Finite Group Databasebeta

← #36714925

Subgroups — #36714925

Order 22784.

2230 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19152133C211yesmaximal, characteristic
2#26023378C212yesmaximal, complemented
3#26023366C212yesmaximal, complemented
4#26023362C211yesmaximal, characteristic, complemented
5#26023362C211yesmaximal, characteristic, complemented
6#26023358C211yesmaximal, characteristic, complemented
7#26023214C212yesmaximal, complemented
8#26023191C212yesmaximal, complemented
9#26023133C212yesmaximal, complemented
10#26023107C212yesmaximal, complemented
11#26022981C212yesmaximal, complemented
12#26022951C212yesmaximal
13#26022884C212yesmaximal, complemented
14C4×#15667997C212yesmaximal, complemented
15#26022773C212yesmaximal, complemented
16#26022644C211yesmaximal, characteristic, complemented
17#26022612C212yesmaximal, complemented
18#376×D89C211yesmaximal, characteristic, complemented
19C89×#2371C211yesmaximal, characteristic, complemented
20#19152133C4116yescomplemented
21C2×#15668007C2212yes—
22C2×#15668000C2211yescharacteristic
23C2×#15667997C2212yes—
24C2×#15667992C2211yescharacteristic
25C2×#15667987C2211yescharacteristic
26C2×#15667977C2211yescharacteristic
27C2×C4×D356C2212yes—
28C2×#15667974C2212yes—
29C2×#15667974C2211yescharacteristic
30C2×#15667974C2212yes—
31C2×#15667970C2212yes—
32C2×C42×D89C2212yes—
33C2×C42×D89C2211yescharacteristic
34#19151502C2212yes—
35#19151502C2212yes—
36#19151496C2212yes—
37#19151494C2212yes—
38#19151490C2212yes—
39#19151489C2212yes—
40#19151489C2212yes—
41#19151489C2212yes—
42#19151488C2212yes—
43#19151487C2212yes—
44#19151487C2212yes—
45#19151487C2212yes—
46#19151485C2212yes—
47#19151484C2212yes—
48#19151484C2212yes—
49#19151484C2212yes—
50#19151484C2212yes—
51#19151483C2212yes—
52#19151481C2212yes—
53#19151479C2212yes—
54#19151476C2212yes—
55#19151476C2212yes—
56#19151476C2212yes—
57#19151476C2212yes—
58#19151472C2212yes—
59#19151472C2212yes—
60#19151469C2212yes—
61#19151469C2212yes—
62#19151465C2212yes—
63#19151465C2212yes—
64#19151462C2212yes—
65#19151462C2211yescharacteristic
66#19151462C2211yescharacteristic
67#19151460C2212yes—
68#19151460C2211yescharacteristic
69#19151460C2211yescharacteristic
70#19151457C2212yes—
71#19151455C2212yes—
72C4⋊C4×Dic89C2212yes—
73C4⋊C4×Dic89C2212yes—
74C4⋊C4×Dic89C2212yes—
75C4×#13083553C2212yes—
76C4×#13083553C2212yes—
77#19151449C2212yes—
78C4×#13083551C2212yes—
79C4×#13083551C2212yes—
80C4×#13083551C2212yes—
81C4×#13083551C2212yes—
82C4×#13083551C2212yes—
83C4×#13083551C2212yes—
84#19151445C2212yes—
85#19151445C2212yes—
86#19151445C2212yes—
87#19151445C2212yes—
