Finite Group Databasebeta

← #674729

Subgroups — #674729

Order 512.

4242 conjugacy classes of subgroups.

The subgroup lattice has 1315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2561C212yesmaximal, complemented
2C2×#2452C211yesmaximal, characteristic, complemented
3C2×D4×C22⋊C4C211yesmaximal, characteristic
4#15471C212yesmaximal, complemented
5#15468C212yesmaximal, complemented
6#15467C212yesmaximal, complemented
7#15297C212yesmaximal, complemented
8#15245C212yesmaximal, complemented
9#15144C211yesmaximal, characteristic, complemented
10#15138C211yesmaximal, characteristic, complemented
11#15132C211yesmaximal, characteristic, complemented
12#15125C211yesmaximal, characteristic, complemented
13#14765C212yesmaximal, complemented
14#14700C211yesmaximal, characteristic, complemented
15#14022C211yesmaximal, characteristic, complemented
16#13974C211yesmaximal, characteristic, complemented
17#13971C212yesmaximal, complemented
18#13916C211yesmaximal, characteristic, complemented
19#13916C211yesmaximal, characteristic, complemented
20#13902C211yesmaximal, characteristic
21#13902C211yesmaximal, characteristic
22C4×#390C211yesmaximal, characteristic, complemented
23C4×#388C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic, complemented
26C22×C22⋊Q8C2212yescomplemented
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C23×C22⋊C4C2212yes—
30#2561—216no—
31#2452—28no—
32C2×#397C2212yes—
33C2×#397C2212yescomplemented
34C2×#396C2212yescomplemented
35C2×#393C2212yes—
36C2×#393C2212yescomplemented
37C2×#393C2212yescomplemented
38C2×#393C2212yescomplemented
39D4×C22⋊C4—28no—
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#389C2211yescharacteristic, complemented
51C2×#389C2211yescharacteristic, complemented
52C2×#388C2212yes—
53C2×#388C2211yescharacteristic
54C2×#388C2211yescharacteristic
55C2×#388C2212yescomplemented
56C2×#388C2212yescomplemented
57C2×#388C2212yescomplemented
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#385C2212yescomplemented
61C2×#381C2212yescomplemented
62C2×#381C2212yescomplemented
63C2×#380C2211yescharacteristic
64C2×#380C2211yescharacteristic
65C2×#380C2211yescharacteristic
66C2×#379C2212yes—
67C2×#379C2212yes—
68C2×#379C2212yes—
69C2×#379C2212yes—
70C2×#379C2212yes—
71C2×C4×C4⋊C4C2211yescharacteristic, complemented
72C2×C4×C4⋊C4C2211yescharacteristic, complemented
73C2×C4×C22⋊C4C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75C2×C4×C22⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2212yescomplemented
77C2×C4×C22⋊C4C2212yescomplemented
78C2×C43C2211yescharacteristic, complemented
79#1446C2212yescomplemented
80#1443C2212yescomplemented
81#1443C2212yescomplemented
82#1442C2212yescomplemented
83#1442C2212yescomplemented
84#1440C2212yes—
85#1440C2212yes—
86#1440C2212yescomplemented
87#1440C2212yescomplemented
88#1440C2212yescomplemented
89#1440C2212yescomplemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1439C2212yes—
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1438C2212yes—
102#1437C2211yescharacteristic
103#1437C2211yescharacteristic
104#1437C2212yescomplemented
105#1437C2212yescomplemented
106#1437C2212yescomplemented
107#1437C2212yescomplemented
108#1437C2212yescomplemented
109#1436C2211yescharacteristic, complemented
110#1436C2212yescomplemented
111#1436C2211yescharacteristic, complemented
112C4⋊#95C2211yescharacteristic, complemented
113C4⋊#95C2211yescharacteristic, complemented
114C4⋊#95C2211yescharacteristic, complemented
115C4⋊#95C2211yescharacteristic, complemented
116C4⋊#95C2211yescharacteristic, complemented
117C4⋊#95C2211yescharacteristic, complemented
118C4⋊#95C2211yescharacteristic, complemented
119C4⋊#95C2211yescharacteristic, complemented
120#1434C2211yescharacteristic, complemented
