Finite Group Databasebeta

← #1259497

Subgroups — #1259497

Order 512.

5062 conjugacy classes of subgroups.

The subgroup lattice has 1421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2561C211yesmaximal, characteristic, complemented
2C2×#2404C211yesmaximal, characteristic, complemented
3C2×#2407C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
5#17077C211yesmaximal, characteristic, complemented
6#16810C211yesmaximal, characteristic, complemented
7#16632C211yesmaximal, characteristic, complemented
8#16395C211yesmaximal, characteristic, complemented
9#15418C212yesmaximal, complemented
10#15369C212yesmaximal, complemented
11#15281C212yesmaximal, complemented
12#15266C212yesmaximal, complemented
13#15160C211yesmaximal, characteristic, complemented
14#14885C211yesmaximal, characteristic, complemented
15#14820C211yesmaximal, characteristic, complemented
16#14762C211yesmaximal, characteristic, complemented
17#14730C212yesmaximal, complemented
18#14716C211yesmaximal, characteristic, complemented
19#14715C212yesmaximal, complemented
20#14534C212yesmaximal, complemented
21#14391C212yesmaximal, complemented
22#14319C211yesmaximal, characteristic, complemented
23#13886C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic, complemented
25C24×D4C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic, complemented
27C22×#121C2211yescharacteristic, complemented
28C22×#120C2212yes—
29C22×#120C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34#2561—28no—
35#2407—28no—
36#2404—28no—
37C2×#397C2211yescharacteristic
38C2×#397C2211yescharacteristic, complemented
39C2×#397C2211yescharacteristic, complemented
40C2×#394C2212yes—
41C2×#394C2212yescomplemented
42C2×#394C2212yescomplemented
43C2×#393C2211yescharacteristic
44C2×#393C2211yescharacteristic, complemented
45C2×#393C2211yescharacteristic, complemented
46C2×#392C2211yescharacteristic
47C2×#392C2212yes—
48C2×#392C2212yes—
49C2×#392C2212yes—
50C2×#392C2212yes—
51C2×#392C2211yescharacteristic, complemented
52C2×#392C2211yescharacteristic, complemented
53D4×C22⋊C4—28no—
54C2×#391C2211yescharacteristic, complemented
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic, complemented
58C2×#390C2212yescomplemented
59C2×#388C2212yes—
60C2×#388C2212yescomplemented
61C2×#388C2212yescomplemented
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#386C2211yescharacteristic
65C2×#386C2211yescharacteristic
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#386C2212yescomplemented
69C2×#386C2212yescomplemented
70C2×#386C2212yescomplemented
71C2×#386C2212yescomplemented
72C2×#386C2212yescomplemented
73C2×#385C2212yescomplemented
74C2×#381C2212yescomplemented
75C2×#381C2211yescharacteristic, complemented
76C2×#380C2211yescharacteristic
77C2×#380C2211yescharacteristic, complemented
78C2×#379C2212yes—
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×#379C2212yes—
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2211yescharacteristic, complemented
84#1446C2211yescharacteristic, complemented
85#1445C2211yescharacteristic, complemented
86#1444C2211yescharacteristic, complemented
87#1443C2212yescomplemented
88#1443C2212yescomplemented
89#1442C2212yescomplemented
90#1442C2212yescomplemented
91#1440C2212yes—
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1439C2211yescharacteristic
95#1439C2212yes—
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2211yescharacteristic, complemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2211yescharacteristic, complemented
105#1439C2212yescomplemented
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1438C2212yes—
111#1438C2212yescomplemented
112#1438C2211yescharacteristic, complemented
113#1438C2212yescomplemented
114#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1437C2212yescomplemented
117#1437C2212yescomplemented
118#1436C2212yescomplemented
119#1436C2212yescomplemented
120C4⋊#95C2211yescharacteristic, complemented
121#1434C2211yescharacteristic, complemented
122C22⋊#95C2212yes—
123C22⋊#95C2212yescomplemented
