Finite Group Databasebeta

← #1294283

Subgroups — #1294283

Order 512.

4528 conjugacy classes of subgroups.

The subgroup lattice has 1349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2548C211yesmaximal, characteristic, complemented
2C2×#2435C211yesmaximal, characteristic, complemented
3C2×#2465C211yesmaximal, characteristic, complemented
4C2×#2433C211yesmaximal, characteristic
5#17011C211yesmaximal, characteristic, complemented
6#16503C211yesmaximal, characteristic, complemented
7#16503C211yesmaximal, characteristic, complemented
8#16253C211yesmaximal, characteristic, complemented
9#15428C212yesmaximal, complemented
10#15317C212yesmaximal, complemented
11#15268C212yesmaximal, complemented
12#15259C212yesmaximal, complemented
13#15140C211yesmaximal, characteristic, complemented
14#14928C212yesmaximal, complemented
15#14928C212yesmaximal, complemented
16#14883C211yesmaximal, characteristic, complemented
17#14813C211yesmaximal, characteristic, complemented
18#14764C211yesmaximal, characteristic, complemented
19#14724C211yesmaximal, characteristic, complemented
20#14358C212yesmaximal, complemented
21#14358C212yesmaximal, complemented
22#14325C211yesmaximal, characteristic, complemented
23#13822C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#127C2211yescharacteristic
26C22×#127C2211yescharacteristic
27C22×#124C2212yes—
28C22×#124C2212yescomplemented
29C22×C22⋊Q8C2211yescharacteristic
30C22×#121C2211yescharacteristic
31C22×#120C2212yes—
32C22×#120C2212yes—
33C22×C4×Q8C2211yescharacteristic, complemented
34#2548—28no—
35#2465—28no—
36#2435—28no—
37#2433—28no—
38C2×#396C2211yescharacteristic
39C2×#395C2211yescharacteristic, complemented
40C2×#395C2211yescharacteristic, complemented
41C2×#394C2211yescharacteristic
42C2×#394C2211yescharacteristic
43C2×#394C2211yescharacteristic
44C2×#394C2211yescharacteristic
45C2×#394C2211yescharacteristic
46C2×#394C2212yes—
47C2×#394C2211yescharacteristic
48C2×#394C2211yescharacteristic, complemented
49C2×#394C2211yescharacteristic, complemented
50C2×#394C2211yescharacteristic, complemented
51C2×#394C2212yescomplemented
52C2×#394C2212yescomplemented
53C2×#393C2211yescharacteristic
54C2×#393C2212yescomplemented
55C2×#393C2212yescomplemented
56C2×#392C2212yes—
57C2×#392C2212yes—
58C2×#391C2211yescharacteristic, complemented
59C2×#390C2211yescharacteristic
60C2×#390C2212yes—
61C2×#390C2211yescharacteristic
62C2×#390C2212yescomplemented
63C2×#390C2212yescomplemented
64C2×#390C2212yescomplemented
65C2×#390C2212yescomplemented
66C2×#390C2212yescomplemented
67C2×#389C2211yescharacteristic, complemented
68C2×#388C2211yescharacteristic
69C2×#388C2211yescharacteristic
70C2×#388C2212yes—
71C2×#388C2212yescomplemented
72C2×#388C2212yescomplemented
73C2×#387C2211yescharacteristic, complemented
74C2×#387C2211yescharacteristic, complemented
75C2×#387C2211yescharacteristic, complemented
76C2×#385C2211yescharacteristic
77C2×#379C2212yes—
78C2×#379C2212yes—
79C2×#379C2212yes—
80C2×#379C2212yes—
81C2×C4×C4⋊C4C2211yescharacteristic, complemented
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2211yescharacteristic
84#1442C2211yescharacteristic, complemented
85#1441C2211yescharacteristic, complemented
86#1441C2211yescharacteristic, complemented
87#1441C2211yescharacteristic, complemented
88#1440C2212yescomplemented
89#1440C2212yescomplemented
90#1440C2212yescomplemented
91#1439C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2211yescharacteristic
104#1438C2211yescharacteristic
105#1438C2212yescomplemented
106#1438C2212yescomplemented
107#1438C2212yescomplemented
108#1438C2212yescomplemented
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1438C2212yescomplemented
112#1438C2212yescomplemented