88#19151444C2212yes—
89#19151444C2211yescharacteristic
90#19151444C2212yes—
91#19151444C2211yescharacteristic
92#19151443C2212yes—
93#19151443C2211yescharacteristic
94#19151443C2211yescharacteristic
95#95×D89C2212yes—
96#95×D89C2212yes—
97#95×D89C2211yescharacteristic
98#95×D89C2211yescharacteristic
99C2×#125×C89C2211yescharacteristic
100#387×C89C2212yes—
101#387×C89C2212yes—
102#387×C89C2212yes—
103#387×C89C2212yes—
104C4×C4⋊C4×C89C2212yes—
105C4×C4⋊C4×C89C2212yes—
106#376×C89C2211yescharacteristic
107#376×C89C2211yescharacteristic
108C22×Dic178C2311yescharacteristic
109C22×D356C2312yes—
110C22×D356C2311yescharacteristic
111C22×C4×D89C2311yescharacteristic
112C22×C4×D89C2312yes—
113C22×C4×D89C2312yes—
114C22×C4×D89C2312yes—
115C22×C4×D89C2311yescharacteristic
116C22×C4×D89C2311yescharacteristic
117C22×C4×D89C2312yes—
118C22×C4×D89C2312yes—
119#15668007C2×C4116yescomplemented
120#15668000C2×C418yescomplemented
121#15667997C2×C4116yescomplemented
122#15667992C2×C418yescomplemented
123#15667987C2×C418yes—
124#15667977C2×C418yescomplemented
125C4×D356—28no—
126#15667974—28no—
127#15667974C2×C418yescomplemented
128#15667974C2×C4116yescomplemented
129#15667970C2×C4116yescomplemented
130C2×C4⋊Dic89C2312yes—
131C2×C4⋊Dic89C2312yes—
132C2×C4⋊Dic89C2312yes—
133C2×#13083553C2312yes—
134C2×#13083553C2312yes—
135C2×#13083553C2312yes—
136C2×#13083553C2312yes—
137C2×#13083553C2312yes—
138C2×#13083551C2312yes—
139C2×#13083551C2312yes—
140C2×#13083551C2312yes—
141C2×#13083551C2312yes—
142C2×#13083551C2312yes—
143C2×#13083551C2312yes—
144C2×#13083551C2312yes—
145C2×#13083551C2312yes—
146C2×#13083551C2312yes—
147C2×#13083551C2312yes—
148C2×#13083551C2312yes—
149C2×#13083551C2312yes—
150C2×#13083551C2312yes—
151C2×C4×Dic89C2312yes—
152C2×C4×Dic89C2312yes—
153C2×C4×Dic89C2312yes—
154C2×C4×Dic89C2312yes—
155C2×C4×Dic89C2312yes—
156C2×C4×Dic89C2312yes—
157C2×C4×Dic89C2312yes—
158C2×C4×Dic89C2312yes—
159C2×C4×Dic89C2311yescharacteristic
160C2×C4×Dic89C2311yescharacteristic
161C2×C4×Dic89C2311yescharacteristic
162C2×C4×Dic89C2312yes—
163C42×D89—28no—
164C42×D89C2×C418yescomplemented
165#15667919C2312yes—
166#15667919C2311yescharacteristic
167#15667919C2312yes—
168#15667919C2312yes—
169#15667919C2312yes—
170#15667919C2312yes—
171#15667919C2311yescharacteristic
172#15667919C2312yes—
173#15667919C2312yes—
174#15667919C2312yes—
175#15667919C2312yes—
176#15667919C2311yescharacteristic
177#15667919C2312yes—
178#15667919C2311yescharacteristic
179#15667919C2312yes—
180#15667919C2312yes—
181#15667919C2312yes—
182#15667919C2312yes—
183#15667919C2312yes—
184#15667919C2312yes—
185#15667919C2312yes—
