Finite Group Databasebeta

← #4474857

Subgroups — #4474857

Order 512.

2030 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17250C212yesmaximal, complemented
2#17194C212yesmaximal, complemented
3#17059C211yesmaximal, characteristic, complemented
4#16926C212yesmaximal, complemented
5#16902C211yesmaximal, characteristic, complemented
6#16859C212yesmaximal, complemented
7#16765C212yesmaximal, complemented
8#16579C212yesmaximal, complemented
9#16222C212yesmaximal, complemented
10#15750C212yesmaximal, complemented
11#15557C212yesmaximal, complemented
12#15546C212yesmaximal, complemented
13#15297C212yesmaximal
14#15282C212yesmaximal
15#14820C211yesmaximal, characteristic
16#14820C211yesmaximal, characteristic
17#14423C211yesmaximal, characteristic, complemented
18#14422C211yesmaximal, characteristic, complemented
19#14341C211yesmaximal, characteristic
20C23×C22⋊C4C2211yescharacteristic
21C2×#397C2211yescharacteristic
22C2×#397C2211yescharacteristic
23C2×#397C2212yes—
24C2×#397C2212yes—
25C2×#397C2211yescharacteristic
26C2×#397C2211yescharacteristic
27C2×#396C2212yes—
28C2×#388C2212yes—
29C2×#388C2212yes—
30C2×#388C2212yes—
31C2×#380C2211yescharacteristic
32C2×#380C2211yescharacteristic
33C2×#379C2211yescharacteristic
34C2×#379C2211yescharacteristic
35C2×#379C2212yes—
36C2×#379C2212yes—
37#1445C2212yescomplemented
38#1445C2212yescomplemented
39#1445C2212yescomplemented
40#1445C2212yescomplemented
41#1445C2212yescomplemented
42#1445C2212yescomplemented
43#1444C2212yescomplemented
44#1444C2212yescomplemented
45#1443C2212yescomplemented
46#1443C2212yescomplemented
47#1443C2212yescomplemented
48#1443C2212yescomplemented
49#1443C2212yescomplemented
50#1443C2212yescomplemented
51#1442C2212yescomplemented
52#1442C2212yescomplemented
53#1442C2212yescomplemented
54#1442C2212yescomplemented
55#1442C2212yescomplemented
56#1441C2212yescomplemented
57#1441C2212yescomplemented
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#1440C2212yes—
71#1440C2212yes—
72#1440C2212yes—
73#1440C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2211yescharacteristic
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2211yescharacteristic
82#1439C2212yes—
83#1439C2211yescharacteristic
84#1439C2212yes—
85#1439C2212yes—
86#1439C2211yescharacteristic
87#1439C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1437C2212yes—
91#1436C2212yescomplemented
92#1436C2212yescomplemented
93#1436C2212yescomplemented
94#1436C2212yescomplemented
95#1436C2212yescomplemented
96#1434C2212yescomplemented
97#1434C2212yescomplemented
98#1434C2212yescomplemented
99C22⋊#95C2211yescharacteristic
100C22⋊#95C2211yescharacteristic
101C22⋊#95C2211yescharacteristic
102C22⋊#95C2211yescharacteristic
103C22⋊#95C2211yescharacteristic
104C22⋊#95C2211yescharacteristic
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C26C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—42no—
122C22×C22⋊C4—42no—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2311yescharacteristic
126C22×C22⋊C4C2311yescharacteristic
127C22×C22⋊C4C2311yescharacteristic
128C22×C22⋊C4C2311yescharacteristic
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C42C2312yes—
148C22×C42C2312yes—
149#397—42no—
150#397—42no—
151#397—42no—
152#397—42no—
153#397—44no—
154#397—44no—
155#396—44no—
156#388—44no—
157#388—44no—
158#388—44no—
159#380—24no—
160#380—24no—
161#379—42no—
162#379—44no—
163#379—44no—
164#379—42no—
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2311yescharacteristic
169C2×#95C2312yes—
170C2×#95C2311yescharacteristic
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2311yescharacteristic
174C2×#95C2311yescharacteristic
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×#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—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—41no—
219C25—41no—
220C25—42no—
221C25—42no—
222C25—42no—
223C25—42no—
224C25C2411yescharacteristic
225C25C2411yescharacteristic
226C25C2411yescharacteristic
227C23×C4—22no—
228C23×C4—41no—
229C23×C4—41no—
230C23×C4—41no—
231C23×C4—41no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—42no—
235C23×C4—42no—
236C23×C4#4114yes—
237C23×C4C2412yes—
238C23×C4C2412yes—
239C23×C4C2412yes—
240C23×C4C2412yes—
241C23×C4C2412yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2411yescharacteristic
252C23×C4C2411yescharacteristic
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—42no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4—42no—
260C2×C4⋊C4—42no—
261C2×C4⋊C4—42no—
262C2×C4⋊C4—42no—
263C2×C4⋊C4—42no—
264C2×C4⋊C4—42no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—41no—
276C2×C4⋊C4—41no—
277C2×C4⋊C4—41no—
278C2×C4⋊C4—41no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—41no—
308C2×C22⋊C4—41no—
309C2×C22⋊C4—41no—
310C2×C22⋊C4—41no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—416no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—41no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—41no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—41no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4—41no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—41no—
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×C42—42no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42—42no—
360#95—24no—
361#95—24no—
362#95—42no—
363#95—42no—
364#95—42no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—42no—
373#95—42no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95—42no—
