Finite Group Databasebeta

← #1259315

Subgroups — #1259315

Order 512.

4879 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2540C211yesmaximal, characteristic, complemented
2C2×#2408C211yesmaximal, characteristic, complemented
3C2×#2459C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
5#16809C211yesmaximal, characteristic, complemented
6#16801C211yesmaximal, characteristic, complemented
7#16509C211yesmaximal, characteristic, complemented
8#16398C211yesmaximal, characteristic, complemented
9#15281C212yesmaximal, complemented
10#15280C212yesmaximal, complemented
11#15278C212yesmaximal, complemented
12#15268C212yesmaximal, complemented
13#14860C211yesmaximal, characteristic, complemented
14#14825C211yesmaximal, characteristic, complemented
15#14813C211yesmaximal, characteristic, complemented
16#14806C211yesmaximal, characteristic, complemented
17#14717C212yesmaximal, complemented
18#14716C212yesmaximal, complemented
19#14715C211yesmaximal, characteristic, complemented
20#14521C212yesmaximal, complemented
21#14363C212yesmaximal, complemented
22#14299C211yesmaximal, characteristic, complemented
23#13891C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#124C2211yescharacteristic, complemented
26C22×C22⋊Q8C2212yescomplemented
27C22×#121C2212yes—
28C22×#121C2212yescomplemented
29C22×#120C2212yes—
30C22×#120C2212yes—
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C23×C22⋊C4C2212yes—
35#2540—28no—
36#2459—28no—
37#2408—28no—
38C2×#400C2211yescharacteristic, complemented
39C2×#399C2211yescharacteristic, complemented
40C2×#399C2211yescharacteristic, complemented
41C2×#396C2212yescomplemented
42C2×#394C2211yescharacteristic
43C2×#394C2211yescharacteristic
44C2×#394C2211yescharacteristic
45C2×#394C2211yescharacteristic
46C2×#394C2212yescomplemented
47C2×#394C2212yescomplemented
48C2×#393C2211yescharacteristic
49C2×#393C2212yescomplemented
50C2×#392C2211yescharacteristic
51C2×#392C2211yescharacteristic
52C2×#392C2211yescharacteristic
53C2×#392C2212yes—
54C2×#392C2211yescharacteristic
55C2×#392C2211yescharacteristic
56C2×#392C2212yescomplemented
57D4×C22⋊C4—28no—
58C2×#391C2211yescharacteristic, complemented
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#390C2212yes—
62C2×#390C2212yescomplemented
63C2×#390C2212yescomplemented
64C2×#388C2212yes—
65C2×#388C2211yescharacteristic, complemented
66C2×#388C2211yescharacteristic, complemented
67C2×#388C2211yescharacteristic, complemented
68C2×#388C2212yescomplemented
69C2×#387C2211yescharacteristic, complemented
70C2×#386C2211yescharacteristic
71C2×#386C2212yes—
72C2×#386C2212yes—
73C2×#386C2211yescharacteristic, complemented
74C2×#386C2212yescomplemented
75C2×#386C2212yescomplemented
76C2×#381C2211yescharacteristic, complemented
77C2×#380C2211yescharacteristic
78C2×#380C2211yescharacteristic
79C2×#379C2212yes—
80C2×#379C2212yes—
81C2×#379C2212yes—
82C2×C4×C4⋊C4C2211yescharacteristic, complemented
83C2×C4×C22⋊C4C2211yescharacteristic
84#1445C2211yescharacteristic, complemented
85#1444C2212yescomplemented
86#1442C2211yescharacteristic, complemented
87#1441C2212yescomplemented
88#1441C2211yescharacteristic, complemented
89#1440C2212yescomplemented
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yescomplemented
94#1439C2211yescharacteristic, complemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2211yescharacteristic, complemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1438C2211yescharacteristic
105#1438C2212yes—
106#1438C2212yes—
107#1438C2211yescharacteristic
108#1438C2212yes—
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1438C2212yescomplemented
112#1438C2212yescomplemented
113#1438C2212yescomplemented
114#1438C2212yescomplemented
115#1437C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118C4⋊#95C2211yescharacteristic, complemented
119#1434C2211yescharacteristic, complemented
120#1434C2211yescharacteristic, complemented
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2312yes—
128C23×Q8C2311yescharacteristic
129C23×D4—28no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—42no—
133C23×D4—44no—
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C23×D4C2311yescharacteristic
141C23×D4C2312yes—
142C23×D4C2312yes—
143C23×D4C2312yes—
144C24×C4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2312yes—
148C2×#124—24no—
149C2×#124—24no—
150C2×#124—42no—
151C2×C22⋊Q8—28no—
152C2×C22⋊Q8—44no—
153C2×C22⋊Q8—44no—
