Finite Group Databasebeta

← #36713356

Subgroups — #36713356

Order 22784.

2202 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19152133C211yesmaximal, characteristic
2#26023065C211yesmaximal, characteristic, complemented
3#26023062C211yesmaximal, characteristic, complemented
4#26023058C211yesmaximal, characteristic, complemented
5#26023048C212yesmaximal, complemented
6#26023036C212yesmaximal, complemented
7#26023032C212yesmaximal, complemented
8#26023020C212yesmaximal, complemented
9#26023016C212yesmaximal
10#26023004C212yesmaximal, complemented
11#26022744C212yesmaximal, complemented
12#26022725C212yesmaximal, complemented
13#26022710C212yesmaximal, complemented
14#26022690C212yesmaximal, complemented
15#26022690C212yesmaximal, complemented
16#26022649C211yesmaximal, characteristic, complemented
17C4×#15667970C212yesmaximal, complemented
18C4×#15667970C211yesmaximal, characteristic, complemented
19C89×#2336C211yesmaximal, characteristic, complemented
20#19152133C4116yescomplemented
21C2×#15668007C2212yes—
22C2×#15668000C2211yescharacteristic
23C2×#15667997C2212yes—
24C2×#15667992C2211yescharacteristic
25C2×#15667987C2211yescharacteristic
26C2×#15667977C2211yescharacteristic
27C2×#15667974C2211yescharacteristic
28C2×#15667974C2212yes—
29C2×#15667970C2212yes—
30C2×#15667970C2212yes—
31C2×#15667970C2212yes—
32C2×C42×D89C2212yes—
33C2×C42×D89C2211yescharacteristic
34#19151502C2212yes—
35#19151502C2212yes—
36#19151500C2212yes—
37#19151499C2212yes—
38#19151497C2212yes—
39#19151495C2212yes—
40#19151493C2212yes—
41#19151490C2212yes—
42#19151490C2212yes—
43#19151490C2212yes—
44#19151489C2212yes—
45#19151489C2212yes—
46#19151489C2212yes—
47#19151488C2212yes—
48#19151488C2212yes—
49#19151488C2212yes—
50#19151487C2212yes—
51#19151487C2212yes—
52#19151487C2212yes—
53#19151484C2212yes—
54#19151484C2212yes—
55#19151484C2212yes—
56#19151484C2212yes—
57#19151483C2212yes—
58#19151482C2212yes—
59#19151481C2212yes—
60#19151480C2212yes—
61#19151476C2212yes—
62#19151476C2212yes—
63#19151476C2212yes—
64#19151476C2212yes—
65#19151472C2212yes—
66#19151472C2212yes—
67#19151469C2212yes—
68#19151469C2212yes—
69#19151466C2211yescharacteristic
70#19151462C2211yescharacteristic
71#19151462C2211yescharacteristic
72#19151460C2212yes—
73#19151457C2212yes—
74C4⋊C4×Dic89C2212yes—
75C4⋊C4×Dic89C2212yes—
76C4⋊C4×Dic89C2212yes—
77C4⋊C4×Dic89C2212yes—
78C4×C4⋊Dic89C2212yes—
79C4×C4⋊Dic89C2211yescharacteristic
80#19151449C2212yes—
81#19151449C2212yes—
82C4×#13083551C2212yes—
83C4×#13083551C2211yescharacteristic
84C4×#13083551C2212yes—
85C4×#13083551C2211yescharacteristic
86#19151445C2212yes—
87#19151445C2211yescharacteristic
88#19151445C2212yes—
89#19151445C2211yescharacteristic
90#19151445C2212yes—
91#19151445C2212yes—
