Finite Group Databasebeta

← #36717689

Subgroups — #36717689

Order 22784.

1990 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19152129C211yesmaximal, characteristic
2#26023402C212yesmaximal, complemented
3#26023395C212yesmaximal, complemented
4#26023374C212yesmaximal, complemented
5#26023370C212yesmaximal, complemented
6#26023224C212yesmaximal, complemented
7#26023190C212yesmaximal, complemented
8#26023134C212yesmaximal, complemented
9#26023106C212yesmaximal, complemented
10#26023061C212yesmaximal, complemented
11#26023052C212yesmaximal, complemented
12#26023019C211yesmaximal, characteristic
13#26023008C211yesmaximal, characteristic, complemented
14#26023005C211yesmaximal, characteristic, complemented
15#26022901C212yesmaximal, complemented
16#26022878C212yesmaximal, complemented
17#26022646C211yesmaximal, characteristic, complemented
18#26022643C211yesmaximal, characteristic, complemented
19C89×#2333C211yesmaximal, characteristic
20#19152129C4116yescomplemented
21C2×#15668005C2212yes—
22C2×#15668003C2211yescharacteristic
23C2×#15667999C2211yescharacteristic
24C2×#15667993C2212yes—
25C2×#15667991C2211yescharacteristic
26C2×#15667977C2211yescharacteristic
27C2×D4×Dic89C2211yescharacteristic
28C2×D4×Dic89C2212yes—
29C2×#15667968C2212yes—
30C22×C4×Dic89C2211yescharacteristic
31#19151502C2212yes—
32#19151502C2212yes—
33#19151501C2212yes—
34#19151495C2212yes—
35#19151495C2212yes—
36#19151493C2212yes—
37#19151493C2212yes—
38#19151492C2212yes—
39#19151492C2212yes—
40#19151492C2212yes—
41#19151492C2212yes—
42#19151492C2212yes—
43#19151491C2212yes—
44#19151486C2212yes—
45#19151486C2212yes—
46#19151486C2212yes—
47#19151486C2212yes—
48#19151486C2212yes—
49#19151484C2212yes—
50#19151483C2212yes—
51#19151483C2212yes—
52#19151482C2212yes—
53#19151482C2212yes—
54#19151482C2212yes—
55#19151481C2212yes—
56#19151481C2212yes—
57#19151480C2212yes—
58#19151480C2212yes—
59#19151480C2212yes—
60#19151478C2212yes—
61#19151478C2212yes—
62#19151471C2212yes—
63#19151471C2212yes—
64#19151470C2212yes—
65#19151470C2212yes—
66#19151465C2212yes—
67#19151465C2212yes—
68#19151465C2212yes—
69#19151463C2212yes—
70#19151462C2212yes—
71#19151462C2212yes—
72#19151461C2211yescharacteristic
73#19151459C2212yes—
74#19151459C2212yes—
75#19151456C2212yes—
76#19151456C2211yescharacteristic
77#19151456C2212yes—
78#19151456C2211yescharacteristic
79C4⋊C4×Dic89C2212yes—
80C4×#13083553C2212yes—
81C4×#13083553C2212yes—
82C4×#13083553C2211yescharacteristic
83C4×#13083553C2211yescharacteristic
84C4×C4⋊Dic89C2212yes—
85#19151449C2212yes—
86#19151449C2212yes—
87C22⋊C4×Dic89C2211yescharacteristic
