Finite Group Databasebeta

← #947066

Subgroups — #947066

Order 512.

2776 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2494C211yesmaximal, characteristic, complemented
2C2×#2432C211yesmaximal, characteristic
3#17145C214yesmaximal, complemented
4#16446C214yesmaximal, complemented
5#16416C214yesmaximal, complemented
6#15997C214yesmaximal, complemented
7#15244C211yesmaximal, characteristic, complemented
8#15236C211yesmaximal, characteristic, complemented
9#15226C211yesmaximal, characteristic, complemented
10#15188C211yesmaximal, characteristic, complemented
11#15184C211yesmaximal, characteristic, complemented
12#15182C211yesmaximal, characteristic, complemented
13#14274C211yesmaximal, characteristic, complemented
14#14260C211yesmaximal, characteristic, complemented
15#14153C211yesmaximal, characteristic, complemented
16#14003C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic
18#13937C211yesmaximal, characteristic
19#13842C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24#2494—28no—
25#2432—28no—
26C2×#401C2212yes—
27C2×#397C2212yes—
28C2×#394C2212yes—
29C2×#394C2212yes—
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#388C2212yes—
47C2×#387C2212yes—
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#384C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×#376C2211yescharacteristic
61#1445C2214yes—
62#1445C2214yes—
63#1443C2212yes—
64#1443C2214yes—
65#1442C2212yes—
66#1442C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1440C2212yes—
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2212yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1438C2214yes—
84#1438C2214yes—
85#1437C2214yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88#1434C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C22×#41—24no—
94C22×#41—24no—
95C22×#41—24no—
96C22×#41—42no—
97C22×#41—42no—
98C22×#41—42no—
99C22×#41—42no—
100C23×Q8C2311yescharacteristic
101C23×Q8C2311yescharacteristic
102C23×D4C2311yescharacteristic
103C23×D4C2312yes—
104C24×C4C2311yescharacteristic
105C24×C4C2312yes—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—24no—
108C2×C4⋊Q8—42no—
109C2×#124—24no—
110C2×#124—24no—
111C2×#124—42no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—42no—
114C2×C22⋊Q8—42no—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2312yes—
149#401—28no—
150#397—28no—
151#394—28no—
152#394—28no—
153#391—24no—
154#391—24no—
155#391—42no—
156#391—42no—
157#391—42no—
158#391—42no—
159#391—42no—
160#391—42no—
161#391—42no—
162#390—24no—
163#390—24no—
164#390—42no—
165#390—42no—
166#390—42no—
167#389—24no—
168#389—24no—
169#388—28no—
170#387—28no—
171#385—28no—
172#385—28no—
173#384—42no—
174#382—24no—
175#382—42no—
176#380—24no—
177#380—24no—
178C4×C4⋊C4—24no—
179C4×C4⋊C4—42no—
180C4×C22⋊C4—42no—
181C4×C22⋊C4—42no—
182C4×C22⋊C4D418yes—
183#376—42no—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C25C2411yescharacteristic
216C25C2412yes—
217C2×#41—416no—
218C2×#41—416no—
219C2×#41—416no—
220C2×#41—416no—
221C2×#41—416no—
222C2×#41—416no—
223C2×#41—416no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8#4114yes—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—42no—
248C22×D4—42no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4#4114yes—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4C2×D414yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C4⋊Q8—416no—
284#124—416no—
285C22⋊Q8—416no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—44no—
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—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4C2×D414yes—
358C2×C22⋊C4C2×D414yes—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—24no—
376C2×C42—44no—
377C2×C42C2×D414yes—
378C2×C42C2×D414yes—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—28no—
389#95—24no—
390#95—42no—
391#95—42no—
392#95—42no—
393#95—44no—
394#95—44no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95C2×D414yes—
409#95C2×D414yes—
410C24—22no—
411C24—21no—
412C24—21no—
413C24—22no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—24no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—24no—
428C24—24no—
429C24—24no—
430C24C22×D412yes—
431C24C2×#4114yes—
432C24C2511yescharacteristic
433#41—4128no—
434C2×Q8—28no—
