Finite Group Databasebeta

← #719674

Subgroups — #719674

Order 512.

3524 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2540C211yesmaximal, characteristic
2C2×#2502C211yesmaximal, characteristic, complemented
3C2×#2501C211yesmaximal, characteristic, complemented
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5#16531C214yesmaximal, complemented
6#15358C214yesmaximal, complemented
7#15271C214yesmaximal, complemented
8#15236C211yesmaximal, characteristic, complemented
9#15219C211yesmaximal, characteristic, complemented
10#15182C211yesmaximal, characteristic, complemented
11#15130C211yesmaximal, characteristic, complemented
12#14721C214yesmaximal, complemented
13#14273C211yesmaximal, characteristic, complemented
14#14153C211yesmaximal, characteristic, complemented
15#14139C211yesmaximal, characteristic, complemented
16#14137C211yesmaximal, characteristic, complemented
17#13910C211yesmaximal, characteristic, complemented
18#13847C211yesmaximal, characteristic, complemented
19#13779C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×#123C2214yes—
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2212yes—
28C23×C4⋊C4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30#2540—28no—
31#2502—28no—
32#2501—28no—
33C2×#399C2212yes—
34C2×#399C2214yes—
35C2×#398C2214yes—
36C2×#394C2214yes—
37C2×#392C2212yes—
38D4×C4⋊C4—28no—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2212yes—
45C2×#390C2212yes—
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#389C2212yes—
50C2×#389C2214yes—
51C2×#386C2214yes—
52C2×#385C2212yes—
53C2×#385C2212yes—
54C2×#385C2214yes—
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×#376C2211yescharacteristic
70#1445C2212yes—
71#1444C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1440C2214yes—
76#1440C2214yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1439C2214yes—
85#1438C2212yes—
86#1438C2214yes—
87#1437C2214yes—
88#1436C2214yes—
89#1436C2214yes—
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C22⋊#95C2214yes—
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C23×D4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C24×C4C2312yes—
104C2×#124—24no—
105C2×#124—24no—
106C2×#124—24no—
107C2×#123—216no—
108C2×#123—48no—
109C2×#123—48no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—42no—
115C2×C22⋊Q8—42no—
116C2×#121—24no—
117C2×#121—24no—
118C2×#121—24no—
119C2×#121—24no—
120C2×#121—42no—
121C2×#121—42no—
122C2×C4×D4—28no—
123C2×C4×D4—24no—
124C2×C4×D4—24no—
125C2×C4×D4—48no—
126C2×C4×D4D418yes—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—24no—
131C22×C4⋊C4—42no—
132C22×C4⋊C4—42no—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2314yes—
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⋊C4C2314yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2314yes—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2312yes—
173C22×C42C2312yes—
174C22×C42C2311yescharacteristic
175#399—216no—
176#399—28no—
177#398—216no—
178#394—48no—
179#392—28no—
180#391—24no—
181#391—24no—
182#391—42no—
183#391—42no—
184#390—24no—
185#390—28no—
186#390—28no—
187#390—24no—
188#390—42no—
189#390—42no—
190#389—28no—
191#389—48no—
192#386—48no—
193#385—216no—
194#385—28no—
195#385—28no—
196#384—24no—
197#384—24no—
198#384—24no—
199#384D418yescomplemented
200#382—24no—
201#380—24no—
202#380—24no—
203C4×C4⋊C4—24no—
204C4×C4⋊C4—24no—
205C4×C4⋊C4—24no—
206C4×C22⋊C4—24no—
207C4×C22⋊C4—24no—
208C4×C22⋊C4—42no—
209C4×C22⋊C4—42no—
210#376—24no—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C25C2412yes—
232C25C2411yescharacteristic
233C25C2411yescharacteristic
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—28no—
246C22×D4—28no—
247C22×D4—22no—
248C22×D4—24no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—24no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—42no—
259C22×D4—42no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4C2×D414yes—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—28no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—44no—
283C23×C4—44no—
284C23×C4—44no—
285C23×C4C2×D414yes—
286C23×C4C2×D414yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303#124—416no—
304#123—464no—
305C22⋊Q8—416no—
306C22⋊Q8—416no—
307#121—416no—
308#121—416no—
309C4×D4—232no—
310C4×D4—432no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
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—24no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—416no—
345C2×C4⋊C4—416no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4C2×D414yes—
358C2×C4⋊C4C2×D414yes—
359C2×C4⋊C4C2×D414yes—
360C2×C4⋊C4C2×D4116yes—
361C2×C4⋊C4#4114yes—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—28no—
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—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4C2×D414yes—
413C2×C22⋊C4C2×D414yes—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—24no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—24no—
427C2×C42—44no—
428C2×C42—44no—
429C2×C42C2×D414yes—
430C2×C42C2×D414yes—
431C2×C42#4114yes—
432C2×C42#4114yes—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—28no—
440#95—28no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—28no—
445#95—28no—
446#95—42no—
447#95—42no—
448#95—44no—
449#95—44no—
450#95—44no—
451#95—44no—
452#95—44no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—22no—
462C24—22no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—22no—
467C24—21no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—24no—
477C24—24no—
478C24—22no—
