Finite Group Databasebeta

← #665577

Subgroups — #665577

Order 512.

4246 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2482C212yesmaximal, complemented
2C2×D4×C22⋊C4C211yesmaximal, characteristic
3C2×#2293C211yesmaximal, characteristic, complemented
4#15345C212yesmaximal, complemented
5#15343C212yesmaximal, complemented
6#15284C212yesmaximal, complemented
7#15282C212yesmaximal, complemented
8#15148C211yesmaximal, characteristic, complemented
9#15138C211yesmaximal, characteristic, complemented
10#15135C211yesmaximal, characteristic, complemented
11#15132C211yesmaximal, characteristic, complemented
12#15113C212yesmaximal, complemented
13#14974C212yesmaximal, complemented
14#14700C211yesmaximal, characteristic, complemented
15#14018C211yesmaximal, characteristic, complemented
16#14001C211yesmaximal, characteristic, complemented
17#13994C211yesmaximal, characteristic, complemented
18#13991C212yesmaximal, complemented
19#13977C211yesmaximal, characteristic, complemented
20#13916C211yesmaximal, characteristic, complemented
21#13902C211yesmaximal, characteristic
22#13902C211yesmaximal, characteristic
23C4×#388C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2212yescomplemented
28C23×C22⋊C4C2212yes—
29#2482—216no—
30C2×#399C2212yes—
31C2×#399C2212yescomplemented
32C2×#397C2212yes—
33C2×#397C2212yescomplemented
34D4×C22⋊C4—28no—
35#2293—28no—
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#389C2211yescharacteristic, complemented
47C2×#389C2211yescharacteristic, complemented
48C2×#389C2211yescharacteristic, complemented
49C2×#389C2211yescharacteristic, complemented
50C2×#388C2212yes—
51C2×#388C2211yescharacteristic
52C2×#388C2211yescharacteristic
53C2×#388C2212yescomplemented
54C2×#388C2212yescomplemented
55C2×#388C2212yescomplemented
56C2×#388C2212yescomplemented
57C2×#388C2212yescomplemented
58C2×#388C2212yescomplemented
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#385C2212yescomplemented
62C2×#385C2212yescomplemented
63C2×#385C2212yescomplemented
64C2×#384C2211yescharacteristic, complemented
65C2×#381C2212yescomplemented
66C2×#380C2211yescharacteristic
67C2×#380C2211yescharacteristic
68C2×#380C2211yescharacteristic
69C2×#379C2212yes—
70C2×#379C2212yes—
71C2×#379C2212yes—
72C2×#379C2212yes—
73C2×#379C2212yes—
74C2×C4×C4⋊C4C2211yescharacteristic, complemented
75C2×C4×C4⋊C4C2211yescharacteristic, complemented
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2212yescomplemented
80C2×C43C2211yescharacteristic, complemented
81#1445C2212yescomplemented
82#1444C2212yescomplemented
83#1443C2212yescomplemented
84#1442C2212yescomplemented
85#1442C2212yescomplemented
86#1440C2212yes—
87#1440C2212yes—
88#1440C2212yescomplemented
89#1440C2212yescomplemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1439C2212yes—
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yes—
107#1437C2211yescharacteristic
108#1437C2211yescharacteristic
109#1437C2212yescomplemented
110#1437C2212yescomplemented
111#1436C2211yescharacteristic, complemented
112#1436C2211yescharacteristic, complemented
113C4⋊#95C2211yescharacteristic, complemented
114C4⋊#95C2211yescharacteristic, complemented
115C4⋊#95C2211yescharacteristic, complemented
116C4⋊#95C2211yescharacteristic, complemented
117C4⋊#95C2211yescharacteristic, complemented
118C4⋊#95C2211yescharacteristic, complemented
119#1434C2211yescharacteristic, complemented
120#1434C2212yescomplemented
121#1434C2211yescharacteristic, complemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C4×#95C2211yescharacteristic, complemented
