Finite Group Databasebeta

← #773927

Subgroups — #773927

Order 512.

5128 conjugacy classes of subgroups.

The subgroup lattice has 1486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2548C211yesmaximal, characteristic, complemented
2C2×#2538C211yesmaximal, characteristic, complemented
3C2×#2433C211yesmaximal, characteristic
4C2×#2472C212yesmaximal, complemented
5C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
6#16340C212yesmaximal, complemented
7#15304C212yesmaximal, complemented
8#15268C212yesmaximal, complemented
9#15268C212yesmaximal, complemented
10#15264C212yesmaximal, complemented
11#15140C211yesmaximal, characteristic, complemented
12#15138C211yesmaximal, characteristic, complemented
13#15130C211yesmaximal, characteristic, complemented
14#14754C212yesmaximal, complemented
15#14725C212yesmaximal, complemented
16#14025C211yesmaximal, characteristic, complemented
17#14025C211yesmaximal, characteristic, complemented
18#14001C211yesmaximal, characteristic, complemented
19#13998C211yesmaximal, characteristic, complemented
20#13974C211yesmaximal, characteristic, complemented
21#13902C211yesmaximal, characteristic, complemented
22C4×#393C211yesmaximal, characteristic, complemented
23#13820C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#127C2211yescharacteristic
26C22×#127C2211yescharacteristic
27C22×#124C2212yescomplemented
28C22×C22⋊Q8C2212yescomplemented
29C22×#121C2211yescharacteristic
30C22×#120C2212yes—
31C22×#120C2212yes—
32C22×C4×Q8C2211yescharacteristic, complemented
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C23×C22⋊C4C2212yes—
36#2548—28no—
37#2538—28no—
38#2472—216no—
39#2433—28no—
40C2×#397C2212yescomplemented
41C2×#396C2212yescomplemented
42C2×#396C2212yescomplemented
43C2×#394C2212yes—
44C2×#394C2212yes—
45C2×#394C2212yescomplemented
46C2×#394C2212yescomplemented
47C2×#394C2212yescomplemented
48C2×#394C2212yescomplemented
49C2×#393C2211yescharacteristic
50C2×#392C2212yes—
51C2×#392C2212yes—
52D4×C22⋊C4—28no—
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#390C2212yes—
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#390C2211yescharacteristic
62C2×#390C2211yescharacteristic, complemented
63C2×#390C2212yescomplemented
64C2×#390C2211yescharacteristic, complemented
65C2×#390C2211yescharacteristic, complemented
66C2×#390C2211yescharacteristic, complemented
67C2×#389C2211yescharacteristic, complemented
68C2×#389C2211yescharacteristic, complemented
69C2×#388C2212yes—
70C2×#388C2212yescomplemented
71C2×#388C2212yescomplemented
72C2×#386C2212yes—
73C2×#386C2212yes—
74C2×#386C2212yescomplemented
75C2×#386C2212yescomplemented
76C2×#386C2212yescomplemented
77C2×#386C2212yescomplemented
78C2×#384C2211yescharacteristic, complemented
79C2×#380C2211yescharacteristic
80C2×#380C2211yescharacteristic
81C2×#380C2212yescomplemented
82C2×#379C2212yes—
83C2×#379C2212yes—
84C2×#379C2212yes—
85C2×C4×C4⋊C4C2211yescharacteristic, complemented
86C2×C4×C4⋊C4C2211yescharacteristic, complemented
87C2×C4×C22⋊C4C2211yescharacteristic
88C2×C4×C22⋊C4C2211yescharacteristic
89C2×C4×C22⋊C4C2211yescharacteristic
90C2×C4×C22⋊C4C2212yescomplemented
91#1446C2211yescharacteristic, complemented
92#1443C2212yescomplemented
93#1442C2211yescharacteristic, complemented
94#1442C2211yescharacteristic, complemented
