Finite Group Databasebeta

← #774458

Subgroups — #774458

Order 512.

4210 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×#2421C211yesmaximal, characteristic, complemented
2C2×#2435C211yesmaximal, characteristic
3C2×#2367C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic
5#16273C212yesmaximal, complemented
6#15556C212yesmaximal, complemented
7#15380C212yesmaximal, complemented
8#15284C212yesmaximal, complemented
9#15282C212yesmaximal, complemented
10#15226C211yesmaximal, characteristic, complemented
11#15179C211yesmaximal, characteristic, complemented
12#15148C211yesmaximal, characteristic, complemented
13#14798C212yesmaximal, complemented
14#14727C212yesmaximal, complemented
15#14027C211yesmaximal, characteristic, complemented
16#14026C211yesmaximal, characteristic, complemented
17#14002C211yesmaximal, characteristic, complemented
18#13994C211yesmaximal, characteristic, complemented
19#13979C211yesmaximal, characteristic, complemented
20#13920C211yesmaximal, characteristic, complemented
21#13902C211yesmaximal, characteristic
22#13873C212yesmaximal, complemented
23C4×#397C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic, complemented
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C23×C22⋊C4C2212yes—
32#2435—28no—
33#2421—28no—
34C2×#400C2212yescomplemented
35C2×#399C2212yescomplemented
36C2×#397C2211yescharacteristic
37C2×#397C2212yes—
38C2×#394C2212yes—
39C2×#394C2212yes—
40#2367—28no—
41D4×C22⋊C4—28no—
42C2×#391C2211yescharacteristic, complemented
43C2×#391C2211yescharacteristic, complemented
44C2×#391C2211yescharacteristic, complemented
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#389C2211yescharacteristic, complemented
54C2×#389C2211yescharacteristic, complemented
55C2×#389C2211yescharacteristic, complemented
56C2×#388C2212yes—
57C2×#388C2212yes—
58C2×#388C2212yescomplemented
59C2×#388C2212yescomplemented
60C2×#387C2212yescomplemented
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#385C2212yescomplemented
64C2×#382C2211yescharacteristic, complemented
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×#380C2212yescomplemented
68C2×#379C2212yes—
69C2×#379C2212yes—
70C2×#379C2212yes—
71C2×#379C2212yes—
72C2×#379C2212yes—
73C2×C4×C4⋊C4C2211yescharacteristic, complemented
74C2×C4×C4⋊C4C2211yescharacteristic, complemented
75C2×C4×C22⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2212yescomplemented
79#1445C2211yescharacteristic, complemented
80#1443C2211yescharacteristic, complemented
81#1443C2211yescharacteristic, complemented
82#1442C2211yescharacteristic, complemented
83#1442C2212yescomplemented
84#1442C2212yescomplemented
85#1441C2212yescomplemented
86#1440C2211yescharacteristic
87#1440C2211yescharacteristic
88#1440C2212yes—
89#1440C2212yes—
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1439C2211yescharacteristic
97#1439C2212yes—
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1438C2212yes—
110#1438C2212yes—
111#1437C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115C4⋊#95C2211yescharacteristic, complemented
116C4⋊#95C2211yescharacteristic, complemented
117C4⋊#95C2211yescharacteristic, complemented
118#1434C2212yescomplemented
119C22⋊#95C2212yescomplemented
120C22⋊#95C2212yescomplemented
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C4×#95C2211yescharacteristic, complemented
125C4×#95C2211yescharacteristic, complemented
126C4×#95C2211yescharacteristic, complemented
127C26C2312yes—
128C23×Q8C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—24no—
134C23×D4—42no—
135C23×D4—42no—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2312yes—
141C24×C4C2312yes—
142C2×#124—24no—
143C2×#124—24no—
144C2×#124—24no—
145C2×#124—24no—
146C2×#124—42no—
147C2×#124D418yes—
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—42no—
151C2×C4×Q8—24no—
152C2×C4×Q8—24no—
153C2×C4×Q8—42no—
154C2×C4×D4—24no—
155C2×C4×D4—24no—
156C2×C4×D4—24no—
157C2×C4×D4—24no—
158C2×C4×D4—42no—
159C2×C4×D4—42no—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C22⋊C4—28no—
173C22×C22⋊C4—28no—
174C22×C22⋊C4—44no—
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2312yes—
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214#400—28no—
215#399—44no—
216#397—28no—
217#397—24no—
218#394—28no—
219#394—28no—
220#391—24no—
221#391—24no—