88C22⋊C4×Dic89C2212yes—
89C22⋊C4×Dic89C2211yescharacteristic
90C22⋊C4×Dic89C2212yes—
91C22⋊C4×Dic89C2212yes—
92C4×C22⋊Dic89C2212yes—
93C4×C22⋊Dic89C2211yescharacteristic
94#19151444C2211yescharacteristic
95#19151444C2211yescharacteristic
96#19151443C2212yes—
97#19151443C2212yes—
98C2×#15667919C2212yes—
99C2×#121×C89C2211yescharacteristic
100#390×C89C2212yes—
101#388×C89C2212yes—
102#387×C89C2212yes—
103#386×C89C2212yes—
104#386×C89C2212yes—
105#381×C89C2211yescharacteristic
106C4×C22⋊C4×C89C2211yescharacteristic
107C4×C22⋊C4×C89C2212yes—
108C22×Dic178C2311yescharacteristic
109C23×Dic89C2312yes—
110C23×Dic89C2312yes—
111C23×Dic89C2311yescharacteristic
112C23×Dic89C2311yescharacteristic
113#15668005C2×C4116yescomplemented
114#15668003C2×C418yescomplemented
115#15667999C2×C418yes—
116#15667993C2×C4116yescomplemented
117#15667991C2×C418yescomplemented
118#15667977C2×C418yescomplemented
119D4×Dic89C2×C418yes—
120D4×Dic89C2×C4116yescomplemented
121#15667968C2×C4116yescomplemented
122C2×C4⋊Dic89C2312yes—
123C2×C4⋊Dic89C2312yes—
124C2×C4⋊Dic89C2311yescharacteristic
125C2×#13083553C2312yes—
126C2×#13083553C2312yes—
127C2×#13083553C2312yes—
128C2×#13083553C2312yes—
129C2×#13083553C2312yes—
130C2×#13083553C2312yes—
131C2×#13083553C2312yes—
132C2×#13083553C2312yes—
133C2×#13083553C2312yes—
134C2×#13083553C2312yes—
135C2×#13083553C2312yes—
136C2×C22⋊Dic89C2312yes—
137C2×C22⋊Dic89C2312yes—
138C2×C22⋊Dic89C2311yescharacteristic
139C2×C22⋊Dic89C2311yescharacteristic
140C2×C22⋊Dic89C2312yes—
141C2×C22⋊Dic89C2312yes—
142C2×C22⋊Dic89C2312yes—
143C2×C22⋊Dic89C2312yes—
144C2×C22⋊Dic89C2312yes—
145C2×C22⋊Dic89C2312yes—
146C2×C4×Dic89C2×C418yescomplemented
147C2×C4×Dic89C2312yes—
148C2×C4×Dic89C2312yes—
149C2×C4×Dic89C2312yes—
150C2×C4×Dic89C2312yes—
151C2×C4×Dic89C2311yescharacteristic
152C2×C4×Dic89C2311yescharacteristic
153C2×C4×Dic89C2312yes—
154C2×C4×Dic89C2312yes—
155C2×C4×Dic89C2312yes—
156C2×C4×Dic89C2311yescharacteristic
157C2×C4×Dic89C2312yes—
158C2×C4×Dic89C2311yescharacteristic
159C2×C4×Dic89C2311yescharacteristic
160C2×C4×Dic89C2311yescharacteristic
161#15667919C2312yes—
162#15667919C2312yes—
163#15667919C2312yes—
164#15667919C2312yes—
165#15667919C2312yes—
166#15667919C2312yes—
167#15667919C2312yes—
168#15667919C2312yes—
169#15667919C2312yes—
170#15667919C2312yes—
171#15667919C2312yes—
172#15667919C2312yes—
173#15667919C2312yes—
174#15667919C2312yes—
175#15667919C2312yes—
176#15667919C2312yes—
177#15667919C2312yes—
178#15667919C2312yes—
179#15667919C2312yes—
180#15667919C2312yes—
181#15667919C2312yes—
182#15667919C2312yes—
183#15667919C2312yes—
