Finite Group Databasebeta

← #36717713

Subgroups — #36717713

Order 22784.

2118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19152133C211yesmaximal, characteristic
2#26023443C212yesmaximal, complemented
3#26023442C212yesmaximal, complemented
4#26023249C212yesmaximal, complemented
5#26023237C212yesmaximal, complemented
6#26023191C212yesmaximal, complemented
7#26023161C212yesmaximal, complemented
8#26023141C212yesmaximal, complemented
9#26023111C212yesmaximal, complemented
10#26023065C211yesmaximal, characteristic, complemented
11#26023062C211yesmaximal, characteristic, complemented
12#26023058C211yesmaximal, characteristic, complemented
13#26022981C212yesmaximal, complemented
14#26022951C212yesmaximal
15#26022901C212yesmaximal, complemented
16#26022884C212yesmaximal, complemented
17#26022656C211yesmaximal, characteristic, complemented
18#383×D89C211yesmaximal, characteristic, complemented
19C89×#2336C211yesmaximal, characteristic, complemented
20#19152133C4116yescomplemented
21C2×#15668007C2212yes—
22C2×#15668000C2211yescharacteristic
23C2×#15667997C2212yes—
24C2×#15667992C2211yescharacteristic
25C2×#15667987C2211yescharacteristic
26C2×#15667977C2211yescharacteristic
27C2×C4×D356C2212yes—
28C2×#15667974C2212yes—
29C2×#15667974C2212yes—
30C2×#15667974C2211yescharacteristic
31C2×#15667970C2212yes—
32C2×#15667969C2211yescharacteristic
33C2×#15667969C2211yescharacteristic
34C2×C42×D89C2211yescharacteristic
35#19151502C2212yes—
36#19151502C2212yes—
37#19151497C2212yes—
38#19151496C2212yes—
39#19151495C2212yes—
40#19151494C2212yes—
41#19151493C2212yes—
42#19151490C2212yes—
43#19151489C2212yes—
44#19151489C2212yes—
45#19151489C2212yes—
46#19151488C2212yes—
47#19151487C2212yes—
48#19151487C2212yes—
49#19151487C2212yes—
50#19151484C2212yes—
51#19151484C2212yes—
52#19151484C2212yes—
53#19151484C2212yes—
54#19151483C2212yes—
55#19151482C2212yes—
56#19151481C2212yes—
57#19151480C2212yes—
58#19151476C2212yes—
59#19151476C2212yes—
60#19151476C2212yes—
61#19151476C2212yes—
62#19151472C2212yes—
63#19151472C2212yes—
64#19151472C2212yes—
65#19151472C2212yes—
66#19151469C2212yes—
67#19151469C2212yes—
68#19151469C2212yes—
69#19151469C2212yes—
70#19151467C2212yes—
71#19151466C2211yescharacteristic
72#19151465C2211yescharacteristic
73#19151465C2211yescharacteristic
74#19151465C2212yes—
75#19151465C2212yes—
76#19151465C2212yes—
77#19151463C2212yes—
78#19151462C2212yes—
79#19151460C2212yes—
80#19151457C2212yes—
81#19151455C2212yes—
82#19151455C2212yes—
83C4⋊C4×Dic89C2212yes—
84C4×#13083553C2211yescharacteristic
85C4×#13083553C2211yescharacteristic
86C4×#13083553C2212yes—
87C4×C4⋊Dic89C2211yescharacteristic
88C4×#13083551C2212yes—
89C4×#13083551C2212yes—
90C4×#13083551C2212yes—
91#19151445C2212yes—
92#19151445C2212yes—
93#19151443C2212yes—
94#95×D89C2211yescharacteristic
95#95×D89C2212yes—
96#95×D89C2212yes—
97#95×D89C2212yes—
98#95×D89C2211yescharacteristic
