Finite Group Databasebeta

← #36717137

Subgroups — #36717137

Order 22784.

2024 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19152352C211yesmaximal, characteristic
2#26023443C212yesmaximal, complemented
3#26023442C212yesmaximal, complemented
4#26023437C211yesmaximal, characteristic, complemented
5#26023430C212yesmaximal, complemented
6#26023423C211yesmaximal, characteristic
7#26023417C212yesmaximal, complemented
8#26023416C212yesmaximal, complemented
9#26023397C212yesmaximal
10#26022823C212yesmaximal, complemented
11#125×Dic89C211yesmaximal, characteristic, complemented
12#26022807C211yesmaximal, characteristic, complemented
13#26022802C212yesmaximal, complemented
14#26022802C212yesmaximal, complemented
15#26022791C211yesmaximal, characteristic
16#26022786C212yesmaximal, complemented
17#26022782C212yesmaximal, complemented
18#26022773C212yesmaximal
19C89×#2382C211yesmaximal, characteristic, complemented
20#19152352C4116yescomplemented
21C2×#15668011C2212yes—
22C2×#15668007C2212yes—
23C2×#15668007C2212yes—
24C2×#15668004C2211yescharacteristic
25C2×#15668000C2211yescharacteristic
26C2×#15667997C2212yes—
27C2×#15667992C2212yes—
28C2×#15667990C2212yes—
29C2×#15667977C2212yes—
30C2×#15667977C2211yescharacteristic
31C2×#15667974C2211yescharacteristic
32C2×C42×D89C2212yes—
33#19151504C2212yes—
34#19151503C2211yescharacteristic
35#19151502C2212yes—
36#19151502C2212yes—
37#19151502C2212yes—
38#19151499C2211yescharacteristic
39#19151497C2211yescharacteristic
40#19151497C2211yescharacteristic
41#19151496C2212yes—
42#19151495C2212yes—
43#19151494C2211yescharacteristic
44#19151494C2211yescharacteristic
45#19151493C2212yes—
46#19151493C2212yes—
47#19151490C2212yes—
48#19151490C2212yes—
49#19151490C2212yes—
50#19151489C2212yes—
51#19151489C2212yes—
52#19151489C2212yes—
53#19151488C2212yes—
54#19151488C2212yes—
55#19151487C2212yes—
56#19151487C2212yes—
57#19151485C2212yes—
58#19151485C2212yes—
59#19151484C2212yes—
60#19151484C2212yes—
61#19151483C2212yes—
62#19151483C2212yes—
63#19151482C2212yes—
64#19151481C2212yes—
65#19151481C2212yes—
66#19151480C2212yes—
67#19151480C2212yes—
68#19151479C2212yes—
69#19151476C2212yes—
70#19151472C2212yes—
71#19151472C2212yes—
72#19151469C2212yes—
73#19151469C2212yes—
74#19151469C2212yes—
75#19151467C2212yes—
76#19151465C2212yes—
77#19151465C2212yes—
78#19151464C2211yescharacteristic
79#19151460C2212yes—
80#19151457C2212yes—
81#19151455C2212yes—
82C4⋊C4×Dic89C2212yes—
83C4⋊C4×Dic89C2211yescharacteristic
84C4⋊C4×Dic89C2212yes—
85C4⋊C4×Dic89C2212yes—
86C4⋊C4×Dic89C2211yescharacteristic
87C4⋊C4×Dic89C2211yescharacteristic
88C4⋊C4×Dic89C2211yescharacteristic
89#19151449C2212yes—
90#19151449C2212yes—
91#19151449C2212yes—
92#19151445C2212yes—
93#19151445C2212yes—
94#19151445C2212yes—
95#19151445C2212yes—
96#19151445C2212yes—
97C42×Dic89C2211yescharacteristic
98C42×Dic89C2212yes—
