Finite Group Databasebeta

← #1117575

Subgroups — #1117575

Order 512.

2432 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16903C211yesmaximal, characteristic, complemented
2#16429C212yesmaximal, complemented
3#16124C212yesmaximal, complemented
4#16117C212yesmaximal, complemented
5#16005C212yesmaximal, complemented
6#15991C212yesmaximal, complemented
7#15540C212yesmaximal, complemented
8#15485C212yesmaximal, complemented
9#15061C211yesmaximal, characteristic, complemented
10#15018C212yesmaximal, complemented
11#14820C212yesmaximal
12#14820C211yesmaximal, characteristic
13#14525C212yesmaximal, complemented
14#14423C211yesmaximal, characteristic, complemented
15#13991C211yesmaximal, characteristic
16#13990C212yesmaximal, complemented
17#13971C212yesmaximal
18#13947C211yesmaximal, characteristic, complemented
19#13794C211yesmaximal, characteristic
20C23×C22⋊C4C2212yes—
21C23×C22⋊C4C2211yescharacteristic
22C2×#397C2212yes—
23C2×#397C2212yes—
24C2×#397C2212yes—
25C2×#388C2212yes—
26C2×#388C2212yes—
27C2×#388C2212yes—
28C2×#385C2212yes—
29C2×#385C2211yescharacteristic
30C2×#383C2212yescomplemented
31C2×#380C2211yescharacteristic
32C2×#380C2212yes—
33C2×#379C2212yes—
34C2×#379C2211yescharacteristic
35C2×#379C2211yescharacteristic
36C2×C4×C22⋊C4C2211yescharacteristic
37C2×C4×C22⋊C4C2212yes—
38#1445C2212yescomplemented
39#1445C2212yescomplemented
40#1445C2212yescomplemented
41#1445C2211yescharacteristic, complemented
42#1445C2211yescharacteristic, complemented
43#1444C2211yescharacteristic, complemented
44#1443C2212yescomplemented
45#1443C2212yescomplemented
46#1443C2212yescomplemented
47#1443C2212yescomplemented
48#1443C2212yescomplemented
49#1443C2212yescomplemented
50#1442C2212yescomplemented
51#1442C2212yescomplemented
52#1442C2212yescomplemented
53#1442C2212yescomplemented
54#1442C2211yescharacteristic, complemented
55#1442C2212yescomplemented
56#1442C2212yescomplemented
57#1442C2212yescomplemented
58#1441C2212yescomplemented
59#1441C2212yescomplemented
60#1441C2212yescomplemented
61#1440C2212yes—
62#1440C2212yes—
63#1440C2212yes—
64#1440C2212yes—
65#1440C2212yes—
66#1440C2212yes—
67#1440C2212yes—
68#1440C2212yes—
69#1440C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1437C2212yes—
77#1437C2212yes—
78#1437C2212yes—
79#1436C2212yescomplemented
80#1436C2212yescomplemented
81#1436C2212yescomplemented
82#1436C2212yescomplemented
83#1436C2212yescomplemented
84#1434C2211yescharacteristic, complemented
85#1434C2212yescomplemented
86#1434C2211yescharacteristic, complemented
87#1434C2211yescharacteristic, complemented
88#1434C2212yescomplemented
89#1434C2212yescomplemented
90C22⋊#95C2211yescharacteristic
91C22⋊#95C2211yescharacteristic
92C22⋊#95C2211yescharacteristic
93C22⋊#95C2212yes—
94C22⋊#95C2212yes—
95C22⋊#95C2211yescharacteristic
96C22⋊#95C2212yes—
97C22⋊#95C2212yes—
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2211yescharacteristic
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C4×#95C2211yescharacteristic, complemented
107C26C2311yescharacteristic
108C24×C4C2312yes—
109C24×C4C2312yes—
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—28no—
121C22×C22⋊C4—44no—
122C22×C22⋊C4—44no—
123C22×C22⋊C4—44no—
124C22×C22⋊C4C2311yescharacteristic
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C42C2312yes—
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2312yes—
148#397—28no—
149#397—44no—
150#397—44no—
151#388—28no—
152#388—44no—
153#388—44no—
154#385—42no—
155#385—44no—
156#383—44no—
157#380—24no—
158#380—44no—
159#379—28no—
160#379—24no—
161#379—42no—
162C4×C22⋊C4—24no—
163C4×C22⋊C4—44no—
164C2×#95C2312yes—
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2311yescharacteristic
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2311yescharacteristic
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2311yescharacteristic
181C2×#95C2312yes—
182C2×#95C2311yescharacteristic
183C2×#95C2311yescharacteristic
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2311yescharacteristic
190C2×#95C2311yescharacteristic
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2311yescharacteristic
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C25—22no—
216C25—24no—
217C25—24no—
218C25—22no—
219C25—41no—
220C25—42no—
221C25—42no—
222C25—41no—
223C25—41no—
224C25—41no—
225C25#4114yes—
226C25C2411yescharacteristic
227C25C2412yes—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—22no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—41no—
239C23×C4—41no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—41no—
249C23×C4—42no—
250C23×C4—41no—
251C23×C4#4114yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—41no—
274C2×C4⋊C4—41no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—41no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—41no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—432no—
339C2×C22⋊C4—416no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—41no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4#4118yes—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42—42no—
360C2×C42—42no—
