Finite Group Databasebeta

← #846252

Subgroups — #846252

Order 512.

5251 conjugacy classes of subgroups.

The subgroup lattice has 1381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic, complemented
2C2×#2472C211yesmaximal, characteristic, complemented
3C2×#2412C211yesmaximal, characteristic, complemented
4C22×#386C211yesmaximal, characteristic, complemented
5#16333C212yesmaximal, complemented
6#16266C212yesmaximal, complemented
7#15376C212yesmaximal, complemented
8#15323C212yesmaximal, complemented
9#15293C212yesmaximal, complemented
10#15264C212yesmaximal, complemented
11#14934C211yesmaximal, characteristic, complemented
12#14927C211yesmaximal, characteristic, complemented
13#14921C211yesmaximal, characteristic, complemented
14#14918C211yesmaximal, characteristic, complemented
15#14911C211yesmaximal, characteristic, complemented
16#14715C211yesmaximal, characteristic
17#14694C211yesmaximal, characteristic, complemented
18#14519C212yesmaximal, complemented
19#14391C212yesmaximal, complemented
20#14040C211yesmaximal, characteristic, complemented
21#13903C211yesmaximal, characteristic, complemented
22#13877C211yesmaximal, characteristic, complemented
23#13867C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#124C2211yescharacteristic, complemented
27C22×#123C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2212yescomplemented
30C22×#120C2211yescharacteristic
31C22×#120C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2848—28no—
37#2472—28no—
38#2412—28no—
39C2×#397C2212yescomplemented
40C2×#397C2211yescharacteristic, complemented
41C2×#394C2211yescharacteristic, complemented
42C2×#394C2212yescomplemented
43C2×#394C2211yescharacteristic, complemented
44C2×#393C2211yescharacteristic, complemented
45C2×#392C2212yes—
46C2×#392C2212yes—
47C2×#390C2211yescharacteristic, complemented
48C2×#388C2211yescharacteristic, complemented
49C2×#388C2211yescharacteristic, complemented
50C2×#386—28no—
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#386C2211yescharacteristic
55C2×#386C2211yescharacteristic
56C2×#386C2211yescharacteristic
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2211yescharacteristic
61C2×#386C2212yescomplemented
62C2×#386C2212yescomplemented
63C2×#386C2212yescomplemented
64C2×#385C2211yescharacteristic
65C2×#385C2211yescharacteristic
66C2×#385C2212yescomplemented
67C2×#385C2212yescomplemented
68C2×#385C2212yescomplemented
69C2×#381C2211yescharacteristic
70C2×#381C2211yescharacteristic
71C2×#381C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×#380C2211yescharacteristic
74C2×#380C2212yescomplemented
75C2×#380C2212yescomplemented
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic
82C22×#95C2211yescharacteristic
83C22×#95C2211yescharacteristic
84#1446C2212yescomplemented
85#1445C2212yescomplemented
86#1443C2212yescomplemented
87#1443C2212yescomplemented
88#1442C2212yescomplemented
89#1442C2212yescomplemented
90#1442C2212yescomplemented
91#1442C2212yescomplemented
92#1441C2212yescomplemented
93#1441C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1438C2212yes—
109#1438C2212yes—
110#1438C2212yes—
111#1438C2212yes—
112#1438C2212yescomplemented
113#1438C2212yescomplemented
114#1437C2212yescomplemented
115#1437C2212yescomplemented
116#1436C2212yescomplemented
117#1434C2212yescomplemented
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—28no—
132C23×D4—24no—
133C23×D4—42no—
134C23×D4—44no—
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2311yescharacteristic
141C24×C4—24no—
142C24×C4—24no—
143C24×C4—44no—
144C24×C4—42no—
145C24×C4—44no—
146C24×C4C2311yescharacteristic
147C24×C4C2312yes—
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C24×C4C2312yes—
151C24×C4C2312yes—
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C2×#124—24no—
155C2×#124—44no—
156C2×#123—24no—
157C2×#123—42no—
158C2×#123—42no—
159C2×C22⋊Q8—24no—
160C2×C22⋊Q8—28no—
161C2×C22⋊Q8—24no—
162C2×C22⋊Q8—42no—
163C2×C22⋊Q8—44no—
164C2×C22⋊Q8—44no—
165C2×#120—24no—
166C2×#120—24no—
167C2×#120—24no—
168C2×#120—42no—
169C2×#120—42no—
170C2×#120—42no—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—24no—
184C22×C22⋊C4—44no—
185C22×C22⋊C4—42no—
186C22×C22⋊C4—42no—
187C22×C22⋊C4—42no—
188C22×C22⋊C4—42no—
189C22×C22⋊C4D418yescomplemented
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2311yescharacteristic
228C22×C42C2311yescharacteristic
