Finite Group Databasebeta

← #760288

Subgroups — #760288

Order 512.

4006 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic
2C2×#2500C211yesmaximal, characteristic
3C2×#2499C211yesmaximal, characteristic, complemented
4C2×#2296C211yesmaximal, characteristic, complemented
5#16657C214yesmaximal, complemented
6#15228C211yesmaximal, characteristic, complemented
7#15228C211yesmaximal, characteristic, complemented
8#15226C211yesmaximal, characteristic, complemented
9#15226C211yesmaximal, characteristic, complemented
10#15072C214yesmaximal, complemented
11#14731C214yesmaximal, complemented
12#14138C211yesmaximal, characteristic, complemented
13#14136C211yesmaximal, characteristic
14#14063C214yesmaximal, complemented
15#13979C211yesmaximal, characteristic, complemented
16#13978C211yesmaximal, characteristic, complemented
17#13977C211yesmaximal, characteristic, complemented
18#13976C211yesmaximal, characteristic, complemented
19C4×#381C211yesmaximal, characteristic, complemented
20C2×#529—28no—
21C2×#529—28no—
22C2×#529—28no—
23C22×#126C2212yes—
24C22×#125C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×#123C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×D4C2212yes—
31C22×C4×D4C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C22×#117C2212yes—
34C22×#117C2211yescharacteristic
35C23×C42C2211yescharacteristic
36#2500—28no—
37#2499—28no—
38C2×#397C2214yes—
39C2×#394C2214yes—
40#2296—28no—
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#388C2214yes—
54C2×#387C2214yes—
55C2×#385C2212yes—
56C2×#385C2212yes—
57C2×#385C2214yes—
58C2×#384C2211yescharacteristic
59C2×#384C2211yescharacteristic
60C2×#382C2211yescharacteristic
61C2×#382C2211yescharacteristic
62C2×#381C2212yes—
63C2×C4×C4⋊C4C2212yes—
64C2×C4×C4⋊C4C2212yes—
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67#1444C2214yes—
68#1444C2214yes—
69#1444C2214yes—
70#1442C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2214yes—
81#1437C2214yes—
82#1436C2214yes—
83#1436C2214yes—
84#1436C2214yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89#1434C2212yes—
90#1434C2212yes—
91C22⋊#95C2212yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C23×D4C2312yes—
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104#529—2128no—
105C2×#126—28no—
106C2×#126—28no—
107C2×#126—28no—
108C2×#125—24no—
109C2×#125—24no—
110C2×#125—24no—
111C2×#124—24no—
112C2×#124—24no—
113C2×#124—24no—
114C2×#123—28no—
115C2×#123—28no—
116C2×#123—28no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8D418yes—
120C2×#121—24no—
121C2×#121—24no—
122C2×#121D418yes—
123C2×C4×Q8—24no—
124C2×C4×Q8—24no—
125C2×C4×Q8—24no—
126C2×C4×D4—28no—
127C2×C4×D4—24no—
128C2×C4×D4—28no—
129C2×C4×D4—24no—
130C2×C4×D4—28no—
131C2×C4×D4—24no—
132C2×#117—24no—
133C2×#117—24no—
134C2×#117—24no—
135C2×#117—24no—
136C2×#117—28no—
137C2×#117—24no—
138C2×#117—24no—
139C2×#117—28no—
140C2×#117—28no—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2314yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2314yes—
170C22×C42—24no—
171C22×C42—24no—
172C22×C42D418yes—
173C22×C42C2312yes—
174C22×C42C2312yes—
175C22×C42C2312yes—
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180C22×C42C2311yescharacteristic
181C22×C42C2311yescharacteristic
182C22×C42C2311yescharacteristic
183C22×C42C2311yescharacteristic
184#397—216no—
185#394—216no—
186#391—24no—
187#391—24no—
188#391—24no—
189#391—24no—
190#390—24no—
191#390—24no—
192#390—24no—
193#390—24no—
194#389—24no—
195#389—24no—
196#389—24no—
197#389—24no—
198#388—216no—
199#387—216no—
200#385—28no—
201#385—28no—
202#385—216no—
203#384—24no—
204#384—24no—
205#382—24no—
206#382—24no—
207#381—28no—
208C4×C4⋊C4—28no—
209C4×C4⋊C4—28no—
210C4×C22⋊C4—24no—
211C4×C22⋊C4—24no—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2312yes—
236C25C2412yes—
237C25C2411yescharacteristic
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8C2×D414yes—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4C2×D414yes—
256C22×D4C2×D418yes—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—24no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—28no—
270C23×C4—44no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296#126—264no—
297#125—232no—
298#124—232no—
299#123—264no—
300C22⋊Q8—232no—
301#121—232no—
302C4×Q8—232no—
303C4×D4—264no—
304C4×D4—232no—
305#117—232no—
306#117—264no—
307#117—416no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
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—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4C2×D418yes—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4C2×D414yes—
350C2×C4⋊C4#4114yes—
351C2×C4⋊C4#4114yes—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
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—24no—
365C2×C22⋊C4—24no—
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—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4C2×D418yes—
390C2×C22⋊C4C2×D418yes—
391C2×C42—232no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42C2×D414yes—
422C2×C42C2×D414yes—
423C2×C42C2×D414yes—
424C2×C42C2×D414yes—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—28no—
432#95—28no—
433#95—28no—
434#95—28no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—28no—
439#95—28no—
440#95—28no—
441#95—42no—
