Finite Group Databasebeta

← #648754

Subgroups — #648754

Order 512.

4122 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C2×#2421C211yesmaximal, characteristic, complemented
3C2×#2360C211yesmaximal, characteristic, complemented
4C22×#380C211yesmaximal, characteristic
5#15960C212yesmaximal, complemented
6#15956C212yesmaximal, complemented
7#15296C212yesmaximal, complemented
8#15290C212yesmaximal, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15223C211yesmaximal, characteristic, complemented
11#15179C211yesmaximal, characteristic, complemented
12#15132C211yesmaximal, characteristic, complemented
13#14738C212yesmaximal, complemented
14#14727C212yesmaximal
15#14139C211yesmaximal, characteristic, complemented
16#14028C212yesmaximal, complemented
17#13974C211yesmaximal, characteristic, complemented
18#13969C211yesmaximal, characteristic, complemented
19#13907C211yesmaximal, characteristic, complemented
20#13881C211yesmaximal, characteristic, complemented
21#13875C211yesmaximal, characteristic, complemented
22#13873C212yesmaximal
23C4×#379C211yesmaximal, characteristic
24C25×C4C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic, complemented
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2212yes—
32#2848—28no—
33#2421—28no—
34C2×#400C2212yescomplemented
35C2×#397C2212yes—
36C2×#397C2212yes—
37#2360—28no—
38C2×#391C2211yescharacteristic, complemented
39C2×#391C2211yescharacteristic, complemented
40C2×#391C2211yescharacteristic, complemented
41C2×#389C2211yescharacteristic, complemented
42C2×#389C2211yescharacteristic, complemented
43C2×#389C2212yescomplemented
44C2×#389C2211yescharacteristic, complemented
45C2×#388C2212yes—
46C2×#388C2212yes—
47C2×#387C2212yescomplemented
48C2×#387C2212yescomplemented
49C2×#385C2212yes—
50C2×#385C2212yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#382C2211yescharacteristic, complemented
54C2×#382C2211yescharacteristic, complemented
55C2×#380—28no—
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2212yes—
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2212yes—
64C2×#380C2212yes—
65C2×#380C2211yescharacteristic
66C2×#379C2212yes—
67C2×#379C2211yescharacteristic
68C2×#379C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic, complemented
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2212yes—
72C2×C4×C22⋊C4C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75C2×C4×C22⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C22×#95C2212yes—
78#1445C2212yescomplemented
79#1445C2212yescomplemented
80#1443C2212yescomplemented
81#1443C2212yescomplemented
82#1443C2212yescomplemented
83#1442C2212yescomplemented
84#1442C2212yescomplemented
85#1442C2212yescomplemented
86#1442C2212yescomplemented
87#1442C2212yescomplemented
88#1442C2212yescomplemented
89#1441C2212yescomplemented
90#1441C2212yescomplemented
91#1441C2212yescomplemented
92#1441C2212yescomplemented
93#1441C2212yescomplemented
94#1441C2212yescomplemented
95#1440C2212yes—
96#1440C2212yes—
97#1440C2212yes—
98#1440C2212yes—
99#1440C2212yes—
100#1440C2212yes—
101#1439C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1437C2212yes—
106#1437C2212yes—
107#1436C2212yescomplemented
108#1436C2212yescomplemented
109C4⋊#95C2211yescharacteristic, complemented
110C4⋊#95C2211yescharacteristic, complemented
111C4⋊#95C2211yescharacteristic, complemented
112C4⋊#95C2211yescharacteristic, complemented
113C4⋊#95C2211yescharacteristic, complemented
114C4⋊#95C2211yescharacteristic, complemented
115#1434C2212yescomplemented
116C22⋊#95C2212yes—
117C22⋊#95C2212yes—
118C22⋊#95C2212yes—
119C22⋊#95C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C26C2311yescharacteristic
128C23×Q8C2311yescharacteristic
129C24×C4—24no—
130C24×C4—24no—
131C24×C4—24no—
132C24×C4—24no—
133C24×C4—24no—
134C24×C4—42no—
135C24×C4—42no—
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2312yes—
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144C2×C22⋊Q8—24no—
145C2×C22⋊Q8—24no—
146C2×C22⋊Q8—24no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—42no—
151C2×C22⋊Q8—42no—
152C2×C22⋊Q8D418yes—
153C2×C4×Q8—24no—
154C2×C4×Q8—24no—
