Finite Group Databasebeta

← #705231

Subgroups — #705231

Order 512.

3360 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2563C211yesmaximal, characteristic, complemented
2C2×#2492C211yesmaximal, characteristic, complemented
3C2×#2432C211yesmaximal, characteristic
4C2×#2339C211yesmaximal, characteristic
5#16368C214yesmaximal, complemented
6#15371C214yesmaximal, complemented
7#15291C214yesmaximal, complemented
8#15236C211yesmaximal, characteristic, complemented
9#15233C211yesmaximal, characteristic, complemented
10#15191C211yesmaximal, characteristic, complemented
11#15180C211yesmaximal, characteristic, complemented
12#14767C214yesmaximal, complemented
13#14274C211yesmaximal, characteristic, complemented
14#14027C211yesmaximal, characteristic, complemented
15#14027C211yesmaximal, characteristic, complemented
16#14003C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic
18#13842C211yesmaximal, characteristic, complemented
19#13785C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27#2563—28no—
28#2492—28no—
29#2432—28no—
30C2×#400C2212yes—
31C2×#394C2214yes—
32C2×#393C2214yes—
33C2×#393C2212yes—
34#2339—28no—
35C2×#391C2212yes—
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#388C2212yes—
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#385C2214yes—
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#381C2212yes—
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2214yes—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×#376C2211yescharacteristic
64C22×#95C2212yes—
65#1446C2214yes—
66#1445C2214yes—
67#1445C2214yes—
68#1443C2212yes—
69#1443C2214yes—
70#1443C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1442C2212yes—
74#1442C2214yes—
75#1441C2214yes—
76#1440C2214yes—
77#1440C2214yes—
78#1440C2212yes—
79#1440C2214yes—
80#1440C2214yes—
81#1439C2212yes—
82#1438C2214yes—
83#1437C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88#1434C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—24no—
99C22×#41—24no—
100C22×#41—42no—
101C22×#41—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×Q8C2312yes—
105C23×D4C2312yes—
106C23×D4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2312yes—
109C24×C4C2312yes—
110C24×C4C2312yes—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—42no—
116C2×C4⋊Q8—42no—
117C2×#124—24no—
118C2×#124—24no—
119C2×#124—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—42no—
123C2×C4×D4—24no—
124C2×C4×D4—24no—
125C2×C4×D4—24no—
126C2×C4×D4—24no—
127C2×C4×D4—42no—
128C2×C4×D4—42no—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2314yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158#400—28no—
159#394—216no—
160#393—216no—
161#393—28no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—24no—
166#391—24no—
167#391—24no—
168#391—28no—
169#391—42no—
170#391—42no—
171#391—42no—
172#390—24no—
173#390—24no—
174#390D418yes—
175#388—28no—
176#386—28no—
177#386—28no—
178#385—216no—
179#382—24no—
180#382—24no—
181#381—28no—
182#380—24no—
183#380—24no—
184#380—216no—
185C4×C4⋊C4—24no—
186C4×C4⋊C4—24no—
187C4×C22⋊C4—24no—
188C4×C22⋊C4—42no—
189C4×C22⋊C4D418yes—
190#376—42no—
191C2×#95—28no—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C25C2411yescharacteristic
226C25C2412yes—
227C2×#41—232no—
228C2×#41—416no—
229C2×#41—416no—
230C2×#41—416no—
231C2×#41—416no—
232C2×#41—416no—
233C2×#41—416no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—24no—
239C22×Q8—24no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—42no—
250C22×Q8—44no—
251C22×Q8—44no—
252C22×Q8#4114yes—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—24no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4C2×D414yes—
265C22×D4#4114yes—
266C22×D4#4114yes—
267C23×C4—24no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—28no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4C2×D414yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C4⋊Q8—416no—
309C4⋊Q8—416no—
310#124—416no—
311C22⋊Q8—416no—
312C4×D4—416no—
313C4×D4—416no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4C2×D414yes—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4C2×D414yes—
374C2×C22⋊C4C2×D414yes—
375C2×C22⋊C4C2×D4116yes—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—44no—
393C2×C42C2×D414yes—
394C2×C42C2×D414yes—
395C2×C42C2×D414yes—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—28no—
403#95—28no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—28no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—28no—
413#95—24no—
414#95—44no—
415#95—42no—
416#95—44no—
417#95—42no—
418#95—42no—
419#95—44no—
420#95—44no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—44no—
425#95—44no—