184C22×D4×C89C2311yescharacteristic
185C22×D4×C89C2312yes—
186C23×C4×C89C2312yes—
187C23×C4×C89C2311yescharacteristic
188#121×C89C2×C418yes—
189C2×C4⋊C4×C89C2312yes—
190C2×C4⋊C4×C89C2311yescharacteristic
191C2×C22⋊C4×C89C2312yes—
192C2×C22⋊C4×C89C2312yes—
193C2×C22⋊C4×C89C2311yescharacteristic
194C2×C22⋊C4×C89C2311yescharacteristic
195C2×C22⋊C4×C89C2312yes—
196C2×C22⋊C4×C89C2312yes—
197C2×C22⋊C4×C89C2312yes—
198C2×C42×C89C2311yescharacteristic
199C2×C42×C89C2312yes—
200C2×C42×C89C2311yescharacteristic
201#95×C89C2312yes—
202#95×C89C2312yes—
203#95×C89C2312yes—
204#95×C89C2312yes—
205#95×C89C2312yes—
206C2×Dic178—41no—
207C2×Dic178—41no—
208C2×Dic178C22×C414yes—
209C22×Dic89—42no—
210C22×Dic89—42no—
211C22×Dic89—42no—
212C22×Dic89—42no—
213C22×Dic89—42no—
214C22×Dic89—42no—
215C22×Dic89—42no—
216C22×Dic89C22×C418yes—
217C22×Dic89C22×C414yes—
218C22×Dic89C22×C414yes—
219C22×Dic89C2412yes—
220C22×Dic89C2412yes—
221C22×Dic89C2412yes—
222C22×Dic89C2412yes—
223C22×Dic89C2411yescharacteristic
224C22×Dic89C2411yescharacteristic
225C22×Dic89C2411yescharacteristic
226C22×Dic89C2411yescharacteristic
227C22×Dic89C2412yes—
228C22×Dic89C2412yes—
229C4⋊Dic89—42no—
230C4⋊Dic89C22×C414yes—
231C4⋊Dic89C22×C418yes—
232#13083553—42no—
233#13083553—42no—
234#13083553—42no—
235#13083553—42no—
236#13083553—42no—
237#13083553—42no—
238#13083553—42no—
239#13083553—42no—
240#13083553C22×C418yes—
241#13083553C22×C418yes—
242#13083553C22×C418yes—
243C22⋊Dic89—42no—
244C22⋊Dic89—42no—
245C22⋊Dic89—42no—
246C22⋊Dic89—41no—
247C22⋊Dic89—41no—
248C22⋊Dic89—42no—
249C22⋊Dic89C22×C418yes—
250C22⋊Dic89C22×C418yes—
251C22⋊Dic89C22×C418yes—
252C22⋊Dic89C22×C418yes—
253C4×Dic89—42no—
254C4×Dic89—42no—
255C4×Dic89—42no—
256C4×Dic89—42no—
257C4×Dic89—42no—
258C4×Dic89—42no—
259C4×Dic89—41no—
260C4×Dic89—42no—
261C4×Dic89—41no—
262C4×Dic89C22×C414yes—
263C4×Dic89C22×C418yes—
264C4×Dic89C22×C414yes—
265C4×Dic89C22×C414yes—
266C4×Dic89C22×C414yes—
267C24×C89C2411yescharacteristic
268C24×C89C2412yes—
269C2×D4×C89—42no—
270C2×D4×C89—42no—
271C2×D4×C89—41no—
272C2×D4×C89—41no—
273C2×D4×C89C22×C414yes—
274C2×D4×C89C22×C418yes—
275C22×C4×C89—41no—
276C22×C4×C89—41no—
277C22×C4×C89—42no—
278C22×C4×C89—42no—
279C22×C4×C89—42no—
280C22×C4×C89C22×C414yes—
281C22×C4×C89C2412yes—
282C22×C4×C89C2412yes—
283C22×C4×C89C2412yes—
284C22×C4×C89C2412yes—
285C22×C4×C89C2411yescharacteristic
286C22×C4×C89C2411yescharacteristic
287C22×C4×C89C2412yes—
288C4⋊C4×C89—42no—
289C4⋊C4×C89C22×C414yes—
290C22⋊C4×C89—42no—
291C22⋊C4×C89—42no—
292C22⋊C4×C89—42no—
293C22⋊C4×C89—41no—
294C22⋊C4×C89—42no—
295C22⋊C4×C89—41no—
