Finite Group Databasebeta

← #36720582

Subgroups — #36720582

Order 22784.

2008 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#26023438C211yesmaximal, characteristic, complemented
3#26023437C211yesmaximal, characteristic, complemented
4#26023423C211yesmaximal, characteristic
5#26023371C212yesmaximal, complemented
6#26023366C212yesmaximal, complemented
7#26023334C212yesmaximal, complemented
8#26023311C212yesmaximal, complemented
9#26023280C212yesmaximal, complemented
10#26023249C212yesmaximal
11#26023041C212yesmaximal
12#26023021C212yesmaximal, complemented
13#26023020C212yesmaximal, complemented
14#26022997C212yesmaximal, complemented
15#26022986C212yesmaximal, complemented
16#26022935C212yesmaximal, complemented
17C4×#15668004C211yesmaximal, characteristic, complemented
18C4×#15668000C211yesmaximal, characteristic
19C4×#125×C89C211yesmaximal, characteristic, complemented
20#19152352C4116yescomplemented
21C2×#15668011C2212yes—
22C2×#15668007C2212yes—
23C2×#15668007C2212yes—
24C2×#15668004C2211yescharacteristic
25C2×#15668000C2211yescharacteristic
26C2×#15667997C2212yes—
27C2×#15667992C2212yes—
28C2×#15667990C2212yes—
29C2×C4×Dic178C2212yes—
30C2×C4×Dic178C2211yescharacteristic
31C2×C4×D356C2211yescharacteristic
32C2×#15667969C2212yes—
33#19151504C2211yescharacteristic
34#19151503C2212yes—
35#19151502C2212yes—
36#19151502C2212yes—
37#19151502C2212yes—
38#19151500C2211yescharacteristic
39#19151497C2212yes—
40#19151497C2212yes—
41#19151496C2211yescharacteristic
42#19151496C2212yes—
43#19151496C2211yescharacteristic
44#19151495C2212yes—
45#19151493C2212yes—
46#19151493C2212yes—
47#19151490C2212yes—
48#19151490C2212yes—
49#19151490C2212yes—
50#19151490C2212yes—
51#19151489C2212yes—
52#19151489C2212yes—
53#19151489C2212yes—
54#19151489C2212yes—
55#19151488C2212yes—
56#19151487C2212yes—
57#19151485C2212yes—
58#19151485C2212yes—
59#19151484C2212yes—
60#19151484C2212yes—
61#19151484C2212yes—
62#19151484C2212yes—
63#19151483C2212yes—
64#19151483C2212yes—
65#19151482C2212yes—
66#19151482C2212yes—
67#19151482C2212yes—
68#19151481C2212yes—
69#19151481C2212yes—
70#19151479C2212yes—
71#19151476C2212yes—
72#19151472C2212yes—
73#19151469C2212yes—
74#19151469C2212yes—
75#19151469C2212yes—
76#19151469C2212yes—
77#19151464C2211yescharacteristic
78#19151464C2211yescharacteristic
79#19151462C2212yes—
80#19151455C2212yes—
81C4⋊C4×Dic89C2212yes—
82C4⋊C4×Dic89C2212yes—
83C4×#13083553C2212yes—
84C4×#13083553C2212yes—
85C4×#13083553C2212yes—
86C4×C4⋊Dic89C2211yescharacteristic
87C4×C4⋊Dic89C2211yescharacteristic
88#19151449C2212yes—
89C4×#13083551C2212yes—
90C4×#13083551C2212yes—
91C4×#13083551C2212yes—
92#19151445C2212yes—
93#19151445C2212yes—
94#19151445C2212yes—
95#19151443C2212yes—
96#95×D89C2212yes—
97C2×#125×C89C2211yescharacteristic
98#389×C89C2211yescharacteristic
99#389×C89C2211yescharacteristic
100#387×C89C2212yes—
101#387×C89C2212yes—
102#382×C89C2211yescharacteristic
103C4×C4⋊C4×C89C2212yes—