92#19151445C2212yes—
93#19151443C2212yes—
94#19151443C2212yes—
95#19151443C2212yes—
96C42×Dic89C2212yes—
97C42×Dic89C2211yescharacteristic
98C42×Dic89C2211yescharacteristic
99C2×#125×C89C2211yescharacteristic
100#389×C89C2212yes—
101#387×C89C2212yes—
102#387×C89C2212yes—
103#387×C89C2212yes—
104#387×C89C2212yes—
105#383×C89C2211yescharacteristic
106C4×C4⋊C4×C89C2212yes—
107C4×C4⋊C4×C89C2211yescharacteristic
108C22×Dic178C2311yescharacteristic
109C22×D356C2311yescharacteristic
110C22×D356C2312yes—
111C22×C4×D89C2311yescharacteristic
112C22×C4×D89C2312yes—
113C22×C4×D89C2312yes—
114C22×C4×D89C2312yes—
115C22×C4×D89C2311yescharacteristic
116C22×C4×D89C2311yescharacteristic
117#15668007C2×C4116yescomplemented
118#15668000C2×C418yes—
119#15667997C2×C4116yescomplemented
120#15667992C2×C418yescomplemented
121#15667987C2×C418yes—
122#15667977C2×C418yescomplemented
123#15667974C2×C418yes—
124#15667974C2×C4116yescomplemented
125#15667970—28no—
126#15667970—28no—
127#15667970C2×C4116yescomplemented
128C2×C4⋊Dic89C2312yes—
129C2×C4⋊Dic89C2312yes—
130C2×C4⋊Dic89C2312yes—
131C2×C4⋊Dic89C2312yes—
132C2×#13083553C2312yes—
133C2×#13083553C2312yes—
134C2×#13083553C2312yes—
135C2×#13083553C2312yes—
136C2×#13083553C2312yes—
137C2×#13083551C2312yes—
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×#13083551C2312yes—
152C2×C4×Dic89C2312yes—
153C2×C4×Dic89C2312yes—
154C2×C4×Dic89C2312yes—
155C2×C4×Dic89C2312yes—
156C2×C4×Dic89C2311yescharacteristic
157C2×C4×Dic89C2312yes—
158C2×C4×Dic89C2312yes—
159C2×C4×Dic89C2312yes—
160C2×C4×Dic89C2312yes—
161C2×C4×Dic89C2311yescharacteristic
162C2×C4×Dic89C2312yes—
163C2×C4×Dic89C2311yescharacteristic
164C2×C4×Dic89C2312yes—
165C2×C4×Dic89C2311yescharacteristic
166C2×C4×Dic89C2311yescharacteristic
167C2×C4×Dic89C2312yes—
168C42×D89—28no—
169C42×D89C2×C418yescomplemented
170#15667919C2312yes—
171#15667919C2312yes—
172#15667919C2312yes—
173#15667919C2312yes—
174#15667919C2312yes—
175#15667919C2312yes—
176#15667919C2312yes—
177#15667919C2312yes—
178#15667919C2312yes—
179#15667919C2311yescharacteristic
180#15667919C2311yescharacteristic
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×C4⋊C4×C89C2312yes—
195C2×C42×C89C2312yes—
196C2×C42×C89C2311yescharacteristic
197C2×C42×C89C2311yescharacteristic
198C2×C42×C89C2312yes—
199C2×C42×C89C2311yescharacteristic
200#95×C89C2312yes—
201#95×C89C2312yes—
202#95×C89C2312yes—
203#95×C89C2311yescharacteristic
204#95×C89C2312yes—
205#95×C89C2311yescharacteristic
206#95×C89C2312yes—
207#95×C89C2312yes—
208#95×C89C2312yes—
209C23×D89C2411yescharacteristic
210C23×D89C2412yes—
211C2×Dic178—42no—
212C2×Dic178C22×C414yes—
213C2×D356—42no—
214C2×D356—42no—
215C2×D356—42no—
216C2×D356C22×C414yes—
217C2×D356C22×C418yes—