186#15667919C2312yes—
187#125×C89C2×C418yescomplemented
188C2×C4⋊C4×C89C2312yes—
189C2×C4⋊C4×C89C2312yes—
190C2×C4⋊C4×C89C2312yes—
191C2×C4⋊C4×C89C2312yes—
192C2×C4⋊C4×C89C2311yescharacteristic
193C2×C4⋊C4×C89C2311yescharacteristic
194C2×C42×C89C2312yes—
195C2×C42×C89C2312yes—
196C2×C42×C89C2312yes—
197C2×C42×C89C2312yes—
198C2×C42×C89C2311yescharacteristic
199#95×C89C2311yescharacteristic
200#95×C89C2311yescharacteristic
201#95×C89C2312yes—
202#95×C89C2311yescharacteristic
203#95×C89C2311yescharacteristic
204#95×C89C2312yes—
205#95×C89C2312yes—
206#95×C89C2312yes—
207#95×C89C2312yes—
208#95×C89C2312yes—
209C23×D89C2412yes—
210C23×D89C2411yescharacteristic
211C2×Dic178—41no—
212C2×Dic178—41no—
213C2×Dic178C22×C414yes—
214C2×D356—24no—
215C2×D356—24no—
216C2×D356—41no—
217C2×D356—41no—
218C2×D356C22×C418yes—
219C2×D356C22×C414yes—
220C22×Dic89C2412yes—
221C22×Dic89C2412yes—
222C22×Dic89C2412yes—
223C22×Dic89C2411yescharacteristic
224C22×Dic89C2411yescharacteristic
225C22×Dic89C2411yescharacteristic
226C22×Dic89C2412yes—
227C22×Dic89C2412yes—
228C2×C4×D89—24no—
229C2×C4×D89—24no—
230C2×C4×D89—24no—
231C2×C4×D89—24no—
232C2×C4×D89—41no—
233C2×C4×D89—41no—
234C2×C4×D89—42no—
235C2×C4×D89—42no—
236C2×C4×D89—42no—
237C2×C4×D89—42no—
238C2×C4×D89—42no—
239C2×C4×D89—42no—
240C2×C4×D89—42no—
241C2×C4×D89—42no—
242C2×C4×D89—42no—
243C2×C4×D89—42no—
244C2×C4×D89—42no—
245C2×C4×D89C22×C414yes—
246C2×C4×D89C22×C418yes—
247C2×C4×D89C22×C414yes—
248C2×C4×D89C22×C414yes—
249C2×C4×D89#4118yes—
250C4⋊Dic89—24no—
251C4⋊Dic89—42no—
252C4⋊Dic89C22×C418yes—
253#13083553—42no—
254#13083553—42no—
255#13083553—42no—
256#13083553—42no—
257#13083553C22×C418yes—
258#13083551—24no—
259#13083551—24no—
260#13083551—24no—
261#13083551—24no—
262#13083551—42no—
263#13083551—42no—
264#13083551—42no—
265#13083551—42no—
266#13083551C22×C418yes—
267#13083551C22×C418yes—
268#13083551C22×C418yes—
269#13083551C22×C418yes—
270#13083551C22×C418yes—
271C4×Dic89—24no—
272C4×Dic89—24no—
273C4×Dic89—24no—
274C4×Dic89—24no—
275C4×Dic89—42no—
276C4×Dic89—42no—
277C4×Dic89—42no—
278C4×Dic89—42no—
279C4×Dic89C22×C414yes—
280C4×Dic89C22×C418yes—
281C4×Dic89C22×C414yes—
282C4×Dic89C22×C414yes—
283C22×C4×C89C2412yes—
284C22×C4×C89C2412yes—
285C22×C4×C89C2412yes—
286C22×C4×C89C2411yescharacteristic
287C22×C4×C89C2411yescharacteristic
288C22×C4×C89C2411yescharacteristic
289C22×C4×C89C2412yes—
290C22×C4×C89C2412yes—
291C22×C4×C89C2412yes—
292C4⋊C4×C89—24no—
293C4⋊C4×C89—42no—
294C4⋊C4×C89C22×C418yes—
295C4⋊C4×C89C22×C414yes—
296C4⋊C4×C89C22×C418yes—
297C4⋊C4×C89C22×C414yes—
298C42×C89—24no—
299C42×C89—24no—
300C42×C89—42no—
