Finite Group Databasebeta

← #576033

Subgroups — #576033

Order 512.

6162 conjugacy classes of subgroups.

The subgroup lattice has 1291 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#534C211yesmaximal, characteristic
2C2×#2377C211yesmaximal, characteristic, complemented
3C2×#2363C211yesmaximal, characteristic, complemented
4#14363C212yesmaximal, complemented
5#14363C212yesmaximal, complemented
6#14360C212yesmaximal, complemented
7#14359C212yesmaximal, complemented
8#14358C212yesmaximal, complemented
9#14357C212yesmaximal, complemented
10#14290C211yesmaximal, characteristic, complemented
11#14257C211yesmaximal, characteristic, complemented
12#14096C212yesmaximal, complemented
13#14095C212yesmaximal, complemented
14#13995C212yesmaximal, complemented
15#13967C212yesmaximal, complemented
16#13903C211yesmaximal, characteristic, complemented
17#13902C212yesmaximal, complemented
18#13868C211yesmaximal, characteristic, complemented
19#13867C212yesmaximal, complemented
20C24×D4C2212yes—
21C2×#534—28no—
22C2×#534—28no—
23C2×#534C4116yescomplemented
24C22×#123C2212yes—
25C22×#123C2212yes—
26C22×#121C2212yes—
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#120C2212yes—
30C22×#120C2212yes—
31C22×C4×D4C2211yescharacteristic, complemented
32C22×#117C2211yescharacteristic, complemented
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2212yescomplemented
35#2377—28no—
36#2363—28no—
37C2×#390C2212yes—
38C2×#390C2212yes—
39C2×#390C2211yescharacteristic, complemented
40C2×#390C2212yescomplemented
41C2×#390C2212yescomplemented
42C2×#390C2212yescomplemented
43C2×#389C2211yescharacteristic, complemented
44C2×#388C2212yescomplemented
45C2×#388C2212yescomplemented
46C2×#387C2212yescomplemented
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2212yescomplemented
50C2×#386C2212yescomplemented
51C2×#386C2212yescomplemented
52C2×#386C2212yescomplemented
53C2×#386C2212yescomplemented
54C2×#385C2212yescomplemented
55C2×#381C2211yescharacteristic, complemented
56C2×#381C2211yescharacteristic, complemented
57C2×#381C2211yescharacteristic, complemented
58C2×#380C2211yescharacteristic, complemented
59C2×#380C2212yescomplemented
60C2×#379C2211yescharacteristic
61C2×#379C2212yes—
62C2×#379C2211yescharacteristic
63C2×#379C2212yescomplemented
64C2×#379C2212yescomplemented
65C2×#379C2212yescomplemented
66C2×C4×C4⋊C4C2211yescharacteristic, complemented
67C2×C4×C22⋊C4C2212yescomplemented
68C2×C4×C22⋊C4C2211yescharacteristic, complemented
69C2×C4×C22⋊C4C2212yescomplemented
70#1445C2211yescharacteristic, complemented
71#1445C2211yescharacteristic, complemented
72#1441C2212yescomplemented
73#1441C2212yescomplemented
74#1440C2212yescomplemented
75#1440C2212yescomplemented
76#1439C2212yescomplemented
77#1439C2212yescomplemented
78#1439C2212yescomplemented
79#1439C2212yescomplemented
80#1439C2212yescomplemented
81#1439C2212yescomplemented
82#1439C2212yescomplemented
83#1439C2212yescomplemented
84#1438C2212yes—
85#1438C2212yes—
86#1438C2212yes—
87#1438C2212yes—
88#1438C2212yescomplemented
89#1438C2211yescharacteristic, complemented
90#1438C2212yescomplemented
91#1438C2212yescomplemented
92#1438C2212yescomplemented