99C2×#125×C89C2211yescharacteristic
100#389×C89C2212yes—
101#389×C89C2212yes—
102#387×C89C2212yes—
103#387×C89C2212yes—
104#387×C89C2212yes—
105#387×C89C2212yes—
106#382×C89C2211yescharacteristic
107#382×C89C2211yescharacteristic
108C22×Dic178C2311yescharacteristic
109C22×Dic178C2312yes—
110C22×D356C2311yescharacteristic
111C22×C4×D89C2312yes—
112C22×C4×D89C2312yes—
113C22×C4×D89C2312yes—
114#15668011C2×C4116yescomplemented
115#15668007C2×C4116yescomplemented
116#15668007C2×C4116yescomplemented
117#15668004C2×C418yescomplemented
118#15668000C2×C418yes—
119#15667997C2×C4116yes—
120#15667992C2×C4116yescomplemented
121#15667990C2×C4116yescomplemented
122#15667977—42no—
123#15667977—44no—
124#15667974—42no—
125C2×C4⋊Dic89C2312yes—
126C2×C4⋊Dic89C2311yescharacteristic
127C2×C4⋊Dic89C2311yescharacteristic
128C2×C4⋊Dic89C2312yes—
129C2×C4⋊Dic89C2312yes—
130C2×C4⋊Dic89C2311yescharacteristic
131C2×C4⋊Dic89C2311yescharacteristic
132C2×#13083553C2312yes—
133C2×#13083553C2312yes—
134C2×#13083553C2312yes—
135C2×#13083553C2312yes—
136C2×#13083553C2312yes—
137C2×#13083553C2312yes—
138C2×#13083553C2312yes—
139C2×#13083553C2312yes—
140C2×#13083553C2312yes—
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×Dic89C2311yescharacteristic
154C2×C4×Dic89C2312yes—
155C2×C4×Dic89C2311yescharacteristic
156C2×C4×Dic89C2312yes—
157C2×C4×Dic89C2311yescharacteristic
158C2×C4×Dic89C2312yes—
159C2×C4×Dic89C2312yes—
160C2×C4×Dic89C2311yescharacteristic
161C2×C4×Dic89C2311yescharacteristic
162C2×C4×Dic89C2312yes—
163C2×C4×Dic89C2312yes—
164C2×C4×Dic89C2311yescharacteristic
165C2×C4×Dic89C2312yes—
166C2×C4×Dic89C2312yes—
167C42×D89—44no—
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—
184#15667919C2312yes—
185#15667919C2312yes—
186#125×C89C2×C418yescomplemented
187C2×C4⋊C4×C89C2311yescharacteristic
188C2×C4⋊C4×C89C2311yescharacteristic
189C2×C4⋊C4×C89C2311yescharacteristic
190C2×C4⋊C4×C89C2311yescharacteristic
191C2×C4⋊C4×C89C2312yes—
192C2×C4⋊C4×C89C2312yes—
193C2×C4⋊C4×C89C2311yescharacteristic
194C2×C4⋊C4×C89C2311yescharacteristic
195C2×C4⋊C4×C89C2312yes—
196C2×C4⋊C4×C89C2312yes—
197C2×C42×C89C2312yes—
198C2×C42×C89C2312yes—
199C2×C42×C89C2311yescharacteristic
200#95×C89C2312yes—
201#95×C89C2312yes—
202#95×C89C2312yes—
203#95×C89C2312yes—
204#95×C89C2312yes—
205#95×C89C2312yes—
206#95×C89C2312yes—
207#95×C89C2312yes—
208C23×D89C2412yes—
209C2×Dic178—42no—
210C2×Dic178—41no—
211C2×Dic178—41no—
212C2×Dic178—42no—
213C2×Dic178C22×C418yes—
214C2×Dic178C22×C414yes—
215C2×D356—41no—
216C2×D356—41no—
217C2×D356C22×C414yes—
218C22×Dic89C2412yes—
219C22×Dic89C2411yescharacteristic
220C22×Dic89C2411yescharacteristic
221C22×Dic89C2412yes—
222C22×Dic89C2411yescharacteristic
223C22×Dic89C2412yes—
224C22×Dic89C2412yes—
225C22×Dic89C2412yes—
226C22×Dic89C2411yescharacteristic
227C2×C4×D89—24no—
228C2×C4×D89—24no—
229C2×C4×D89—24no—
