Finite Group Databasebeta

← #719675

Subgroups — #719675

Order 512.

3104 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2540C211yesmaximal, characteristic
2C2×#2500C211yesmaximal, characteristic, complemented
3C2×#2499C211yesmaximal, characteristic, complemented
4C2×#2354C211yesmaximal, characteristic, complemented
5#16526C214yesmaximal, complemented
6#15348C214yesmaximal, complemented
7#15346C214yesmaximal, complemented
8#15182C211yesmaximal, characteristic, complemented
9#15182C211yesmaximal, characteristic, complemented
10#15130C211yesmaximal, characteristic, complemented
11#15130C211yesmaximal, characteristic, complemented
12#14793C214yesmaximal, complemented
13#14273C211yesmaximal, characteristic, complemented
14#14153C211yesmaximal, characteristic, complemented
15#14138C211yesmaximal, characteristic, complemented
16#14136C211yesmaximal, characteristic, complemented
17#13910C211yesmaximal, characteristic, complemented
18#13847C211yesmaximal, characteristic, complemented
19#13779C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C22×#117C2211yescharacteristic
28#2540—28no—
29#2500—28no—
30#2499—28no—
31C2×#399C2212yes—
32C2×#397C2214yes—
33C2×#394C2214yes—
34C2×#394C2214yes—
35C2×#394C2214yes—
36C2×#392C2212yes—
37#2354—28no—
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2212yes—
45C2×#390C2212yes—
46C2×#390C2212yes—
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#389C2214yes—
50C2×#388C2212yes—
51C2×#388C2212yes—
52C2×#388C2214yes—
53C2×#387C2214yes—
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2212yes—
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#1441C2214yes—
73#1441C2214yes—
74#1440C2214yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1438C2212yes—
85#1438C2214yes—
86#1437C2214yes—
87#1437C2214yes—
88#1436C2214yes—
89#1436C2214yes—
90#1436C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C23×D4C2312yes—
99C23×D4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C2×#124—24no—
103C2×#124—24no—
104C2×#124—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—42no—
110C2×C22⋊Q8—42no—
111C2×#121—24no—
112C2×#121—24no—
113C2×#121—24no—
114C2×#121—24no—
115C2×#121—42no—
116C2×#121—42no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4D418yes—
120C2×#117—24no—
121C2×#117—24no—
122C2×#117—24no—
123C2×#117—24no—
124C2×#117—42no—
125C2×#117—42no—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2314yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2312yes—
168C22×C42C2312yes—
169C22×C42C2311yescharacteristic
170#399—28no—
171#397—216no—
172#394—216no—
173#394—48no—
174#394—48no—
175#392—28no—
176#391—24no—
177#391—24no—
178#391—42no—
179#391—42no—
180#390—28no—
181#390—24no—
182#390—28no—
183#390—28no—
184#390—24no—
185#390—42no—
186#390—42no—
187#389—48no—
188#388—28no—
189#388—28no—
190#388—216no—
191#387—216no—
192#384—24no—
193#384—24no—
194#384—24no—
195#384—24no—
196#382D418yescomplemented
197#380—24no—
198#380—24no—
199C4×C4⋊C4—28no—
200C4×C4⋊C4—24no—
201C4×C4⋊C4—24no—
202C4×C4⋊C4—24no—
203C4×C22⋊C4—24no—
204C4×C22⋊C4—24no—
205C4×C22⋊C4—42no—
206C4×C22⋊C4—42no—
207#376—24no—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C25C2412yes—
229C25C2411yescharacteristic
230C25C2411yescharacteristic
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—24no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—42no—
252C22×D4—42no—
253C22×D4—42no—
254C22×D4—42no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4C2×D414yes—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
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×C4C2×D414yes—
273C23×C4C2×D414yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290#124—416no—
291C22⋊Q8—416no—
292C22⋊Q8—416no—
293#121—416no—
294#121—416no—
295C4×D4—232no—
296#117—416no—
297#117—416no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4C2×D414yes—
338C2×C4⋊C4C2×D414yes—
339C2×C4⋊C4C2×D414yes—
340C2×C4⋊C4#4114yes—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
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—28no—
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—28no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—44no—
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—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4C2×D414yes—
398C2×C22⋊C4C2×D414yes—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—24no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—24no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—44no—
419C2×C42—44no—
420C2×C42C2×D414yes—
421C2×C42C2×D414yes—
422C2×C42#4114yes—
423C2×C42#4114yes—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—28no—
431#95—28no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—28no—
