Finite Group Databasebeta

← #36713188

Subgroups — #36713188

Order 22784.

3134 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19152111C211yesmaximal, characteristic
2C2×C4×#13083575C211yesmaximal, characteristic, complemented
3C2×#117×D89C211yesmaximal, characteristic, complemented
4#26022946C211yesmaximal, characteristic, complemented
5#26022945C211yesmaximal, characteristic, complemented
6#26022943C211yesmaximal, characteristic, complemented
7#26022941C211yesmaximal, characteristic, complemented
8#26022937C211yesmaximal, characteristic, complemented
9#26022936C211yesmaximal, characteristic, complemented
10#26022928C211yesmaximal, characteristic, complemented
11#26022925C212yesmaximal, complemented
12#26022916C212yesmaximal, complemented
13#26022914C212yesmaximal, complemented
14#26022905C212yesmaximal, complemented
15#26022741C211yesmaximal, characteristic, complemented
16#26022733C211yesmaximal, characteristic, complemented
17#26022712C212yesmaximal, complemented
18#26022710C212yesmaximal, complemented
19#26022694C212yesmaximal, complemented
20#26022690C212yesmaximal, complemented
21#26022634C211yesmaximal, characteristic, complemented
22C4×#15667970C211yesmaximal, characteristic, complemented
23C89×#2323C211yesmaximal, characteristic, complemented
24C22×#13083575C2211yescharacteristic
25C23×C4×D89C2211yescharacteristic
26#19152111C4116yescomplemented
27C2×#15667997C2212yes—
28C2×#15667988C2211yescharacteristic
29C2×#15667987C2211yescharacteristic
30C2×#15667986C2211yescharacteristic
31C2×#15667982C2212yes—
32C4×#13083575—28no—
33C2×Q8×Dic89C2211yescharacteristic, complemented
34C2×C4×D356C2212yes—
35C2×C4×D356C2211yescharacteristic, complemented
36C2×#15667974C2212yes—
37C2×#15667974C2212yes—
38C2×#15667974C2211yescharacteristic, complemented
39C2×#15667972C2212yes—
40C2×#15667971C2211yescharacteristic
41C2×#15667970C2211yescharacteristic
42C2×#15667970C2211yescharacteristic
43C2×#15667970C2211yescharacteristic
44C2×#15667970C2211yescharacteristic
45C2×#15667970C2211yescharacteristic
46C2×#15667970C2212yescomplemented
47C2×#15667969C2211yescharacteristic
48C2×#15667969C2211yescharacteristic
49C2×#15667968C2211yescharacteristic
50C2×#15667968C2211yescharacteristic
51#117×D89—28no—
52C2×C4⋊C4×D89C2211yescharacteristic
53C2×C4⋊C4×D89C2211yescharacteristic
54C2×C22⋊C4×D89C2211yescharacteristic
55C2×C22⋊C4×D89C2211yescharacteristic
56C2×C42×D89C2211yescharacteristic
57C2×C42×D89C2211yescharacteristic
58C2×C42×D89C2212yescomplemented
59#19151505C2211yescharacteristic, complemented
60#19151500C2212yes—
61#19151500C2211yescharacteristic, complemented
62#19151499C2212yes—
63#19151499C2211yescharacteristic, complemented
64#19151498C2212yes—
65#19151498C2212yes—
66#19151497C2212yescomplemented
67#19151497C2211yescharacteristic, complemented
68#19151496C2211yescharacteristic, complemented
69#19151495C2212yescomplemented
70#19151494C2211yescharacteristic, complemented
71#19151493C2212yescomplemented
72#19151491C2212yes—
73#19151491C2212yes—
74#19151490C2212yes—
75#19151490C2212yescomplemented
76#19151489C2212yes—
77#19151489C2212yescomplemented
78#19151488C2212yes—
79#19151488C2212yescomplemented
80#19151487C2212yes—
81#19151487C2212yescomplemented
82#19151484C2212yescomplemented
83#19151482C2212yescomplemented
84#19151480C2212yescomplemented
85#19151476C2212yes—
86#19151476C2212yes—
87#19151476C2212yes—
88#19151476C2212yes—
89#19151474C2212yes—
90#19151474C2212yes—
91#19151472C2212yes—
92#19151472C2212yescomplemented
93#19151472C2212yescomplemented
94#19151469C2212yes—
95#19151469C2212yescomplemented
