Finite Group Databasebeta

← #759337

Subgroups — #759337

Order 512.

4246 conjugacy classes of subgroups.

The subgroup lattice has 1331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2439C211yesmaximal, characteristic, complemented
2C2×#2440C211yesmaximal, characteristic, complemented
3C2×#2280C211yesmaximal, characteristic
4C22×#380C211yesmaximal, characteristic
5#16302C212yesmaximal, complemented
6#16299C212yesmaximal, complemented
7#15223C211yesmaximal, characteristic, complemented
8#15220C211yesmaximal, characteristic, complemented
9#15131C211yesmaximal, characteristic, complemented
10#15125C211yesmaximal, characteristic, complemented
11#14775C212yesmaximal, complemented
12#14770C212yesmaximal, complemented
13#14726C212yesmaximal
14#14717C212yesmaximal
15#14130C211yesmaximal, characteristic, complemented
16#14129C211yesmaximal, characteristic, complemented
17#14052C212yesmaximal, complemented
18#14028C212yesmaximal, complemented
19#13951C211yesmaximal, characteristic, complemented
20#13907C211yesmaximal, characteristic, complemented
21#13881C211yesmaximal, characteristic, complemented
22#13879C211yesmaximal, characteristic, complemented
23C4×#379C211yesmaximal, characteristic
24C25×C4C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic, complemented
26C22×C22⋊Q8C2212yes—
27C22×#117C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2212yes—
32#2440—28no—
33#2439—28no—
34C2×#398C2212yescomplemented
35C2×#396C2212yes—
36C2×#396C2212yes—
37C2×#395C2212yescomplemented
38C2×#393C2212yes—
39C2×#393C2212yes—
40C2×#391C2212yescomplemented
41C2×#389C2211yescharacteristic, complemented
42C2×#389C2211yescharacteristic, complemented
43C2×#389C2211yescharacteristic, complemented
44C2×#389C2211yescharacteristic, complemented
45C2×#389C2211yescharacteristic, complemented
46C2×#389C2211yescharacteristic, complemented
47C2×#387C2212yescomplemented
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#384C2211yescharacteristic, complemented
51C2×#382C2211yescharacteristic, complemented
52C2×#382C2211yescharacteristic, complemented
53#2280—28no—
54C2×#381C2212yes—
55C2×#380—28no—
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2212yes—
62C2×#380C2211yescharacteristic
63C2×#380C2212yes—
64C2×#380C2212yes—
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×#379C2211yescharacteristic
68C2×#379C2212yes—
69C2×#379C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic
74C2×C4×C22⋊C4C2212yes—
75C2×C4×C22⋊C4C2212yes—
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C22×#95C2212yes—
79#1446C2212yescomplemented
80#1445C2212yescomplemented
81#1445C2212yescomplemented
82#1444C2212yescomplemented
83#1443C2212yescomplemented
84#1442C2212yescomplemented
85#1442C2212yescomplemented
86#1442C2212yescomplemented
87#1442C2212yescomplemented
88#1441C2212yescomplemented
89#1441C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1441C2212yescomplemented
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1436C2212yescomplemented
106#1436C2212yescomplemented
107#1436C2212yescomplemented
108#1436C2212yescomplemented
109C4⋊#95C2211yescharacteristic, complemented
110C4⋊#95C2211yescharacteristic, complemented
111C4⋊#95C2211yescharacteristic, complemented
112C4⋊#95C2211yescharacteristic, complemented
113C4⋊#95C2211yescharacteristic, complemented
114C4⋊#95C2211yescharacteristic, complemented
115C4⋊#95C2212yescomplemented
116#1434C2212yescomplemented
117C22⋊#95C2212yes—
118C22⋊#95C2212yes—
119C22⋊#95C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C26C2311yescharacteristic
128C23×Q8C2312yes—
129C24×C4—24no—
130C24×C4—24no—
131C24×C4—24no—
132C24×C4—24no—
133C24×C4—42no—
134C24×C4—42no—
135C24×C4Q818yescomplemented
136C24×C4C2311yescharacteristic
137C24×C4C2312yes—
138C24×C4C2312yes—
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C2×C4⋊Q8—24no—
145C2×C4⋊Q8—24no—
146C2×C4⋊Q8—42no—
147C2×C22⋊Q8—28no—
148C2×C22⋊Q8—28no—
149C2×C22⋊Q8—44no—
150C2×#117—24no—
151C2×#117—24no—
