Finite Group Databasebeta

← #894674

Subgroups — #894674

Order 512.

2188 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2532C212yesmaximal, complemented
2#17077C211yesmaximal, characteristic
3#17076C211yesmaximal, characteristic, complemented
4#17062C212yesmaximal, complemented
5#15689C212yesmaximal
6#15675C212yesmaximal, complemented
7#15517C212yesmaximal, complemented
8#15499C212yesmaximal, complemented
9#15084C212yesmaximal
10#15081C212yesmaximal, complemented
11#15077C212yesmaximal, complemented
12#14703C211yesmaximal, characteristic, complemented
13#14700C211yesmaximal, characteristic
14#14467C211yesmaximal, characteristic, complemented
15#14445C211yesmaximal, characteristic
16#14413C212yesmaximal, complemented
17#14079C212yesmaximal, complemented
18#13900C212yesmaximal, complemented
19C4×#384C211yesmaximal, characteristic, complemented
20#2532—216no—
21C2×#400C2212yes—
22C2×#399C2212yes—
23C2×#399C2212yes—
24C2×#398C2212yes—
25C2×#398C2212yes—
26C2×#397C2212yes—
27C2×#397C2212yes—
28C2×#393C2212yes—
29C2×#391C2211yescharacteristic
30C2×#391C2212yes—
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#388C2212yes—
39C2×#388C2212yes—
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#388C2212yes—
43C2×#388C2212yes—
44C2×#388C2212yes—
45C2×#388C2212yes—
46C2×#388C2212yes—
47C2×#387C2212yes—
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#383C2212yes—
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×#376C2212yes—
56C2×C43C2211yescharacteristic
57#1445C2212yes—
58#1445C2212yes—
59#1445C2212yes—
60#1444C2212yes—
61#1444C2212yes—
62#1444C2212yes—
63#1444C2212yes—
64#1442C2212yes—
65#1442C2212yes—
66#1442C2212yes—
67#1442C2212yes—
68#1441C2212yes—
69#1441C2212yes—
70#1441C2212yes—
71#1441C2212yes—
72#1440C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1438C2212yes—
84#1438C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1437C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95C4⋊#95C2212yes—
96C4⋊#95C2212yes—
97C4⋊#95C2212yes—
98C4⋊#95C2211yescharacteristic
99C4⋊#95C2211yescharacteristic
100C4⋊#95C2211yescharacteristic
101C4⋊#95C2211yescharacteristic
102C4⋊#95C2211yescharacteristic
103C4⋊#95C2211yescharacteristic
104#1434C2212yes—
105#1434C2212yes—
106#1434C2212yes—
107#1434C2212yes—
108C23×Q8C2311yescharacteristic
109C23×D4C2311yescharacteristic
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C42C2312yes—
145C22×C42C2312yes—
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2312yes—
154C22×C42C2311yescharacteristic
155#400—28no—
156#399—44no—
157#399—44no—
158#398—28no—
159#398—44no—
160#397—28no—
161#397—44no—
162#393—28no—
163#391—28no—
164#391—24no—
165#391—42no—
166#391D418yescomplemented
167#390—24no—
168#390—24no—
169#390—42no—
170#389—42no—
171#389—42no—
172#388—28no—
173#388—28no—
174#388—28no—
175#388—28no—
176#388—28no—
177#388—28no—
178#388—28no—
179#388—44no—
180#388—44no—
181#387—28no—
182#384—24no—
183#384—24no—
184#383—28no—
185C4×C4⋊C4—28no—
186C4×C4⋊C4—28no—
187C4×C4⋊C4—42no—
188C4×C4⋊C4—42no—
189#376—28no—
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—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C43—24no—
231C25C2412yes—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—41no—
235C22×Q8—41no—
236C22×Q8—41no—
237C22×Q8—41no—
238C22×Q8C2×D414yes—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—41no—
243C22×D4—41no—
244C22×D4—41no—
245C22×D4—41no—
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258C23×C4C2411yescharacteristic
259C23×C4C2411yescharacteristic
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4C2×D414yes—
323C2×C4⋊C4#4114yes—
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—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
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×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
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×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—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—41no—
389C2×C42—41no—
390C2×C42—41no—
391C2×C42—41no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42C2×D414yes—
396C2×C42#4114yes—
397C2×C42#4114yes—
398C2×C42#4114yes—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95C2×D418yes—
438#95C2×D418yes—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24C2511yescharacteristic
455C2×Q8—28no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×Q8—82no—
459C2×Q8—82no—
460C2×Q8—82no—
461C2×Q8—82no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—82no—