435C2×Q8—28no—
436C2×Q8—28no—
437C2×Q8—44no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×D4—28no—
449C2×D4—28no—
450C2×D4—28no—
451C2×D4—48no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—44no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
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—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
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—24no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C2×#4114yes—
570C22×C4C2×#4112yes—
571C22×C4C2×#4112yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C4H(5,𝔽2)12yes—
574C22×C4H(5,𝔽2)12yes—
575C22×C4H(5,𝔽2)12yes—
576C22×C42−1+414yes—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—48no—
580C4⋊C4—48no—
581C4⋊C4—48no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—84no—
588C4⋊C4—88no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—88no—
600C22⋊C4—84no—
601C22⋊C4—88no—
602C22⋊C4—88no—
603C22⋊C4—88no—
604C42—28no—
605C42—28no—
606C42—44no—
607C42—44no—
608C42—44no—
609C42—44no—
610C42—84no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—24no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—22no—
620C23—22no—
621C23—28no—
622C23—28no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—44no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—44no—
639C23—42no—
640C23—41no—
641C23—42no—
642C23—44no—
643C23—42no—
644C23—42no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—42no—
649C23—42no—
650C23—44no—
651C23—44no—
652C23—42no—
653C23—44no—
654C23—44no—
655C23—42no—
656C23—42no—
657C23C23×D411yescharacteristic
658C23C22×#4111yescharacteristic
659C23C22×#4111yescharacteristic
660C23C2×H(5,𝔽2)11yescharacteristic
661C23C2×H(5,𝔽2)11yescharacteristic
662C23C2×H(5,𝔽2)11yescharacteristic
663C23C2×H(5,𝔽2)11yescharacteristic
664C23C2×2−1+412yes—
665C23#58512yes—
666C23#58512yes—
667C23#58512yes—
668Q8—416no—
669Q8—88no—
670D4—432no—
671D4—416no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—432no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—416no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
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—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4#53514yes—
769C2×C4#53814yes—
770C2×C4#53814yes—
771C2×C4#54614yes—
772C2×C4#54614yes—
773C2×C4#55114yes—
774C2×C4#56014yes—
775C22—42no—
776C22—42no—
777C22—48no—
778C22—44no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—44no—
786C22—48no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—84no—
792C22—82no—
793C22—84no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22C2×#53511yescharacteristic
798C22#344911yescharacteristic
799C22#344911yescharacteristic
800C22C2×#53811yescharacteristic
801C22C2×#53811yescharacteristic
802C22C2×#54611yescharacteristic
803C22C2×#54611yescharacteristic
804C22C2×#55111yescharacteristic
805C22#349911yescharacteristic
806C22#350011yescharacteristic
807C22#351512yes—
808C22#351812yes—
809C22#352112yes—
810C22#352412yes—
811C22C2×#56011yescharacteristic
812C22#353912yes—
813C22#354112yes—
814C22#354112yes—
815C22#355112yes—
816C22#355412yes—
817C22#356112yes—
818C22#356212yes—
819C22#356212yes—
820C4—42no—
821C4—42no—
822C4—44no—
823C4—44no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4#268518yes—
837C2—82no—
838C2—84no—
839C2#3739111yescharacteristic
840C2#3754411yescharacteristic
841C2#3808811yescharacteristic
842C2#3809111yescharacteristic
843C2#3809211yescharacteristic
844C2#3894811yescharacteristic
845C2#4270612yes—
846C2#4290012yes—
847C2#4519212yes—
848C2C2×#268511yescharacteristic
849C2#5315212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×#41C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2494C2semidirect
3. #17145C2semidirect
4. #16446C2semidirect
5. #16416C2semidirect
6. #15997C2semidirect
7. #15244C2semidirect
8. #15236C2semidirect
9. #15226C2semidirect
10. #15188C2semidirect
11. #15184C2semidirect
12. #15182C2semidirect
13. #14274C2semidirect
14. #14260C2semidirect
15. #14153C2semidirect
16. #14003C2semidirect
19. #13842C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24942
C2×#24322
#171452
#164462
#164162
#159972
#152442
#152362
#152262
#151882
#151842
#151822
#142742
#142602
#141532
#140032
#139372
#138422