104C4×C4⋊C4×C89C2212yes—
105C4×C4⋊C4×C89C2211yescharacteristic
106C4×C4⋊C4×C89C2211yescharacteristic
107C43×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
122C4×Dic178—44no—
123C4×Dic178—42no—
124C4×D356—42no—
125#15667969—44no—
126C2×C4⋊Dic89C2311yescharacteristic
127C2×C4⋊Dic89C2311yescharacteristic
128C2×C4⋊Dic89C2312yes—
129C2×C4⋊Dic89C2312yes—
130C2×C4⋊Dic89C2311yescharacteristic
131C2×C4⋊Dic89C2311yescharacteristic
132C2×C4⋊Dic89C2312yes—
133C2×C4⋊Dic89C2311yescharacteristic
134C2×C4⋊Dic89C2311yescharacteristic
135C2×#13083553C2312yes—
136C2×#13083553C2312yes—
137C2×#13083553C2312yes—
138C2×#13083553C2312yes—
139C2×#13083553C2312yes—
140C2×#13083553C2312yes—
141C2×#13083553C2312yes—
142C2×#13083553C2312yes—
143C2×#13083553C2312yes—
144C2×#13083551C2312yes—
145C2×#13083551C2312yes—
146C2×#13083551C2312yes—
147C2×#13083551C2312yes—
148C2×#13083551C2312yes—
149C2×#13083551C2312yes—
150C2×#13083551C2312yes—
151C2×#13083551C2312yes—
152C2×#13083551C2312yes—
153C2×#13083551C2312yes—
154C2×#13083551C2312yes—
155C2×C4×Dic89C2312yes—
156C2×C4×Dic89C2312yes—
157C2×C4×Dic89C2312yes—
158C2×C4×Dic89C2312yes—
159C2×C4×Dic89C2312yes—
160C2×C4×Dic89C2312yes—
161C2×C4×Dic89C2312yes—
162C2×C4×Dic89C2312yes—
163C2×C4×Dic89C2312yes—
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—
184#125×C89C2×C418yescomplemented
185C2×C4⋊C4×C89C2312yes—
186C2×C4⋊C4×C89C2311yescharacteristic
187C2×C4⋊C4×C89C2311yescharacteristic
188C2×C4⋊C4×C89C2312yes—
189C2×C4⋊C4×C89C2312yes—
190C2×C4⋊C4×C89C2312yes—
191C2×C4⋊C4×C89C2311yescharacteristic
192C2×C4⋊C4×C89C2311yescharacteristic
193C2×C42×C89C2311yescharacteristic
194C2×C42×C89C2311yescharacteristic
195C2×C42×C89C2311yescharacteristic
196C2×C42×C89C2312yes—
197C2×C42×C89C2311yescharacteristic
198C2×C42×C89C2311yescharacteristic
199C2×C42×C89C2311yescharacteristic
200C2×C42×C89C2312yes—
201C2×C42×C89C2311yescharacteristic
202#95×C89C2312yes—
203#95×C89C2312yes—
204#95×C89C2312yes—
205#95×C89C2312yes—
206#95×C89C2312yes—
207#95×C89C2312yes—
208C23×D89C2412yes—
209C2×Dic178—41no—
210C2×Dic178—42no—
211C2×Dic178—42no—
212C2×Dic178—41no—
213C2×Dic178C22×C418yes—
214C2×Dic178C22×C414yes—
215C2×D356—41no—
216C2×D356—41no—
217C2×D356C22×C414yes—
218C22×Dic89C2412yes—
219C22×Dic89C2412yes—
220C22×Dic89C2412yes—
221C22×Dic89C2412yes—
222C22×Dic89C2412yes—
223C22×Dic89C2412yes—
224C22×Dic89C2412yes—
225C2×C4×D89—24no—
226C2×C4×D89—42no—
227C2×C4×D89—42no—
228C2×C4×D89—42no—
229C2×C4×D89—42no—
230C2×C4×D89—42no—
231C2×C4×D89—42no—
232C2×C4×D89—42no—
233C2×C4×D89C22×C418yes—
234C4⋊Dic89—41no—
235C4⋊Dic89—42no—
236C4⋊Dic89—41no—
237C4⋊Dic89—42no—
238C4⋊Dic89—41no—
239C4⋊Dic89—41no—
240C4⋊Dic89C22×C414yes—
241C4⋊Dic89C22×C418yes—
242C4⋊Dic89C22×C414yes—
243#13083553—24no—
244#13083553—24no—
245#13083553—42no—
246#13083553—42no—
247#13083553—42no—
248#13083553—42no—
249#13083553C22×C418yes—
250#13083553C22×C418yes—
251#13083553C22×C418yes—
252#13083551—24no—
253#13083551—24no—