124C22⋊#95C2211yescharacteristic, complemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2211yescharacteristic, complemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C22×#41—24no—
130C22×#41—24no—
131C22×#41—44no—
132C22×#41—44no—
133C22×#41—42no—
134C23×Q8C2311yescharacteristic
135C23×D4—24no—
136C23×D4—24no—
137C23×D4—24no—
138C23×D4—44no—
139C23×D4—44no—
140C23×D4C2311yescharacteristic
141C23×D4C2311yescharacteristic
142C23×D4C2311yescharacteristic
143C23×D4C2312yes—
144C23×D4C2311yescharacteristic
145C23×D4C2312yes—
146C23×D4C2312yes—
147C23×D4C2312yes—
148C23×D4C2312yes—
149C23×D4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C24×C4C2312yes—
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2311yescharacteristic
156C2×C22⋊Q8—24no—
157C2×C22⋊Q8—24no—
158C2×C22⋊Q8—42no—
159C2×#121—24no—
160C2×#121—44no—
161C2×#120—28no—
162C2×#120—44no—
163C2×#120—44no—
164C2×#120—44no—
165C2×#120—44no—
166C2×#120—44no—
167C2×C4×D4—24no—
168C2×C4×D4—44no—
169C2×C4×D4—44no—
170C2×C4×D4D418yescomplemented
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—42no—
183C22×C22⋊C4—42no—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2312yes—
225C22×C42C2311yescharacteristic
226#397—24no—
227#397—24no—
228#397—42no—
229#394—28no—
230#394—44no—
231#394—44no—
232#393—24no—
233#393—24no—
234#393D418yescomplemented
235#392—28no—
236#392—28no—
237#392—24no—
238#392—24no—
239#392—42no—
240#392—44no—
241#392—44no—
242#391—24no—
243#390—24no—
244#390—24no—
245#390—24no—
246#390—44no—
247#388—28no—
248#388—28no—
249#388—44no—
250#386—24no—
251#386—24no—
252#386—28no—
253#386—24no—
254#386—24no—
255#386—28no—
256#386—28no—
257#386—28no—
258#386—28no—
259#386—44no—
260#386—44no—
261#385—28no—
262#381—28no—
263#381—24no—
264#380—24no—
265#380—24no—
266#379—28no—
267#379—24no—
268#379—24no—
269#379—44no—
270C4×C22⋊C4—24no—
271C4×C22⋊C4—24no—
272C2×#95C2311yescharacteristic
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
302C2×#95C2312yes—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—24no—
313C25—24no—
314C25—22no—
315C25—41no—
316C25—41no—
317C25—42no—
318C25—42no—
319C25—41no—
320C25—41no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25C2411yescharacteristic
326C25C2411yescharacteristic
327C25C2412yes—
328C25C2411yescharacteristic
329C25C2411yescharacteristic
330C25C2411yescharacteristic
331C2×#41—416no—
332C2×#41—416no—
333C2×#41—416no—
334C2×#41—432no—
335C2×#41—432no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—42no—
339C22×Q8—42no—
340C22×Q8C2×D414yescomplemented
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—232no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
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—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—24no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—22no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
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—432no—
401C22×D4—432no—
402C22×D4—416no—
403C22×D4—416no—
404C22×D4C2×D414yes—
405C22×D4#4114yescomplemented
406C23×C4—24no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—24no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—24no—
417C23×C4—22no—
418C23×C4—24no—
419C23×C4—24no—
420C23×C4—22no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4—41no—
429C23×C4—41no—
430C23×C4—42no—
431C23×C4—42no—
432C23×C4—42no—
433C23×C4—42no—
434C23×C4—42no—
435C23×C4C2×D414yes—
436C23×C4C2×D414yes—
437C23×C4#4114yescomplemented
438C23×C4C2412yes—
439C23×C4C2411yescharacteristic
440C23×C4C2412yes—
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2412yes—
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2412yes—
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2412yes—
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C22⋊Q8—416no—
456#121—416no—
457#120—432no—
458#120—432no—
459C4×D4—416no—
460C4×D4—416no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
