Finite Group Databasebeta

← #846251

Subgroups — #846251

Order 512.

5165 conjugacy classes of subgroups.

The subgroup lattice has 1357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic, complemented
2C2×#2488C211yesmaximal, characteristic, complemented
3C2×#2411C211yesmaximal, characteristic, complemented
4C22×#386C211yesmaximal, characteristic, complemented
5#16352C212yesmaximal, complemented
6#16272C212yesmaximal, complemented
7#15453C212yesmaximal, complemented
8#15442C212yesmaximal, complemented
9#15307C212yesmaximal, complemented
10#15280C212yesmaximal, complemented
11#14921C211yesmaximal, characteristic, complemented
12#14918C211yesmaximal, characteristic, complemented
13#14911C211yesmaximal, characteristic, complemented
14#14725C211yesmaximal, characteristic, complemented
15#14717C211yesmaximal, characteristic, complemented
16#14715C211yesmaximal, characteristic
17#14694C211yesmaximal, characteristic, complemented
18#14534C212yesmaximal, complemented
19#14377C212yesmaximal, complemented
20#14040C211yesmaximal, characteristic, complemented
21#13902C211yesmaximal, characteristic, complemented
22#13878C211yesmaximal, characteristic, complemented
23#13868C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2212yescomplemented
29C22×#120C2211yescharacteristic
30C22×#120C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35#2848—28no—
36#2488—28no—
37#2411—28no—
38C2×#400C2211yescharacteristic, complemented
39C2×#400C2211yescharacteristic, complemented
40C2×#397C2211yescharacteristic, complemented
41C2×#396C2212yescomplemented
42C2×#394C2212yescomplemented
43C2×#394C2212yescomplemented
44C2×#393C2211yescharacteristic, complemented
45C2×#393C2212yescomplemented
46C2×#392C2212yes—
47C2×#392C2212yes—
48C2×#391C2211yescharacteristic, complemented
49C2×#390C2212yes—
50C2×#390C2212yes—
51C2×#390C2212yescomplemented
52C2×#388C2212yescomplemented
53C2×#388C2211yescharacteristic, complemented
54C2×#388C2211yescharacteristic, complemented
55C2×#386—28no—
56C2×#386C2212yes—
57C2×#386C2211yescharacteristic
58C2×#386C2211yescharacteristic
59C2×#386C2212yes—
60C2×#386C2211yescharacteristic
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2211yescharacteristic
64C2×#386C2212yescomplemented
65C2×#386C2212yescomplemented
66C2×#385C2211yescharacteristic
67C2×#385C2211yescharacteristic
68C2×#385C2212yescomplemented
69C2×#385C2212yescomplemented
70C2×#382C2211yescharacteristic, complemented
71C2×#381C2211yescharacteristic
72C2×#381C2211yescharacteristic
73C2×#380C2211yescharacteristic
74C2×#380C2211yescharacteristic
75C2×#380C2212yescomplemented
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×#379C2211yescharacteristic
82C2×C4×C22⋊C4C2211yescharacteristic
83C22×#95C2211yescharacteristic
84C22×#95C2211yescharacteristic
85#1445C2212yescomplemented
86#1444C2212yescomplemented
87#1443C2212yescomplemented
88#1443C2212yescomplemented
89#1442C2212yescomplemented
90#1441C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1438C2212yescomplemented
111#1438C2212yescomplemented
112#1438C2212yescomplemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118#1434C2212yescomplemented
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—28no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—42no—
134C23×D4—44no—
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2312yes—
140C24×C4—24no—
141C24×C4—24no—
142C24×C4—44no—
143C24×C4—42no—
144C24×C4—44no—
145C24×C4C2311yescharacteristic
146C24×C4C2312yes—
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2312yes—
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C2×#123—24no—
153C2×#123—24no—
154C2×#123—42no—
155C2×C22⋊Q8—24no—
156C2×C22⋊Q8—28no—
157C2×C22⋊Q8—24no—
158C2×C22⋊Q8—42no—
159C2×C22⋊Q8—44no—
160C2×C22⋊Q8—44no—
161C2×#120—24no—
162C2×#120—24no—