155C2×C4×Q8—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⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C22⋊C4—28no—
179C22×C22⋊C4—28no—
180C22×C22⋊C4—44no—
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C42C2311yescharacteristic
204C22×C42C2311yescharacteristic
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2312yes—
208C22×C42C2312yes—
209#400—28no—
210#397—28no—
211#397—44no—
212#391—24no—
213#391—24no—
214#391—42no—
215#389—24no—
216#389—28no—
217#389—24no—
218#389—42no—
219#388—28no—
220#388—44no—
221#387—28no—
222#387—28no—
223#385—28no—
224#385—28no—
225#385—28no—
226#385—28no—
227#382—24no—
228#382—42no—
229#380—24no—
230#380—24no—
231#380—24no—
232#380—24no—
233#380—24no—
234#380—24no—
235#380—28no—
236#380—28no—
237#380—28no—
238#380D418yes—
239#379—24no—
240#379—28no—
241#379—24no—
242C4×C4⋊C4—24no—
243C4×C22⋊C4—24no—
244C4×C22⋊C4—24no—
245C4×C22⋊C4—24no—
246C4×C22⋊C4—24no—
247C4×C22⋊C4—28no—
248C4×C22⋊C4—42no—
249C4×C22⋊C4—42no—
250C2×#95—28no—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2311yescharacteristic
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2311yescharacteristic
258C2×#95C2311yescharacteristic
259C2×#95C2311yescharacteristic
260C2×#95C2311yescharacteristic
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C25—22no—
297C25—22no—
298C25—22no—
299C25—22no—
300C25—22no—
301C25—22no—
302C25—22no—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—41no—
307C25—41no—
308C25—41no—
309C25—41no—
310C25#4114yes—
311C25C2411yescharacteristic
312C25C2411yescharacteristic
313C25C2411yescharacteristic
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8C2×D414yes—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—232no—
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—22no—
335C23×C4—22no—
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—24no—
350C23×C4—24no—
351C23×C4—24no—
352C23×C4—24no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—41no—
362C23×C4—41no—
363C23×C4—41no—
364C23×C4—41no—
365C23×C4—41no—
366C23×C4—41no—
367C23×C4—416no—
368C23×C4—416no—
369C23×C4—416no—
370C23×C4—416no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4—42no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—416no—
378C23×C4—416no—
379C23×C4C2×D414yes—
380C23×C4C2×D414yes—
381C23×C4#4114yes—
382C23×C4#4114yes—
383C23×C4#4114yes—
384C23×C4C2411yescharacteristic
385C23×C4C2412yes—
386C23×C4C2412yes—
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2411yescharacteristic
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C22⋊Q8—232no—
405C22⋊Q8—416no—
406C22⋊Q8—416no—
407C4×Q8—416no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—416no—
443C2×C4⋊C4—416no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
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⋊C4C2×D414yes—
455C2×C4⋊C4C2×D414yes—
456C2×C4⋊C4C2×D414yes—
457C2×C4⋊C4C2×D418yes—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—432no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—41no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—41no—
514C2×C22⋊C4—41no—
515C2×C22⋊C4—41no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4—41no—
520C2×C22⋊C4—41no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4C2×D418yes—
523C2×C22⋊C4C2×D418yes—
524C2×C22⋊C4#4114yes—
525C2×C42—24no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—24no—
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—22no—
539C2×C42—24no—
540C2×C42—42no—
541C2×C42—42no—
542C2×C42—42no—
543#95—24no—
544#95—24no—
545#95—24no—
546#95—22no—
547#95—22no—
548#95—24no—
549#95—22no—
550#95—24no—
551#95—22no—
552#95—24no—
553#95—24no—
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—22no—
563#95—22no—
564#95—22no—
565#95—22no—
566#95—24no—
567#95—24no—
568#95—42no—
569#95—42no—
570#95—42no—
571#95—42no—
572#95—42no—
573#95—41no—
574#95—41no—
575#95—41no—
576#95—41no—
577#95—42no—
578#95—42no—
579#95—42no—
580#95—42no—
581#95—42no—
582#95—42no—
583#95—42no—
584#95—42no—
585#95—42no—
586#95—42no—
587#95C2×D418yes—
588C24—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24—21no—
593C24—21no—
594C24—21no—
595C24—21no—
596C24—28no—
597C24—28no—
