Finite Group Databasebeta

← #763411

Subgroups — #763411

Order 512.

3014 conjugacy classes of subgroups.

The subgroup lattice has 929 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2444C212yesmaximal
2C2×#2322C212yesmaximal, complemented
3#15981C211yesmaximal, characteristic, complemented
4#15961C211yesmaximal, characteristic, complemented
5#15953C212yesmaximal, complemented
6#15780C211yesmaximal, characteristic, complemented
7#15532C212yesmaximal, complemented
8#15521C211yesmaximal, characteristic, complemented
9#15410C212yesmaximal, complemented
10#15405C212yesmaximal, complemented
11#15400C212yesmaximal, complemented
12#15398C212yesmaximal, complemented
13#14936C211yesmaximal, characteristic, complemented
14#14926C211yesmaximal, characteristic
15#14912C212yesmaximal, complemented
16#14140C212yesmaximal, complemented
17#14044C212yesmaximal, complemented
18#13975C212yesmaximal, complemented
19C2×#1442C211yesmaximal, characteristic, complemented
20C22×#123C2212yes—
21C22×#121C2211yescharacteristic
22C22×C4×D4C2212yes—
23C23×C4⋊C4C2211yescharacteristic
24#2444—216no—
25C2×#400C2212yes—
26C2×#397C2212yes—
27C2×#397C2212yes—
28C2×#394C2212yes—
29#2322—216no—
30C2×#389C2212yes—
31C2×#389C2212yes—
32C2×#388C2212yes—
33C2×#388C2212yes—
34C2×#388C2212yes—
35C2×#388C2212yes—
36C2×#387C2212yes—
37C2×#387C2212yes—
38C2×#387C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#381C2212yes—
51C2×#381C2212yes—
52C2×#380C2211yescharacteristic
53C2×C4×C22⋊C4C2212yes—
54C22×#95C2211yescharacteristic
55C22×#95C2212yes—
56C22×#95C2212yes—
57C22×#95C2211yescharacteristic
58#1445C2211yescharacteristic
59#1445C2212yes—
60#1445C2212yes—
61#1445C2211yescharacteristic
62#1444C2212yes—
63#1444C2211yescharacteristic
64#1444C2211yescharacteristic
65#1444C2211yescharacteristic
66#1444C2211yescharacteristic
67#1443C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1442C2211yescharacteristic
71#1442C2211yescharacteristic
72#1442C2211yescharacteristic
73#1442C2211yescharacteristic
74#1442C2212yes—
75#1442C2212yes—
76#1442C2212yes—
77#1442C2212yes—
78#1442C2212yes—
79#1442C2212yes—
80#1441C2212yes—
81#1441C2212yes—
82#1441C2212yes—
83#1441C2212yes—
84#1440C2212yes—
85#1440C2212yes—
86#1440C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1438C2211yescharacteristic
95#1438C2211yescharacteristic
96#1437C2212yes—
97#1436C2212yes—
98#1436C2212yes—
99#1436C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102C4⋊#95C2212yes—
103C4⋊#95C2212yes—
104#1434C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2211yescharacteristic
107C22⋊#95C2212yes—
108C22⋊#95C2211yescharacteristic
109C23×D4C2312yes—
110C23×D4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2312yes—
115C24×C4C2312yes—
116C24×C4C2312yes—
117C2×#123—28no—
118C2×#123—28no—
119C2×#123—28no—
120C2×#121—28no—
121C2×#121—42no—
122C2×C4×D4—28no—
123C2×C4×D4—28no—
124C2×C4×D4—44no—
125C22×C4⋊C4—28no—
126C22×C4⋊C4—42no—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2312yes—
160#400—28no—
161#397—28no—
162#397—28no—
163#394—28no—
164#389—28no—
165#389—28no—
166#388—28no—
167#388—28no—
168#388—28no—
169#388—44no—
170#387—28no—
171#387—28no—
172#387—28no—
173#386—28no—
174#386—28no—
175#386—28no—
176#386—28no—
177#386D4116yes—
178#385—28no—
179#385—28no—
180#385—28no—
181#385—28no—
182#385—28no—
183#385—44no—
184#381—28no—
185#381—28no—
186#380—42no—
187C4×C22⋊C4—28no—
188C2×#95—28no—
189C2×#95—24no—
190C2×#95—44no—
191C2×#95—42no—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2312yes—
202C2×#95C2311yescharacteristic
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2311yescharacteristic
233C2×#95C2311yescharacteristic
234C2×#95C2311yescharacteristic
235C2×#95C2311yescharacteristic
236C2×#95C2312yes—
237C2×#95C2312yes—
238C25C2412yes—
239C25C2411yescharacteristic
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—22no—
248C22×D4—41no—
249C22×D4—42no—
250C22×D4—41no—
251C22×D4C2×D418yes—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—42no—
270C23×C4—41no—
271C23×C4—41no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4C2×D418yes—
287C23×C4#4114yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305#123—264no—
306#121—416no—
307C4×D4—432no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
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—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—41no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—41no—
335C2×C4⋊C4—416no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—41no—
347C2×C4⋊C4—41no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
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—24no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4C2×D418yes—
392C2×C22⋊C4C2×D418yes—
393C2×C22⋊C4C2×D418yes—
394C2×C22⋊C4#4118yes—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
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—22no—
423#95—22no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—22no—
