Finite Group Databasebeta

← #920689

Subgroups — #920689

Order 512.

4305 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2410C211yesmaximal, characteristic
2C22×#394C211yesmaximal, characteristic, complemented
3#17193C212yesmaximal, complemented
4#17087C212yesmaximal, complemented
5#16512C212yesmaximal, complemented
6#16465C212yesmaximal, complemented
7#16426C212yesmaximal, complemented
8#16259C212yesmaximal, complemented
9#15383C212yesmaximal, complemented
10#15312C212yesmaximal, complemented
11#15092C211yesmaximal, characteristic, complemented
12#15091C211yesmaximal, characteristic, complemented
13#14727C211yesmaximal, characteristic, complemented
14#14718C211yesmaximal, characteristic, complemented
15#14718C211yesmaximal, characteristic, complemented
16#14718C211yesmaximal, characteristic, complemented
17#14265C211yesmaximal, characteristic, complemented
18#14259C211yesmaximal, characteristic, complemented
19#14134C211yesmaximal, characteristic, complemented
20#14127C211yesmaximal, characteristic, complemented
21#13877C211yesmaximal, characteristic, complemented
22#13869C211yesmaximal, characteristic, complemented
23#13867C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×#120C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2410—28no—
37C2×#397C2212yescomplemented
38C2×#394—28no—
39C2×#394C2212yes—
40C2×#394C2211yescharacteristic
41C2×#394C2212yes—
42C2×#394C2212yes—
43C2×#394C2211yescharacteristic
44C2×#394C2212yes—
45C2×#394C2212yescomplemented
46C2×#394C2212yescomplemented
47C2×#394C2212yescomplemented
48C2×#392C2211yescharacteristic
49C2×#392C2211yescharacteristic
50C2×#386C2211yescharacteristic
51C2×#386C2211yescharacteristic
52C2×#386C2211yescharacteristic
53C2×#386C2211yescharacteristic
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#386C2211yescharacteristic
57C2×#386C2211yescharacteristic
58C2×#386C2211yescharacteristic
59C2×#386C2212yescomplemented
60C2×#385C2211yescharacteristic
61C2×#385C2211yescharacteristic
62C2×#385C2211yescharacteristic
63C2×#385C2211yescharacteristic
64C2×#385C2211yescharacteristic
65C2×#385C2212yescomplemented
66C2×#381C2212yescomplemented
67C2×#380C2212yescomplemented
68C2×#379C2211yescharacteristic
69C2×#379C2211yescharacteristic
70C2×#379C2211yescharacteristic
71C2×#379C2211yescharacteristic
72C22×#95C2211yescharacteristic
73#1445C2212yescomplemented
74#1444C2212yescomplemented
75#1444C2212yescomplemented
76#1443C2212yescomplemented
77#1443C2212yescomplemented
78#1442C2212yescomplemented
79#1442C2212yescomplemented
80#1442C2212yescomplemented
81#1442C2212yescomplemented
82#1441C2212yescomplemented
83#1441C2212yescomplemented
84#1441C2212yescomplemented
85#1440C2212yescomplemented
86#1440C2212yescomplemented
87#1440C2212yescomplemented
88#1440C2212yescomplemented
89#1440C2212yescomplemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yescomplemented
108#1438C2212yescomplemented
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111C22⋊#95C2211yescharacteristic
112C22⋊#95C2211yescharacteristic
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—42no—
128C23×D4—42no—
129C23×D4—44no—
130C23×D4—44no—
131C23×D4D418yes—
132C23×D4C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2312yes—
148C24×C4C2311yescharacteristic
149C2×#121—24no—
150C2×#121—24no—
151C2×#121—44no—
152C2×#121—44no—
153C2×#120—24no—
154C2×#120—24no—
155C2×#120—24no—
156C2×#120—42no—
157C2×#120—42no—
158C2×#120—42no—
159C22×C4⋊C4—24no—
160C22×C4⋊C4—42no—
161C22×C4⋊C4—42no—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C22⋊C4—24no—
171C22×C22⋊C4—24no—
172C22×C22⋊C4—24no—
173C22×C22⋊C4—24no—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—44no—
178C22×C22⋊C4—44no—
179C22×C22⋊C4—42no—
180C22×C22⋊C4—42no—
181C22×C22⋊C4—42no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222#397—44no—
223#394—28no—
224#394—28no—
225#394—28no—
226#394—28no—
227#394—24no—
228#394—24no—
229#394—44no—
230#394—44no—
231#394—44no—
232#392—24no—
233#392—24no—
234#386—24no—
235#386—24no—
236#386—24no—
237#386—24no—
238#386—44no—
239#386—42no—
240#386—42no—
241#386—42no—
242#386—44no—
243#386—44no—
244#385—24no—
245#385—24no—
246#385—42no—
247#385—42no—
248#385—42no—
249#385—44no—
250#381—44no—
251#380—44no—
252#379—24no—
253#379—24no—
254#379—42no—
255#379—42no—
256C2×#95—24no—
257C2×#95C2311yescharacteristic
258C2×#95C2311yescharacteristic
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2312yes—
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×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C25—24no—
292C25—24no—
293C25—22no—
294C25—22no—
295C25—22no—
296C25—22no—
297C25—22no—
298C25—22no—
299C25—22no—
300C25—22no—
301C25—22no—
302C25—22no—
303C25—22no—
304C25—22no—
305C25—42no—
306C25—42no—