96#19151469C2212yescomplemented
97#19151460C2212yes—
98#19151458C2211yescharacteristic
99#19151455C2211yescharacteristic
100#19151455C2211yescharacteristic
101#19151453C2212yes—
102C4⋊C4×Dic89C2211yescharacteristic, complemented
103C4⋊C4×Dic89C2211yescharacteristic, complemented
104C4⋊C4×Dic89C2212yescomplemented
105C4×C4⋊Dic89C2211yescharacteristic, complemented
106#19151449C2212yescomplemented
107C22⋊C4×Dic89C2212yes—
108C4×#13083551C2212yes—
109#19151445C2212yes—
110#19151445C2212yes—
111#19151445C2212yescomplemented
112#19151445C2212yescomplemented
113#19151443C2212yescomplemented
114C42×Dic89C2212yescomplemented
115C2×C22⋊Q8×C89C2211yescharacteristic
116C2×C4×Q8×C89C2211yescharacteristic, complemented
117C2×#117×C89C2211yescharacteristic
118#391×C89C2211yescharacteristic, complemented
119#389×C89C2212yescomplemented
120#389×C89C2211yescharacteristic, complemented
121#388×C89C2212yes—
122#388×C89C2212yes—
123#387×C89C2212yescomplemented
124#380×C89C2211yescharacteristic
125C4×C4⋊C4×C89C2211yescharacteristic, complemented
126C24×D89C2311yescharacteristic
127C2×#13083575—24no—
128C2×#13083575—24no—
129C2×#13083575C2×C418yes—
130C22×D356C2312yes—
131C22×D356C2311yescharacteristic
132C22×D356C2312yes—
133C22×C22⋊D89C2312yes—
134C23×Dic89C2311yescharacteristic
135C22×C4×D89—24no—
136C22×C4×D89—24no—
137C22×C4×D89C2×C418yescomplemented
138C22×C4×D89C2311yescharacteristic
139C22×C4×D89C2311yescharacteristic
140C22×C4×D89C2311yescharacteristic
141C22×C4×D89C2312yes—
142C22×C4×D89C2311yescharacteristic
143C22×C4×D89C2312yes—
144C22×C4×D89C2312yes—
145C22×C4×D89C2311yescharacteristic
146C22×C4×D89C2311yescharacteristic
147C22×C4×D89C2311yescharacteristic
148C22×C4×D89C2311yescharacteristic
149#15667997C2×C4116yescomplemented
150#15667988C2×C418yescomplemented
151#15667987C2×C418yescomplemented
152#15667986C2×C418yescomplemented
153#15667982C2×C4116yescomplemented
154Q8×Dic89—24no—
155C4×D356—28no—
156C4×D356—24no—
157#15667974—28no—
158#15667974—24no—
159#15667974C2×C4116yescomplemented
160#15667972C2×C4116yescomplemented
161#15667971—24no—
162#15667970—24no—
163#15667970—24no—
164#15667970—24no—
165#15667970—24no—
166#15667970—28no—
167#15667970C2×C418yescomplemented
168#15667969—24no—
169#15667969—24no—
170#15667968—24no—
171#15667968—24no—
172C2×C4⋊Dic89C2311yescharacteristic
173C2×C4⋊Dic89C2311yescharacteristic
174C2×C4⋊Dic89C2311yescharacteristic
175C2×C4⋊Dic89C2312yes—
176C2×C4⋊Dic89C2311yescharacteristic
177C2×C4⋊Dic89C2312yes—
178C2×C4⋊Dic89C2311yescharacteristic
179C2×#13083553C2311yescharacteristic
180C2×#13083553C2311yescharacteristic
181C2×#13083553C2311yescharacteristic
182C2×#13083553C2311yescharacteristic
183C2×#13083553C2312yes—
184C2×#13083553C2312yes—
185C2×#13083553C2312yes—
186C4⋊C4×D89—24no—
187C4⋊C4×D89—24no—
188C2×C22⋊Dic89C2311yescharacteristic
189C2×C22⋊Dic89C2311yescharacteristic
190C2×C22⋊Dic89C2312yes—
191C2×#13083551C2312yes—
192C2×#13083551C2312yes—
193C2×#13083551C2311yescharacteristic
194C2×#13083551C2311yescharacteristic
195C2×#13083551C2312yes—
196C2×#13083551C2311yescharacteristic
197C2×#13083551C2312yes—
198C2×#13083551C2311yescharacteristic
199C2×#13083551C2312yes—
200C2×#13083551C2312yes—
201C2×#13083551C2312yes—
202C2×#13083551C2312yes—
203C2×#13083551C2312yes—
204C2×#13083551C2312yes—
205C2×#13083551C2312yes—
206C2×#13083551C2312yes—
207C2×#13083551C2312yes—
208C2×#13083551C2312yes—
209C22⋊C4×D89—24no—
210C22⋊C4×D89—24no—
211C2×C4×Dic89C2312yes—
212C2×C4×Dic89C2312yes—
213C2×C4×Dic89C2311yescharacteristic
214C2×C4×Dic89C2311yescharacteristic
215C2×C4×Dic89C2312yes—
216C2×C4×Dic89C2311yescharacteristic