230C2×C4×D89—42no—
231C2×C4×D89—42no—
232C2×C4×D89—42no—
233C2×C4×D89—42no—
234C2×C4×D89—42no—
235C2×C4×D89C22×C418yes—
236C4⋊Dic89—41no—
237C4⋊Dic89—42no—
238C4⋊Dic89—42no—
239C4⋊Dic89—41no—
240C4⋊Dic89C22×C414yes—
241C4⋊Dic89C22×C418yes—
242C4⋊Dic89C22×C414yes—
243#13083553—42no—
244#13083553—42no—
245#13083553—42no—
246#13083553—42no—
247#13083553—42no—
248#13083553—42no—
249#13083553C22×C418yes—
250#13083553C22×C418yes—
251#13083553C22×C418yes—
252#13083551—42no—
253#13083551—42no—
254#13083551—42no—
255#13083551—42no—
256#13083551—42no—
257#13083551—42no—
258#13083551C22×C418yes—
259#13083551C22×C418yes—
260#13083551C22×C418yes—
261#13083551C22×C418yes—
262#13083551C22×C418yes—
263C4×Dic89—22no—
264C4×Dic89—24no—
265C4×Dic89—24no—
266C4×Dic89—24no—
267C4×Dic89—24no—
268C4×Dic89—22no—
269C4×Dic89—22no—
270C4×Dic89—24no—
271C4×Dic89—42no—
272C4×Dic89—42no—
273C4×Dic89—42no—
274C4×Dic89—41no—
275C4×Dic89—41no—
276C4×Dic89—41no—
277C4×Dic89C22×C418yes—
278C22×C4×C89C2412yes—
279C22×C4×C89C2412yes—
280C22×C4×C89C2412yes—
281C22×C4×C89C2412yes—
282C22×C4×C89C2412yes—
283C22×C4×C89C2411yescharacteristic
284C22×C4×C89C2411yescharacteristic
285C22×C4×C89C2412yes—
286C22×C4×C89C2411yescharacteristic
287C4⋊C4×C89—41no—
288C4⋊C4×C89—42no—
289C4⋊C4×C89—41no—
290C4⋊C4×C89—42no—
291C4⋊C4×C89—41no—
292C4⋊C4×C89—41no—
293C4⋊C4×C89C22×C414yes—
294C4⋊C4×C89C22×C418yes—
295C4⋊C4×C89C22×C418yes—
296C4⋊C4×C89C22×C414yes—
297C42×C89—42no—
298C42×C89—42no—
299C42×C89C22×C414yes—
300C23×C89C2511yescharacteristic
301C22×D89—22no—
302C22×D89—22no—
303C22×D89—22no—
304C22×D89—22no—
305C22×D89—22no—
306C22×D89—22no—
307C22×D89C23×C414yes—
308C2×C4×C89—22no—
309C2×C4×C89—21no—
310C2×C4×C89—21no—
311C2×C4×C89—22no—
312C2×C4×C89—21no—
313C2×C4×C89—22no—
314C2×C4×C89—21no—
315C2×C4×C89—21no—
316C2×C4×C89—21no—
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—22no—
325C2×C4×C89—22no—
326C2×C4×C89—22no—
327C2×C4×C89—22no—
328C2×C4×C89—22no—
329C2×C4×C89—22no—
330C2×C4×C89C23×C412yes—
331C2×C4×C89C23×C412yes—
332C2×C4×C89C23×C412yes—
333C2×C4×C89C23×C414yes—
334C2×C4×C89C23×C414yes—
335C2×Dic89—22no—
336C2×Dic89—22no—
337C2×Dic89—22no—
338C2×Dic89—22no—
339C2×Dic89—22no—
340C2×Dic89—22no—
341C2×Dic89—22no—
342C2×Dic89—21no—
343C2×Dic89—21no—
344C2×Dic89—21no—
345C2×Dic89—22no—
346C2×Dic89—21no—
347C2×Dic89—21no—
348C2×Dic89—22no—
349C2×Dic89—22no—
350C2×Dic89—21no—
351C2×Dic89—21no—
352C2×Dic89—21no—
353C2×Dic89—21no—
354C2×Dic89—22no—
355C2×Dic89—22no—
356C2×Dic89C23×C414yes—
357C2×Dic89C23×C414yes—
358C2×Dic89C23×C414yes—
359C2×Dic89H(5,𝔽2)12yes—
360C2×Dic892−1+412yes—
361C2×Dic892−1+412yes—
362D356—44no—
363C4×D89—48no—
364C4×D89—48no—
365C4×D89—48no—
366Dic178—44no—
367Dic178—48no—
368C22×C89C24×C411yescharacteristic
369C22×C89C2×H(5,𝔽2)11yescharacteristic
370C22×C89C2×2−1+411yescharacteristic
371C22×C89C2×2−1+411yescharacteristic
