Finite Group Databasebeta

← #712423

Subgroups — #712423

Order 512.

4513 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×#2430C211yesmaximal, characteristic, complemented
2C2×#2411C211yesmaximal, characteristic, complemented
3C2×#2404C211yesmaximal, characteristic, complemented
4C2×#2623C211yesmaximal, characteristic, complemented
5C22×#397C211yesmaximal, characteristic, complemented
6C2×#2311C211yesmaximal, characteristic, complemented
7#16812C212yesmaximal, complemented
8#16810C212yesmaximal, complemented
9#15526C214yesmaximal, complemented
10#15493C214yesmaximal, complemented
11#15167C212yesmaximal, complemented
12#15007C212yesmaximal, complemented
13#14946C212yesmaximal, complemented
14#14716C212yesmaximal, complemented
15#14152C212yesmaximal, complemented
16#13995C212yesmaximal, complemented
17#13799C211yesmaximal, characteristic, complemented
18C23×#41C2211yescharacteristic
19C22×#123C2211yescharacteristic
20C22×#121C2212yes—
21C22×#120C2212yes—
22C22×#120C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2212yes—
27#2623—28no—
28#2430—28no—
29#2411—28no—
30#2404—28no—
31C2×#400C2212yescomplemented
32C2×#399C2212yescomplemented
33C2×#398C2212yescomplemented
34C2×#397—28no—
35C2×#397C2212yes—
36C2×#397C2214yes—
37C2×#397C2212yes—
38C2×#397C2212yescomplemented
39C2×#396C2212yes—
40C2×#395C2211yescharacteristic, complemented
41C2×#394C2212yes—
42C2×#394C2211yescharacteristic, complemented
43C2×#393C2212yes—
44C2×#393C2211yescharacteristic, complemented
45C2×#392C2212yes—
46C2×#392C2214yes—
47C2×#392C2211yescharacteristic, complemented
48#2311—28no—
49C2×#391C2212yescomplemented
50C2×#390C2212yes—
51C2×#390C2214yes—
52C2×#390C2212yescomplemented
53C2×#388C2212yes—
54C2×#386C2212yes—
55C2×#386C2211yescharacteristic
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2214yes—
61C2×#386C2212yescomplemented
62C2×#385C2212yes—
63C2×#385C2211yescharacteristic
64C2×#385C2212yescomplemented
65C2×#381C2211yescharacteristic
66C2×#380C2214yescomplemented
67C2×#379C2211yescharacteristic
68C2×C4×C22⋊C4C2212yes—
69C22×#95C2212yes—
70C22×#95C2211yescharacteristic
71#1445C2214yescomplemented
72#1445C2214yescomplemented
73#1445C2214yescomplemented
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yescomplemented
77#1439C2214yescomplemented
78#1438C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81#1438C2214yescomplemented
82#1437C2214yes—
83#1437C2214yescomplemented
84#1437C2214yescomplemented
85#1436C2214yescomplemented
86#1434C2212yescomplemented
87C22⋊#95C2212yes—
88C4×#95C2212yescomplemented
89C26C2311yescharacteristic
90C22×#41—28no—
91C22×#41—24no—
92C22×#41—24no—
93C22×#41—24no—
94C22×#41—44no—
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C23×D4C2311yescharacteristic
99C23×D4C2314yes—
100C23×D4C2312yes—
101C23×D4C2312yes—
102C24×C4C2312yes—
103C24×C4C2311yescharacteristic
104C24×C4C2312yes—
105C24×C4C2311yescharacteristic
106C24×C4C2312yes—
107C2×#123—24no—
108C2×#123—24no—
109C2×#123—24no—
110C2×#121—28no—
111C2×#121—28no—
112C2×#121—44no—
113C2×#120—28no—
114C2×#120—28no—
115C2×#120—24no—
116C2×#120—44no—
117C2×#120—44no—
118C2×#117—44no—
119C2×#117D418yescomplemented
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C22⋊C4—28no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—48no—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C42C2314yes—
160C22×C42C2312yes—
161#400—28no—
162#399—28no—
163#398—28no—
164#397—28no—
165#397—216no—
166#397—28no—
167#397—28no—
168#396—28no—
169#395—24no—
170#394—28no—
171#394—24no—
172#393—28no—
173#393—24no—
174#392—28no—
175#392—24no—
176#392—48no—
177#391—28no—
178#390—28no—
179#390—28no—
180#390—48no—
181#388—28no—
182#386—28no—
183#386—28no—
184#386—28no—
185#386—28no—
186#386—28no—
187#386—24no—
188#386—216no—
189#386—28no—
190#385—28no—
191#385—24no—
192#385—28no—
193#381D418yescomplemented
194#380—216no—
195#379—24no—
196C4×C22⋊C4—44no—
197C2×#95—28no—
198C2×#95D418yescomplemented
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2312yes—
217C2×#95C2312yes—
218C25—22no—