95#1442C2211yescharacteristic, complemented
96#1440C2212yes—
97#1440C2212yescomplemented
98#1440C2212yescomplemented
99#1439C2211yescharacteristic
100#1439C2211yescharacteristic
101#1439C2211yescharacteristic
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1438C2212yes—
109#1438C2212yes—
110#1438C2212yes—
111#1438C2212yescomplemented
112#1438C2212yescomplemented
113#1438C2212yescomplemented
114#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1438C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1437C2212yescomplemented
120#1436C2212yescomplemented
121C4⋊#95C2211yescharacteristic, complemented
122C4⋊#95C2211yescharacteristic, complemented
123C4⋊#95C2211yescharacteristic, complemented
124C22⋊#95C2212yescomplemented
125C4×#95C2211yescharacteristic, complemented
126C4×#95C2211yescharacteristic, complemented
127C4×#95C2211yescharacteristic, complemented
128C26C2312yes—
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—24no—
134C23×D4—24no—
135C23×D4—42no—
136C23×D4—42no—
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2312yes—
142C23×D4C2312yes—
143C23×D4C2312yes—
144C23×D4C2311yescharacteristic
145C23×D4C2312yes—
146C24×C4C2311yescharacteristic
147C24×C4C2312yes—
148C24×C4C2312yes—
149C2×#127—24no—
150C2×#127—24no—
151C2×#127—24no—
152C2×#127—24no—
153C2×#127—24no—
154C2×#127—42no—
155C2×#124—28no—
156C2×#124—28no—
157C2×#124—44no—
158C2×C22⋊Q8—28no—
159C2×C22⋊Q8—28no—
160C2×C22⋊Q8—44no—
161C2×#121—24no—
162C2×#121—24no—
163C2×#121—42no—
164C2×#120—28no—
165C2×#120—28no—
166C2×#120—28no—
167C2×#120—44no—
168C2×#120—44no—
169C2×#120—44no—
170C2×C4×Q8—24no—
171C2×C4×Q8—24no—
172C2×C4×Q8—42no—
173C2×C4×D4—24no—
174C2×C4×D4—24no—
175C2×C4×D4—24no—
176C2×C4×D4—24no—
177C2×C4×D4—42no—
178C2×C4×D4—42no—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2312yes—
191C22×C22⋊C4—28no—
192C22×C22⋊C4—28no—
193C22×C22⋊C4—44no—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
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×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
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×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2312yes—
229C22×C42C2311yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2312yes—
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2312yes—
237#397—28no—
238#396—28no—
239#396—28no—
240#394—28no—
241#394—28no—
242#394—28no—
243#394—28no—
244#394—44no—
245#394—44no—
246#393D418yescomplemented
247#392—28no—
248#392—28no—
249#390—24no—
250#390—24no—
251#390—24no—
252#390—24no—
253#390—24no—
254#390—24no—
255#390—28no—
256#390—28no—
257#390—24no—
258#390—42no—
259#390—42no—
260#390—42no—
261#390D418yes—
262#390D418yescomplemented
263#389—24no—
264#389—24no—
265#388—28no—
266#388—28no—
267#388—44no—
268#386—28no—
269#386—28no—
270#386—28no—
271#386—28no—
272#386—44no—
273#386—44no—
274#384—24no—
275#380—24no—
276#380—24no—
277#380—28no—
278#379—28no—
279#379—28no—
280#379—44no—
281C4×C4⋊C4—24no—
282C4×C4⋊C4—42no—
283C4×C22⋊C4—24no—
284C4×C22⋊C4—24no—
285C4×C22⋊C4—28no—
286C4×C22⋊C4—42no—
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C2×#95C2311yescharacteristic
309C2×#95C2311yescharacteristic
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2311yescharacteristic
313C2×#95C2311yescharacteristic
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C2×#95C2311yescharacteristic