229C22×C42C2311yescharacteristic
230#397—24no—
231#397—28no—
232#394—28no—
233#394—24no—
234#394—24no—
235#393—24no—
236#392—28no—
237#392—44no—
238#390—24no—
239#388—24no—
240#388—24no—
241#386—28no—
242#386—24no—
243#386—24no—
244#386—24no—
245#386—28no—
246#386—28no—
247#386—28no—
248#386—28no—
249#386—28no—
250#386—44no—
251#386—44no—
252#386—42no—
253#386—44no—
254#385—24no—
255#385—28no—
256#385—28no—
257#385—44no—
258#385D418yescomplemented
259#381—24no—
260#381—42no—
261#381—42no—
262#380—28no—
263#380—24no—
264#380—28no—
265#380—42no—
266#379—24no—
267#379—24no—
268#379—24no—
269#379—42no—
270#379—42no—
271C4×C22⋊C4—24no—
272C2×#95—24no—
273C2×#95—24no—
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C25—22no—
309C25—24no—
310C25—22no—
311C25—24no—
312C25—22no—
313C25—24no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25C2×D414yes—
329C25#4114yes—
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C25C2411yescharacteristic
333C25C2412yes—
334C25C2411yescharacteristic
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—24no—
338C22×Q8—42no—
339C22×Q8—41no—
340C22×D4—232no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—24no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—24no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—41no—
370C22×D4—41no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—432no—
379C22×D4—416no—
380C22×D4—432no—
381C22×D4—416no—
382C22×D4#4118yes—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—24no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—24no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—416no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4—42no—
429C23×C4—432no—
430C23×C4—416no—
431C23×C4—416no—
432C23×C4—432no—
433C23×C4C2×D414yes—
434C23×C4C2×D414yes—
435C23×C4C2×D414yes—
436C23×C4C2411yescharacteristic
437C23×C4C2412yes—
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2412yes—
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2412yes—
445C23×C4C2412yes—
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C23×C4C2411yescharacteristic
450C23×C4C2412yes—
451C23×C4C2411yescharacteristic
452C23×C4C2412yes—
453C23×C4C2411yescharacteristic
454#124—416no—
455#123—416no—
456C22⋊Q8—416no—
457C22⋊Q8—432no—
458#120—416no—
459#120—416no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—41no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—41no—
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⋊C4C2×D418yescomplemented
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
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—24no—
504C2×C22⋊C4—22no—
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—24no—
514C2×C22⋊C4—24no—
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—24no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—416no—
544C2×C22⋊C4—416no—
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—41no—
556C2×C22⋊C4—41no—
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—416no—
566C2×C22⋊C4—416no—
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⋊C4C2×D414yes—
585C2×C22⋊C4C2×D414yes—
586C2×C22⋊C4C2×D414yes—
587C2×C22⋊C4C2×D414yes—
588C2×C22⋊C4C2×D414yes—
589C2×C22⋊C4C2×D414yes—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—42no—
593C2×C42—42no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—22no—
599#95—22no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—24no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95—42no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95C2×D418yescomplemented
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—28no—
633C24—28no—
634C24—216no—
635C24—28no—
636C24—216no—
637C24—22no—
638C24—21no—
639C24—22no—
640C24—22no—
641C24—21no—
642C24—22no—
643C24—22no—
644C24—21no—
645C24—22no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—21no—
652C24—22no—
653C24—21no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—28no—
659C24—28no—
660C24—28no—
661C24—21no—
662C24—22no—
663C24—21no—
664C24—22no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—22no—
669C24—21no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—28no—
674C24—21no—
675C24—21no—
676C24—22no—
677C24—21no—
678C24—22no—
679C24—21no—
680C24—22no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—22no—
685C24—48no—
686C24—44no—
687C24—44no—
688C24—44no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—48no—