99C2×#125×C89C2211yescharacteristic
100#389×C89C2212yes—
101#387×C89C2212yes—
102#387×C89C2212yes—
103#387×C89C2212yes—
104#387×C89C2212yes—
105#383×C89C2211yescharacteristic
106C4×C4⋊C4×C89C2211yescharacteristic
107C4×C4⋊C4×C89C2212yes—
108C22×Dic178C2311yescharacteristic
109C22×D356C2312yes—
110C22×D356C2311yescharacteristic
111C22×C4×D89C2311yescharacteristic
112C22×C4×D89C2312yes—
113C22×C4×D89C2312yes—
114C22×C4×D89C2312yes—
115C22×C4×D89C2312yes—
116C22×C4×D89C2311yescharacteristic
117C22×C4×D89C2311yescharacteristic
118C22×C4×D89C2312yes—
119#15668007C2×C4116yescomplemented
120#15668000C2×C418yescomplemented
121#15667997C2×C4116yescomplemented
122#15667992C2×C418yescomplemented
123#15667987C2×C418yes—
124#15667977C2×C418yescomplemented
125C4×D356—44no—
126#15667974—44no—
127#15667974C2×C418yescomplemented
128#15667974C2×C4116yescomplemented
129#15667970C2×C4116yescomplemented
130#15667969—42no—
131#15667969—42no—
132C2×C4⋊Dic89C2312yes—
133C2×C4⋊Dic89C2312yes—
134C2×C4⋊Dic89C2312yes—
135C2×C4⋊Dic89C2312yes—
136C2×#13083553C2312yes—
137C2×#13083553C2312yes—
138C2×#13083553C2312yes—
139C2×#13083553C2312yes—
140C2×#13083553C2312yes—
141C2×#13083553C2312yes—
142C2×#13083553C2312yes—
143C2×#13083551C2312yes—
144C2×#13083551C2312yes—
145C2×#13083551C2312yes—
146C2×#13083551C2312yes—
147C2×#13083551C2312yes—
148C2×#13083551C2312yes—
149C2×#13083551C2312yes—
150C2×#13083551C2312yes—
151C2×#13083551C2312yes—
152C2×#13083551C2312yes—
153C2×#13083551C2312yes—
154C2×#13083551C2312yes—
155C2×#13083551C2312yes—
156C2×C4×Dic89C2312yes—
157C2×C4×Dic89C2312yes—
158C2×C4×Dic89C2311yescharacteristic
159C2×C4×Dic89C2312yes—
160C2×C4×Dic89C2311yescharacteristic
161C2×C4×Dic89C2312yes—
162C2×C4×Dic89C2312yes—
163C2×C4×Dic89C2311yescharacteristic
164C2×C4×Dic89C2311yescharacteristic
165C2×C4×Dic89C2311yescharacteristic
166C42×D89C2×C418yescomplemented
167#15667919C2312yes—
168#15667919C2312yes—
169#15667919C2312yes—
170#15667919C2312yes—
171#15667919C2312yes—
172#15667919C2312yes—
173#15667919C2312yes—
174#15667919C2312yes—
175#15667919C2311yescharacteristic
176#15667919C2312yes—
177#15667919C2311yescharacteristic
178#15667919C2312yes—
179#15667919C2312yes—
180#15667919C2312yes—
181#15667919C2312yes—
182#15667919C2312yes—
183#15667919C2312yes—
184#15667919C2312yes—
185#15667919C2312yes—
186#15667919C2312yes—
187#15667919C2312yes—
188#125×C89C2×C418yescomplemented
189C2×C4⋊C4×C89C2312yes—
190C2×C4⋊C4×C89C2312yes—
191C2×C4⋊C4×C89C2312yes—
192C2×C4⋊C4×C89C2312yes—
193C2×C4⋊C4×C89C2311yescharacteristic
194C2×C4⋊C4×C89C2311yescharacteristic
195C2×C4⋊C4×C89C2312yes—
196C2×C42×C89C2311yescharacteristic
197C2×C42×C89C2311yescharacteristic
198C2×C42×C89C2312yes—
199C2×C42×C89C2312yes—
200C2×C42×C89C2311yescharacteristic
201#95×C89C2312yes—
202#95×C89C2312yes—
203#95×C89C2312yes—
204#95×C89C2312yes—
205#95×C89C2311yescharacteristic
206#95×C89C2311yescharacteristic
