Finite Group Databasebeta

← #5063449

Subgroups — #5063449

Order 512.

2644 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17282C212yesmaximal, complemented
2#17224C212yesmaximal, complemented
3#17137C211yesmaximal, characteristic, complemented
4#16741C212yesmaximal, complemented
5#16741C212yesmaximal, complemented
6#16656C212yesmaximal, complemented
7#16133C212yesmaximal, complemented
8#16004C212yesmaximal, complemented
9#15986C212yesmaximal, complemented
10#15948C211yesmaximal, characteristic
11#15671C212yesmaximal, complemented
12#15610C212yesmaximal, complemented
13#15323C212yesmaximal, complemented
14#15262C211yesmaximal, characteristic, complemented
15#15259C211yesmaximal, characteristic
16#14717C212yesmaximal, complemented
17#14658C211yesmaximal, characteristic, complemented
18#14492C211yesmaximal, characteristic, complemented
19#14255C211yesmaximal, characteristic
20C22×#126C2212yes—
21C22×#124C2211yescharacteristic
22C22×#123C2211yescharacteristic
23C22×C22⋊Q8C2212yes—
24C22×#120C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C2×#401C2212yescomplemented
27C2×#395C2212yescomplemented
28C2×#393C2211yescharacteristic
29C2×#393C2211yescharacteristic
30C2×#393C2212yes—
31C2×#393C2212yes—
32C2×#393C2212yescomplemented
33C2×#391C2212yescomplemented
34C2×#386C2211yescharacteristic
35C2×#386C2211yescharacteristic
36C2×#386C2212yes—
37C2×#385C2212yescomplemented
38C2×#380C2212yescomplemented
39C2×#379C2212yes—
40C2×#379C2211yescharacteristic
41C2×#379C2212yes—
42#1446C2212yescomplemented
43#1446C2212yescomplemented
44#1446C2212yescomplemented
45#1445C2212yescomplemented
46#1445C2212yescomplemented
47#1445C2212yescomplemented
48#1443C2212yescomplemented
49#1443C2212yescomplemented
50#1443C2212yescomplemented
51#1442C2212yescomplemented
52#1442C2212yescomplemented
53#1442C2212yescomplemented
54#1441C2212yescomplemented
55#1441C2212yescomplemented
56#1441C2212yescomplemented
57#1441C2212yescomplemented
58#1441C2212yescomplemented
59#1440C2212yes—
60#1440C2212yes—
61#1440C2212yes—
62#1440C2212yes—
63#1440C2211yescharacteristic
64#1440C2212yes—
65#1440C2212yes—
66#1440C2211yescharacteristic
67#1440C2212yescomplemented
68#1440C2212yescomplemented
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yescomplemented
84#1439C2212yescomplemented
85#1438C2211yescharacteristic
86#1438C2211yescharacteristic
87#1438C2211yescharacteristic
88#1438C2212yes—
89#1438C2212yes—
90#1438C2211yescharacteristic
91#1438C2211yescharacteristic
92#1438C2212yes—
93#1438C2211yescharacteristic
94#1437C2211yescharacteristic
95#1437C2212yes—
96#1437C2211yescharacteristic
97#1437C2212yes—
98#1437C2212yescomplemented
99#1436C2212yescomplemented
100#1436C2212yescomplemented
101#1434C2212yescomplemented
102#1434C2212yescomplemented
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C26C2311yescharacteristic
108C23×Q8C2311yescharacteristic
109C23×Q8C2312yes—
110C23×D4C2311yescharacteristic
111C23×D4C2311yescharacteristic
112C23×D4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2312yes—
115C2×#126—44no—
116C2×#126—44no—
117C2×#126—44no—
118C2×#124—24no—
119C2×#124—44no—
120C2×#123—24no—
121C2×#123—44no—
122C2×C22⋊Q8—44no—
123C2×C22⋊Q8—44no—
124C2×C22⋊Q8—44no—
125C2×#120—24no—
126C2×#120—42no—
127C2×#120—42no—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C22⋊C4—44no—
136C22×C22⋊C4—42no—
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2312yes—
168#401—44no—
169#395—44no—
170#393—44no—
171#393—44no—
172#393—44no—
173#393—42no—
174#393—42no—
175#391—44no—
176#386—44no—
177#386—42no—
178#386—42no—
179#385—44no—
180#380—44no—
181#379—44no—
182#379—44no—
183#379—42no—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2311yescharacteristic