163C2×#120—42no—
164C2×#120—42no—
165C2×#120—42no—
166C2×#120—42no—
167C2×#117—24no—
168C2×#117—42no—
169C2×#117—42no—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—24no—
184C22×C22⋊C4—24no—
185C22×C22⋊C4—44no—
186C22×C22⋊C4—42no—
187C22×C22⋊C4—42no—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
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⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2312yes—
225C22×C42C2311yescharacteristic
226#400—24no—
227#400—24no—
228#397—24no—
229#396—28no—
230#394—28no—
231#394—44no—
232#393—24no—
233#393—44no—
234#392—28no—
235#392—44no—
236#391—24no—
237#390—28no—
238#390—28no—
239#390—44no—
240#388—24no—
241#388—24no—
242#388—28no—
243#386—24no—
244#386—24no—
245#386—24no—
246#386—28no—
247#386—28no—
248#386—28no—
249#386—28no—
250#386—44no—
251#386—42no—
252#386—44no—
253#385—24no—
254#385—28no—
255#385—28no—
256#385D418yescomplemented
257#382—24no—
258#381—24no—
259#381—42no—
260#380—24no—
261#380—28no—
262#380—42no—
263#379—24no—
264#379—24no—
265#379—24no—
266#379—42no—
267#379—42no—
268#379—42no—
269C4×C22⋊C4—24no—
270C2×#95—24no—
271C2×#95D418yescomplemented
272C2×#95C2312yes—
273C2×#95C2311yescharacteristic
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2312yes—
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2312yes—
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×#95C2312yes—
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2312yes—
308C25—22no—
309C25—24no—
310C25—22no—
311C25—24no—
312C25—22no—
313C25—22no—
314C25—24no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25#4114yes—
330C25C2411yescharacteristic
331C25C2412yes—
332C25C2412yes—
333C25C2411yescharacteristic
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—24no—
337C22×Q8—42no—
338C22×Q8—41no—
339C22×D4—232no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—24no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—24no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—416no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—432no—
376C22×D4—416no—
377C22×D4—432no—
378C22×D4#4118yes—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—24no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—416no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—432no—
418C23×C4—416no—
419C23×C4—416no—
420C23×C4—432no—
421C23×C4C2×D414yes—
422C23×C4C2×D414yes—
423C23×C4C2×D414yes—
424C23×C4C2×D414yes—
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2411yescharacteristic
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444#123—416no—
445C22⋊Q8—416no—
446C22⋊Q8—432no—
447#120—416no—
448#120—416no—
449#117—416no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—41no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—41no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4C2×D418yescomplemented
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—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—22no—
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—41no—
555C2×C22⋊C4—41no—
556C2×C22⋊C4—416no—
557C2×C22⋊C4—416no—
558C2×C22⋊C4—416no—
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⋊C4C2×D414yes—
583C2×C22⋊C4C2×D414yes—
584C2×C42—24no—
585C2×C42—22no—
586C2×C42—24no—
587C2×C42—22no—
588C2×C42—42no—
589C2×C42—42no—
590C2×C42—42no—
591#95—24no—
592#95—24no—
593#95—22no—
594#95—22no—
595#95—24no—
596#95—24no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—24no—
604#95—22no—
605#95—22no—
606#95—24no—
607#95—24no—
608#95—42no—
609#95—42no—
610#95—42no—
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#95C2×D414yes—
623#95C2×D414yes—
624#95C2×D414yes—
625#95C2×D414yes—
626#95C2×D418yescomplemented
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—28no—
632C24—28no—
633C24—216no—
634C24—28no—