207#95×C89C2312yes—
208#95×C89C2312yes—
209#95×C89C2312yes—
210C23×D89C2412yes—
211C23×D89C2411yescharacteristic
212C2×Dic178—42no—
213C2×Dic178C22×C414yes—
214C2×D356—24no—
215C2×D356—24no—
216C2×D356—42no—
217C2×D356C22×C418yes—
218C2×D356C22×C414yes—
219C22×Dic89C2412yes—
220C22×Dic89C2412yes—
221C22×Dic89C2412yes—
222C22×Dic89C2412yes—
223C22×Dic89C2411yescharacteristic
224C22×Dic89C2411yescharacteristic
225C22×Dic89C2411yescharacteristic
226C22×Dic89C2412yes—
227C2×C4×D89—22no—
228C2×C4×D89—22no—
229C2×C4×D89—24no—
230C2×C4×D89—24no—
231C2×C4×D89—42no—
232C2×C4×D89—42no—
233C2×C4×D89—42no—
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—
249C4⋊Dic89—42no—
250C4⋊Dic89—42no—
251C4⋊Dic89—42no—
252C4⋊Dic89C22×C418yes—
253#13083553—42no—
254#13083553—42no—
255#13083553—42no—
256#13083553—42no—
257#13083553—42no—
258#13083553—42no—
259#13083553C22×C418yes—
260#13083551—24no—
261#13083551—24no—
262#13083551—42no—
263#13083551—42no—
264#13083551—42no—
265#13083551—42no—
266#13083551—42no—
267#13083551—42no—
268#13083551C22×C418yes—
269#13083551C22×C418yes—
270#13083551C22×C418yes—
271#13083551C22×C418yes—
272#13083551C22×C418yes—
273C4×Dic89—41no—
274C4×Dic89—41no—
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×C89C2412yes—
287C22×C4×C89C2411yescharacteristic
288C22×C4×C89C2411yescharacteristic
289C22×C4×C89C2412yes—
290C22×C4×C89C2411yescharacteristic
291C22×C4×C89C2412yes—
292C4⋊C4×C89—42no—
293C4⋊C4×C89—42no—
294C4⋊C4×C89—42no—
295C4⋊C4×C89C22×C418yes—
296C4⋊C4×C89C22×C414yes—
297C4⋊C4×C89C22×C418yes—
298C4⋊C4×C89C22×C414yes—
299C42×C89—41no—
300C42×C89—41no—
301C42×C89—42no—
302C42×C89—42no—
303C42×C89C22×C414yes—
304C23×C89C2511yescharacteristic
305C22×D89—22no—
306C22×D89—22no—
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×D89H(5,𝔽2)12yes—
316C22×D892−1+412yes—
317C2×C4×C89—21no—
318C2×C4×C89—22no—
319C2×C4×C89—21no—
320C2×C4×C89—22no—
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—22no—
334C2×C4×C89—22no—
335C2×C4×C89—22no—
336C2×C4×C89—22no—
337C2×C4×C89C23×C412yes—
338C2×C4×C89C23×C412yes—
339C2×C4×C89C23×C412yes—
340C2×C4×C89C23×C414yes—
341C2×C4×C89C23×C414yes—
342C2×Dic89—21no—
343C2×Dic89—21no—
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—22no—
359C2×Dic89—22no—
360C2×Dic89C23×C412yes—
361C2×Dic89C23×C412yes—
362C2×Dic89C23×C412yes—
363C2×Dic89C23×C414yes—
364D356—216no—
365D356—44no—
366C4×D89—28no—
367C4×D89—44no—
368C4×D89—48no—
369C4×D89—44no—
370C4×D89—84no—
371C4×D89—84no—
372C4×D89—84no—
373C4×D89—84no—
374Dic178—44no—
375C22×C89C24×C411yescharacteristic
376C22×C89C2×H(5,𝔽2)11yescharacteristic
377C22×C89C2×2−1+411yescharacteristic
378C22×C89#58512yes—
379C22×C89#58512yes—
380C2×D89—22no—
381C2×D89—22no—
382C2×D89—24no—
383C2×D89—24no—
384C2×D89—24no—
385C2×D89—24no—
386C2×D89—24no—
387C2×D89—42no—
388C2×D89—42no—
389C2×D89—42no—
390C2×D89—42no—
391C2×D89#52014yes—
392C4×C89—22no—