125C4×#95C2211yescharacteristic, complemented
126C26C2312yes—
127C23×D4—24no—
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—42no—
133C23×D4—42no—
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2312yes—
139C24×C4C2312yes—
140C2×C4×D4—24no—
141C2×C4×D4—24no—
142C2×C4×D4—24no—
143C2×C4×D4—42no—
144C2×C4×D4—42no—
145C2×C4×D4D418yes—
146C2×#117—28no—
147C2×#117—28no—
148C2×#117—44no—
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C22⋊C4—28no—
164C22×C22⋊C4—28no—
165C22×C22⋊C4—44no—
166C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C42C2312yes—
198C22×C42C2311yescharacteristic
199C22×C42C2311yescharacteristic
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
202C22×C42C2311yescharacteristic
203C22×C42C2311yescharacteristic
204C22×C42C2311yescharacteristic
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208#399—28no—
209#399—28no—
210#397—28no—
211#397—28no—
212#390—24no—
213#390—24no—
214#390—24no—
215#390—24no—
216#390—24no—
217#390—24no—
218#390—24no—
219#390—24no—
220#390—42no—
221#390—42no—
222#389—24no—
223#389—24no—
224#389—42no—
225#389—42no—
226#388—28no—
227#388—28no—
228#388—28no—
229#388—24no—
230#388—28no—
231#388—28no—
232#388—44no—
233#388—44no—
234#388D418yescomplemented
235#386—28no—
236#386—28no—
237#385—28no—
238#385—28no—
239#385—44no—
240#384—42no—
241#381—28no—
242#380—24no—
243#380—24no—
244#380—42no—
245#379—28no—
246#379—28no—
247#379—28no—
248#379—28no—
249#379—44no—
250C4×C4⋊C4—24no—
251C4×C4⋊C4—42no—
252C4×C22⋊C4—28no—
253C4×C22⋊C4—24no—
254C4×C22⋊C4—24no—
255C4×C22⋊C4—42no—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C2×#95C2312yes—
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2311yescharacteristic
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C43—24no—
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×D4—232no—
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—24no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—416no—
328C22×D4—416no—
329C22×D4—42no—
330C22×D4—42no—
331C22×D4—416no—
332C22×D4—416no—
333C22×D4—416no—
334C22×D4—416no—
335C22×D4C2×D414yes—
336C22×D4#4114yes—
337C22×D4#4114yes—
338C22×D4#4114yes—
339C23×C4—24no—
340C23×C4—24no—
341C23×C4—24no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—24no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—24no—
350C23×C4—24no—
351C23×C4—42no—
352C23×C4—42no—
353C23×C4—42no—
354C23×C4—42no—
355C23×C4—42no—
356C23×C4—42no—
357C23×C4—42no—
358C23×C4C2×D418yes—
359C23×C4#4114yes—
360C23×C4C2412yes—
361C23×C4C2412yes—
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2411yescharacteristic
365C23×C4C2411yescharacteristic
366C23×C4C2412yes—
367C23×C4C2411yescharacteristic
368C23×C4C2411yescharacteristic
369C23×C4C2411yescharacteristic
370C23×C4C2411yescharacteristic
371C23×C4C2411yescharacteristic
372C23×C4C2412yes—
373C23×C4C2411yescharacteristic
374C23×C4C2411yescharacteristic
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C4×D4—232no—
381C4×D4—416no—
382#117—432no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—41no—
409C2×C4⋊C4—41no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4—41no—
413C2×C4⋊C4—41no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4C2×D414yes—
424C2×C4⋊C4C2×D414yescomplemented
425C2×C22⋊C4—24no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—22no—
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—24no—
475C2×C22⋊C4—432no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—41no—
479C2×C22⋊C4—41no—