317C25—24no—
318C25—24no—
319C25—24no—
320C25—24no—
321C25—24no—
322C25—24no—
323C25—24no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25—42no—
330C25—42no—
331C25—42no—
332C25C2412yes—
333C25C2412yes—
334C25C2412yes—
335C25C2411yescharacteristic
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—41no—
341C22×Q8—41no—
342C22×Q8C2×D414yescomplemented
343C22×D4—232no—
344C22×D4—24no—
345C22×D4—24no—
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—24no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—22no—
369C22×D4—24no—
370C22×D4—22no—
371C22×D4—22no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—24no—
381C22×D4—22no—
382C22×D4—22no—
383C22×D4—24no—
384C22×D4—416no—
385C22×D4—416no—
386C22×D4—42no—
387C22×D4—42no—
388C22×D4—42no—
389C22×D4—42no—
390C22×D4—42no—
391C22×D4—42no—
392C22×D4—42no—
393C22×D4—42no—
394C22×D4—42no—
395C22×D4—42no—
396C22×D4—42no—
397C22×D4—42no—
398C22×D4—42no—
399C22×D4—42no—
400C22×D4—42no—
401C22×D4—42no—
402C22×D4—42no—
403C22×D4—42no—
404C22×D4—42no—
405C22×D4—416no—
406C22×D4—416no—
407C22×D4—416no—
408C22×D4—416no—
409C22×D4C2×D414yes—
410C22×D4C2×D414yes—
411C22×D4#4114yes—
412C22×D4#4114yes—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—24no—
420C23×C4—24no—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—24no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4—42no—
429C23×C4—42no—
430C23×C4—42no—
431C23×C4—42no—
432C23×C4—42no—
433C23×C4#4114yes—
434C23×C4C2412yes—
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453#127—416no—
454#127—416no—
455#124—432no—
456C22⋊Q8—432no—
457#121—416no—
458#120—432no—
459#120—432no—
460C4×Q8—416no—
461C4×D4—416no—
462C4×D4—416no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4—41no—
492C2×C4⋊C4—41no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4C2×D414yes—
498C2×C4⋊C4C2×D414yes—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
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—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
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—24no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—432no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—41no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—41no—
557C2×C22⋊C4—41no—
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—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—42no—
587C2×C22⋊C4—42no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4C2×D414yes—
599C2×C22⋊C4C2×D418yes—
600C2×C22⋊C4C2×D414yes—
601C2×C22⋊C4C2×D418yes—
602C2×C22⋊C4C2×D418yes—
603C2×C22⋊C4C2×D414yes—
604C2×C22⋊C4C2×D418yes—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—24no—
613C2×C42—24no—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618C2×C42—22no—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42—24no—
624C2×C42—42no—
625C2×C42—42no—
626C2×C42—42no—
627C2×C42C2×D414yes—
628C2×C42C2×D414yes—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—24no—
634#95—24no—
635#95—24no—
636#95—24no—
637#95—24no—
638#95—24no—
639#95—24no—
640#95—24no—
641#95—22no—
642#95—22no—
643#95—24no—
644#95—22no—
645#95—22no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95—42no—
654#95—42no—
655#95—42no—
656#95C2×D414yescomplemented
657#95C2×D414yescomplemented
658#95C2×D414yescomplemented
659C24—21no—