194C2×#95C2311yescharacteristic
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—
225C25—22no—
226C25—22no—
227C25—22no—
228C25—24no—
229C25—42no—
230C25—42no—
231C25—42no—
232C25—42no—
233C25—42no—
234C25C2411yescharacteristic
235C25C2411yescharacteristic
236C25C2411yescharacteristic
237C25C2411yescharacteristic
238C22×Q8—22no—
239C22×Q8—24no—
240C22×Q8—24no—
241C22×Q8—42no—
242C22×Q8—42no—
243C22×Q8—42no—
244C22×Q8—42no—
245C22×Q8—42no—
246C22×Q8—41no—
247C22×Q8—42no—
248C22×Q8—41no—
249C22×Q8—42no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—24no—
254C22×D4—22no—
255C22×D4—41no—
256C22×D4—41no—
257C22×D4—41no—
258C22×D4—41no—
259C22×D4—42no—
260C22×D4—42no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4#4114yes—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—41no—
276C23×C4—41no—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292#126—432no—
293#124—416no—
294#123—416no—
295C22⋊Q8—432no—
296#120—416no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
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—41no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
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×C22⋊C4—416no—
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—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—41no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—41no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C42—22no—
400C2×C42—24no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
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—41no—
432#95—41no—
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—
445C24—21no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—28no—
453C24—21no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—48no—
478C24—48no—
479C24—44no—
480C24—48no—
481C24—48no—
482C24—44no—
483C24—84no—
484C24—84no—
485C24—84no—
486C24—84no—
487C24—82no—
488C24—82no—
489C24—84no—
490C24—84no—
491C24—82no—
492C24—82no—
493C24—84no—
494C24—84no—
495C24—84no—
496C24—84no—
497C24C2×#4112yes—
498C24C2×#4112yes—
499C24H(5,𝔽2)12yes—
500C24H(5,𝔽2)12yes—
501C242−1+414yes—
502C24C2511yescharacteristic
503C2×Q8—28no—
504C2×Q8—48no—
505C2×Q8—82no—
506C2×Q8—82no—
507C2×Q8—84no—
508C2×Q8—84no—
509C2×Q8—84no—
510C2×Q8—84no—
511C2×Q8—84no—
512C2×Q8—84no—
513C2×Q8—84no—
514C2×Q8—84no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—48no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—84no—
524C2×D4—82no—
525C2×D4—84no—
526C2×D4—82no—
527C2×D4—84no—
528C2×D4—84no—
529C2×D4—84no—
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—21no—
540C22×C4—21no—
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—28no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
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—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
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—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—84no—
629C22×C4—84no—
630C22×C4—84no—
631C22×C4—84no—
632C22×C4—82no—
633C22×C4—82no—
634C22×C4—84no—
635C22×C4—84no—
636C22×C4—84no—
637C22×C4C2×#4112yes—
638C22×C4H(5,𝔽2)14yes—
639C22×C4H(5,𝔽2)14yes—
640C22×C4H(5,𝔽2)14yes—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—48no—
663C22⋊C4—44no—
664C22⋊C4—84no—
665C22⋊C4—84no—
666C22⋊C4—84no—
667C22⋊C4—82no—
668C22⋊C4—82no—
669C22⋊C4—84no—
670C22⋊C4—82no—
671C22⋊C4—82no—
672C22⋊C4—84no—
673C22⋊C4—84no—
674C22⋊C4—84no—
675C22⋊C4—84no—
676C22⋊C4—84no—
677C42—44no—
678C42—48no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—22no—
702C23—24no—
703C23—22no—
704C23—416no—
705C23—41no—
706C23—41no—
707C23—42no—
