Finite Group Databasebeta

← #1295089

Subgroups — #1295089

Order 512.

4772 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2684C212yesmaximal, complemented
2C2×#2668C212yesmaximal, complemented
3C2×#2427C211yesmaximal, characteristic, complemented
4C2×#2408C211yesmaximal, characteristic, complemented
5#17059C211yesmaximal, characteristic, complemented
6#16814C211yesmaximal, characteristic, complemented
7#16508C211yesmaximal, characteristic, complemented
8#16363C211yesmaximal, characteristic, complemented
9#15696C212yesmaximal, complemented
10#15480C212yesmaximal, complemented
11#15453C212yesmaximal, complemented
12#15283C212yesmaximal, complemented
13#15167C211yesmaximal, characteristic, complemented
14#15160C212yesmaximal, complemented
15#14977C211yesmaximal, characteristic, complemented
16#14839C211yesmaximal, characteristic, complemented
17#14762C212yesmaximal, complemented
18#14757C211yesmaximal, characteristic, complemented
19#14715C211yesmaximal, characteristic, complemented
20#14271C211yesmaximal, characteristic, complemented
21#14228C211yesmaximal, characteristic, complemented
22#13902C211yesmaximal, characteristic, complemented
23#13813C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic, complemented
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×#121C2212yescomplemented
31C22×#120C2212yes—
32C22×#120C2212yes—
33C22×C4×D4C2211yescharacteristic
34#2684—216no—
35#2668—216no—
36#2427—28no—
37#2408—28no—
38C2×#399C2212yescomplemented
39C2×#399C2212yescomplemented
40C2×#399C2211yescharacteristic, complemented
41C2×#397C2212yes—
42C2×#397C2211yescharacteristic
43C2×#397C2212yes—
44C2×#397C2212yes—
45C2×#397C2211yescharacteristic, complemented
46C2×#397C2212yescomplemented
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2211yescharacteristic
50C2×#394C2212yescomplemented
51C2×#394C2212yescomplemented
52C2×#394C2212yescomplemented
53C2×#394C2211yescharacteristic, complemented
54C2×#393C2212yescomplemented
55C2×#393C2212yescomplemented
56C2×#392C2212yes—
57C2×#392C2211yescharacteristic
58C2×#392C2212yes—
59C2×#392C2211yescharacteristic
60C2×#392C2212yescomplemented
61C2×#391C2211yescharacteristic, complemented
62C2×#390C2211yescharacteristic
63C2×#390C2211yescharacteristic
64C2×#390C2212yes—
65C2×#390C2212yes—
66C2×#390C2212yescomplemented
67C2×#389C2211yescharacteristic, complemented
68C2×#388C2212yescomplemented
69C2×#388C2212yescomplemented
70C2×#386C2211yescharacteristic
71C2×#386C2212yes—
72C2×#386C2212yescomplemented
73C2×#386C2212yescomplemented
74C2×#386C2212yescomplemented
75C2×#386C2212yescomplemented
76C2×#386C2211yescharacteristic, complemented
77C2×#386C2212yescomplemented
78C2×#380C2211yescharacteristic
79C2×#380C2211yescharacteristic
80C2×#380C2211yescharacteristic, complemented
81C2×#379C2212yes—
82C2×#379C2212yes—
83C2×#379C2212yes—
84C2×#379C2212yes—
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2211yescharacteristic, complemented
87C2×C4×C22⋊C4C2212yescomplemented
88C22×#95C2211yescharacteristic, complemented
89#1445C2212yescomplemented
90#1445C2211yescharacteristic, complemented
91#1445C2211yescharacteristic, complemented
92#1445C2211yescharacteristic, complemented
93#1444C2212yescomplemented
94#1444C2211yescharacteristic, complemented
95#1444C2211yescharacteristic, complemented
96#1444C2211yescharacteristic, complemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2211yescharacteristic, complemented
106#1438C2212yes—
107#1438C2211yescharacteristic
108#1438C2211yescharacteristic
109#1438C2211yescharacteristic
110#1438C2211yescharacteristic
111#1438C2211yescharacteristic
112#1438C2211yescharacteristic
113#1438C2212yescomplemented
114#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1437C2212yes—
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1437C2212yescomplemented
120#1437C2212yescomplemented
121#1436C2212yescomplemented
122C4⋊#95C2212yescomplemented
123#1434C2211yescharacteristic, complemented
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic, complemented
126C4×#95C2211yescharacteristic, complemented
127C26C2312yes—