426#95—44no—
427#95C2×D414yes—
428#95C2×D414yes—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24C22×D412yes—
448C24C22×D414yes—
449C24C2×#4114yes—
450C24C2×#4114yes—
451C24C2511yescharacteristic
452#41—4128no—
453C2×Q8—28no—
454C2×Q8—28no—
455C2×Q8—28no—
456C2×Q8—48no—
457C2×Q8—48no—
458C2×Q8—44no—
459C2×Q8—44no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—88no—
470C2×Q8—84no—
471C2×Q8—88no—
472C2×D4—216no—
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—28no—
477C2×D4—28no—
478C2×D4—28no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4#124116yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—216no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
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—24no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—416no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—48no—
590C22×C4—84no—
591C22×C4—88no—
592C22×C4—84no—
593C22×C4—88no—
594C22×C4—88no—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D414yes—
600C22×C4C22×D414yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C4H(5,𝔽2)12yes—
610C22×C42−1+414yes—
611C4⋊C4—28no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—416no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C22⋊C4—28no—
621C22⋊C4—44no—
622C22⋊C4—416no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—416no—
629C22⋊C4—88no—
630C22⋊C4—84no—
631C22⋊C4—84no—
632C22⋊C4—88no—
633C42—28no—
634C42—28no—
635C42—28no—
636C42—44no—
637C42—44no—
638C42—44no—
639C42—84no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—28no—
650C23—28no—
651C23—28no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23C2×#12418yes—
686C23C23×D411yescharacteristic
687C23C23×D411yescharacteristic
688C23C22×#4111yescharacteristic
689C23C22×#4111yescharacteristic
690C23C22×#4111yescharacteristic
691C23C2×H(5,𝔽2)11yescharacteristic
692C23C2×H(5,𝔽2)11yescharacteristic
693C23C2×2−1+412yes—
694C23#58512yes—
695C23#58512yes—
696C23#58512yes—
697Q8—416no—
698Q8—816no—
699Q8—88no—
700D4—232no—
701D4—432no—
702C2×C4—22no—
703C2×C4—24no—
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—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—28no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—432no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—41no—
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—44no—
747C2×C4—42no—
748C2×C4—416no—
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—44no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
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—44no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—816no—
798C2×C4—816no—
799C2×C4#52514yes—
800C2×C4C2×#12414yes—
801C2×C4#53614yes—
802C2×C4#53814yes—
803C2×C4D4214yes—
804C2×C4#54614yes—
805C2×C4#54614yes—
806C2×C4#55114yes—
807C22—28no—
808C22—216no—
809C22—48no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—48no—
815C22—44no—
816C22—48no—
817C22—44no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22C2×#52511yescharacteristic
830C22C22×#12411yescharacteristic
831C22C2×#53611yescharacteristic
832C22#344911yescharacteristic
833C22C2×#53811yescharacteristic
834C22C2×D4211yescharacteristic
835C22C2×#54611yescharacteristic
836C22C2×#54611yescharacteristic
837C22C2×#55111yescharacteristic
838C22#348512yes—
839C22#348912yes—
840C22#350011yescharacteristic
841C22#350011yescharacteristic
842C22#351512yes—
843C22#351512yes—
844C22#351812yes—
845C22#352112yes—
846C22#352112yes—
847C22#352412yes—
848C22#354012yes—
849C22#354712yes—
850C22#356112yes—
851C22#356212yes—
852C4—24no—
853C4—42no—
854C4—44no—
855C4—42no—
856C4—44no—
857C4—42no—
858C4—44no—
859C4—42no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4—82no—
868C4#247218yes—
869C2—48no—
870C2—82no—
871C2C2×#247211yescharacteristic
872C2#3520011yescharacteristic
873C2#3562311yescharacteristic
874C2#3604212yes—
875C2#3767611yescharacteristic
876C2#3768211yescharacteristic
877C2#3809411yescharacteristic
878C2#3895511yescharacteristic
879C2#4276712yes—
880C2#4519212yes—
881C2#4538512yes—
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×#2563C2semidirect
2. C2×#2492C2semidirect
5. #16368C2semidirect
6. #15371C2semidirect
7. #15291C2semidirect
8. #15236C2semidirect
9. #15233C2semidirect
10. #15191C2semidirect
11. #15180C2semidirect
12. #14767C2semidirect
13. #14274C2semidirect
14. #14027C2semidirect
15. #14027C2semidirect
16. #14003C2semidirect
18. #13842C2semidirect
19. #13785C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25632
C2×#24922
C2×#24322
C2×#23392
#163682
#153712
#152912
#152362
#152332
#151912
#151802
#147672
#142742
#140272
#140032
#139372
#138422
#137852