217C2×C4×Dic89C2312yes—
218C2×C4×Dic89C2312yes—
219C2×C4×Dic89C2312yes—
220C2×C4×Dic89C2312yes—
221C2×C4×Dic89C2311yescharacteristic
222C2×C4×Dic89C2311yescharacteristic
223C2×C4×Dic89C2311yescharacteristic
224C42×D89—24no—
225C42×D89—28no—
226C42×D89D418yescomplemented
227#15667919C2312yes—
228#15667919C2312yes—
229#15667919C2312yes—
230#15667919C2312yes—
231#15667919C2312yes—
232#15667919C2312yes—
233#15667919C2312yes—
234#15667919C2312yes—
235#15667919C2312yes—
236#15667919C2312yes—
237#15667919C2312yes—
238C22×Q8×C89C2311yescharacteristic
239C23×C4×C89C2311yescharacteristic
240C22⋊Q8×C89C2×C418yescomplemented
241C4×Q8×C89—24no—
242#117×C89—24no—
243C2×C4⋊C4×C89C2311yescharacteristic
244C2×C4⋊C4×C89C2311yescharacteristic
245C2×C4⋊C4×C89C2311yescharacteristic
246C2×C4⋊C4×C89C2312yes—
247C2×C4⋊C4×C89C2311yescharacteristic
248C2×C4⋊C4×C89C2312yes—
249C2×C4⋊C4×C89C2311yescharacteristic
250C2×C4⋊C4×C89C2312yes—
251C2×C22⋊C4×C89C2311yescharacteristic
252C2×C22⋊C4×C89C2311yescharacteristic
253C2×C22⋊C4×C89C2312yes—
254C2×C22⋊C4×C89C2312yes—
255C2×C42×C89C2312yes—
256C2×C42×C89C2311yescharacteristic
257C2×C42×C89C2312yes—
258C2×C42×C89C2311yescharacteristic
259#95×C89C2312yes—
260#95×C89C2312yes—
261#95×C89C2312yes—
262#95×C89C2312yes—
263#95×C89C2312yes—
264C23×D89—22no—
265C23×D89—22no—
266C23×D89—41no—
267C23×D89—41no—
268C23×D89—41no—
269C23×D89—41no—
270C23×D89C22×C414yes—
271C23×D89C2412yes—
272C23×D89C2411yescharacteristic
273C23×D89C2411yescharacteristic
274#13083575—232no—
275C2×D356—24no—
276C2×D356—24no—
277C2×D356—22no—
278C2×D356—22no—
279C2×D356—42no—
280C2×D356—42no—
281C2×D356C22×C418yes—
282C2×D356C22×C414yes—
283C2×D356C22×C418yes—
284C2×C22⋊D89—42no—
285C2×C22⋊D89—42no—
286C2×C22⋊D89C22×C418yes—
287C22×Dic89—22no—
288C22×Dic89—22no—
289C22×Dic89C22×C414yes—
290C22×Dic89C2411yescharacteristic
291C22×Dic89C2412yes—
292C22×Dic89C2411yescharacteristic
293C22×Dic89C2412yes—
294C22×Dic89C2411yescharacteristic
295C22×Dic89C2412yes—
296C22×Dic89C2411yescharacteristic
297C22×Dic89C2411yescharacteristic
298C22×Dic89C2411yescharacteristic
299C2×C4×D89—22no—
300C2×C4×D89—22no—
301C2×C4×D89—22no—
302C2×C4×D89—22no—
303C2×C4×D89—22no—
304C2×C4×D89—24no—
305C2×C4×D89—22no—
306C2×C4×D89—24no—
307C2×C4×D89—232no—
308C2×C4×D89—22no—
309C2×C4×D89—22no—
310C2×C4×D89—24no—
311C2×C4×D89—24no—
312C2×C4×D89—41no—
313C2×C4×D89—41no—
314C2×C4×D89—41no—
315C2×C4×D89—41no—
316C2×C4×D89—42no—
317C2×C4×D89—42no—
318C2×C4×D89—42no—
319C2×C4×D89—42no—
320C2×C4×D89—41no—
321C2×C4×D89—41no—
322C2×C4×D89—41no—
323C2×C4×D89—41no—
324C2×C4×D89C22×C418yes—
325C2×C4×D89C22×C414yes—
326C2×C4×D89C22×C414yes—
327C2×C4×D89C22×C414yes—
328C2×C4×D89C22×C414yes—
329C2×C4×D89C2×D414yes—
330C2×C4×D89C2×D414yes—
331C2×C4×D89C2×D414yes—
332C2×C4×D89#4114yes—
333C4⋊Dic89—22no—
334C4⋊Dic89—22no—
335C4⋊Dic89—22no—
336C4⋊Dic89—22no—
337C4⋊Dic89—24no—
338C4⋊Dic89—42no—
339C4⋊Dic89C22×C414yes—
340#13083553—22no—
341#13083553—22no—
342#13083553—22no—
343#13083553—22no—
344#13083553—42no—
345#13083553—42no—
346#13083553C22×C418yes—
347C22⋊Dic89—22no—
348C22⋊Dic89—22no—
349C22⋊Dic89—42no—
350#13083551—24no—
351#13083551—24no—
352#13083551—22no—
353#13083551—22no—
354#13083551—24no—
355#13083551—22no—
356#13083551—22no—
357#13083551—24no—
358#13083551—42no—
359#13083551—42no—
360#13083551—42no—
361#13083551—42no—
362#13083551—42no—
363#13083551—42no—
364#13083551C22×C418yes—
365#13083551C22×C418yes—
366#13083551C22×C418yes—
367#13083551C22×C418yes—
368C4×Dic89—22no—
369C4×Dic89—22no—
370C4×Dic89—22no—
371C4×Dic89—24no—
372C4×Dic89—24no—
373C4×Dic89—24no—