154C2×#121—28no—
155C2×#121—28no—
156C2×#121—28no—
157C2×#121—44no—
158C2×#121—44no—
159C2×#121—44no—
160C2×#120—28no—
161C2×#120—44no—
162C2×#120—44no—
163C2×#120—44no—
164C2×#120—44no—
165C2×#120—44no—
166C2×C4×D4—24no—
167C2×C4×D4—24no—
168C2×C4×D4—24no—
169C2×C4×D4—24no—
170C2×C4×D4—24no—
171C2×C4×D4—42no—
172C2×C4×D4—42no—
173C2×C4×D4—44no—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C22⋊C4—28no—
185C22×C22⋊C4—44no—
186C22×C22⋊C4—44no—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2312yes—
228C22×C42C2311yescharacteristic
229#400—42no—
230#399—24no—
231#399—24no—
232#396—44no—
233#394—24no—
234#394—24no—
235#394—24no—
236#394—24no—
237#394—44no—
238#394—44no—
239#393—24no—
240#393—44no—
241#392—24no—
242#392—28no—
243#392—24no—
244#392—24no—
245#392—42no—
246#392—44no—
247#392D418yescomplemented
248#391—24no—
249#390—28no—
250#390—28no—
251#390—28no—
252#390—24no—
253#390—24no—
254#388—24no—
255#388—24no—
256#388—24no—
257#388—44no—
258#388—44no—
259#387—24no—
260#386—24no—
261#386—28no—
262#386—28no—
263#386—24no—
264#386—44no—
265#386—44no—
266#381—24no—
267#380—24no—
268#380—24no—
269#379—28no—
270#379—28no—
271#379—44no—
272C4×C4⋊C4—24no—
273C4×C22⋊C4D418yescomplemented
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C25—24no—
306C25—24no—
307C25—24no—
308C25—24no—
309C25—24no—
310C25—24no—
311C25—24no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25—42no—
320C25C2411yescharacteristic
321C25C2411yescharacteristic
322C25C2412yes—
323C25C2412yes—
324C25C2411yescharacteristic
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—24no—
328C22×Q8—42no—
329C22×Q8—41no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—232no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—22no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—24no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—24no—
361C22×D4—22no—
362C22×D4—24no—
363C22×D4—416no—
364C22×D4—41no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—41no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—41no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—42no—
388C22×D4—42no—
389C22×D4—42no—
390C22×D4—42no—
391C22×D4—432no—
392C22×D4—416no—
393C22×D4—432no—
394C22×D4C2×D414yes—
395C22×D4C2×D418yes—
396C22×D4#4118yes—
397C23×C4—22no—
398C23×C4—24no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—24no—
405C23×C4—22no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—41no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4C2×D414yes—
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C23×C4C2412yes—
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439#124—416no—
440C22⋊Q8—432no—
441#121—432no—
442#121—432no—
443#120—432no—
444#120—432no—
445C4×D4—416no—
446C4×D4—416no—
447C4×D4—416no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
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—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—22no—
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—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
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—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—432no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—41no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—41no—
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—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—41no—
558C2×C22⋊C4—41no—
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⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4C2×D414yes—
582C2×C22⋊C4C2×D414yes—
583C2×C22⋊C4C2×D414yes—
584C2×C22⋊C4C2×D418yes—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—24no—
590C2×C42—42no—
591C2×C42—41no—
592C2×C42—42no—
593C2×C42—42no—
594C2×C42C2×D414yes—
595C2×C42C2×D414yes—
596#95—22no—
597#95—24no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—22no—
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#95—42no—
623#95—42no—
624#95C2×D414yes—
625#95C2×D414yes—
626#95C2×D414yes—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—21no—
637C24—22no—
638C24—21no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—21no—
647C24—216no—
648C24—21no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—21no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—22no—
670C24—21no—
671C24—22no—
672C24—21no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24—84no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24—84no—
