Finite Group Databasebeta

← #3955326

Subgroups — #3955326

Order 512.

2658 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2607C211yesmaximal, characteristic, complemented
2C2×#2482C211yesmaximal, characteristic
3#16830C211yesmaximal, characteristic, complemented
4#16675C211yesmaximal, characteristic, complemented
5#16278C212yesmaximal, complemented
6#15956C212yesmaximal, complemented
7#15907C212yesmaximal, complemented
8#15832C212yesmaximal, complemented
9#15586C212yesmaximal, complemented
10#15467C212yesmaximal
11#15371C212yesmaximal, complemented
12#14785C212yesmaximal, complemented
13#14734C211yesmaximal, characteristic
14#14592C211yesmaximal, characteristic, complemented
15#14553C212yesmaximal, complemented
16#14063C212yesmaximal, complemented
17#13983C212yesmaximal, complemented
18#13971C212yesmaximal
19#13869C211yesmaximal, characteristic
20C22×#117C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23#2607—28no—
24#2482—28no—
25C2×#399C2211yescharacteristic
26C2×#399C2211yescharacteristic
27C2×#399C2211yescharacteristic
28C2×#399C2211yescharacteristic
29C2×#397C2211yescharacteristic
30C2×#397C2211yescharacteristic
31C2×#393C2212yes—
32C2×#393C2212yes—
33C2×#393C2212yes—
34C2×#391C2212yescomplemented
35C2×#391C2212yescomplemented
36C2×#388C2212yes—
37C2×#388C2212yes—
38C2×#388C2212yes—
39C2×#388C2212yes—
40C2×#387C2212yescomplemented
41C2×#387C2212yescomplemented
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#381C2211yescharacteristic
46C2×#381C2211yescharacteristic
47C2×#381C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#379C2212yes—
50C2×#379C2212yes—
51C2×#379C2211yescharacteristic
52C2×C4×C4⋊C4C2212yescomplemented
53C2×C4×C22⋊C4C2212yes—
54#1446C2212yescomplemented
55#1446C2212yescomplemented
56#1445C2212yescomplemented
57#1445C2212yescomplemented
58#1444C2212yescomplemented
59#1443C2212yescomplemented
60#1443C2212yescomplemented
61#1443C2212yescomplemented
62#1443C2212yescomplemented
63#1442C2212yescomplemented
64#1442C2212yescomplemented
65#1442C2212yescomplemented
66#1442C2212yescomplemented
67#1442C2212yescomplemented
68#1442C2212yescomplemented
69#1441C2212yescomplemented
70#1441C2212yescomplemented
71#1441C2212yescomplemented
72#1440C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1440C2212yes—
77#1440C2212yes—
78#1440C2212yes—
79#1440C2212yes—
80#1440C2212yes—
81#1440C2212yes—
82#1439C2211yescharacteristic
83#1439C2212yes—
84#1439C2212yes—
85#1439C2211yescharacteristic
86#1439C2212yes—
87#1439C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1437C2212yes—
91#1437C2212yes—
92#1437C2212yes—
93#1436C2212yescomplemented
94#1436C2212yescomplemented
95#1436C2212yescomplemented
96#1436C2212yescomplemented
97#1436C2212yescomplemented
98#1436C2212yescomplemented
99#1436C2212yescomplemented
100#1434C2212yescomplemented
101#1434C2212yescomplemented
102C22⋊#95C2211yescharacteristic
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2211yescharacteristic
107C22⋊#95C2211yescharacteristic
108C22⋊#95C2212yes—
109C26C2311yescharacteristic
110C23×Q8C2312yes—
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C2×#117—24no—
116C2×#117—42no—
117C2×#117—42no—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—24no—
130C22×C22⋊C4—42no—
131C22×C22⋊C4—42no—
132C22×C22⋊C4—42no—
133C22×C22⋊C4—42no—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2312yes—
156C22×C42C2312yes—
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2312yes—
160#399—24no—
161#399—24no—
162#399—42no—
163#399D418yes—
164#397—24no—
165#397—24no—
166#393—28no—
167#393—28no—
168#393—44no—
169#391—28no—
170#391—28no—
171#388—28no—
172#388—28no—
173#388—44no—
174#388—44no—
175#387—28no—
176#387—28no—
177#385—28no—
178#385—28no—
179#385—28no—
180#381—24no—
181#381—24no—
182#381—42no—
183#380—42no—
184#379—28no—
185#379—28no—
186#379—42no—
187C4×C4⋊C4—44no—