128C23×Q8C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—44no—
132C23×D4—42no—
133C23×D4—44no—
134C23×D4C2312yes—
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2312yes—
142C23×D4C2311yescharacteristic
143C23×D4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2312yes—
148C2×#124—24no—
149C2×#124—28no—
150C2×C22⋊Q8—24no—
151C2×C22⋊Q8—44no—
152C2×#121—28no—
153C2×#121—24no—
154C2×#121—24no—
155C2×#121—24no—
156C2×#121—24no—
157C2×#121—28no—
158C2×#121—44no—
159C2×#121—44no—
160C2×#121—44no—
161C2×#121—42no—
162C2×#120—28no—
163C2×#120—28no—
164C2×#120—28no—
165C2×#120—28no—
166C2×#120—44no—
167C2×#120—44no—
168C2×C4×D4—44no—
169C2×C4×D4D418yescomplemented
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224#399—28no—
225#399—42no—
226#399—44no—
227#397—28no—
228#397—24no—
229#397—28no—
230#397—28no—
231#397—24no—
232#397—28no—
233#394—28no—
234#394—28no—
235#394—24no—
236#394—24no—
237#394—28no—
238#394—28no—
239#394—28no—
240#393—28no—
241#393—28no—
242#392—24no—
243#392—28no—
244#392—28no—
245#392—42no—
246#392—44no—
247#391—24no—
248#390—24no—
249#390—24no—
250#390—44no—
251#390—44no—
252#390—44no—
253#389—24no—
254#388—28no—
255#388—28no—
256#386—24no—
257#386—24no—
258#386—28no—
259#386—28no—
260#386—28no—
261#386—28no—
262#386—28no—
263#386D4116yescomplemented
264#380—24no—
265#380—24no—
266#380—24no—
267#379—28no—
268#379—28no—
269#379—28no—
270#379—28no—
271C4×C22⋊C4—24no—
272C4×C22⋊C4—42no—
273C4×C22⋊C4—44no—
274C2×#95—42no—
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C25—24no—
305C25—24no—
306C25—24no—
307C25—24no—
308C25—24no—
309C25—42no—
310C25—42no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25C2412yes—
320C25C2412yes—
321C25C2411yescharacteristic
322C25C2411yescharacteristic
323C25C2411yescharacteristic
324C22×Q8—22no—
325C22×Q8—24no—
326C22×Q8—42no—
327C22×Q8—41no—
328C22×Q8—41no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—22no—
336C22×D4—24no—
337C22×D4—22no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—22no—
360C22×D4—416no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—41no—
368C22×D4—41no—
369C22×D4—416no—
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—41no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—41no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—42no—
388C22×D4—416no—
389C22×D4—432no—
390C22×D4—432no—
391C22×D4C2×D414yes—
392C22×D4C2×D418yes—
393C22×D4#4114yes—
394C23×C4—22no—
395C23×C4—24no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—41no—
408C23×C4—41no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4C2×D414yes—
414C23×C4C2×D414yes—
415C23×C4C2×D418yescomplemented
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2412yes—
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434#124—416no—
435C22⋊Q8—416no—
436#121—416no—
437#121—416no—
438#121—432no—
439#121—416no—
440#120—432no—
441#120—432no—
442C4×D4—416no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4C2×D414yes—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
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—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
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—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
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—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—41no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—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⋊C4C2×D414yes—
572C2×C22⋊C4C2×D414yes—
573C2×C22⋊C4C2×D418yes—
574C2×C22⋊C4C2×D418yes—
575C2×C22⋊C4C2×D418yescomplemented
576C2×C42—22no—
577C2×C42—24no—
578C2×C42—24no—
579C2×C42—42no—
580C2×C42—42no—
581C2×C42—42no—
582C2×C42—42no—
583C2×C42—42no—
584C2×C42—42no—
585C2×C42C2×D414yes—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—22no—
595#95—22no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—24no—
600#95—22no—
601#95—22no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—24no—
609#95—22no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95C2×D418yescomplemented
614#95C2×D418yescomplemented
615C24—21no—
616C24—21no—
617C24—22no—