296C22⋊C4×C89C22×C418yes—
297C42×C89—41no—
298C42×C89—41no—
299C42×C89—42no—
300C23×C89—21no—
301C23×C89—21no—
302C23×C89—22no—
303C23×C89—22no—
304C23×C89—22no—
305C23×C89—22no—
306C23×C89—22no—
307C23×C89—22no—
308C23×C89—22no—
309C23×C89—22no—
310C23×C89C23×C414yes—
311C23×C89C23×C412yes—
312C23×C89C2511yescharacteristic
313D4×C89—44no—
314D4×C89—48no—
315C2×C4×C89—21no—
316C2×C4×C89—21no—
317C2×C4×C89—22no—
318C2×C4×C89—22no—
319C2×C4×C89—21no—
320C2×C4×C89—21no—
321C2×C4×C89—22no—
322C2×C4×C89—22no—
323C2×C4×C89—22no—
324C2×C4×C89—22no—
325C2×C4×C89—22no—
326C2×C4×C89—22no—
327C2×C4×C89—22no—
328C2×C4×C89—22no—
329C2×C4×C89—22no—
330C2×C4×C89—22no—
331C2×C4×C89—22no—
332C2×C4×C89—22no—
333C2×C4×C89—44no—
334C2×C4×C89—84no—
335C2×C4×C89C23×C412yes—
336C2×C4×C89C23×C414yes—
337C2×C4×C89C23×C412yes—
338C2×Dic89—22no—
339C2×Dic89—22no—
340C2×Dic89—22no—
341C2×Dic89—22no—
342C2×Dic89—22no—
343C2×Dic89—22no—
344C2×Dic89—22no—
345C2×Dic89—22no—
346C2×Dic89—22no—
347C2×Dic89—22no—
348C2×Dic89—22no—
349C2×Dic89—22no—
350C2×Dic89—22no—
351C2×Dic89—22no—
352C2×Dic89—22no—
353C2×Dic89—22no—
354C2×Dic89—22no—
355C2×Dic89—22no—
356C2×Dic89—22no—
357C2×Dic89—22no—
358C2×Dic89—48no—
359C2×Dic89—44no—
360C2×Dic89—44no—
361C2×Dic89—84no—
362C2×Dic89C23×C412yes—
363C2×Dic89C23×C412yes—
364C2×Dic89C23×C412yes—
365C2×Dic89C23×C412yes—
366C2×Dic89C23×C414yes—
367C2×Dic89C23×C414yes—
368Dic178—44no—
369C22×C89—22no—
370C22×C89—22no—
371C22×C89—24no—
372C22×C89—22no—
373C22×C89—24no—
374C22×C89—24no—
375C22×C89—42no—
376C22×C89—42no—
377C22×C89—42no—
378C22×C89—42no—
379C22×C89—42no—
380C22×C89—42no—
381C22×C89C24×C411yescharacteristic
382C22×C89#58511yescharacteristic
383C22×C89#58512yes—
384C22×C89#58511yescharacteristic
385C22×C89#58512yes—
386C4×C89—22no—
387C4×C89—22no—
388C4×C89—24no—
389C4×C89—42no—
390C4×C89—42no—
391C4×C89—42no—
392C4×C89—42no—
393Dic89—24no—
394Dic89—22no—
395Dic89—22no—
396Dic89—22no—
397Dic89—22no—
398Dic89—24no—
399Dic89—42no—
400Dic89—42no—
401Dic89—42no—
402Dic89—42no—
403#34400—891nomaximal, Sylow
404C2×C89—42no—
405C2×C89—44no—
406C2×C89#342811yescharacteristic
407C2×C89#342811yescharacteristic
408C2×C89#342811yescharacteristic
409C2×C89#356612yes—
410C2×C89#356612yes—
411C2×#529—891no—
412#2376—892no—
413#2376—892no—
414#2373—892no—
415#2373—892no—
416#2357—892no—
417#2353—892no—
418#2346—892no—
419#2343—892no—
420#2337—892no—
421#2336—892no—
422#2333—891no—
423#2333D8911yescharacteristic
424#2332—891no—
425#2332—891no—
426#2320—892no—
427#2318—892no—
428#2283—891no—
429#2283—891no—
430C89#3440011yescharacteristic, complemented, Sylow