598C24—28no—
599C24—28no—
600C24—28no—
601C24—28no—
602C24—28no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
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—28no—
628C24—28no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24—44no—
634C24—44no—
635C24—44no—
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—
655C24C22×D412yes—
656C24C22×D412yes—
657C24C2×#4112yes—
658C24C2×#4112yes—
659C24C2×#4112yes—
660C24C2×#4112yes—
661C24C2×#4112yes—
662C24C2×#4112yes—
663C24C2×#4112yes—
664C24H(5,𝔽2)12yes—
665C242−1+412yes—
666C242−1+412yes—
667C242−1+412yes—
668C24C2511yescharacteristic
669C2×Q8—28no—
670C2×Q8—28no—
671C2×Q8—28no—
672C2×Q8—44no—
673C2×Q8—44no—
674C2×Q8—44no—
675C2×Q8—44no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—28no—
683C22×C4—28no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—28no—
687C22×C4—28no—
688C22×C4—28no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—22no—
729C22×C4—21no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—21no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—21no—
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—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—4128no—
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—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—84no—
849C22×C4—84no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—84no—
853C22×C4—84no—
854C22×C4#123116yes—
855C22×C4C22×D412yes—
856C22×C4C22×D414yes—
857C22×C4C22×D414yes—
858C22×C4C22×D414yes—
859C22×C4C22×D414yes—
860C22×C4C22×D412yes—
861C22×C4C22×D412yes—
862C22×C4C22×D412yes—
863C22×C4C2×#4112yes—
864C22×C4C2×#4112yes—
865C22×C4C2×#4112yes—
866C22×C4C2×#4112yes—
867C22×C4C2×#4112yes—
868C22×C4C2×#4112yes—
869C22×C4C2×#4112yes—
870C22×C4C2×#4112yes—
871C22×C4H(5,𝔽2)12yes—
872C22×C4H(5,𝔽2)12yes—
873C4⋊C4—28no—
874C4⋊C4—216no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—84no—
888C4⋊C4—84no—
889C22⋊C4—216no—
890C22⋊C4—216no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C42—48no—
912C42—44no—
913C42—44no—
914C42—44no—
915C42—44no—
916C42—84no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
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—232no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
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—416no—
983C23—416no—
984C23—416no—
985C23—416no—
986C23—416no—
987C23—416no—
988C23—416no—
989C23—416no—
990C23—416no—
991C23—416no—
992C23—416no—
993C23—416no—
994C23—416no—
995C23—41no—
996C23—41no—
997C23—416no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
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—
1028C23C2×#12314yes—
1029C23#52914yes—
1030C23#54114yes—
1031C23#54614yes—
1032C23#54814yes—
1033C23#54814yes—
1034C23#55214yes—
1035C23#55214yes—
1036C23#55614yes—
1037C23C23×D411yescharacteristic
1038C23C23×D411yescharacteristic
1039C23C22×#4111yescharacteristic
1040C23C22×#4111yescharacteristic
1041C23C22×#4111yescharacteristic
1042C23C22×#4111yescharacteristic
1043C23C22×#4111yescharacteristic
1044C23C2×H(5,𝔽2)11yescharacteristic
1045C23C2×H(5,𝔽2)11yescharacteristic
1046C23C2×H(5,𝔽2)11yescharacteristic
1047C23C2×2−1+411yescharacteristic
1048C23C2×2−1+411yescharacteristic
1049C23C2×2−1+411yescharacteristic
1050C23#58511yescharacteristic
1051C23#58511yescharacteristic
1052Q8—416no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—232no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—416no—
1085C2×C4—416no—
1086C2×C4—416no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—42no—
1090C2×C4—42no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—42no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—42no—
1100C2×C4—42no—
1101C2×C4—41no—
1102C2×C4—42no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—42no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—42no—
1109C2×C4—42no—
1110C2×C4—42no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—42no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—416no—
1120C2×C4—416no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—42no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—816no—
1192C2×C4—816no—
