Finite Group Databasebeta

← #946463

Subgroups — #946463

Order 512.

3212 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2499C211yesmaximal, characteristic, complemented
2C2×#2415C211yesmaximal, characteristic
3C2×#2434C211yesmaximal, characteristic, complemented
4C2×#2409C211yesmaximal, characteristic
5#17097C214yesmaximal, complemented
6#16325C214yesmaximal, complemented
7#16308C214yesmaximal
8#15973C214yesmaximal, complemented
9#15233C211yesmaximal, characteristic, complemented
10#15184C211yesmaximal, characteristic, complemented
11#15182C211yesmaximal, characteristic, complemented
12#15180C211yesmaximal, characteristic, complemented
13#15178C211yesmaximal, characteristic, complemented
14#15178C211yesmaximal, characteristic, complemented
15#14274C211yesmaximal, characteristic, complemented
16#14261C211yesmaximal, characteristic, complemented
17#14138C211yesmaximal, characteristic, complemented
18#13922C211yesmaximal, characteristic, complemented
19#13847C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×#117C2211yescharacteristic
29#2499—28no—
30#2434—28no—
31#2415—28no—
32#2409—28no—
33C2×#397C2212yes—
34C2×#397C2214yes—
35C2×#395C2212yes—
36C2×#395C2214yes—
37C2×#394C2212yes—
38C2×#393C2212yes—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#389C2212yes—
52C2×#388C2212yes—
53C2×#387C2214yes—
54C2×#386C2212yes—
55C2×#385C2212yes—
56C2×#385C2214yes—
57C2×#384C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×#376C2211yescharacteristic
67#1446C2214yes—
68#1445C2212yes—
69#1445C2214yes—
70#1445C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1443C2214yes—
74#1443C2214yes—
75#1442C2214yes—
76#1442C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1441C2214yes—
81#1440C2214yes—
82#1440C2214yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2214yes—
86#1439C2214yes—
87#1439C2214yes—
88#1438C2212yes—
89#1436C2214yes—
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C22⋊#95C2214yes—
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—42no—
99C23×Q8—42no—
100C23×Q8—42no—
101C23×Q8—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×Q8C2311yescharacteristic
105C23×Q8C2312yes—
106C23×D4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2312yes—
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—42no—
114C2×C4⋊Q8—42no—
115C2×C4⋊Q8—42no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8—42no—
125C2×C22⋊Q8—42no—
126C2×C22⋊Q8—42no—
127C2×C22⋊Q8—42no—
128C2×C4×D4—42no—
129C2×C4×D4—42no—
130C2×C4×D4D418yes—
131C2×#117—24no—
132C2×#117—24no—
133C2×#117—42no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
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×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#397—28no—
169#397—216no—
170#395—28no—
171#395—216no—
172#394—28no—
173#393—28no—
174#391—24no—
175#391—24no—
176#391—24no—
177#391—24no—
178#391—24no—
179#391—42no—
180#391—42no—
181#391—42no—
182#391—42no—
183#391—42no—
184#391D418yescomplemented
185#389—28no—
186#389—24no—
187#388—28no—
188#387—216no—
189#386—28no—
190#385—28no—
191#385—216no—
192#384—24no—
193#382—24no—
194#380—24no—
195#380—24no—
196C4×C4⋊C4—42no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—42no—
200C4×C22⋊C4—42no—
201#376—42no—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2314yes—
231C25C2411yescharacteristic
232C25C2411yescharacteristic
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—24no—
239C22×Q8—24no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—24no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—42no—
256C22×Q8—42no—
257C22×Q8—42no—
258C22×Q8—42no—
259C22×Q8—416no—
260C22×Q8—416no—
261C22×Q8—416no—
262C22×Q8—416no—
263C22×Q8—416no—
264C22×Q8—416no—
265C22×Q8—416no—
266C22×Q8C2×D414yes—
267C22×Q8#4114yes—
268C22×D4—24no—
269C22×D4—41no—
270C22×D4—41no—
271C22×D4—42no—
272C22×D4C2×D414yes—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4C2×D414yes—
293C23×C4C2×D414yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2412yes—
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2411yescharacteristic
311C4⋊Q8—416no—
312C4⋊Q8—416no—
313C22⋊Q8—416no—
314C22⋊Q8—416no—
315C22⋊Q8—416no—
316C22⋊Q8—416no—
317C4×D4—416no—
318#117—416no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—41no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4C2×D414yes—
362C2×C4⋊C4C2×D414yes—
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—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—41no—
388C2×C22⋊C4—41no—
389C2×C22⋊C4—41no—
390C2×C22⋊C4—41no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4C2×D414yes—
399C2×C22⋊C4C2×D414yes—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—42no—
416C2×C42C2×D414yes—
417C2×C42C2×D414yes—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—28no—