219C25—24no—
220C25—22no—
221C25—22no—
222C25—24no—
223C25—24no—
224C25—44no—
225C25—42no—
226C25C2411yescharacteristic
227C25C2412yes—
228C25C2412yes—
229C25C2411yescharacteristic
230C2×#41—232no—
231C2×#41—432no—
232C2×#41—432no—
233C2×#41—416no—
234C2×#41—416no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—24no—
239C22×Q8—42no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—28no—
253C22×D4—28no—
254C22×D4—24no—
255C22×D4—24no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—28no—
260C22×D4—24no—
261C22×D4—24no—
262C22×D4—42no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4—42no—
266C22×D4—44no—
267C22×D4—42no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4#4118yes—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4—44no—
296C23×C4C2×D414yes—
297C23×C4C2×D414yes—
298C23×C4C2×D414yes—
299C23×C4C2×D418yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2414yes—
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2414yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313#123—416no—
314#121—432no—
315#120—432no—
316#120—416no—
317#117—416no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—416no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4C2×D418yes—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
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—28no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—432no—
390C2×C22⋊C4—416no—
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⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4C2×D414yes—
403C2×C22⋊C4C2×D414yes—
404C2×C22⋊C4C2×D418yes—
405C2×C42—44no—
406C2×C42—44no—
407C2×C42—44no—
408C2×C42—44no—
409C2×C42C2×D418yes—
410#95—28no—
411#95—28no—
412#95—28no—
413#95—28no—
414#95—24no—
415#95—24no—
416#95—28no—
417#95—28no—
418#95—24no—
419#95—24no—
420#95—28no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95C2×D418yes—
425#95C2×D414yes—
426#95C2×D414yes—
427#95C2×D418yes—
428#95C2×D418yes—
429C24—22no—
430C24—24no—
431C24—22no—
432C24—28no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—24no—
440C24—22no—
441C24—22no—
442C24—24no—
443C24—24no—
444C24—22no—
445C24—22no—
446C24—24no—
447C24—24no—
448C24—24no—
449C24—22no—
450C24—24no—
451C24—22no—
452C24—24no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—24no—
461C24—48no—
462C24—48no—
463C24—416no—
464C24—416no—
465C24—48no—
466C24—44no—
467C24—44no—
468C24—48no—
469C24—44no—
470C24—44no—
471C24—48no—
472C24—84no—
473C24—84no—
474C24—88no—
475C24—88no—
476C24C22×D412yes—
477C24C22×D412yes—
478C24C22×D412yes—
479C24C2×#4114yes—
480C24C2×#4114yes—
481C24H(5,𝔽2)14yes—
482C24H(5,𝔽2)14yes—
483C24C2511yescharacteristic
484#41—4128no—
485C2×Q8—28no—
486C2×Q8—48no—
487C2×Q8—48no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×D4—28no—
491C2×D4—216no—
492C2×D4—216no—
493C2×D4—216no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—44no—
497C2×D4—416no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—416no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—416no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—44no—
514C2×D4—84no—
515C2×D4—88no—
516C2×D4—84no—
517C2×D4—88no—
518C2×D4—88no—
519C2×D4—88no—
520C2×D4—88no—
521C2×D4—88no—
522C2×D4—88no—
523C2×D4—88no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—216no—
527C22×C4—216no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—216no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—216no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—44no—
600C22×C4—48no—
601C22×C4—88no—
602C22×C4—88no—
603C22×C4—88no—
604C22×C4—88no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4#127116yes—
608C22×C4C22×D414yes—
609C22×C4C22×D418yes—
610C22×C4C22×D414yes—
611C22×C4C22×D414yes—
612C22×C4C22×D414yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C2×#4114yes—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—88no—
627C4⋊C4—84no—
628C22⋊C4—28no—
629C22⋊C4—28no—
630C22⋊C4—216no—
631C22⋊C4—416no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—416no—
