Finite Group Databasebeta

← #648570

Subgroups — #648570

Order 512.

5332 conjugacy classes of subgroups.

The subgroup lattice has 1357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2411C211yesmaximal, characteristic, complemented
2C2×#2419C211yesmaximal, characteristic, complemented
3C2×C4×#120C211yesmaximal, characteristic, complemented
4C22×#386C211yesmaximal, characteristic, complemented
5#15496C212yesmaximal, complemented
6#15461C212yesmaximal, complemented
7#15377C212yesmaximal, complemented
8#15330C212yesmaximal, complemented
9#15014C211yesmaximal, characteristic, complemented
10#14918C211yesmaximal, characteristic, complemented
11#14911C211yesmaximal, characteristic, complemented
12#14756C212yesmaximal, complemented
13#14730C212yesmaximal, complemented
14#14715C211yesmaximal, characteristic
15#14693C211yesmaximal, characteristic, complemented
16#14189C212yesmaximal, complemented
17#14034C212yesmaximal, complemented
18#14020C211yesmaximal, characteristic, complemented
19#13971C211yesmaximal, characteristic, complemented
20#13967C211yesmaximal, characteristic, complemented
21#13902C211yesmaximal, characteristic, complemented
22#13868C211yesmaximal, characteristic, complemented
23#13799C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#120C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2212yescomplemented
31C22×#117C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35#2419—28no—
36#2411—28no—
37C2×#400C2211yescharacteristic, complemented
38C2×#398C2211yescharacteristic, complemented
39C2×#397C2211yescharacteristic, complemented
40C2×#397C2211yescharacteristic, complemented
41C2×#396C2212yescomplemented
42C2×#394C2212yescomplemented
43C2×#392C2212yes—
44C2×#392C2212yes—
45C4×#120—28no—
46C2×#390C2212yes—
47C2×#390C2212yes—
48C2×#390C2212yescomplemented
49C2×#388C2212yescomplemented
50C2×#388C2212yescomplemented
51C2×#387C2211yescharacteristic, complemented
52C2×#387C2211yescharacteristic, complemented
53C2×#386—28no—
54C2×#386C2212yes—
55C2×#386C2211yescharacteristic
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#386C2211yescharacteristic
60C2×#386C2211yescharacteristic
61C2×#386C2212yescomplemented
62C2×#386C2212yescomplemented
63C2×#385C2211yescharacteristic
64C2×#385C2211yescharacteristic
65C2×#385C2211yescharacteristic
66C2×#385C2212yescomplemented
67C2×#385C2211yescharacteristic, complemented
68C2×#385C2212yescomplemented
69C2×#385C2212yescomplemented
70C2×#381C2211yescharacteristic
71C2×#381C2211yescharacteristic
72C2×#381C2211yescharacteristic, complemented
73C2×#380C2211yescharacteristic
74C2×#379C2211yescharacteristic
75C2×#379C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic
82C2×C4×C22⋊C4C2212yescomplemented
83C22×#95C2211yescharacteristic
84C22×#95C2211yescharacteristic
85#1445C2212yescomplemented
86#1444C2212yescomplemented
87#1443C2212yescomplemented
88#1442C2212yescomplemented
89#1442C2212yescomplemented
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#1438C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yescomplemented
107#1438C2212yescomplemented
108#1438C2212yescomplemented
109#1437C2212yescomplemented
110#1437C2212yescomplemented
111#1437C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116#1434C2212yescomplemented
117#1434C2212yescomplemented
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C4×#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×D4—28no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—42no—
133C23×D4—44no—
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2312yes—
139C24×C4—24no—
140C24×C4—24no—
141C24×C4—44no—
142C24×C4—42no—
143C24×C4—44no—
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2312yes—
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C2×#123—24no—
153C2×#123—24no—
154C2×#123—42no—
155C2×#120—24no—
156C2×#120—24no—
157C2×#120—24no—
158C2×#120—24no—
159C2×#120—24no—
160C2×#120—42no—
161C2×C4×D4—24no—