466C2×D4—82no—
467C2×D4—82no—
468C2×D4—82no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
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—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4C22×D414yes—
574C22×C4C22×D414yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C2×#4114yes—
579C22×C4C2×#4112yes—
580C22×C4C2×#4112yes—
581C22×C4C2×#4112yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4C2×#4112yes—
585C22×C4C2×#4112yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4C2×#4112yes—
589C22×C4H(5,𝔽2)12yes—
590C22×C4H(5,𝔽2)12yes—
591C22×C4H(5,𝔽2)12yes—
592C22×C42−1+412yes—
593C22×C42−1+412yes—
594C22×C42−1+412yes—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—48no—
598C4⋊C4—48no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—82no—
607C4⋊C4—82no—
608C4⋊C4—82no—
609C4⋊C4—82no—
610C4⋊C4—84no—
611C4⋊C4—84no—
612C4⋊C4—84no—
613C4⋊C4—84no—
614C4⋊C4—84no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—84no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C22⋊C4—84no—
628C22⋊C4—84no—
629C42—28no—
630C42—28no—
631C42—28no—
632C42—28no—
633C42—44no—
634C42—44no—
635C42—44no—
636C42—48no—
637C42—48no—
638C42—48no—
639C42—48no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23C23×D411yescharacteristic
676C23C22×#4111yescharacteristic
677C23C22×#4111yescharacteristic
678C23C22×#4111yescharacteristic
679C23C22×#4111yescharacteristic
680C23C2×H(5,𝔽2)11yescharacteristic
681C23C2×H(5,𝔽2)11yescharacteristic
682C23C2×H(5,𝔽2)11yescharacteristic
683C23C2×2−1+411yescharacteristic
684C23C2×2−1+411yescharacteristic
685C23C2×2−1+411yescharacteristic
686C23#58511yescharacteristic
687C23#58511yescharacteristic
688C23#58511yescharacteristic
689C23#58511yescharacteristic
690Q8—88no—
691D4—88no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
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—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—41no—
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—42no—
811C2×C4—42no—
812C2×C4#52914yes—
813C2×C4#54714yes—
814C2×C4#55014yes—
815C2×C4#55014yes—
816C2×C4#55214yes—
817C2×C4#55514yes—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22C2×#52911yescharacteristic
834C22#344911yescharacteristic
835C22#345511yescharacteristic
836C22#345911yescharacteristic
837C22#346111yescharacteristic
838C22C2×#54711yescharacteristic
839C22C2×#55011yescharacteristic
840C22C2×#55011yescharacteristic
841C22D4×#4111yescharacteristic
842C22C2×#55211yescharacteristic
843C22C2×#55511yescharacteristic
844C22#347511yescharacteristic
845C22#349111yescharacteristic
846C22#349211yescharacteristic
847C22#349411yescharacteristic
848C22#349411yescharacteristic
849C22#349611yescharacteristic
850C22#349911yescharacteristic
851C22#350611yescharacteristic
852C22#350611yescharacteristic
853C22#350711yescharacteristic
854C22#350711yescharacteristic
855C22#350711yescharacteristic
856C22#350911yescharacteristic
857C22#352211yescharacteristic
858C22#352211yescharacteristic
859C22#352911yescharacteristic
860C22#354411yescharacteristic
861C22#354911yescharacteristic
862C22#356111yescharacteristic
863C22#356111yescharacteristic
864C22#356111yescharacteristic
865C22#356111yescharacteristic
866C22#356411yescharacteristic
867C22#356411yescharacteristic
868C4—24no—
869C4—24no—
870C4—24no—
871C4—24no—
872C4—24no—
873C4—24no—
874C4—44no—
875C4—42no—
876C4—44no—
877C4—44no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4—82no—
886C2—162no—
887C2#3504211yescharacteristic
888C2#3611711yescharacteristic
889C2#3617611yescharacteristic
890C2#3726711yescharacteristic
891C2#3786611yescharacteristic
892C2#3788511yescharacteristic
893C2#3944611yescharacteristic
894C2#3950111yescharacteristic
895C2#3957411yescharacteristic
896C2#3974011yescharacteristic
897C2#4623211yescharacteristic
898C2#4628511yescharacteristic
899C2#5216011yescharacteristic
900C2#5931211yescharacteristic
901C2#5982211yescharacteristic
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
1. C2×#2532C2semidirect
3. #17076C2semidirect
4. #17062C2semidirect
6. #15675C2semidirect
7. #15517C2semidirect
8. #15499C2semidirect
10. #15081C2semidirect
11. #15077C2semidirect
12. #14703C2semidirect
14. #14467C2semidirect
16. #14413C2semidirect
17. #14079C2semidirect
18. #13900C2semidirect
19. C4×#384C2semidirect
166. #391D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25322
#170772
#170762
#170622
#156892
#156752
#155172
#154992
#150842
#150812
#150772
#147032
#147002
#144672
#144452
#144132
#140792
#139002
C4×#3842