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×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4C2×D414yes—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
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—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—416no—
534C2×C22⋊C4—416no—
535C2×C22⋊C4—41no—
536C2×C22⋊C4—41no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—41no—
539C2×C22⋊C4—41no—
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—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—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⋊C4—42no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4C2×D414yes—
587C2×C22⋊C4C2×D414yes—
588C2×C22⋊C4C2×D414yes—
589C2×C22⋊C4C2×D418yes—
590C2×C42—22no—
591C2×C42—24no—
592C2×C42—42no—
593C2×C42—42no—
594C2×C42—42no—
595C2×C42—42no—
596C2×C42C2×D414yes—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—24no—
601#95—22no—
602#95—22no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—22no—
608#95—24no—
609#95—24no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—24no—
614#95—22no—
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#95—42no—
625#95—42no—
626#95C2×D414yescomplemented
627#95C2×D418yescomplemented
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—22no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—21no—
648C24—21no—
649C24—22no—
650C24—22no—
651C24—21no—
652C24—21no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—21no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—21no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—21no—
690C24—44no—
691C24—44no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—44no—
701C24—44no—
702C24—48no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—44no—
707C24—44no—
708C24—44no—
709C24—44no—
710C24—44no—
711C24—44no—
712C24—44no—
713C24—44no—
714C24—84no—
715C24—82no—
716C24—82no—
717C24—84no—
718C24—84no—
719C24—84no—
720C24—82no—
721C24—82no—
722C24—84no—
723C24—84no—
724C24—84no—
725C24—84no—
726C24—84no—
727C24—84no—
728C24—84no—
729C24—84no—
730C24—84no—
731C24—84no—
732C24—84no—
733C24—84no—
734C24C22×D412yes—
735C24C22×D412yes—
736C24C22×D412yes—
737C24C2×#4112yes—
738C24C2×#4112yes—
739C24C2×#4112yes—
740C24H(5,𝔽2)14yes—
741C24H(5,𝔽2)14yes—
742C24H(5,𝔽2)14yes—
743C24H(5,𝔽2)12yes—
744C24C2511yescharacteristic
745#41—4128no—
746C2×Q8—28no—
747C2×Q8—48no—
748C2×Q8—44no—
749C2×Q8—44no—
750C2×Q8—48no—
751C2×D4—216no—
752C2×D4—216no—
753C2×D4—28no—
754C2×D4—28no—
755C2×D4—216no—
756C2×D4—28no—
757C2×D4—28no—
758C2×D4—28no—
759C2×D4—28no—
760C2×D4—28no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—48no—
771C2×D4—44no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—4128no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—48no—
782C2×D4—44no—
783C2×D4—48no—
784C2×D4—44no—
785C2×D4—48no—
786C2×D4—48no—
787C2×D4—48no—
788C2×D4—48no—
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—84no—
798C2×D4—84no—
799C2×D4—84no—
800C2×D4—84no—
801C2×D4—84no—
802C2×D4—84no—
803C2×D4—84no—
804C2×D4—84no—
805C2×D4—84no—
806C2×D4—84no—
807C2×D4—84no—
808C2×D4—84no—
809C2×D4—84no—
810C2×D4—84no—
811C2×D4—84no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—28no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—28no—
850C22×C4—28no—
851C22×C4—28no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—21no—
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—21no—
871C22×C4—21no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—21no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—21no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—44no—
903C22×C4—48no—
904C22×C4—48no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—48no—
908C22×C4—48no—
909C22×C4—48no—
910C22×C4—48no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—48no—
914C22×C4—48no—
915C22×C4—48no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—48no—
919C22×C4—48no—
920C22×C4—48no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—84no—
924C22×C4—84no—
925C22×C4—84no—
926C22×C4—82no—
927C22×C4—82no—
928C22×C4—84no—