372C22×C89#58511yescharacteristic
373C22×C89#58511yescharacteristic
374C22×C89#58511yescharacteristic
375C2×D89—24no—
376C2×D89—24no—
377C2×D89—24no—
378C2×D89—42no—
379C2×D89—42no—
380C2×D89—42no—
381C2×D89—42no—
382C4×C89—24no—
383C4×C89—22no—
384C4×C89—22no—
385C4×C89—24no—
386C4×C89—22no—
387C4×C89—42no—
388C4×C89—42no—
389C4×C89—42no—
390C4×C89—42no—
391Dic89—24no—
392Dic89—24no—
393Dic89—24no—
394Dic89—42no—
395Dic89—41no—
396Dic89—41no—
397Dic89—41no—
398Dic89—42no—
399Dic89#56314yescomplemented
400C4×#563—891nomaximal, Sylow
401C2×C89C4×H(5,𝔽2)11yescharacteristic
402C2×C89C4×2−1+411yescharacteristic
403C2×C89C4×2−1+411yescharacteristic
404C2×C89C2×#56311yescharacteristic
405C2×C89#352911yescharacteristic
406C2×C89#353111yescharacteristic
407C2×C89#353111yescharacteristic
408D89—44no—
409C2×#563—891no—
410#2383—892no—
411#2383—892no—
412#2382—891no—
413#2382D8911yescharacteristic, complemented
414#2381—892no—
415#2379—891no—
416#2378—892no—
417#2378—892no—
418#2376—892no—
419C4×C4⋊Q8—892no—
420C4×#125—891no—
421C4×#125—891no—
422C4×#126—892no—
423C4×#126—892no—
424C4×#124—891no—
425C4×C22⋊Q8—892no—
426C4×C22⋊Q8—892no—
427C4×#123—892no—
428C89C4×#56311yescharacteristic, complemented, Sylow
429#563—8916no—
430C2×C4⋊Q8—892no—
431C2×#126—892no—
432C2×#126—892no—
433C2×#125—891no—
434C2×#125C2×D8911yescharacteristic
435C2×#124—891no—
436C2×#123—892no—
437C2×C22⋊Q8—892no—
438C2×C22⋊Q8—892no—
439C2×C4×Q8—891no—
440C2×C4×Q8—892no—
441C2×C4×D4—891no—
442C22×C42—892no—
443#391—891no—
444#391—892no—
445#391—892no—
446#391—892no—
447#391—892no—
448#390—891no—
449#389—891no—
450#389—891no—
451#389—891no—
452#389—891no—
453#389—892no—
454#389—892no—
455#389—892no—
456#389—892no—
457#389C2×D8912yes—
458#389C2×D8912yes—
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#387—892no—
478#387—892no—
479#387—892no—
480#387—892no—
481#387C2×D8912yes—
482#387C2×D8912yes—
483#387C2×D8912yes—
484#387C2×D8912yes—
485#386—892no—
486#385—892no—
487#385—892no—
488#385—892no—
489#385—892no—
490#385—892no—
491#384—892no—
492#383—892no—
493#383—892no—
494#382—891no—
495#382C2×D8911yescharacteristic
496#382C2×D8911yescharacteristic
497#381—892no—
498#380—892no—
499#380—892no—
500C4×C4⋊C4—891no—
501C4×C4⋊C4—891no—
502C4×C4⋊C4—892no—
503C4×C4⋊C4—892no—
504C4×C4⋊C4—892no—
505C4×C4⋊C4—891no—
506C4×C4⋊C4—891no—
507C4×C4⋊C4—892no—
508C4×C4⋊C4—892no—
509C4×C4⋊C4—892no—
510C4×C22⋊C4—892no—
511C4×C22⋊C4—892no—
512C4×C22⋊C4—892no—
513C4×C22⋊C4—892no—
514C4×C22⋊C4—892no—
515C43—892no—
516C43—891no—
517C22×Q8—892no—
518C22×Q8—891no—
519C22×D4—891no—
520C23×C4—892no—
521C23×C4—892no—
522C23×C4—892no—
523C4⋊Q8—8916no—
524#126—8916no—
525#126—8916no—
526#125—898no—
527#125C4×D8918yescomplemented
528#124—898no—
529#123—8916no—
530C22⋊Q8—8916no—
531C22⋊Q8—8916no—
532C4×Q8—3564no—
533C4×Q8—3562no—
534C4×D4—3562no—
535C2×C4⋊C4—891no—