635C24—216no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—28no—
649C24—28no—
650C24—28no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—21no—
666C24—21no—
667C24—22no—
668C24—21no—
669C24—22no—
670C24—22no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—22no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—44no—
692C24—44no—
693C24—48no—
694C24—44no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—44no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24—44no—
707C24—44no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24—84no—
714C24C22×D412yes—
715C24C22×D412yes—
716C24C2×#4114yes—
717C24C2×#4114yes—
718C24C2×#4114yes—
719C24C2×#4112yes—
720C24H(5,𝔽2)14yes—
721C24H(5,𝔽2)12yes—
722C24H(5,𝔽2)12yes—
723C24H(5,𝔽2)12yes—
724C242−1+412yes—
725C24C2511yescharacteristic
726C2×Q8—44no—
727C2×Q8—48no—
728C2×Q8—44no—
729C2×Q8—82no—
730C2×Q8—84no—
731C2×D4—216no—
732C2×D4—216no—
733C2×D4—216no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—4128no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—48no—
757C2×D4—44no—
758C2×D4—84no—
759C2×D4—84no—
760C2×D4—84no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—84no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—216no—
774C22×C4—28no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
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—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—21no—
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—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—22no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—44no—
878C22×C4—48no—
879C22×C4—44no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—48no—
886C22×C4—48no—
887C22×C4—48no—
888C22×C4—48no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—48no—
897C22×C4—48no—
898C22×C4—4128no—
899C22×C4—48no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—48no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—84no—
909C22×C4—84no—
910C22×C4C22×D412yes—
911C22×C4C22×D412yes—
912C22×C4C22×D412yes—
913C22×C4C22×D414yes—
914C22×C4C22×D412yes—
915C22×C4C22×D414yes—
916C22×C4C22×D412yes—
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C22×D412yes—
920C22×C4C2×#4114yes—
921C22×C4H(5,𝔽2)14yes—
922C4⋊C4—48no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—84no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—84no—
957C22⋊C4—82no—
958C22⋊C4—84no—
959C22⋊C4—82no—
960C22⋊C4—84no—
961C22⋊C4—84no—
962C22⋊C4—84no—
963C22⋊C4—84no—
964C22⋊C4—84no—
965C22⋊C4—84no—
966C22⋊C4—84no—
967C42—48no—
968C42—44no—
969C42—82no—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—24no—
974C23—22no—
975C23—24no—
976C23—22no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—232no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—432no—
1013C23—432no—
1014C23—416no—
1015C23—416no—
1016C23—416no—
1017C23—416no—
1018C23—416no—
1019C23—432no—
1020C23—432no—
1021C23—416no—
1022C23—416no—
1023C23—416no—
1024C23—416no—
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—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—42no—
1067C23—42no—
1068C23—42no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—42no—
1078C23—42no—
1079C23—41no—
1080C23—42no—
1081C23—41no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—41no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—816no—
1093C23—816no—
1094C23—816no—
1095C23—816no—
1096C23—88no—
1097C23—88no—
1098C23—88no—
1099C23—88no—
1100C23#53514yes—
1101C23#53714yes—
1102C23#53814yes—
1103C23D4214yes—
1104C23#54614yes—
1105C23#54814yes—
1106C23#55118yes—
1107C23#56214yes—
1108C23C23×D411yescharacteristic
1109C23C23×D411yescharacteristic
1110C23C22×#4112yes—
1111C23C22×#4111yescharacteristic
1112C23C2×H(5,𝔽2)11yescharacteristic
1113C23C2×H(5,𝔽2)11yescharacteristic
1114C23C2×H(5,𝔽2)12yes—
1115C23C2×H(5,𝔽2)11yescharacteristic
