Finite Group Databasebeta

← #656510

Subgroups — #656510

Order 512.

5012 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2353C211yesmaximal, characteristic, complemented
2C22×#386C211yesmaximal, characteristic, complemented
3#16051C212yesmaximal, complemented
4#15450C212yesmaximal, complemented
5#15369C212yesmaximal, complemented
6#15334C212yesmaximal, complemented
7#14977C212yesmaximal, complemented
8#14921C211yesmaximal, characteristic, complemented
9#14820C211yesmaximal, characteristic, complemented
10#14814C212yesmaximal, complemented
11#14734C211yesmaximal, characteristic, complemented
12#14715C211yesmaximal, characteristic
13#14694C211yesmaximal, characteristic, complemented
14#14207C212yesmaximal, complemented
15#14082C212yesmaximal, complemented
16#14040C211yesmaximal, characteristic, complemented
17#13995C211yesmaximal, characteristic, complemented
18#13991C211yesmaximal, characteristic, complemented
19#13967C211yesmaximal, characteristic, complemented
20#13967C211yesmaximal, characteristic, complemented
21#13902C211yesmaximal, characteristic, complemented
22#13883C211yesmaximal, characteristic, complemented
23C4×#379C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#120C2211yescharacteristic
27C22×#120C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C2×#399C2212yescomplemented
33C2×#397C2212yescomplemented
34C2×#392C2212yes—
35C2×#392C2212yes—
36#2353—28no—
37C2×#390C2212yes—
38C2×#390C2212yes—
39C2×#390C2212yescomplemented
40C2×#388C2211yescharacteristic, complemented
41C2×#388C2211yescharacteristic, complemented
42C2×#388C2212yescomplemented
43C2×#387C2211yescharacteristic, complemented
44C2×#387C2211yescharacteristic, complemented
45C2×#386—28no—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2211yescharacteristic
49C2×#386C2211yescharacteristic
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#386C2211yescharacteristic
53C2×#386C2211yescharacteristic
54C2×#386C2212yescomplemented
55C2×#386C2212yescomplemented
56C2×#386C2212yescomplemented
57C2×#386C2212yescomplemented
58C2×#385C2211yescharacteristic
59C2×#385C2211yescharacteristic
60C2×#383C2211yescharacteristic, complemented
61C2×#381C2211yescharacteristic, complemented
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×#379C2211yescharacteristic
65C2×#379C2211yescharacteristic
66C2×#379C2211yescharacteristic
67C2×#379C2211yescharacteristic
68C2×#379C2211yescharacteristic
69C2×#379C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic, complemented
74C2×C4×C22⋊C4C2212yescomplemented
75C2×C4×C22⋊C4C2212yescomplemented
76C2×#376C2211yescharacteristic, complemented
77C22×#95C2211yescharacteristic
78C22×#95C2211yescharacteristic
79#1445C2212yescomplemented
80#1443C2212yescomplemented
81#1443C2212yescomplemented
82#1443C2212yescomplemented
83#1442C2212yescomplemented
84#1441C2212yescomplemented
85#1440C2212yescomplemented
86#1440C2212yescomplemented
87#1440C2212yescomplemented
88#1439C2212yescomplemented
89#1439C2212yescomplemented
90#1439C2212yescomplemented
91#1439C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yescomplemented
103#1438C2212yescomplemented
104#1438C2212yescomplemented
105#1437C2212yescomplemented
106#1437C2212yescomplemented
107#1437C2212yescomplemented
108#1437C2212yescomplemented
109#1436C2212yescomplemented
110#1436C2212yescomplemented
111#1434C2212yescomplemented
112#1434C2212yescomplemented
113C22⋊#95C2211yescharacteristic
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C26C2311yescharacteristic
126C26C2311yescharacteristic
127C23×D4—28no—
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—42no—
131C23×D4—44no—
132C23×D4C2311yescharacteristic
133C23×D4C2312yes—
134C23×D4C2312yes—
135C23×D4C2312yes—
136C23×D4C2312yes—
137C24×C4—24no—
138C24×C4—24no—
139C24×C4—44no—
140C24×C4—44no—
141C24×C4—42no—
142C24×C4C2311yescharacteristic
143C24×C4C2312yes—