442#95—44no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—44no—
447#95—44no—
448#95#4118yes—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—21no—
453C24—21no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—24no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—24no—
465C24—24no—
466C24—24no—
467C24C22×D414yes—
468C24C22×D412yes—
469C24C22×D412yes—
470C24C22×D412yes—
471C24C2511yescharacteristic
472C2×Q8—28no—
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×D4—216no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—416no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—416no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—216no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
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—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
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—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
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—24no—
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—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—416no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—416no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4#120116yes—
590C22×C4C22×D414yes—
591C22×C4C22×D414yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D414yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C2×#4114yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4114yes—
607C22×C4C2×#4114yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4112yes—
610C22×C42−1+412yes—
611C22×C42−1+412yes—
612C4⋊C4—216no—
613C4⋊C4—216no—
614C4⋊C4—216no—
615C4⋊C4—216no—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—416no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—48no—
627C4⋊C4—88no—
628C22⋊C4—216no—
629C22⋊C4—216no—
630C22⋊C4—216no—
631C22⋊C4—216no—
632C22⋊C4—216no—
633C22⋊C4—216no—
634C22⋊C4—416no—
635C22⋊C4—48no—
636C22⋊C4—416no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—88no—
640C22⋊C4—88no—
641C42—216no—
642C42—216no—
643C42—28no—
644C42—28no—
645C42—28no—
646C42—28no—
647C42—48no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—44no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—28no—
670C23—28no—
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—42no—
685C23—42no—
686C23—42no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23C2×#12014yes—
698C23C23×D411yescharacteristic
699C23C23×D411yescharacteristic
700C23C23×D411yescharacteristic
701C23C22×#4111yescharacteristic
702C23C22×#4111yescharacteristic
703C23C22×#4112yes—
704C23C2×2−1+411yescharacteristic
705C23C2×2−1+411yescharacteristic
706C23#58512yes—
707C23#58512yes—
708C23#58512yes—
709Q8—416no—
710D4—432no—
711D4—416no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—232no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—24no—
743C2×C4—28no—
744C2×C4—24no—
745C2×C4—28no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—28no—
749C2×C4—416no—
750C2×C4—432no—
751C2×C4—416no—
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—44no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—44no—
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—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4C2×#12014yes—
807C2×C4C2×#12014yes—
808C2×C4#52514yes—
809C2×C4#53214yes—
810C2×C4#53614yes—
811C2×C4#54714yes—
812C2×C4#54714yes—
813C2×C4#54714yes—
814C2×C4#54714yes—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—48no—
830C22—48no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—84no—
836C22—84no—
837C22C22×#12011yescharacteristic
838C22C2×#52511yescharacteristic
839C22C2×#53211yescharacteristic
840C22C2×#53611yescharacteristic
841C22#344911yescharacteristic
842C22#344911yescharacteristic
843C22#344911yescharacteristic
844C22C2×#54711yescharacteristic
845C22C2×#54711yescharacteristic
846C22C2×#54711yescharacteristic
847C22C2×#54711yescharacteristic
848C22D4×#4112yes—
849C22D4×#4112yes—
850C22#347512yes—
851C22#348012yes—
852C22#348512yes—
853C22#348712yes—
854C22#351512yes—
855C22#351812yes—
856C22#352112yes—
857C22#352412yes—
858C22#356512yes—
859C22#356512yes—
860C4—24no—
861C4—24no—
862C4—42no—
863C4—42no—
864C4—44no—
865C4—44no—
866C4—44no—
867C4—44no—
868C4—42no—
869C4—44no—
870C4—44no—
871C4—44no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4#240618yes—
877C2—44no—
878C2—84no—
879C2C2×#240611yescharacteristic
880C2#3473811yescharacteristic
881C2#3491011yescharacteristic
882C2#3514911yescharacteristic
883C2#3520111yescharacteristic
884C2#3521111yescharacteristic
885C2#3754511yescharacteristic
886C2#5911812yes—
887C2#5911912yes—
888C2#5912012yes—
889C2#5912112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2499C2semidirect
4. C2×#2296C2semidirect
5. #16657C2semidirect
6. #15228C2semidirect
7. #15228C2semidirect
8. #15226C2semidirect
9. #15226C2semidirect
10. #15072C2semidirect
11. #14731C2semidirect
12. #14138C2semidirect
14. #14063C2semidirect
15. #13979C2semidirect
16. #13978C2semidirect
17. #13977C2semidirect
18. #13976C2semidirect
19. C4×#381C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5292
C2×#25002
C2×#24992
C2×#22962
#166572
#152282
#152262
#150722
#147312
#141382
#141362
#140632
#139792
#139782
#139772
#139762
C4×#3812