93#1438C2212yescomplemented
94#1438C2212yescomplemented
95#1438C2211yescharacteristic, complemented
96#1437C2212yescomplemented
97#1437C2212yescomplemented
98#1437C2212yescomplemented
99#1437C2212yescomplemented
100#1437C2212yescomplemented
101#1437C2212yescomplemented
102#1437C2212yescomplemented
103#1437C2212yescomplemented
104#1436C2212yescomplemented
105#1436C2212yescomplemented
106C4⋊#95C2212yescomplemented
107C22⋊#95C2212yescomplemented
108C22⋊#95C2212yescomplemented
109C22⋊#95C2212yescomplemented
110C22⋊#95C2212yescomplemented
111C22⋊#95C2212yescomplemented
112C26C2311yescharacteristic
113C26C2312yes—
114C23×D4—28no—
115C23×D4—28no—
116C23×D4—44no—
117C23×D4—44no—
118C23×D4—44no—
119C23×D4—44no—
120C23×D4C2×C4116yescomplemented
121C23×D4C2312yes—
122C23×D4C2312yes—
123C23×D4C2312yes—
124C23×D4C2312yes—
125C23×D4C2311yescharacteristic
126C23×D4C2312yes—
127C23×D4C2311yescharacteristic
128C24×C4C2312yes—
129C24×C4C2312yes—
130C24×C4C2311yescharacteristic
131C24×C4C2312yes—
132C24×C4C2311yescharacteristic
133#534—2128no—
134C2×#123—28no—
135C2×#123—28no—
136C2×#123—28no—
137C2×#123—28no—
138C2×#123C2×C4116yescomplemented
139C2×#123C2×C4116yescomplemented
140C2×#121—28no—
141C2×#121—28no—
142C2×#121—24no—
143C2×#121—24no—
144C2×#121C2×C418yes—
145C2×#121C2×C418yescomplemented
146C2×#121C2×C4116yescomplemented
147C2×#121D418yes—
148C2×#121D418yes—
149C2×#120—28no—
150C2×#120—28no—
151C2×#120—28no—
152C2×#120—28no—
153C2×#120C2×C4116yes—
154C2×#120C2×C4116yescomplemented
155C2×C4×D4—24no—
156C2×C4×D4—44no—
157C2×#117—24no—
158C2×#117—44no—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C22⋊C4—24no—
168C22×C22⋊C4—24no—
169C22×C22⋊C4—44no—
170C22×C22⋊C4—44no—
171C22×C22⋊C4—44no—
172C22×C22⋊C4C2×C418yescomplemented
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C42C2312yes—
208C22×C42C2311yescharacteristic
209C22×C42C2312yes—
210C22×C42C2312yes—
211C22×C42C2311yescharacteristic
212#390—24no—
213#390—28no—
214#390—28no—
215#390—44no—
216#390—44no—
217#390—44no—
218#389—24no—
219#388—28no—
220#388—28no—
221#387—28no—
222#386—28no—
223#386—28no—
224#386—28no—
225#386—44no—
226#386—44no—
227#386—44no—
228#386—44no—
229#385—28no—
230#381—24no—
231#381—42no—
232#381—42no—
233#380—24no—
234#380—44no—
235#379—42no—
236#379—44no—
237#379—42no—
238#379—44no—
239#379—44no—
240#379—44no—
241C4×C4⋊C4—24no—
242C4×C22⋊C4—24no—
243C4×C22⋊C4—28no—
244C4×C22⋊C4—44no—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2311yescharacteristic
252C2×#95C2311yescharacteristic
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2311yescharacteristic
256C2×#95C2311yescharacteristic
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C25—22no—
272C25—22no—
273C25—24no—
274C25—24no—
275C25—24no—
276C25—24no—
277C25—24no—
278C25—24no—
279C25—42no—
280C25—42no—
281C25—42no—
282C25—42no—
283C25—42no—
284C25—42no—
285C25—42no—
286C25—41no—
287C25—41no—
288C25—42no—
289C25—42no—
290C25—42no—
291C25—41no—
292C25—41no—
293C25—42no—
294C25—42no—
295C25C22×C414yes—
296C25C22×C418yes—
297C25C2412yes—
298C25C2411yescharacteristic
299C25C2412yes—
300C25C2412yes—
301C22×D4—24no—
302C22×D4—24no—
303C22×D4—24no—
