Finite Group Databasebeta

← #4382000

Subgroups — #4382000

Order 512.

4266 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#538C211yesmaximal, characteristic
2C2×#2538C211yesmaximal, characteristic, complemented
3C2×#2604C211yesmaximal, characteristic, complemented
4C2×#2632C211yesmaximal, characteristic, complemented
5#16363C211yesmaximal, characteristic, complemented
6#16360C211yesmaximal, characteristic, complemented
7#16253C211yesmaximal, characteristic, complemented
8#16251C211yesmaximal, characteristic, complemented
9#16102C212yesmaximal, complemented
10#15397C212yesmaximal, complemented
11#15338C212yesmaximal, complemented
12#15321C212yesmaximal, complemented
13#15316C212yesmaximal, complemented
14#15281C212yesmaximal, complemented
15#15276C212yesmaximal, complemented
16#15268C212yesmaximal, complemented
17#14825C211yesmaximal, characteristic, complemented
18#14734C211yesmaximal, characteristic, complemented
19#14723C211yesmaximal, characteristic, complemented
20#14717C211yesmaximal, characteristic, complemented
21#14665C211yesmaximal, characteristic, complemented
22#14273C211yesmaximal, characteristic, complemented
23#13959C211yesmaximal, characteristic, complemented
24C2×#538—28no—
25C2×#538—28no—
26C2×#538—28no—
27C22×#126C2211yescharacteristic
28C22×#126C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C22×#123C2211yescharacteristic
32C22×#123C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×C22⋊Q8C2211yescharacteristic, complemented
36C22×#121C2211yescharacteristic
37C22×#121C2211yescharacteristic
38C22×#121C2211yescharacteristic
39C22×#120C2211yescharacteristic
40C22×#120C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic, complemented
42C22×C4×D4C2211yescharacteristic
43C22×C4×D4C2211yescharacteristic
44C23×C22⋊C4C2211yescharacteristic
45#2632—28no—
46#2604—28no—
47#2538—28no—
48C2×#400C2211yescharacteristic, complemented
49C2×#399C2211yescharacteristic
50C2×#399C2211yescharacteristic
51C2×#399C2211yescharacteristic, complemented
52C2×#396C2212yes—
53C2×#396C2212yescomplemented
54C2×#395C2212yescomplemented
55C2×#395C2211yescharacteristic, complemented
56C2×#394C2212yes—
57C2×#394C2212yes—
58C2×#394C2212yes—
59C2×#394C2212yes—
60C2×#394C2212yescomplemented
61C2×#393C2211yescharacteristic
62C2×#393C2211yescharacteristic
63C2×#393C2211yescharacteristic, complemented
64C2×#391C2212yescomplemented
65C2×#390C2212yes—
66C2×#390C2212yes—
67C2×#389C2212yescomplemented
68C2×#389C2212yescomplemented
69C2×#388C2212yes—
70C2×#388C2212yes—
71C2×#388C2212yes—
72C2×#388C2212yescomplemented
73C2×#387C2212yescomplemented
74C2×#385C2212yes—
75C2×#385C2212yescomplemented
76C2×#384C2211yescharacteristic, complemented
77C2×#383C2211yescharacteristic, complemented
78C2×#380C2211yescharacteristic
79C2×#380C2211yescharacteristic, complemented
80C2×#379C2212yes—
81C2×#379C2212yes—
82C2×#376C2211yescharacteristic, complemented
83#1445C2212yescomplemented
84#1444C2212yescomplemented
85#1444C2212yescomplemented
86#1441C2212yescomplemented
87#1441C2211yescharacteristic, complemented
88#1441C2211yescharacteristic, complemented
89#1441C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1440C2212yes—
93#1440C2212yescomplemented
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2211yescharacteristic
98#1439C2211yescharacteristic
99#1439C2212yes—
100#1439C2211yescharacteristic
101#1439C2212yes—
102#1439C2211yescharacteristic
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1439C2212yescomplemented
109#1439C2211yescharacteristic, complemented
110#1439C2211yescharacteristic, complemented
111#1439C2212yescomplemented
112#1438C2212yes—
113#1438C2212yes—
114#1438C2212yes—
115#1438C2212yes—
