Finite Group Databasebeta

← #1259473

Subgroups — #1259473

Order 512.

5170 conjugacy classes of subgroups.

The subgroup lattice has 1431 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2539C211yesmaximal, characteristic, complemented
2C2×#2404C211yesmaximal, characteristic, complemented
3C2×#2407C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
5#17068C211yesmaximal, characteristic, complemented
6#16814C211yesmaximal, characteristic, complemented
7#16508C211yesmaximal, characteristic, complemented
8#16392C211yesmaximal, characteristic, complemented
9#15403C212yesmaximal, complemented
10#15281C212yesmaximal, complemented
11#15270C212yesmaximal, complemented
12#15266C212yesmaximal, complemented
13#15161C211yesmaximal, characteristic, complemented
14#14885C211yesmaximal, characteristic, complemented
15#14765C211yesmaximal, characteristic, complemented
16#14734C211yesmaximal, characteristic, complemented
17#14721C212yesmaximal, complemented
18#14717C211yesmaximal, characteristic, complemented
19#14715C212yesmaximal, complemented
20#14534C212yesmaximal, complemented
21#14407C212yesmaximal, complemented
22#14311C211yesmaximal, characteristic, complemented
23#13886C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic, complemented
25C24×D4C2211yescharacteristic
26C22×#123C2212yescomplemented
27C22×C22⋊Q8C2211yescharacteristic, complemented
28C22×#121C2211yescharacteristic, complemented
29C22×#120C2212yes—
30C22×#120C2212yes—
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35#2539—28no—
36#2407—28no—
37#2404—28no—
38C2×#399C2211yescharacteristic
39C2×#399C2211yescharacteristic, complemented
40C2×#399C2211yescharacteristic, complemented
41C2×#394C2212yescomplemented
42C2×#394C2212yescomplemented
43C2×#394C2212yescomplemented
44C2×#394C2212yescomplemented
45C2×#393C2211yescharacteristic
46C2×#393C2211yescharacteristic, complemented
47C2×#393C2211yescharacteristic, complemented
48C2×#392C2212yes—
49C2×#392C2212yes—
50C2×#392C2212yes—
51C2×#392C2212yes—
52C2×#392C2211yescharacteristic
53C2×#392C2211yescharacteristic, complemented
54C2×#392C2211yescharacteristic, complemented
55D4×C22⋊C4—28no—
56C2×#391C2211yescharacteristic, complemented
57C2×#390C2212yes—
58C2×#390C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#390C2212yescomplemented
61C2×#390C2211yescharacteristic, complemented
62C2×#388C2212yescomplemented
63C2×#388C2212yescomplemented
64C2×#386C2211yescharacteristic
65C2×#386C2211yescharacteristic
66C2×#386C2211yescharacteristic
67C2×#386C2211yescharacteristic
68C2×#386C2212yes—
69C2×#386C2212yes—
70C2×#386C2212yescomplemented
71C2×#386C2212yescomplemented
72C2×#386C2212yescomplemented
73C2×#386C2212yescomplemented
74C2×#385C2212yescomplemented
75C2×#385C2212yescomplemented
76C2×#381C2211yescharacteristic, complemented
77C2×#380C2211yescharacteristic
78C2×#380C2211yescharacteristic, complemented
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×#379C2212yes—
82C2×#379C2212yes—
83C2×C4×C22⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic, complemented
85#1446C2211yescharacteristic, complemented
86#1445C2211yescharacteristic, complemented
87#1444C2212yescomplemented
88#1442C2212yescomplemented
89#1442C2211yescharacteristic, complemented
90#1441C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2211yescharacteristic
98#1439C2211yescharacteristic, complemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2211yescharacteristic, complemented
107#1439C2212yescomplemented
108#1438C2212yes—
109#1438C2212yes—
110#1438C2212yes—
111#1438C2212yes—
112#1438C2212yes—
113#1438C2211yescharacteristic, complemented
114#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1437C2212yescomplemented
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119#1436C2212yescomplemented
120C4⋊#95C2211yescharacteristic, complemented
121#1434C2211yescharacteristic, complemented
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic, complemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2211yescharacteristic, complemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C22×#41—24no—