218C22×Dic89C2412yes—
219C22×Dic89C2412yes—
220C22×Dic89C2412yes—
221C22×Dic89C2411yescharacteristic
222C22×Dic89C2411yescharacteristic
223C22×Dic89C2412yes—
224C22×Dic89C2412yes—
225C22×Dic89C2411yescharacteristic
226C2×C4×D89—24no—
227C2×C4×D89—24no—
228C2×C4×D89—24no—
229C2×C4×D89—24no—
230C2×C4×D89—24no—
231C2×C4×D89—42no—
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×D89C22×C418yes—
239C2×C4×D89C22×C414yes—
240C2×C4×D89C22×C414yes—
241C2×C4×D89C22×C414yes—
242C4⋊Dic89—24no—
243C4⋊Dic89—24no—
244C4⋊Dic89—42no—
245C4⋊Dic89C22×C418yes—
246#13083553—42no—
247#13083553—42no—
248#13083553—42no—
249#13083553—42no—
250#13083553C22×C418yes—
251#13083551—24no—
252#13083551—24no—
253#13083551—24no—
254#13083551—24no—
255#13083551—42no—
256#13083551—42no—
257#13083551—42no—
258#13083551—42no—
259#13083551—42no—
260#13083551—42no—
261#13083551C22×C418yes—
262#13083551C22×C418yes—
263#13083551C22×C418yes—
264#13083551C22×C418yes—
265#13083551C22×C418yes—
266C4×Dic89—24no—
267C4×Dic89—24no—
268C4×Dic89—24no—
269C4×Dic89—24no—
270C4×Dic89—42no—
271C4×Dic89—41no—
272C4×Dic89—42no—
273C4×Dic89—42no—
274C4×Dic89—42no—
275C4×Dic89—42no—
276C4×Dic89—41no—
277C4×Dic89C22×C414yes—
278C4×Dic89C22×C418yes—
279C4×Dic89C22×C414yes—
280C4×Dic89C22×C414yes—
281C4×Dic89#4118yes—
282C22×C4×C89C2412yes—
283C22×C4×C89C2412yes—
284C22×C4×C89C2412yes—
285C22×C4×C89C2411yescharacteristic
286C22×C4×C89C2411yescharacteristic
287C22×C4×C89C2412yes—
288C22×C4×C89C2411yescharacteristic
289C22×C4×C89C2412yes—
290C22×C4×C89C2412yes—
291C4⋊C4×C89—24no—
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—41no—
300C42×C89—42no—
301C42×C89—41no—
302C42×C89C22×C414yes—
303C23×C89C2511yescharacteristic
304C22×D89—22no—
305C22×D89—22no—
306C22×D89—22no—
307C22×D89—22no—
308C22×D89—22no—
309C22×D89—22no—
310C22×D89—22no—
311C22×D89—22no—
312C22×D89—21no—
313C22×D89—21no—
314C22×D89C23×C414yes—
315C22×D89C23×C412yes—
316C2×C4×C89—22no—
317C2×C4×C89—22no—
318C2×C4×C89—22no—
319C2×C4×C89—21no—
320C2×C4×C89—22no—
321C2×C4×C89—22no—
322C2×C4×C89—21no—
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×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—22no—
346C2×Dic89—21no—
347C2×Dic89—21no—
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×Dic89C23×C412yes—
358C2×Dic89C23×C412yes—
359C2×Dic89C23×C414yes—
360C2×Dic89C23×C412yes—
361C2×Dic89C2×#4114yes—
362C2×Dic89C2×#4114yes—
363D356—44no—
364D356—48no—
365C4×D89—28no—
366C4×D89—216no—
367C4×D89—44no—
368C4×D89—44no—
369C4×D89—48no—
370C4×D89—48no—
371Dic178—44no—
372C22×C89C24×C411yescharacteristic
373C22×C89C22×#4112yes—
374C22×C89#58511yescharacteristic
375C22×C89#58511yescharacteristic
376C22×C89#58512yes—
377C2×D89—22no—
378C2×D89—24no—
379C2×D89—22no—
380C2×D89—22no—