222#391—42no—
223#390—24no—
224#390—24no—
225#390—24no—
226#390—24no—
227#390—24no—
228#390—24no—
229#390—24no—
230#390—42no—
231#389—24no—
232#389—42no—
233#389—42no—
234#388—28no—
235#388—28no—
236#388—28no—
237#388—44no—
238#387—28no—
239#386—28no—
240#386—28no—
241#385—28no—
242#382—24no—
243#380—44no—
244#380—42no—
245#380D418yes—
246#379—28no—
247#379—28no—
248#379—28no—
249#379—44no—
250#379—44no—
251C4×C4⋊C4—24no—
252C4×C4⋊C4—24no—
253C4×C22⋊C4—24no—
254C4×C22⋊C4—24no—
255C4×C22⋊C4—28no—
256C4×C22⋊C4—24no—
257C2×#95C2311yescharacteristic
258C2×#95C2311yescharacteristic
259C2×#95C2312yes—
260C2×#95C2311yescharacteristic
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2311yescharacteristic
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2312yes—
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C25—24no—
298C25—24no—
299C25—24no—
300C25—24no—
301C25—24no—
302C25—24no—
303C25—24no—
304C25—42no—
305C25—42no—
306C25—42no—
307C25—42no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25—42no—
312C25C2412yes—
313C25C2412yes—
314C25C2411yescharacteristic
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8C2×D414yes—
322C22×D4—232no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—24no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—416no—
339C22×D4—416no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4—416no—
343C22×D4—416no—
344C22×D4—416no—
345C22×D4—416no—
346C22×D4C2×D414yes—
347C22×D4#4114yes—
348C22×D4#4114yes—
349C22×D4#4114yes—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—42no—
363C23×C4—42no—
364C23×C4—42no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4—42no—
368C23×C4—42no—
369C23×C4—42no—
370C23×C4C2×D414yes—
371C23×C4C2412yes—
372C23×C4C2411yescharacteristic
373C23×C4C2411yescharacteristic
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C23×C4C2411yescharacteristic
381C23×C4C2412yes—
382C23×C4C2411yescharacteristic
383C23×C4C2411yescharacteristic
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391#124—232no—
392#124—416no—
393C22⋊Q8—416no—
394C4×Q8—416no—
395C4×D4—416no—
396C4×D4—416no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—24no—
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—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—41no—
421C2×C4⋊C4—41no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4C2×D414yes—
432C2×C4⋊C4C2×D414yes—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
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—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—24no—
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—22no—
462C2×C22⋊C4—22no—
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—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—432no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—41no—
484C2×C22⋊C4—41no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—41no—
487C2×C22⋊C4—41no—
488C2×C22⋊C4—41no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
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⋊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⋊C4C2×D418yes—
524C2×C22⋊C4C2×D418yes—
525C2×C22⋊C4C2×D418yes—
526C2×C22⋊C4#4114yes—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—24no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—24no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—24no—
547C2×C42—42no—
548C2×C42—42no—
549C2×C42—42no—
550C2×C42C2×D414yes—
551#95—22no—
552#95—24no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—24no—
560#95—22no—
561#95—24no—
562#95—24no—
563#95—24no—
564#95—24no—
565#95—24no—
566#95—24no—
567#95—22no—
568#95—22no—
569#95—22no—
570#95—22no—
571#95—41no—
572#95—41no—
573#95—41no—
574#95—41no—
575#95—42no—
576#95—41no—
577#95—41no—
578#95—41no—
579#95—42no—
580#95—41no—
581#95—42no—
582#95—42no—
583#95—42no—
584#95—42no—
585#95—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95C2×D418yes—
591C24—21no—
592C24—22no—
593C24—22no—
594C24—21no—
595C24—21no—
596C24—21no—
597C24—22no—
598C24—22no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—216no—
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—22no—
629C24—22no—
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—48no—
645C24—48no—
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—
662C24—84no—
663C24—84no—