130C22×#41—24no—
131C22×#41—44no—
132C22×#41—42no—
133C22×#41—44no—
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×D4C2312yes—
145C23×D4C2312yes—
146C23×D4C2312yes—
147C23×D4C2312yes—
148C23×D4C2311yescharacteristic
149C23×D4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C24×C4C2312yes—
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2311yescharacteristic
156C2×#123—28no—
157C2×#123—44no—
158C2×#123—44no—
159C2×C22⋊Q8—24no—
160C2×C22⋊Q8—44no—
161C2×#121—24no—
162C2×#121—24no—
163C2×#121—42no—
164C2×#120—28no—
165C2×#120—28no—
166C2×#120—44no—
167C2×#120—44no—
168C2×#120—44no—
169C2×#120—44no—
170C2×C4×D4—24no—
171C2×C4×D4—44no—
172C2×C4×D4—44no—
173C2×C4×D4D418yescomplemented
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2311yescharacteristic
183C22×C22⋊C4—24no—
184C22×C22⋊C4—24no—
185C22×C22⋊C4—24no—
186C22×C22⋊C4—24no—
187C22×C22⋊C4—42no—
188C22×C22⋊C4—42no—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2312yes—
228C22×C42C2311yescharacteristic
229C22×C42C2312yes—
230C22×C42C2311yescharacteristic
231#399—24no—
232#399—24no—
233#399—42no—
234#394—28no—
235#394—44no—
236#394—44no—
237#394—44no—
238#393—24no—
239#393—24no—
240#393—42no—
241#392—28no—
242#392—24no—
243#392—24no—
244#392—28no—
245#392—44no—
246#392—44no—
247#392D418yescomplemented
248#391—24no—
249#390—28no—
250#390—24no—
251#390—28no—
252#390—24no—
253#390—24no—
254#388—44no—
255#388—44no—
256#386—28no—
257#386—24no—
258#386—24no—
259#386—28no—
260#386—24no—
261#386—24no—
262#386—28no—
263#386—28no—
264#386—28no—
265#386—44no—
266#385—28no—
267#385—44no—
268#381—24no—
269#380—24no—
270#380—24no—
271#379—24no—
272#379—24no—
273#379—44no—
274#379—44no—
275C4×C22⋊C4—24no—
276C4×C22⋊C4—24no—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2311yescharacteristic
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2311yescharacteristic
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—24no—
315C25—24no—
316C25—22no—
317C25—22no—
318C25—41no—
319C25—41no—
320C25—42no—
321C25—42no—
322C25—41no—
323C25—41no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25C2412yes—
329C25C2411yescharacteristic
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C25C2411yescharacteristic
333C25C2411yescharacteristic
334C2×#41—416no—
335C2×#41—416no—
336C2×#41—432no—
337C2×#41—416no—
338C2×#41—432no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—24no—
342C22×Q8—22no—
343C22×Q8—42no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—232no—
347C22×D4—24no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
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—22no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—22no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—24no—
375C22×D4—22no—
376C22×D4—24no—
377C22×D4—42no—
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—42no—
401C22×D4—432no—
402C22×D4—432no—
403C22×D4—416no—
404C22×D4—416no—
405C22×D4C2×D414yes—
406C22×D4C2×D418yes—
407C22×D4C2×D414yescomplemented
408C22×D4#4114yescomplemented
409C23×C4—24no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—24no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—24no—
420C23×C4—22no—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—22no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4—42no—
429C23×C4—42no—
430C23×C4—42no—
431C23×C4—41no—
432C23×C4—41no—
433C23×C4—42no—
434C23×C4—42no—
435C23×C4—42no—
436C23×C4—42no—
437C23×C4—42no—
438C23×C4C2×D414yes—
439C23×C4C2×D414yes—
440C23×C4#4114yescomplemented
441C23×C4C2412yes—
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2412yes—
447C23×C4C2412yes—
448C23×C4C2411yescharacteristic
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2412yes—
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2412yes—
455C23×C4C2412yes—
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458#123—432no—
459C22⋊Q8—416no—
460#121—416no—
461#120—432no—
462#120—432no—
463C4×D4—416no—