480C2×C22⋊C4—41no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—41no—
494C2×C22⋊C4—41no—
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⋊C4—42no—
514C2×C22⋊C4C2×D414yes—
515C2×C22⋊C4C2×D418yes—
516C2×C22⋊C4C2×D414yes—
517C2×C22⋊C4C2×D414yes—
518C2×C22⋊C4#4114yes—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—24no—
524C2×C42—24no—
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—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—41no—
547C2×C42—41no—
548C2×C42—41no—
549C2×C42—41no—
550C2×C42C2×D414yes—
551C2×C42C2×D414yescomplemented
552#95—22no—
553#95—22no—
554#95—24no—
555#95—24no—
556#95—24no—
557#95—24no—
558#95—24no—
559#95—24no—
560#95—24no—
561#95—24no—
562#95—24no—
563#95—24no—
564#95—22no—
565#95—22no—
566#95—24no—
567#95—22no—
568#95—22no—
569#95—22no—
570#95—24no—
571#95—22no—
572#95—42no—
573#95—41no—
574#95—41no—
575#95—42no—
576#95—42no—
577#95—41no—
578#95—41no—
579#95—41no—
580#95—41no—
581#95—42no—
582#95—42no—
583#95—42no—
584#95—42no—
585#95—42no—
586#95C2×D414yescomplemented
587#95C2×D414yescomplemented
588C24—22no—
589C24—21no—
590C24—22no—
591C24—21no—
592C24—21no—
593C24—21no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—21no—
599C24—22no—
600C24—21no—
601C24—21no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—216no—
613C24—22no—
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—48no—
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—84no—
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—
661C24C22×D414yes—
662C24C22×D412yes—
663C24C2×#4114yes—
664C24C2×#4114yes—
665C24C2×#4114yes—
666C24C2×#4112yes—
667C24C2×#4112yes—
668C24C2511yescharacteristic
669C2×D4—216no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—28no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—4128no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4#123116yes—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—216no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—22no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
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—22no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
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—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—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
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—28no—
763C22×C4—216no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—48no—
826C22×C4—84no—
827C22×C4—84no—
828C22×C4—84no—
829C22×C4—84no—
830C22×C4—84no—
831C22×C4C22×D412yes—
832C22×C4C22×D412yes—
833C22×C4C22×D414yes—
834C22×C4C22×D412yes—
835C22×C4C22×D412yes—
836C22×C4C22×D412yes—
837C22×C4C22×D412yes—
838C22×C4C22×D412yes—
839C22×C4C22×D412yes—
840C22×C4C22×D412yes—
841C22×C4C2×#4112yes—
842C22×C4C2×#4112yes—
843C22×C4C2×#4112yes—
844C22×C4C2×#4112yes—
845C22×C4C2×#4112yes—
846C22×C4C2×#4112yes—
847C22×C4C2×#4112yes—
848C22×C4H(5,𝔽2)12yes—
849C22×C4H(5,𝔽2)12yes—
850C22×C4H(5,𝔽2)12yes—
851C22×C4H(5,𝔽2)12yes—
852C4⋊C4—28no—
853C4⋊C4—44no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—84no—
863C4⋊C4—84no—
864C4⋊C4—84no—
865C4⋊C4—84no—
866C22⋊C4—216no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—44no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—44no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—84no—
890C22⋊C4—84no—
891C22⋊C4—84no—
892C22⋊C4—84no—
893C22⋊C4—84no—
894C22⋊C4—84no—
895C22⋊C4—84no—
896C22⋊C4—84no—
897C42—28no—
898C42—28no—
899C42—44no—
900C42—44no—
901C42—44no—
902C42—44no—
903C42—44no—
904C42—44no—