431#529—8916no—
432C2×#126—892no—
433C2×#125—891no—
434C2×#124—891no—
435C2×#123—892no—
436C2×C22⋊Q8—891no—
437C2×#121C2×D8911yescharacteristic
438C2×C4×Q8—891no—
439C2×C4×D4—891no—
440C2×C4×D4—892no—
441C2×#117—892no—
442C22×C42—891no—
443#391—892no—
444#391—892no—
445#390—892no—
446#390C2×D8912yes—
447#389—892no—
448#389—892no—
449#389—892no—
450#389—892no—
451#388—892no—
452#388—892no—
453#388—892no—
454#388—892no—
455#388—892no—
456#388—892no—
457#388—892no—
458#388—892no—
459#388—892no—
460#388—892no—
461#388—892no—
462#388C2×D8912yes—
463#387—892no—
464#387—892no—
465#387—892no—
466#387—892no—
467#387—892no—
468#387—892no—
469#387—892no—
470#387—892no—
471#387—892no—
472#387—892no—
473#387—892no—
474#387C2×D8912yes—
475#386—892no—
476#386—892no—
477#386C2×D8912yes—
478#386C2×D8912yes—
479#385—892no—
480#385—892no—
481#385—892no—
482#385—892no—
483#383—892no—
484#383—892no—
485#383—892no—
486#382—892no—
487#382—892no—
488#382—892no—
489#381—891no—
490#381—892no—
491#381—892no—
492#381C2×D8911yescharacteristic
493#380—892no—
494#380—892no—
495#380—891no—
496#380—891no—
497C4×C4⋊C4—892no—
498C4×C4⋊C4—892no—
499C4×C4⋊C4—892no—
500C4×C4⋊C4—892no—
501C4×C4⋊C4—891no—
502C4×C4⋊C4—891no—
503C4×C4⋊C4—892no—
504C4×C4⋊C4—892no—
505C4×C22⋊C4—891no—
506C4×C22⋊C4—892no—
507C4×C22⋊C4—892no—
508C4×C22⋊C4—892no—
509C4×C22⋊C4—892no—
510C4×C22⋊C4—891no—
511C4×C22⋊C4—891no—
512C4×C22⋊C4C2×D8911yescharacteristic
513C4×C22⋊C4C2×D8912yes—
514#376—891no—
515#376—891no—
516#376—892no—
517#376—892no—
518C2×#95—892no—
519C22×Q8—891no—
520C22×D4C22×D8912yes—
521C22×D4C22×D8911yescharacteristic
522C23×C4—892no—
523C23×C4—891no—
524C23×C4—891no—
525C23×C4—892no—
526C23×C4C22×D8912yes—
527C23×C4C22×D8911yescharacteristic
528#126—8916no—
529#125—898no—
530#124—898no—
531#123—8916no—
532C22⋊Q8—898no—
533#121C4×D8918yes—
534C4×Q8—898no—
535C4×D4—898no—
536C4×D4—8916no—
537#117—8916no—
538C2×C4⋊C4—892no—
539C2×C4⋊C4—892no—
540C2×C4⋊C4—891no—
541C2×C4⋊C4—892no—
542C2×C4⋊C4—892no—
543C2×C4⋊C4—892no—
544C2×C4⋊C4—892no—
545C2×C4⋊C4—892no—
546C2×C4⋊C4—892no—
547C2×C4⋊C4—892no—
548C2×C4⋊C4—892no—
549C2×C4⋊C4—892no—
550C2×C4⋊C4—892no—
551C2×C4⋊C4—892no—
552C2×C4⋊C4C22×D8912yes—
553C2×C4⋊C4C22×D8911yescharacteristic
554C2×C22⋊C4—892no—
555C2×C22⋊C4—892no—
556C2×C22⋊C4—892no—
557C2×C22⋊C4—892no—
558C2×C22⋊C4—891no—
559C2×C22⋊C4—892no—
560C2×C22⋊C4—891no—
561C2×C22⋊C4—892no—
562C2×C22⋊C4—892no—
563C2×C22⋊C4—892no—
564C2×C22⋊C4C22×D8911yescharacteristic
565C2×C22⋊C4C22×D8911yescharacteristic
566C2×C22⋊C4C22×D8912yes—
567C2×C22⋊C4C22×D8912yes—
568C2×C22⋊C4C22×D8912yes—
569C2×C22⋊C4C22×D8912yes—