700C24—48no—
701C24—48no—
702C24—48no—
703C24—44no—
704C24—44no—
705C24—48no—
706C24—44no—
707C24—44no—
708C24—44no—
709C24—44no—
710C24—44no—
711C24—44no—
712C24—44no—
713C24—44no—
714C24—84no—
715C24—84no—
716C24—84no—
717C24—84no—
718C24—84no—
719C24—84no—
720C24C22×D412yes—
721C24C22×D412yes—
722C24C22×D412yes—
723C24C22×D412yes—
724C24C2×#4114yes—
725C24C2×#4114yes—
726C24C2×#4114yes—
727C24C2×#4112yes—
728C24H(5,𝔽2)14yes—
729C24H(5,𝔽2)12yes—
730C24H(5,𝔽2)12yes—
731C24H(5,𝔽2)12yes—
732C242−1+412yes—
733C24C2511yescharacteristic
734C2×Q8—44no—
735C2×Q8—48no—
736C2×Q8—44no—
737C2×Q8—82no—
738C2×Q8—84no—
739C2×D4—216no—
740C2×D4—216no—
741C2×D4—216no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—4128no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—44no—
759C2×D4—48no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—48no—
768C2×D4—44no—
769C2×D4—84no—
770C2×D4—82no—
771C2×D4—82no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4—84no—
775C2×D4—84no—
776C2×D4—84no—
777C2×D4—84no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—216no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
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—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—28no—
824C22×C4—28no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—21no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—22no—
874C22×C4—21no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—44no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—48no—
888C22×C4—48no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—48no—
898C22×C4—48no—
899C22×C4—48no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—48no—
903C22×C4—48no—
904C22×C4—44no—
905C22×C4—4128no—
906C22×C4—48no—
907C22×C4—44no—
908C22×C4—48no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—44no—
916C22×C4—84no—
917C22×C4—84no—
918C22×C4—84no—
919C22×C4—84no—
920C22×C4—84no—
921C22×C4—84no—
922C22×C4—84no—
923C22×C4C22×D412yes—
924C22×C4C22×D412yes—
925C22×C4C22×D412yes—
926C22×C4C22×D412yes—
927C22×C4C22×D414yes—
928C22×C4C22×D412yes—
929C22×C4C22×D414yes—
930C22×C4C22×D412yes—
931C22×C4C2×#4114yes—
932C22×C4H(5,𝔽2)14yes—
933C4⋊C4—48no—
934C4⋊C4—44no—
935C4⋊C4—48no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—48no—
939C4⋊C4—48no—
940C4⋊C4—84no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—48no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—82no—
970C22⋊C4—84no—
971C22⋊C4—82no—
972C22⋊C4—84no—
973C22⋊C4—82no—
974C22⋊C4—82no—
975C22⋊C4—84no—
976C22⋊C4—84no—
977C22⋊C4—84no—
978C22⋊C4—84no—
979C42—44no—
980C42—82no—
981C23—22no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23—24no—
987C23—22no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—232no—
998C23—24no—
999C23—22no—
1000C23—22no—
1001C23—24no—
1002C23—22no—
1003C23—24no—
1004C23—22no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—22no—
1012C23—24no—
1013C23—22no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
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—22no—
1033C23—22no—
1034C23—22no—
1035C23—432no—
1036C23—432no—
1037C23—416no—
1038C23—416no—
1039C23—416no—
1040C23—416no—
1041C23—416no—
1042C23—416no—
1043C23—416no—
1044C23—416no—
1045C23—432no—
1046C23—432no—
1047C23—416no—
1048C23—42no—
1049C23—41no—
1050C23—42no—
1051C23—42no—
1052C23—41no—
1053C23—42no—
1054C23—41no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—41no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—416no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—41no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—42no—
1100C23—42no—
1101C23—41no—
1102C23—42no—
1103C23—41no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—41no—
1110C23—42no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—88no—
1115C23—88no—
1116C23—88no—
1117C23—816no—
1118C23—816no—
1119C23—816no—
1120C23—816no—
1121C23#52514yes—
1122C23#53514yes—
1123C23#53714yes—
1124C23#53814yes—
1125C23D4214yes—
1126C23#54614yes—
1127C23#54814yes—
1128C23#55118yes—
1129C23#56214yes—
1130C23C23×D411yescharacteristic
1131C23C23×D411yescharacteristic
1132C23C22×#4112yes—
1133C23C22×#4111yescharacteristic
1134C23C2×H(5,𝔽2)12yes—
1135C23C2×H(5,𝔽2)11yescharacteristic
1136C23C2×H(5,𝔽2)11yescharacteristic
1137C23C2×H(5,𝔽2)11yescharacteristic
1138C23C2×H(5,𝔽2)12yes—
1139C23C2×2−1+411yescharacteristic
1140C23#58512yes—