618C24—21no—
619C24—21no—
620C24—22no—
621C24—22no—
622C24—21no—
623C24—22no—
624C24—21no—
625C24—21no—
626C24—22no—
627C24—21no—
628C24—22no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—21no—
642C24—22no—
643C24—21no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—21no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—21no—
669C24—21no—
670C24—22no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24C22×D414yes—
707C24C22×D412yes—
708C24C22×D412yes—
709C24C22×D414yes—
710C24C2×#4114yes—
711C24H(5,𝔽2)14yes—
712C24H(5,𝔽2)12yes—
713C24C2511yescharacteristic
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—44no—
717C2×Q8—84no—
718C2×Q8—84no—
719C2×D4—28no—
720C2×D4—216no—
721C2×D4—216no—
722C2×D4—28no—
723C2×D4—44no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—4128no—
742C2×D4—48no—
743C2×D4—48no—
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—44no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—48no—
758C2×D4—44no—
759C2×D4—84no—
760C2×D4—84no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—82no—
769C2×D4—84no—
770C2×D4—82no—
771C2×D4—84no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4—84no—
775C2×D4—84no—
776C2×D4—84no—
777C2×D4—84no—
778C2×D4—84no—
779C2×D4#127116yes—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—21no—
872C22×C4—44no—
873C22×C4—48no—
874C22×C4—48no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4—84no—
888C22×C4—84no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4C22×D414yes—
892C22×C4C22×D414yes—
893C22×C4C22×D414yes—
894C22×C4C22×D412yes—
895C22×C4C22×D414yes—
896C22×C4C22×D412yes—
897C22×C4C22×D414yes—
898C22×C4C22×D412yes—
899C22×C4C22×D412yes—
900C22×C4C22×D412yes—
901C22×C4C2×#4112yes—
902C22×C4H(5,𝔽2)14yes—
903C22×C4H(5,𝔽2)12yes—
904C4⋊C4—28no—
905C4⋊C4—44no—
906C4⋊C4—48no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—82no—
912C4⋊C4—82no—
913C4⋊C4—84no—
914C4⋊C4—84no—
915C4⋊C4—84no—
916C22⋊C4—28no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C22⋊C4—84no—
948C22⋊C4—84no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C42—44no—
955C42—44no—
956C42—84no—
957C42—84no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—22no—
969C23—22no—
970C23—24no—
971C23—22no—
972C23—22no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—22no—
981C23—22no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—22no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—22no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—22no—
1000C23—24no—
1001C23—42no—
1002C23—42no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—41no—
1012C23—42no—
1013C23—42no—
1014C23—41no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—41no—
1019C23—42no—
1020C23—41no—
1021C23—432no—
1022C23—42no—
1023C23—42no—
1024C23—41no—
1025C23—41no—
1026C23—42no—
1027C23—42no—
1028C23—41no—
1029C23—42no—
1030C23—42no—
1031C23—41no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—41no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—41no—
1067C23—42no—
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—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—41no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—816no—
1097C23—816no—
1098C23—816no—
1099C23—816no—
1100C23—816no—
1101C23—816no—
1102C23—816no—
1103C23—816no—
1104C23—816no—
1105C23—816no—
1106C23—816no—
1107C23—816no—
1108C23—816no—
1109C23—816no—
1110C23C2×#12714yes—
1111C23C2×#12714yes—
1112C23C23×D411yescharacteristic
1113C23C23×D412yes—
1114C23C22×#4111yescharacteristic
1115C23C2×H(5,𝔽2)12yes—
1116C23C2×H(5,𝔽2)11yescharacteristic
1117C23C2×H(5,𝔽2)12yes—
1118C23C2×H(5,𝔽2)11yescharacteristic
1119C23#58511yescharacteristic
1120C23#58511yescharacteristic
1121C23#58512yes—
1122C23#58511yescharacteristic
1123Q8—88no—
1124D4—416no—
1125D4—416no—
1126D4—416no—
1127D4—432no—
1128D4—816no—
1129D4—816no—
1130D4—88no—
1131D4—816no—
1132D4—88no—
1133D4—816no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—416no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—42no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—42no—
1215C2×C4—41no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—41no—