152C2×#117—24no—
153C2×#117—24no—
154C2×#117—42no—
155C2×#117—42no—
156C22×C4⋊C4—24no—
157C22×C4⋊C4—24no—
158C22×C4⋊C4—24no—
159C22×C4⋊C4—24no—
160C22×C4⋊C4—42no—
161C22×C4⋊C4—42no—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C22⋊C4—28no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2312yes—
211C22×C42C2312yes—
212#398—28no—
213#396—28no—
214#396—44no—
215#395—28no—
216#393—28no—
217#393—44no—
218#391—28no—
219#389—24no—
220#389—24no—
221#389—24no—
222#389—24no—
223#389—42no—
224#389—42no—
225#387—28no—
226#385—28no—
227#385—44no—
228#384—24no—
229#382—24no—
230#382—42no—
231#381—28no—
232#380—24no—
233#380—24no—
234#380—24no—
235#380—24no—
236#380—24no—
237#380—24no—
238#380—28no—
239#380—28no—
240#380—28no—
241#380D418yes—
242#380D418yes—
243#379—28no—
244#379—24no—
245#379—24no—
246C4×C22⋊C4—24no—
247C4×C22⋊C4—24no—
248C4×C22⋊C4—24no—
249C4×C22⋊C4—24no—
250C4×C22⋊C4—28no—
251C4×C22⋊C4—28no—
252C4×C22⋊C4—42no—
253C4×C22⋊C4—42no—
254C2×#95—28no—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2311yescharacteristic
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2311yescharacteristic
262C2×#95C2312yes—
263C2×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C2×#95C2311yescharacteristic
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C25—22no—
298C25—22no—
299C25—22no—
300C25—22no—
301C25—22no—
302C25—22no—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—41no—
308C25—41no—
309C25—41no—
310C25—41no—
311C25C2×Q814yes—
312C25C2411yescharacteristic
313C25C2411yescharacteristic
314C25C2411yescharacteristic
315C22×Q8—24no—
316C22×Q8—24no—
317C22×Q8—24no—
318C22×Q8—42no—
319C22×Q8—42no—
320C22×Q8—42no—
321C22×Q8—42no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—232no—
335C23×C4—232no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—24no—
351C23×C4—24no—
352C23×C4—24no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—416no—
359C23×C4—41no—
360C23×C4—41no—
361C23×C4—41no—
362C23×C4—41no—
363C23×C4—41no—
364C23×C4—41no—
365C23×C4—416no—
366C23×C4—416no—
367C23×C4—416no—
368C23×C4—416no—
369C23×C4—42no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4—42no—
374C23×C4—42no—
375C23×C4C2×D414yes—
376C23×C4C2×D414yes—
377C23×C4C2×Q814yes—
378C23×C4C2×Q814yes—
379C23×C4C2×Q814yes—
380C23×C4C2×Q814yes—
381C23×C4C2×Q814yes—
382C23×C4C2×Q814yes—
383C23×C4#4114yes—
384C23×C4#4114yes—
385C23×C4C2411yescharacteristic
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C4⋊Q8—416no—
406C22⋊Q8—432no—
407#117—416no—
408#117—416no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—416no—
447C2×C4⋊C4—416no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4C2×D414yes—
465C2×C4⋊C4C2×D414yes—
466C2×C4⋊C4C2×D414yes—
467C2×C4⋊C4C2×D414yes—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—22no—
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—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—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—41no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—41no—
527C2×C22⋊C4—41no—
528C2×C22⋊C4—41no—
529C2×C22⋊C4—41no—
530C2×C22⋊C4—432no—
531C2×C22⋊C4C2×D418yes—
532C2×C22⋊C4C2×D418yes—
533C2×C22⋊C4#4114yes—
534C2×C22⋊C4#4114yes—
535C2×C42—24no—
536C2×C42—24no—
537C2×C42—24no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—24no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—42no—
552C2×C42—42no—
553#95—24no—
554#95—24no—
555#95—24no—
556#95—24no—
557#95—24no—
558#95—24no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563#95—24no—
564#95—24no—
565#95—24no—
566#95—24no—
567#95—24no—
568#95—24no—
569#95—22no—
570#95—22no—
571#95—22no—
572#95—22no—
573#95—24no—
574#95—24no—
575#95—42no—
576#95—42no—
577#95—42no—
578#95—42no—
579#95—41no—
580#95—41no—
581#95—41no—
582#95—41no—
583#95—42no—
584#95—42no—
585#95—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95—42no—
593#95C2×D418yes—
594#95C2×D418yes—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—28no—
