Finite Group Databasebeta

← #893850

Subgroups — #893850

Order 512.

2974 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16718C212yesmaximal, complemented
2#16391C211yesmaximal, characteristic
3#16297C211yesmaximal, characteristic
4#16017C212yesmaximal, complemented
5#15990C212yesmaximal, complemented
6#15989C212yesmaximal, complemented
7#15930C212yesmaximal, complemented
8#15050C211yesmaximal, characteristic, complemented
9#15043C212yesmaximal, complemented
10#15017C211yesmaximal, characteristic, complemented
11#14768C212yesmaximal, complemented
12#14681C212yesmaximal
13#14596C211yesmaximal, characteristic, complemented
14#14581C211yesmaximal, characteristic, complemented
15#14365C212yesmaximal
16#14103C212yesmaximal, complemented
17#14038C212yesmaximal, complemented
18#13917C212yesmaximal, complemented
19C4×#379C211yesmaximal, characteristic
20C25×C4C2211yescharacteristic
21C2×#397C2211yescharacteristic
22C2×#393C2211yescharacteristic
23C2×#393C2212yes—
24C2×#391C2211yescharacteristic, complemented
25C2×#388C2212yes—
26C2×#388C2212yes—
27C2×#387C2212yescomplemented
28C2×#382C2211yescharacteristic, complemented
29C2×#381C2212yes—
30C2×#381C2212yes—
31C2×#381C2212yes—
32C2×#381C2212yes—
33C2×#379C2212yes—
34C2×#379C2211yescharacteristic
35C2×#379C2211yescharacteristic
36C2×#379C2212yes—
37C2×C4×C22⋊C4C2212yes—
38C2×C4×C22⋊C4C2212yes—
39C2×C4×C22⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41#1446C2212yescomplemented
42#1446C2211yescharacteristic, complemented
43#1445C2212yescomplemented
44#1445C2212yescomplemented
45#1445C2211yescharacteristic, complemented
46#1444C2211yescharacteristic, complemented
47#1443C2212yescomplemented
48#1443C2212yescomplemented
49#1443C2212yescomplemented
50#1443C2212yescomplemented
51#1443C2212yescomplemented
52#1443C2212yescomplemented
53#1443C2212yescomplemented
54#1443C2212yescomplemented
55#1443C2212yescomplemented
56#1442C2212yescomplemented
57#1442C2212yescomplemented
58#1442C2211yescharacteristic, complemented
59#1442C2212yescomplemented
60#1441C2212yescomplemented
61#1440C2212yes—
62#1440C2212yes—
63#1440C2212yes—
64#1440C2212yes—
65#1440C2212yes—
66#1439C2211yescharacteristic
67#1439C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2211yescharacteristic
78#1437C2212yes—
79#1437C2212yes—
80#1437C2212yes—
81#1437C2212yes—
82#1436C2212yescomplemented
83#1436C2212yescomplemented
84#1436C2212yescomplemented
85#1436C2212yescomplemented
86#1436C2212yescomplemented
87#1434C2212yescomplemented
88#1434C2211yescharacteristic, complemented
89#1434C2212yescomplemented
90#1434C2212yescomplemented
91#1434C2212yescomplemented
92#1434C2212yescomplemented
93#1434C2211yescharacteristic, complemented
94C22⋊#95C2212yes—
95C22⋊#95C2211yescharacteristic
96C22⋊#95C2212yes—
97C22⋊#95C2212yes—
98C22⋊#95C2212yes—
99C22⋊#95C2211yescharacteristic
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C4×#95C2212yescomplemented
107C26C2311yescharacteristic
108C23×Q8C2311yescharacteristic
109C24×C4—24no—
110C24×C4—28no—
111C24×C4—42no—
112C24×C4—42no—
113C24×C4—44no—
114C24×C4C2311yescharacteristic
115C24×C4C2312yes—
116C24×C4C2312yes—
117C24×C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2311yescharacteristic
148C22×C42C2312yes—
149#397—24no—
150#393—24no—
151#393—44no—
152#391—42no—
153#388—28no—
154#388—44no—
155#387—44no—
156#382—42no—
157#381—28no—
158#381—44no—
159#381—44no—
160#381—44no—
161#379—28no—
162#379—24no—
163#379—24no—
164#379—44no—
165C4×C22⋊C4—28no—
166C4×C22⋊C4—42no—
167C4×C22⋊C4—42no—
168C4×C22⋊C4—44no—
169C2×#95C2311yescharacteristic
170C2×#95C2312yes—
171C2×#95C2311yescharacteristic
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2311yescharacteristic
