Finite Group Databasebeta

← #581562

Subgroups — #581562

Order 512.

6256 conjugacy classes of subgroups.

The subgroup lattice has 1299 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#534C211yesmaximal, characteristic
2C2×#2321C212yesmaximal, complemented
3#14657C211yesmaximal, characteristic, complemented
4#14506C211yesmaximal, characteristic, complemented
5#14506C211yesmaximal, characteristic, complemented
6#14505C212yesmaximal, complemented
7#14417C212yesmaximal, complemented
8#14361C212yesmaximal, complemented
9#14359C212yesmaximal, complemented
10#14357C212yesmaximal, complemented
11#14134C211yesmaximal, characteristic, complemented
12#14100C212yesmaximal, complemented
13#14096C212yesmaximal, complemented
14#13970C212yesmaximal, complemented
15#13967C212yesmaximal, complemented
16#13902C211yesmaximal, characteristic, complemented
17#13873C212yesmaximal, complemented
18#13867C212yesmaximal, complemented
19#13867C211yesmaximal, characteristic, complemented
20C24×D4C2211yescharacteristic
21C24×D4C2211yescharacteristic
22C2×#534—216no—
23C2×#534C4116yescomplemented
24C22×#123C2212yes—
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#121C2212yes—
28C22×#121C2212yes—
29C22×#120C2212yes—
30C22×#120C2211yescharacteristic
31C22×#120C2211yescharacteristic
32C22×C4×D4C2212yescomplemented
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2212yescomplemented
35C23×C22⋊C4C2211yescharacteristic, complemented
36#2321—216no—
37C2×#390C2212yes—
38C2×#390C2212yescomplemented
39C2×#390C2212yescomplemented
40C2×#388C2212yescomplemented
41C2×#388C2212yescomplemented
42C2×#388C2212yescomplemented
43C2×#388C2212yescomplemented
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yescomplemented
48C2×#386C2212yescomplemented
49C2×#386C2212yescomplemented
50C2×#386C2212yescomplemented
51C2×#386C2212yescomplemented
52C2×#386C2212yescomplemented
53C2×#386C2212yescomplemented
54C2×#385C2212yescomplemented
55C2×#380C2211yescharacteristic, complemented
56C2×#380C2212yescomplemented
57C2×#379C2212yes—
58C2×#379C2212yes—
59C2×#379C2212yescomplemented
60C2×#379C2211yescharacteristic, complemented
61C2×#379C2212yescomplemented
62C2×C4×C22⋊C4C2212yescomplemented
63C2×C4×C22⋊C4C2211yescharacteristic, complemented
64C2×C4×C22⋊C4C2212yescomplemented
65#1445C2212yescomplemented
66#1445C2212yescomplemented
67#1441C2212yescomplemented
68#1441C2212yescomplemented
69#1440C2212yescomplemented
70#1440C2212yescomplemented
71#1440C2212yescomplemented
72#1440C2212yescomplemented
73#1440C2212yescomplemented
74#1440C2212yescomplemented
75#1439C2212yescomplemented
76#1439C2212yescomplemented
77#1439C2212yescomplemented
78#1439C2212yescomplemented
79#1438C2212yes—
80#1438C2212yes—
81#1438C2211yescharacteristic
82#1438C2211yescharacteristic
83#1438C2211yescharacteristic
84#1438C2211yescharacteristic
85#1438C2211yescharacteristic, complemented
86#1438C2212yescomplemented
87#1438C2212yescomplemented
88#1438C2211yescharacteristic, complemented
89#1438C2212yescomplemented
90#1438C2212yescomplemented
91#1438C2211yescharacteristic, complemented
92#1438C2211yescharacteristic, complemented
93#1437C2212yescomplemented