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2312yes—
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C2×#120—24no—
151C2×#120—24no—
152C2×#120—24no—
153C2×#120—24no—
154C2×#120—42no—
155C2×#120—42no—
156C2×C4×D4—24no—
157C2×C4×D4—24no—
158C2×C4×D4—24no—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C22⋊C4—24no—
166C22×C22⋊C4—24no—
167C22×C22⋊C4—24no—
168C22×C22⋊C4—44no—
169C22×C22⋊C4—44no—
170C22×C22⋊C4—44no—
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2311yescharacteristic
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2312yes—
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211#399—44no—
212#397—44no—
213#392—28no—
214#392—44no—
215#390—28no—
216#390—44no—
217#390—44no—
218#388—24no—
219#388—24no—
220#388—44no—
221#387—24no—
222#387—24no—
223#386—24no—
224#386—24no—
225#386—28no—
226#386—28no—
227#386—28no—
228#386—28no—
229#386—44no—
230#386—44no—
231#386—44no—
232#386—44no—
233#386—42no—
234#386—42no—
235#385—24no—
236#385—42no—
237#383—24no—
238#381—24no—
239#380—24no—
240#380—42no—
241#379—24no—
242#379—24no—
243#379—24no—
244#379—42no—
245#379—42no—
246#379—42no—
247C4×C22⋊C4—24no—
248C4×C22⋊C4—24no—
249C4×C22⋊C4—24no—
250C4×C22⋊C4—44no—
251C4×C22⋊C4—44no—
252C4×C22⋊C4—42no—
253#376—24no—
254C2×#95—24no—
255C2×#95D418yescomplemented
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C25—22no—
295C25—24no—
296C25—24no—
297C25—22no—
298C25—22no—
299C25—22no—
300C25—24no—
301C25—22no—
302C25—22no—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—42no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25#4114yes—
316C25C2412yes—
317C25C2411yescharacteristic
318C25C2412yes—
319C25C2411yescharacteristic
320C22×D4—232no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—42no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—42no—
347C22×D4—416no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—432no—
356C22×D4—416no—
357C22×D4—432no—
358C22×D4#4114yes—
359C22×D4#4118yes—
360C23×C4—22no—
361C23×C4—24no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—416no—
402C23×C4—416no—
403C23×C4—432no—
404C23×C4—416no—
405C23×C4—432no—
406C23×C4C2×D414yes—
407C23×C4C2×D414yes—
408C23×C4C2×D414yes—
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2412yes—
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428#120—416no—
429#120—416no—
430C4×D4—232no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—42no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
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—24no—
506C2×C22⋊C4—24no—
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—416no—
521C2×C22⋊C4—416no—
522C2×C22⋊C4—416no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4#4114yes—
547C2×C22⋊C4#4114yes—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—24no—
554C2×C42—24no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—24no—
558C2×C42—42no—
559C2×C42—42no—
560C2×C42—42no—
561C2×C42—42no—
562#95—24no—
563#95—24no—
564#95—22no—
565#95—22no—
566#95—22no—
567#95—22no—
568#95—22no—
569#95—22no—
570#95—22no—
571#95—22no—
572#95—22no—
573#95—22no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—42no—
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#95—42no—
591#95—42no—
592#95—42no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95C2×D414yes—
597#95C2×D414yes—
598#95C2×D414yes—
599#95C2×D414yes—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—28no—
605C24—28no—
606C24—216no—
607C24—28no—
608C24—216no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—28no—
622C24—28no—
623C24—28no—
624C24—21no—
625C24—22no—
626C24—22no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—48no—
649C24—48no—
650C24—48no—
651C24—48no—
652C24—48no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24—48no—
657C24—48no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—48no—
663C24—44no—