383#95—42no—
384#95—42no—
385#95—42no—
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—41no—
395#95—41no—
396#95—41no—
397#95—41no—
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—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—28no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—22no—
426C24—22no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—44no—
438C24—44no—
439C24—44no—
440C24—44no—
441C24—44no—
442C24—48no—
443C24—48no—
444C24—44no—
445C24—82no—
446C24—82no—
447C24—82no—
448C24—82no—
449C24—84no—
450C24—84no—
451C24—84no—
452C24—84no—
453C24—84no—
454C24—84no—
455C24—84no—
456C24—84no—
457C24—84no—
458C24—84no—
459C24C2×#4112yes—
460C24H(5,𝔽2)12yes—
461C24H(5,𝔽2)12yes—
462C24H(5,𝔽2)12yes—
463C24H(5,𝔽2)12yes—
464C24C2511yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
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—22no—
525C22×C4—22no—
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—22no—
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—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—84no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—84no—
577C22×C4C2×#4112yes—
578C22×C4C2×#4112yes—
579C4⋊C4—82no—
580C4⋊C4—82no—
581C4⋊C4—82no—
582C4⋊C4—82no—
583C4⋊C4—84no—
584C4⋊C4—84no—
585C4⋊C4—84no—
586C4⋊C4—84no—
587C4⋊C4—84no—
588C4⋊C4—84no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—84no—
597C22⋊C4—84no—
598C22⋊C4—82no—
599C22⋊C4—84no—
600C22⋊C4—82no—
601C22⋊C4—82no—
602C22⋊C4—82no—
603C22⋊C4—84no—
604C22⋊C4—84no—
605C22⋊C4—84no—
606C22⋊C4—84no—
607C22⋊C4—84no—
608C22⋊C4—84no—
609C22⋊C4—84no—
610C22⋊C4—84no—
611C22⋊C4—84no—
612C22⋊C4—84no—
613C42—84no—
614C42—84no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—416no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
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—42no—
682C23—42no—
683C23—42no—
684C23—88no—
685C23—88no—
686C23—88no—
687C23—88no—
688C23—816no—
689C23—816no—
690C23—816no—
691C23—816no—
692C23—88no—
693C23—88no—
694C23#54014yes—
695C23C22×#4111yescharacteristic
696C23C2×H(5,𝔽2)11yescharacteristic
697C23C2×H(5,𝔽2)11yescharacteristic
698C23C2×H(5,𝔽2)11yescharacteristic
699C23C2×H(5,𝔽2)11yescharacteristic
700C23#58512yes—
701C23#58512yes—
702C23#58511yescharacteristic
703C23#58511yescharacteristic
704C23#58512yes—
705C23#58512yes—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
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—41no—
731C2×C4—41no—
732C2×C4—41no—
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—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
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—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
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—88no—
811C2×C4—88no—
812C22—24no—
813C22—24no—
814C22—24no—
815C22—44no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—42no—
823C22—44no—
824C22—42no—
825C22—42no—
826C22—44no—
827C22—42no—
828C22—42no—
829C22—44no—
830C22—44no—
831C22—42no—
832C22—42no—
833C22—832no—
834C22—82no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22C2×#54011yescharacteristic
847C22#349011yescharacteristic
848C22#349111yescharacteristic
849C22#349111yescharacteristic
850C22#349311yescharacteristic
851C22#351011yescharacteristic
852C22#351011yescharacteristic
853C22#353312yes—
854C22#353312yes—
855C22#353312yes—
856C22#353411yescharacteristic
857C22#353411yescharacteristic
858C22#353411yescharacteristic
859C22#353411yescharacteristic
860C22#354512yes—
861C22#356012yes—
862C22#356012yes—
863C22#356012yes—
864C22#356012yes—
865C22#356612yes—
866C22#356612yes—
867C22#356612yes—
868C22#356812yes—
869C4—42no—
870C4—42no—
871C4—82no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—81no—
884C4—81no—
885C2—44no—
886C2—82no—
887C2—82no—
888C2#3673111yescharacteristic
889C2#4138911yescharacteristic
890C2#4138911yescharacteristic
891C2#4638811yescharacteristic
892C2#4703511yescharacteristic
893C2#5018611yescharacteristic
894C2#5018911yescharacteristic
895C2#5414212yes—
896C2#5442512yes—
897C2#5555512yes—
898C2#5765212yes—
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. #17250C2semidirect
2. #17194C2semidirect
3. #17059C2semidirect
4. #16926C2semidirect
5. #16902C2semidirect
6. #16859C2semidirect
7. #16765C2semidirect
8. #16579C2semidirect
9. #16222C2semidirect
10. #15750C2semidirect
11. #15557C2semidirect
12. #15546C2semidirect
17. #14423C2semidirect
18. #14422C2semidirect
37. #1445C22semidirect
38. #1445C22semidirect
39. #1445C22semidirect
40. #1445C22semidirect
41. #1445C22semidirect
42. #1445C22semidirect
43. #1444C22semidirect
44. #1444C22semidirect
45. #1443C22semidirect
46. #1443C22semidirect
47. #1443C22semidirect
48. #1443C22semidirect
49. #1443C22semidirect
50. #1443C22semidirect
51. #1442C22semidirect
52. #1442C22semidirect
53. #1442C22semidirect
54. #1442C22semidirect
55. #1442C22semidirect
56. #1441C22semidirect
57. #1441C22semidirect
58. #1441C22semidirect
59. #1441C22semidirect
60. #1441C22semidirect
91. #1436C22semidirect
92. #1436C22semidirect
93. #1436C22semidirect
94. #1436C22semidirect
95. #1436C22semidirect
96. #1434C22semidirect
97. #1434C22semidirect
98. #1434C22semidirect

Maximal subgroups

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

subgroupindex
#172502
#171942
#170592
#169262
#169022
#168592
#167652
#165792
#162222
#157502
#155572
#155462
#152972
#152822
#148202
#144232
#144222
#143412