374C4×Dic89—42no—
375C4×Dic89—42no—
376C4×Dic89—42no—
377C4×Dic89C22×C418yes—
378C4×Dic89C2×D414yes—
379C4×Dic89C2×D414yes—
380C4×Dic89C2×D414yes—
381C24×C89C2411yescharacteristic
382C2×Q8×C89—22no—
383C2×Q8×C89—22no—
384C2×Q8×C89C22×C414yes—
385C22×C4×C89—22no—
386C22×C4×C89—22no—
387C22×C4×C89C22×C414yes—
388C22×C4×C89C2411yescharacteristic
389C22×C4×C89C2411yescharacteristic
390C22×C4×C89C2412yes—
391C22×C4×C89C2412yes—
392C22×C4×C89C2411yescharacteristic
393C22×C4×C89C2412yes—
394C22×C4×C89C2412yes—
395C22×C4×C89C2411yescharacteristic
396C22×C4×C89C2411yescharacteristic
397C22×C4×C89C2411yescharacteristic
398C4⋊C4×C89—24no—
399C4⋊C4×C89—22no—
400C4⋊C4×C89—22no—
401C4⋊C4×C89—22no—
402C4⋊C4×C89—22no—
403C4⋊C4×C89—42no—
404C4⋊C4×C89C22×C414yes—
405C4⋊C4×C89C22×C418yes—
406C22⋊C4×C89—22no—
407C22⋊C4×C89—22no—
408C22⋊C4×C89—42no—
409C22⋊C4×C89C22×C418yes—
410C42×C89—22no—
411C42×C89—24no—
412C42×C89—42no—
413C42×C89C2×D414yes—
414C23×C89—21no—
415C23×C89—21no—
416C23×C89—21no—
417C23×C89—21no—
418C23×C89—21no—
419C23×C89—21no—
420C23×C89C23×C412yes—
421C23×C89C2511yescharacteristic
422C22×D89—21no—
423C22×D89—21no—
424C22×D89—21no—
425C22×D89—21no—
426C22×D89—21no—
427C22×D89—22no—
428C22×D89—21no—
429C22×D89—22no—
430C22×D89—21no—
431C22×D89—21no—
432C22×D89—22no—
433C22×D89—22no—
434C22×D89—22no—
435C22×D89—22no—
436C22×D89—21no—
437C22×D89—21no—
438C22×D89—28no—
439C22×D89—44no—
440C22×D89—44no—
441C22×D89—44no—
442C22×D89—44no—
443C22×D89—44no—
444C22×D89—44no—
445C22×D89C23×C412yes—
446C22×D89C23×C414yes—
447C22×D89C23×C412yes—
448C22×D89C22×D412yes—
449C22×D89C2×#4112yes—
450Q8×C89—28no—
451C2×C4×C89—22no—
452C2×C4×C89—21no—
453C2×C4×C89—21no—
454C2×C4×C89—22no—
455C2×C4×C89—21no—
456C2×C4×C89—22no—
457C2×C4×C89—21no—
458C2×C4×C89—22no—
459C2×C4×C89—21no—
460C2×C4×C89—21no—
461C2×C4×C89—28no—
462C2×C4×C89—21no—
463C2×C4×C89—21no—
464C2×C4×C89—22no—
465C2×C4×C89—22no—
466C2×C4×C89—22no—
467C2×C4×C89—22no—
468C2×C4×C89—21no—
469C2×C4×C89—22no—
470C2×C4×C89—21no—
471C2×C4×C89—21no—
472C2×C4×C89—22no—
473C2×C4×C89—21no—
474C2×C4×C89C23×C414yes—
475C2×C4×C89C23×C414yes—
476C2×C4×C89C23×C412yes—
477C2×C4×C89C23×C412yes—
478C2×C4×C89C22×D412yes—
479C2×C4×C89C22×D412yes—
480C2×C4×C89C22×D412yes—
481C2×C4×C89C2×#4112yes—
482C22⋊D89—48no—
483C2×Dic89—21no—
484C2×Dic89—21no—
485C2×Dic89—21no—
486C2×Dic89—21no—
487C2×Dic89—22no—
488C2×Dic89—22no—
489C2×Dic89—21no—
490C2×Dic89—21no—
491C2×Dic89—28no—
492C2×Dic89—22no—
493C2×Dic89—21no—
494C2×Dic89—21no—
495C2×Dic89—22no—
496C2×Dic89—22no—
497C2×Dic89—22no—
498C2×Dic89—21no—
499C2×Dic89—21no—
500C2×Dic89—22no—
501C2×Dic89—22no—
502C2×Dic89—21no—
503C2×Dic89—21no—
504C2×Dic89C23×C414yes—
505C2×Dic89C23×C412yes—
506C2×Dic89C23×C412yes—
507C2×Dic89C22×D412yes—
508C2×Dic89C22×D412yes—
509C2×Dic89C22×D412yes—
510C2×Dic89C2×#4112yes—
511D356—216no—
512D356—28no—
513D356—48no—
514C4×D89—28no—
515C4×D89—28no—
516C4×D89—28no—
517C4×D89—216no—
518C4×D89—44no—
519C4×D89—44no—
520C4×D89—48no—
521C4×D89—48no—
522C4×D89—44no—
523C4×D89—44no—
524C4×D89C4×D4116yes—
525C22×C89—22no—
526C22×C89—22no—
527C22×C89—22no—
528C22×C89—41no—
529C22×C89—41no—
530C22×C89—41no—
531C22×C89—41no—
532C22×C89C24×C411yescharacteristic
533C22×C89C23×D411yescharacteristic
534C22×C89C22×#4111yescharacteristic
535C22×C89#58511yescharacteristic
536C22×C89#58511yescharacteristic
537C22×C89#58511yescharacteristic
538C22×C89#58511yescharacteristic
539C2×D89—22no—
540C2×D89—22no—
541C2×D89—22no—
542C2×D89—22no—
543C2×D89—22no—
544C2×D89—22no—
545C2×D89—22no—
546C2×D89—24no—
547C2×D89—22no—
548C2×D89—24no—