664C24—44no—
665C24—48no—
666C24—44no—
667C24—44no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—44no—
672C24—44no—
673C24—44no—
674C24—44no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24—44no—
679C24—44no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24C22×D412yes—
687C24C2×#4114yes—
688C24C2×#4112yes—
689C24C2×#4114yes—
690C24C2×#4114yes—
691C24C2×#4112yes—
692C24C2×#4112yes—
693C24C2×#4112yes—
694C24C2×#4112yes—
695C24H(5,𝔽2)14yes—
696C24H(5,𝔽2)12yes—
697C24H(5,𝔽2)12yes—
698C24C2511yescharacteristic
699C2×D4—216no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—216no—
704C2×D4—216no—
705C2×D4—48no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—4128no—
717C2×D4—48no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—84no—
729C2×D4—84no—
730C2×D4—84no—
731C2×D4—84no—
732C2×D4—84no—
733C2×D4—84no—
734C2×D4—84no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—28no—
742C22×C4—216no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—22no—
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—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—44no—
860C22×C4—48no—
861C22×C4—4128no—
862C22×C4—48no—
863C22×C4—44no—
864C22×C4—48no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—82no—
869C22×C4—82no—
870C22×C4—84no—
871C22×C4—84no—
872C22×C4—84no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4C22×D412yes—
877C22×C4C22×D412yes—
878C22×C4C22×D412yes—
879C22×C4C22×D412yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C2×#4114yes—
883C22×C4C2×#4112yes—
884C22×C4C2×#4112yes—
885C22×C4C2×#4112yes—
886C22×C4C2×#4114yes—
887C22×C4H(5,𝔽2)14yes—
888C22×C4H(5,𝔽2)14yes—
889C4⋊C4—28no—
890C4⋊C4—84no—
891C4⋊C4—82no—
892C4⋊C4—82no—
893C4⋊C4—84no—
894C4⋊C4—84no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—82no—
919C22⋊C4—82no—
920C22⋊C4—84no—
921C22⋊C4—84no—
922C22⋊C4—84no—
923C22⋊C4—84no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—84no—
929C42—28no—
930C42—44no—
931C42—44no—
932C42—82no—
933C42—82no—
934C42—84no—
935C23—22no—
936C23—22no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—22no—
942C23—22no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—232no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—22no—
971C23—24no—
972C23—22no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—432no—
983C23—432no—
984C23—416no—
985C23—416no—
986C23—432no—
987C23—416no—
988C23—416no—
989C23—416no—
990C23—432no—
991C23—416no—
992C23—416no—
993C23—416no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—416no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—41no—
1012C23—42no—
1013C23—41no—
1014C23—42no—
1015C23—42no—
1016C23—41no—
1017C23—41no—
1018C23—42no—
1019C23—42no—
1020C23—41no—
1021C23—41no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—41no—
1034C23—41no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—816no—
1058C23—816no—
1059C23—816no—
1060C23—816no—
1061C23—88no—
1062C23—88no—
1063C23—88no—
1064C23—88no—
1065C23#52514yes—
1066C23#52914yes—
1067C23#54014yes—
1068C23#54614yes—
1069C23#55014yes—
1070C23#55118yes—
1071C23#55114yes—
1072C23#55114yes—
1073C23C23×D411yescharacteristic
1074C23C22×#4111yescharacteristic
1075C23C22×#4111yescharacteristic
1076C23C22×#4112yes—
1077C23C22×#4111yescharacteristic
1078C23C22×#4111yescharacteristic
1079C23C2×H(5,𝔽2)12yes—
1080C23C2×H(5,𝔽2)11yescharacteristic
1081C23C2×H(5,𝔽2)11yescharacteristic
1082C23C2×H(5,𝔽2)12yes—
1083C23C2×H(5,𝔽2)12yes—
1084D4—432no—
1085D4—432no—
1086D4—416no—
1087D4—816no—
1088D4—816no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—416no—
1123C2×C4—416no—
1124C2×C4—432no—
1125C2×C4—416no—
1126C2×C4—432no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—42no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—41no—
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—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—88no—