464C4×D4—416no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4C2×D414yes—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—24no—
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—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
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—22no—
528C2×C22⋊C4—22no—
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—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—416no—
549C2×C22⋊C4—416no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C22⋊C4—41no—
554C2×C22⋊C4—41no—
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⋊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⋊C4C2×D414yes—
597C2×C22⋊C4C2×D414yes—
598C2×C22⋊C4C2×D414yes—
599C2×C22⋊C4C2×D418yescomplemented
600C2×C42—22no—
601C2×C42—24no—
602C2×C42—42no—
603C2×C42—42no—
604C2×C42—42no—
605C2×C42—42no—
606C2×C42C2×D414yes—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—24no—
611#95—22no—
612#95—22no—
613#95—24no—
614#95—22no—
615#95—24no—
616#95—24no—
617#95—24no—
618#95—24no—
619#95—24no—
620#95—24no—
621#95—24no—
622#95—24no—
623#95—24no—
624#95—22no—
625#95—42no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95—42no—
630#95—42no—
631#95—42no—
632#95—42no—
633#95—42no—
634#95—42no—
635#95C2×D414yescomplemented
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—22no—
645C24—22no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—28no—
663C24—28no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—21no—
694C24—21no—
695C24—22no—
696C24—21no—
697C24—21no—
698C24—44no—
699C24—44no—
700C24—48no—
701C24—48no—
702C24—48no—
703C24—48no—
704C24—44no—
705C24—44no—
706C24—44no—
707C24—44no—
708C24—44no—
709C24—44no—
710C24—48no—
711C24—48no—
712C24—48no—
713C24—48no—
714C24—44no—
715C24—44no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24—44no—
720C24—44no—
721C24—44no—
722C24—82no—
723C24—84no—
724C24—84no—
725C24—82no—
726C24—82no—
727C24—82no—
728C24—84no—
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—
742C24C22×D414yes—
743C24C22×D412yes—
744C24C22×D412yes—
745C24C22×D412yes—
746C24C2×#4112yes—
747C24C2×#4112yes—
748C24C2×#4112yes—
749C24H(5,𝔽2)14yes—
750C24H(5,𝔽2)14yes—
751C242−1+412yes—
752C24C2511yescharacteristic
753#41—4128no—
754C2×Q8—28no—
755C2×Q8—48no—
756C2×Q8—48no—
757C2×Q8—44no—
758C2×Q8—44no—
759C2×D4—216no—
760C2×D4—216no—
761C2×D4—28no—
762C2×D4—28no—
763C2×D4—216no—
764C2×D4—28no—
765C2×D4—28no—
766C2×D4—216no—
767C2×D4—28no—
768C2×D4—28no—
769C2×D4—28no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—48no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—4128no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—48no—
794C2×D4—44no—
795C2×D4—48no—
796C2×D4—44no—
797C2×D4—48no—
798C2×D4—48no—
799C2×D4—48no—
800C2×D4—48no—
801C2×D4—48no—
802C2×D4—48no—
803C2×D4—48no—
804C2×D4—84no—
805C2×D4—84no—
806C2×D4—84no—
807C2×D4—84no—
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—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—28no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—21no—
862C22×C4—22no—
863C22×C4—28no—
864C22×C4—28no—
865C22×C4—28no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—22no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
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—21no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
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—22no—
900C22×C4—22no—
901C22×C4—21no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—44no—
910C22×C4—48no—
911C22×C4—48no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—48no—
915C22×C4—48no—
916C22×C4—48no—
917C22×C4—48no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—48no—
921C22×C4—48no—
922C22×C4—48no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—48no—
926C22×C4—48no—
927C22×C4—48no—
928C22×C4—44no—
929C22×C4—44no—
930C22×C4—84no—
931C22×C4—84no—
932C22×C4—84no—
933C22×C4—82no—
934C22×C4—82no—
935C22×C4—84no—
936C22×C4—84no—
937C22×C4C22×D412yes—
938C22×C4C22×D412yes—
939C22×C4C22×D414yes—
940C22×C4C22×D412yes—
941C22×C4C22×D412yes—