1234C2×C4—88no—
1235C2×C4—88no—
1236C2×C4—816no—
1237C2×C4C2×#12714yes—
1238C2×C4#53414yes—
1239C2×C4#54614yes—
1240C22—24no—
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—24no—
1245C22—24no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—42no—
1261C22—42no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—42no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—42no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—42no—
1280C22—44no—
1281C22—864no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—81no—
1287C22—82no—
1288C22—81no—
1289C22—82no—
1290C22—81no—
1291C22—82no—
1292C22—82no—
1293C22—81no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22—82no—
1298C22—82no—
1299C22—82no—
1300C22—82no—
1301C22—82no—
1302C22—82no—
1303C22—82no—
1304C22C22×#12711yescharacteristic
1305C22C2×#53411yescharacteristic
1306C22#344911yescharacteristic
1307C22C2×#54611yescharacteristic
1308C22D4×#4112yes—
1309C22#348412yes—
1310C22#348411yescharacteristic
1311C22#348812yes—
1312C22#348811yescharacteristic
1313C22#349012yes—
1314C22#349612yes—
1315C22#349612yes—
1316C22#349612yes—
1317C22#350011yescharacteristic
1318C22#351311yescharacteristic
1319C22#352111yescharacteristic
1320C22#353212yes—
1321C22#354512yes—
1322C22#355812yes—
1323C22#355811yescharacteristic
1324C22#356012yes—
1325C22#356212yes—
1326C22#356211yescharacteristic
1327C4—24no—
1328C4—24no—
1329C4—24no—
1330C4—44no—
1331C4—42no—
1332C4—42no—
1333C4—44no—
1334C4—44no—
1335C4—44no—
1336C4—81no—
1337C4—82no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—82no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C2—44no—
1346C2—44no—
1347C2—82no—
1348C2—84no—
1349C2—84no—
1350C2#3500111yescharacteristic
1351C2#3592111yescharacteristic
1352C2#3626011yescharacteristic
1353C2#3783211yescharacteristic
1354C2#3890211yescharacteristic
1355C2#4238711yescharacteristic
1356C2#4297911yescharacteristic
1357C2#4301312yes—
1358C2#4303412yes—
1359C2#4784812yes—
1360C2#4786112yes—
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×#2684C2semidirect
2. C2×#2668C2semidirect
3. C2×#2427C2semidirect
4. C2×#2408C2semidirect
5. #17059C2semidirect
6. #16814C2semidirect
7. #16508C2semidirect
8. #16363C2semidirect
9. #15696C2semidirect
10. #15480C2semidirect
11. #15453C2semidirect
12. #15283C2semidirect
13. #15167C2semidirect
14. #15160C2semidirect
15. #14977C2semidirect
16. #14839C2semidirect
17. #14762C2semidirect
18. #14757C2semidirect
19. #14715C2semidirect
20. #14271C2semidirect
21. #14228C2semidirect
22. #13902C2semidirect
23. #13813C2semidirect
26. C22×C22⋊Q8C22semidirect
30. C22×#121C22semidirect
38. C2×#399C22semidirect
39. C2×#399C22semidirect
40. C2×#399C22semidirect
45. C2×#397C22semidirect
46. C2×#397C22semidirect
50. C2×#394C22semidirect
51. C2×#394C22semidirect
52. C2×#394C22semidirect
53. C2×#394C22semidirect
54. C2×#393C22semidirect
55. C2×#393C22semidirect
60. C2×#392C22semidirect
61. C2×#391C22semidirect
66. C2×#390C22semidirect
67. C2×#389C22semidirect
68. C2×#388C22semidirect
69. C2×#388C22semidirect
72. C2×#386C22semidirect
73. C2×#386C22semidirect
74. C2×#386C22semidirect
75. C2×#386C22semidirect
76. C2×#386C22semidirect
77. C2×#386C22semidirect
80. C2×#380C22semidirect
86. C2×C4×C22⋊C4C22semidirect
87. C2×C4×C22⋊C4C22semidirect
88. C22×#95C22semidirect
89. #1445C22semidirect
90. #1445C22semidirect
91. #1445C22semidirect
92. #1445C22semidirect
93. #1444C22semidirect
94. #1444C22semidirect
95. #1444C22semidirect
96. #1444C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1437C22semidirect
120. #1437C22semidirect
121. #1436C22semidirect
122. C4⋊#95C22semidirect
123. #1434C22semidirect
125. C22⋊#95C22semidirect
126. C4×#95C22semidirect
169. C2×C4×D4D4semidirect
263. #386D4semidirect
415. C23×C4C2×D4semidirect
575. C2×C22⋊C4C2×D4semidirect
613. #95C2×D4semidirect
614. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#26842
C2×#26682
C2×#24272
C2×#24082
#170592
#168142
#165082
#163632
#156962
#154802
#154532
#152832
#151672
#151602
#149772
#148392
#147622
#147572
#147152
#142712
#142282
#139022
#138132