113#1438C2211yescharacteristic, complemented
114#1437C2212yes—
115#1437C2212yescomplemented
116#1437C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1437C2212yescomplemented
120#1437C2212yescomplemented
121#1436C2212yescomplemented
122#1434C2211yescharacteristic, complemented
123#1434C2211yescharacteristic, complemented
124C22⋊#95C2211yescharacteristic
125C4×#95C2211yescharacteristic, complemented
126C4×#95C2212yescomplemented
127C26C2312yes—
128C23×Q8C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—44no—
133C23×D4—42no—
134C23×D4—44no—
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2311yescharacteristic
141C23×D4C2312yes—
142C23×D4C2312yes—
143C23×D4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C2×#127—24no—
146C2×#127—24no—
147C2×#127—24no—
148C2×#127—42no—
149C2×#127—44no—
150C2×#124—28no—
151C2×#124—28no—
152C2×#124—44no—
153C2×#124—44no—
154C2×#124—44no—
155C2×#124—44no—
156C2×C22⋊Q8—24no—
157C2×C22⋊Q8—24no—
158C2×C22⋊Q8—42no—
159C2×#121—24no—
160C2×#121—44no—
161C2×#120—28no—
162C2×#120—28no—
163C2×#120—28no—
164C2×#120—28no—
165C2×#120—44no—
166C2×#120—44no—
167C2×C4×Q8—24no—
168C2×C4×Q8—24no—
169C2×C4×Q8—42no—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2312yes—
225C22×C42C2311yescharacteristic
226#396—24no—
227#395—24no—
228#395—24no—
229#394—24no—
230#394—24no—
231#394—24no—
232#394—24no—
233#394—24no—
234#394—24no—
235#394—44no—
236#394—42no—
237#394—44no—
238#394—42no—
239#394—44no—
240#394D418yescomplemented
241#393—24no—
242#393—44no—
243#393—44no—
244#392—28no—
245#392—28no—
246#391—24no—
247#390—28no—
248#390—28no—
249#390—28no—
250#390—28no—
251#390—24no—
252#390—24no—
253#390—44no—
254#390—44no—
255#389—24no—
256#388—24no—
257#388—24no—
258#388—28no—
259#388—44no—
260#388—44no—
261#387—24no—
262#387—24no—
263#387—24no—
264#385—24no—
265#379—28no—
266#379—28no—
267#379—44no—
268#379—44no—
269C4×C4⋊C4—24no—
270C4×C22⋊C4—24no—
271C4×C22⋊C4D418yes—
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C25—24no—
303C25—24no—
304C25—24no—
305C25—24no—
306C25—24no—
307C25—42no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25C2412yes—
318C25C2412yes—
319C25C2412yes—
320C25C2411yescharacteristic
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—24no—
329C22×Q8—41no—
330C22×Q8—41no—
331C22×Q8—41no—
332C22×Q8—42no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—22no—
359C22×D4—24no—
360C22×D4—22no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—22no—
364C22×D4—416no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—416no—
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×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—42no—
388C22×D4—42no—
389C22×D4—42no—
390C22×D4—42no—
391C22×D4—416no—
392C22×D4—432no—
393C22×D4—432no—
394C22×D4C2×D414yes—
395C23×C4—22no—
396C23×C4—24no—
397C23×C4—22no—
398C23×C4—42no—
399C23×C4C2×D414yes—
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2412yes—
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2412yes—
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419#127—416no—
420#127—416no—
421#124—432no—
422#124—432no—
423C22⋊Q8—416no—
424#121—416no—
425#120—432no—
426#120—432no—
427C4×Q8—416no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4C2×D414yes—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—22no—
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—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—41no—
512C2×C22⋊C4—41no—
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⋊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⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
565C2×C22⋊C4C2×D418yes—
566C2×C22⋊C4C2×D418yes—
567C2×C22⋊C4C2×D414yes—
568C2×C22⋊C4#4118yes—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—24no—