301C42×C89—42no—
302C42×C89C22×C414yes—
303C23×C89C2511yescharacteristic
304C22×D89—22no—
305C22×D89—21no—
306C22×D89—21no—
307C22×D89—22no—
308C22×D89—22no—
309C22×D89—22no—
310C22×D89—22no—
311C22×D89—22no—
312C22×D89—22no—
313C22×D89C23×C414yes—
314C22×D89C23×C412yes—
315C22×D89C2×#4114yes—
316C2×C4×C89—22no—
317C2×C4×C89—22no—
318C2×C4×C89—22no—
319C2×C4×C89—22no—
320C2×C4×C89—22no—
321C2×C4×C89—22no—
322C2×C4×C89—22no—
323C2×C4×C89—22no—
324C2×C4×C89—21no—
325C2×C4×C89—21no—
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—22no—
334C2×C4×C89—22no—
335C2×C4×C89C23×C412yes—
336C2×C4×C89C23×C412yes—
337C2×C4×C89C23×C412yes—
338C2×C4×C89C23×C414yes—
339C2×C4×C89C23×C414yes—
340C2×C4×C89C2×#4114yes—
341C2×Dic89—22no—
342C2×Dic89—22no—
343C2×Dic89—22no—
344C2×Dic89—22no—
345C2×Dic89—21no—
346C2×Dic89—21no—
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×Dic89C23×C412yes—
359C2×Dic89C23×C412yes—
360C2×Dic89C23×C412yes—
361C2×Dic89C23×C414yes—
362C2×Dic89C2×#4114yes—
363D356—216no—
364D356—44no—
365C4×D89—28no—
366C4×D89—44no—
367C4×D89—48no—
368C4×D89—44no—
369C4×D89—48no—
370C4×D89—48no—
371C4×D89—84no—
372C4×D89—84no—
373Dic178—44no—
374C22×C89C24×C411yescharacteristic
375C22×C89C22×#4112yes—
376C22×C89#58511yescharacteristic
377C22×C89#58512yes—
378C22×C89#58511yescharacteristic
379C2×D89—22no—
380C2×D89—22no—
381C2×D89—24no—
382C2×D89—24no—
383C2×D89—24no—
384C2×D89—24no—
385C2×D89—24no—
386C2×D89—42no—
387C2×D89—42no—
388C2×D89—42no—
389C2×D89—42no—
390C2×D89C4×#4114yes—
391C4×C89—22no—
392C4×C89—24no—
393C4×C89—22no—
394C4×C89—22no—
395C4×C89—24no—
396C4×C89—24no—
397C4×C89—42no—
398C4×C89—42no—
399C4×C89—42no—
400Dic89—22no—
401Dic89—24no—
402Dic89—22no—
403Dic89—22no—
404Dic89—24no—
405Dic89—42no—
406Dic89—42no—
407Dic89—42no—
408#34219—891nomaximal, Sylow
409C2×C89C2×C4×#4111yescharacteristic
410C2×C89#342811yescharacteristic
411C2×C89#342811yescharacteristic
412C2×C89#349112yes—
413C2×C89#349312yes—
414D89—24no—
415D89—44no—
416C2×#529—891no—
417#2373—892no—
418#2373—892no—
419#2372—891no—
420#2372—891no—
421#2371—891no—
422#2371D8911yescharacteristic, complemented
423#2356—892no—
424#2353—892no—
425#2346—892no—
426#2343—892no—
427#2329—892no—
428#2325—892no—
429#2318—892no—
430C4×#123—892no—
431C4×#123—892no—
432#2283—891no—
433#2275—892no—
434C2×#376—891no—
435C89#3421911yescharacteristic, complemented, Sylow
436#529—8916no—
437C2×#126—892no—
438C2×#125C2×D8911yescharacteristic
439C2×#124—891no—
440C2×#123—892no—
441C2×C22⋊Q8—891no—
442C2×#121—891no—
443C2×C4×Q8—891no—
444C2×C4×D4—892no—
445C2×C4×D4—891no—
446C2×C4×D4—892no—