381C2×D89—24no—
382C2×D89—24no—
383C2×D89—42no—
384C2×D89—42no—
385C2×D89—42no—
386C2×D89—42no—
387C2×D89—42no—
388C2×D89—42no—
389C4×C89—24no—
390C4×C89—22no—
391C4×C89—22no—
392C4×C89—22no—
393C4×C89—24no—
394C4×C89—24no—
395C4×C89—42no—
396C4×C89—42no—
397C4×C89—42no—
398Dic89—24no—
399Dic89—22no—
400Dic89—22no—
401Dic89—24no—
402Dic89—42no—
403Dic89—42no—
404Dic89—42no—
405Dic89C4×#4114yes—
406#34081—891nomaximal, Sylow
407C2×C89C2×C4×#4111yescharacteristic
408C2×C89#342811yescharacteristic
409C2×C89#342811yescharacteristic
410C2×C89#345512yes—
411C2×C89#345512yes—
412D89—42no—
413D89—44no—
414C2×#529—891no—
415#2337—891no—
416#2337—891no—
417#2336—891no—
418#2336D8911yescharacteristic, complemented
419#2335—892no—
420#2335—892no—
421#2334—892no—
422#2334—892no—
423#2333—892no—
424#2332—892no—
425#2298—892no—
426#2295—892no—
427#2293—892no—
428#2290—892no—
429#2290—892no—
430#2283—891no—
431C4×#117—892no—
432C4×#117—891no—
433C89#3408111yescharacteristic, complemented, Sylow
434#529—8916no—
435C2×#126—892no—
436C2×#125C2×D8911yescharacteristic
437C2×#124—891no—
438C2×#123—892no—
439C2×C22⋊Q8—891no—
440C2×#121—891no—
441C2×C4×Q8—891no—
442C2×C4×D4—891no—
443C2×C4×D4—892no—
444C2×#117—892no—
445C2×#117—892no—
446C2×#117—892no—
447C22×C42—891no—
448C22×C42—892no—
449#391—892no—
450#391—892no—
451#390—892no—
452#390—892no—
453#389—892no—
454#389—892no—
455#389—892no—
456#389C2×D8912yes—
457#388—892no—
458#388—892no—
459#388—892no—
460#388—892no—
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#383—891no—
490#383C2×D8911yescharacteristic
491#382—891no—
492#382—891no—
493#381—892no—
494#380—892no—
495C4×C4⋊C4—892no—
496C4×C4⋊C4—892no—
497C4×C4⋊C4—892no—
498C4×C4⋊C4—892no—
499C4×C4⋊C4—892no—
500C4×C4⋊C4—891no—
501C4×C4⋊C4—892no—
502C4×C4⋊C4—892no—
503C4×C4⋊C4C2×D8912yes—
504C4×C4⋊C4C2×D8911yescharacteristic
505C4×C22⋊C4—892no—
506C4×C22⋊C4—891no—
507C4×C22⋊C4—891no—
508C4×C22⋊C4—892no—
509C4×C22⋊C4—892no—
510C4×C22⋊C4—892no—
511C4×C22⋊C4—892no—
512C4×C22⋊C4—891no—
513C4×C22⋊C4—891no—
514C4×C22⋊C4—892no—
515C4×C22⋊C4—892no—
516#376—892no—
517#376—892no—
518#376—892no—
519C43—891no—
520C43—892no—
521C43—891no—
522C22×Q8—891no—
523C22×D4—892no—
524C22×D4—891no—
525C23×C4—891no—
526C23×C4—891no—
527C23×C4—891no—
528C23×C4—892no—
529C23×C4—892no—
530C23×C4—892no—
531#126—8916no—
532#125C4×D8918yescomplemented
533#124—898no—
534#123—8916no—
535C22⋊Q8—898no—
536#121—898no—
537C4×Q8—898no—
538C4×D4—898no—
539C4×D4—8916no—
540#117—8916no—
541#117—1788no—
542#117—1788no—
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×D8912yes—
554C2×C4⋊C4C22×D8912yes—
555C2×C4⋊C4C22×D8912yes—
556C2×C4⋊C4C22×D8911yescharacteristic
557C2×C4⋊C4C22×D8912yes—
558C2×C4⋊C4C22×D8911yescharacteristic