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2311yescharacteristic
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2311yescharacteristic
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C25—24no—
220C25—22no—
221C25—22no—
222C25—24no—
223C25—41no—
224C25—41no—
225C25—42no—
226C25—42no—
227C25—41no—
228C25—41no—
229C25#4114yes—
230C25C2411yescharacteristic
231C25C2412yes—
232C22×Q8—22no—
233C22×Q8—42no—
234C22×Q8—41no—
235C22×Q8—41no—
236C22×Q8—42no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—41no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—41no—
260C23×C4—416no—
261C23×C4—432no—
262C23×C4—432no—
263C23×C4—416no—
264C23×C4—416no—
265C23×C4#4118yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—41no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—41no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
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—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—41no—
326C2×C22⋊C4—41no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—41no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—41no—
335C2×C22⋊C4—41no—
336C2×C22⋊C4—41no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
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—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4#4114yes—
358C2×C22⋊C4#4114yes—
359C2×C42—24no—
360C2×C42—22no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—22no—
364C2×C42—42no—
365C2×C42—42no—
366C2×C42—42no—
367C2×C42—42no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—42no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—22no—
381#95—24no—
382#95—22no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—41no—
390#95—41no—
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—41no—
404#95—41no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—28no—
443C24—216no—
444C24—44no—
445C24—48no—
446C24—44no—
447C24—44no—
448C24—48no—
449C24—44no—
450C24—48no—
451C24—48no—
452C24—48no—
453C24—48no—
454C24—48no—
455C24—44no—
456C24—44no—
457C24—48no—
458C24—44no—
459C24—44no—
460C24—48no—
461C24—48no—
462C24—44no—
463C24—44no—
464C24—48no—
465C24C2×#4112yes—
466C24C2×#4112yes—
467C24C2×#4112yes—
468C24C2×#4114yes—
469C24C2×#4114yes—
470C24H(5,𝔽2)14yes—
471C24C2511yescharacteristic
472C2×Q8—44no—
473C2×Q8—82no—
474C2×Q8—84no—
475C2×Q8—82no—
476C2×Q8—84no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—28no—
481C22×C4—216no—
482C22×C4—216no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—216no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
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—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
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—21no—
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—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—44no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—44no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—44no—
598C22×C4—4128no—
599C22×C4—44no—
600C22×C4—48no—
601C22×C4—44no—
602C22×C4C2×#4112yes—
603C22×C4C2×#4114yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4114yes—
607C22×C4H(5,𝔽2)12yes—
608C22×C4H(5,𝔽2)12yes—
609C4⋊C4—48no—
610C4⋊C4—82no—
611C4⋊C4—82no—
612C4⋊C4—82no—
613C4⋊C4—84no—
614C4⋊C4—84no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C22⋊C4—84no—
628C22⋊C4—84no—
629C22⋊C4—84no—
630C22⋊C4—84no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C22⋊C4—84no—
635C42—44no—
636C42—84no—
637C42—82no—
638C42—84no—
639C42—84no—
640C23—24no—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—24no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—416no—
671C23—432no—
672C23—432no—
673C23—416no—
674C23—416no—
675C23—416no—
676C23—432no—