660C24—22no—
661C24—22no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—22no—
666C24—21no—
667C24—22no—
668C24—21no—
669C24—21no—
670C24—22no—
671C24—21no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—21no—
677C24—22no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—22no—
682C24—22no—
683C24—216no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—22no—
703C24—22no—
704C24—22no—
705C24—22no—
706C24—22no—
707C24—22no—
708C24—22no—
709C24—22no—
710C24—22no—
711C24—22no—
712C24—22no—
713C24—48no—
714C24—48no—
715C24—48no—
716C24—48no—
717C24—48no—
718C24—48no—
719C24—48no—
720C24—48no—
721C24—48no—
722C24—48no—
723C24—48no—
724C24—48no—
725C24—48no—
726C24—48no—
727C24—48no—
728C24—48no—
729C24—84no—
730C24—84no—
731C24—84no—
732C24—84no—
733C24—84no—
734C24—84no—
735C24—84no—
736C24—84no—
737C24—84no—
738C24—84no—
739C24—84no—
740C24—84no—
741C24—84no—
742C24—84no—
743C24—84no—
744C24—84no—
745C24—84no—
746C24—84no—
747C24C22×D414yes—
748C24C22×D414yes—
749C24C22×D412yes—
750C24C2×#4114yes—
751C24C2×#4114yes—
752C24C2×#4112yes—
753C24H(5,𝔽2)12yes—
754C24C2511yescharacteristic
755C2×Q8—28no—
756C2×Q8—28no—
757C2×Q8—44no—
758C2×Q8—44no—
759C2×Q8—44no—
760C2×Q8—44no—
761C2×Q8—44no—
762C2×D4—216no—
763C2×D4—28no—
764C2×D4—28no—
765C2×D4—28no—
766C2×D4—28no—
767C2×D4—28no—
768C2×D4—28no—
769C2×D4—28no—
770C2×D4—28no—
771C2×D4—28no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—48no—
787C2×D4—48no—
788C2×D4—4128no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—48no—
793C2×D4—48no—
794C2×D4—48no—
795C2×D4—48no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—48no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—84no—
809C2×D4—84no—
810C2×D4—84no—
811C2×D4—84no—
812C2×D4—84no—
813C2×D4—84no—
814C2×D4—84no—
815C2×D4—84no—
816C2×D4—84no—
817C2×D4—84no—
818C2×D4—84no—
819C2×D4—84no—
820C2×D4—84no—
821C2×D4—84no—
822C2×D4—84no—
823C2×D4—84no—
824C2×D4—84no—
825C2×D4#124116yescomplemented
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—22no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—22no—
894C22×C4—28no—
895C22×C4—28no—
896C22×C4—28no—
897C22×C4—22no—
898C22×C4—21no—
899C22×C4—22no—
900C22×C4—21no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—22no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—22no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—22no—
937C22×C4—21no—
938C22×C4—22no—
939C22×C4—48no—
940C22×C4—48no—
941C22×C4—48no—
942C22×C4—48no—
943C22×C4—48no—
944C22×C4—48no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—48no—
950C22×C4—84no—
951C22×C4—84no—
952C22×C4—84no—
953C22×C4—84no—
954C22×C4—84no—
955C22×C4—84no—
956C22×C4—84no—
957C22×C4C22×D412yes—
958C22×C4C22×D412yes—
959C22×C4C22×D412yes—
960C22×C4C22×D414yes—
961C22×C4C22×D412yes—
962C22×C4C22×D414yes—
963C22×C4C22×D412yes—
964C22×C4C22×D412yes—
965C22×C4C22×D412yes—
966C22×C4C22×D412yes—
967C22×C4C22×D412yes—
968C22×C4C22×D412yes—
969C22×C4C22×D412yes—
970C22×C4C22×D412yes—
971C22×C4C2×#4112yes—
972C22×C4C2×#4112yes—
973C22×C4C2×#4112yes—
974C22×C4C2×#4112yes—
975C22×C4H(5,𝔽2)12yes—
976C22×C4H(5,𝔽2)12yes—
977C22×C4H(5,𝔽2)12yes—
978C22×C4H(5,𝔽2)12yes—
979C22×C4H(5,𝔽2)12yes—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—48no—
986C4⋊C4—48no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—48no—