604C24—28no—
605C24—28no—
606C24—28no—
607C24—28no—
608C24—28no—
609C24—28no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—28no—
635C24—28no—
636C24—44no—
637C24—44no—
638C24—44no—
639C24—44no—
640C24—44no—
641C24—44no—
642C24—44no—
643C24—44no—
644C24—44no—
645C24—44no—
646C24—44no—
647C24—44no—
648C24—44no—
649C24—44no—
650C24—44no—
651C24—44no—
652C24—44no—
653C24—44no—
654C24—44no—
655C24—44no—
656C24—44no—
657C24—44no—
658C24—44no—
659C24—44no—
660C24—44no—
661C24—44no—
662C24C22×D412yes—
663C24C22×D412yes—
664C24C22×Q812yes—
665C24C22×Q812yes—
666C24C22×Q812yes—
667C24C2×#4112yes—
668C24C2×#4112yes—
669C24C2×#4112yes—
670C24C2×#4112yes—
671C24H(5,𝔽2)12yes—
672C24H(5,𝔽2)12yes—
673C242−1+412yes—
674C242−1+412yes—
675C24C2511yescharacteristic
676C2×Q8—48no—
677C2×Q8—48no—
678C2×Q8—48no—
679C2×Q8—84no—
680C2×Q8—84no—
681C2×Q8—84no—
682C2×Q8—84no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—28no—
692C22×C4—28no—
693C22×C4—28no—
694C22×C4—28no—
695C22×C4—28no—
696C22×C4—28no—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—28no—
700C22×C4—28no—
701C22×C4—28no—
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—4128no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—84no—
853C22×C4—84no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4C22⋊Q8116yes—
857C22×C4C22⋊Q8116yescomplemented
858C22×C4C22×D414yes—
859C22×C4C22×D414yes—
860C22×C4C22×D414yes—
861C22×C4C22×D414yes—
862C22×C4C22×D412yes—
863C22×C4C22×D412yes—
864C22×C4C22×D412yes—
865C22×C4C22×D412yes—
866C22×C4C22×Q812yes—
867C22×C4C22×Q812yes—
868C22×C4C22×Q812yes—
869C22×C4C22×Q812yes—
870C22×C4C2×#4112yes—
871C22×C4C2×#4112yes—
872C22×C4C2×#4112yes—
873C22×C4C2×#4112yes—
874C22×C4C2×#4112yes—
875C22×C4C2×#4112yes—
876C22×C4C2×#4112yes—
877C22×C4C2×#4112yes—
878C22×C4H(5,𝔽2)12yes—
879C22×C4H(5,𝔽2)12yes—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—48no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—84no—
896C4⋊C4—84no—
897C4⋊C4—84no—
898C4⋊C4—84no—
899C22⋊C4—216no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C42—48no—
922C42—48no—
923C42—44no—
924C42—44no—
925C42—44no—
926C42—44no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—232no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—416no—
993C23—416no—
994C23—416no—
995C23—416no—
996C23—416no—
997C23—416no—
998C23—416no—
999C23—416no—
1000C23—416no—
1001C23—416no—
1002C23—416no—
1003C23—416no—
1004C23—416no—
1005C23—41no—
1006C23—416no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23C2×C22⋊Q814yes—
1039C23C2×C22⋊Q814yes—
1040C23#53314yes—
1041C23#54414yes—
1042C23#54414yes—
1043C23#54614yes—
1044C23#54814yes—
1045C23#55514yes—
1046C23#55614yes—
1047C23C23×D411yescharacteristic
1048C23C23×D411yescharacteristic
1049C23C23×Q811yescharacteristic
1050C23C22×#4111yescharacteristic
1051C23C22×#4111yescharacteristic
1052C23C22×#4111yescharacteristic
1053C23C22×#4111yescharacteristic
1054C23C2×H(5,𝔽2)11yescharacteristic
1055C23C2×H(5,𝔽2)11yescharacteristic
1056C23C2×H(5,𝔽2)11yescharacteristic
1057C23C2×H(5,𝔽2)11yescharacteristic
1058C23C2×2−1+411yescharacteristic
1059C23C2×2−1+411yescharacteristic
1060C23#58511yescharacteristic
1061C23#58511yescharacteristic
1062Q8—816no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—232no—
1076C2×C4—232no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—416no—
1105C2×C4—416no—
1106C2×C4—416no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—42no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—42no—
1116C2×C4—41no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—42no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—42no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—416no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—816no—
1201C2×C4—816no—
1202C2×C4C2×C22⋊Q814yes—
1203C2×C4C2×C22⋊Q814yes—
1204C2×C4C2×C22⋊Q814yes—
1205C2×C4C2×C22⋊Q814yes—
1206C2×C4#54314yes—
1207C2×C4D4214yes—
1208C2×C4#54614yes—
1209C2×C4#54614yes—
1210C2×C4#55114yes—