559C2×C22⋊C4—892no—
560C2×C22⋊C4—892no—
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—892no—
577C2×C42—891no—
578C2×C42—891no—
579C2×C42—898no—
580C2×C42—891no—
581C2×C42—892no—
582C2×C42—892no—
583C2×C42—891no—
584C2×C42—892no—
585C2×C42—892no—
586C2×C42—892no—
587C2×C42—892no—
588C2×C42—892no—
589C2×C42—892no—
590C2×C42—892no—
591C2×C42—1788no—
592C2×C42C22×D8912yes—
593C2×C42C22×D8911yescharacteristic
594C2×C42C22×D8912yes—
595C2×C42C22×D8911yescharacteristic
596C2×C42C22×D8911yescharacteristic
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—891no—
607#95—891no—
608#95—892no—
609#95—892no—
610#95—892no—
611#95—892no—
612#95—892no—
613#95—892no—
614#95C22×D8912yes—
615#95C22×D8912yes—
616#95C22×D8912yes—
617#95C22×D8911yescharacteristic
618#95C22×D8911yescharacteristic
619#95C22×D8912yes—
620#95C22×D8912yes—
621#95C22×D8912yes—
622#95C22×D8912yes—
623C24—892no—
624C24—891no—
625C2×Q8—894no—
626C2×Q8—3562no—
627C2×D4—898no—
628C2×D4—894no—
629C2×D4—3562no—
630C2×D4—3562no—
631C2×D4—3562no—
632C22×C4—891no—
633C22×C4—891no—
634C22×C4—892no—
635C22×C4—892no—
636C22×C4—891no—
637C22×C4—894no—
638C22×C4—894no—
639C22×C4—894no—
640C22×C4—898no—
641C22×C4—892no—
642C22×C4—892no—
643C22×C4—892no—
644C22×C4—3562no—
645C22×C4—3561no—
646C22×C4—3562no—
647C22×C4—3561no—
648C22×C4—3562no—
649C22×C4—3562no—
650C22×C4—3562no—
651C22×C4—1784no—
652C22×C4—1784no—
653C22×C4—1784no—
654C22×C4—1784no—
655C22×C4—1784no—
656C22×C4C23×D8912yes—
657C22×C4C23×D8912yes—
658C22×C4C23×D8912yes—
659C22×C4C23×D8911yescharacteristic
660C22×C4C23×D8911yescharacteristic
661C22×C4C23×D8912yes—
662C22×C4C23×D8912yes—
663C22×C4C23×D8911yescharacteristic
664C22×C4C23×D8912yes—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—42no—
668C4⋊C4—898no—
669C4⋊C4—898no—
670C4⋊C4—3562no—
671C4⋊C4—3562no—
672C4⋊C4—3562no—
673C4⋊C4—3562no—
674C4⋊C4—3562no—
675C4⋊C4—1784no—
676C4⋊C4—1784no—
677C4⋊C4C2×C4×D8918yes—
678C4⋊C4C2×C4×D8914yes—
679C4⋊C4C2×C4×D8918yes—
680C4⋊C4C2×C4×D8914yes—
681C22⋊C4—898no—
682C22⋊C4—898no—
683C22⋊C4—898no—
684C22⋊C4—898no—
685C22⋊C4—898no—
686C22⋊C4—3562no—
687C22⋊C4—3562no—
688C22⋊C4—3562no—
689C22⋊C4—3562no—
690C22⋊C4—3562no—
691C22⋊C4—3562no—
692C22⋊C4—1784no—
693C22⋊C4—1784no—
694C22⋊C4—1784no—
695C22⋊C4—1784no—
696C42—24no—
697C42—41no—
698C42—42no—
699C42—41no—
700C42—894no—
701C42—894no—
702C42—894no—
703C42—898no—
704C42—898no—
705C42—3562no—
706C42—3561no—
707C42—3561no—
708C42—3562no—
709C42—3562no—
710C42—3562no—
711C42—3562no—
712C42—1784no—
713C42—1784no—
714C42—1784no—
715C42—1784no—
716C42C2×C4×D8914yes—
717C23—894no—
718C23—892no—
719C23—1782no—
720C23—1782no—
721C23—1782no—
722C23—1782no—
723C23—1781no—
724C23—1782no—
725C23—1782no—
726C23—1782no—
727C23—1782no—
728C23—1781no—