94#1437C2212yescomplemented
95#1437C2212yescomplemented
96#1437C2212yescomplemented
97#1436C2212yescomplemented
98#1436C2212yescomplemented
99C4⋊#95C2212yescomplemented
100C4⋊#95C2212yescomplemented
101C22⋊#95C2212yescomplemented
102C22⋊#95C2212yescomplemented
103C22⋊#95C2212yescomplemented
104C22⋊#95C2212yescomplemented
105C22⋊#95C2212yescomplemented
106C22⋊#95C2212yescomplemented
107C22⋊#95C2212yescomplemented
108C22⋊#95C2212yescomplemented
109C22⋊#95C2212yescomplemented
110C26C2311yescharacteristic
111C26C2311yescharacteristic
112C26C2311yescharacteristic
113C23×D4—28no—
114C23×D4—28no—
115C23×D4—42no—
116C23×D4—42no—
117C23×D4—42no—
118C23×D4—42no—
119C23×D4—44no—
120C23×D4—44no—
121C23×D4C2×C418yescomplemented
122C23×D4C2×C418yescomplemented
123C23×D4C2312yes—
124C23×D4C2312yes—
125C23×D4C2311yescharacteristic
126C23×D4C2311yescharacteristic
127C23×D4C2311yescharacteristic
128C23×D4C2312yes—
129C23×D4C2311yescharacteristic
130C23×D4C2312yes—
131C24×C4C2311yescharacteristic
132C24×C4C2312yes—
133C24×C4C2312yes—
134C24×C4C2311yescharacteristic
135C24×C4C2312yes—
136C24×C4C2312yes—
137#534—2128no—
138C2×#123—28no—
139C2×#123—28no—
140C2×#123—28no—
141C2×#123—28no—
142C2×#123C2×C418yescomplemented
143C2×#123C2×C4116yescomplemented
144C2×#123C2×C418yescomplemented
145C2×#121—28no—
146C2×#121—28no—
147C2×#121—28no—
148C2×#121—28no—
149C2×#121C2×C4116yescomplemented
150C2×#121C2×C4116yescomplemented
151C2×#120—28no—
152C2×#120—28no—
153C2×#120—28no—
154C2×#120C2×C418yes—
155C2×#120C2×C418yescomplemented
156C2×#120C2×C4116yescomplemented
157C2×#120D4116yes—
158C2×C4×D4—28no—
159C2×C4×D4—44no—
160C2×C4×D4—44no—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C22⋊C4—28no—
167C22×C22⋊C4—28no—
168C22×C22⋊C4—44no—
169C22×C22⋊C4—44no—
170C22×C22⋊C4—44no—
171C22×C22⋊C4—42no—
172C22×C22⋊C4C2×C418yescomplemented
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C42C2312yes—
208C22×C42C2312yes—
209C22×C42C2312yes—
210#390—28no—
211#390—28no—
212#390—44no—
213#388—28no—
214#388—28no—
215#388—28no—
216#388—28no—
217#386—28no—
218#386—28no—
219#386—28no—
220#386—44no—
221#386—44no—
222#386—44no—
223#386—44no—
224#386—44no—
225#386—44no—
226#386—44no—
227#385—28no—
228#380—44no—
229#380—42no—
230#379—28no—
231#379—44no—
232#379—44no—
233#379—44no—
234#379—42no—
235C4×C22⋊C4—28no—
236C4×C22⋊C4—44no—
237C4×C22⋊C4—42no—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2311yescharacteristic
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2311yescharacteristic
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C2×#95C2312yes—
266C25—24no—
267C25—24no—
268C25—22no—
269C25—22no—
270C25—22no—
271C25—22no—
272C25—24no—
273C25—42no—
274C25—42no—
275C25—42no—
276C25—41no—
277C25—42no—
278C25—41no—
279C25—42no—
280C25—42no—
281C25—42no—
282C25—42no—
283C25—42no—
284C25—42no—
285C25—42no—
286C25—42no—
287C25—42no—
288C25—42no—
289C25C22×C414yes—
290C25C22×C414yes—
291C25C22×C414yes—
292C25C2×D418yes—
293C25C2411yescharacteristic
294C25C2411yescharacteristic
295C25C2411yescharacteristic
296C25C2412yes—
297C25C2411yescharacteristic
298C25C2411yescharacteristic
299C22×D4—232no—
300C22×D4—24no—