393C4×C89—24no—
394C4×C89—22no—
395C4×C89—24no—
396C4×C89—22no—
397C4×C89—42no—
398C4×C89—42no—
399C4×C89—42no—
400C4×C89—42no—
401Dic89—22no—
402Dic89—24no—
403Dic89—22no—
404Dic89—22no—
405Dic89—42no—
406Dic89—42no—
407Dic89—42no—
408Dic89—42no—
409#34401—891nomaximal, Sylow
410C2×C89C2×#52011yescharacteristic
411C2×C89#342811yescharacteristic
412C2×C89#342811yescharacteristic
413C2×C89#356012yes—
414C2×C89#356412yes—
415D89—24no—
416D89—44no—
417C2×#529—891no—
418#2383—892no—
419#2383—892no—
420#2359—892no—
421#2359—892no—
422#2353—892no—
423#2349—892no—
424#2347—892no—
425#2343—892no—
426#2337—891no—
427#2337—891no—
428#2336—891no—
429#2336D8911yescharacteristic, complemented
430#2329—892no—
431#2325—892no—
432#2320—892no—
433#2318—892no—
434#2285—891no—
435C2×#383—891no—
436C89#3440111yescharacteristic, complemented, Sylow
437#529—8916no—
438C2×#126—892no—
439C2×#125C2×D8911yescharacteristic
440C2×#124—891no—
441C2×#123—892no—
442C2×C22⋊Q8—891no—
443C2×#121—891no—
444C2×C4×Q8—891no—
445C2×C4×D4—891no—
446C2×C4×D4—892no—
447C2×C4×D4—892no—
448C2×C4×D4—892no—
449C2×#117—892no—
450C2×#117—891no—
451C2×#117—891no—
452C22×C42—891no—
453#391—892no—
454#391—892no—
455#389—892no—
456#389—892no—
457#389—892no—
458#389—892no—
459#389—892no—
460#389C2×D8912yes—
461#388—892no—
462#388—892no—
463#388—892no—
464#388—892no—
465#388—892no—
466#388—892no—
467#388—892no—
468#388—892no—
469#387—892no—
470#387—892no—
471#387—892no—
472#387—892no—
473#387—892no—
474#387—892no—
475#387—892no—
476#387—892no—
477#387C2×D8912yes—
478#387C2×D8912yes—
479#387C2×D8912yes—
480#387C2×D8912yes—
481#386—892no—
482#386—892no—
483#386—892no—
484#386—892no—
485#385—892no—
486#385—892no—
487#385—892no—
488#385—892no—
489#385—892no—
490#385—892no—
491#385—892no—
492#385—892no—
493#384—892no—
494#383—891no—
495#383—892no—
496#383—892no—
497#383—892no—
498#383—891no—
499#383—891no—
500#383C2×D8911yescharacteristic
501#382—892no—
502#382—892no—
503#381—892no—
504#380—892no—
505#380—892no—
506#380—892no—
507C4×C4⋊C4—892no—
508C4×C4⋊C4—892no—
509C4×C4⋊C4—891no—
510C4×C4⋊C4—891no—
511C4×C4⋊C4—891no—
512C4×C4⋊C4C2×D8911yescharacteristic
513C4×C4⋊C4C2×D8912yes—
514C4×C22⋊C4—892no—
515C4×C22⋊C4—892no—
516C4×C22⋊C4—892no—
517C4×C22⋊C4—892no—
518C4×C22⋊C4—892no—
519#376—892no—
520C2×#95—892no—
521C2×#95—892no—
522C2×#95—891no—
523C2×#95—891no—
524C2×#95—892no—
525C22×Q8—891no—
526C22×D4—891no—
527C22×D4—892no—
528C23×C4—892no—
529C23×C4—891no—
530C23×C4—891no—
531C23×C4—891no—
532C23×C4—892no—
533C23×C4—892no—
534C23×C4—892no—
535C23×C4—892no—
536#126—8916no—
537#125C4×D8918yescomplemented
538#124—898no—
539#123—8916no—
540C22⋊Q8—898no—
541#121—898no—
542C4×Q8—898no—
543C4×D4—898no—
544C4×D4—8916no—
545C4×D4—3564no—
546C4×D4—3564no—
547#117—8916no—
548#117—3562no—
549#117—3562no—
550C2×C4⋊C4—892no—
551C2×C4⋊C4—892no—
552C2×C4⋊C4—892no—
553C2×C4⋊C4—892no—
554C2×C4⋊C4—892no—
