Finite Group Databasebeta

← #696708

Subgroups — #696708

Order 512.

3680 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic
2C2×#2499C211yesmaximal, characteristic, complemented
3C2×#2485C211yesmaximal, characteristic
4C2×#2317C211yesmaximal, characteristic, complemented
5#16657C214yesmaximal
6#16104C214yesmaximal, complemented
7#16102C214yesmaximal, complemented
8#15236C211yesmaximal, characteristic, complemented
9#15228C211yesmaximal, characteristic, complemented
10#15228C211yesmaximal, characteristic, complemented
11#15182C211yesmaximal, characteristic, complemented
12#14892C214yesmaximal, complemented
13#14258C211yesmaximal, characteristic, complemented
14#13978C211yesmaximal, characteristic, complemented
15#13976C211yesmaximal, characteristic, complemented
16#13924C211yesmaximal, characteristic, complemented
17#13879C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19#13839C211yesmaximal, characteristic
20C2×#552—28no—
21C2×#552—28no—
22C2×#552—28no—
23C22×#126C2212yes—
24C22×#125C2211yescharacteristic
25C22×#125C2212yes—
26C22×#123C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C22×#117C2212yes—
34C22×#117C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36#2499—28no—
37#2485—28no—
38C2×#397C2214yes—
39C2×#397C2212yes—
40C2×#394C2212yes—
41#2317—28no—
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#389C2214yes—
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#388C2212yes—
50C2×#387C2212yes—
51C2×#387C2214yes—
52C2×#385C2214yes—
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65#1445C2214yes—
66#1444C2214yes—
67#1444C2214yes—
68#1444C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1441C2212yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1440C2212yes—
77#1440C2214yes—
78#1440C2214yes—
79#1439C2212yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1438C2212yes—
84#1436C2214yes—
85#1436C2214yes—
86#1436C2214yes—
87#1436C2214yes—
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C22⋊#95C2214yes—
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102#552—2128no—
103C2×#126—28no—
104C2×#126—28no—
105C2×#126—28no—
106C2×#125—28no—
107C2×#125—28no—
108C2×#125—28no—
109C2×#125—24no—
110C2×#125—24no—
111C2×#125—24no—
112C2×#123—28no—
113C2×#123—28no—
114C2×#123—28no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8D418yes—
121C2×C4×Q8—24no—
122C2×C4×Q8—24no—
123C2×C4×Q8—24no—
124C2×C4×D4—24no—
125C2×C4×D4—24no—
126C2×C4×D4D418yes—
127C2×#117—24no—
128C2×#117—24no—
129C2×#117—28no—
130C2×#117—24no—
131C2×#117—24no—
132C2×#117—24no—
133C2×#117—24no—
134C2×#117—24no—
135C2×#117—28no—
136C2×#117—28no—
137C2×#117—24no—
138C2×#117—24no—
139C22×C4⋊C4—24no—
140C22×C4⋊C4—24no—
141C22×C4⋊C4D418yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2314yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2314yes—
161C22×C4⋊C4C2314yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2311yescharacteristic
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C42C2312yes—
176C22×C42C2312yes—
177C22×C42C2312yes—
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180C22×C42C2311yescharacteristic
181C22×C42C2311yescharacteristic
182C22×C42C2311yescharacteristic
183#397—28no—
184#397—216no—
185#394—28no—
186#391—24no—
187#391—24no—
188#391—24no—
189#391—24no—
190#389—216no—
191#389—24no—
192#389—24no—
193#388—28no—
194#387—28no—
195#387—216no—
196#385—216no—
197#384—24no—
198#384—24no—
199#384—24no—
200#382—24no—
201#382—24no—
202#382—24no—
203#380—24no—
204#380—24no—
205#380—24no—
206C4×C22⋊C4—24no—
207C4×C22⋊C4—24no—
208C4×C22⋊C4—24no—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C25C2411yescharacteristic
235C25C2411yescharacteristic
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8C2×D414yes—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—42no—
246C22×D4—42no—
247C22×D4C2×D414yes—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4C2×D414yes—
263C23×C4C2×D414yes—
264C23×C4C2×D414yes—
265C23×C4C2×D414yes—
266C23×C4C2×D418yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284#126—264no—
285#125—264no—
286#125—232no—
287#123—264no—
288C22⋊Q8—232no—
289C22⋊Q8—232no—
290C4×Q8—232no—
291C4×D4—232no—
292#117—232no—
293#117—232no—
294#117—264no—
295#117—416no—
296C2×C4⋊C4—232no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4C2×D414yes—
350C2×C4⋊C4C2×D414yes—
351C2×C4⋊C4C2×D418yes—
352C2×C4⋊C4C2×D414yes—
353C2×C4⋊C4C2×D414yes—
354C2×C4⋊C4C2×D418yes—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4C2×D414yes—
389C2×C22⋊C4C2×D418yes—
390C2×C22⋊C4C2×D414yes—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42C2×D414yes—
413C2×C42#4114yes—
414C2×C42#4114yes—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—28no—
420#95—28no—
421#95—28no—
422#95—24no—
423#95—28no—
424#95—28no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—28no—
429#95—28no—