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—24no—
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—232no—
315C22×D4—24no—
316C22×D4—42no—
317C22×D4—42no—
318C22×D4—416no—
319C22×D4—41no—
320C22×D4—41no—
321C22×D4—42no—
322C22×D4—41no—
323C22×D4—41no—
324C22×D4—41no—
325C22×D4—41no—
326C22×D4—41no—
327C22×D4—41no—
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—42no—
338C22×D4—42no—
339C22×D4—416no—
340C22×D4—416no—
341C22×D4—416no—
342C22×D4—432no—
343C22×D4—432no—
344C22×D4—432no—
345C22×D4—432no—
346C22×D4C22×C418yes—
347C22×D4C22×C414yes—
348C22×D4C22×C418yes—
349C22×D4C22×C414yes—
350C22×D4C22×C418yes—
351C22×D4C22×C414yes—
352C22×D4C22×C418yes—
353C22×D4C22×C414yes—
354C22×D4C2×D418yes—
355C22×D4C2×D418yes—
356C22×D4C2×D418yes—
357C23×C4—24no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—42no—
370C23×C4—41no—
371C23×C4—42no—
372C23×C4—41no—
373C23×C4—42no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4C22×C414yes—
393C23×C4C22×C418yes—
394C23×C4C22×C414yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2412yes—
400C23×C4C2412yes—
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2411yescharacteristic
408#123—232no—
409#123—264no—
410#123—232no—
411#121—264no—
412#121—264no—
413#120—232no—
414#120—264no—
415#120C22⋊C4164yescomplemented
416C4×D4—432no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4C22×C418yes—
431C2×C4⋊C4C22×C418yes—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
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—232no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
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—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
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—41no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—41no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—432no—
491C2×C22⋊C4—416no—
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—42no—
508C2×C22⋊C4—41no—
509C2×C22⋊C4—41no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4C22×C414yes—
522C2×C22⋊C4C22×C418yes—
523C2×C22⋊C4C22×C418yes—
524C2×C22⋊C4C22×C418yes—
525C2×C22⋊C4C22×C418yes—
526C2×C22⋊C4C22×C414yes—
527C2×C22⋊C4C22×C418yes—
528C2×C22⋊C4C2×D418yes—
529C2×C22⋊C4C2×D418yes—
530C2×C22⋊C4C2×D418yes—
531C2×C42—24no—
532C2×C42—24no—
533C2×C42—24no—
534C2×C42—24no—
535C2×C42—42no—
536C2×C42—42no—
537C2×C42—42no—
538C2×C42—42no—
539C2×C42—42no—
540#95—24no—
541#95—24no—
542#95—24no—
543#95—24no—
544#95—24no—
545#95—24no—
546#95—24no—
547#95—24no—
548#95—42no—
549#95—42no—
550#95—42no—
551#95—41no—
552#95—41no—
553#95—42no—
554#95—41no—
555#95—41no—
556#95—42no—
557#95—42no—
558#95—42no—
559#95—42no—
560#95—42no—
561#95—42no—
562#95—42no—
563#95—42no—
564#95—42no—
565#95—42no—
566#95—42no—
567#95—42no—
568C24—216no—
569C24—216no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—21no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—21no—
591C24—21no—
592C24—22no—
593C24—21no—
594C24—22no—
595C24—21no—
596C24—21no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—28no—
610C24—28no—
611C24—28no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—21no—
