
136. #19151462C22semidirect
137. #19151460C22semidirect
138. #19151457C22semidirect
139. C4×#13083553C22semidirect
140. C4×#13083553C22semidirect
141. C4×#13083553C22semidirect
142. C4×#13083553C22semidirect
143. C4×C4⋊Dic89C22semidirect
144. C4×C4⋊Dic89C22semidirect
145. #19151449C22semidirect
146. #19151449C22semidirect
159. C4×#13083551C22semidirect
160. C4×#13083551C22semidirect
162. C4×C22⋊Dic89C22semidirect
163. C4×C22⋊Dic89C22semidirect
168. #19151445C22semidirect
169. #19151445C22semidirect
170. #19151444C22semidirect
172. C42×Dic89C22semidirect
176. C4×C4⋊C4×C89C22semidirect
177. C4×C4⋊C4×C89C22semidirect
178. C4×C4⋊C4×C89C22semidirect
182. C4×C22⋊C4×C89C22semidirect
183. C4×C22⋊C4×C89C22semidirect
184. C4×C22⋊C4×C89C22semidirect
185. #376×C89C22semidirect
187. C2×#95×C89C22semidirect
206. #15668007C2×C4semidirect
207. #15668006C2×C4semidirect
208. #15668000C2×C4semidirect
209. #15667998C2×C4semidirect
210. #15667997C2×C4semidirect
211. #15667995C2×C4semidirect
212. #15667989C2×C4semidirect
213. #15667986C2×C4semidirect
214. #15667985C2×C4semidirect
215. #15667984C2×C4semidirect
216. #15667982C2×C4semidirect
217. #15667980C2×C4semidirect
224. C4×C22⋊D89C2×C4semidirect
258. C2×#13083551C2×C4semidirect
347. C4×D4×C89C2×C4semidirect
831. #2275D89semidirect
834. C89#34283semidirect
953. C4×C4⋊C4C2×D89semidirect
954. C4×C4⋊C4C2×D89semidirect
955. C4×C4⋊C4C2×D89semidirect
982. C4×C22⋊C4C2×D89semidirect
983. C4×C22⋊C4C2×D89semidirect
984. C4×C22⋊C4C2×D89semidirect
986. #376C2×D89semidirect
989. C2×#95C2×D89semidirect
1039. C4×D4C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#191521812
#260233832
#260233722
#260233682
#260233622
#260233302
#260233212
#260232992
#260232972
#260232882
#260232692
#260232582
#260232402
#260232342
#260232292
#260230602
#260230362
#260230212
#260230122
#260228862
C4×#156680072
C4×#156679982
C4×#156679972
C4×#156679852
#260226972
C2×#191514872
#260226042
C4×#156679722
C89×#22752
#3428389