447C2×C4×D4—892no—
448C2×#117—892no—
449C22×C42—891no—
450C22×C42—892no—
451#391—892no—
452#391—892no—
453#389—892no—
454#389—892no—
455#388—892no—
456#388—892no—
457#388—892no—
458#388—892no—
459#388—892no—
460#388—892no—
461#388—892no—
462#388—892no—
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#387C2×D8912yes—
472#387C2×D8912yes—
473#387C2×D8912yes—
474#387C2×D8912yes—
475#386—892no—
476#386—892no—
477#386—892no—
478#386—892no—
479#385—892no—
480#385—892no—
481#385—892no—
482#385—892no—
483#383—892no—
484#383—892no—
485#382—892no—
486#382—891no—
487#382—891no—
488#381—892no—
489#381—891no—
490#381—891no—
491#380—892no—
492#380—892no—
493C4×C4⋊C4—892no—
494C4×C4⋊C4—892no—
495C4×C4⋊C4—892no—
496C4×C4⋊C4—892no—
497C4×C4⋊C4—892no—
498C4×C4⋊C4—892no—
499C4×C4⋊C4C2×D8912yes—
500C4×C4⋊C4C2×D8912yes—
501C4×C22⋊C4—892no—
502C4×C22⋊C4—892no—
503C4×C22⋊C4—892no—
504C4×C22⋊C4—892no—
505C4×C22⋊C4—892no—
506C4×C22⋊C4—892no—
507C4×C22⋊C4—892no—
508C4×C22⋊C4—892no—
509C4×C22⋊C4—892no—
510C4×C22⋊C4—892no—
511#376—892no—
512#376—892no—
513#376—891no—
514#376—891no—
515#376—892no—
516#376—891no—
517#376—891no—
518#376C2×D8911yescharacteristic
519#376C2×D8911yescharacteristic
520C2×#95—891no—
521C2×#95—892no—
522C2×#95—892no—
523C2×#95—891no—
524C22×Q8—891no—
525C22×D4—891no—
526C22×D4—892no—
527C23×C4—892no—
528C23×C4—891no—
529C23×C4—892no—
530C23×C4—891no—
531C23×C4—891no—
532C23×C4—892no—
533C23×C4—892no—
534C23×C4—892no—
535#126—8916no—
536#125C4×D8918yescomplemented
537#124—898no—
538#123—8916no—
539C22⋊Q8—898no—
540#121—898no—
541C4×Q8—898no—
542C4×D4—898no—
543C4×D4—8916no—
544C4×D4—1788no—
545C4×D4—1788no—
546#117—8916no—
547C2×C4⋊C4—892no—
548C2×C4⋊C4—892no—
549C2×C4⋊C4—892no—
550C2×C4⋊C4—892no—
551C2×C4⋊C4—892no—
552C2×C4⋊C4—892no—
553C2×C4⋊C4—892no—
554C2×C4⋊C4—892no—
555C2×C4⋊C4C22×D8912yes—
556C2×C4⋊C4C22×D8912yes—
557C2×C4⋊C4C22×D8912yes—
558C2×C4⋊C4C22×D8911yescharacteristic
559C2×C4⋊C4C22×D8912yes—
560C2×C4⋊C4C22×D8911yescharacteristic
561C2×C22⋊C4—892no—
562C2×C22⋊C4—892no—
563C2×C22⋊C4—892no—
564C2×C22⋊C4—892no—
565C2×C22⋊C4—892no—
566C2×C22⋊C4—892no—
567C2×C22⋊C4—892no—
568C2×C22⋊C4—892no—
569C2×C22⋊C4—892no—
570C2×C22⋊C4—892no—
571C2×C22⋊C4—892no—
572C2×C22⋊C4—892no—
573C2×C22⋊C4—892no—
574C2×C42—891no—
575C2×C42—892no—
576C2×C42—891no—
577C2×C42—891no—
578C2×C42—898no—
579C2×C42—892no—
580C2×C42—892no—
581C2×C42—892no—
582C2×C42—892no—
583C2×C42—892no—
584C2×C42—892no—
585C2×C42—892no—
586C2×C42—892no—
587C2×C42—1788no—
588C2×C42C22×D8912yes—
589C2×C42C22×D8912yes—
590C2×C42C22×D8912yes—
591C2×C42C22×D8912yes—
592C2×C42C22×D8911yescharacteristic
593#95—892no—