549C2×D89—24no—
550C2×D89—22no—
551C2×D89—416no—
552C2×D89—42no—
553C2×D89—42no—
554C2×D89—41no—
555C2×D89—41no—
556C2×D89—42no—
557C2×D89—42no—
558C2×D89—41no—
559C2×D89—41no—
560C2×D89C2×C4×D414yes—
561C4×C89—22no—
562C4×C89—24no—
563C4×C89—24no—
564C4×C89—22no—
565C4×C89—22no—
566C4×C89—42no—
567C4×C89—41no—
568C4×C89—41no—
569C4×C89—42no—
570C4×C89C2×C4×D414yes—
571Dic89—22no—
572Dic89—24no—
573Dic89—22no—
574Dic89—22no—
575Dic89—41no—
576Dic89—42no—
577Dic89—41no—
578Dic89—42no—
579Dic89C2×C4×D414yes—
580#34065—891nomaximal, Sylow
581C2×C89—42no—
582C2×C89C22×C4×D411yescharacteristic
583C2×C89#342811yescharacteristic
584C2×C89#342811yescharacteristic
585C2×C89#344911yescharacteristic
586C2×C89#344911yescharacteristic
587C2×C89#345511yescharacteristic
588C2×C89#345511yescharacteristic
589D89—24no—
590D89—44no—
591D89—42no—
592C2×#525—891no—
593C2×C4×#41—891no—
594C22×#117—891no—
595#2324—891no—
596#2324—891no—
597#2324—891no—
598#2324—891no—
599#2323—891no—
600#2323—891no—
601#2323—891no—
602#2323D8911yescharacteristic, complemented
603#2322—892no—
604#2322—892no—
605#2321—892no—
606#2321—892no—
607#2297—891no—
608#2296—891no—
609#2293—892no—
610#2293—892no—
611#2290—892no—
612#2290—892no—
613#2280—891no—
614C4×#117—891no—
615C89#3406511yescharacteristic, complemented, Sylow
616C22×#41—891no—
617C24×C4—891no—
618#525—8916no—
619C2×#123—892no—
620C2×C22⋊Q8—891no—
621C2×C22⋊Q8C2×D8911yescharacteristic
622C2×#121—891no—
623C2×#121—891no—
624C2×#120—892no—
625C4×#41—1788no—
626C2×C4×Q8—891no—
627C2×C4×Q8C2×D8911yescharacteristic, complemented
628C2×C4×D4—892no—
629C2×C4×D4—892no—
630C2×C4×D4—891no—
631C2×C4×D4—892no—
632C2×C4×D4—892no—
633C2×C4×D4—891no—
634C2×#117—891no—
635C2×#117—891no—
636C2×#117—891no—
637C2×#117—891no—
638C2×#117—891no—
639C2×#117—892no—
640C2×#117—891no—
641C2×#117—891no—
642C2×#117—891no—
643C2×#117—891no—
644C2×#117—891no—
645C2×#117—1788no—
646C2×#117C2×D8911yescharacteristic
647C22×C4⋊C4—891no—
648C22×C4⋊C4—891no—
649C22×C22⋊C4—891no—
650C22×C22⋊C4—891no—
651C22×C42—891no—
652C22×C42—891no—
653C22×C42—892no—
654#391—891no—
655#391C2×D8911yescharacteristic, complemented
656#390—892no—
657#390—891no—
658#390—892no—
659#390—892no—
660#390—892no—
661#390—891no—
662#389—892no—
663#389—892no—
664#389—891no—
665#389—891no—
666#389—891no—
667#389—892no—
668#389C2×D8912yescomplemented
669#389C2×D8911yescharacteristic, complemented
670#388—892no—
671#388—892no—
672#388—892no—
673#388—892no—
674#388—892no—
675#388—892no—
676#388—892no—
677#388—892no—
678#388—892no—
679#388—892no—
680#388C2×D8912yes—
681#388C2×D8912yes—
682#387—892no—
683#387—892no—
684#387—892no—
685#387C2×D8912yescomplemented
686#386—892no—
687#386—892no—
688#386—892no—
689#386—892no—
690#386—892no—
691#386—892no—
692#385—892no—
693#385—892no—
694#385—892no—
695#385—892no—
696#385—892no—
697#385—892no—
698#381—892no—
699#380—891no—
700#380—891no—
701#380—891no—
702#380C2×D8911yescharacteristic
703#379—892no—
704C4×C4⋊C4—891no—
705C4×C4⋊C4—891no—
706C4×C4⋊C4—892no—
707C4×C4⋊C4—891no—
708C4×C4⋊C4—892no—
709C4×C4⋊C4C2×D8911yescharacteristic, complemented
710C4×C22⋊C4—892no—
711C4×C22⋊C4—892no—
712C4×C22⋊C4—892no—
713C4×C22⋊C4—892no—
714C4×C22⋊C4—892no—
715C4×C22⋊C4—892no—
716#376—892no—
717C43—892no—
718C25—891no—
719C2×#41—898no—
720C2×#41—1784no—
721C2×#41—1784no—
722C22×Q8C22×D8911yescharacteristic
723C22×D4—892no—
724C22×D4—892no—
725C22×D4—892no—
726C22×D4—891no—
727C23×C4—891no—
728C23×C4—891no—
729C23×C4—891no—
730C23×C4—891no—
731C23×C4—898no—
732C23×C4—891no—
733C23×C4—891no—
734C23×C4—891no—
735C23×C4—892no—
736C23×C4—891no—