576C2×C42—24no—
577C2×C42—24no—
578C2×C42—24no—
579C2×C42—24no—
580C2×C42—41no—
581C2×C42—41no—
582C2×C42—42no—
583C2×C42—42no—
584C2×C42—42no—
585C2×C42—42no—
586C2×C42—42no—
587C2×C42C2×D414yes—
588C2×C42C2×D414yes—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—22no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95C2×D414yes—
617#95C2×D414yes—
618#95C2×D414yes—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24C22×D414yes—
707C24C22×D412yes—
708C24C2×#4114yes—
709C24H(5,𝔽2)14yes—
710C24C2511yescharacteristic
711C2×Q8—28no—
712C2×Q8—44no—
713C2×Q8—44no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—44no—
717C2×Q8—48no—
718C2×Q8—44no—
719C2×Q8—44no—
720C2×Q8—44no—
721C2×Q8—82no—
722C2×Q8—84no—
723C2×D4—216no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—4128no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—84no—
769C2×D4—84no—
770C2×D4—84no—
771C2×D4—84no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4—84no—
775C2×D4—84no—
776C2×D4—84no—
777C2×D4—84no—
778C2×D4—84no—
779C2×D4—84no—
780C2×D4—84no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—28no—
823C22×C4—28no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—21no—
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—21no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—21no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—21no—
879C22×C4—44no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4C22×D412yes—
883C22×C4C22×D414yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C22×D412yes—
888C22×C4C22×D412yes—
889C22×C4C22×D412yes—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C2×#4114yes—
893C22×C4C2×#4114yes—
894C22×C4H(5,𝔽2)12yes—
895C22×C4H(5,𝔽2)12yes—
896C22×C4H(5,𝔽2)14yes—
897C22×C4H(5,𝔽2)12yes—
898C22×C4H(5,𝔽2)12yes—
899C4⋊C4—28no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—82no—
910C4⋊C4—82no—
911C22⋊C4—28no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
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—48no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—82no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C22⋊C4#124116yescomplemented
948C42—28no—
949C42—44no—
950C42—44no—
951C42—44no—
952C42—48no—
953C42—48no—
954C42—84no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—24no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—42no—
982C23—41no—
983C23—41no—
984C23—42no—
985C23—41no—
986C23—42no—
987C23—41no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—432no—
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—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—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—816no—
1084C23—816no—
1085C23—816no—
1086C23—816no—
1087C23—816no—
1088C23—816no—
1089C23—816no—
1090C23—816no—
1091C23—816no—
1092C23—816no—
1093C23—816no—
1094C23—816no—
1095C23—816no—
1096C23—816no—
1097C23C2×#12414yes—
1098C23C23×D411yescharacteristic
1099C23C23×D411yescharacteristic
1100C23C22×#4112yes—
1101C23C2×H(5,𝔽2)12yes—
1102C23C2×H(5,𝔽2)11yescharacteristic
1103C23C2×H(5,𝔽2)11yescharacteristic
1104C23C2×H(5,𝔽2)11yescharacteristic
1105C23C2×H(5,𝔽2)12yes—
1106C23C2×H(5,𝔽2)11yescharacteristic
1107C23#58512yes—
1108C23#58511yescharacteristic
1109Q8—416no—
1110Q8—88no—
1111D4—432no—
1112D4—416no—
1113D4—416no—
1114D4—816no—
1115D4—816no—
1116D4—816no—
1117D4—88no—
1118D4—816no—
1119D4—816no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—416no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—41no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—41no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4C2×#12414yes—
1230C2×C4C2×#12414yes—
1231C2×C4#53514yes—
1232C2×C4#53514yes—
1233C2×C4D4214yes—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—42no—