635C22⋊C4—416no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—44no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—84no—
645C22⋊C4—88no—
646C22⋊C4—88no—
647C22⋊C4—88no—
648C22⋊C4—84no—
649C22⋊C4—84no—
650C22⋊C4—88no—
651C42—48no—
652C42—88no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—28no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—28no—
671C23—28no—
672C23—28no—
673C23—28no—
674C23—416no—
675C23—432no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—44no—
684C23—44no—
685C23—42no—
686C23—42no—
687C23—44no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—44no—
692C23—44no—
693C23—42no—
694C23—42no—
695C23—44no—
696C23—42no—
697C23—42no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—816no—
729C23—816no—
730C23—832no—
731C23—88no—
732C23—816no—
733C23—88no—
734C23#52514yes—
735C23C2×#12714yes—
736C23#53414yes—
737C23#54618yes—
738C23#54618yes—
739C23C23×D411yescharacteristic
740C23C23×D411yescharacteristic
741C23C23×D411yescharacteristic
742C23C22×#4112yes—
743C23C2×H(5,𝔽2)12yes—
744C23C2×H(5,𝔽2)12yes—
745C23#58514yes—
746C23#58512yes—
747Q8—416no—
748D4—416no—
749D4—432no—
750D4—832no—
751D4—816no—
752D4—816no—
753D4—88no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—232no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—28no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—28no—
778C2×C4—24no—
779C2×C4—28no—
780C2×C4—24no—
781C2×C4—432no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—816no—
825C2×C4—88no—
826C2×C4—816no—
827C2×C4C2×#12714yes—
828C2×C4C2×#12714yes—
829C22—24no—
830C22—28no—
831C22—28no—
832C22—28no—
833C22—216no—
834C22—24no—
835C22—28no—
836C22—44no—
837C22—48no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—48no—
842C22—48no—
843C22—44no—
844C22—44no—
845C22—48no—
846C22—832no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—84no—
853C22—84no—
854C22—82no—
855C22—84no—
856C22—84no—
857C22—82no—
858C22—82no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—84no—
865C22—81no—
866C22—82no—
867C22#253918yes—
868C22C2×#52511yescharacteristic
869C22C22×#12711yescharacteristic
870C22C2×#53411yescharacteristic
871C22#344912yes—
872C22C2×#54612yes—
873C22C2×#54612yes—
874C22#348411yescharacteristic
875C22#348711yescharacteristic
876C22#348812yes—
877C22#348812yes—
878C22#350012yes—
879C22#350012yes—
880C22#351314yes—
881C22#352114yes—
882C22#353414yes—
883C22#356014yes—
884C4—24no—
885C4—24no—
886C4—44no—
887C4—44no—
888C4—44no—
889C4—48no—
890C4—44no—
891C4—44no—
892C4—81no—
893C4—82no—
894C4—81no—
895C4—81no—
896C4—84no—
897C2—28no—
898C2—84no—
899C2—84no—
900C2—161no—
901C2C2×#253911yescharacteristic
902C2#3532911yescharacteristic
903C2#3556511yescharacteristic
904C2#3597912yes—
905C2#3803112yes—
906C2#3890012yes—
907C2#4193612yes—
908C2#4399814yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2430C2semidirect
2. C2×#2411C2semidirect
3. C2×#2404C2semidirect
4. C2×#2623C2semidirect
5. C22×#397C2semidirect
6. C2×#2311C2semidirect
7. #16812C2semidirect
8. #16810C2semidirect
9. #15526C2semidirect
10. #15493C2semidirect
11. #15167C2semidirect
12. #15007C2semidirect
13. #14946C2semidirect
14. #14716C2semidirect
15. #14152C2semidirect
16. #13995C2semidirect
17. #13799C2semidirect
31. C2×#400C22semidirect
32. C2×#399C22semidirect
33. C2×#398C22semidirect
38. C2×#397C22semidirect
40. C2×#395C22semidirect
42. C2×#394C22semidirect
44. C2×#393C22semidirect
47. C2×#392C22semidirect
49. C2×#391C22semidirect
52. C2×#390C22semidirect
61. C2×#386C22semidirect
64. C2×#385C22semidirect
66. C2×#380C22semidirect
71. #1445C22semidirect
72. #1445C22semidirect
73. #1445C22semidirect
76. #1439C22semidirect
77. #1439C22semidirect
81. #1438C22semidirect
83. #1437C22semidirect
84. #1437C22semidirect
85. #1436C22semidirect
86. #1434C22semidirect
88. C4×#95C22semidirect
119. C2×#117D4semidirect
193. #381D4semidirect
198. C2×#95D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24302
C2×#24112
C2×#24042
C2×#26232
C22×#3972
C2×#23112
#168122
#168102
#155262
#154932
#151672
#150072
#149462
#147162
#141522
#139952
#137992