162C2×C4×D4—24no—
163C2×C4×D4—28no—
164C2×C4×D4—44no—
165C2×C4×D4—42no—
166C2×C4×D4—44no—
167C2×#117—24no—
168C2×#117—24no—
169C2×#117—42no—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—24no—
184C22×C22⋊C4—24no—
185C22×C22⋊C4—44no—
186C22×C22⋊C4—42no—
187C22×C22⋊C4—42no—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2312yes—
225C22×C42C2312yes—
226#400—24no—
227#398—24no—
228#397—24no—
229#397—24no—
230#396—28no—
231#394—28no—
232#392—28no—
233#392—44no—
234#390—28no—
235#390—28no—
236#390—44no—
237#388—28no—
238#388—44no—
239#387—24no—
240#387—24no—
241#386—24no—
242#386—28no—
243#386—28no—
244#386—28no—
245#386—28no—
246#386—28no—
247#386—44no—
248#386—42no—
249#386D418yescomplemented
250#385—24no—
251#385—24no—
252#385—24no—
253#385—24no—
254#385—28no—
255#385—44no—
256#385—44no—
257#381—24no—
258#381—24no—
259#381—24no—
260#380—24no—
261#379—24no—
262#379—24no—
263#379—24no—
264#379—24no—
265#379—42no—
266#379—42no—
267C4×C22⋊C4—24no—
268C4×C22⋊C4—28no—
269C4×C22⋊C4—42no—
270C2×#95—24no—
271C2×#95D418yescomplemented
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2312yes—
308C25—22no—
309C25—24no—
310C25—22no—
311C25—24no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—24no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25#4114yes—
330C25C2411yescharacteristic
331C25C2412yes—
332C25C2412yes—
333C25C2411yescharacteristic
334C22×D4—232no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—24no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—416no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—432no—
370C22×D4—416no—
371C22×D4—432no—
372C22×D4C2×D414yes—
373C22×D4#4118yes—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—24no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—24no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—22no—
401C23×C4—24no—
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×C4—416no—
413C23×C4—42no—
414C23×C4—41no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—432no—
418C23×C4—416no—
419C23×C4—416no—
420C23×C4—432no—
421C23×C4C2×D414yes—
422C23×C4C2×D414yes—
423C23×C4C2×D414yes—
424C23×C4C2×D414yes—
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2412yes—
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2412yes—
441C23×C4C2412yes—
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444#123—416no—
445#120—232no—
446#120—416no—
447C4×D4—416no—
448C4×D4—432no—
449#117—416no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—41no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—24no—
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—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—416no—
556C2×C22⋊C4—416no—
557C2×C22⋊C4—416no—
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—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4C2×D414yes—
576C2×C22⋊C4C2×D418yescomplemented
577C2×C22⋊C4#4114yes—
578C2×C22⋊C4#4114yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—24no—
584C2×C42—24no—
585C2×C42—24no—
586C2×C42—42no—
587C2×C42—42no—
588C2×C42—41no—
589C2×C42—42no—
590C2×C42—42no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—24no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—24no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95—42no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95C2×D414yes—
623#95C2×D414yes—
624#95C2×D414yes—
625#95C2×D414yes—
626#95C2×D418yescomplemented
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—28no—
632C24—28no—
633C24—216no—
634C24—28no—
635C24—216no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—28no—
649C24—28no—
650C24—28no—
651C24—21no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—21no—
666C24—22no—
667C24—22no—
668C24—21no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—44no—
691C24—44no—
692C24—48no—
693C24—44no—
694C24—44no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—44no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24—44no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24C22×D412yes—