594#95—891no—
595#95—892no—
596#95—892no—
597#95—892no—
598#95—892no—
599#95—891no—
600#95—892no—
601#95—892no—
602#95—892no—
603#95—891no—
604#95—892no—
605#95—892no—
606#95—891no—
607#95—892no—
608#95—892no—
609#95—892no—
610#95—892no—
611#95—892no—
612#95—892no—
613#95—892no—
614#95—892no—
615#95C22×D8911yescharacteristic
616#95C22×D8912yes—
617#95C22×D8911yescharacteristic
618#95C22×D8912yes—
619#95C22×D8911yescharacteristic
620#95C22×D8911yescharacteristic
621#95C22×D8912yes—
622#95C22×D8912yes—
623#95C22×D8912yes—
624#95C22×D8912yes—
625C24—891no—
626C24—892no—
627C2×Q8—894no—
628C2×Q8—3561no—
629C2×Q8—3561no—
630C2×D4—894no—
631C2×D4—898no—
632C2×D4—3561no—
633C2×D4—3561no—
634C2×D4—1784no—
635C2×D4—1784no—
636C22×C4—891no—
637C22×C4—892no—
638C22×C4—891no—
639C22×C4—892no—
640C22×C4—891no—
641C22×C4—894no—
642C22×C4—894no—
643C22×C4—898no—
644C22×C4—898no—
645C22×C4—894no—
646C22×C4—892no—
647C22×C4—892no—
648C22×C4—892no—
649C22×C4—3562no—
650C22×C4—3562no—
651C22×C4—3562no—
652C22×C4—3562no—
653C22×C4—3562no—
654C22×C4—3561no—
655C22×C4—3561no—
656C22×C4—3562no—
657C22×C4—3562no—
658C22×C4—3562no—
659C22×C4—3562no—
660C22×C4—3562no—
661C22×C4—3562no—
662C22×C4—1784no—
663C22×C4—1784no—
664C22×C4—1784no—
665C22×C4—1784no—
666C22×C4C23×D8912yes—
667C22×C4C23×D8912yes—
668C22×C4C23×D8912yes—
669C22×C4C23×D8911yescharacteristic
670C22×C4C23×D8911yescharacteristic
671C22×C4C23×D8911yescharacteristic
672C22×C4C23×D8912yes—
673C22×C4C23×D8912yes—
674C22×C4C23×D8912yes—
675C4⋊C4—24no—
676C4⋊C4—42no—
677C4⋊C4—898no—
678C4⋊C4—898no—
679C4⋊C4—3562no—
680C4⋊C4—3562no—
681C4⋊C4—3562no—
682C4⋊C4—3562no—
683C4⋊C4—3562no—
684C4⋊C4—1784no—
685C4⋊C4C2×C4×D8918yes—
686C4⋊C4C2×C4×D8914yes—
687C4⋊C4C2×C4×D8918yes—
688C4⋊C4C2×C4×D8914yes—
689C22⋊C4—898no—
690C22⋊C4—898no—
691C22⋊C4—898no—
692C22⋊C4—898no—
693C22⋊C4—898no—
694C22⋊C4—3562no—
695C22⋊C4—3562no—
696C22⋊C4—3562no—
697C22⋊C4—3562no—
698C22⋊C4—1784no—
699C22⋊C4—1784no—
700C22⋊C4—1784no—
701C22⋊C4—1784no—
702C42—24no—
703C42—24no—
704C42—42no—
705C42—42no—
706C42—894no—
707C42—894no—
708C42—894no—
709C42—898no—
710C42—3562no—
711C42—3562no—
712C42—3562no—
713C42—3562no—
714C42—1784no—
715C42—1784no—
716C42—1784no—
717C42—1784no—
718C42C2×C4×D8914yes—
719C23—892no—
720C23—894no—
721C23—894no—
722C23—1782no—
723C23—1782no—
724C23—1782no—
725C23—1782no—
726C23—1782no—
727C23—1782no—
728C23—1782no—
729C23—1781no—
730C23—1781no—
731C23C24×D8911yescharacteristic
732Q8—3564no—
733D4—3564no—
734D4—17816no—
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—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—892no—