714C24—84no—
715C24—84no—
716C24—84no—
717C24C22×D412yes—
718C24C22×D412yes—
719C24C22×D414yes—
720C24C2×#4114yes—
721C24C2×#4114yes—
722C24H(5,𝔽2)12yes—
723C24H(5,𝔽2)14yes—
724C242−1+412yes—
725C24C2511yescharacteristic
726C2×Q8—48no—
727C2×Q8—44no—
728C2×Q8—44no—
729C2×Q8—82no—
730C2×Q8—84no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—216no—
734C2×D4—216no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—216no—
738C2×D4—216no—
739C2×D4—216no—
740C2×D4—28no—
741C2×D4—48no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—44no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—44no—
757C2×D4—48no—
758C2×D4—4128no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—44no—
768C2×D4—48no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4—82no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4—84no—
775C2×D4—84no—
776C2×D4—84no—
777C2×D4—84no—
778C2×D4—84no—
779C2×D4—84no—
780C2×D4—82no—
781C2×D4—84no—
782C2×D4—84no—
783C2×D4—82no—
784C2×D4—84no—
785C2×D4—84no—
786C2×D4—84no—
787C2×D4—84no—
788C2×D4—84no—
789C2×D4—84no—
790C2×D4—84no—
791C2×D4—84no—
792C2×D4—84no—
793C2×D4—84no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—28no—
839C22×C4—28no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—21no—
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—22no—
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—22no—
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—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—21no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—21no—
883C22×C4—22no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—44no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—44no—
893C22×C4—48no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—48no—
898C22×C4—44no—
899C22×C4—48no—
900C22×C4—82no—
901C22×C4—84no—
902C22×C4—84no—
903C22×C4—84no—
904C22×C4—84no—
905C22×C4—84no—
906C22×C4—84no—
907C22×C4—84no—
908C22×C4—84no—
909C22×C4—84no—
910C22×C4C22×D412yes—
911C22×C4C22×D412yes—
912C22×C4C22×D412yes—
913C22×C4C22×D414yes—
914C22×C4C22×D412yes—
915C22×C4C22×D412yes—
916C22×C4C22×D412yes—
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C2×#4114yes—
920C22×C4H(5,𝔽2)12yes—
921C22×C4H(5,𝔽2)14yes—
922C22×C4H(5,𝔽2)14yes—
923C22×C4H(5,𝔽2)12yes—
924C4⋊C4—216no—
925C4⋊C4—44no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—82no—
933C4⋊C4—84no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—44no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—48no—
960C22⋊C4—44no—
961C22⋊C4—82no—
962C22⋊C4—82no—
963C22⋊C4—84no—
964C22⋊C4—84no—
965C22⋊C4—82no—
966C22⋊C4—84no—
967C22⋊C4—82no—
968C22⋊C4—84no—
969C22⋊C4—84no—
970C22⋊C4—84no—
971C22⋊C4—84no—
972C42—28no—
973C42—44no—
974C42—44no—
975C42—84no—
976C23—22no—
977C23—24no—
978C23—22no—
979C23—22no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—22no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—22no—
1003C23—24no—
1004C23—24no—
1005C23—22no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—22no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—22no—
1014C23—22no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—432no—
1021C23—432no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—41no—
1047C23—42no—
1048C23—41no—
1049C23—41no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—41no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—41no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—41no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—41no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—41no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
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—42no—
1109C23—42no—
1110C23—41no—
1111C23—41no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—816no—
1116C23—816no—
1117C23—816no—
1118C23—816no—
1119C23—816no—
1120C23—816no—
1121C23—816no—
1122C23—816no—
1123C23—816no—
1124C23—816no—
1125C23—816no—
1126C23—816no—
1127C23—816no—
1128C23#53714yes—
1129C23#54618yes—
1130C23C23×D411yescharacteristic
1131C23C23×D411yescharacteristic
1132C23C22×#4112yes—
1133C23C2×H(5,𝔽2)12yes—
1134C23C2×H(5,𝔽2)11yescharacteristic
1135C23C2×H(5,𝔽2)11yescharacteristic
1136C23C2×H(5,𝔽2)12yes—
1137C23C2×H(5,𝔽2)11yescharacteristic
1138C23C2×H(5,𝔽2)12yes—
1139C23C2×2−1+411yescharacteristic
1140C23#58511yescharacteristic
1141Q8—88no—
1142D4—232no—
1143D4—432no—
1144D4—416no—
1145D4—416no—