714C24C22×D412yes—
715C24C22×D412yes—
716C24C2×#4114yes—
717C24C2×#4114yes—
718C24C2×#4114yes—
719C24C2×#4112yes—
720C24C2×#4112yes—
721C24C2×#4112yes—
722C24H(5,𝔽2)14yes—
723C24H(5,𝔽2)12yes—
724C24H(5,𝔽2)12yes—
725C24C2511yescharacteristic
726C2×D4—216no—
727C2×D4—216no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—216no—
732C2×D4—216no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—4128no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—44no—
757C2×D4—48no—
758C2×D4—84no—
759C2×D4—84no—
760C2×D4—84no—
761C2×D4—84no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—216no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—28no—
826C22×C4—28no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
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—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—21no—
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—44no—
872C22×C4—48no—
873C22×C4—44no—
874C22×C4—48no—
875C22×C4—48no—
876C22×C4—48no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—48no—
886C22×C4—48no—
887C22×C4—48no—
888C22×C4—44no—
889C22×C4—48no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—4128no—
895C22×C4—48no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—48no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—82no—
906C22×C4—84no—
907C22×C4—84no—
908C22×C4—84no—
909C22×C4C22×D412yes—
910C22×C4C22×D412yes—
911C22×C4C22×D412yes—
912C22×C4C22×D414yes—
913C22×C4C22×D412yes—
914C22×C4C22×D414yes—
915C22×C4C22×D412yes—
916C22×C4C22×D412yes—
917C22×C4C22×D412yes—
918C22×C4C2×#4114yes—
919C22×C4C2×#4114yes—
920C22×C4C2×#4114yes—
921C22×C4H(5,𝔽2)14yes—
922C4⋊C4—48no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—48no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—82no—
930C4⋊C4—84no—
931C4⋊C4—82no—
932C22⋊C4—216no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—48no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—48no—
958C22⋊C4—84no—
959C22⋊C4—82no—
960C22⋊C4—84no—
961C22⋊C4—84no—
962C22⋊C4—84no—
963C22⋊C4—84no—
964C22⋊C4—84no—
965C22⋊C4—84no—
966C42—48no—
967C42—44no—
968C42—48no—
969C42—84no—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—22no—
977C23—24no—
978C23—22no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—232no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—22no—
1006C23—24no—
1007C23—22no—
1008C23—22no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—432no—
1018C23—432no—
1019C23—416no—
1020C23—416no—
1021C23—416no—
1022C23—416no—
1023C23—432no—
1024C23—416no—
1025C23—432no—
1026C23—416no—
1027C23—416no—
1028C23—416no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—416no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—41no—
1047C23—42no—
1048C23—41no—
1049C23—42no—
1050C23—42no—
1051C23—41no—
1052C23—41no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—41no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—41no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—41no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—41no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—816no—
1093C23—816no—
1094C23—816no—
1095C23—816no—
1096C23—88no—
1097C23—88no—
1098C23—88no—
1099C23—88no—
1100C23#52514yes—
1101C23#53214yes—
1102C23#54014yes—
1103C23D4214yes—
1104C23#54614yes—
1105C23#54614yes—
1106C23#55118yes—
1107C23#55314yes—
1108C23C23×D411yescharacteristic
1109C23C23×D411yescharacteristic
1110C23C22×#4111yescharacteristic
1111C23C22×#4111yescharacteristic
1112C23C22×#4112yes—
1113C23C22×#4111yescharacteristic
1114C23C2×H(5,𝔽2)12yes—
1115C23C2×H(5,𝔽2)11yescharacteristic
1116C23C2×H(5,𝔽2)11yescharacteristic
1117C23C2×H(5,𝔽2)12yes—
1118C23#58512yes—
1119D4—432no—
1120D4—432no—
1121D4—432no—
1122D4—416no—
1123D4—816no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—416no—
1160C2×C4—416no—
1161C2×C4—432no—