536C2×C4⋊C4—892no—
537C2×C4⋊C4—892no—
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—891no—
547C2×C4⋊C4—891no—
548C2×C4⋊C4—892no—
549C2×C4⋊C4—892no—
550C2×C4⋊C4—892no—
551C2×C4⋊C4C22×D8911yescharacteristic
552C2×C4⋊C4C22×D8912yes—
553C2×C4⋊C4C22×D8911yescharacteristic
554C2×C4⋊C4C22×D8911yescharacteristic
555C2×C4⋊C4C22×D8911yescharacteristic
556C2×C4⋊C4C22×D8912yes—
557C2×C4⋊C4C22×D8911yescharacteristic
558C2×C4⋊C4C22×D8912yes—
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×C42—892no—
573C2×C42—891no—
574C2×C42—892no—
575C2×C42—891no—
576C2×C42—891no—
577C2×C42—892no—
578C2×C42—892no—
579C2×C42—891no—
580C2×C42—892no—
581C2×C42—892no—
582C2×C42—892no—
583C2×C42—892no—
584C2×C42—892no—
585C2×C42—891no—
586C2×C42—891no—
587C2×C42—3564no—
588C2×C42C22×D8912yes—
589C2×C42C22×D8912yes—
590C2×C42C22×D8911yescharacteristic
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#95C22×D8912yes—
610#95C22×D8912yes—
611#95C22×D8912yes—
612#95C22×D8912yes—
613#95C22×D8912yes—
614#95C22×D8912yes—
615#95C22×D8912yes—
616#95C22×D8912yes—
617C24—892no—
618C2×Q8—898no—
619C2×Q8—894no—
620C2×Q8—3562no—
621C2×Q8—3561no—
622C2×Q8—3561no—
623C2×Q8—3562no—
624C2×D4—894no—
625C2×D4—3561no—
626C2×D4—3561no—
627C22×C4—891no—
628C22×C4—892no—
629C22×C4—892no—
630C22×C4—892no—
631C22×C4—898no—
632C22×C4—891no—
633C22×C4—891no—
634C22×C4—892no—
635C22×C4—892no—
636C22×C4—891no—
637C22×C4—3562no—
638C22×C4—3562no—
639C22×C4—3562no—
640C22×C4—3562no—
641C22×C4—3562no—
642C22×C4—1784no—
643C22×C4—1784no—
644C22×C4—1784no—
645C22×C4C23×D8912yes—
646C22×C4C23×D8912yes—
647C22×C4C23×D8912yes—
648C22×C4C23×D8912yes—
649C22×C4C23×D8912yes—
650C22×C4C23×D8911yescharacteristic
651C22×C4C23×D8911yescharacteristic
652C22×C4C23×D8912yes—
653C22×C4C23×D8911yescharacteristic
654C4⋊C4—41no—
655C4⋊C4—42no—
656C4⋊C4—41no—
657C4⋊C4—42no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—894no—
661C4⋊C4—898no—
662C4⋊C4—898no—
663C4⋊C4—898no—
664C4⋊C4—898no—
665C4⋊C4—894no—
666C4⋊C4—3562no—
667C4⋊C4—3562no—
668C4⋊C4—3562no—
669C4⋊C4—3562no—
670C4⋊C4—3562no—
671C4⋊C4—3562no—
672C4⋊C4—3562no—
673C4⋊C4—3561no—
674C4⋊C4—3561no—
675C4⋊C4—3562no—
676C4⋊C4C2×C4×D8914yes—
677C4⋊C4C2×C4×D8918yes—
678C4⋊C4C2×C4×D8918yes—
679C4⋊C4C2×C4×D8914yes—
680C22⋊C4—898no—
681C22⋊C4—898no—
682C22⋊C4—898no—
683C22⋊C4—898no—
684C22⋊C4—898no—
685C22⋊C4—3562no—
686C22⋊C4—3562no—
687C22⋊C4—3562no—
688C22⋊C4—3562no—
689C22⋊C4—3562no—
690C22⋊C4—3562no—
691C42—42no—
692C42—42no—
693C42—898no—
694C42—3562no—
695C42—3561no—
696C42—3561no—
697C42—3561no—
698C42—3562no—
699C42—3562no—
700C42—1784no—
701C42—1784no—
702C42—1782no—
703C42—1784no—
704C42—1782no—
705C42—1784no—
706C42—1782no—
707C42—1784no—
708C42C2×C4×D8914yes—
709C23—894no—
710C23—1782no—
711C23—1782no—
712C23—1782no—
713C23—1782no—
714C23—1782no—
715C23—1782no—
716C23C24×D8911yescharacteristic
717Q8—3568no—