929C22×C4—84no—
930C22×C4C22×D412yes—
931C22×C4C22×D412yes—
932C22×C4C22×D414yes—
933C22×C4C22×D412yes—
934C22×C4C22×D414yes—
935C22×C4C22×D412yes—
936C22×C4C22×D412yes—
937C22×C4C22×D412yes—
938C22×C4C22×D412yes—
939C22×C4C2×#4112yes—
940C22×C4C2×#4112yes—
941C22×C4C2×#4112yes—
942C22×C4H(5,𝔽2)12yes—
943C4⋊C4—44no—
944C4⋊C4—48no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—84no—
949C4⋊C4—84no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—44no—
953C22⋊C4—48no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—44no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4—44no—
966C22⋊C4—48no—
967C22⋊C4—48no—
968C22⋊C4—48no—
969C22⋊C4—44no—
970C22⋊C4—48no—
971C22⋊C4—48no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—82no—
975C22⋊C4—82no—
976C22⋊C4—84no—
977C22⋊C4—84no—
978C22⋊C4—84no—
979C22⋊C4—84no—
980C22⋊C4—84no—
981C22⋊C4—82no—
982C22⋊C4—82no—
983C22⋊C4—84no—
984C22⋊C4—84no—
985C22⋊C4—84no—
986C22⋊C4—84no—
987C22⋊C4—84no—
988C22⋊C4—84no—
989C42—44no—
990C42—44no—
991C42—84no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—24no—
1002C23—24no—
1003C23—22no—
1004C23—22no—
1005C23—24no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—24no—
1021C23—24no—
1022C23—24no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—24no—
1033C23—24no—
1034C23—24no—
1035C23—24no—
1036C23—24no—
1037C23—24no—
1038C23—24no—
1039C23—24no—
1040C23—22no—
1041C23—22no—
1042C23—24no—
1043C23—24no—
1044C23—24no—
1045C23—416no—
1046C23—416no—
1047C23—416no—
1048C23—416no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—42no—
1056C23—41no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—41no—
1068C23—41no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—42no—
1086C23—41no—
1087C23—41no—
1088C23—42no—
1089C23—42no—
1090C23—41no—
1091C23—41no—
1092C23—42no—
1093C23—42no—
1094C23—41no—
1095C23—41no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—41no—
1103C23—41no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—42no—
1110C23—42no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—41no—
1115C23—41no—
1116C23—42no—
1117C23—42no—
1118C23—41no—
1119C23—41no—
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—88no—
1144C23—88no—
1145C23—816no—
1146C23—816no—
1147C23—88no—
1148C23—88no—
1149C23—88no—
1150C23—88no—
1151C23—816no—
1152C23—816no—
1153C23—816no—
1154C23—816no—
1155C23—88no—
1156C23—816no—
1157C23—816no—
1158C23—88no—
1159C23—88no—
1160C23—88no—
1161C23#53414yes—
1162C23#53514yes—
1163C23#55014yes—
1164C23C23×D411yescharacteristic
1165C23C23×D411yescharacteristic
1166C23C22×#4111yescharacteristic
1167C23C22×#4111yescharacteristic
1168C23C2×H(5,𝔽2)12yes—
1169C23C2×H(5,𝔽2)12yes—
1170C23C2×H(5,𝔽2)11yescharacteristic
1171C23C2×H(5,𝔽2)11yescharacteristic
1172C23C2×H(5,𝔽2)12yes—
1173C23#58511yescharacteristic
1174C23#58512yes—
1175Q8—416no—
1176D4—232no—
1177D4—416no—
1178D4—416no—
1179D4—416no—
1180D4—416no—
1181D4—432no—
1182D4—816no—
1183D4—816no—
1184D4—816no—
1185D4—816no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—416no—
1214C2×C4—416no—
1215C2×C4—432no—
1216C2×C4—41no—
1217C2×C4—42no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—41no—
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—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—42no—
1241C2×C4—41no—
1242C2×C4—41no—
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—41no—
1252C2×C4—42no—
1253C2×C4—41no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—42no—
1263C2×C4—42no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—42no—
1267C2×C4—42no—
1268C2×C4—42no—
1269C2×C4—42no—
1270C2×C4—42no—
1271C2×C4—42no—
1272C2×C4—42no—
1273C2×C4—42no—
1274C2×C4—42no—
1275C2×C4—42no—
1276C2×C4—42no—
1277C2×C4—42no—
1278C2×C4—42no—
1279C2×C4—42no—
1280C2×C4—42no—
1281C2×C4—42no—
1282C2×C4—42no—
1283C2×C4—42no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—88no—
1287C2×C4—88no—
1288C2×C4—88no—
1289C2×C4#52514yes—
1290C2×C4D4214yes—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—28no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—44no—