617C24—21no—
618C24—22no—
619C24—22no—
620C24—28no—
621C24—28no—
622C24—48no—
623C24—44no—
624C24—44no—
625C24—44no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—48no—
630C24—48no—
631C24—48no—
632C24—48no—
633C24—48no—
634C24—48no—
635C24—48no—
636C24—48no—
637C24—48no—
638C24—48no—
639C24—44no—
640C24—44no—
641C24—48no—
642C24—84no—
643C24—84no—
644C24—84no—
645C24—84no—
646C24—84no—
647C24—84no—
648C24—84no—
649C24—84no—
650C24—82no—
651C24—82no—
652C24—84no—
653C24—84no—
654C24—84no—
655C24—84no—
656C24—84no—
657C24—82no—
658C24—82no—
659C24—82no—
660C24—82no—
661C24—84no—
662C24—84no—
663C24—82no—
664C24—82no—
665C24—84no—
666C24—84no—
667C24—84no—
668C24—84no—
669C24—84no—
670C24—84no—
671C24—82no—
672C24—82no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24C2×C22⋊C4116yescomplemented
678C24C23×C412yes—
679C24C23×C412yes—
680C24C23×C414yes—
681C24C23×C412yes—
682C24C23×C412yes—
683C24C23×C412yes—
684C24C22×D414yes—
685C24C22×D414yes—
686C24C22×D414yes—
687C24C22×D414yes—
688C24H(5,𝔽2)12yes—
689C24H(5,𝔽2)12yes—
690C24H(5,𝔽2)14yes—
691C24C2511yescharacteristic
692C2×D4—216no—
693C2×D4—28no—
694C2×D4—28no—
695C2×D4—216no—
696C2×D4—28no—
697C2×D4—216no—
698C2×D4—28no—
699C2×D4—216no—
700C2×D4—216no—
701C2×D4—28no—
702C2×D4—48no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—44no—
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—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—4128no—
733C2×D4—4128no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—84no—
737C2×D4—84no—
738C2×D4—84no—
739C2×D4—84no—
740C2×D4C2×C22⋊C4132yes—
741C2×D4C2×C22⋊C4116yes—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—28no—
750C22×C4—28no—
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—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—216no—
780C22×C4—28no—
781C22×C4—216no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
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—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—48no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—84no—
837C22×C4—84no—
838C22×C4—84no—
839C22×C4—84no—
840C22×C4—84no—
841C22×C4—84no—
842C22×C4—84no—
843C22×C4—84no—
844C22×C4—84no—
845C22×C4—84no—
846C22×C4—84no—
847C22×C4—84no—
848C22×C4—84no—
849C22×C4—84no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—84no—
853C22×C4—84no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4C23×C414yes—
858C22×C4C23×C412yes—
859C22×C4C23×C414yes—
860C22×C4C23×C414yes—
861C22×C4C23×C412yes—
862C22×C4C22×D414yes—
863C22×C4C22×D414yes—
864C22×C4C22×D414yes—
865C22×C4H(5,𝔽2)14yes—
866C22×C4H(5,𝔽2)14yes—
867C4⋊C4—216no—
868C4⋊C4—216no—
869C4⋊C4—48no—
870C4⋊C4—84no—
871C4⋊C4—84no—
872C22⋊C4—28no—
873C22⋊C4—216no—
874C22⋊C4—216no—
875C22⋊C4—216no—
876C22⋊C4—216no—
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—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—44no—
890C22⋊C4—84no—
891C22⋊C4—84no—
892C22⋊C4—84no—
893C22⋊C4—84no—
894C22⋊C4—84no—
895C22⋊C4—84no—
896C22⋊C4—84no—
897C22⋊C4—84no—
898C22⋊C4—84no—
899C22⋊C4—84no—
900C22⋊C4—84no—
901C22⋊C4—82no—
902C22⋊C4—82no—
903C22⋊C4—84no—
904C22⋊C4C2×C22⋊C4116yescomplemented