729C23C24×D8911yescharacteristic
730Q8—3564no—
731D4—3568no—
732D4—3564no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
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—892no—
753C2×C4—894no—
754C2×C4—892no—
755C2×C4—892no—
756C2×C4—894no—
757C2×C4—894no—
758C2×C4—3568no—
759C2×C4—3564no—
760C2×C4—3564no—
761C2×C4—3568no—
762C2×C4—1788no—
763C2×C4—17816no—
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—1781no—
774C2×C4—1782no—
775C2×C4—1782no—
776C2×C4—1782no—
777C2×C4—1782no—
778C2×C4—1782no—
779C2×C4—1781no—
780C2×C4C22×C4×D8912yes—
781C2×C4C22×C4×D8912yes—
782C2×C4C22×C4×D8912yes—
783C2×C4C22×C4×D8914yes—
784C2×C4C22×C4×D8914yes—
785C2×C4#41×D8914yes—
786C22—3562no—
787C22—3562no—
788C22—3562no—
789C22—3562no—
790C22—3562no—
791C22—3562no—
792C22—1784no—
793C22—1782no—
794C22—1782no—
795C22—1784no—
796C22—1782no—
797C22—1784no—
798C22C23×C4×D8911yescharacteristic
799C22C2×#41×D8912yes—
800C22#1915243311yescharacteristic
801C22#1915243511yescharacteristic
802C22#1915243512yes—
803C4—24no—
804C4—22no—
805C4—22no—
806C4—24no—
807C4—22no—
808C4—24no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—894no—
813C4—3562no—
814C4—3562no—
815C4—3562no—
816C4—1782no—
817C4—1782no—
818C4—1784no—
819C4—1784no—
820C2—3564no—
821C2—3562no—
822C2C4×#41×D8911yescharacteristic
823C2#2603345211yescharacteristic
824C2#2603345411yescharacteristic
825C2#2603363812yes—
826C2#2603364312yes—
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC89×#2336C2
socle, cosocleC23×C89C25
prime radicalC2×#15667987C22
hypercenter#2336D89
hypocenterC89#34081
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2336

Complements

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

NH ≅ G/Ntype
2. #26023065C2semidirect
3. #26023062C2semidirect
4. #26023058C2semidirect
5. #26023048C2semidirect
6. #26023036C2semidirect
7. #26023032C2semidirect
8. #26023020C2semidirect
10. #26023004C2semidirect
11. #26022744C2semidirect
12. #26022725C2semidirect
13. #26022710C2semidirect
14. #26022690C2semidirect
15. #26022690C2semidirect
16. #26022649C2semidirect
17. C4×#15667970C2semidirect
18. C4×#15667970C2semidirect
19. C89×#2336C2semidirect
20. #19152133C4semidirect
117. #15668007C2×C4semidirect
119. #15667997C2×C4semidirect
120. #15667992C2×C4semidirect
122. #15667977C2×C4semidirect
124. #15667974C2×C4semidirect
127. #15667970C2×C4semidirect
169. C42×D89C2×C4semidirect
187. #125×C89C2×C4semidirect
418. #2336D89semidirect
433. C89#34081semidirect
532. #125C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#191521332
#260230652
#260230622
#260230582
#260230482
#260230362
#260230322
#260230202
#260230162
#260230042
#260227442
#260227252
#260227102
#260226902
#260226492
C4×#156679702
C89×#23362
#3408189