555C2×C4⋊C4—892no—
556C2×C4⋊C4—892no—
557C2×C4⋊C4—892no—
558C2×C4⋊C4—892no—
559C2×C4⋊C4—892no—
560C2×C4⋊C4—892no—
561C2×C4⋊C4C22×D8912yes—
562C2×C4⋊C4C22×D8912yes—
563C2×C4⋊C4C22×D8912yes—
564C2×C4⋊C4C22×D8912yes—
565C2×C4⋊C4C22×D8911yescharacteristic
566C2×C4⋊C4C22×D8912yes—
567C2×C4⋊C4C22×D8911yescharacteristic
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×C22⋊C4—892no—
575C2×C22⋊C4—892no—
576C2×C22⋊C4—892no—
577C2×C22⋊C4—892no—
578C2×C22⋊C4—892no—
579C2×C22⋊C4—892no—
580C2×C22⋊C4—892no—
581C2×C42—891no—
582C2×C42—892no—
583C2×C42—891no—
584C2×C42—891no—
585C2×C42—898no—
586C2×C42—891no—
587C2×C42—891no—
588C2×C42—892no—
589C2×C42—892no—
590C2×C42—892no—
591C2×C42—892no—
592C2×C42C22×D8911yescharacteristic
593C2×C42C22×D8911yescharacteristic
594C2×C42C22×D8912yes—
595C2×C42C22×D8912yes—
596C2×C42C22×D8911yescharacteristic
597#95—892no—
598#95—892no—
599#95—892no—
600#95—892no—
601#95—891no—
602#95—892no—
603#95—892no—
604#95—892no—
605#95—892no—
606#95—892no—
607#95—891no—
608#95—892no—
609#95—892no—
610#95—892no—
611#95—892no—
612#95—892no—
613#95—892no—
614#95—892no—
615#95—892no—
616#95—892no—
617#95—892no—
618#95C22×D8912yes—
619#95C22×D8911yescharacteristic
620#95C22×D8912yes—
621#95C22×D8911yescharacteristic
622#95C22×D8912yes—
623#95C22×D8912yes—
624#95C22×D8912yes—
625#95C22×D8912yes—
626#95C22×D8912yes—
627C24—891no—
628C24—892no—
629C2×Q8—894no—
630C2×Q8—3562no—
631C2×D4—894no—
632C2×D4—898no—
633C2×D4—3562no—
634C2×D4—1784no—
635C2×D4—1784no—
636C22×C4—891no—
637C22×C4—892no—
638C22×C4—891no—
639C22×C4—891no—
640C22×C4—894no—
641C22×C4—894no—
642C22×C4—898no—
643C22×C4—894no—
644C22×C4—892no—
645C22×C4—892no—
646C22×C4—892no—
647C22×C4—892no—
648C22×C4—3562no—
649C22×C4—3562no—
650C22×C4—3562no—
651C22×C4—3562no—
652C22×C4—3562no—
653C22×C4—3562no—
654C22×C4—3562no—
655C22×C4—3562no—
656C22×C4—3562no—
657C22×C4—3562no—
658C22×C4—3562no—
659C22×C4—3562no—
660C22×C4—3562no—
661C22×C4—3562no—
662C22×C4—1782no—
663C22×C4—1782no—
664C22×C4—1784no—
665C22×C4—1784no—
666C22×C4C23×D8912yes—
667C22×C4C23×D8912yes—
668C22×C4C23×D8912yes—
669C22×C4C23×D8912yes—
670C22×C4C23×D8911yescharacteristic
671C22×C4C23×D8911yescharacteristic
672C22×C4C23×D8912yes—
673C22×C4C23×D8912yes—
674C22×C4C23×D8911yescharacteristic
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—898no—
679C4⋊C4—898no—
680C4⋊C4—3562no—
681C4⋊C4—3562no—
682C4⋊C4—3562no—
683C4⋊C4—3562no—
684C4⋊C4—3562no—
685C4⋊C4—3562no—
686C4⋊C4—3562no—
687C4⋊C4—3562no—
688C4⋊C4—3562no—
689C4⋊C4C2×C4×D8918yes—
690C4⋊C4C2×C4×D8914yes—
691C4⋊C4C2×C4×D8918yes—
692C4⋊C4C2×C4×D8914yes—
693C22⋊C4—898no—
694C22⋊C4—898no—
695C22⋊C4—898no—
696C22⋊C4—898no—
697C22⋊C4—898no—
698C22⋊C4—3562no—
699C22⋊C4—3562no—
700C22⋊C4—3562no—
701C22⋊C4—3562no—
702C22⋊C4—3562no—
703C22⋊C4—3562no—
704C22⋊C4—1784no—
705C22⋊C4—1784no—
706C42—41no—
707C42—41no—
708C42—42no—
709C42—42no—
710C42—894no—
711C42—894no—