942C22×C4C22×D412yes—
943C22×C4C22×D412yes—
944C22×C4C22×D412yes—
945C22×C4C2×#4112yes—
946C22×C4C2×#4112yes—
947C22×C4C2×#4112yes—
948C22×C4H(5,𝔽2)14yes—
949C22×C4H(5,𝔽2)14yes—
950C22×C4H(5,𝔽2)12yes—
951C4⋊C4—44no—
952C4⋊C4—48no—
953C4⋊C4—48no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—48no—
957C4⋊C4—44no—
958C4⋊C4—84no—
959C4⋊C4—84no—
960C22⋊C4—216no—
961C22⋊C4—28no—
962C22⋊C4—28no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—48no—
968C22⋊C4—44no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—48no—
974C22⋊C4—48no—
975C22⋊C4—48no—
976C22⋊C4—48no—
977C22⋊C4—48no—
978C22⋊C4—48no—
979C22⋊C4—48no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—48no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—82no—
986C22⋊C4—82no—
987C22⋊C4—84no—
988C22⋊C4—84no—
989C22⋊C4—82no—
990C22⋊C4—82no—
991C22⋊C4—84no—
992C22⋊C4—84no—
993C22⋊C4—84no—
994C22⋊C4—84no—
995C22⋊C4—84no—
996C22⋊C4—84no—
997C22⋊C4—84no—
998C22⋊C4—84no—
999C42—44no—
1000C42—44no—
1001C42—84no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—24no—
1012C23—22no—
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—22no—
1026C23—22no—
1027C23—22no—
1028C23—24no—
1029C23—22no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—24no—
1034C23—24no—
1035C23—24no—
1036C23—24no—
1037C23—24no—
1038C23—22no—
1039C23—22no—
1040C23—24no—
1041C23—24no—
1042C23—22no—
1043C23—22no—
1044C23—24no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—22no—
1054C23—22no—
1055C23—416no—
1056C23—416no—
1057C23—416no—
1058C23—416no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—42no—
1066C23—42no—
1067C23—41no—
1068C23—42no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—41no—
1078C23—41no—
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—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—42no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—42no—
1101C23—42no—
1102C23—41no—
1103C23—41no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—41no—
1109C23—41no—
1110C23—42no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—42no—
1116C23—42no—
1117C23—41no—
1118C23—41no—
1119C23—42no—
1120C23—41no—
1121C23—41no—
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—88no—
1154C23—88no—
1155C23—816no—
1156C23—816no—
1157C23—88no—
1158C23—88no—
1159C23—88no—
1160C23—88no—
1161C23—816no—
1162C23—816no—
1163C23—816no—
1164C23—816no—
1165C23—88no—
1166C23—88no—
1167C23—816no—
1168C23—816no—
1169C23—88no—
1170C23—88no—
1171C23#53414yes—
1172C23#53514yes—
1173C23#54714yes—
1174C23C23×D411yescharacteristic
1175C23C23×D411yescharacteristic
1176C23C22×#4111yescharacteristic
1177C23C22×#4111yescharacteristic
1178C23C2×H(5,𝔽2)12yes—
1179C23C2×H(5,𝔽2)12yes—
1180C23C2×H(5,𝔽2)11yescharacteristic
1181C23C2×H(5,𝔽2)12yes—
1182C23C2×H(5,𝔽2)12yes—
1183C23C2×2−1+411yescharacteristic
1184C23#58511yescharacteristic
1185Q8—416no—
1186D4—232no—
1187D4—416no—
1188D4—416no—
1189D4—416no—
1190D4—416no—
1191D4—432no—
1192D4—816no—
1193D4—816no—
1194D4—816no—
1195D4—816no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—416no—
1227C2×C4—416no—
1228C2×C4—432no—
1229C2×C4—41no—
1230C2×C4—42no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—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—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—42no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—42no—
1263C2×C4—42no—
1264C2×C4—42no—
1265C2×C4—42no—
1266C2×C4—41no—
1267C2×C4—42no—
1268C2×C4—42no—
1269C2×C4—42no—
1270C2×C4—41no—
1271C2×C4—42no—
1272C2×C4—42no—
1273C2×C4—42no—
1274C2×C4—41no—
1275C2×C4—41no—
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—42no—
1287C2×C4—42no—
1288C2×C4—42no—
1289C2×C4—42no—
1290C2×C4—42no—
1291C2×C4—42no—
1292C2×C4—42no—
1293C2×C4—42no—
1294C2×C4—42no—
1295C2×C4—42no—
1296C2×C4—88no—
1297C2×C4—88no—
1298C2×C4—88no—
1299C2×C4#52514yes—
1300C2×C4D4214yes—
1301C22—24no—
1302C22—24no—
1303C22—24no—
1304C22—28no—
1305C22—24no—
1306C22—24no—
1307C22—24no—
1308C22—24no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—44no—