1238C22—42no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—42no—
1243C22—44no—
1244C22—42no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—864no—
1260C22—82no—
1261C22—82no—
1262C22—82no—
1263C22—82no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—82no—
1274C22—82no—
1275C22—82no—
1276C22—82no—
1277C22—82no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22—82no—
1290C22—82no—
1291C22C22×#12411yescharacteristic
1292C22C2×#53511yescharacteristic
1293C22C2×#53511yescharacteristic
1294C22C2×D4211yescharacteristic
1295C22D4×#4112yes—
1296C22#348411yescharacteristic
1297C22#348412yes—
1298C22#348411yescharacteristic
1299C22#348811yescharacteristic
1300C22#348811yescharacteristic
1301C22#350011yescharacteristic
1302C22#350812yes—
1303C22#350812yes—
1304C22#351312yes—
1305C22#351412yes—
1306C22#351912yes—
1307C22#353212yes—
1308C22#353711yescharacteristic
1309C22#354012yes—
1310C22#354211yescharacteristic
1311C22#354212yes—
1312C22#354612yes—
1313C22#355812yes—
1314C4—24no—
1315C4—24no—
1316C4—24no—
1317C4—24no—
1318C4—24no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—44no—
1323C4—42no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—82no—
1328C4—82no—
1329C4—82no—
1330C4—81no—
1331C4—82no—
1332C4—81no—
1333C2—44no—
1334C2—84no—
1335C2—84no—
1336C2—162no—
1337C2#3528511yescharacteristic
1338C2#3590311yescharacteristic
1339C2D4×#12411yescharacteristic
1340C2#3764511yescharacteristic
1341C2#3765011yescharacteristic
1342C2#4242611yescharacteristic
1343C2#4298711yescharacteristic
1344C2#4310512yes—
1345C2#4311312yes—
1346C2#5085012yes—
1347C2#5114312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2433C2
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×#2548C2semidirect
2. C2×#2435C2semidirect
3. C2×#2465C2semidirect
5. #17011C2semidirect
6. #16503C2semidirect
7. #16503C2semidirect
8. #16253C2semidirect
9. #15428C2semidirect
10. #15317C2semidirect
11. #15268C2semidirect
12. #15259C2semidirect
13. #15140C2semidirect
14. #14928C2semidirect
15. #14928C2semidirect
16. #14883C2semidirect
17. #14813C2semidirect
18. #14764C2semidirect
19. #14724C2semidirect
20. #14358C2semidirect
21. #14358C2semidirect
22. #14325C2semidirect
23. #13822C2semidirect
28. C22×#124C22semidirect
33. C22×C4×Q8C22semidirect
39. C2×#395C22semidirect
40. C2×#395C22semidirect
48. C2×#394C22semidirect
49. C2×#394C22semidirect
50. C2×#394C22semidirect
51. C2×#394C22semidirect
52. C2×#394C22semidirect
54. C2×#393C22semidirect
55. C2×#393C22semidirect
58. C2×#391C22semidirect
62. C2×#390C22semidirect
63. C2×#390C22semidirect
64. C2×#390C22semidirect
65. C2×#390C22semidirect
66. C2×#390C22semidirect
67. C2×#389C22semidirect
71. C2×#388C22semidirect
72. C2×#388C22semidirect
73. C2×#387C22semidirect
74. C2×#387C22semidirect
75. C2×#387C22semidirect
81. C2×C4×C4⋊C4C22semidirect
84. #1442C22semidirect
85. #1441C22semidirect
86. #1441C22semidirect
87. #1441C22semidirect
88. #1440C22semidirect
89. #1440C22semidirect
90. #1440C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
105. #1438C22semidirect
106. #1438C22semidirect
107. #1438C22semidirect
108. #1438C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
115. #1437C22semidirect
116. #1437C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1437C22semidirect
120. #1437C22semidirect
121. #1436C22semidirect
122. #1434C22semidirect
123. #1434C22semidirect
125. C4×#95C22semidirect
126. C4×#95C22semidirect
240. #394D4semidirect
947. C22⋊C4#124semidirect

Maximal subgroups

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

subgroupindex
C2×#25482
C2×#24352
C2×#24652
C2×#24332
#170112
#165032
#162532
#154282
#153172
#152682
#152592
#151402
#149282
#148832
#148132
#147642
#147242
#143582
#143252
#138222