905C22⋊C4C2×C22⋊C4132yescomplemented
906C42—48no—
907C42—84no—
908C42—84no—
909C23—232no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—24no—
916C23—22no—
917C23—24no—
918C23—22no—
919C23—22no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—22no—
961C23—22no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—24no—
974C23—24no—
975C23—416no—
976C23—432no—
977C23—416no—
978C23—416no—
979C23—42no—
980C23—42no—
981C23—42no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—41no—
988C23—42no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—42no—
993C23—41no—
994C23—41no—
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—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—42no—
1021C23—41no—
1022C23—41no—
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—42no—
1038C23—42no—
1039C23—41no—
1040C23—41no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—41no—
1046C23—41no—
1047C23—42no—
1048C23—42no—
1049C23—88no—
1050C23—88no—
1051C23—88no—
1052C23—816no—
1053C23—816no—
1054C23—816no—
1055C23—816no—
1056C23—816no—
1057C23—816no—
1058C23—816no—
1059C23—816no—
1060C23—816no—
1061C23—816no—
1062C23—816no—
1063C23—88no—
1064C23—88no—
1065C23—816no—
1066C23—816no—
1067C23—816no—
1068C23—816no—
1069C23—816no—
1070C23—816no—
1071C23C22×C22⋊C414yes—
1072C23C22×C22⋊C414yes—
1073C23C22×C22⋊C418yes—
1074C23#51814yes—
1075C23#51814yes—
1076C23C24×C411yescharacteristic
1077C23C23×D412yes—
1078C23C2×H(5,𝔽2)11yescharacteristic
1079C23C2×H(5,𝔽2)12yes—
1080C23C2×H(5,𝔽2)11yescharacteristic
1081C23C2×H(5,𝔽2)12yes—
1082C23C2×H(5,𝔽2)12yes—
1083C23#58512yes—
1084C23#58512yes—
1085D4—416no—
1086D4—432no—
1087D4—416no—
1088D4—432no—
1089D4—416no—
1090D4—432no—
1091D4—416no—
1092D4—816no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—416no—
1119C2×C4—416no—
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—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
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—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—816no—
1181C2×C4—816no—
1182C2×C4—816no—
1183C2×C4—816no—
1184C2×C4C22×C22⋊C418yes—
1185C2×C4C22×C22⋊C414yes—
1186C22—24no—
1187C22—24no—
1188C22—24no—
1189C22—24no—
1190C22—24no—
1191C22—24no—
1192C22—28no—
1193C22—28no—
1194C22—28no—
1195C22—28no—
1196C22—28no—
1197C22—28no—
1198C22—44no—
1199C22—44no—
1200C22—44no—
1201C22—44no—
1202C22—44no—
1203C22—44no—
1204C22—44no—
1205C22—44no—
1206C22—44no—
1207C22—44no—
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—42no—
1223C22—44no—
1224C22—42no—
1225C22—42no—
1226C22—44no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—44no—
1241C22—44no—
1242C22—832no—
1243C22—832no—
1244C22—832no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22C23×C22⋊C411yescharacteristic
1250C22C2×#51811yescharacteristic
1251C22C2×#51811yescharacteristic
1252C22C4×H(5,𝔽2)12yes—
1253C22C4×H(5,𝔽2)12yes—
1254C22#348412yes—
1255C22#348412yes—
1256C22#348412yes—
1257C22#348512yes—
1258C22#349612yes—
1259C22#349612yes—
1260C22#353211yescharacteristic
1261C22#353311yescharacteristic
1262C22#353412yes—
1263C22#353412yes—
1264C22#353712yes—
1265C22#354212yes—
1266C22#354311yescharacteristic