677C23—416no—
678C23—416no—
679C23—416no—
680C23—432no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—41no—
696C23—42no—
697C23—41no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—41no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23#52914yes—
708C23#55118yes—
709C23C22×#4111yescharacteristic
710C23C22×#4111yescharacteristic
711C23C22×#4111yescharacteristic
712C23C22×#4112yes—
713C23C2×H(5,𝔽2)11yescharacteristic
714C23C2×H(5,𝔽2)11yescharacteristic
715C23C2×H(5,𝔽2)12yes—
716C23#58511yescharacteristic
717C23#58512yes—
718C23#58511yescharacteristic
719C23#58512yes—
720Q8—88no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—432no—
738C2×C4—416no—
739C2×C4—432no—
740C2×C4—416no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—42no—
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—41no—
768C2×C4—42no—
769C2×C4—42no—
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—41no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4#55114yes—
832C22—28no—
833C22—28no—
834C22—28no—
835C22—28no—
836C22—24no—
837C22—464no—
838C22—42no—
839C22—44no—
840C22—42no—
841C22—44no—
842C22—42no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—42no—
848C22—44no—
849C22—44no—
850C22—42no—
851C22—44no—
852C22—42no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22C2×#52911yescharacteristic
860C22#345512yes—
861C22#345911yescharacteristic
862C22#346011yescharacteristic
863C22C2×#55111yescharacteristic
864C22C2×#55112yes—
865C22#347512yes—
866C22#347512yes—
867C22#349012yes—
868C22#349011yescharacteristic
869C22#349112yes—
870C22#349111yescharacteristic
871C22#349312yes—
872C22#350511yescharacteristic
873C22#350611yescharacteristic
874C22#351312yes—
875C22#351312yes—
876C22#352911yescharacteristic
877C22#353211yescharacteristic
878C22#353312yes—
879C22#353312yes—
880C22#354011yescharacteristic
881C22#354012yes—
882C4—24no—
883C4—44no—
884C4—42no—
885C4—42no—
886C4—44no—
887C4—42no—
888C4—81no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4—81no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—82no—
899C2—48no—
900C2—44no—
901C2#3504311yescharacteristic
902C2#3616912yes—
903C2#3687211yescharacteristic
904C2#3785512yes—
905C2#3798812yes—
906C2#3991612yes—
907C2#4546011yescharacteristic
908C2#4569411yescharacteristic
909C2#5217811yescharacteristic
910C2#5919211yescharacteristic
911C2#5920211yescharacteristic
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. #16718C2semidirect
4. #16017C2semidirect
5. #15990C2semidirect
6. #15989C2semidirect
7. #15930C2semidirect
8. #15050C2semidirect
9. #15043C2semidirect
10. #15017C2semidirect
11. #14768C2semidirect
13. #14596C2semidirect
14. #14581C2semidirect
16. #14103C2semidirect
17. #14038C2semidirect
18. #13917C2semidirect
24. C2×#391C22semidirect
27. C2×#387C22semidirect
28. C2×#382C22semidirect
41. #1446C22semidirect
42. #1446C22semidirect
43. #1445C22semidirect
44. #1445C22semidirect
45. #1445C22semidirect
46. #1444C22semidirect
47. #1443C22semidirect
48. #1443C22semidirect
49. #1443C22semidirect
50. #1443C22semidirect
51. #1443C22semidirect
52. #1443C22semidirect
53. #1443C22semidirect
54. #1443C22semidirect
55. #1443C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1441C22semidirect
82. #1436C22semidirect
83. #1436C22semidirect
84. #1436C22semidirect
85. #1436C22semidirect
86. #1436C22semidirect
87. #1434C22semidirect
88. #1434C22semidirect
89. #1434C22semidirect
90. #1434C22semidirect
91. #1434C22semidirect
92. #1434C22semidirect
93. #1434C22semidirect
106. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
#167182
#163912
#162972
#160172
#159902
#159892
#159302
#150502
#150432
#150172
#147682
#146812
#145962
#145812
#143652
#141032
#140382
#139172
C4×#3792