307C25—42no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25C2×D414yes—
312C25C2×D414yes—
313C25C2411yescharacteristic
314C25C2411yescharacteristic
315C25C2411yescharacteristic
316C25C2411yescharacteristic
317C25C2411yescharacteristic
318C25C2411yescharacteristic
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—24no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—416no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4—42no—
343C22×D4—41no—
344C22×D4—41no—
345C22×D4—41no—
346C22×D4—41no—
347C22×D4—41no—
348C22×D4—41no—
349C22×D4—41no—
350C22×D4—41no—
351C22×D4—41no—
352C22×D4—41no—
353C22×D4—41no—
354C22×D4—41no—
355C22×D4—41no—
356C22×D4—41no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—416no—
364C22×D4—416no—
365C22×D4—432no—
366C22×D4—432no—
367C22×D4C2×D414yes—
368C22×D4C2×D414yes—
369C22×D4C2×D414yes—
370C22×D4C2×D414yes—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—24no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—24no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—24no—
392C23×C4—22no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—41no—
399C23×C4—41no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4C2×D414yes—
413C23×C4C2412yes—
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418C23×C4C2412yes—
419C23×C4C2411yescharacteristic
420C23×C4C2412yes—
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2412yes—
430#121—416no—
431#121—416no—
432#120—416no—
433#120—416no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
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—416no—
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⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
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—22no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
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—24no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—416no—
518C2×C22⋊C4—416no—
519C2×C22⋊C4—41no—
520C2×C22⋊C4—41no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
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—41no—
533C2×C22⋊C4—41no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—41no—
536C2×C22⋊C4—41no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—416no—
542C2×C22⋊C4—416no—
543C2×C22⋊C4—416no—
544C2×C22⋊C4—416no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4#4114yes—
570C2×C22⋊C4#4114yes—
571#95—24no—
572#95—24no—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—24no—
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#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—22no—
614C24—22no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—22no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—22no—
623C24—21no—
624C24—21no—
625C24—22no—
626C24—22no—
627C24—28no—
628C24—28no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—21no—
641C24—21no—
642C24—22no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—28no—
650C24—28no—
651C24—28no—
652C24—28no—
653C24—28no—
654C24—28no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—22no—
666C24—44no—
667C24—44no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—44no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—44no—
685C24—44no—
686C24—44no—
687C24—44no—
688C24—44no—
689C24—44no—
690C24—44no—
691C24—44no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24C22×D412yes—
705C24C22×D412yes—
706C24C22×D412yes—
707C24C22×D412yes—
708C24C22×D412yes—
709C24C2×#4112yes—
710C24C2×#4112yes—
711C24H(5,𝔽2)14yes—
712C24H(5,𝔽2)14yes—
713C24H(5,𝔽2)12yes—
714C24H(5,𝔽2)12yes—
715C24H(5,𝔽2)12yes—
716C242−1+412yes—
717C24C2511yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—4128no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—84no—
756C2×D4—82no—
757C2×D4—82no—
758C2×D4—84no—
759C2×D4—82no—
760C2×D4—82no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
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—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—44no—
875C22×C4—48no—
876C22×C4—48no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4—82no—
892C22×C4—82no—
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—
905C22×C4C22×D412yes—
906C22×C4C22×D412yes—
907C22×C4C2×#4112yes—
908C22×C4C2×#4114yes—
909C22×C4C2×#4112yes—
910C22×C4H(5,𝔽2)14yes—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—84no—
916C4⋊C4—84no—
917C4⋊C4—84no—
918C4⋊C4—84no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—84no—
947C22⋊C4—84no—
948C22⋊C4—84no—
949C22⋊C4—82no—
950C22⋊C4—82no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—416no—
1012C23—416no—
1013C23—416no—
1014C23—416no—
1015C23—416no—
1016C23—416no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—41no—
1028C23—41no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—41no—