712C42—894no—
713C42—898no—
714C42—3561no—
715C42—3561no—
716C42—3562no—
717C42—3562no—
718C42—3562no—
719C42—3562no—
720C42C2×C4×D8914yes—
721C23—892no—
722C23—892no—
723C23—892no—
724C23—894no—
725C23—1782no—
726C23—1782no—
727C23—1782no—
728C23—1782no—
729C23—1782no—
730C23—1782no—
731C23—1782no—
732C23—1782no—
733C23C24×D8911yescharacteristic
734Q8—3564no—
735D4—3564no—
736D4—17816no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
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—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—892no—
758C2×C4—892no—
759C2×C4—892no—
760C2×C4—894no—
761C2×C4—3568no—
762C2×C4—3564no—
763C2×C4—3564no—
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—1781no—
778C2×C4—1781no—
779C2×C4—1782no—
780C2×C4—1782no—
781C2×C4—1782no—
782C2×C4—1782no—
783C2×C4—7124no—
784C2×C4—7124no—
785C2×C4—7124no—
786C2×C4—7124no—
787C2×C4C22×C4×D8912yes—
788C2×C4C22×C4×D8912yes—
789C2×C4C22×C4×D8912yes—
790C2×C4C22×C4×D8914yes—
791C2×C4C22×C4×D8914yes—
792C22—894no—
793C22—3562no—
794C22—3562no—
795C22—3562no—
796C22—3562no—
797C22—1784no—
798C22—1784no—
799C22—1784no—
800C22—1782no—
801C22—1782no—
802C22—1784no—
803C22—1784no—
804C22C23×C4×D8911yescharacteristic
805C22H(5,𝔽2)×D8911yescharacteristic
806C222−1+4×D8911yescharacteristic
807C22#1915243412yes—
808C22#1915243512yes—
809C4—22no—
810C4—24no—
811C4—24no—
812C4—22no—
813C4—22no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—3562no—
819C4—3562no—
820C4—3562no—
821C4—3562no—
822C4—1782no—
823C4—1782no—
824C4—1782no—
825C4—1784no—
826C2—3564no—
827C2—1784no—
828C2#520×D8911yescharacteristic
829C2#2603345111yescharacteristic
830C2#2603345411yescharacteristic
831C2#2603480512yes—
832C2#2603486512yes—
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC89×#2336C2
socle, cosocleC23×C89C25
prime radicalC2×#15667987C22
hypercenter#2336D89
hypocenterC89#34401
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2336

Complements

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

NH ≅ G/Ntype
2. #26023443C2semidirect
3. #26023442C2semidirect
4. #26023249C2semidirect
5. #26023237C2semidirect
6. #26023191C2semidirect
7. #26023161C2semidirect
8. #26023141C2semidirect
9. #26023111C2semidirect
10. #26023065C2semidirect
11. #26023062C2semidirect
12. #26023058C2semidirect
13. #26022981C2semidirect
15. #26022901C2semidirect
16. #26022884C2semidirect
17. #26022656C2semidirect
18. #383×D89C2semidirect
19. C89×#2336C2semidirect
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
166. C42×D89C2×C4semidirect
188. #125×C89C2×C4semidirect
429. #2336D89semidirect
436. C89#34401semidirect
537. #125C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#191521332
#260234432
#260234422
#260232492
#260232372
#260231912
#260231612
#260231412
#260231112
#260230652
#260230622
#260230582
#260229812
#260229512
#260229012
#260228842
#260226562
#383×D892
C89×#23362
#3440189