432#95—22no—
433#95—42no—
434#95—42no—
435#95—41no—
436#95—41no—
437#95—41no—
438#95—41no—
439#95—42no—
440#95—42no—
441#95—41no—
442#95—42no—
443#95—41no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95C2×D418yes—
449#95C2×D418yes—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—21no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C22×D414yes—
471C24C22×D414yes—
472C24C2×#4112yes—
473C24C2×#4114yes—
474C24H(5,𝔽2)12yes—
475C242−1+412yes—
476C24C2511yescharacteristic
477C2×D4—216no—
478C2×D4—216no—
479C2×D4—216no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—44no—
486C2×D4—82no—
487C2×D4—84no—
488C2×D4—82no—
489C22×C4—216no—
490C22×C4—28no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
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—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
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—21no—
525C22×C4—21no—
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—21no—
535C22×C4—21no—
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—216no—
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—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—48no—
596C22×C4—44no—
597C22×C4—48no—
598C22×C4—44no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—84no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4—84no—
610C22×C4—84no—
611C22×C4—84no—
612C22×C4—82no—
613C22×C4—84no—
614C22×C4—82no—
615C22×C4—84no—
616C22×C4—84no—
617C22×C4—84no—
618C22×C4—84no—
619C22×C4—84no—
620C22×C4—84no—
621C22×C4C22×D414yes—
622C22×C4C22×D414yes—
623C22×C4C22×D414yes—
624C22×C4C22×D414yes—
625C22×C4C22×D414yes—
626C22×C4C2×#4114yes—
627C22×C4C2×#4112yes—
628C22×C4C2×#4112yes—
629C22×C4C2×#4114yes—
630C22×C4H(5,𝔽2)12yes—
631C22×C42−1+412yes—
632C4⋊C4—216no—
633C4⋊C4—216no—
634C4⋊C4—48no—
635C4⋊C4—44no—
636C4⋊C4—48no—
637C4⋊C4—44no—
638C4⋊C4—48no—
639C4⋊C4—44no—
640C4⋊C4—84no—
641C4⋊C4—84no—
642C4⋊C4—84no—
643C4⋊C4—84no—
644C4⋊C4—84no—
645C4⋊C4—82no—
646C4⋊C4—82no—
647C22⋊C4—216no—
648C22⋊C4—216no—
649C22⋊C4—216no—
650C22⋊C4—216no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—84no—
658C22⋊C4—84no—
659C22⋊C4—84no—
660C22⋊C4—84no—
661C22⋊C4—84no—
662C42—48no—
663C42—84no—
664C42—84no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—24no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23#52518yes—
719C23#53914yes—
720C23D4214yes—
721C23#54718yes—
722C23#55914yes—
723C23C23×D412yes—
724C23C22×#4111yescharacteristic
725C23C22×#4112yes—
726C23C2×H(5,𝔽2)11yescharacteristic
727C23C2×H(5,𝔽2)11yescharacteristic
728C23C2×2−1+411yescharacteristic
729C23C2×2−1+411yescharacteristic
730C23#58511yescharacteristic
731C23#58512yes—
732C23#58512yes—
733C23#58511yescharacteristic
734D4—432no—
735D4—88no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—416no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
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—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—816no—
845C2×C4—88no—
846C2×C4—88no—
847C2×C4—816no—
848C2×C4—816no—
849C22—24no—
850C22—24no—
851C22—28no—
852C22—24no—
853C22—28no—
854C22—24no—
855C22—28no—
856C22—24no—
857C22—24no—
858C22—28no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22#245518yes—
875C22C2×#52512yes—
876C22C2×#53911yescharacteristic
877C22C2×D4211yescharacteristic
878C22C2×#54712yes—
879C22C2×#55911yescharacteristic
880C22#348512yes—
881C22#348912yes—
882C22#349312yes—
883C22#349612yes—
884C22#350012yes—
885C22#350611yescharacteristic
886C22#350711yescharacteristic
887C22#351312yes—
888C22#351512yes—
889C22#352112yes—
890C22#352112yes—
891C22#353411yescharacteristic
892C22#353511yescharacteristic
893C22#354511yescharacteristic
894C22#354511yescharacteristic
895C22#355211yescharacteristic
896C22#355312yes—
897C22#355311yescharacteristic
898C4—44no—
899C4—44no—
900C4—44no—
901C4—44no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—44no—
906C4—44no—
907C4—42no—
908C4—44no—
909C4—82no—
910C4—82no—
911C4—82no—
912C4—81no—
913C4—82no—
914C4—81no—
915C2—28no—
916C2—84no—
917C2C2×#245511yescharacteristic
918C2#3536412yes—
919C2#3545012yes—
920C2#3712411yescharacteristic
921C2#3714111yescharacteristic
922C2#4301711yescharacteristic
923C2#4302712yes—
924C2#4332511yescharacteristic
925C2#4349512yes—
926C2#4371011yescharacteristic
927C2#4476011yescharacteristic
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
2. C2×#2322C2semidirect
3. #15981C2semidirect
4. #15961C2semidirect
5. #15953C2semidirect
6. #15780C2semidirect
7. #15532C2semidirect
8. #15521C2semidirect
9. #15410C2semidirect
10. #15405C2semidirect
11. #15400C2semidirect
12. #15398C2semidirect
13. #14936C2semidirect
15. #14912C2semidirect
16. #14140C2semidirect
17. #14044C2semidirect
18. #13975C2semidirect
19. C2×#1442C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24442
C2×#23222
#159812
#159612
#159532
#157802
#155322
#155212
#154102
#154052
#154002
#153982
#149362
#149262
#149122
#141402
#140442
#139752
C2×#14422