479C24—22no—
480C24—24no—
481C24—24no—
482C24C22×D412yes—
483C24C22×D412yes—
484C24H(5,𝔽2)14yes—
485C242−1+414yes—
486C24C2511yescharacteristic
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×D4—216no—
495C2×D4—216no—
496C2×D4—28no—
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—416no—
502C2×D4—416no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—84no—
513C2×D4—84no—
514C2×D4—88no—
515C2×D4—88no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
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—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—28no—
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—24no—
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—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—22no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—416no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—88no—
611C22×C4—84no—
612C22×C4—84no—
613C22×C4—88no—
614C22×C4—88no—
615C22×C4C22×D414yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D414yes—
619C22×C4C22×D414yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C2×#4114yes—
625C22×C4C2×#4112yes—
626C22×C4C2×#4112yes—
627C22×C4C2×#4112yes—
628C22×C4C2×#4112yes—
629C22×C4C2×#4112yes—
630C22×C4C2×#4112yes—
631C22×C4C2×#4112yes—
632C22×C4H(5,𝔽2)14yes—
633C22×C4H(5,𝔽2)12yes—
634C22×C4H(5,𝔽2)12yes—
635C22×C42−1+414yes—
636C4⋊C4—216no—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—416no—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4—416no—
647C4⋊C4—48no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—84no—
652C4⋊C4—88no—
653C22⋊C4—216no—
654C22⋊C4—216no—
655C22⋊C4—28no—
656C22⋊C4—28no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—416no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—416no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—88no—
670C22⋊C4—88no—
671C42—28no—
672C42—48no—
673C42—44no—
674C42—44no—
675C42—44no—
676C42—84no—
677C42#123116yescomplemented
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—42no—
737C23—42no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23#53514yes—
746C23#53614yes—
747C23C23×D411yescharacteristic
748C23C23×D411yescharacteristic
749C23C22×#4111yescharacteristic
750C23C22×#4111yescharacteristic
751C23C22×#4111yescharacteristic
752C23C2×H(5,𝔽2)12yes—
753C23C2×H(5,𝔽2)11yescharacteristic
754C23C2×H(5,𝔽2)11yescharacteristic
755C23C2×H(5,𝔽2)12yes—
756C23C2×2−1+412yes—
757C23C2×2−1+412yes—
758Q8—88no—
759D4—232no—
760D4—816no—
761D4—816no—
762D4—88no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—28no—
784C2×C4—28no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—28no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
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—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—416no—
822C2×C4—416no—
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—44no—
838C2×C4—44no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—44no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—42no—
852C2×C4—816no—
853C2×C4—816no—
854C2×C4C2×#12314yes—
855C2×C4C2×#12314yes—
856C2×C4C2×#12314yes—
857C2×C4#53214yes—
858C2×C4#54014yes—
859C2×C4D4214yes—
860C2×C4#54614yes—
861C2×C4#55014yes—
862C2×C4#55914yes—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—24no—
869C22—42no—
870C22—42no—
871C22—44no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—42no—
876C22—42no—
877C22—44no—
878C22—44no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—82no—
886C22—82no—
887C22—84no—
888C22—84no—
889C22—82no—
890C22—82no—
891C22—84no—
892C22—82no—
893C22—82no—
894C22—82no—
895C22—84no—
896C22C22×#12311yescharacteristic
897C22C2×#53211yescharacteristic
898C22C2×#53511yescharacteristic
899C22C2×#53611yescharacteristic
900C22C2×#54011yescharacteristic
901C22C2×D4211yescharacteristic
902C22C2×#54611yescharacteristic
903C22C2×#55011yescharacteristic
904C22C2×#55911yescharacteristic
905C22#348412yes—
906C22#348612yes—
907C22#349212yes—
908C22#349212yes—
909C22#349212yes—
910C22#349811yescharacteristic
911C22#349911yescharacteristic
912C22#351112yes—
913C22#352012yes—
914C22#352212yes—
915C22#353612yes—
916C22#353612yes—
917C22#354312yes—
918C22#355212yes—
919C4—24no—
920C4—24no—
921C4—44no—
922C4—44no—
923C4—44no—
924C4—44no—
925C4—44no—
926C4—42no—
927C4—42no—
928C4—44no—
929C4—82no—
930C4—82no—
931C4—82no—
932C4—82no—
933C4—82no—
934C4#244518yes—
935C2—44no—
936C2—44no—
937C2—162no—
938C2C2×#244511yescharacteristic
939C2#3522711yescharacteristic
940C2#3553011yescharacteristic
941C2#3569712yes—
942C2#3767411yescharacteristic
943C2#3767511yescharacteristic
944C2#3807811yescharacteristic
945C2#3807911yescharacteristic
946C2#4246012yes—
947C2#4498512yes—
948C2#4535612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2540C2
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×#2502C2semidirect
3. C2×#2501C2semidirect
4. C2×D4×C4⋊C4C2semidirect
5. #16531C2semidirect
6. #15358C2semidirect
7. #15271C2semidirect
8. #15236C2semidirect
9. #15219C2semidirect
10. #15182C2semidirect
11. #15130C2semidirect
12. #14721C2semidirect
13. #14273C2semidirect
14. #14153C2semidirect
15. #14139C2semidirect
16. #14137C2semidirect
17. #13910C2semidirect
18. #13847C2semidirect
19. #13779C2semidirect
199. #384D4semidirect
677. C42#123semidirect

Maximal subgroups

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

subgroupindex
C2×#25402
C2×#25022
C2×#25012
C2×D4×C4⋊C42
#165312
#153582
#152712
#152362
#152192
#151822
#151302
#147212
#142732
#141532
#141392
#141372
#139102
#138472
#137792