1141Q8—88no—
1142D4—432no—
1143D4—432no—
1144D4—88no—
1145D4—88no—
1146D4—816no—
1147D4—88no—
1148C2×C4—22no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—416no—
1175C2×C4—432no—
1176C2×C4—416no—
1177C2×C4—416no—
1178C2×C4—432no—
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—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—42no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—42no—
1223C2×C4—41no—
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—41no—
1233C2×C4—42no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—41no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—88no—
1259C2×C4—816no—
1260C2×C4—88no—
1261C2×C4#53414yes—
1262C22—24no—
1263C22—24no—
1264C22—24no—
1265C22—24no—
1266C22—24no—
1267C22—24no—
1268C22—28no—
1269C22—28no—
1270C22—28no—
1271C22—28no—
1272C22—24no—
1273C22—24no—
1274C22—28no—
1275C22—24no—
1276C22—28no—
1277C22—28no—
1278C22—464no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—42no—
1283C22—44no—
1284C22—42no—
1285C22—44no—
1286C22—42no—
1287C22—44no—
1288C22—42no—
1289C22—44no—
1290C22—44no—
1291C22—44no—
1292C22—44no—
1293C22—44no—
1294C22—44no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—44no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—832no—
1307C22—82no—
1308C22—82no—
1309C22—82no—
1310C22—82no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—82no—
1319C22—82no—
1320C22—82no—
1321C22—82no—
1322C22#267618yes—
1323C22C2×#52511yescharacteristic
1324C22C2×#53411yescharacteristic
1325C22C2×#53511yescharacteristic
1326C22C2×#53711yescharacteristic
1327C22C2×#53811yescharacteristic
1328C22C2×D4211yescharacteristic
1329C22C2×#54611yescharacteristic
1330C22C2×#54811yescharacteristic
1331C22D4×#4112yes—
1332C22C2×#55112yes—
1333C22#348411yescharacteristic
1334C22#348412yes—
1335C22#348511yescharacteristic
1336C22#349012yes—
1337C22#350512yes—
1338C22#351312yes—
1339C22#351912yes—
1340C22#352012yes—
1341C22C2×#56211yescharacteristic
1342C22#353212yes—
1343C22#353412yes—
1344C22#353512yes—
1345C22#354212yes—
1346C4—24no—
1347C4—42no—
1348C4—42no—
1349C4—44no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—44no—
1354C4—44no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—82no—
1360C4—81no—
1361C4—82no—
1362C4—82no—
1363C4—82no—
1364C2—28no—
1365C2—48no—
1366C2—44no—
1367C2—82no—
1368C2—161no—
1369C2#3507711yescharacteristic
1370C2#3609911yescharacteristic
1371C2#3615811yescharacteristic
1372C2#3670911yescharacteristic
1373C2#3764411yescharacteristic
1374C2#3810812yes—
1375C2#3835812yes—
1376C2#3946611yescharacteristic
1377C2#4552812yes—
1378C2C2×#267611yescharacteristic
1379C2#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×#2472C2semidirect
3. C2×#2412C2semidirect
4. C22×#386C2semidirect
5. #16333C2semidirect
6. #16266C2semidirect
7. #15376C2semidirect
8. #15323C2semidirect
9. #15293C2semidirect
10. #15264C2semidirect
11. #14934C2semidirect
12. #14927C2semidirect
13. #14921C2semidirect
14. #14918C2semidirect
15. #14911C2semidirect
17. #14694C2semidirect
18. #14519C2semidirect
19. #14391C2semidirect
20. #14040C2semidirect
21. #13903C2semidirect
22. #13877C2semidirect
23. #13867C2semidirect
26. C22×#124C22semidirect
29. C22×C22⋊Q8C22semidirect
39. C2×#397C22semidirect
40. C2×#397C22semidirect
41. C2×#394C22semidirect
42. C2×#394C22semidirect
43. C2×#394C22semidirect
44. C2×#393C22semidirect
47. C2×#390C22semidirect
48. C2×#388C22semidirect
49. C2×#388C22semidirect
61. C2×#386C22semidirect
62. C2×#386C22semidirect
63. C2×#386C22semidirect
66. C2×#385C22semidirect
67. C2×#385C22semidirect
68. C2×#385C22semidirect
74. C2×#380C22semidirect
75. C2×#380C22semidirect
84. #1446C22semidirect
85. #1445C22semidirect
86. #1443C22semidirect
87. #1443C22semidirect
88. #1442C22semidirect
89. #1442C22semidirect
90. #1442C22semidirect
91. #1442C22semidirect
92. #1441C22semidirect
93. #1441C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
114. #1437C22semidirect
115. #1437C22semidirect
116. #1436C22semidirect
117. #1434C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
189. C22×C22⋊C4D4semidirect
258. #385D4semidirect
483. C2×C4⋊C4C2×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×#28482
C2×#24722
C2×#24122
C22×#3862
#163332
#162662
#153762
#153232
#152932
#152642
#149342
#149272
#149212
#149182
#149112
#147152
#146942
#145192
#143912
#140402
#139032
#138772
#138672