1146D4—88no—
1147D4—816no—
1148D4—816no—
1149D4—88no—
1150D4—816no—
1151D4—816no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—416no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—42no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
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—41no—
1224C2×C4—41no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—41no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—41no—
1232C2×C4—42no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—88no—
1257C2×C4—816no—
1258C2×C4—816no—
1259C2×C4#52514yes—
1260C2×C4#53514yes—
1261C2×C4D4214yes—
1262C22—28no—
1263C22—24no—
1264C22—24no—
1265C22—28no—
1266C22—28no—
1267C22—24no—
1268C22—42no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—42no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—42no—
1286C22—44no—
1287C22—42no—
1288C22—42no—
1289C22—44no—
1290C22—44no—
1291C22—42no—
1292C22—42no—
1293C22—44no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—44no—
1299C22—44no—
1300C22—864no—
1301C22—82no—
1302C22—82no—
1303C22—82no—
1304C22—81no—
1305C22—82no—
1306C22—82no—
1307C22—82no—
1308C22—82no—
1309C22—82no—
1310C22—82no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—82no—
1315C22—81no—
1316C22—82no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—82no—
1321C22—82no—
1322C22—82no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22C2×#52511yescharacteristic
1327C22C2×#53511yescharacteristic
1328C22C2×#53711yescharacteristic
1329C22C2×D4211yescharacteristic
1330C22C2×#54612yes—
1331C22#348411yescharacteristic
1332C22#348411yescharacteristic
1333C22#348412yes—
1334C22#348811yescharacteristic
1335C22#348911yescharacteristic
1336C22#349012yes—
1337C22#349811yescharacteristic
1338C22#351412yes—
1339C22#351912yes—
1340C22#351912yes—
1341C22#352012yes—
1342C22#353212yes—
1343C22#353611yescharacteristic
1344C22#353612yes—
1345C22#354211yescharacteristic
1346C22#354312yes—
1347C22#354312yes—
1348C22#355812yes—
1349C4—24no—
1350C4—24no—
1351C4—24no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—42no—
1356C4—44no—
1357C4—44no—
1358C4—42no—
1359C4—81no—
1360C4—81no—
1361C4—82no—
1362C4—81no—
1363C4—82no—
1364C4—82no—
1365C4—81no—
1366C4—82no—
1367C2—48no—
1368C2—44no—
1369C2—82no—
1370C2—84no—
1371C2—161no—
1372C2#3523611yescharacteristic
1373C2#3600411yescharacteristic
1374C2#3609811yescharacteristic
1375C2#3764811yescharacteristic
1376C2#3767411yescharacteristic
1377C2#4048811yescharacteristic
1378C2#4248411yescharacteristic
1379C2#4309512yes—
1380C2#4310112yes—
1381C2#4868512yes—
1382C2#4993412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2540C2semidirect
2. C2×#2408C2semidirect
3. C2×#2459C2semidirect
4. C2×D4×C22⋊C4C2semidirect
5. #16809C2semidirect
6. #16801C2semidirect
7. #16509C2semidirect
8. #16398C2semidirect
9. #15281C2semidirect
10. #15280C2semidirect
11. #15278C2semidirect
12. #15268C2semidirect
13. #14860C2semidirect
14. #14825C2semidirect
15. #14813C2semidirect
16. #14806C2semidirect
17. #14717C2semidirect
18. #14716C2semidirect
19. #14715C2semidirect
20. #14521C2semidirect
21. #14363C2semidirect
22. #14299C2semidirect
23. #13891C2semidirect
25. C22×#124C22semidirect
26. C22×C22⋊Q8C22semidirect
28. C22×#121C22semidirect
38. C2×#400C22semidirect
39. C2×#399C22semidirect
40. C2×#399C22semidirect
41. C2×#396C22semidirect
46. C2×#394C22semidirect
47. C2×#394C22semidirect
49. C2×#393C22semidirect
56. C2×#392C22semidirect
58. C2×#391C22semidirect
62. C2×#390C22semidirect
63. C2×#390C22semidirect
65. C2×#388C22semidirect
66. C2×#388C22semidirect
67. C2×#388C22semidirect
68. C2×#388C22semidirect
69. C2×#387C22semidirect
73. C2×#386C22semidirect
74. C2×#386C22semidirect
75. C2×#386C22semidirect
76. C2×#381C22semidirect
82. C2×C4×C4⋊C4C22semidirect
84. #1445C22semidirect
85. #1444C22semidirect
86. #1442C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
89. #1440C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
115. #1437C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. C4⋊#95C22semidirect
119. #1434C22semidirect
120. #1434C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
247. #392D4semidirect
273. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25402
C2×#24082
C2×#24592
C2×D4×C22⋊C42
#168092
#168012
#165092
#163982
#152812
#152802
#152782
#152682
#148602
#148252
#148132
#148062
#147172
#147162
#147152
#145212
#143632
#142992
#138912