121#1434C2211yescharacteristic, complemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C4×#95C2211yescharacteristic, complemented
125C4×#95C2211yescharacteristic, complemented
126C26C2312yes—
127C23×Q8C2312yes—
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—42no—
134C23×D4—42no—
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2312yes—
140C24×C4C2312yes—
141C2×C4⋊Q8—24no—
142C2×C4⋊Q8—42no—
143C2×C4⋊Q8—42no—
144C2×C22⋊Q8—28no—
145C2×C22⋊Q8—28no—
146C2×C22⋊Q8—44no—
147C2×C4×D4—24no—
148C2×C4×D4—24no—
149C2×C4×D4—24no—
150C2×C4×D4—42no—
151C2×C4×D4—42no—
152C2×C4×D4D418yes—
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C22⋊C4—28no—
165C22×C22⋊C4—28no—
166C22×C22⋊C4—44no—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C42C2311yescharacteristic
199C22×C42C2311yescharacteristic
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
202C22×C42C2311yescharacteristic
203C22×C42C2311yescharacteristic
204C22×C42C2311yescharacteristic
205C22×C42C2311yescharacteristic
206C22×C42C2312yes—
207C22×C42C2311yescharacteristic
208C22×C42C2311yescharacteristic
209#397—28no—
210#397—28no—
211#396—28no—
212#393—28no—
213#393—28no—
214#393—28no—
215#393—44no—
216#390—24no—
217#390—24no—
218#390—24no—
219#390—24no—
220#390—24no—
221#390—24no—
222#390—24no—
223#390—24no—
224#390—42no—
225#390—42no—
226#389—24no—
227#389—24no—
228#388—28no—
229#388—28no—
230#388—24no—
231#388—28no—
232#388—44no—
233#388D418yescomplemented
234#386—28no—
235#386—28no—
236#385—28no—
237#381—28no—
238#381—28no—
239#380—24no—
240#380—24no—
241#380—42no—
242#379—28no—
243#379—28no—
244#379—28no—
245#379—28no—
246#379—44no—
247C4×C4⋊C4—24no—
248C4×C4⋊C4—42no—
249C4×C22⋊C4—24no—
250C4×C22⋊C4—24no—
251C4×C22⋊C4—28no—
252C4×C22⋊C4—44no—
253C4×C22⋊C4—42no—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2311yescharacteristic
258C2×#95C2311yescharacteristic
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C43—42no—
293C25—24no—
294C25—24no—
295C25—24no—
296C25—24no—
297C25—24no—
298C25—24no—
299C25—24no—
300C25—42no—
301C25—42no—
302C25—42no—
303C25—42no—
304C25—42no—
305C25—42no—
306C25—42no—
307C25—42no—
308C25C2412yes—
309C25C2411yescharacteristic
310C25C2412yes—
311C22×Q8—24no—
312C22×Q8—24no—
313C22×Q8—42no—
314C22×Q8—42no—
315C22×Q8—42no—
316C22×Q8—42no—
317C22×Q8—42no—
318C22×D4—232no—
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—24no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—416no—
335C22×D4—416no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4—416no—
339C22×D4—416no—
340C22×D4—416no—
341C22×D4—416no—
342C22×D4C2×D414yes—
343C22×D4#4114yes—
344C22×D4#4114yes—
345C22×D4#4114yes—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—24no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—42no—
359C23×C4—42no—
360C23×C4—42no—
361C23×C4—42no—
362C23×C4—42no—
363C23×C4—42no—
364C23×C4—42no—
365C23×C4C2×D418yes—
366C23×C4#4114yes—
367C23×C4C2412yes—
368C23×C4C2412yes—
369C23×C4C2412yes—
370C23×C4C2412yes—
371C23×C4C2411yescharacteristic
372C23×C4C2411yescharacteristic
373C23×C4C2412yes—
374C23×C4C2411yescharacteristic
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2412yes—
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382C23×C4C2411yescharacteristic
383C23×C4C2411yescharacteristic
384C23×C4C2411yescharacteristic
385C23×C4C2411yescharacteristic
386C23×C4C2411yescharacteristic
387C4⋊Q8—416no—
388C22⋊Q8—432no—
389C4×D4—416no—
390C4×D4—416no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—41no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4C2×D414yes—
423C2×C4⋊C4C2×D414yescomplemented
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
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—22no—