304C22×D4—24no—
305C22×D4—24no—
306C22×D4—24no—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—264no—
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—42no—
317C22×D4—432no—
318C22×D4—42no—
319C22×D4—42no—
320C22×D4—42no—
321C22×D4—42no—
322C22×D4—42no—
323C22×D4—42no—
324C22×D4—42no—
325C22×D4—42no—
326C22×D4—42no—
327C22×D4—42no—
328C22×D4—42no—
329C22×D4—42no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4—42no—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—432no—
338C22×D4—432no—
339C22×D4—432no—
340C22×D4—432no—
341C22×D4—432no—
342C22×D4C22×C418yes—
343C22×D4C22×C418yes—
344C22×D4C22×C418yes—
345C22×D4C22×C414yes—
346C22×D4C22×C418yes—
347C22×D4C22×C414yes—
348C22×D4C22×C418yes—
349C22×D4C2×D414yes—
350C22×D4C2×D414yes—
351C22×D4C2×D418yes—
352C22×D4C2×D418yes—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—42no—
364C23×C4—42no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4—42no—
368C23×C4—42no—
369C23×C4—42no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4—41no—
374C23×C4—41no—
375C23×C4—41no—
376C23×C4—41no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4C22×C418yes—
382C23×C4C22×C414yes—
383C23×C4C22×C414yes—
384C23×C4C2×D414yes—
385C23×C4C2×D414yes—
386C23×C4C2412yes—
387C23×C4C2411yescharacteristic
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2411yescharacteristic
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2411yescharacteristic
396C23×C4C2412yes—
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2412yes—
401#123—264no—
402#123—264no—
403#121—264no—
404#121—232no—
405#121C22⋊C4164yescomplemented
406#120—264no—
407#120—264no—
408C4×D4—416no—
409#117—416no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4C22×C418yes—
428C2×C4⋊C4C22×C414yes—
429C2×C4⋊C4C22×C414yes—
430C2×C4⋊C4C2×D414yes—
431C2×C4⋊C4C2×D414yes—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—232no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—41no—
486C2×C22⋊C4—41no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—432no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—41no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—41no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—41no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4C22×C418yes—
529C2×C22⋊C4C22×C418yes—
530C2×C22⋊C4C22×C418yes—
531C2×C22⋊C4C22×C418yes—
532C2×C22⋊C4C22×C418yes—
533C2×C22⋊C4C22×C418yes—
534C2×C22⋊C4C2×D418yes—
535C2×C22⋊C4C2×D418yes—
536C2×C42—24no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—24no—
540C2×C42—24no—
541C2×C42—24no—
542C2×C42—42no—
543C2×C42—42no—
544C2×C42—42no—
545C2×C42—42no—
546C2×C42—42no—
547C2×C42—42no—
548C2×C42—42no—
549#95—22no—
550#95—24no—
551#95—22no—
552#95—24no—
553#95—24no—
554#95—22no—
555#95—24no—
556#95—22no—
557#95—24no—
558#95—24no—
559#95—24no—
560#95—24no—
561#95—42no—
562#95—42no—
563#95—42no—
564#95—42no—
565#95—42no—
566#95—42no—
567#95—42no—
568#95—42no—
569#95—42no—
570#95—42no—
571#95—42no—
572#95—42no—
573#95—42no—
574#95—42no—
575C24—28no—
576C24—28no—
577C24—216no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—21no—
582C24—21no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—21no—