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—24no—
264C4×Dic89—42no—
265C4×Dic89—42no—
266C4×Dic89—42no—
267C4×Dic89—42no—
268C4×Dic89—42no—
269C4×Dic89—42no—
270C4×Dic89—42no—
271C4×Dic89C22×C418yes—
272C22×C4×C89C2412yes—
273C22×C4×C89C2412yes—
274C22×C4×C89C2411yescharacteristic
275C22×C4×C89C2412yes—
276C22×C4×C89C2411yescharacteristic
277C22×C4×C89C2411yescharacteristic
278C22×C4×C89C2412yes—
279C22×C4×C89C2411yescharacteristic
280C22×C4×C89C2411yescharacteristic
281C22×C4×C89C2411yescharacteristic
282C22×C4×C89C2411yescharacteristic
283C4⋊C4×C89—24no—
284C4⋊C4×C89—41no—
285C4⋊C4×C89—41no—
286C4⋊C4×C89—42no—
287C4⋊C4×C89C22×C414yes—
288C4⋊C4×C89C22×C418yes—
289C4⋊C4×C89C22×C418yes—
290C4⋊C4×C89C22×C414yes—
291C42×C89—24no—
292C42×C89—22no—
293C42×C89—22no—
294C42×C89—22no—
295C42×C89—42no—
296C42×C89—41no—
297C42×C89—41no—
298C42×C89—41no—
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—21no—
309C2×C4×C89—22no—
310C2×C4×C89—21no—
311C2×C4×C89—21no—
312C2×C4×C89—21no—
313C2×C4×C89—21no—
314C2×C4×C89—21no—
315C2×C4×C89—22no—
316C2×C4×C89—21no—
317C2×C4×C89—21no—
318C2×C4×C89—21no—
319C2×C4×C89—22no—
320C2×C4×C89—21no—
321C2×C4×C89—21no—
322C2×C4×C89—21no—
323C2×C4×C89—22no—
324C2×C4×C89—22no—
325C2×C4×C89—22no—
326C2×C4×C89—21no—
327C2×C4×C89—21no—
328C2×C4×C89—22no—
329C2×C4×C89—21no—
330C2×C4×C89—22no—
331C2×C4×C89—22no—
332C2×C4×C89—22no—
333C2×C4×C89C23×C412yes—
334C2×C4×C89C23×C412yes—
335C2×C4×C89C23×C412yes—
336C2×C4×C89C23×C414yes—
337C2×C4×C89C23×C414yes—
338C2×C4×C89H(5,𝔽2)12yes—
339C2×C4×C892−1+412yes—
340C2×C4×C892−1+412yes—
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—22no—
359C2×Dic89C23×C414yes—
360C2×Dic89C23×C414yes—
361C2×Dic89C23×C414yes—
362D356—44no—
363C4×D89—48no—
364C4×D89—84no—
365C4×D89—84no—
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—22no—
388C4×C89—22no—
389C4×C89—22no—
390C4×C89—42no—
391C4×C89—42no—
392C4×C89—41no—
393Dic89—24no—
394Dic89—24no—
395Dic89—24no—
396Dic89—42no—
397Dic89—42no—
398Dic89—42no—
399Dic89—42no—
400#34528—891nomaximal, Sylow
401C2×C89C4×H(5,𝔽2)11yescharacteristic
402C2×C89C4×2−1+411yescharacteristic
403C2×C89C4×2−1+411yescharacteristic
404C2×C89#355911yescharacteristic
405C2×C89#356111yescharacteristic
406C2×C89#356311yescharacteristic
407C2×C89#356811yescharacteristic
408D89—44no—
409C2×#563—891no—
410#2382—891no—
411#2382—891no—
412#2379—891no—
413#2373—892no—
414#2373—892no—
415#2368—892no—
416#2365—892no—
417#2362—892no—
418#2359—892no—
419#2335—892no—
420#2334—892no—
421#2334—892no—
422#2331—892no—
423#2329—892no—
424#2323—892no—
425C4×#125—891no—
426C4×#125D8911yescharacteristic, complemented
427C4×#124—891no—
428C89#3452811yescharacteristic, 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—892no—
440C2×C4×Q8—891no—
441C2×C4×D4—891no—
442C2×#117—892no—
443#391—892no—
444#391—891no—
445#391—892no—
446#391—892no—
447#391—892no—
448#390—891no—
449#389—892no—
450#389—892no—
451#389—892no—