905C42—48no—
906C42—44no—
907C42—44no—
908C23—22no—
909C23—24no—
910C23—24no—
911C23—22no—
912C23—22no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23—22no—
917C23—24no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—22no—
928C23—24no—
929C23—24no—
930C23—22no—
931C23—22no—
932C23—24no—
933C23—24no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—22no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—432no—
952C23—432no—
953C23—41no—
954C23—42no—
955C23—41no—
956C23—42no—
957C23—42no—
958C23—41no—
959C23—41no—
960C23—42no—
961C23—41no—
962C23—41no—
963C23—42no—
964C23—42no—
965C23—42no—
966C23—42no—
967C23—42no—
968C23—42no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—42no—
973C23—41no—
974C23—42no—
975C23—41no—
976C23—41no—
977C23—42no—
978C23—41no—
979C23—42no—
980C23—41no—
981C23—42no—
982C23—41no—
983C23—42no—
984C23—41no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
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—816no—
1014C23—816no—
1015C23—816no—
1016C23—816no—
1017C23—816no—
1018C23—816no—
1019C23—816no—
1020C23—816no—
1021C23—816no—
1022C23—816no—
1023C23—816no—
1024C23—816no—
1025C23—816no—
1026C23C2×#12318yes—
1027C23#53214yes—
1028C23C23×D411yescharacteristic
1029C23C23×D411yescharacteristic
1030C23C22×#4111yescharacteristic
1031C23C22×#4111yescharacteristic
1032C23C22×#4111yescharacteristic
1033C23C22×#4111yescharacteristic
1034C23C22×#4111yescharacteristic
1035C23C2×H(5,𝔽2)11yescharacteristic
1036C23C2×H(5,𝔽2)11yescharacteristic
1037C23C2×H(5,𝔽2)11yescharacteristic
1038C23C2×H(5,𝔽2)11yescharacteristic
1039C23#58511yescharacteristic
1040C23#58511yescharacteristic
1041C23#58511yescharacteristic
1042C23#58511yescharacteristic
1043D4—232no—
1044D4—432no—
1045D4—416no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—22no—
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—24no—
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—22no—
1084C2×C4—22no—
1085C2×C4—432no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—42no—
1096C2×C4—42no—
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—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—42no—
1116C2×C4—42no—
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—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—416no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—816no—
1181C2×C4C2×#12314yes—
1182C2×C4#52514yes—
1183C2×C4#53514yes—
1184C2×C4D4214yes—
1185C2×C4#55114yes—
1186C2×C4#55114yes—
1187C2×C4#55114yes—
1188C2×C4#55114yes—
1189C22—28no—
1190C22—24no—
1191C22—24no—
1192C22—24no—
1193C22—28no—
1194C22—28no—
1195C22—44no—
1196C22—42no—
1197C22—44no—
1198C22—42no—
1199C22—44no—
1200C22—42no—
1201C22—44no—
1202C22—42no—
1203C22—44no—
1204C22—42no—
1205C22—42no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—44no—
1210C22—42no—
1211C22—44no—
1212C22—42no—
1213C22—44no—
1214C22—42no—
1215C22—44no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—864no—
1227C22—82no—
1228C22—82no—
1229C22—82no—
1230C22—82no—
1231C22—82no—
1232C22—82no—
1233C22—82no—
1234C22—82no—
1235C22C22×#12311yescharacteristic
1236C22C2×#52511yescharacteristic
1237C22C2×#53211yescharacteristic
1238C22C2×#53511yescharacteristic
1239C22#346011yescharacteristic
1240C22C2×D4211yescharacteristic
1241C22D4×#4111yescharacteristic
1242C22D4×#4111yescharacteristic
1243C22D4×#4111yescharacteristic
1244C22D4×#4111yescharacteristic
1245C22C2×#55111yescharacteristic
1246C22C2×#55111yescharacteristic
1247C22C2×#55111yescharacteristic