718Q8—3564no—
719D4—3564no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
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—892no—
743C2×C4—892no—
744C2×C4—892no—
745C2×C4—894no—
746C2×C4—894no—
747C2×C4—894no—
748C2×C4—3568no—
749C2×C4—3568no—
750C2×C4—3568no—
751C2×C4—1782no—
752C2×C4—1781no—
753C2×C4—1781no—
754C2×C4—1781no—
755C2×C4—1782no—
756C2×C4—1781no—
757C2×C4—1781no—
758C2×C4—1782no—
759C2×C4—1781no—
760C2×C4—1782no—
761C2×C4—1782no—
762C2×C4—1781no—
763C2×C4—1781no—
764C2×C4—1781no—
765C2×C4—1782no—
766C2×C4—1782no—
767C2×C4—1782no—
768C2×C4—1782no—
769C2×C4—1782no—
770C2×C4—1782no—
771C2×C4—1782no—
772C2×C4C22×C4×D8914yes—
773C2×C4C22×C4×D8912yes—
774C2×C4C22×C4×D8912yes—
775C2×C4C22×C4×D8912yes—
776C2×C4C22×C4×D8914yes—
777C22—3562no—
778C22—3562no—
779C22—3562no—
780C22—3562no—
781C22—1784no—
782C22—1784no—
783C22—1784no—
784C22C23×C4×D8911yescharacteristic
785C22H(5,𝔽2)×D8911yescharacteristic
786C222−1+4×D8911yescharacteristic
787C222−1+4×D8911yescharacteristic
788C22#1915243311yescharacteristic
789C22#1915243511yescharacteristic
790C22#1915243511yescharacteristic
791C4—24no—
792C4—22no—
793C4—22no—
794C4—24no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—894no—
801C4—3562no—
802C4—3561no—
803C4—3561no—
804C4—3561no—
805C4—3562no—
806C4—1784no—
807C4—1784no—
808C4—1784no—
809C2—3564no—
810C2#2603345811yescharacteristic
811C2#2603346111yescharacteristic
812C2#2603346311yescharacteristic
813C2#563×D8911yescharacteristic
814C2#2603438911yescharacteristic
815C2#2603439811yescharacteristic
816C2#2603440011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC89×#2382C2
socle, cosocleC23×C89C25
prime radicalC22×D356C23
hypercenter#2382D89
hypocenterC89C4×#563
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ #2382

Complements

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

NH ≅ G/Ntype
2. #26023443C2semidirect
3. #26023442C2semidirect
4. #26023437C2semidirect
5. #26023430C2semidirect
7. #26023417C2semidirect
8. #26023416C2semidirect
10. #26022823C2semidirect
11. #125×Dic89C2semidirect
12. #26022807C2semidirect
13. #26022802C2semidirect
14. #26022802C2semidirect
16. #26022786C2semidirect
17. #26022782C2semidirect
19. C89×#2382C2semidirect
20. #19152352C4semidirect
114. #15668011C2×C4semidirect
115. #15668007C2×C4semidirect
116. #15668007C2×C4semidirect
117. #15668004C2×C4semidirect
120. #15667992C2×C4semidirect
121. #15667990C2×C4semidirect
186. #125×C89C2×C4semidirect
399. Dic89#563semidirect
413. #2382D89semidirect
428. C89C4×#563semidirect
527. #125C4×D89semidirect

Maximal subgroups

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

subgroupindex
C2×#191523522
#260234432
#260234422
#260234372
#260234302
#260234232
#260234172
#260234162
#260233972
#260228232
#125×Dic892
#260228072
#260228022
#260227912
#260227862
#260227822
#260227732
C89×#23822
C4×#56389