737C23×C4—891no—
738C23×C4—892no—
739C23×C4—892no—
740C23×C4—1784no—
741C23×C4—1784no—
742C23×C4C22×D8911yescharacteristic
743#123—8916no—
744C22⋊Q8—898no—
745C22⋊Q8C4×D8918yescomplemented
746#121—898no—
747#121—898no—
748#120—8916no—
749C4×Q8—24no—
750C4×Q8—1784no—
751C4×D4—8916no—
752C4×D4—8916no—
753C4×D4—1788no—
754C4×D4—1784no—
755C4×D4—1788no—
756C4×D4—1784no—
757#117—24no—
758#117—898no—
759#117—1784no—
760#117—1784no—
761#117—1784no—
762#117—1784no—
763#117—1784no—
764#117—1788no—
765#117—1784no—
766#117—1784no—
767#117—1784no—
768#117—1784no—
769C2×C4⋊C4—891no—
770C2×C4⋊C4—892no—
771C2×C4⋊C4—892no—
772C2×C4⋊C4—892no—
773C2×C4⋊C4—892no—
774C2×C4⋊C4—891no—
775C2×C4⋊C4—891no—
776C2×C4⋊C4—891no—
777C2×C4⋊C4—891no—
778C2×C4⋊C4—891no—
779C2×C4⋊C4—891no—
780C2×C4⋊C4—891no—
781C2×C4⋊C4—892no—
782C2×C4⋊C4—891no—
783C2×C4⋊C4—1784no—
784C2×C4⋊C4—1784no—
785C2×C4⋊C4C22×D8911yescharacteristic
786C2×C4⋊C4C22×D8911yescharacteristic
787C2×C4⋊C4C22×D8911yescharacteristic
788C2×C4⋊C4C22×D8912yes—
789C2×C4⋊C4C22×D8911yescharacteristic
790C2×C4⋊C4C22×D8912yes—
791C2×C4⋊C4C22×D8911yescharacteristic
792C2×C4⋊C4C22×D8912yes—
793C2×C22⋊C4—892no—
794C2×C22⋊C4—892no—
795C2×C22⋊C4—892no—
796C2×C22⋊C4—892no—
797C2×C22⋊C4—892no—
798C2×C22⋊C4—892no—
799C2×C22⋊C4—892no—
800C2×C22⋊C4—892no—
801C2×C22⋊C4—892no—
802C2×C22⋊C4—892no—
803C2×C22⋊C4—892no—
804C2×C22⋊C4—891no—
805C2×C22⋊C4—891no—
806C2×C22⋊C4—891no—
807C2×C22⋊C4—891no—
808C2×C22⋊C4—891no—
809C2×C22⋊C4—891no—
810C2×C22⋊C4—892no—
811C2×C22⋊C4—892no—
812C2×C22⋊C4—892no—
813C2×C22⋊C4—892no—
814C2×C22⋊C4—1784no—
815C2×C22⋊C4—1784no—
816C2×C22⋊C4C22×D8911yescharacteristic
817C2×C22⋊C4C22×D8911yescharacteristic
818C2×C22⋊C4C22×D8912yes—
819C2×C22⋊C4C22×D8912yes—
820C2×C42—891no—
821C2×C42—891no—
822C2×C42—891no—
823C2×C42—892no—
824C2×C42—898no—
825C2×C42—892no—
826C2×C42—892no—
827C2×C42—892no—
828C2×C42—891no—
829C2×C42—892no—
830C2×C42—891no—
831C2×C42—891no—
832C2×C42—892no—
833C2×C42—892no—
834C2×C42—1788no—
835C2×C42—1784no—
836C2×C42C22×D8911yescharacteristic
837C2×C42C22×D8912yes—
838C2×C42C22×D8912yes—
839C2×C42C22×D8911yescharacteristic
840#95—892no—
841#95—892no—
842#95—892no—
843#95—892no—
844#95—892no—
845#95—892no—
846#95—892no—
847#95—892no—
848#95—892no—
849#95—892no—
850#95—892no—
851#95C22×D8912yes—
852#95C22×D8912yes—
853#95C22×D8912yes—
854#95C22×D8912yes—
855#95C22×D8912yes—
856C24—891no—
857C24—894no—
858C24—891no—
859C24—892no—
860C24—3561no—
861C24—3561no—
862C24—3561no—
863C24—3561no—
864C24—1782no—
865C24—1782no—
866C24C23×D8911yescharacteristic
867#41—17832no—
868C2×Q8—22no—
869C2×Q8—22no—
870C2×Q8C2×C4×D8914yes—
871C2×D4—898no—
872C2×D4—898no—
873C2×D4—898no—
874C2×D4—894no—
875C2×D4—3562no—
876C2×D4—3562no—
877C2×D4—3562no—
878C2×D4—3562no—
879C2×D4—1784no—
880C2×D4—1784no—
881C2×D4—1782no—
882C2×D4—1782no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—891no—
886C22×C4—894no—
887C22×C4—894no—
888C22×C4—894no—
889C22×C4—894no—
890C22×C4—891no—
891C22×C4—892no—
892C22×C4—891no—
893C22×C4—891no—
894C22×C4—894no—
895C22×C4—894no—
896C22×C4—894no—
897C22×C4—898no—
898C22×C4—894no—
899C22×C4—894no—
900C22×C4—892no—
901C22×C4—891no—
902C22×C4—891no—
903C22×C4—892no—
904C22×C4—3561no—
905C22×C4—3561no—
906C22×C4—3562no—
907C22×C4—3562no—
908C22×C4—3561no—
909C22×C4—3561no—
910C22×C4—3562no—
911C22×C4—3561no—
912C22×C4—3561no—
913C22×C4—3561no—
914C22×C4—3562no—
915C22×C4—3561no—
916C22×C4—1784no—
917C22×C4—1784no—
918C22×C4—1782no—
919C22×C4—1782no—
920C22×C4—17832no—
921C22×C4—1784no—
922C22×C4—1782no—
923C22×C4—1782no—
924C22×C4—1782no—
925C22×C4—1782no—