1038C23—41no—
1039C23—416no—
1040C23—416no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—41no—
1054C23—41no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—41no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—88no—
1095C23—88no—
1096C23—88no—
1097C23—88no—
1098C23—88no—
1099C23—88no—
1100C23—816no—
1101C23—816no—
1102C23—816no—
1103C23—816no—
1104C23—816no—
1105C23—816no—
1106C23—816no—
1107C23—816no—
1108C23#53414yes—
1109C23#53414yes—
1110C23#53414yes—
1111C23#53814yes—
1112C23#54214yes—
1113C23#54614yes—
1114C23#54714yes—
1115C23#55514yes—
1116C23#56214yes—
1117C23C23×D411yescharacteristic
1118C23C22×#4111yescharacteristic
1119C23C22×#4111yescharacteristic
1120C23C2×H(5,𝔽2)11yescharacteristic
1121C23C2×H(5,𝔽2)11yescharacteristic
1122C23C2×H(5,𝔽2)12yes—
1123C23C2×H(5,𝔽2)12yes—
1124C23C2×H(5,𝔽2)11yescharacteristic
1125C23C2×H(5,𝔽2)12yes—
1126C23C2×2−1+411yescharacteristic
1127C23#58512yes—
1128D4—416no—
1129D4—416no—
1130D4—416no—
1131D4—416no—
1132D4—88no—
1133D4—88no—
1134D4—88no—
1135D4—88no—
1136D4—88no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—416no—
1154C2×C4—416no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
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—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—41no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—88no—
1243C2×C4—816no—
1244C2×C4—88no—
1245C2×C4—88no—
1246C2×C4—88no—
1247C2×C4—88no—
1248C22—28no—
1249C22—24no—
1250C22—28no—
1251C22—28no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—28no—
1257C22—24no—
1258C22—24no—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—24no—
1263C22—24no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—44no—
1277C22—44no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—832no—
1295C22—832no—
1296C22—82no—
1297C22—82no—
1298C22—82no—
1299C22—82no—
1300C22—82no—
1301C22—82no—
1302C22—82no—
1303C22—82no—
1304C22—82no—
1305C22—81no—
1306C22—82no—
1307C22—82no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—82no—
1314C22—81no—
1315C22#268618yes—
1316C22C2×#53411yescharacteristic
1317C22C2×#53411yescharacteristic
1318C22C2×#53411yescharacteristic
1319C22C2×#53811yescharacteristic
1320C22C2×#54211yescharacteristic
1321C22C2×#54611yescharacteristic
1322C22C2×#54711yescharacteristic
1323C22C2×#55511yescharacteristic
1324C22#348411yescharacteristic
1325C22#348511yescharacteristic
1326C22#351312yes—
1327C22#351312yes—
1328C22#351912yes—
1329C22#351912yes—
1330C22C2×#56211yescharacteristic
1331C22#353212yes—
1332C22#353212yes—
1333C22#353412yes—
1334C22#353412yes—
1335C22#353412yes—
1336C22#353512yes—
1337C22#353612yes—
1338C22#353712yes—
1339C4—42no—
1340C4—42no—
1341C4—44no—
1342C4—42no—
1343C4—42no—
1344C4—44no—
1345C4—82no—
1346C4—82no—
1347C4—81no—
1348C4—82no—
1349C4—81no—
1350C4—82no—
1351C4—81no—
1352C4—81no—
1353C4—82no—
1354C4—82no—
1355C4—81no—
1356C2—28no—
1357C2—44no—
1358C2—44no—
1359C2—82no—
1360C2—82no—
1361C2—161no—
1362C2#3711711yescharacteristic
1363C2#3743611yescharacteristic
1364C2#3802011yescharacteristic
1365C2#3802211yescharacteristic
1366C2#3803611yescharacteristic
1367C2#3803811yescharacteristic
1368C2#4078312yes—
1369C2#4078512yes—
1370C2#4326512yes—
1371C2C2×#268611yescharacteristic
1372C2#5239412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2410C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×#394C2semidirect
3. #17193C2semidirect
4. #17087C2semidirect
5. #16512C2semidirect
6. #16465C2semidirect
7. #16426C2semidirect
8. #16259C2semidirect
9. #15383C2semidirect
10. #15312C2semidirect
11. #15092C2semidirect
12. #15091C2semidirect
13. #14727C2semidirect
14. #14718C2semidirect
15. #14718C2semidirect
16. #14718C2semidirect
17. #14265C2semidirect
18. #14259C2semidirect
19. #14134C2semidirect
20. #14127C2semidirect
21. #13877C2semidirect
22. #13869C2semidirect
23. #13867C2semidirect
37. C2×#397C22semidirect
45. C2×#394C22semidirect
46. C2×#394C22semidirect
47. C2×#394C22semidirect
59. C2×#386C22semidirect
65. C2×#385C22semidirect
66. C2×#381C22semidirect
67. C2×#380C22semidirect
73. #1445C22semidirect
74. #1444C22semidirect
75. #1444C22semidirect
76. #1443C22semidirect
77. #1443C22semidirect
78. #1442C22semidirect
79. #1442C22semidirect
80. #1442C22semidirect
81. #1442C22semidirect
82. #1441C22semidirect
83. #1441C22semidirect
84. #1441C22semidirect
85. #1440C22semidirect
86. #1440C22semidirect
87. #1440C22semidirect
88. #1440C22semidirect
89. #1440C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
107. #1438C22semidirect
108. #1438C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24102
C22×#3942
#171932
#170872
#165122
#164652
#164262
#162592
#153832
#153122
#150922
#150912
#147272
#147182
#142652
#142592
#141342
#141272
#138772
#138692
#138672