361#95—22no—
362#95—22no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—42no—
372#95—42no—
373#95—41no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—41no—
379#95—42no—
380#95—41no—
381#95—41no—
382#95—42no—
383#95—42no—
384#95—41no—
385#95—41no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412C24—216no—
413C24—28no—
414C24—28no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—21no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—28no—
436C24—216no—
437C24—44no—
438C24—44no—
439C24—48no—
440C24—82no—
441C24—82no—
442C24—82no—
443C24—82no—
444C24—84no—
445C24—84no—
446C24—84no—
447C24—84no—
448C24—84no—
449C24—84no—
450C24—84no—
451C24—84no—
452C24—82no—
453C24—82no—
454C24—84no—
455C24C2×#4112yes—
456C24C2×#4114yes—
457C24C2×#4114yes—
458C24C2×#4112yes—
459C24H(5,𝔽2)12yes—
460C24H(5,𝔽2)14yes—
461C24C2511yescharacteristic
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—44no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—84no—
573C22×C4—84no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—84no—
577C22×C4—84no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4—84no—
584C22×C4—84no—
585C22×C4—84no—
586C22×C4—84no—
587C22×C4—84no—
588C22×C4C2×#4114yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4114yes—
591C22×C4C2×#4112yes—
592C22×C4H(5,𝔽2)12yes—
593C4⋊C4—82no—
594C4⋊C4—84no—
595C4⋊C4—84no—
596C4⋊C4—82no—
597C4⋊C4—84no—
598C4⋊C4—84no—
599C4⋊C4—84no—
600C22⋊C4—48no—
601C22⋊C4—44no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—44no—
609C22⋊C4—48no—
610C22⋊C4—44no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—84no—
616C22⋊C4—84no—
617C22⋊C4—84no—
618C22⋊C4—84no—
619C22⋊C4—82no—
620C42—48no—
621C42—82no—
622C42—82no—
623C42—84no—
624C23—232no—
625C23—22no—
626C23—24no—
627C23—22no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—88no—
682C23—816no—
683C23—816no—
684C23—88no—
685C23—88no—
686C23—816no—
687C23—88no—
688C23—88no—
689C23—88no—
690C23—816no—
691C23#55314yes—
692C23#55318yes—
693C23C22×#4111yescharacteristic
694C23C22×#4112yes—
695C23C22×#4111yescharacteristic
696C23C2×H(5,𝔽2)11yescharacteristic
697C23C2×H(5,𝔽2)12yes—
698C23C2×H(5,𝔽2)11yescharacteristic
699C23#58511yescharacteristic
700C23#58512yes—
701C23#58511yescharacteristic
702C23#58511yescharacteristic
703C23#58512yes—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—88no—
812C2×C4—816no—
813C2×C4—816no—
814C2×C4—88no—
815C22—24no—
816C22—28no—
817C22—28no—
818C22—24no—
819C22—28no—
820C22—24no—
821C22—42no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—42no—
832C22—44no—
833C22—42no—
834C22—44no—
835C22—42no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—832no—
842C22#344411yescharacteristic
843C22#345911yescharacteristic
844C22C2×#55311yescharacteristic
845C22C2×#55312yes—
846C22#349012yes—
847C22#349011yescharacteristic
848C22#349111yescharacteristic
849C22#349111yescharacteristic
850C22#349111yescharacteristic
851C22#349112yes—
852C22#349411yescharacteristic
853C22#351011yescharacteristic
854C22#351312yes—
855C22#352112yes—
856C22#352112yes—
857C22#352112yes—
858C22#353312yes—
859C22#354212yes—
860C22#354512yes—
861C22#354512yes—
862C22#355811yescharacteristic
863C22#356011yescharacteristic
864C22#356012yes—
865C4—42no—
866C4—44no—
867C4—42no—
868C4—42no—
869C4—44no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4—81no—
876C4—82no—
877C4—81no—
878C4—82no—
879C4—82no—
880C4—81no—
881C4—82no—
882C2—44no—
883C2—48no—
884C2#3548811yescharacteristic
885C2#3585111yescharacteristic
886C2#3660711yescharacteristic
887C2#3794211yescharacteristic
888C2#3821012yes—
889C2#4351111yescharacteristic
890C2#4359712yes—
891C2#4661612yes—
892C2#4683711yescharacteristic
893C2#4811912yes—
894C2#5104111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #16903C2semidirect
2. #16429C2semidirect
3. #16124C2semidirect
4. #16117C2semidirect
5. #16005C2semidirect
6. #15991C2semidirect
7. #15540C2semidirect
8. #15485C2semidirect
9. #15061C2semidirect
10. #15018C2semidirect
13. #14525C2semidirect
14. #14423C2semidirect
16. #13990C2semidirect
18. #13947C2semidirect
30. C2×#383C22semidirect
38. #1445C22semidirect
39. #1445C22semidirect
40. #1445C22semidirect
41. #1445C22semidirect
42. #1445C22semidirect
43. #1444C22semidirect
44. #1443C22semidirect
45. #1443C22semidirect
46. #1443C22semidirect
47. #1443C22semidirect
48. #1443C22semidirect
49. #1443C22semidirect
50. #1442C22semidirect
51. #1442C22semidirect
52. #1442C22semidirect
53. #1442C22semidirect
54. #1442C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1441C22semidirect
59. #1441C22semidirect
60. #1441C22semidirect
79. #1436C22semidirect
80. #1436C22semidirect
81. #1436C22semidirect
82. #1436C22semidirect
83. #1436C22semidirect
84. #1434C22semidirect
85. #1434C22semidirect
86. #1434C22semidirect
87. #1434C22semidirect
88. #1434C22semidirect
89. #1434C22semidirect
106. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
#169032
#164292
#161242
#161172
#160052
#159912
#155402
#154852
#150612
#150182
#148202
#145252
#144232
#139912
#139902
#139712
#139472
#137942