755C2×C4—892no—
756C2×C4—892no—
757C2×C4—894no—
758C2×C4—894no—
759C2×C4—3568no—
760C2×C4—3568no—
761C2×C4—3564no—
762C2×C4—3564no—
763C2×C4—3568no—
764C2×C4—1788no—
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—1782no—
777C2×C4—1782no—
778C2×C4—1782no—
779C2×C4—1781no—
780C2×C4—1781no—
781C2×C4—1782no—
782C2×C4—7124no—
783C2×C4—7124no—
784C2×C4C22×C4×D8912yes—
785C2×C4C22×C4×D8912yes—
786C2×C4C22×C4×D8912yes—
787C2×C4C22×C4×D8914yes—
788C2×C4C22×C4×D8914yes—
789C2×C4#41×D8914yes—
790C22—894no—
791C22—3562no—
792C22—3562no—
793C22—3562no—
794C22—3562no—
795C22—1784no—
796C22—1784no—
797C22—1784no—
798C22—1784no—
799C22—1782no—
800C22—1782no—
801C22—1784no—
802C22C23×C4×D8911yescharacteristic
803C22C2×#41×D8912yes—
804C22#1915243412yes—
805C22#1915243511yescharacteristic
806C22#1915243511yescharacteristic
807C4—22no—
808C4—24no—
809C4—24no—
810C4—22no—
811C4—24no—
812C4—22no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—3562no—
817C4—3562no—
818C4—3562no—
819C4—1782no—
820C4—1784no—
821C4—1782no—
822C4—1782no—
823C4—1784no—
824C2—3564no—
825C2—1784no—
826C2C4×#41×D8911yescharacteristic
827C2#2603345111yescharacteristic
828C2#2603345411yescharacteristic
829C2#2603394712yes—
830C2#2603397012yes—
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC89×#2371C2
socle, cosocleC23×C89C25
prime radicalC2×#15667987C22
hypercenter#2371D89
hypocenterC89#34219
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2371

Complements

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

NH ≅ G/Ntype
2. #26023378C2semidirect
3. #26023366C2semidirect
4. #26023362C2semidirect
5. #26023362C2semidirect
6. #26023358C2semidirect
7. #26023214C2semidirect
8. #26023191C2semidirect
9. #26023133C2semidirect
10. #26023107C2semidirect
11. #26022981C2semidirect
13. #26022884C2semidirect
14. C4×#15667997C2semidirect
15. #26022773C2semidirect
16. #26022644C2semidirect
17. #26022612C2semidirect
18. #376×D89C2semidirect
19. C89×#2371C2semidirect
20. #19152133C4semidirect
119. #15668007C2×C4semidirect
120. #15668000C2×C4semidirect
121. #15667997C2×C4semidirect
122. #15667992C2×C4semidirect
124. #15667977C2×C4semidirect
127. #15667974C2×C4semidirect
128. #15667974C2×C4semidirect
129. #15667970C2×C4semidirect
164. C42×D89C2×C4semidirect
187. #125×C89C2×C4semidirect
422. #2371D89semidirect
435. C89#34219semidirect
536. #125C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#191521332
#260233782
#260233662
#260233622
#260233582
#260232142
#260231912
#260231332
#260231072
#260229812
#260229512
#260228842
C4×#156679972
#260227732
#260226442
#260226122
#376×D892
C89×#23712
#3421989