436#95—44no—
437#95—42no—
438#95—42no—
439#95—44no—
440#95—44no—
441#95—44no—
442#95—44no—
443#95C2×D4116yes—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—22no—
453C24—22no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—24no—
470C24—22no—
471C24—22no—
472C24—24no—
473C24—24no—
474C24—24no—
475C24C22×D412yes—
476C24C22×D412yes—
477C24C2511yescharacteristic
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×D4—28no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—88no—
502C2×D4—88no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4—88no—
506C2×D4—88no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
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—22no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4C22×D414yes—
597C22×C4C22×D414yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D414yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4112yes—
609C22×C4C2×#4112yes—
610C22×C4C2×#4112yes—
611C22×C4C2×#4112yes—
612C22×C4C2×#4112yes—
613C22×C4H(5,𝔽2)14yes—
614C22×C4H(5,𝔽2)12yes—
615C22×C4H(5,𝔽2)12yes—
616C22×C42−1+414yes—
617C4⋊C4—216no—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—416no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—84no—
630C4⋊C4—88no—
631C4⋊C4—88no—
632C22⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—416no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—88no—
648C22⋊C4—88no—
649C22⋊C4—84no—
650C22⋊C4—84no—
651C22⋊C4—88no—
652C42—28no—
653C42—48no—
654C42—48no—
655C42—48no—
656C42—44no—
657C42—44no—
658C42—44no—
659C42—84no—
660C42#123116yes—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
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—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23C23×D411yescharacteristic
731C23C23×D411yescharacteristic
732C23C22×#4111yescharacteristic
733C23C22×#4111yescharacteristic
734C23C22×#4111yescharacteristic
735C23C2×H(5,𝔽2)11yescharacteristic
736C23C2×H(5,𝔽2)11yescharacteristic
737C23C2×H(5,𝔽2)12yes—
738C23C2×2−1+412yes—
739C23#58512yes—
740C23#58512yes—
741Q8—88no—
742D4—416no—
743D4—816no—
744D4—816no—
745D4—88no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—24no—
768C2×C4—28no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—28no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
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—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—416no—
805C2×C4—416no—
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—44no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—44no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4C2×#12314yes—
836C2×C4C2×#12314yes—
837C2×C4C2×#12314yes—
838C2×C4#53214yes—
839C2×C4#54014yes—
840C2×C4D4214yes—
841C2×C4#54614yes—
842C2×C4#55014yes—
843C2×C4#55914yes—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—84no—
871C22—84no—
872C22—84no—
873C22—84no—
874C22—82no—
875C22—82no—
876C22—82no—
877C22C22×#12311yescharacteristic
878C22C2×#53211yescharacteristic
879C22#344911yescharacteristic
880C22#344911yescharacteristic
881C22C2×#54011yescharacteristic
882C22C2×D4211yescharacteristic
883C22C2×#54611yescharacteristic
884C22C2×#55011yescharacteristic
885C22C2×#55911yescharacteristic
886C22#348812yes—
887C22#348912yes—
888C22#349212yes—
889C22#349312yes—
890C22#349312yes—
891C22#349811yescharacteristic
892C22#349911yescharacteristic
893C22#351112yes—
894C22#351412yes—
895C22#351812yes—
896C22#354112yes—
897C22#354212yes—
898C22#354612yes—
899C22#355412yes—
900C4—24no—
901C4—24no—
902C4—44no—
903C4—44no—
904C4—42no—
905C4—42no—
906C4—44no—
907C4—44no—
908C4—44no—
909C4—44no—
910C4—82no—
911C4—82no—
912C4—82no—
913C4—82no—
914C4—82no—
915C4#244518yes—
916C2—82no—
917C2—82no—
918C2—162no—
919C2C2×#244511yescharacteristic
920C2#3515711yescharacteristic
921C2#3553011yescharacteristic
922C2#3602812yes—
923C2#3768011yescharacteristic
924C2#3768111yescharacteristic
925C2#3809011yescharacteristic
926C2#3809111yescharacteristic
927C2#4265812yes—
928C2#4498012yes—
929C2#4498612yes—
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×#2500C2semidirect
3. C2×#2499C2semidirect
4. C2×#2354C2semidirect
5. #16526C2semidirect
6. #15348C2semidirect
7. #15346C2semidirect
8. #15182C2semidirect
9. #15182C2semidirect
10. #15130C2semidirect
11. #15130C2semidirect
12. #14793C2semidirect
13. #14273C2semidirect
14. #14153C2semidirect
15. #14138C2semidirect
16. #14136C2semidirect
17. #13910C2semidirect
18. #13847C2semidirect
19. #13779C2semidirect
196. #382D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25402
C2×#25002
C2×#24992
C2×#23542
#165262
#153482
#153462
#151822
#151302
#147932
#142732
#141532
#141382
#141362
#139102
#138472
#137792