1116C23C2×H(5,𝔽2)12yes—
1117C23C2×2−1+411yescharacteristic
1118C23#58512yes—
1119Q8—88no—
1120D4—432no—
1121D4—432no—
1122D4—816no—
1123D4—816no—
1124D4—88no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—416no—
1156C2×C4—416no—
1157C2×C4—432no—
1158C2×C4—416no—
1159C2×C4—432no—
1160C2×C4—41no—
1161C2×C4—416no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—41no—
1231C2×C4—42no—
1232C2×C4—42no—
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—88no—
1243C2×C4#52514yes—
1244C2×C4#53514yes—
1245C22—24no—
1246C22—24no—
1247C22—24no—
1248C22—24no—
1249C22—24no—
1250C22—24no—
1251C22—28no—
1252C22—28no—
1253C22—28no—
1254C22—28no—
1255C22—28no—
1256C22—28no—
1257C22—28no—
1258C22—464no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—832no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—82no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22—82no—
1298C22#267618yes—
1299C22C2×#52511yescharacteristic
1300C22C2×#53511yescharacteristic
1301C22C2×#53511yescharacteristic
1302C22C2×#53711yescharacteristic
1303C22C2×#53811yescharacteristic
1304C22C2×D4211yescharacteristic
1305C22C2×#54611yescharacteristic
1306C22C2×#54811yescharacteristic
1307C22D4×#4112yes—
1308C22C2×#55112yes—
1309C22#348411yescharacteristic
1310C22#348412yes—
1311C22#348711yescharacteristic
1312C22#349012yes—
1313C22#350512yes—
1314C22#351312yes—
1315C22#351912yes—
1316C22#352012yes—
1317C22C2×#56211yescharacteristic
1318C22#353212yes—
1319C22#353412yes—
1320C22#353512yes—
1321C22#354212yes—
1322C4—24no—
1323C4—24no—
1324C4—42no—
1325C4—42no—
1326C4—44no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—44no—
1332C4—81no—
1333C4—81no—
1334C4—82no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—82no—
1339C4—82no—
1340C4—82no—
1341C2—28no—
1342C2—48no—
1343C2—84no—
1344C2—161no—
1345C2#3523611yescharacteristic
1346C2#3610211yescharacteristic
1347C2#3615811yescharacteristic
1348C2#3672211yescharacteristic
1349C2#3764511yescharacteristic
1350C2#3810812yes—
1351C2#3835812yes—
1352C2#3946711yescharacteristic
1353C2#4556212yes—
1354C2C2×#267611yescharacteristic
1355C2#5913312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14715C2
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×#2848C2semidirect
2. C2×#2488C2semidirect
3. C2×#2411C2semidirect
4. C22×#386C2semidirect
5. #16352C2semidirect
6. #16272C2semidirect
7. #15453C2semidirect
8. #15442C2semidirect
9. #15307C2semidirect
10. #15280C2semidirect
11. #14921C2semidirect
12. #14918C2semidirect
13. #14911C2semidirect
14. #14725C2semidirect
15. #14717C2semidirect
17. #14694C2semidirect
18. #14534C2semidirect
19. #14377C2semidirect
20. #14040C2semidirect
21. #13902C2semidirect
22. #13878C2semidirect
23. #13868C2semidirect
28. C22×C22⋊Q8C22semidirect
38. C2×#400C22semidirect
39. C2×#400C22semidirect
40. C2×#397C22semidirect
41. C2×#396C22semidirect
42. C2×#394C22semidirect
43. C2×#394C22semidirect
44. C2×#393C22semidirect
45. C2×#393C22semidirect
48. C2×#391C22semidirect
51. C2×#390C22semidirect
52. C2×#388C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
64. C2×#386C22semidirect
65. C2×#386C22semidirect
68. C2×#385C22semidirect
69. C2×#385C22semidirect
70. C2×#382C22semidirect
75. C2×#380C22semidirect
85. #1445C22semidirect
86. #1444C22semidirect
87. #1443C22semidirect
88. #1443C22semidirect
89. #1442C22semidirect
90. #1441C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. #1434C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
256. #385D4semidirect
271. C2×#95D4semidirect
479. C2×C4⋊C4C2×D4semidirect
626. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#24882
C2×#24112
C22×#3862
#163522
#162722
#154532
#154422
#153072
#152802
#149212
#149182
#149112
#147252
#147172
#147152
#146942
#145342
#143772
#140402
#139022
#138782
#138682