990C4⋊C4—44no—
991C4⋊C4—84no—
992C22⋊C4—28no—
993C22⋊C4—28no—
994C22⋊C4—216no—
995C22⋊C4—28no—
996C22⋊C4—216no—
997C22⋊C4—48no—
998C22⋊C4—44no—
999C22⋊C4—48no—
1000C22⋊C4—48no—
1001C22⋊C4—48no—
1002C22⋊C4—48no—
1003C22⋊C4—48no—
1004C22⋊C4—48no—
1005C22⋊C4—44no—
1006C22⋊C4—48no—
1007C22⋊C4—48no—
1008C22⋊C4—48no—
1009C22⋊C4—48no—
1010C22⋊C4—48no—
1011C22⋊C4—48no—
1012C22⋊C4—44no—
1013C22⋊C4—48no—
1014C22⋊C4—48no—
1015C22⋊C4—84no—
1016C22⋊C4—84no—
1017C22⋊C4—84no—
1018C22⋊C4—84no—
1019C22⋊C4—84no—
1020C22⋊C4—84no—
1021C22⋊C4—84no—
1022C22⋊C4—84no—
1023C22⋊C4—84no—
1024C22⋊C4—84no—
1025C22⋊C4—84no—
1026C22⋊C4—84no—
1027C42—28no—
1028C42—28no—
1029C42—48no—
1030C42—44no—
1031C42—44no—
1032C42—44no—
1033C42—44no—
1034C42—84no—
1035C23—22no—
1036C23—24no—
1037C23—24no—
1038C23—22no—
1039C23—24no—
1040C23—22no—
1041C23—24no—
1042C23—24no—
1043C23—22no—
1044C23—24no—
1045C23—24no—
1046C23—24no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—24no—
1051C23—22no—
1052C23—24no—
1053C23—22no—
1054C23—24no—
1055C23—22no—
1056C23—22no—
1057C23—24no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—24no—
1062C23—24no—
1063C23—22no—
1064C23—24no—
1065C23—24no—
1066C23—24no—
1067C23—24no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—24no—
1072C23—24no—
1073C23—24no—
1074C23—24no—
1075C23—24no—
1076C23—24no—
1077C23—24no—
1078C23—432no—
1079C23—432no—
1080C23—41no—
1081C23—41no—
1082C23—42no—
1083C23—41no—
1084C23—41no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—41no—
1089C23—41no—
1090C23—42no—
1091C23—42no—
1092C23—41no—
1093C23—42no—
1094C23—41no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—42no—
1103C23—41no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—41no—
1109C23—41no—
1110C23—42no—
1111C23—41no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—42no—
1116C23—42no—
1117C23—42no—
1118C23—42no—
1119C23—42no—
1120C23—42no—
1121C23—42no—
1122C23—42no—
1123C23—42no—
1124C23—42no—
1125C23—42no—
1126C23—42no—
1127C23—42no—
1128C23—42no—
1129C23—42no—
1130C23—42no—
1131C23—42no—
1132C23—42no—
1133C23—42no—
1134C23—42no—
1135C23—42no—
1136C23—42no—
1137C23—42no—
1138C23—42no—
1139C23—42no—
1140C23—42no—
1141C23—42no—
1142C23—42no—
1143C23—42no—
1144C23—42no—
1145C23—42no—
1146C23—42no—
1147C23—42no—
1148C23—42no—
1149C23—42no—
1150C23—42no—
1151C23—42no—
1152C23—42no—
1153C23—42no—
1154C23—42no—
1155C23—42no—
1156C23—42no—
1157C23—42no—
1158C23—42no—
1159C23—42no—
1160C23—42no—
1161C23—42no—
1162C23—42no—
1163C23—42no—
1164C23—42no—
1165C23—42no—
1166C23—42no—
1167C23—42no—
1168C23—42no—
1169C23—42no—
1170C23—42no—
1171C23—42no—
1172C23—42no—
1173C23—42no—
1174C23—42no—
1175C23—816no—
1176C23—816no—
1177C23—816no—
1178C23—816no—
1179C23—816no—
1180C23—816no—
1181C23—816no—
1182C23—816no—
1183C23—816no—
1184C23—816no—
1185C23—816no—
1186C23—816no—
1187C23—816no—
1188C23C2×#12418yes—
1189C23#55014yes—
1190C23C23×D411yescharacteristic
1191C23C23×D411yescharacteristic
1192C23C23×D411yescharacteristic
1193C23C22×#4111yescharacteristic
1194C23C22×#4111yescharacteristic
1195C23C22×#4111yescharacteristic
1196C23C2×H(5,𝔽2)11yescharacteristic
1197C23C2×H(5,𝔽2)11yescharacteristic
1198C23C2×H(5,𝔽2)11yescharacteristic
1199C23C2×H(5,𝔽2)11yescharacteristic
1200C23C2×H(5,𝔽2)11yescharacteristic
1201C23C2×H(5,𝔽2)11yescharacteristic