570C2×C22⋊C4C22×D8912yes—
571C2×C42—898no—
572C2×C42—891no—
573C2×C42—892no—
574C2×C42—891no—
575C2×C42—891no—
576C2×C42—891no—
577C2×C42—892no—
578C2×C42—891no—
579C2×C42—892no—
580C2×C42—891no—
581C2×C42—892no—
582C2×C42—892no—
583C2×C42—892no—
584C2×C42—892no—
585C2×C42—892no—
586C2×C42C22×D8911yescharacteristic
587C2×C42C22×D8911yescharacteristic
588C2×C42C22×D8912yes—
589#95—892no—
590#95—892no—
591#95—892no—
592#95—892no—
593#95—892no—
594#95—892no—
595#95—892no—
596#95—892no—
597#95—892no—
598#95—892no—
599#95—892no—
600#95—892no—
601#95—892no—
602#95—892no—
603#95—892no—
604#95—892no—
605#95—892no—
606#95—892no—
607#95—892no—
608#95—892no—
609#95—892no—
610#95—892no—
611#95—892no—
612#95C22×D8912yes—
613#95C22×D8912yes—
614#95C22×D8912yes—
615#95C22×D8912yes—
616#95C22×D8912yes—
617C24C23×D8911yescharacteristic
618C24C23×D8912yes—
619C2×Q8—894no—
620C2×Q8—3561no—
621C2×Q8—3561no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4C2×C4×D8918yes—
627C2×D4C2×C4×D8914yes—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—894no—
634C22×C4—894no—
635C22×C4—898no—
636C22×C4—891no—
637C22×C4—891no—
638C22×C4—892no—
639C22×C4—891no—
640C22×C4—891no—
641C22×C4—892no—
642C22×C4—892no—
643C22×C4—892no—
644C22×C4—892no—
645C22×C4—892no—
646C22×C4—3562no—
647C22×C4—3562no—
648C22×C4—3562no—
649C22×C4—3562no—
650C22×C4—3562no—
651C22×C4—3562no—
652C22×C4—3562no—
653C22×C4C2×C4×D8914yes—
654C22×C4C23×D8912yes—
655C22×C4C23×D8912yes—
656C22×C4C23×D8912yes—
657C22×C4C23×D8912yes—
658C22×C4C23×D8911yescharacteristic
659C22×C4C23×D8911yescharacteristic
660C22×C4C23×D8912yes—
661C4⋊C4—42no—
662C4⋊C4—898no—
663C4⋊C4—898no—
664C4⋊C4—894no—
665C4⋊C4—898no—
666C4⋊C4—898no—
667C4⋊C4—3562no—
668C4⋊C4—3562no—
669C4⋊C4—3562no—
670C4⋊C4—3562no—
671C4⋊C4—3562no—
672C4⋊C4—3562no—
673C4⋊C4—3562no—
674C4⋊C4—3562no—
675C4⋊C4—3562no—
676C4⋊C4C2×C4×D8914yes—
677C22⋊C4—42no—
678C22⋊C4—41no—
679C22⋊C4—41no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—898no—
684C22⋊C4—898no—
685C22⋊C4—898no—
686C22⋊C4—898no—
687C22⋊C4—3562no—
688C22⋊C4—3561no—
689C22⋊C4—3561no—
690C22⋊C4—3562no—
691C22⋊C4—3562no—
692C22⋊C4—3562no—
693C22⋊C4C2×C4×D8918yes—
694C42—41no—
695C42—41no—
696C42—42no—
697C42—894no—
698C42—894no—
699C42—894no—
700C42—894no—
701C42—898no—
702C42—3561no—
703C42—3561no—
704C42—3562no—
705C42—3562no—
706C42—3562no—
707C42—3562no—
708C42—3562no—
709C42—3562no—
710C42—3562no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23C22×C4×D8914yes—
722C23C22×C4×D8912yes—
723C23C24×D8911yescharacteristic
724Q8—3564no—
725D4—44no—