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—22no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—432no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—41no—
478C2×C22⋊C4—41no—
479C2×C22⋊C4—41no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—41no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—41no—
492C2×C22⋊C4—41no—
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—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4C2×D414yes—
514C2×C22⋊C4C2×D414yes—
515C2×C22⋊C4C2×D418yes—
516C2×C22⋊C4C2×D414yes—
517C2×C22⋊C4#4114yes—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—24no—
539C2×C42—41no—
540C2×C42—41no—
541C2×C42—41no—
542C2×C42—41no—
543C2×C42—41no—
544C2×C42—41no—
545C2×C42—41no—
546C2×C42—41no—
547C2×C42—42no—
548C2×C42—42no—
549C2×C42C2×D414yes—
550C2×C42C2×D414yescomplemented
551#95—22no—
552#95—22no—
553#95—24no—
554#95—24no—
555#95—22no—
556#95—22no—
557#95—24no—
558#95—24no—
559#95—24no—
560#95—24no—
561#95—24no—
562#95—24no—
563#95—24no—
564#95—24no—
565#95—24no—
566#95—22no—
567#95—22no—
568#95—24no—
569#95—22no—
570#95—22no—
571#95—24no—
572#95—22no—
573#95—42no—
574#95—41no—
575#95—41no—
576#95—41no—
577#95—42no—
578#95—42no—
579#95—42no—
580#95—41no—
581#95—41no—
582#95—42no—
583#95—42no—
584#95—42no—
585#95—42no—
586#95—42no—
587#95C2×D414yescomplemented
588#95C2×D414yescomplemented
589C24—22no—
590C24—21no—
591C24—22no—
592C24—21no—
593C24—21no—
594C24—21no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—22no—
601C24—21no—
602C24—21no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—216no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—48no—
629C24—48no—
630C24—48no—
631C24—48no—
632C24—48no—
633C24—48no—
634C24—48no—
635C24—48no—
636C24—48no—
637C24—48no—
638C24—48no—
639C24—48no—
640C24—48no—
641C24—48no—
642C24—48no—
643C24—48no—
644C24—84no—
645C24—84no—
646C24—84no—
647C24—84no—
648C24—84no—
649C24—84no—
650C24—84no—
651C24—84no—
652C24—84no—
653C24—84no—
654C24—84no—
655C24—84no—
656C24—84no—
657C24—84no—
658C24—84no—
659C24—84no—
660C24—84no—
661C24—84no—
662C24C22×D414yes—
663C24C22×D412yes—
664C24C2×#4114yes—
665C24C2×#4114yes—
666C24C2×#4114yes—
667C24C2×#4112yes—
668C24C2×#4112yes—
669C24C2511yescharacteristic
670C2×Q8—48no—
671C2×Q8—48no—
672C2×Q8—84no—
673C2×Q8—84no—
674C2×Q8—84no—
675C2×Q8—84no—
676C2×Q8—84no—
677C2×D4—216no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—28no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—4128no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4#124116yes—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—216no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
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—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—21no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—48no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—48no—
826C22×C4—48no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—48no—
832C22×C4—84no—
833C22×C4—84no—
834C22×C4—84no—
835C22×C4—84no—
836C22×C4—84no—
837C22×C4—84no—
838C22×C4—84no—
839C22×C4C22×D412yes—
840C22×C4C22×D412yes—
841C22×C4C22×D412yes—
842C22×C4C22×D412yes—
843C22×C4C22×D412yes—
844C22×C4C22×D412yes—
845C22×C4C22×D414yes—
846C22×C4C22×D412yes—
847C22×C4C22×D412yes—
848C22×C4C22×D412yes—
849C22×C4C2×#4112yes—
850C22×C4C2×#4112yes—
851C22×C4C2×#4112yes—
852C22×C4C2×#4112yes—
853C22×C4C2×#4112yes—
854C22×C4C2×#4112yes—
855C22×C4C2×#4112yes—
856C22×C4H(5,𝔽2)12yes—
857C22×C4H(5,𝔽2)12yes—
858C22×C4H(5,𝔽2)12yes—
859C22×C4H(5,𝔽2)12yes—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—44no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—48no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—44no—
874C22⋊C4—48no—