1202C23#58511yescharacteristic
1203C23#58511yescharacteristic
1204C23#58511yescharacteristic
1205Q8—416no—
1206D4—232no—
1207D4—432no—
1208D4—416no—
1209D4—816no—
1210D4—816no—
1211D4—816no—
1212D4—816no—
1213D4—816no—
1214D4—88no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—42no—
1267C2×C4—42no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—42no—
1276C2×C4—42no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—42no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—42no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—42no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—42no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—416no—
1298C2×C4—42no—
1299C2×C4—41no—
1300C2×C4—42no—
1301C2×C4—41no—
1302C2×C4—42no—
1303C2×C4—42no—
1304C2×C4—42no—
1305C2×C4—42no—
1306C2×C4—41no—
1307C2×C4—42no—
1308C2×C4—42no—
1309C2×C4—42no—
1310C2×C4—42no—
1311C2×C4—41no—
1312C2×C4—42no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—42no—
1316C2×C4—41no—
1317C2×C4—42no—
1318C2×C4—42no—
1319C2×C4—41no—
1320C2×C4—42no—
1321C2×C4—42no—
1322C2×C4—41no—
1323C2×C4—42no—
1324C2×C4—42no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—42no—
1330C2×C4—41no—
1331C2×C4—42no—
1332C2×C4—41no—
1333C2×C4—41no—
1334C2×C4—41no—
1335C2×C4—41no—
1336C2×C4—42no—
1337C2×C4—41no—
1338C2×C4—41no—
1339C2×C4—41no—
1340C2×C4—816no—
1341C2×C4—816no—
1342C2×C4#52514yes—
1343C2×C4C2×#12414yes—
1344C2×C4#53814yes—
1345C2×C4D4214yes—
1346C2×C4D4214yes—
1347C2×C4D4214yes—
1348C2×C4#54614yes—
1349C2×C4#54614yes—
1350C2×C4#55114yes—
1351C22—24no—
1352C22—28no—
1353C22—28no—
1354C22—28no—
1355C22—24no—
1356C22—24no—
1357C22—44no—
1358C22—42no—
1359C22—44no—
1360C22—42no—
1361C22—44no—
1362C22—42no—
1363C22—44no—
1364C22—42no—
1365C22—42no—
1366C22—44no—
1367C22—42no—
1368C22—44no—
1369C22—42no—
1370C22—42no—
1371C22—44no—
1372C22—42no—
1373C22—44no—
1374C22—42no—
1375C22—44no—
1376C22—44no—
1377C22—42no—
1378C22—44no—
1379C22—42no—
1380C22—44no—
1381C22—44no—
1382C22—44no—
1383C22—44no—
1384C22—44no—
1385C22—44no—
1386C22—44no—
1387C22—44no—
1388C22—864no—
1389C22—82no—
1390C22—82no—
1391C22—82no—
1392C22—82no—
1393C22—82no—
1394C22—82no—
1395C22—82no—
1396C22—82no—
1397C22—82no—
1398C22—82no—
1399C22—82no—
1400C22—82no—
1401C22—82no—
1402C22—82no—
1403C22—82no—
1404C22—82no—
1405C22—82no—
1406C22—82no—
1407C22—82no—
1408C22—82no—
1409C22—82no—
1410C22—82no—
1411C22—82no—
1412C22C2×#52511yescharacteristic
1413C22C22×#12411yescharacteristic
1414C22C2×#53811yescharacteristic
1415C22C2×D4211yescharacteristic
1416C22C2×D4211yescharacteristic
1417C22C2×D4211yescharacteristic
1418C22C2×#54611yescharacteristic
1419C22C2×#54611yescharacteristic
1420C22C2×#55011yescharacteristic
1421C22D4×#4111yescharacteristic
1422C22D4×#4111yescharacteristic
1423C22C2×#55111yescharacteristic
1424C22#348411yescharacteristic
1425C22#348811yescharacteristic
1426C22#348811yescharacteristic
1427C22#348811yescharacteristic
1428C22#349611yescharacteristic
1429C22#349611yescharacteristic
1430C22#349811yescharacteristic
1431C22#350011yescharacteristic
1432C22#350611yescharacteristic
1433C22#350811yescharacteristic
1434C22#351011yescharacteristic
1435C22#351311yescharacteristic
1436C22#351311yescharacteristic
1437C22#351411yescharacteristic
1438C22#351411yescharacteristic
1439C22#351911yescharacteristic