726D4—48no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—44no—
746C2×C4—84no—
747C2×C4—892no—
748C2×C4—892no—
749C2×C4—892no—
750C2×C4—892no—
751C2×C4—894no—
752C2×C4—894no—
753C2×C4—3564no—
754C2×C4—3564no—
755C2×C4—3568no—
756C2×C4—1782no—
757C2×C4—1782no—
758C2×C4—1782no—
759C2×C4—1782no—
760C2×C4—1782no—
761C2×C4—1782no—
762C2×C4—1782no—
763C2×C4—1782no—
764C2×C4—1782no—
765C2×C4—1782no—
766C2×C4—1782no—
767C2×C4—1782no—
768C2×C4—1782no—
769C2×C4—1782no—
770C2×C4—1782no—
771C2×C4—1782no—
772C2×C4—1782no—
773C2×C4—1782no—
774C2×C4—1782no—
775C2×C4—1782no—
776C2×C4—7124no—
777C2×C4C22×C4×D8912yes—
778C2×C4C22×C4×D8912yes—
779C2×C4C22×C4×D8914yes—
780C22—22no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—22no—
785C22—24no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C23×C4×D8911yescharacteristic
793C22#1915243311yescharacteristic
794C22#1915243312yes—
795C22#1915243311yescharacteristic
796C22#1915243412yes—
797C4—22no—
798C4—22no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—3562no—
805C4—3562no—
806C4—3562no—
807C4—3562no—
808C4—1782no—
809C4—1782no—
810C4—1784no—
811C4—1782no—
812C4—1782no—
813C4—1784no—
814C2—42no—
815C2—44no—
816C2#2603345011yescharacteristic
817C2#2603345011yescharacteristic
818C2#2603345111yescharacteristic
819C2#2603491612yes—
820C2#2603492412yes—
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC89×#2333C2
socle, cosocleC23×C89C25
prime radicalC2×#121×C89C22
hypercenter#2333D89
hypocenterC89#34400
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2333

Complements

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

NH ≅ G/Ntype
2. #26023402C2semidirect
3. #26023395C2semidirect
4. #26023374C2semidirect
5. #26023370C2semidirect
6. #26023224C2semidirect
7. #26023190C2semidirect
8. #26023134C2semidirect
9. #26023106C2semidirect
10. #26023061C2semidirect
11. #26023052C2semidirect
13. #26023008C2semidirect
14. #26023005C2semidirect
15. #26022901C2semidirect
16. #26022878C2semidirect
17. #26022646C2semidirect
18. #26022643C2semidirect
20. #19152129C4semidirect
113. #15668005C2×C4semidirect
114. #15668003C2×C4semidirect
116. #15667993C2×C4semidirect
117. #15667991C2×C4semidirect
118. #15667977C2×C4semidirect
120. D4×Dic89C2×C4semidirect
121. #15667968C2×C4semidirect
146. C2×C4×Dic89C2×C4semidirect
430. C89#34400semidirect

Maximal subgroups

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

subgroupindex
C2×#191521292
#260234022
#260233952
#260233742
#260233702
#260232242
#260231902
#260231342
#260231062
#260230612
#260230522
#260230192
#260230082
#260230052
#260229012
#260228782
#260226462
#260226432
C89×#23332
#3440089