875C22⋊C4—44no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—44no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
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—84no—
902C42—28no—
903C42—44no—
904C42—44no—
905C42—44no—
906C42—44no—
907C42—44no—
908C42—44no—
909C42—44no—
910C42—44no—
911C42—44no—
912C42—84no—
913C23—22no—
914C23—24no—
915C23—24no—
916C23—22no—
917C23—22no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—22no—
922C23—24no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—22no—
933C23—24no—
934C23—24no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—24no—
940C23—22no—
941C23—24no—
942C23—22no—
943C23—22no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—22no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—432no—
957C23—432no—
958C23—41no—
959C23—42no—
960C23—41no—
961C23—42no—
962C23—42no—
963C23—41no—
964C23—41no—
965C23—42no—
966C23—42no—
967C23—42no—
968C23—41no—
969C23—42no—
970C23—41no—
971C23—42no—
972C23—42no—
973C23—41no—
974C23—42no—
975C23—42no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—42no—
980C23—41no—
981C23—41no—
982C23—42no—
983C23—41no—
984C23—42no—
985C23—41no—
986C23—42no—
987C23—41no—
988C23—42no—
989C23—41no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—816no—
1019C23—816no—
1020C23—816no—
1021C23—816no—
1022C23—816no—
1023C23—816no—
1024C23—816no—
1025C23—816no—
1026C23—816no—
1027C23—816no—
1028C23—816no—
1029C23—816no—
1030C23—816no—
1031C23C2×#12418yes—
1032C23#53214yes—
1033C23C23×D411yescharacteristic
1034C23C23×D411yescharacteristic
1035C23C22×#4111yescharacteristic
1036C23C22×#4111yescharacteristic
1037C23C22×#4111yescharacteristic
1038C23C22×#4111yescharacteristic
1039C23C22×#4111yescharacteristic
1040C23C2×H(5,𝔽2)11yescharacteristic
1041C23C2×H(5,𝔽2)11yescharacteristic
1042C23C2×H(5,𝔽2)11yescharacteristic
1043C23C2×H(5,𝔽2)11yescharacteristic
1044C23#58511yescharacteristic
1045C23#58511yescharacteristic
1046C23#58511yescharacteristic
1047C23#58511yescharacteristic
1048Q8—816no—
1049D4—232no—
1050D4—432no—
1051D4—416no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—24no—
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—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—42no—
1109C2×C4—41no—
1110C2×C4—42no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—42no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—42no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—416no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—41no—
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—41no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—816no—
1186C2×C4—816no—
1187C2×C4#52514yes—
1188C2×C4C2×#12414yes—
1189C2×C4#53414yes—
1190C2×C4D4214yes—
1191C2×C4#55114yes—
1192C2×C4#55114yes—
1193C2×C4#55114yes—
1194C2×C4#55114yes—
1195C22—28no—
1196C22—28no—
1197C22—24no—
1198C22—28no—
1199C22—24no—
1200C22—24no—
1201C22—42no—
1202C22—44no—
1203C22—42no—
1204C22—42no—
1205C22—44no—
1206C22—42no—
1207C22—44no—
1208C22—42no—
1209C22—44no—
1210C22—42no—
1211C22—44no—
1212C22—44no—
1213C22—42no—
1214C22—42no—
1215C22—44no—
1216C22—42no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—42no—
1221C22—44no—
1222C22—42no—
1223C22—44no—
1224C22—42no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—864no—
1233C22—82no—
1234C22—82no—
1235C22—82no—
1236C22—82no—
1237C22—82no—
1238C22—82no—
1239C22—82no—
1240C22—82no—
1241C22C2×#52511yescharacteristic
1242C22C22×#12411yescharacteristic
1243C22C2×#53211yescharacteristic
1244C22C2×#53411yescharacteristic
1245C22#346011yescharacteristic
1246C22C2×D4211yescharacteristic
1247C22D4×#4111yescharacteristic
1248C22D4×#4111yescharacteristic
1249C22D4×#4111yescharacteristic
1250C22D4×#4111yescharacteristic
1251C22C2×#55111yescharacteristic