1248C22C2×#55111yescharacteristic
1249C22#347511yescharacteristic
1250C22#348111yescharacteristic
1251C22#348111yescharacteristic
1252C22#348511yescharacteristic
1253C22#348811yescharacteristic
1254C22#349411yescharacteristic
1255C22#349611yescharacteristic
1256C22#349811yescharacteristic
1257C22#350511yescharacteristic
1258C22#351011yescharacteristic
1259C22#351311yescharacteristic
1260C22#351311yescharacteristic
1261C22#351311yescharacteristic
1262C22#351411yescharacteristic
1263C22#351411yescharacteristic
1264C22#352111yescharacteristic
1265C22#352111yescharacteristic
1266C22#354611yescharacteristic
1267C22#354911yescharacteristic
1268C22#355111yescharacteristic
1269C22#356211yescharacteristic
1270C4—24no—
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—44no—
1282C4—81no—
1283C4—82no—
1284C4—82no—
1285C4—82no—
1286C4—82no—
1287C4—82no—
1288C4—81no—
1289C4#248218yescomplemented
1290C2—48no—
1291C2—44no—
1292C2—84no—
1293C2#3468111yescharacteristic
1294C2C2×#248211yescharacteristic
1295C2#3552311yescharacteristic
1296C2D4×#12311yescharacteristic
1297C2#3621611yescharacteristic
1298C2#3626211yescharacteristic
1299C2#3626411yescharacteristic
1300C2#3820611yescharacteristic
1301C2#3825411yescharacteristic
1302C2#3934211yescharacteristic
1303C2#3988111yescharacteristic
1304C2#5947611yescharacteristic
1305C2#5948811yescharacteristic
1306C2#5984311yescharacteristic
1307C2#5994511yescharacteristic
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×#2482C2semidirect
3. C2×#2293C2semidirect
4. #15345C2semidirect
5. #15343C2semidirect
6. #15284C2semidirect
7. #15282C2semidirect
8. #15148C2semidirect
9. #15138C2semidirect
10. #15135C2semidirect
11. #15132C2semidirect
12. #15113C2semidirect
13. #14974C2semidirect
14. #14700C2semidirect
15. #14018C2semidirect
16. #14001C2semidirect
17. #13994C2semidirect
18. #13991C2semidirect
19. #13977C2semidirect
20. #13916C2semidirect
23. C4×#388C2semidirect
27. C22×#117C22semidirect
31. C2×#399C22semidirect
33. C2×#397C22semidirect
46. C2×#389C22semidirect
47. C2×#389C22semidirect
48. C2×#389C22semidirect
49. C2×#389C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
55. C2×#388C22semidirect
56. C2×#388C22semidirect
57. C2×#388C22semidirect
58. C2×#388C22semidirect
61. C2×#385C22semidirect
62. C2×#385C22semidirect
63. C2×#385C22semidirect
64. C2×#384C22semidirect
65. C2×#381C22semidirect
74. C2×C4×C4⋊C4C22semidirect
75. C2×C4×C4⋊C4C22semidirect
79. C2×C4×C22⋊C4C22semidirect
80. C2×C43C22semidirect
81. #1445C22semidirect
82. #1444C22semidirect
83. #1443C22semidirect
84. #1442C22semidirect
85. #1442C22semidirect
88. #1440C22semidirect
89. #1440C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
109. #1437C22semidirect
110. #1437C22semidirect
111. #1436C22semidirect
112. #1436C22semidirect
113. C4⋊#95C22semidirect
114. C4⋊#95C22semidirect
115. C4⋊#95C22semidirect
116. C4⋊#95C22semidirect
117. C4⋊#95C22semidirect
118. C4⋊#95C22semidirect
119. #1434C22semidirect
120. #1434C22semidirect
121. #1434C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C4×#95C22semidirect
125. C4×#95C22semidirect
234. #388D4semidirect
424. C2×C4⋊C4C2×D4semidirect
551. C2×C42C2×D4semidirect
586. #95C2×D4semidirect
587. #95C2×D4semidirect
1289. C4#2482semidirect

Maximal subgroups

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

subgroupindex
C2×#24822
C2×D4×C22⋊C42
C2×#22932
#153452
#153432
#152842
#152822
#151482
#151382
#151352
#151322
#151132
#149742
#147002
#140182
#140012
#139942
#139912
#139772
#139162
#139022
C4×#3882