Finite Group Databasebeta

← #765931

Subgroups — #765931

Order 512.

3426 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2502C211yesmaximal, characteristic, complemented
2C2×#2432C211yesmaximal, characteristic
3C2×#2323C211yesmaximal, characteristic, complemented
4C2×#2311C211yesmaximal, characteristic
5#15512C214yesmaximal, complemented
6#15436C214yesmaximal, complemented
7#15411C214yesmaximal, complemented
8#15301C214yesmaximal, complemented
9#15217C211yesmaximal, characteristic, complemented
10#15184C211yesmaximal, characteristic, complemented
11#15180C211yesmaximal, characteristic, complemented
12#15134C211yesmaximal, characteristic, complemented
13#14026C211yesmaximal, characteristic, complemented
14#14024C211yesmaximal, characteristic, complemented
15#14001C211yesmaximal, characteristic, complemented
16#14000C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic
18#13904C211yesmaximal, characteristic, complemented
19#13852C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#2502—28no—
28#2432—28no—
29C2×#398C2214yes—
30C2×#396C2214yes—
31C2×#394C2214yes—
32#2323—28no—
33#2311—28no—
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#389C2212yes—
49C2×#388C2212yes—
50C2×#388C2212yes—
51C2×#388C2214yes—
52C2×#387C2212yes—
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#385C2214yes—
56C2×#385C2214yes—
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#381C2214yes—
60C2×#380C2211yescharacteristic
61C2×#380C2212yes—
62C2×#380C2212yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68#1445C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1441C2212yes—
72#1441C2212yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1440C2214yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1438C2214yes—
85#1437C2214yes—
86#1436C2214yes—
87#1436C2214yes—
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—24no—
99C22×#41—24no—
100C22×#41—42no—
101C22×#41—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×D4C2311yescharacteristic
105C23×D4C2312yes—
106C24×C4C2312yes—
107C24×C4C2311yescharacteristic
108C24×C4C2312yes—
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—42no—
112C2×#124—24no—
113C2×#124—24no—
114C2×#124—42no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8D418yes—
118C2×C4×Q8—24no—
119C2×C4×Q8—42no—
120C2×C4×Q8—42no—
121C2×#117—42no—
122C2×#117—42no—
123C2×#117D418yes—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2312yes—
164C22×C42C2312yes—
165#398—216no—
166#396—48no—
167#394—216no—
168#391—24no—
169#391—24no—
170#391—24no—
171#391—24no—
172#391—24no—
173#391—24no—
174#391—24no—
175#391—42no—
176#390—24no—
177#390—24no—
178#390—24no—
179#390—24no—
180#390—42no—
181#389—28no—
182#389—24no—
183#388—28no—
184#388—28no—
185#388—48no—
186#387—28no—
187#386—28no—
188#386—28no—
189#385—216no—
190#385—216no—
191#384—24no—
192#384—24no—
193#381—48no—
194#380—24no—
195#380—28no—
196#380—28no—
197C4×C4⋊C4—24no—
198C4×C4⋊C4—42no—
199C4×C4⋊C4—42no—
200C4×C22⋊C4—24no—
201C4×C22⋊C4—24no—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C25C2412yes—
229C25C2411yescharacteristic
230C2×#41—232no—
231C2×#41—416no—
232C2×#41—416no—
233C2×#41—416no—
234C2×#41—416no—
235C2×#41—416no—
236C2×#41—416no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8C2×D414yes—
250C22×Q8#4114yes—
251C22×D4—24no—
252C22×D4—24no—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—24no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4#4114yes—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4#4114yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C4⋊Q8—416no—
302#124—416no—
303C22⋊Q8—232no—
304C4×Q8—416no—
305#117—416no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—41no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4—41no—
338C2×C4⋊C4—41no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—416no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4C2×D414yes—
351C2×C4⋊C4C2×D418yes—
352C2×C4⋊C4C2×D414yes—
353C2×C4⋊C4C2×D414yes—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4C2×D418yes—
389C2×C22⋊C4C2×D414yes—
390C2×C22⋊C4C2×D414yes—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—24no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—44no—
412C2×C42C2×D414yes—
413C2×C42C2×D414yes—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—28no—
423#95—28no—
424#95—28no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—28no—
429#95—28no—
430#95—28no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—44no—
438#95—44no—
439#95—44no—
440C24—21no—
441C24—21no—
442C24—22no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—24no—
453C24—22no—
454C24—22no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24C22×D412yes—
459C24C22×D412yes—
460C24C2×#4114yes—
461C24C2×#4112yes—
462C24C2511yescharacteristic