926C22×C4—1782no—
927C22×C4—1782no—
928C22×C4—1784no—
929C22×C4—1782no—
930C22×C4—1782no—
931C22×C4C2×C4×D8914yes—
932C22×C4C23×D8912yes—
933C22×C4C23×D8911yescharacteristic
934C22×C4C23×D8912yes—
935C22×C4C23×D8911yescharacteristic
936C22×C4C23×D8912yes—
937C22×C4C23×D8912yes—
938C22×C4C23×D8911yescharacteristic
939C22×C4C23×D8911yescharacteristic
940C22×C4C23×D8911yescharacteristic
941C22×C4C23×D8911yescharacteristic
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—24no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—42no—
948C4⋊C4—894no—
949C4⋊C4—898no—
950C4⋊C4—3562no—
951C4⋊C4—3562no—
952C4⋊C4—3562no—
953C4⋊C4—1782no—
954C4⋊C4—1782no—
955C4⋊C4—1782no—
956C4⋊C4—1782no—
957C4⋊C4—1784no—
958C4⋊C4—1782no—
959C4⋊C4—1782no—
960C4⋊C4—1782no—
961C4⋊C4—1782no—
962C4⋊C4C2×C4×D8914yes—
963C4⋊C4C2×C4×D8918yes—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—42no—
967C22⋊C4—898no—
968C22⋊C4—898no—
969C22⋊C4—898no—
970C22⋊C4—898no—
971C22⋊C4—3562no—
972C22⋊C4—3562no—
973C22⋊C4—3562no—
974C22⋊C4—3562no—
975C22⋊C4—3562no—
976C22⋊C4—3562no—
977C22⋊C4—3562no—
978C22⋊C4—1782no—
979C22⋊C4—1782no—
980C22⋊C4—1784no—
981C22⋊C4—1784no—
982C22⋊C4—1784no—
983C22⋊C4—1782no—
984C22⋊C4—1782no—
985C22⋊C4—1782no—
986C22⋊C4—1782no—
987C22⋊C4—1784no—
988C22⋊C4C2×C4×D8918yes—
989C42—22no—
990C42—24no—
991C42—42no—
992C42—898no—
993C42—894no—
994C42—894no—
995C42—894no—
996C42—3562no—
997C42—3562no—
998C42—3562no—
999C42—1782no—
1000C42—1782no—
1001C42—1784no—
1002C42—1784no—
1003C42—1784no—
1004C42—1782no—
1005C42D4×D8914yes—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—892no—
1013C23—892no—
1014C23—892no—
1015C23—892no—
1016C23—894no—
1017C23—3564no—
1018C23—3564no—
1019C23—3564no—
1020C23—3564no—
1021C23—3564no—
1022C23—3564no—
1023C23—1788no—
1024C23—1781no—
1025C23—1782no—
1026C23—1781no—
1027C23—1782no—
1028C23—1782no—
1029C23—1781no—
1030C23—1781no—
1031C23—1781no—
1032C23—1782no—
1033C23—1782no—
1034C23—1782no—
1035C23—1781no—
1036C23—1781no—
1037C23—1781no—
1038C23—1781no—
1039C23—1781no—
1040C23C22×C4×D8912yes—
1041C23C24×D8911yescharacteristic
1042Q8—28no—
1043D4—3568no—
1044D4—3568no—
1045D4—17816no—
1046D4—1788no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—28no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—892no—
1071C2×C4—892no—
1072C2×C4—892no—
1073C2×C4—8916no—
1074C2×C4—894no—
1075C2×C4—892no—
1076C2×C4—892no—
1077C2×C4—892no—
1078C2×C4—3568no—
1079C2×C4—3564no—
1080C2×C4—3564no—
1081C2×C4—3564no—
1082C2×C4—3564no—
1083C2×C4—3568no—
1084C2×C4—1788no—
1085C2×C4—17816no—
1086C2×C4—1788no—
1087C2×C4—1788no—
1088C2×C4—1781no—
1089C2×C4—1782no—
1090C2×C4—1781no—
1091C2×C4—1782no—
1092C2×C4—1781no—
1093C2×C4—1782no—
1094C2×C4—1782no—
1095C2×C4—1781no—
1096C2×C4—1782no—
1097C2×C4—1782no—
1098C2×C4—1781no—
1099C2×C4—1781no—
1100C2×C4—1781no—
1101C2×C4—1781no—
1102C2×C4—1781no—
1103C2×C4—1781no—
1104C2×C4—1781no—
1105C2×C4—1782no—
1106C2×C4—1782no—
1107C2×C4—1781no—
1108C2×C4—1788no—
1109C2×C4C22×C4×D8914yes—
1110C2×C4C22×C4×D8912yes—
1111C2×C4C22×C4×D8914yes—
1112C2×C4C22×C4×D8912yes—
1113C2×C4C2×D4×D8912yes—
1114C2×C4C2×D4×D8912yes—
1115C2×C4C2×D4×D8912yes—
1116C2×C4#41×D8912yes—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—894no—
1125C22—35616no—
1126C22—3562no—
1127C22—3561no—
1128C22—3562no—
1129C22—3561no—
1130C22—3561no—
1131C22—3562no—
1132C22—3561no—
1133C22—3562no—
1134C22—1782no—
1135C22—1784no—
1136C22—1782no—
1137C22—1784no—
1138C22—1784no—
1139C22—1782no—
1140C22—1782no—
1141C22—1782no—
1142C22—1782no—
1143C22—1782no—
1144C22—1782no—
1145C22—1782no—
1146C22C23×C4×D8911yescharacteristic