601C24—21no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—28no—
611C24—216no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—216no—
627C24—216no—
628C24—48no—
629C24—48no—
630C24—48no—
631C24—48no—
632C24—44no—
633C24—44no—
634C24—48no—
635C24—48no—
636C24—48no—
637C24—48no—
638C24—48no—
639C24—48no—
640C24—48no—
641C24—48no—
642C24—48no—
643C24—48no—
644C24—82no—
645C24—84no—
646C24—82no—
647C24—84no—
648C24—82no—
649C24—82no—
650C24—84no—
651C24—84no—
652C24—84no—
653C24—84no—
654C24—84no—
655C24—82no—
656C24—84no—
657C24—82no—
658C24—84no—
659C24—84no—
660C24—84no—
661C24—84no—
662C24—84no—
663C24—84no—
664C24—84no—
665C24—84no—
666C24—84no—
667C24—84no—
668C24—84no—
669C24—84no—
670C24—84no—
671C24—84no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24C23×C414yes—
680C24C23×C414yes—
681C24C23×C412yes—
682C24C23×C414yes—
683C24C22×D414yes—
684C24C22×D414yes—
685C24C22×D412yes—
686C24C22×D412yes—
687C24H(5,𝔽2)14yes—
688C24H(5,𝔽2)14yes—
689C24C2511yescharacteristic
690C2×D4—216no—
691C2×D4—216no—
692C2×D4—216no—
693C2×D4—216no—
694C2×D4—216no—
695C2×D4—216no—
696C2×D4—28no—
697C2×D4—44no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—44no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—4256no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—82no—
728C2×D4—82no—
729C2×D4—84no—
730C2×D4—84no—
731C2×D4—84no—
732C2×D4—84no—
733C2×D4—84no—
734C2×D4C2×C22⋊C4116yes—
735C2×D4C2×C22⋊C4132yescomplemented
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—216no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—28no—
772C22×C4—216no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—44no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—44no—
822C22×C4—48no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—48no—
826C22×C4—48no—
827C22×C4—48no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—84no—
834C22×C4—84no—
835C22×C4—84no—
836C22×C4—82no—
837C22×C4—82no—
838C22×C4—82no—
839C22×C4—82no—
840C22×C4—84no—
841C22×C4—84no—
842C22×C4—84no—
843C22×C4—84no—
844C22×C4—84no—
845C22×C4—84no—
846C22×C4—84no—
847C22×C4C2×C22⋊C4116yescomplemented
848C22×C4C23×C414yes—
849C22×C4C23×C414yes—
850C22×C4C23×C412yes—
851C22×C4C23×C412yes—
852C22×C4C23×C414yes—
853C22×C4C22×D412yes—
854C22×C4C22×D412yes—
855C22×C4C22×D414yes—
856C22×C4C22×D414yes—
857C22×C4C22×D412yes—
858C22×C4C22×D412yes—
859C22×C4H(5,𝔽2)12yes—
860C22×C4H(5,𝔽2)12yes—
861C22×C4H(5,𝔽2)14yes—
862C4⋊C4—28no—
863C4⋊C4—216no—
864C4⋊C4—28no—
865C4⋊C4—44no—
866C4⋊C4—84no—
867C4⋊C4—84no—
868C4⋊C4—84no—
869C4⋊C4C2×C22⋊C4116yescomplemented
870C22⋊C4—216no—
871C22⋊C4—216no—
872C22⋊C4—216no—
873C22⋊C4—216no—
874C22⋊C4—216no—
875C22⋊C4—44no—
876C22⋊C4—48no—
877C22⋊C4—44no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—84no—
887C22⋊C4—84no—
888C22⋊C4—84no—
889C22⋊C4—84no—
890C22⋊C4—84no—
891C22⋊C4—84no—
892C22⋊C4—82no—
893C22⋊C4—84no—
894C22⋊C4—82no—
895C22⋊C4—84no—
896C22⋊C4—84no—
897C22⋊C4—84no—
898C22⋊C4—84no—
899C22⋊C4—84no—
900C22⋊C4—84no—
901C22⋊C4—84no—
902C22⋊C4—84no—
903C22⋊C4C2×C22⋊C4132yescomplemented
904C42—48no—
905C42—44no—
906C42—44no—
907C42—84no—
908C42—84no—
909C23—232no—
910C23—24no—