1440C22#351911yescharacteristic
1441C22#353711yescharacteristic
1442C22#354211yescharacteristic
1443C22#354311yescharacteristic
1444C22#354611yescharacteristic
1445C22#354611yescharacteristic
1446C22#356211yescharacteristic
1447C4—24no—
1448C4—24no—
1449C4—42no—
1450C4—44no—
1451C4—42no—
1452C4—42no—
1453C4—42no—
1454C4—42no—
1455C4—42no—
1456C4—42no—
1457C4—42no—
1458C4—44no—
1459C4—81no—
1460C4—82no—
1461C4—81no—
1462C4—81no—
1463C4—82no—
1464C4—82no—
1465C4#247218yescomplemented
1466C2—48no—
1467C2—44no—
1468C2—84no—
1469C2—162no—
1470C2C2×#247211yescharacteristic
1471C2#3580811yescharacteristic
1472C2#3590311yescharacteristic
1473C2#3610111yescharacteristic
1474C2D4×#12411yescharacteristic
1475C2#3939611yescharacteristic
1476C2#4258111yescharacteristic
1477C2#4486811yescharacteristic
1478C2#4495511yescharacteristic
1479C2#4505711yescharacteristic
1480C2#4536711yescharacteristic
1481C2#5899711yescharacteristic
1482C2#5912411yescharacteristic
1483C2#5941211yescharacteristic
1484C2#5982011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2433C2
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×#2548C2semidirect
2. C2×#2538C2semidirect
4. C2×#2472C2semidirect
5. C2×D4×C22⋊C4C2semidirect
6. #16340C2semidirect
7. #15304C2semidirect
8. #15268C2semidirect
9. #15268C2semidirect
10. #15264C2semidirect
11. #15140C2semidirect
12. #15138C2semidirect
13. #15130C2semidirect
14. #14754C2semidirect
15. #14725C2semidirect
16. #14025C2semidirect
17. #14025C2semidirect
18. #14001C2semidirect
19. #13998C2semidirect
20. #13974C2semidirect
21. #13902C2semidirect
22. C4×#393C2semidirect
23. #13820C2semidirect
27. C22×#124C22semidirect
28. C22×C22⋊Q8C22semidirect
32. C22×C4×Q8C22semidirect
40. C2×#397C22semidirect
41. C2×#396C22semidirect
42. C2×#396C22semidirect
45. C2×#394C22semidirect
46. C2×#394C22semidirect
47. C2×#394C22semidirect
48. C2×#394C22semidirect
62. C2×#390C22semidirect
63. C2×#390C22semidirect
64. C2×#390C22semidirect
65. C2×#390C22semidirect
66. C2×#390C22semidirect
67. C2×#389C22semidirect
68. C2×#389C22semidirect
70. C2×#388C22semidirect
71. C2×#388C22semidirect
74. C2×#386C22semidirect
75. C2×#386C22semidirect
76. C2×#386C22semidirect
77. C2×#386C22semidirect
78. C2×#384C22semidirect
81. C2×#380C22semidirect
85. C2×C4×C4⋊C4C22semidirect
86. C2×C4×C4⋊C4C22semidirect
90. C2×C4×C22⋊C4C22semidirect
91. #1446C22semidirect
92. #1443C22semidirect
93. #1442C22semidirect
94. #1442C22semidirect
95. #1442C22semidirect
97. #1440C22semidirect
98. #1440C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
116. #1438C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1437C22semidirect
120. #1436C22semidirect
121. C4⋊#95C22semidirect
122. C4⋊#95C22semidirect
123. C4⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C4×#95C22semidirect
126. C4×#95C22semidirect
127. C4×#95C22semidirect
246. #393D4semidirect
262. #390D4semidirect
342. C22×Q8C2×D4semidirect
656. #95C2×D4semidirect
657. #95C2×D4semidirect
658. #95C2×D4semidirect
825. C2×D4#124semidirect
1465. C4#2472semidirect

Maximal subgroups

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

subgroupindex
C2×#25482
C2×#25382
C2×#24332
C2×#24722
C2×D4×C22⋊C42
#163402
#153042
#152682
#152642
#151402
#151382
#151302
#147542
#147252
#140252
#140012
#139982
#139742
#139022
C4×#3932
#138202