188C4×C22⋊C4—28no—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2311yescharacteristic
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
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—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2311yescharacteristic
234C25—22no—
235C25—22no—
236C25—22no—
237C25—22no—
238C25—24no—
239C25—22no—
240C25—41no—
241C25—42no—
242C25—41no—
243C25—42no—
244C25—42no—
245C25C2411yescharacteristic
246C25C2411yescharacteristic
247C25C2411yescharacteristic
248C22×Q8—24no—
249C22×Q8—24no—
250C22×Q8—42no—
251C22×Q8—42no—
252C22×Q8—42no—
253C22×Q8—42no—
254C22×Q8—42no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—42no—
265C23×C4—41no—
266C23×C4—41no—
267C23×C4—41no—
268C23×C4—41no—
269C23×C4—41no—
270C23×C4—42no—
271C23×C4—41no—
272C23×C4—41no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4#4114yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293#117—416no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4C2×D414yes—
322C2×C4⋊C4C2×D418yes—
323C2×C22⋊C4—22no—
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—22no—
339C2×C22⋊C4—22no—
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—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—416no—
375C2×C22⋊C4—416no—
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—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4C2×D414yes—
389C2×C22⋊C4C2×D418yes—
390C2×C22⋊C4#4118yes—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—22no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—22no—
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—42no—
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#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—41no—
447#95C2×D414yes—
448C24—21no—
449C24—22no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—22no—
458C24—21no—
459C24—21no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—28no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—44no—
477C24—48no—
478C24—44no—
479C24—48no—
480C24—44no—
481C24—44no—
482C24—48no—
483C24—48no—
484C24—44no—
485C24—44no—
486C24—44no—
487C24—44no—
488C24—84no—
489C24—84no—
490C24—84no—
491C24—84no—
492C24—82no—
493C24—82no—
494C24—84no—
495C24—84no—
496C24—84no—
497C24—84no—
498C24C22×D412yes—
499C24C2×#4112yes—
500C24C2×#4114yes—
501C24H(5,𝔽2)12yes—
502C24H(5,𝔽2)12yes—
503C242−1+412yes—
504C24C2511yescharacteristic
505C2×Q8—48no—
506C2×Q8—48no—
507C2×Q8—84no—
508C2×Q8—84no—
509C2×Q8—84no—
510C2×Q8—84no—
511C2×Q8—84no—
512C22×C4—28no—
513C22×C4—22no—
514C22×C4—22no—
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—22no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
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—28no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
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×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—84no—
620C22×C4—82no—
621C22×C4—82no—
622C22×C4—82no—
623C22×C4—82no—
624C22×C4—82no—
625C22×C4—84no—
626C22×C4—84no—
627C22×C4—82no—
628C22×C4—82no—
629C22×C4—84no—
630C22×C4C22×D412yes—
631C22×C4C22×D414yes—
632C22×C4C22×D412yes—
633C22×C4C22×D414yes—
634C22×C4C2×#4114yes—
635C22×C4C2×#4114yes—
636C22×C4C2×#4114yes—
637C22×C4H(5,𝔽2)12yes—
638C4⋊C4—48no—
639C4⋊C4—44no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—44no—
644C4⋊C4—82no—
645C4⋊C4—84no—
646C4⋊C4—84no—
647C4⋊C4—82no—
648C22⋊C4—44no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—44no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—44no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—44no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—84no—
665C22⋊C4—84no—
666C22⋊C4—82no—
667C22⋊C4—84no—
668C22⋊C4—82no—
669C22⋊C4—84no—
670C42—48no—
671C42—48no—
672C42—84no—
673C42—84no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—22no—
680C23—22no—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—24no—
701C23—22no—
702C23—24no—