1202C2×C4—88no—
1203C2×C4—88no—
1204C2×C4#52514yes—
1205C2×C4#53514yes—
1206C22—24no—
1207C22—24no—
1208C22—28no—
1209C22—28no—
1210C22—24no—
1211C22—28no—
1212C22—24no—
1213C22—24no—
1214C22—24no—
1215C22—28no—
1216C22—28no—
1217C22—28no—
1218C22—28no—
1219C22—464no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—42no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—42no—
1238C22—44no—
1239C22—44no—
1240C22—42no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—832no—
1245C22—82no—
1246C22—81no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22—82no—
1252C22—82no—
1253C22—81no—
1254C22—81no—
1255C22—82no—
1256C22—81no—
1257C22—82no—
1258C22—82no—
1259C22#247118yes—
1260C22C2×#52511yescharacteristic
1261C22C2×#52511yescharacteristic
1262C22C2×#52911yescharacteristic
1263C22C2×#53511yescharacteristic
1264C22C2×#54011yescharacteristic
1265C22C2×#54611yescharacteristic
1266C22C2×#55011yescharacteristic
1267C22C2×#55112yes—
1268C22C2×#55111yescharacteristic
1269C22C2×#55111yescharacteristic
1270C22#348112yes—
1271C22#348112yes—
1272C22#348112yes—
1273C22#348411yescharacteristic
1274C22#348411yescharacteristic
1275C22#349012yes—
1276C22#349012yes—
1277C22#351912yes—
1278C22#351912yes—
1279C22#351912yes—
1280C22#351912yes—
1281C22#353212yes—
1282C22#353712yes—
1283C4—24no—
1284C4—24no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—44no—
1293C4—44no—
1294C4—82no—
1295C4—82no—
1296C4—82no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—82no—
1302C2—28no—
1303C2—48no—
1304C2—82no—
1305C2—84no—
1306C2C2×#247111yescharacteristic
1307C2#3496311yescharacteristic
1308C2#3535511yescharacteristic
1309C2#3615811yescharacteristic
1310C2#3624412yes—
1311C2#3652911yescharacteristic
1312C2#3783311yescharacteristic
1313C2#3851012yes—
1314C2#3913211yescharacteristic
1315C2#5926712yes—
1316C2#5937012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14715C2
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×#2353C2semidirect
2. C22×#386C2semidirect
3. #16051C2semidirect
4. #15450C2semidirect
5. #15369C2semidirect
6. #15334C2semidirect
7. #14977C2semidirect
8. #14921C2semidirect
9. #14820C2semidirect
10. #14814C2semidirect
11. #14734C2semidirect
13. #14694C2semidirect
14. #14207C2semidirect
15. #14082C2semidirect
16. #14040C2semidirect
17. #13995C2semidirect
18. #13991C2semidirect
19. #13967C2semidirect
20. #13967C2semidirect
21. #13902C2semidirect
22. #13883C2semidirect
23. C4×#379C2semidirect
32. C2×#399C22semidirect
33. C2×#397C22semidirect
39. C2×#390C22semidirect
40. C2×#388C22semidirect
41. C2×#388C22semidirect
42. C2×#388C22semidirect
43. C2×#387C22semidirect
44. C2×#387C22semidirect
54. C2×#386C22semidirect
55. C2×#386C22semidirect
56. C2×#386C22semidirect
57. C2×#386C22semidirect
60. C2×#383C22semidirect
61. C2×#381C22semidirect
73. C2×C4×C22⋊C4C22semidirect
74. C2×C4×C22⋊C4C22semidirect
75. C2×C4×C22⋊C4C22semidirect
76. C2×#376C22semidirect
79. #1445C22semidirect
80. #1443C22semidirect
81. #1443C22semidirect
82. #1443C22semidirect
83. #1442C22semidirect
84. #1441C22semidirect
85. #1440C22semidirect
86. #1440C22semidirect
87. #1440C22semidirect
88. #1439C22semidirect
89. #1439C22semidirect
90. #1439C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
102. #1438C22semidirect
103. #1438C22semidirect
104. #1438C22semidirect
105. #1437C22semidirect
106. #1437C22semidirect
107. #1437C22semidirect
108. #1437C22semidirect
109. #1436C22semidirect
110. #1436C22semidirect
111. #1434C22semidirect
112. #1434C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
255. C2×#95D4semidirect

Maximal subgroups

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

subgroupindex
C2×#23532
C22×#3862
#160512
#154502
#153692
#153342
#149772
#149212
#148202
#148142
#147342
#147152
#146942
#142072
#140822
#140402
#139952
#139912
#139672
#139022
#138832
C4×#3792