1267C22#354511yescharacteristic
1268C22#355812yes—
1269C22#356012yes—
1270C4—24no—
1271C4—28no—
1272C4—44no—
1273C4—44no—
1274C4—42no—
1275C4—44no—
1276C4—44no—
1277C4—82no—
1278C4—82no—
1279C4—82no—
1280C4—82no—
1281C4—82no—
1282C4—82no—
1283C2—44no—
1284C2—48no—
1285C2—44no—
1286C2—44no—
1287C2—44no—
1288C2—82no—
1289C2#3417111yescharacteristic
1290C2#3425612yes—
1291C2#3440711yescharacteristic
1292C2#3440811yescharacteristic
1293C2#3443712yes—
1294C2#4635012yes—
1295C2#4635112yes—
1296C2#4635212yes—
1297C2#4641312yes—
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×#2321C2semidirect
3. #14657C2semidirect
4. #14506C2semidirect
5. #14506C2semidirect
6. #14505C2semidirect
7. #14417C2semidirect
8. #14361C2semidirect
9. #14359C2semidirect
10. #14357C2semidirect
11. #14134C2semidirect
12. #14100C2semidirect
13. #14096C2semidirect
14. #13970C2semidirect
15. #13967C2semidirect
16. #13902C2semidirect
17. #13873C2semidirect
18. #13867C2semidirect
19. #13867C2semidirect
23. C2×#534C4semidirect
32. C22×C4×D4C22semidirect
34. C23×C22⋊C4C22semidirect
35. C23×C22⋊C4C22semidirect
38. C2×#390C22semidirect
39. C2×#390C22semidirect
40. C2×#388C22semidirect
41. C2×#388C22semidirect
42. C2×#388C22semidirect
43. C2×#388C22semidirect
47. C2×#386C22semidirect
48. C2×#386C22semidirect
49. C2×#386C22semidirect
50. C2×#386C22semidirect
51. C2×#386C22semidirect
52. C2×#386C22semidirect
53. C2×#386C22semidirect
54. C2×#385C22semidirect
55. C2×#380C22semidirect
56. C2×#380C22semidirect
59. C2×#379C22semidirect
60. C2×#379C22semidirect
61. C2×#379C22semidirect
62. C2×C4×C22⋊C4C22semidirect
63. C2×C4×C22⋊C4C22semidirect
64. C2×C4×C22⋊C4C22semidirect
65. #1445C22semidirect
66. #1445C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1440C22semidirect
70. #1440C22semidirect
71. #1440C22semidirect
72. #1440C22semidirect
73. #1440C22semidirect
74. #1440C22semidirect
75. #1439C22semidirect
76. #1439C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect
85. #1438C22semidirect
86. #1438C22semidirect
87. #1438C22semidirect
88. #1438C22semidirect
89. #1438C22semidirect
90. #1438C22semidirect
91. #1438C22semidirect
92. #1438C22semidirect
93. #1437C22semidirect
94. #1437C22semidirect
95. #1437C22semidirect
96. #1437C22semidirect
97. #1436C22semidirect
98. #1436C22semidirect
99. C4⋊#95C22semidirect
100. C4⋊#95C22semidirect
101. C22⋊#95C22semidirect
102. C22⋊#95C22semidirect
103. C22⋊#95C22semidirect
104. C22⋊#95C22semidirect
105. C22⋊#95C22semidirect
106. C22⋊#95C22semidirect
107. C22⋊#95C22semidirect
108. C22⋊#95C22semidirect
109. C22⋊#95C22semidirect
121. C23×D4C2×C4semidirect
122. C23×D4C2×C4semidirect
142. C2×#123C2×C4semidirect
143. C2×#123C2×C4semidirect
144. C2×#123C2×C4semidirect
149. C2×#121C2×C4semidirect
150. C2×#121C2×C4semidirect
155. C2×#120C2×C4semidirect
156. C2×#120C2×C4semidirect
172. C22×C22⋊C4C2×C4semidirect
415. #120C22⋊C4semidirect
677. C24C2×C22⋊C4semidirect
904. C22⋊C4C2×C22⋊C4semidirect
905. 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×#23212
#146572
#145062
#145052
#144172
#143612
#143592
#143572
#141342
#141002
#140962
#139702
#139672
#139022
#138732
#138672