116#1438C2212yes—
117#1438C2212yes—
118#1438C2212yescomplemented
119#1437C2212yes—
120#1437C2212yescomplemented
121#1436C2212yescomplemented
122#1436C2212yescomplemented
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2212yes—
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2212yescomplemented
127C22⋊#95C2211yescharacteristic, complemented
128C22⋊#95C2211yescharacteristic, complemented
129C26C2311yescharacteristic
130C23×Q8C2311yescharacteristic
131C23×Q8C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143#538—2128no—
144C2×#126—24no—
145C2×#126—24no—
146C2×#126—24no—
147C2×#126—24no—
148C2×#126—24no—
149C2×#126D418yes—
150C2×#124—24no—
151C2×#124—24no—
152C2×#124—24no—
153C2×#124—24no—
154C2×#124—24no—
155C2×#124D418yes—
156C2×#123—24no—
157C2×#123—24no—
158C2×#123—24no—
159C2×#123—24no—
160C2×#123—24no—
161C2×#123—24no—
162C2×C22⋊Q8—24no—
163C2×C22⋊Q8—24no—
164C2×C22⋊Q8—24no—
165C2×C22⋊Q8—24no—
166C2×C22⋊Q8—24no—
167C2×C22⋊Q8—44no—
168C2×C22⋊Q8—44no—
169C2×#121—24no—
170C2×#121—24no—
171C2×#121—24no—
172C2×#121—24no—
173C2×#121—24no—
174C2×#121—24no—
175C2×#121—24no—
176C2×#121—24no—
177C2×#121—24no—
178C2×#120—24no—
179C2×#120—24no—
180C2×#120—24no—
181C2×#120—24no—
182C2×#120—24no—
183C2×#120—24no—
184C2×C4×Q8—24no—
185C2×C4×Q8—24no—
186C2×C4×Q8—24no—
187C2×C4×D4—24no—
188C2×C4×D4—24no—
189C2×C4×D4—24no—
190C2×C4×D4—24no—
191C2×C4×D4—24no—
192C2×C4×D4D418yes—
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2312yes—
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2312yes—
211C22×C22⋊C4—24no—
212C22×C22⋊C4—24no—
213C22×C22⋊C4—24no—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C22⋊C4C2312yes—
240C22×C22⋊C4C2312yes—
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2312yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2312yes—
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2312yes—
248C22×C42C2311yescharacteristic
249C22×C42C2312yes—
250C22×C42C2312yes—
251C22×C42C2311yescharacteristic
252#400—24no—
253#399—24no—
254#399—24no—
255#399—24no—
256#396—28no—
257#396—28no—
258#395—28no—
259#395—24no—
260#394—28no—
261#394—44no—
262#394—44no—
263#394—44no—
264#394—44no—
265#393—24no—
266#393—24no—
267#393—24no—
268#391—44no—
269#390—28no—
270#390—44no—
271#389—28no—
272#389—28no—
273#388—28no—
274#388—28no—
275#388—28no—
276#388—28no—
277#387—28no—
278#385—44no—
279#385—44no—
280#384—24no—
281#383—24no—
282#380—24no—
283#380—24no—
284#379—44no—
285#379—44no—
286#376—24no—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—22no—
320C25—22no—
321C25—41no—
322C25—41no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C25C2411yescharacteristic
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—24no—
338C22×Q8—42no—
339C22×Q8—42no—
340C22×Q8—42no—
341C22×Q8C2×D414yes—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—41no—
366C22×D4—41no—
367C22×D4—41no—
368C22×D4—41no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4C2×D414yes—
380C22×D4C2×D414yes—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4C2×D414yes—
400C23×C4C2×D414yes—
401C23×C4C2412yes—
402C23×C4C2412yes—
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419#126—232no—
420#126—232no—
421#124—232no—
422#124—232no—
423#123—232no—
424#123—232no—
425C22⋊Q8—232no—
426C22⋊Q8—416no—
427C22⋊Q8—416no—
428#121—232no—
429#121—232no—
430#121—232no—
431#120—232no—
432#120—232no—
433C4×Q8—416no—
434C4×D4—232no—
435C4×D4—232no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4C2×D414yes—
485C2×C4⋊C4C2×D414yes—
486C2×C4⋊C4C2×D414yes—
487C2×C4⋊C4C2×D414yes—
488C2×C22⋊C4—232no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4C2×D414yes—
583C2×C22⋊C4C2×D414yes—
584C2×C22⋊C4C2×D414yes—