1252C22C2×#55111yescharacteristic
1253C22C2×#55111yescharacteristic
1254C22C2×#55111yescharacteristic
1255C22#347511yescharacteristic
1256C22#348111yescharacteristic
1257C22#348111yescharacteristic
1258C22#349411yescharacteristic
1259C22#349611yescharacteristic
1260C22#349611yescharacteristic
1261C22#349811yescharacteristic
1262C22#350011yescharacteristic
1263C22#350511yescharacteristic
1264C22#351011yescharacteristic
1265C22#351311yescharacteristic
1266C22#351411yescharacteristic
1267C22#351411yescharacteristic
1268C22#351411yescharacteristic
1269C22#351411yescharacteristic
1270C22#352111yescharacteristic
1271C22#352111yescharacteristic
1272C22#353711yescharacteristic
1273C22#354011yescharacteristic
1274C22#355811yescharacteristic
1275C22#356211yescharacteristic
1276C4—24no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—44no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—82no—
1289C4—81no—
1290C4—82no—
1291C4—82no—
1292C4—81no—
1293C4—82no—
1294C4—82no—
1295C4#256118yescomplemented
1296C2—48no—
1297C2—44no—
1298C2—84no—
1299C2#3468111yescharacteristic
1300C2C2×#256111yescharacteristic
1301C2#3561111yescharacteristic
1302C2D4×#12411yescharacteristic
1303C2#3623811yescharacteristic
1304C2#3626211yescharacteristic
1305C2#3626411yescharacteristic
1306C2#3904211yescharacteristic
1307C2#3907011yescharacteristic
1308C2#3935811yescharacteristic
1309C2#3996011yescharacteristic
1310C2#5937511yescharacteristic
1311C2#5937811yescharacteristic
1312C2#5947611yescharacteristic
1313C2#5948411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2561C2semidirect
2. C2×#2452C2semidirect
4. #15471C2semidirect
5. #15468C2semidirect
6. #15467C2semidirect
7. #15297C2semidirect
8. #15245C2semidirect
9. #15144C2semidirect
10. #15138C2semidirect
11. #15132C2semidirect
12. #15125C2semidirect
13. #14765C2semidirect
14. #14700C2semidirect
15. #14022C2semidirect
16. #13974C2semidirect
17. #13971C2semidirect
18. #13916C2semidirect
19. #13916C2semidirect
22. C4×#390C2semidirect
23. C4×#388C2semidirect
25. C22×C4⋊Q8C22semidirect
26. C22×C22⋊Q8C22semidirect
33. C2×#397C22semidirect
34. C2×#396C22semidirect
36. C2×#393C22semidirect
37. C2×#393C22semidirect
38. C2×#393C22semidirect
50. C2×#389C22semidirect
51. C2×#389C22semidirect
55. C2×#388C22semidirect
56. C2×#388C22semidirect
57. C2×#388C22semidirect
60. C2×#385C22semidirect
61. C2×#381C22semidirect
62. C2×#381C22semidirect
71. C2×C4×C4⋊C4C22semidirect
72. C2×C4×C4⋊C4C22semidirect
76. C2×C4×C22⋊C4C22semidirect
77. C2×C4×C22⋊C4C22semidirect
78. C2×C43C22semidirect
79. #1446C22semidirect
80. #1443C22semidirect
81. #1443C22semidirect
82. #1442C22semidirect
83. #1442C22semidirect
86. #1440C22semidirect
87. #1440C22semidirect
88. #1440C22semidirect
89. #1440C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
104. #1437C22semidirect
105. #1437C22semidirect
106. #1437C22semidirect
107. #1437C22semidirect
108. #1437C22semidirect
109. #1436C22semidirect
110. #1436C22semidirect
111. #1436C22semidirect
112. C4⋊#95C22semidirect
113. C4⋊#95C22semidirect
114. C4⋊#95C22semidirect
115. C4⋊#95C22semidirect
116. C4⋊#95C22semidirect
117. C4⋊#95C22semidirect
118. C4⋊#95C22semidirect
119. C4⋊#95C22semidirect
120. #1434C22semidirect
121. #1434C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C4×#95C22semidirect
125. C4×#95C22semidirect
233. #388D4semidirect
423. C2×C4⋊C4C2×D4semidirect
550. C2×C42C2×D4semidirect
587. #95C2×D4semidirect
588. #95C2×D4semidirect
1295. C4#2561semidirect

Maximal subgroups

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

subgroupindex
C2×#25612
C2×#24522
C2×D4×C22⋊C42
#154712
#154682
#154672
#152972
#152452
#151442
#151382
#151322
#151252
#147652
#147002
#140222
#139742
#139712
#139162
#139022
C4×#3902
C4×#3882