703C23—416no—
704C23—416no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—41no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—41no—
726C23—41no—
727C23—42no—
728C23—42no—
729C23—41no—
730C23—41no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—88no—
744C23—88no—
745C23—816no—
746C23—88no—
747C23—816no—
748C23—816no—
749C23—88no—
750C23—816no—
751C23—88no—
752C23#54814yes—
753C23#55914yes—
754C23C23×D411yescharacteristic
755C23C22×#4111yescharacteristic
756C23C22×#4112yes—
757C23C2×H(5,𝔽2)11yescharacteristic
758C23C2×H(5,𝔽2)11yescharacteristic
759C23C2×H(5,𝔽2)11yescharacteristic
760C23C2×2−1+411yescharacteristic
761C23#58511yescharacteristic
762C23#58512yes—
763C23#58512yes—
764C23#58512yes—
765Q8—816no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—416no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
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—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
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—41no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—88no—
872C2×C4—88no—
873C2×C4—88no—
874C22—24no—
875C22—24no—
876C22—24no—
877C22—24no—
878C22—28no—
879C22—44no—
880C22—44no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—44no—
886C22—44no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—44no—
891C22—44no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—44no—
897C22—42no—
898C22—42no—
899C22—44no—
900C22—42no—
901C22—832no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—82no—
906C22—81no—
907C22—82no—
908C22#345911yescharacteristic
909C22C2×#54811yescharacteristic
910C22D4×#4112yes—
911C22#347512yes—
912C22C2×#55911yescharacteristic
913C22#348411yescharacteristic
914C22#348512yes—
915C22#348811yescharacteristic
916C22#349011yescharacteristic
917C22#349112yes—
918C22#349512yes—
919C22#351012yes—
920C22#351312yes—
921C22#351312yes—
922C22#353311yescharacteristic
923C22#353311yescharacteristic
924C22#353311yescharacteristic
925C22#353511yescharacteristic
926C22#353611yescharacteristic
927C22#354012yes—
928C22#354512yes—
929C22#356412yes—
930C22#356812yes—
931C4—44no—
932C4—44no—
933C4—42no—
934C4—42no—
935C4—44no—
936C4—42no—
937C4—44no—
938C4—44no—
939C4—82no—
940C4—82no—
941C4—81no—
942C4—82no—
943C4—82no—
944C4—82no—
945C4—82no—
946C4—82no—
947C2—44no—
948C2—44no—
949C2—82no—
950C2#3775211yescharacteristic
951C2#3875212yes—
952C2#4354112yes—
953C2#4359811yescharacteristic
954C2#4703511yescharacteristic
955C2#4986512yes—
956C2#5205411yescharacteristic
957C2#5759411yescharacteristic
958C2#5913212yes—
959C2#5918911yescharacteristic
960C2#5936711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
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×#2607C2semidirect
3. #16830C2semidirect
4. #16675C2semidirect
5. #16278C2semidirect
6. #15956C2semidirect
7. #15907C2semidirect
8. #15832C2semidirect
9. #15586C2semidirect
11. #15371C2semidirect
12. #14785C2semidirect
14. #14592C2semidirect
15. #14553C2semidirect
16. #14063C2semidirect
17. #13983C2semidirect
34. C2×#391C22semidirect
35. C2×#391C22semidirect
40. C2×#387C22semidirect
41. C2×#387C22semidirect
52. C2×C4×C4⋊C4C22semidirect
54. #1446C22semidirect
55. #1446C22semidirect
56. #1445C22semidirect
57. #1445C22semidirect
58. #1444C22semidirect
59. #1443C22semidirect
60. #1443C22semidirect
61. #1443C22semidirect
62. #1443C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1442C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
93. #1436C22semidirect
94. #1436C22semidirect
95. #1436C22semidirect
96. #1436C22semidirect
97. #1436C22semidirect
98. #1436C22semidirect
99. #1436C22semidirect
100. #1434C22semidirect
101. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#26072
C2×#24822
#168302
#166752
#162782
#159562
#159072
#158322
#155862
#154672
#153712
#147852
#147342
#145922
#145532
#140632
#139832
#139712
#138692