585C2×C22⋊C4C2×D414yes—
586C2×C22⋊C4C2×D414yes—
587C2×C22⋊C4C2×D414yes—
588C2×C22⋊C4C2×D414yes—
589C2×C22⋊C4C2×D414yes—
590C2×C22⋊C4C2×D414yes—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—24no—
595C2×C42—24no—
596C2×C42—24no—
597C2×C42—24no—
598C2×C42—24no—
599C2×C42—42no—
600C2×C42C2×D414yes—
601C2×C42C2×D414yes—
602C2×C42C2×D414yes—
603#95—24no—
604#95—22no—
605#95—22no—
606#95—24no—
607#95—24no—
608#95—24no—
609#95—22no—
610#95—22no—
611#95—24no—
612#95—24no—
613#95—24no—
614#95—24no—
615#95—24no—
616#95—24no—
617#95—24no—
618#95—24no—
619#95—24no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95—42no—
630#95—42no—
631#95—42no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—21no—
639C24—21no—
640C24—28no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—44no—
682C24—44no—
683C24—44no—
684C24—44no—
685C24—44no—
686C24—48no—
687C24—48no—
688C24—44no—
689C24—82no—
690C24—82no—
691C24—82no—
692C24—82no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24C22×D412yes—
704C24C22×D412yes—
705C24C22×D412yes—
706C24C22×D412yes—
707C24C22×D412yes—
708C242−1+412yes—
709C242−1+412yes—
710C24C2511yescharacteristic
711C2×Q8—28no—
712C2×Q8—28no—
713C2×Q8—48no—
714C2×Q8—48no—
715C2×Q8—48no—
716C2×Q8—44no—
717C2×Q8—44no—
718C2×Q8—84no—
719C2×Q8—82no—
720C2×Q8—82no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—48no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—84no—
742C2×D4—82no—
743C2×D4—82no—
744C2×D4—82no—
745C2×D4—82no—
746C2×D4—84no—
747C2×D4—84no—
748C2×D4—84no—
749C2×D4—82no—
750C2×D4—82no—
751C2×D4—84no—
752C2×D4—84no—
753C2×D4—84no—
754C2×D4—84no—
755C2×D4—84no—
756C2×D4—82no—
757C2×D4—82no—
758C2×D4—82no—
759C2×D4—82no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
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—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
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—28no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—28no—
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—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—84no—
861C22×C4—84no—
862C22×C4—84no—
863C22×C4—84no—
864C22×C4—82no—
865C22×C4—82no—
866C22×C4—84no—
867C22×C4—84no—
868C22×C4—84no—
869C22×C4—84no—
870C22×C4—82no—
871C22×C4—82no—
872C22×C4C22×D412yes—
873C22×C4C22×D412yes—
874C22×C4C22×D412yes—
875C22×C4C22×D412yes—
876C22×C4C22×D412yes—
877C22×C4C22×D412yes—
878C22×C4C22×D412yes—
879C22×C4C22×D412yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C22×D412yes—
888C22×C4H(5,𝔽2)14yes—
889C22×C4H(5,𝔽2)14yes—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—84no—
906C4⋊C4—84no—
907C4⋊C4—84no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C42—28no—
943C42—48no—
944C42—48no—
945C42#120116yes—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—24no—
979C23—24no—
980C23—22no—
981C23—22no—
982C23—416no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—42no—
1022C23—42no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—88no—
1062C23—88no—
1063C23—88no—
1064C23—88no—
1065C23—816no—
1066C23—816no—
1067C23—816no—
1068C23—816no—
1069C23—88no—
1070C23—88no—
1071C23#53614yes—
1072C23C23×D411yescharacteristic
1073C23C23×D411yescharacteristic
1074C23C23×D411yescharacteristic
1075C23C2×H(5,𝔽2)12yes—
1076C23C2×H(5,𝔽2)12yes—
1077C23C2×2−1+411yescharacteristic
1078C23C2×2−1+411yescharacteristic
1079C23#58511yescharacteristic
1080C23#58511yescharacteristic
1081C23#58512yes—
1082C23#58512yes—
1083Q8—416no—
1084Q8—88no—
1085D4—416no—
1086D4—416no—
1087D4—88no—
1088D4—88no—
1089D4—88no—
1090D4—88no—
1091D4—88no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—42no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