1211C22—24no—
1212C22—24no—
1213C22—24no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—24no—
1229C22—24no—
1230C22—24no—
1231C22—464no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22#243918yescomplemented
1257C22C22×C22⋊Q811yescharacteristic
1258C22C22×C22⋊Q811yescharacteristic
1259C22C2×#53311yescharacteristic
1260C22C2×#54311yescharacteristic
1261C22C2×#54411yescharacteristic
1262C22C2×#54411yescharacteristic
1263C22#345811yescharacteristic
1264C22C2×D4211yescharacteristic
1265C22C2×#54611yescharacteristic
1266C22C2×#54611yescharacteristic
1267C22C2×#54611yescharacteristic
1268C22C2×#54811yescharacteristic
1269C22D4×#4111yescharacteristic
1270C22D4×#4111yescharacteristic
1271C22C2×#55111yescharacteristic
1272C22C2×#55511yescharacteristic
1273C22C2×#55611yescharacteristic
1274C22#347511yescharacteristic
1275C22#347511yescharacteristic
1276C22#348411yescharacteristic
1277C22#348611yescharacteristic
1278C22#348811yescharacteristic
1279C22#348911yescharacteristic
1280C22#349211yescharacteristic
1281C22#349211yescharacteristic
1282C22#349411yescharacteristic
1283C22#349511yescharacteristic
1284C22#351911yescharacteristic
1285C22#351911yescharacteristic
1286C22#352011yescharacteristic
1287C22#352011yescharacteristic
1288C22#354111yescharacteristic
1289C22#354111yescharacteristic
1290C22#354211yescharacteristic
1291C22#354211yescharacteristic
1292C4—24no—
1293C4—24no—
1294C4—42no—
1295C4—44no—
1296C4—44no—
1297C4—42no—
1298C4—42no—
1299C4—44no—
1300C4—42no—
1301C4—42no—
1302C4—44no—
1303C4—81no—
1304C4—81no—
1305C4—82no—
1306C4—82no—
1307C4—82no—
1308C4—81no—
1309C4—81no—
1310C4—82no—
1311C4#243718yes—
1312C2—28no—
1313C2—44no—
1314C2—44no—
1315C2C2×#243711yescharacteristic
1316C2C2×#243911yescharacteristic
1317C2#3473911yescharacteristic
1318C2#3507911yescharacteristic
1319C2#3522411yescharacteristic
1320C2#3525311yescharacteristic
1321C2#3747611yescharacteristic
1322C2#5900411yescharacteristic
1323C2#5900511yescharacteristic
1324C2#5902311yescharacteristic
1325C2#5902411yescharacteristic
1326C2#5902511yescharacteristic
1327C2#5902611yescharacteristic
1328C2#5920311yescharacteristic
1329C2#5920411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
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×#2439C2semidirect
2. C2×#2440C2semidirect
5. #16302C2semidirect
6. #16299C2semidirect
7. #15223C2semidirect
8. #15220C2semidirect
9. #15131C2semidirect
10. #15125C2semidirect
11. #14775C2semidirect
12. #14770C2semidirect
15. #14130C2semidirect
16. #14129C2semidirect
17. #14052C2semidirect
18. #14028C2semidirect
19. #13951C2semidirect
20. #13907C2semidirect
21. #13881C2semidirect
22. #13879C2semidirect
25. C22×C4⋊Q8C22semidirect
34. C2×#398C22semidirect
37. C2×#395C22semidirect
40. C2×#391C22semidirect
41. C2×#389C22semidirect
42. C2×#389C22semidirect
43. C2×#389C22semidirect
44. C2×#389C22semidirect
45. C2×#389C22semidirect
46. C2×#389C22semidirect
47. C2×#387C22semidirect
50. C2×#384C22semidirect
51. C2×#382C22semidirect
52. C2×#382C22semidirect
79. #1446C22semidirect
80. #1445C22semidirect
81. #1445C22semidirect
82. #1444C22semidirect
83. #1443C22semidirect
84. #1442C22semidirect
85. #1442C22semidirect
86. #1442C22semidirect
87. #1442C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
92. #1441C22semidirect
105. #1436C22semidirect
106. #1436C22semidirect
107. #1436C22semidirect
108. #1436C22semidirect
109. C4⋊#95C22semidirect
110. C4⋊#95C22semidirect
111. C4⋊#95C22semidirect
112. C4⋊#95C22semidirect
113. C4⋊#95C22semidirect
114. C4⋊#95C22semidirect
115. C4⋊#95C22semidirect
116. #1434C22semidirect
135. C24×C4Q8semidirect
857. C22×C4C22⋊Q8semidirect
1256. C22#2439semidirect

Maximal subgroups

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

subgroupindex
C2×#24392
C2×#24402
C2×#22802
C22×#3802
#163022
#162992
#152232
#152202
#151312
#151252
#147752
#147702
#147262
#147172
#141302
#141292
#140522
#140282
#139512
#139072
#138812
#138792
C4×#3792