911C23—24no—
912C23—24no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23—22no—
917C23—22no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—22no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—22no—
937C23—22no—
938C23—24no—
939C23—22no—
940C23—24no—
941C23—22no—
942C23—22no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—22no—
949C23—24no—
950C23—22no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—432no—
968C23—432no—
969C23—42no—
970C23—42no—
971C23—42no—
972C23—42no—
973C23—42no—
974C23—42no—
975C23—42no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—42no—
981C23—42no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—816no—
1038C23—816no—
1039C23—816no—
1040C23—88no—
1041C23—816no—
1042C23—88no—
1043C23—816no—
1044C23—88no—
1045C23—88no—
1046C23—88no—
1047C23—88no—
1048C23—816no—
1049C23—816no—
1050C23—816no—
1051C23—816no—
1052C23—816no—
1053C23—816no—
1054C23—816no—
1055C23—816no—
1056C23—816no—
1057C23—816no—
1058C23—816no—
1059C23—816no—
1060C23C22×C22⋊C418yes—
1061C23C22×C22⋊C414yes—
1062C23#51818yes—
1063C23C24×C411yescharacteristic
1064C23C23×D411yescharacteristic
1065C23C23×D411yescharacteristic
1066C23C2×H(5,𝔽2)12yes—
1067C23C2×H(5,𝔽2)12yes—
1068C23C2×H(5,𝔽2)12yes—
1069C23C2×H(5,𝔽2)11yescharacteristic
1070C23C2×H(5,𝔽2)11yescharacteristic
1071C23#58512yes—
1072C23#58511yescharacteristic
1073C23#58511yescharacteristic
1074D4—432no—
1075D4—416no—
1076D4—432no—
1077D4—432no—
1078D4—432no—
1079D4—88no—
1080D4—816no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—416no—
1109C2×C4—432no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—42no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—41no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—88no—
1174C2×C4—816no—
1175C2×C4—816no—
1176C2×C4C22×C22⋊C414yes—
1177C2×C4C22×C22⋊C414yes—
1178C2×C4C22×C22⋊C418yes—
1179C22—28no—
1180C22—28no—
1181C22—28no—
1182C22—24no—
1183C22—28no—
1184C22—24no—
1185C22—28no—
1186C22—24no—
1187C22—28no—
1188C22—44no—
1189C22—44no—
1190C22—44no—
1191C22—44no—
1192C22—44no—
1193C22—44no—
1194C22—44no—
1195C22—44no—
1196C22—44no—
1197C22—42no—
1198C22—44no—
1199C22—44no—
1200C22—42no—
1201C22—44no—
1202C22—44no—
1203C22—44no—
1204C22—44no—
1205C22—42no—
1206C22—44no—
1207C22—42no—
1208C22—44no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—832no—
1228C22—864no—
1229C22—82no—
1230C22—82no—
1231C22—82no—
1232C22—82no—
1233C22—82no—
1234C22—82no—
1235C22—82no—
1236C22—82no—
1237C22C23×C22⋊C411yescharacteristic
1238C22C2×#51812yes—
1239C22C4×H(5,𝔽2)11yescharacteristic
1240C22C4×H(5,𝔽2)12yes—
1241C22C4×H(5,𝔽2)11yescharacteristic
1242C22#348411yescharacteristic
1243C22#348411yescharacteristic
1244C22#348412yes—
1245C22#348411yescharacteristic
1246C22#348511yescharacteristic
1247C22#348811yescharacteristic
1248C22#348811yescharacteristic
1249C22#349612yes—
1250C22#349811yescharacteristic
1251C22#350011yescharacteristic
1252C22#353212yes—
1253C22#353312yes—
1254C22#353412yes—
1255C22#353412yes—
1256C22#354212yes—
1257C22#354212yes—
1258C22#354312yes—
1259C22#354512yes—
1260C4—28no—
1261C4—24no—
1262C4—24no—
1263C4—44no—
1264C4—42no—
1265C4—44no—
1266C4—44no—