423#95—24no—
424#95—24no—
425#95—28no—
426#95—24no—
427#95—24no—
428#95—28no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—28no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—44no—
442#95—44no—
443#95—44no—
444#95—44no—
445#95—44no—
446#95C2×D4116yes—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24C22×D412yes—
467C24C22×D412yes—
468C242−1+414yes—
469C24C2511yescharacteristic
470C2×Q8—28no—
471C2×Q8—28no—
472C2×Q8—28no—
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—28no—
476C2×Q8—48no—
477C2×Q8—48no—
478C2×Q8—48no—
479C2×Q8—48no—
480C2×Q8—48no—
481C2×Q8—48no—
482C2×Q8—4128no—
483C2×Q8—48no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×D4—28no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—48no—
503C2×D4—48no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
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—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
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—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—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D414yes—
616C22×C4C22×D412yes—
617C22×C4C22×D414yes—
618C22×C4C22×D414yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C2×#4114yes—
623C22×C4C2×#4112yes—
624C22×C4H(5,𝔽2)12yes—
625C22×C4H(5,𝔽2)12yes—
626C22×C4H(5,𝔽2)12yes—
627C22×C4H(5,𝔽2)12yes—
628C22×C42−1+414yes—
629C22×C42−1+414yes—
630C4⋊C4—28no—
631C4⋊C4—44no—
632C4⋊C4—416no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—416no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—416no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—44no—
645C22⋊C4—216no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C42—28no—
659C42—28no—
660C42—48no—
661C42—44no—
662C42—44no—
663C42—44no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—42no—
687C23—42no—
688C23—41no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—41no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23#53614yes—
710C23C23×D411yescharacteristic
711C23C23×D411yescharacteristic
712C23C22×#4111yescharacteristic
713C23C2×H(5,𝔽2)11yescharacteristic
714C23C2×H(5,𝔽2)11yescharacteristic
715C23C2×H(5,𝔽2)11yescharacteristic
716C23C2×H(5,𝔽2)11yescharacteristic
717C23C2×2−1+412yes—
718C23C2×2−1+412yes—
719C23C2×2−1+412yes—
720C23#58512yes—
721Q8—432no—
722Q8—416no—
723Q8—416no—
724Q8—88no—
725D4—416no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—28no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—432no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
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—44no—
791C2×C4—416no—
792C2×C4—416no—
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—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—42no—
827C2×C4#53414yes—
828C2×C4#53514yes—
829C2×C4#53814yes—
830C2×C4D4214yes—
831C2×C4#54614yes—
832C2×C4#54614yes—
833C2×C4#56014yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—42no—
838C22—42no—
839C22—44no—
840C22—44no—
841C22—42no—
842C22—44no—
843C22—42no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22C2×#53411yescharacteristic
857C22C2×#53511yescharacteristic
858C22C2×#53611yescharacteristic
859C22#344911yescharacteristic
860C22C2×#53811yescharacteristic
861C22C2×D4211yescharacteristic
862C22C2×#54611yescharacteristic
863C22C2×#54611yescharacteristic
864C22#348612yes—
865C22#348912yes—
866C22#349911yescharacteristic
867C22#349911yescharacteristic
868C22#351812yes—
869C22#352312yes—
870C22C2×#56011yescharacteristic
871C22#353812yes—
872C22#353812yes—
873C22#354112yes—
874C22#354112yes—
875C22#354112yes—
876C22#355012yes—
877C22#355212yes—
878C22#355412yes—
879C4—42no—
880C4—44no—
881C4—44no—
882C4—44no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—44no—
887C4—44no—
888C4—44no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4—82no—
895C4#267818yes—
896C2—44no—
897C2—82no—
898C2#3738611yescharacteristic
899C2#3744911yescharacteristic
900C2#3767511yescharacteristic
901C2#3768011yescharacteristic
902C2#3808111yescharacteristic
903C2#3809111yescharacteristic
904C2#4280812yes—
905C2#4285112yes—
906C2#4529112yes—
907C2C2×#267811yescharacteristic
908C2#5313612yes—
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×#2499C2semidirect
3. C2×#2434C2semidirect
5. #17097C2semidirect
6. #16325C2semidirect
8. #15973C2semidirect
9. #15233C2semidirect
10. #15184C2semidirect
11. #15182C2semidirect
12. #15180C2semidirect
13. #15178C2semidirect
14. #15178C2semidirect
15. #14274C2semidirect
16. #14261C2semidirect
17. #14138C2semidirect
18. #13922C2semidirect
184. #391D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24992
C2×#24152
C2×#24342
C2×#24092
#170972
#163252
#163082
#159732
#152332
#151842
#151822
#151802
#151782
#142742
#142612
#141382
#139222
#138472