1193C2×C4C2×#12314yes—
1194C2×C4C2×#12314yes—
1195C2×C4#52514yes—
1196C2×C4#53814yes—
1197C2×C4D4214yes—
1198C2×C4#54614yes—
1199C2×C4#54614yes—
1200C2×C4#55114yes—
1201C22—24no—
1202C22—24no—
1203C22—24no—
1204C22—24no—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—24no—
1211C22—24no—
1212C22—24no—
1213C22—24no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—464no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
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#242118yescomplemented
1247C22C22×#12311yescharacteristic
1248C22C2×#52511yescharacteristic
1249C22C2×#52911yescharacteristic
1250C22C2×#53811yescharacteristic
1251C22C2×#54111yescharacteristic
1252C22C2×D4211yescharacteristic
1253C22C2×#54611yescharacteristic
1254C22C2×#54611yescharacteristic
1255C22C2×#54611yescharacteristic
1256C22C2×#54811yescharacteristic
1257C22C2×#54811yescharacteristic
1258C22D4×#4111yescharacteristic
1259C22C2×#55111yescharacteristic
1260C22C2×#55211yescharacteristic
1261C22C2×#55211yescharacteristic
1262C22C2×#55611yescharacteristic
1263C22#347511yescharacteristic
1264C22#348611yescharacteristic
1265C22#348811yescharacteristic
1266C22#348911yescharacteristic
1267C22#348911yescharacteristic
1268C22#349211yescharacteristic
1269C22#349211yescharacteristic
1270C22#349311yescharacteristic
1271C22#349411yescharacteristic
1272C22#349511yescharacteristic
1273C22#349511yescharacteristic
1274C22#350511yescharacteristic
1275C22#350511yescharacteristic
1276C22#351911yescharacteristic
1277C22#352011yescharacteristic
1278C22#353611yescharacteristic
1279C22#353811yescharacteristic
1280C22#354111yescharacteristic
1281C22#354111yescharacteristic
1282C4—24no—
1283C4—44no—
1284C4—42no—
1285C4—42no—
1286C4—44no—
1287C4—44no—
1288C4—42no—
1289C4—42no—
1290C4—44no—
1291C4—82no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—82no—
1297C4—82no—
1298C4—81no—
1299C4—82no—
1300C4—81no—
1301C4#241818yes—
1302C2—28no—
1303C2—44no—
1304C2—44no—
1305C2C2×#241811yescharacteristic
1306C2C2×#242111yescharacteristic
1307C2#3551611yescharacteristic
1308C2#3610711yescharacteristic
1309C2#3616311yescharacteristic
1310C2#3616711yescharacteristic
1311C2#3643911yescharacteristic
1312C2#3766311yescharacteristic
1313C2#3785011yescharacteristic
1314C2#3915411yescharacteristic
1315C2#3947711yescharacteristic
1316C2#5899611yescharacteristic
1317C2#5900511yescharacteristic
1318C2#5901411yescharacteristic
1319C2#5902411yescharacteristic
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
2. C2×#2421C2semidirect
3. C2×#2360C2semidirect
5. #15960C2semidirect
6. #15956C2semidirect
7. #15296C2semidirect
8. #15290C2semidirect
9. #15236C2semidirect
10. #15223C2semidirect
11. #15179C2semidirect
12. #15132C2semidirect
13. #14738C2semidirect
15. #14139C2semidirect
16. #14028C2semidirect
17. #13974C2semidirect
18. #13969C2semidirect
19. #13907C2semidirect
20. #13881C2semidirect
21. #13875C2semidirect
28. C22×C4×Q8C22semidirect
34. C2×#400C22semidirect
38. C2×#391C22semidirect
39. C2×#391C22semidirect
40. C2×#391C22semidirect
41. C2×#389C22semidirect
42. C2×#389C22semidirect
43. C2×#389C22semidirect
44. C2×#389C22semidirect
47. C2×#387C22semidirect
48. C2×#387C22semidirect
53. C2×#382C22semidirect
54. C2×#382C22semidirect
69. C2×C4×C4⋊C4C22semidirect
78. #1445C22semidirect
79. #1445C22semidirect
80. #1443C22semidirect
81. #1443C22semidirect
82. #1443C22semidirect
83. #1442C22semidirect
84. #1442C22semidirect
85. #1442C22semidirect
86. #1442C22semidirect
87. #1442C22semidirect
88. #1442C22semidirect
89. #1441C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
92. #1441C22semidirect
93. #1441C22semidirect
94. #1441C22semidirect
107. #1436C22semidirect
108. #1436C22semidirect
109. C4⋊#95C22semidirect
110. C4⋊#95C22semidirect
111. C4⋊#95C22semidirect
112. C4⋊#95C22semidirect
113. C4⋊#95C22semidirect
114. C4⋊#95C22semidirect
115. #1434C22semidirect
1246. C22#2421semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#24212
C2×#23602
C22×#3802
#159602
#159562
#152962
#152902
#152362
#152232
#151792
#151322
#147382
#147272
#141392
#140282
#139742
#139692
#139072
#138812
#138752
#138732
C4×#3792