708C23—42no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—41no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—41no—
744C23—41no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—816no—
764C23—88no—
765C23—88no—
766C23—816no—
767C23—816no—
768C23—816no—
769C23—816no—
770C23—816no—
771C23#56314yes—
772C23C22×#4111yescharacteristic
773C23C2×H(5,𝔽2)11yescharacteristic
774C23C2×H(5,𝔽2)11yescharacteristic
775C23C2×H(5,𝔽2)12yes—
776C23C2×H(5,𝔽2)12yes—
777C23C2×H(5,𝔽2)12yes—
778C23C2×2−1+412yes—
779C23#58512yes—
780C23#58512yes—
781Q8—88no—
782Q8—816no—
783D4—88no—
784D4—88no—
785D4—88no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
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—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—41no—
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—41no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—41no—
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—42no—
856C2×C4—42no—
857C2×C4—41no—
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—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—88no—
886C2×C4—816no—
887C22—28no—
888C22—24no—
889C22—44no—
890C22—44no—
891C22—44no—
892C22—44no—
893C22—44no—
894C22—42no—
895C22—42no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—832no—
912C22—82no—
913C22—82no—
914C22—82no—
915C22—82no—
916C22—82no—
917C22—82no—
918C22—82no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22—82no—
923C22—82no—
924C22#349011yescharacteristic
925C22#349011yescharacteristic
926C22#349011yescharacteristic
927C22#352012yes—
928C22#352112yes—
929C22C2×#56311yescharacteristic
930C22#353212yes—
931C22#353211yescharacteristic
932C22#353212yes—
933C22#353311yescharacteristic
934C22#353612yes—
935C22#354112yes—
936C22#354112yes—
937C22#354212yes—
938C22#354511yescharacteristic
939C22#354512yes—
940C22#354612yes—
941C22#354612yes—
942C22#355812yes—
943C22#356112yes—
944C22#356112yes—
945C4—44no—
946C4—44no—
947C4—42no—
948C4—44no—
949C4—82no—
950C4—82no—
951C4—82no—
952C4—82no—
953C4—82no—
954C4—82no—
955C4—82no—
956C4—82no—
957C4—82no—
958C4—81no—
959C4—81no—
960C2—44no—
961C2—82no—
962C2—82no—
963C2—82no—
964C2#4572811yescharacteristic
965C2#4661412yes—
966C2#4699611yescharacteristic
967C2#4866812yes—
968C2#4899711yescharacteristic
969C2#5231812yes—
970C2#5506912yes—
971C2#5532812yes—
972C2#5641212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #17282C2semidirect
2. #17224C2semidirect
3. #17137C2semidirect
4. #16741C2semidirect
5. #16741C2semidirect
6. #16656C2semidirect
7. #16133C2semidirect
8. #16004C2semidirect
9. #15986C2semidirect
11. #15671C2semidirect
12. #15610C2semidirect
13. #15323C2semidirect
14. #15262C2semidirect
16. #14717C2semidirect
17. #14658C2semidirect
18. #14492C2semidirect
26. C2×#401C22semidirect
27. C2×#395C22semidirect
32. C2×#393C22semidirect
33. C2×#391C22semidirect
37. C2×#385C22semidirect
38. C2×#380C22semidirect
42. #1446C22semidirect
43. #1446C22semidirect
44. #1446C22semidirect
45. #1445C22semidirect
46. #1445C22semidirect
47. #1445C22semidirect
48. #1443C22semidirect
49. #1443C22semidirect
50. #1443C22semidirect
51. #1442C22semidirect
52. #1442C22semidirect
53. #1442C22semidirect
54. #1441C22semidirect
55. #1441C22semidirect
56. #1441C22semidirect
57. #1441C22semidirect
58. #1441C22semidirect
67. #1440C22semidirect
68. #1440C22semidirect
83. #1439C22semidirect
84. #1439C22semidirect
98. #1437C22semidirect
99. #1436C22semidirect
100. #1436C22semidirect
101. #1434C22semidirect
102. #1434C22semidirect

Maximal subgroups

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

subgroupindex
#172822
#172242
#171372
#167412
#166562
#161332
#160042
#159862
#159482
#156712
#156102
#153232
#152622
#152592
#147172
#146582
#144922
#142552