1162C2×C4—416no—
1163C2×C4—432no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—416no—
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—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
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—88no—
1242C2×C4—88no—
1243C2×C4#52514yes—
1244C2×C4#53514yes—
1245C22—24no—
1246C22—24no—
1247C22—24no—
1248C22—24no—
1249C22—24no—
1250C22—28no—
1251C22—28no—
1252C22—24no—
1253C22—28no—
1254C22—28no—
1255C22—28no—
1256C22—28no—
1257C22—28no—
1258C22—464no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—42no—
1272C22—44no—
1273C22—42no—
1274C22—44no—
1275C22—42no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—832no—
1284C22—82no—
1285C22—81no—
1286C22—82no—
1287C22—81no—
1288C22—81no—
1289C22—82no—
1290C22—82no—
1291C22—82no—
1292C22—82no—
1293C22—82no—
1294C22—81no—
1295C22—82no—
1296C22—82no—
1297C22—82no—
1298C22#246418yes—
1299C22C2×#52511yescharacteristic
1300C22C2×#52511yescharacteristic
1301C22C2×#53211yescharacteristic
1302C22C2×#53511yescharacteristic
1303C22C2×#54011yescharacteristic
1304C22C2×D4211yescharacteristic
1305C22C2×#54611yescharacteristic
1306C22C2×#54611yescharacteristic
1307C22D4×#4112yes—
1308C22C2×#55112yes—
1309C22C2×#55311yescharacteristic
1310C22#348112yes—
1311C22#348112yes—
1312C22#348411yescharacteristic
1313C22#348412yes—
1314C22#348711yescharacteristic
1315C22#349012yes—
1316C22#350512yes—
1317C22#351312yes—
1318C22#351312yes—
1319C22#351312yes—
1320C22#353212yes—
1321C22#354212yes—
1322C4—24no—
1323C4—24no—
1324C4—42no—
1325C4—44no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—44no—
1331C4—44no—
1332C4—44no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—82no—
1338C4—81no—
1339C4—82no—
1340C4—81no—
1341C2—28no—
1342C2—48no—
1343C2—82no—
1344C2—84no—
1345C2C2×#246411yescharacteristic
1346C2#3496511yescharacteristic
1347C2#3539611yescharacteristic
1348C2#3610211yescharacteristic
1349C2#3615811yescharacteristic
1350C2#3622012yes—
1351C2#3764511yescharacteristic
1352C2#3853412yes—
1353C2#3946711yescharacteristic
1354C2#5902912yes—
1355C2#5985012yes—
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×#2411C2semidirect
2. C2×#2419C2semidirect
3. C2×C4×#120C2semidirect
4. C22×#386C2semidirect
5. #15496C2semidirect
6. #15461C2semidirect
7. #15377C2semidirect
8. #15330C2semidirect
9. #15014C2semidirect
10. #14918C2semidirect
11. #14911C2semidirect
12. #14756C2semidirect
13. #14730C2semidirect
15. #14693C2semidirect
16. #14189C2semidirect
17. #14034C2semidirect
18. #14020C2semidirect
19. #13971C2semidirect
20. #13967C2semidirect
21. #13902C2semidirect
22. #13868C2semidirect
23. #13799C2semidirect
30. C22×C4×D4C22semidirect
37. C2×#400C22semidirect
38. C2×#398C22semidirect
39. C2×#397C22semidirect
40. C2×#397C22semidirect
41. C2×#396C22semidirect
42. C2×#394C22semidirect
48. C2×#390C22semidirect
49. C2×#388C22semidirect
50. C2×#388C22semidirect
51. C2×#387C22semidirect
52. C2×#387C22semidirect
61. C2×#386C22semidirect
62. C2×#386C22semidirect
66. C2×#385C22semidirect
67. C2×#385C22semidirect
68. C2×#385C22semidirect
69. C2×#385C22semidirect
72. C2×#381C22semidirect
82. C2×C4×C22⋊C4C22semidirect
85. #1445C22semidirect
86. #1444C22semidirect
87. #1443C22semidirect
88. #1442C22semidirect
89. #1442C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
106. #1438C22semidirect
107. #1438C22semidirect
108. #1438C22semidirect
109. #1437C22semidirect
110. #1437C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. #1434C22semidirect
117. #1434C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C4×#95C22semidirect
249. #386D4semidirect
271. C2×#95D4semidirect
576. C2×C22⋊C4C2×D4semidirect
626. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24112
C2×#24192
C2×C4×#1202
C22×#3862
#154962
#154612
#153772
#153302
#150142
#149182
#149112
#147562
#147302
#147152
#146932
#141892
#140342
#140202
#139712
#139672
#139022
#138682
#137992