463#41—4128no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—28no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×D4—216no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—216no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
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—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—24no—
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—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
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—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—416no—
587C22×C4—48no—
588C22×C4—88no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4#121116yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D414yes—
596C22×C4C22×D412yes—
597C22×C4C22×D414yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C2×#4114yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4H(5,𝔽2)14yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C4H(5,𝔽2)12yes—
610C22×C42−1+414yes—
611C22×C42−1+414yes—
612C4⋊C4—28no—
613C4⋊C4—216no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—48no—
617C4⋊C4—416no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—88no—
626C4⋊C4—88no—
627C4⋊C4—84no—
628C22⋊C4—216no—
629C22⋊C4—216no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—416no—
633C22⋊C4—48no—
634C22⋊C4—416no—
635C22⋊C4—416no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—88no—
641C22⋊C4—84no—
642C42—28no—
643C42—28no—
644C42—48no—
645C42—44no—
646C42—44no—
647C42—44no—
648C42—44no—
649C42—84no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—28no—
668C23—28no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—44no—
682C23—44no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23C2×#12114yes—
696C23C23×D411yescharacteristic
697C23C23×D411yescharacteristic
698C23C22×#4111yescharacteristic
699C23C22×#4111yescharacteristic
700C23C22×#4111yescharacteristic
701C23C2×H(5,𝔽2)11yescharacteristic
702C23C2×H(5,𝔽2)11yescharacteristic
703C23C2×H(5,𝔽2)12yes—
704C23C2×2−1+412yes—
705C23C2×2−1+412yes—
706C23#58512yes—
707Q8—416no—
708Q8—416no—
709D4—432no—
710D4—416no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—232no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—28no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—432no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
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—44no—
787C2×C4—44no—
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—44no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—816no—
807C2×C4C2×#12114yes—
808C2×C4C2×#12114yes—
809C2×C4#52514yes—
810C2×C4#53414yes—
811C2×C4#54614yes—
812C2×C4#54614yes—
813C2×C4#55114yes—
814C2×C4#55114yes—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—42no—
819C22—42no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—42no—
824C22—44no—
825C22—42no—
826C22—44no—
827C22—44no—
828C22—48no—
829C22—48no—
830C22—44no—
831C22—82no—
832C22—82no—
833C22—84no—
834C22—84no—
835C22—82no—
836C22—82no—
837C22C22×#12111yescharacteristic
838C22C2×#52511yescharacteristic
839C22C2×#53411yescharacteristic
840C22C2×#54611yescharacteristic
841C22C2×#54611yescharacteristic
842C22C2×#55111yescharacteristic
843C22C2×#55111yescharacteristic
844C22#348612yes—
845C22#348812yes—
846C22#349811yescharacteristic
847C22#349911yescharacteristic
848C22#349911yescharacteristic
849C22#350011yescharacteristic
850C22#350612yes—
851C22#350912yes—
852C22#351512yes—
853C22#351612yes—
854C22#352012yes—
855C22#352212yes—
856C22#353612yes—
857C22#354112yes—
858C22#354712yes—
859C22#354812yes—
860C4—24no—
861C4—44no—
862C4—44no—
863C4—42no—
864C4—42no—
865C4—44no—
866C4—44no—
867C4—42no—
868C4—42no—
869C4—44no—
870C4—44no—
871C4—82no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4#253418yes—
877C2—44no—
878C2—84no—
879C2C2×#253411yescharacteristic
880C2#3553311yescharacteristic
881C2#3553511yescharacteristic
882C2#3562211yescharacteristic
883C2#3566711yescharacteristic
884C2#3729611yescharacteristic
885C2#3738811yescharacteristic
886C2#4496212yes—
887C2#4499612yes—
888C2#4536612yes—
889C2#4541712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×#41C22
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×#2502C2semidirect
3. C2×#2323C2semidirect
5. #15512C2semidirect
6. #15436C2semidirect
7. #15411C2semidirect
8. #15301C2semidirect
9. #15217C2semidirect
10. #15184C2semidirect
11. #15180C2semidirect
12. #15134C2semidirect
13. #14026C2semidirect
14. #14024C2semidirect
15. #14001C2semidirect
16. #14000C2semidirect
18. #13904C2semidirect
19. #13852C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25022
C2×#24322
C2×#23232
C2×#23112
#155122
#154362
#154112
#153012
#152172
#151842
#151802
#151342
#140262
#140242
#140012
#140002
#139372
#139042
#138522