664C24C22×D414yes—
665C24C22×D412yes—
666C24C2×#4114yes—
667C24C2×#4114yes—
668C24C2×#4114yes—
669C24C2×#4112yes—
670C24H(5,𝔽2)12yes—
671C24C2511yescharacteristic
672C2×Q8—28no—
673C2×Q8—28no—
674C2×Q8—28no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×D4—216no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—28no—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—4128no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4#123116yes—
701C22×C4—21no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—22no—
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—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
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—22no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—22no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—84no—
839C22×C4—84no—
840C22×C4—84no—
841C22×C4—84no—
842C22×C4—84no—
843C22×C4—84no—
844C22×C4—84no—
845C22×C4—84no—
846C22×C4C22×D412yes—
847C22×C4C22×D414yes—
848C22×C4C22×D412yes—
849C22×C4C22×D412yes—
850C22×C4C22×D414yes—
851C22×C4C22×D414yes—
852C22×C4C22×D412yes—
853C22×C4C22×D412yes—
854C22×C4C2×#4112yes—
855C22×C4C2×#4112yes—
856C22×C4C2×#4112yes—
857C22×C4C2×#4112yes—
858C22×C4C2×#4112yes—
859C22×C4H(5,𝔽2)12yes—
860C22×C4H(5,𝔽2)12yes—
861C22×C4H(5,𝔽2)12yes—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—48no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—84no—
873C4⋊C4—84no—
874C22⋊C4—216no—
875C22⋊C4—216no—
876C22⋊C4—28no—
877C22⋊C4—216no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—48no—
883C22⋊C4—44no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—84no—
892C22⋊C4—84no—
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—
902C22⋊C4—84no—
903C22⋊C4—84no—
904C22⋊C4—84no—
905C42—28no—
906C42—48no—
907C42—44no—
908C42—44no—
909C42—44no—
910C42—44no—
911C42—44no—
912C42—84no—
913C23—22no—
914C23—24no—
915C23—24no—
916C23—22no—
917C23—24no—
918C23—24no—
919C23—22no—
920C23—24no—
921C23—22no—
922C23—24no—
923C23—24no—
924C23—22no—
925C23—22no—
926C23—24no—
927C23—24no—
928C23—22no—
929C23—22no—
930C23—24no—
931C23—22no—
932C23—22no—
933C23—24no—
934C23—24no—
935C23—22no—
936C23—24no—
937C23—24no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—24no—
942C23—22no—
943C23—22no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—22no—
948C23—22no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—432no—
957C23—432no—
958C23—41no—
959C23—41no—
960C23—42no—
961C23—41no—
962C23—41no—
963C23—42no—
964C23—42no—
965C23—42no—
966C23—41no—
967C23—42no—
968C23—41no—
969C23—42no—
970C23—42no—
971C23—42no—
972C23—42no—
973C23—41no—
974C23—41no—
975C23—42no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—42no—
981C23—42no—
982C23—42no—
983C23—41no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—41no—
988C23—41no—
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×#12318yes—
1032C23#54614yes—
1033C23C23×D411yescharacteristic
1034C23C23×D411yescharacteristic
1035C23C22×#4111yescharacteristic
1036C23C22×#4111yescharacteristic
1037C23C22×#4111yescharacteristic
1038C23C22×#4111yescharacteristic
1039C23C2×H(5,𝔽2)11yescharacteristic
1040C23C2×H(5,𝔽2)11yescharacteristic
1041C23C2×H(5,𝔽2)11yescharacteristic
1042C23C2×H(5,𝔽2)11yescharacteristic
1043C23#58511yescharacteristic
1044C23#58511yescharacteristic
1045C23#58511yescharacteristic
1046C23#58511yescharacteristic
1047C23#58511yescharacteristic
1048Q8—416no—
1049D4—232no—
1050D4—432no—
1051D4—416no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
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—24no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—41no—
1080C2×C4—42no—
1081C2×C4—41no—
1082C2×C4—42no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—42no—
1088C2×C4—42no—
1089C2×C4—41no—
1090C2×C4—42no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—42no—
1094C2×C4—41no—
1095C2×C4—42no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—42no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—42no—
1106C2×C4—42no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—42no—
1111C2×C4—41no—
1112C2×C4—42no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—416no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—42no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—42no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—42no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—816no—