452#389—892no—
453#389—891no—
454#389—891no—
455#389—892no—
456#389—892no—
457#389C2×D8911yescharacteristic
458#389C2×D8911yescharacteristic
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#387—892no—
482#387—892no—
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#382—891no—
492#382—891no—
493#382—892no—
494#382C2×D8911yescharacteristic
495#380—892no—
496C4×C4⋊C4—892no—
497C4×C4⋊C4—892no—
498C4×C4⋊C4—892no—
499C4×C4⋊C4—892no—
500C4×C4⋊C4—891no—
501C4×C4⋊C4—891no—
502C4×C4⋊C4—892no—
503C4×C4⋊C4—892no—
504C4×C4⋊C4C2×D8912yes—
505C4×C4⋊C4C2×D8912yes—
506C4×C4⋊C4C2×D8911yescharacteristic
507C4×C4⋊C4C2×D8911yescharacteristic
508C4×C22⋊C4—892no—
509C4×C22⋊C4—892no—
510C4×C22⋊C4—892no—
511C4×C22⋊C4—892no—
512C4×C22⋊C4—892no—
513C4×C22⋊C4—892no—
514#376—892no—
515C2×#95—892no—
516C43C2×D8911yescharacteristic
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—
535#117—3564no—
536C2×C4⋊C4—891no—
537C2×C4⋊C4—892no—
538C2×C4⋊C4—892no—
539C2×C4⋊C4—892no—
540C2×C4⋊C4—892no—
541C2×C4⋊C4—891no—
542C2×C4⋊C4—892no—
543C2×C4⋊C4—891no—
544C2×C4⋊C4—892no—
545C2×C4⋊C4—891no—
546C2×C4⋊C4—891no—
547C2×C4⋊C4—892no—
548C2×C4⋊C4—892no—
549C2×C4⋊C4—891no—
550C2×C4⋊C4—892no—
551C2×C4⋊C4—892no—
552C2×C4⋊C4—892no—
553C2×C4⋊C4—892no—
554C2×C4⋊C4C22×D8912yes—
555C2×C4⋊C4C22×D8912yes—
556C2×C4⋊C4C22×D8911yescharacteristic
557C2×C4⋊C4C22×D8911yescharacteristic
558C2×C4⋊C4C22×D8911yescharacteristic
559C2×C4⋊C4C22×D8912yes—
560C2×C4⋊C4C22×D8912yes—
561C2×C4⋊C4C22×D8911yescharacteristic
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×C42—892no—
574C2×C42—892no—
575C2×C42—892no—
576C2×C42—892no—
577C2×C42—892no—
578C2×C42—892no—
579C2×C42—892no—
580C2×C42—892no—
581C2×C42—892no—
582C2×C42C22×D8912yes—
583C2×C42C22×D8911yescharacteristic
584C2×C42C22×D8911yescharacteristic
585C2×C42C22×D8911yescharacteristic
586C2×C42C22×D8911yescharacteristic
587C2×C42C22×D8911yescharacteristic
588C2×C42C22×D8911yescharacteristic
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#95—892no—
610#95—892no—
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—892no—
628C22×C4—892no—
629C22×C4—892no—
630C22×C4—898no—
631C22×C4—892no—
632C22×C4—892no—
633C22×C4—892no—
634C22×C4—892no—
635C22×C4—3562no—
636C22×C4—3562no—
637C22×C4—3562no—
638C22×C4—3562no—
639C22×C4—3562no—
640C22×C4—3562no—
641C22×C4—3562no—
642C22×C4—1784no—
643C22×C4C23×D8912yes—
644C22×C4C23×D8911yescharacteristic
645C22×C4C23×D8912yes—
646C22×C4C23×D8911yescharacteristic
647C22×C4C23×D8912yes—
648C22×C4C23×D8912yes—
649C22×C4C23×D8911yescharacteristic
650C22×C4C23×D8911yescharacteristic
651C22×C4C23×D8911yescharacteristic
652C22×C4C23×D8911yescharacteristic
653C22×C4C23×D8911yescharacteristic
654C4⋊C4—24no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—42no—
658C4⋊C4—894no—
659C4⋊C4—898no—
660C4⋊C4—898no—
661C4⋊C4—898no—
662C4⋊C4—898no—
663C4⋊C4—894no—
664C4⋊C4—3562no—
665C4⋊C4—3561no—
666C4⋊C4—3562no—
667C4⋊C4—3561no—
668C4⋊C4—3562no—
669C4⋊C4—3562no—