1267C4—42no—
1268C4—81no—
1269C4—81no—
1270C4—82no—
1271C4—82no—
1272C4—82no—
1273C4—82no—
1274C4—82no—
1275C2—44no—
1276C2—48no—
1277C2—48no—
1278C2—84no—
1279C2#3417111yescharacteristic
1280C2#3425611yescharacteristic
1281C2#3425811yescharacteristic
1282C2#3440712yes—
1283C2#3440812yes—
1284C2#4783011yescharacteristic
1285C2#4783111yescharacteristic
1286C2#4785312yes—
1287C2#4785412yes—
1288C2#4877611yescharacteristic
1289C2#4877711yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#534C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2377C2semidirect
3. C2×#2363C2semidirect
4. #14363C2semidirect
5. #14363C2semidirect
6. #14360C2semidirect
7. #14359C2semidirect
8. #14358C2semidirect
9. #14357C2semidirect
10. #14290C2semidirect
11. #14257C2semidirect
12. #14096C2semidirect
13. #14095C2semidirect
14. #13995C2semidirect
15. #13967C2semidirect
16. #13903C2semidirect
17. #13902C2semidirect
18. #13868C2semidirect
19. #13867C2semidirect
23. C2×#534C4semidirect
31. C22×C4×D4C22semidirect
32. C22×#117C22semidirect
34. C23×C22⋊C4C22semidirect
39. C2×#390C22semidirect
40. C2×#390C22semidirect
41. C2×#390C22semidirect
42. C2×#390C22semidirect
43. C2×#389C22semidirect
44. C2×#388C22semidirect
45. C2×#388C22semidirect
46. C2×#387C22semidirect
49. C2×#386C22semidirect
50. C2×#386C22semidirect
51. C2×#386C22semidirect
52. C2×#386C22semidirect
53. C2×#386C22semidirect
54. C2×#385C22semidirect
55. C2×#381C22semidirect
56. C2×#381C22semidirect
57. C2×#381C22semidirect
58. C2×#380C22semidirect
59. C2×#380C22semidirect
63. C2×#379C22semidirect
64. C2×#379C22semidirect
65. C2×#379C22semidirect
66. C2×C4×C4⋊C4C22semidirect
67. C2×C4×C22⋊C4C22semidirect
68. C2×C4×C22⋊C4C22semidirect
69. C2×C4×C22⋊C4C22semidirect
70. #1445C22semidirect
71. #1445C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
74. #1440C22semidirect
75. #1440C22semidirect
76. #1439C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect
79. #1439C22semidirect
80. #1439C22semidirect
81. #1439C22semidirect
82. #1439C22semidirect
83. #1439C22semidirect
88. #1438C22semidirect
89. #1438C22semidirect
90. #1438C22semidirect
91. #1438C22semidirect
92. #1438C22semidirect
93. #1438C22semidirect
94. #1438C22semidirect
95. #1438C22semidirect
96. #1437C22semidirect
97. #1437C22semidirect
98. #1437C22semidirect
99. #1437C22semidirect
100. #1437C22semidirect
101. #1437C22semidirect
102. #1437C22semidirect
103. #1437C22semidirect
104. #1436C22semidirect
105. #1436C22semidirect
106. C4⋊#95C22semidirect
107. C22⋊#95C22semidirect
108. C22⋊#95C22semidirect
109. C22⋊#95C22semidirect
110. C22⋊#95C22semidirect
111. C22⋊#95C22semidirect
120. C23×D4C2×C4semidirect
138. C2×#123C2×C4semidirect
139. C2×#123C2×C4semidirect
145. C2×#121C2×C4semidirect
146. C2×#121C2×C4semidirect
154. C2×#120C2×C4semidirect
172. C22×C22⋊C4C2×C4semidirect
405. #121C22⋊C4semidirect
735. C2×D4C2×C22⋊C4semidirect
847. C22×C4C2×C22⋊C4semidirect
869. C4⋊C4C2×C22⋊C4semidirect
903. C22⋊C4C2×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#5342
C2×#23772
C2×#23632
#143632
#143602
#143592
#143582
#143572
#142902
#142572
#140962
#140952
#139952
#139672
#139032
#139022
#138682
#138672