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—41no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
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—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—88no—
1200C2×C4—88no—
1201C2×C4—88no—
1202C2×C4—88no—
1203C2×C4C2×#12014yes—
1204C2×C4C2×#12014yes—
1205C2×C4C2×#12014yes—
1206C22—24no—
1207C22—24no—
1208C22—24no—
1209C22—42no—
1210C22—44no—
1211C22—44no—
1212C22—42no—
1213C22—44no—
1214C22—42no—
1215C22—42no—
1216C22—44no—
1217C22—42no—
1218C22—42no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—42no—
1224C22—42no—
1225C22—44no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—44no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—832no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22C22×#12011yescharacteristic
1263C22C2×#53611yescharacteristic
1264C22#344911yescharacteristic
1265C22#348411yescharacteristic
1266C22#348511yescharacteristic
1267C22#348812yes—
1268C22#348812yes—
1269C22#348812yes—
1270C22#348911yescharacteristic
1271C22#348911yescharacteristic
1272C22#348911yescharacteristic
1273C22#348911yescharacteristic
1274C22#349612yes—
1275C22#349811yescharacteristic
1276C22#350011yescharacteristic
1277C22#353512yes—
1278C22#354112yes—
1279C22#354112yes—
1280C22#354212yes—
1281C22#354612yes—
1282C22#356112yes—
1283C22#356612yes—
1284C22#356812yes—
1285C4—24no—
1286C4—24no—
1287C4—24no—
1288C4—44no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—44no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—82no—
1298C4—82no—
1299C4—82no—
1300C4—82no—
1301C4—82no—
1302C4—82no—
1303C2—44no—
1304C2—82no—
1305C2—82no—
1306C2—82no—
1307C2—82no—
1308C2#3530511yescharacteristic
1309C2#3551211yescharacteristic
1310C2#3551311yescharacteristic
1311C2#4049111yescharacteristic
1312C2#4050111yescharacteristic
1313C2#4137011yescharacteristic
1314C2#4138011yescharacteristic
1315C2#4767512yes—
1316C2#4767912yes—
1317C2#5064112yes—
1318C2#5086212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#538C2
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×#2538C2semidirect
3. C2×#2604C2semidirect
4. C2×#2632C2semidirect
5. #16363C2semidirect
6. #16360C2semidirect
7. #16253C2semidirect
8. #16251C2semidirect
9. #16102C2semidirect
10. #15397C2semidirect
11. #15338C2semidirect
12. #15321C2semidirect
13. #15316C2semidirect
14. #15281C2semidirect
15. #15276C2semidirect
16. #15268C2semidirect
17. #14825C2semidirect
18. #14734C2semidirect
19. #14723C2semidirect
20. #14717C2semidirect
21. #14665C2semidirect
22. #14273C2semidirect
23. #13959C2semidirect
35. C22×C22⋊Q8C22semidirect
41. C22×C4×Q8C22semidirect
48. C2×#400C22semidirect
51. C2×#399C22semidirect
53. C2×#396C22semidirect
54. C2×#395C22semidirect
55. C2×#395C22semidirect
60. C2×#394C22semidirect
63. C2×#393C22semidirect
64. C2×#391C22semidirect
67. C2×#389C22semidirect
68. C2×#389C22semidirect
72. C2×#388C22semidirect
73. C2×#387C22semidirect
75. C2×#385C22semidirect
76. C2×#384C22semidirect
77. C2×#383C22semidirect
79. C2×#380C22semidirect
82. C2×#376C22semidirect
83. #1445C22semidirect
84. #1444C22semidirect
85. #1444C22semidirect
86. #1441C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
93. #1440C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
118. #1438C22semidirect
120. #1437C22semidirect
121. #1436C22semidirect
122. #1436C22semidirect
126. C22⋊#95C22semidirect
127. C22⋊#95C22semidirect
128. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C22×#5382
C2×#25382
C2×#26042
C2×#26322
#163632
#163602
#162532
#162512
#161022
#153972
#153382
#153212
#153162
#152812
#152762
#152682
#148252
#147342
#147232
#147172
#146652
#142732
#139592