670C4⋊C4—3562no—
671C4⋊C4—3562no—
672C4⋊C4—3561no—
673C4⋊C4—3561no—
674C4⋊C4—1784no—
675C4⋊C4—1784no—
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—1784no—
690C22⋊C4—1784no—
691C42—24no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—42no—
696C42—41no—
697C42—41no—
698C42—41no—
699C42—898no—
700C42—3562no—
701C42—3562no—
702C42—3562no—
703C42—3562no—
704C42—3562no—
705C42—3562no—
706C42—3562no—
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—21no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—894no—
746C2×C4—894no—
747C2×C4—894no—
748C2×C4—3568no—
749C2×C4—1782no—
750C2×C4—1782no—
751C2×C4—1782no—
752C2×C4—1782no—
753C2×C4—1782no—
754C2×C4—1782no—
755C2×C4—1782no—
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—7124no—
768C2×C4—7124no—
769C2×C4C22×C4×D8914yes—
770C2×C4C22×C4×D8912yes—
771C2×C4C22×C4×D8912yes—
772C2×C4C22×C4×D8912yes—
773C2×C4C22×C4×D8914yes—
774C2×C4#1566805812yes—
775C2×C4#1566805912yes—
776C2×C4#1566806012yes—
777C22—3562no—
778C22—3562no—
779C22—3562no—
780C22—3562no—
781C22—1784no—
782C22—1784no—
783C22—1784no—
784C22C23×C4×D8911yescharacteristic
785C22C2×#1566805811yescharacteristic
786C22C2×#1566805911yescharacteristic
787C22C2×#1566806011yescharacteristic
788C22#1915243411yescharacteristic
789C22#1915243411yescharacteristic
790C22#1915243411yescharacteristic
791C4—24no—
792C4—22no—
793C4—22no—
794C4—24no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—22no—
799C4—42no—
800C4—41no—
801C4—42no—
802C4—3562no—
803C4—3562no—
804C4—3562no—
805C4—3562no—
806C4—1784no—
807C4—1784no—
808C4—1784no—
809C2—3564no—
810C2C4×#1566805811yescharacteristic
811C2C4×#1566805911yescharacteristic
812C2C4×#1566806011yescharacteristic
813C2#2603478611yescharacteristic
814C2#2603482211yescharacteristic
815C2#2603486211yescharacteristic
816C2#2603494811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingC4×#125×C89C2
socle, cosocleC23×C89C25
prime radicalC22×D356C23
hypercenterC4×#125D89
hypocenterC89#34528
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
2. #26023438C2semidirect
3. #26023437C2semidirect
5. #26023371C2semidirect
6. #26023366C2semidirect
7. #26023334C2semidirect
8. #26023311C2semidirect
9. #26023280C2semidirect
12. #26023021C2semidirect
13. #26023020C2semidirect
14. #26022997C2semidirect
15. #26022986C2semidirect
16. #26022935C2semidirect
17. C4×#15668004C2semidirect
19. C4×#125×C89C2semidirect
20. #19152352C4semidirect
114. #15668011C2×C4semidirect
115. #15668007C2×C4semidirect
116. #15668007C2×C4semidirect
117. #15668004C2×C4semidirect
120. #15667992C2×C4semidirect
121. #15667990C2×C4semidirect
184. #125×C89C2×C4semidirect
426. C4×#125D89semidirect
428. C89#34528semidirect
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
#260234382
#260234372
#260234232
#260233712
#260233662
#260233342
#260233112
#260232802
#260232492
#260230412
#260230212
#260230202
#260229972
#260229862
#260229352
C4×#156680042
C4×#156680002
C4×#125×C892
#3452889