430#95—24no—
431#95—44no—
432#95—42no—
433#95—42no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95—42no—
438#95—44no—
439#95—44no—
440C24—21no—
441C24—21no—
442C24—22no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—22no—
453C24—21no—
454C24—21no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24C22×D412yes—
459C24C22×D412yes—
460C24C22×D412yes—
461C24C22×D412yes—
462C24C2511yescharacteristic
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×D4—28no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—48no—
474C2×D4—48no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—216no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
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—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
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—24no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—416no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—416no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4#120116yes—
575C22×C4C22×D412yes—
576C22×C4C22×D414yes—
577C22×C4C22×D412yes—
578C22×C4C22×D414yes—
579C22×C4C22×D414yes—
580C22×C4C22×D412yes—
581C22×C4C22×D414yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C2×#4114yes—
589C22×C4C2×#4114yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C42−1+414yes—
593C22×C42−1+412yes—
594C22×C42−1+412yes—
595C4⋊C4—216no—
596C4⋊C4—216no—
597C4⋊C4—216no—
598C4⋊C4—216no—
599C4⋊C4—216no—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—216no—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—216no—
606C4⋊C4—416no—
607C4⋊C4—48no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—88no—
613C4⋊C4—88no—
614C4⋊C4—84no—
615C22⋊C4—216no—
616C22⋊C4—216no—
617C22⋊C4—216no—
618C22⋊C4—28no—
619C22⋊C4—216no—
620C22⋊C4—28no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—84no—
627C22⋊C4—84no—
628C42—216no—
629C42—216no—
630C42—28no—
631C42—28no—
632C42—28no—
633C42—48no—
634C42—44no—
635C42—44no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
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—
681C23C2×#12014yes—
682C23C23×D411yescharacteristic
683C23C23×D411yescharacteristic
684C23C23×D411yescharacteristic
685C23C22×#4111yescharacteristic
686C23C22×#4111yescharacteristic
687C23C2×2−1+411yescharacteristic
688C23C2×2−1+411yescharacteristic
689C23C2×2−1+412yes—
690C23#58512yes—
691C23#58512yes—
692C23#58512yes—
693Q8—416no—
694D4—416no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—232no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—24no—
720C2×C4—28no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—432no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
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—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—416no—
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—44no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4C2×#12014yes—
792C2×C4C2×#12014yes—
793C2×C4#52514yes—
794C2×C4#53614yes—
795C2×C4#54714yes—
796C2×C4#54714yes—
797C2×C4#54714yes—
798C2×C4#54714yes—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—42no—
803C22—42no—
804C22—44no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22C22×#12011yescharacteristic
822C22C2×#52511yescharacteristic
823C22C2×#53611yescharacteristic
824C22#344911yescharacteristic
825C22#344911yescharacteristic
826C22C2×#54711yescharacteristic
827C22C2×#54711yescharacteristic
828C22C2×#54711yescharacteristic
829C22C2×#54711yescharacteristic
830C22#348512yes—
831C22#348712yes—
832C22#348912yes—
833C22#349312yes—
834C22#349512yes—
835C22#349712yes—
836C22#349911yescharacteristic
837C22#350011yescharacteristic
838C22#350712yes—
839C22#351212yes—
840C22#355512yes—
841C22#356312yes—
842C22#356512yes—
843C22#356512yes—
844C4—24no—
845C4—42no—
846C4—44no—
847C4—44no—
848C4—44no—
849C4—42no—
850C4—42no—
851C4—44no—
852C4—44no—
853C4—44no—
854C4—44no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4—82no—
860C4#240618yes—
861C2—44no—
862C2—82no—
863C2C2×#240611yescharacteristic
864C2#3514911yescharacteristic
865C2#3566011yescharacteristic
866C2#3575812yes—
867C2#3786811yescharacteristic
868C2#3787111yescharacteristic
869C2#3948411yescharacteristic
870C2#3948511yescharacteristic
871C2#4264412yes—
872C2#4526112yes—
873C2#4526412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2499C2semidirect
4. C2×#2317C2semidirect
6. #16104C2semidirect
7. #16102C2semidirect
8. #15236C2semidirect
9. #15228C2semidirect
10. #15228C2semidirect
11. #15182C2semidirect
12. #14892C2semidirect
13. #14258C2semidirect
14. #13978C2semidirect
15. #13976C2semidirect
16. #13924C2semidirect
17. #13879C2semidirect
18. #13879C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5522
C2×#24992
C2×#24852
C2×#23172
#166572
#161042
#161022
#152362
#152282
#151822
#148922
#142582
#139782
#139762
#139242
#138792
#138392