1147C22C22×D4×D8911yescharacteristic
1148C22C2×#41×D8911yescharacteristic
1149C22#1915243311yescharacteristic
1150C22#1915243511yescharacteristic
1151C22#1915243511yescharacteristic
1152C22#1915243511yescharacteristic
1153C4—22no—
1154C4—24no—
1155C4—24no—
1156C4—22no—
1157C4—22no—
1158C4—41no—
1159C4—42no—
1160C4—41no—
1161C4—42no—
1162C4—894no—
1163C4—3561no—
1164C4—3562no—
1165C4—3561no—
1166C4—3562no—
1167C4—1782no—
1168C4—1784no—
1169C4—1782no—
1170C4—1782no—
1171C4C4×D4×D8914yes—
1172C2—42no—
1173C2—3562no—
1174C2—3564no—
1175C2—1784no—
1176C2C2×C4×D4×D8911yescharacteristic
1177C2#2603345211yescharacteristic
1178C2#2603345411yescharacteristic
1179C2#2603358011yescharacteristic
1180C2#2603358411yescharacteristic
1181C2#2603363911yescharacteristic
1182C2#2603364311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC89×#2323C2
socle, cosocleC23×C89C25
prime radicalC2×#19152111C2
hypercenter#2323D89
hypocenterC89#34065
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×C4×#13083575C2semidirect
3. C2×#117×D89C2semidirect
4. #26022946C2semidirect
5. #26022945C2semidirect
6. #26022943C2semidirect
7. #26022941C2semidirect
8. #26022937C2semidirect
9. #26022936C2semidirect
10. #26022928C2semidirect
11. #26022925C2semidirect
12. #26022916C2semidirect
13. #26022914C2semidirect
14. #26022905C2semidirect
15. #26022741C2semidirect
16. #26022733C2semidirect
17. #26022712C2semidirect
18. #26022710C2semidirect
19. #26022694C2semidirect
20. #26022690C2semidirect
21. #26022634C2semidirect
22. C4×#15667970C2semidirect
23. C89×#2323C2semidirect
26. #19152111C4semidirect
33. C2×Q8×Dic89C22semidirect
35. C2×C4×D356C22semidirect
38. C2×#15667974C22semidirect
46. C2×#15667970C22semidirect
58. C2×C42×D89C22semidirect
59. #19151505C22semidirect
61. #19151500C22semidirect
63. #19151499C22semidirect
66. #19151497C22semidirect
67. #19151497C22semidirect
68. #19151496C22semidirect
69. #19151495C22semidirect
70. #19151494C22semidirect
71. #19151493C22semidirect
75. #19151490C22semidirect
77. #19151489C22semidirect
79. #19151488C22semidirect
81. #19151487C22semidirect
82. #19151484C22semidirect
83. #19151482C22semidirect
84. #19151480C22semidirect
92. #19151472C22semidirect
93. #19151472C22semidirect
95. #19151469C22semidirect
96. #19151469C22semidirect
102. C4⋊C4×Dic89C22semidirect
103. C4⋊C4×Dic89C22semidirect
104. C4⋊C4×Dic89C22semidirect
105. C4×C4⋊Dic89C22semidirect
106. #19151449C22semidirect
111. #19151445C22semidirect
112. #19151445C22semidirect
113. #19151443C22semidirect
114. C42×Dic89C22semidirect
116. C2×C4×Q8×C89C22semidirect
118. #391×C89C22semidirect
119. #389×C89C22semidirect
120. #389×C89C22semidirect
123. #387×C89C22semidirect
125. C4×C4⋊C4×C89C22semidirect
137. C22×C4×D89C2×C4semidirect
149. #15667997C2×C4semidirect
150. #15667988C2×C4semidirect
151. #15667987C2×C4semidirect
152. #15667986C2×C4semidirect
153. #15667982C2×C4semidirect
159. #15667974C2×C4semidirect
160. #15667972C2×C4semidirect
167. #15667970C2×C4semidirect
226. C42×D89D4semidirect
240. C22⋊Q8×C89C2×C4semidirect
602. #2323D89semidirect
615. C89#34065semidirect
627. C2×C4×Q8C2×D89semidirect
655. #391C2×D89semidirect
668. #389C2×D89semidirect
669. #389C2×D89semidirect
685. #387C2×D89semidirect
709. C4×C4⋊C4C2×D89semidirect
745. C22⋊Q8C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#191521112
C2×C4×#130835752
C2×#117×D892
#260229462
#260229452
#260229432
#260229412
#260229372
#260229362
#260229282
#260229252
#260229162
#260229142
#260229052
#260227412
#260227332
#260227122
#260227102
#260226942
#260226902
#260226342
C4×#156679702
C89×#23232
#3406589