1316C22—44no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22—44no—
1322C22—44no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22—42no—
1328C22—44no—
1329C22—44no—
1330C22—44no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—44no—
1335C22—42no—
1336C22—42no—
1337C22—44no—
1338C22—44no—
1339C22—44no—
1340C22—44no—
1341C22—44no—
1342C22—44no—
1343C22—44no—
1344C22—44no—
1345C22—42no—
1346C22—42no—
1347C22—44no—
1348C22—44no—
1349C22—42no—
1350C22—42no—
1351C22—832no—
1352C22—832no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—82no—
1358C22—82no—
1359C22—82no—
1360C22—82no—
1361C22—82no—
1362C22—82no—
1363C22—82no—
1364C22—81no—
1365C22—81no—
1366C22—82no—
1367C22—82no—
1368C22—82no—
1369C22—82no—
1370C22—81no—
1371C22—81no—
1372C22—82no—
1373C22C2×#52511yescharacteristic
1374C22C2×#53411yescharacteristic
1375C22C2×#53511yescharacteristic
1376C22C2×D4211yescharacteristic
1377C22C2×#54711yescharacteristic
1378C22D4×#4111yescharacteristic
1379C22#348412yes—
1380C22#348411yescharacteristic
1381C22#348412yes—
1382C22#348911yescharacteristic
1383C22#349012yes—
1384C22#349012yes—
1385C22#349811yescharacteristic
1386C22#350611yescharacteristic
1387C22#350812yes—
1388C22#351912yes—
1389C22#352011yescharacteristic
1390C22#353212yes—
1391C22#353412yes—
1392C22#353612yes—
1393C22#353612yes—
1394C22#354312yes—
1395C22#355812yes—
1396C4—24no—
1397C4—24no—
1398C4—42no—
1399C4—44no—
1400C4—42no—
1401C4—42no—
1402C4—44no—
1403C4—44no—
1404C4—42no—
1405C4—42no—
1406C4—81no—
1407C4—81no—
1408C4—82no—
1409C4—82no—
1410C4—82no—
1411C4—81no—
1412C4—82no—
1413C2—44no—
1414C2—44no—
1415C2—44no—
1416C2—84no—
1417C2—82no—
1418C2—82no—
1419C2#3505011yescharacteristic
1420C2#3574111yescharacteristic
1421C2#3610011yescharacteristic
1422C2#3764411yescharacteristic
1423C2#3767411yescharacteristic
1424C2#4059311yescharacteristic
1425C2#4195211yescharacteristic
1426C2#4307912yes—
1427C2#4311812yes—
1428C2#4800512yes—
1429C2#5008712yes—
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×#2539C2semidirect
2. C2×#2404C2semidirect
3. C2×#2407C2semidirect
4. C2×D4×C22⋊C4C2semidirect
5. #17068C2semidirect
6. #16814C2semidirect
7. #16508C2semidirect
8. #16392C2semidirect
9. #15403C2semidirect
10. #15281C2semidirect
11. #15270C2semidirect
12. #15266C2semidirect
13. #15161C2semidirect
14. #14885C2semidirect
15. #14765C2semidirect
16. #14734C2semidirect
17. #14721C2semidirect
18. #14717C2semidirect
19. #14715C2semidirect
20. #14534C2semidirect
21. #14407C2semidirect
22. #14311C2semidirect
23. #13886C2semidirect
24. C23×#41C22semidirect
26. C22×#123C22semidirect
27. C22×C22⋊Q8C22semidirect
28. C22×#121C22semidirect
39. C2×#399C22semidirect
40. C2×#399C22semidirect
41. C2×#394C22semidirect
42. C2×#394C22semidirect
43. C2×#394C22semidirect
44. C2×#394C22semidirect
46. C2×#393C22semidirect
47. C2×#393C22semidirect
53. C2×#392C22semidirect
54. C2×#392C22semidirect
56. C2×#391C22semidirect
60. C2×#390C22semidirect
61. C2×#390C22semidirect
62. C2×#388C22semidirect
63. C2×#388C22semidirect
70. C2×#386C22semidirect
71. C2×#386C22semidirect
72. C2×#386C22semidirect
73. C2×#386C22semidirect
74. C2×#385C22semidirect
75. C2×#385C22semidirect
76. C2×#381C22semidirect
78. C2×#380C22semidirect
84. C2×C4×C22⋊C4C22semidirect
85. #1446C22semidirect
86. #1445C22semidirect
87. #1444C22semidirect
88. #1442C22semidirect
89. #1442C22semidirect
90. #1441C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
116. #1437C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. #1436C22semidirect
120. C4⋊#95C22semidirect
121. #1434C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
173. C2×C4×D4D4semidirect
247. #392D4semidirect
407. C22×D4C2×D4semidirect
408. C22×D4#41semidirect
440. C23×C4#41semidirect
599. C2×C22⋊C4C2×D4semidirect
635. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25392
C2×#24042
C2×#24072
C2×D4×C22⋊C42
#170682
#168142
#165082
#163922
#154032
#152812
#152702
#152662
#151612
#148852
#147652
#147342
#147212
#147172
#147152
#145342
#144072
#143112
#138862