1304C22—44no—
1305C22—44no—
1306C22—42no—
1307C22—42no—
1308C22—44no—
1309C22—44no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—44no—
1316C22—44no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—44no—
1327C22—44no—
1328C22—44no—
1329C22—44no—
1330C22—44no—
1331C22—42no—
1332C22—42no—
1333C22—44no—
1334C22—44no—
1335C22—44no—
1336C22—44no—
1337C22—44no—
1338C22—44no—
1339C22—42no—
1340C22—42no—
1341C22—832no—
1342C22—832no—
1343C22—82no—
1344C22—81no—
1345C22—81no—
1346C22—82no—
1347C22—82no—
1348C22—82no—
1349C22—82no—
1350C22—81no—
1351C22—81no—
1352C22—82no—
1353C22—82no—
1354C22—82no—
1355C22—81no—
1356C22—81no—
1357C22—82no—
1358C22—82no—
1359C22—82no—
1360C22—81no—
1361C22—81no—
1362C22—82no—
1363C22C2×#52511yescharacteristic
1364C22C2×#53411yescharacteristic
1365C22C2×#53511yescharacteristic
1366C22C2×D4211yescharacteristic
1367C22C2×#55011yescharacteristic
1368C22D4×#4111yescharacteristic
1369C22#348412yes—
1370C22#348411yescharacteristic
1371C22#348811yescharacteristic
1372C22#348812yes—
1373C22#349012yes—
1374C22#349012yes—
1375C22#349412yes—
1376C22#350011yescharacteristic
1377C22#350611yescharacteristic
1378C22#351312yes—
1379C22#351911yescharacteristic
1380C22#353212yes—
1381C22#353212yes—
1382C22#353412yes—
1383C22#353412yes—
1384C22#355812yes—
1385C22#356012yes—
1386C4—24no—
1387C4—24no—
1388C4—42no—
1389C4—44no—
1390C4—42no—
1391C4—42no—
1392C4—44no—
1393C4—42no—
1394C4—42no—
1395C4—82no—
1396C4—81no—
1397C4—81no—
1398C4—82no—
1399C4—82no—
1400C4—81no—
1401C4—82no—
1402C4—82no—
1403C2—44no—
1404C2—44no—
1405C2—44no—
1406C2—84no—
1407C2—82no—
1408C2—82no—
1409C2#3505011yescharacteristic
1410C2#3573011yescharacteristic
1411C2#3610111yescharacteristic
1412C2#3764411yescharacteristic
1413C2#3767711yescharacteristic
1414C2#4058811yescharacteristic
1415C2#4193611yescharacteristic
1416C2#4309912yes—
1417C2#4423112yes—
1418C2#4788912yes—
1419C2#4855512yes—
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×#2561C2semidirect
2. C2×#2404C2semidirect
3. C2×#2407C2semidirect
4. C2×D4×C22⋊C4C2semidirect
5. #17077C2semidirect
6. #16810C2semidirect
7. #16632C2semidirect
8. #16395C2semidirect
9. #15418C2semidirect
10. #15369C2semidirect
11. #15281C2semidirect
12. #15266C2semidirect
13. #15160C2semidirect
14. #14885C2semidirect
15. #14820C2semidirect
16. #14762C2semidirect
17. #14730C2semidirect
18. #14716C2semidirect
19. #14715C2semidirect
20. #14534C2semidirect
21. #14391C2semidirect
22. #14319C2semidirect
23. #13886C2semidirect
24. C23×#41C22semidirect
26. C22×C22⋊Q8C22semidirect
27. C22×#121C22semidirect
38. C2×#397C22semidirect
39. C2×#397C22semidirect
41. C2×#394C22semidirect
42. C2×#394C22semidirect
44. C2×#393C22semidirect
45. C2×#393C22semidirect
51. C2×#392C22semidirect
52. C2×#392C22semidirect
54. C2×#391C22semidirect
57. C2×#390C22semidirect
58. C2×#390C22semidirect
60. C2×#388C22semidirect
61. C2×#388C22semidirect
68. C2×#386C22semidirect
69. C2×#386C22semidirect
70. C2×#386C22semidirect
71. C2×#386C22semidirect
72. C2×#386C22semidirect
73. C2×#385C22semidirect
74. C2×#381C22semidirect
75. C2×#381C22semidirect
77. C2×#380C22semidirect
83. C2×C4×C22⋊C4C22semidirect
84. #1446C22semidirect
85. #1445C22semidirect
86. #1444C22semidirect
87. #1443C22semidirect
88. #1443C22semidirect
89. #1442C22semidirect
90. #1442C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
116. #1437C22semidirect
117. #1437C22semidirect
118. #1436C22semidirect
119. #1436C22semidirect
120. C4⋊#95C22semidirect
121. #1434C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
170. C2×C4×D4D4semidirect
234. #393D4semidirect
340. C22×Q8C2×D4semidirect
405. C22×D4#41semidirect
437. C23×C4#41semidirect
626. #95C2×D4semidirect
627. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25612
C2×#24042
C2×#24072
C2×D4×C22⋊C42
#170772
#168102
#166322
#163952
#154182
#153692
#152812
#152662
#151602
#148852
#148202
#147622
#147302
#147162
#147152
#145342
#143912
#143192
#138862