1187C2×C4—816no—
1188C2×C4C2×#12314yes—
1189C2×C4#52514yes—
1190C2×C4#53814yes—
1191C2×C4D4214yes—
1192C2×C4#54614yes—
1193C2×C4#54614yes—
1194C2×C4#55114yes—
1195C22—24no—
1196C22—28no—
1197C22—28no—
1198C22—28no—
1199C22—24no—
1200C22—24no—
1201C22—44no—
1202C22—42no—
1203C22—44no—
1204C22—42no—
1205C22—44no—
1206C22—44no—
1207C22—42no—
1208C22—42no—
1209C22—44no—
1210C22—42no—
1211C22—44no—
1212C22—42no—
1213C22—42no—
1214C22—44no—
1215C22—42no—
1216C22—44no—
1217C22—42no—
1218C22—42no—
1219C22—44no—
1220C22—44no—
1221C22—42no—
1222C22—44no—
1223C22—42no—
1224C22—44no—
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—
1241C22C22×#12311yescharacteristic
1242C22C2×#52511yescharacteristic
1243C22C2×#53811yescharacteristic
1244C22C2×D4211yescharacteristic
1245C22C2×#54611yescharacteristic
1246C22C2×#54611yescharacteristic
1247C22C2×#54611yescharacteristic
1248C22D4×#4111yescharacteristic
1249C22C2×#55111yescharacteristic
1250C22#347511yescharacteristic
1251C22#347511yescharacteristic
1252C22#348111yescharacteristic
1253C22#348711yescharacteristic
1254C22#348811yescharacteristic
1255C22#348811yescharacteristic
1256C22#348811yescharacteristic
1257C22#350011yescharacteristic
1258C22#350011yescharacteristic
1259C22#351311yescharacteristic
1260C22#351311yescharacteristic
1261C22#351311yescharacteristic
1262C22#351411yescharacteristic
1263C22#351411yescharacteristic
1264C22#351411yescharacteristic
1265C22#351411yescharacteristic
1266C22#352111yescharacteristic
1267C22#352111yescharacteristic
1268C22#352111yescharacteristic
1269C22#352111yescharacteristic
1270C22#354311yescharacteristic
1271C22#355811yescharacteristic
1272C22#355811yescharacteristic
1273C22#356211yescharacteristic
1274C22#356211yescharacteristic
1275C22#356211yescharacteristic
1276C4—42no—
1277C4—44no—
1278C4—42no—
1279C4—42no—
1280C4—44no—
1281C4—42no—
1282C4—42no—
1283C4—44no—
1284C4—42no—
1285C4—81no—
1286C4—82no—
1287C4—81no—
1288C4—81no—
1289C4—82no—
1290C4—81no—
1291C4—81no—
1292C4—82no—
1293C4—81no—
1294C4—81no—
1295C4#241818yes—
1296C2—48no—
1297C2—44no—
1298C2—84no—
1299C2C2×#241811yescharacteristic
1300C2#3597611yescharacteristic
1301C2#3607511yescharacteristic
1302C2#3616211yescharacteristic
1303C2#3621611yescharacteristic
1304C2#3903411yescharacteristic
1305C2#4257511yescharacteristic
1306C2#4505711yescharacteristic
1307C2#4517111yescharacteristic
1308C2#4518711yescharacteristic
1309C2#4526311yescharacteristic
1310C2#5903011yescharacteristic
1311C2#5913111yescharacteristic
1312C2#5941611yescharacteristic
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×#2421C2semidirect
3. C2×#2367C2semidirect
5. #16273C2semidirect
6. #15556C2semidirect
7. #15380C2semidirect
8. #15284C2semidirect
9. #15282C2semidirect
10. #15226C2semidirect
11. #15179C2semidirect
12. #15148C2semidirect
13. #14798C2semidirect
14. #14727C2semidirect
15. #14027C2semidirect
16. #14026C2semidirect
17. #14002C2semidirect
18. #13994C2semidirect
19. #13979C2semidirect
20. #13920C2semidirect
22. #13873C2semidirect
23. C4×#397C2semidirect
28. C22×C4×Q8C22semidirect
34. C2×#400C22semidirect
35. C2×#399C22semidirect
42. C2×#391C22semidirect
43. C2×#391C22semidirect
44. C2×#391C22semidirect
53. C2×#389C22semidirect
54. C2×#389C22semidirect
55. C2×#389C22semidirect
58. C2×#388C22semidirect
59. C2×#388C22semidirect
60. C2×#387C22semidirect
63. C2×#385C22semidirect
64. C2×#382C22semidirect
67. C2×#380C22semidirect
73. C2×C4×C4⋊C4C22semidirect
74. C2×C4×C4⋊C4C22semidirect
78. C2×C4×C22⋊C4C22semidirect
79. #1445C22semidirect
80. #1443C22semidirect
81. #1443C22semidirect
82. #1442C22semidirect
83. #1442C22semidirect
84. #1442C22semidirect
85. #1441C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. C4⋊#95C22semidirect
116. C4⋊#95C22semidirect
117. C4⋊#95C22semidirect
118. #1434C22semidirect
119. C22⋊#95C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C4×#95C22semidirect
125. C4×#95C22semidirect
126. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24212
C2×#24352
C2×#23672
C2×D4×C22⋊C42
#162732
#155562
#153802
#152842
#152822
#152262
#151792
#151482
#147982
#147272
#140272
#140262
#140022
#139942
#139792
#139202
#139022
#138732
C4×#3972