Finite Group Databasebeta

← #917565

Subgroups — #917565

Order 512.

4297 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2561C211yesmaximal, characteristic, complemented
2C2×#2472C211yesmaximal, characteristic, complemented
3C2×#2613C211yesmaximal, characteristic
4C22×#394C211yesmaximal, characteristic, complemented
5#17107C212yesmaximal, complemented
6#17090C212yesmaximal, complemented
7#16537C212yesmaximal, complemented
8#16504C212yesmaximal, complemented
9#16438C212yesmaximal, complemented
10#16438C212yesmaximal, complemented
11#15780C212yesmaximal, complemented
12#15655C212yesmaximal, complemented
13#15069C211yesmaximal, characteristic, complemented
14#14934C211yesmaximal, characteristic, complemented
15#14918C211yesmaximal, characteristic, complemented
16#14911C211yesmaximal, characteristic, complemented
17#14911C211yesmaximal, characteristic, complemented
18#14725C211yesmaximal, characteristic, complemented
19#14335C211yesmaximal, characteristic, complemented
20#13996C211yesmaximal, characteristic, complemented
21#13991C211yesmaximal, characteristic, complemented
22#13904C211yesmaximal, characteristic, complemented
23#13873C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#124C2211yescharacteristic, complemented
26C22×#123C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C22×#120C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2613—28no—
37#2561—28no—
38#2472—28no—
39C2×#397C2212yescomplemented
40C2×#397C2211yescharacteristic, complemented
41C2×#394—28no—
42C2×#394C2212yes—
43C2×#394C2212yes—
44C2×#394C2212yes—
45C2×#394C2212yes—
46C2×#394C2212yes—
47C2×#394C2212yes—
48C2×#394C2211yescharacteristic, complemented
49C2×#394C2211yescharacteristic, complemented
50C2×#394C2212yescomplemented
51C2×#393C2212yescomplemented
52C2×#393C2211yescharacteristic, complemented
53C2×#392C2212yes—
54C2×#392C2212yes—
55C2×#390C2211yescharacteristic, complemented
56C2×#388C2212yescomplemented
57C2×#388C2212yescomplemented
58C2×#388C2211yescharacteristic, complemented
59C2×#388C2211yescharacteristic, complemented
60C2×#388C2212yescomplemented
61C2×#388C2212yescomplemented
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#386C2211yescharacteristic
65C2×#385C2211yescharacteristic
66C2×#381C2211yescharacteristic
67C2×#381C2211yescharacteristic
68C2×#381C2211yescharacteristic
69C2×#381C2211yescharacteristic
70C2×#381C2211yescharacteristic
71C2×#381C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×#379C2211yescharacteristic
74C2×#379C2211yescharacteristic
75C2×#379C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C22×#95C2211yescharacteristic
82#1446C2212yescomplemented
83#1445C2212yescomplemented
84#1445C2212yescomplemented
85#1445C2212yescomplemented
86#1444C2212yescomplemented
87#1444C2212yescomplemented
88#1442C2212yescomplemented
89#1442C2212yescomplemented
90#1442C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1439C2212yescomplemented
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#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1438C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1437C2212yescomplemented
120C4⋊#95C2212yescomplemented
121C4⋊#95C2212yescomplemented
122C4⋊#95C2212yescomplemented
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—42no—
134C23×D4—42no—
135C23×D4—42no—
136C23×D4—42no—
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2311yescharacteristic
141C23×D4C2311yescharacteristic
142C23×D4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C2×#124—24no—
149C2×#124—44no—
150C2×#123—24no—
151C2×#123—24no—
152C2×#123—42no—
153C2×#123—42no—
154C2×#123—42no—
155C2×#123—42no—
156C2×C22⋊Q8—24no—
157C2×C22⋊Q8—24no—
158C2×C22⋊Q8—42no—
159C2×#120—24no—
160C2×#120—24no—
161C2×#120—24no—
162C2×#120—42no—
163C2×#120—42no—
164C2×#120—42no—
165C22×C4⋊C4—24no—
166C22×C4⋊C4—24no—
167C22×C4⋊C4—42no—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4—42no—
184C22×C22⋊C4—42no—
185C22×C22⋊C4—42no—
186C22×C22⋊C4D418yescomplemented
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2311yescharacteristic
228C22×C42C2311yescharacteristic
229C22×C42C2311yescharacteristic
230C22×C42C2312yes—
231#397—28no—
232#397—24no—
233#394—28no—
234#394—28no—
235#394—28no—
236#394—28no—
237#394—28no—
238#394—28no—
239#394—24no—
240#394—24no—
241#394—44no—
242#393—28no—
243#393—24no—
244#392—28no—
245#392—28no—
246#390—24no—
247#388—28no—
248#388—28no—
249#388—24no—
250#388—24no—
251#388—44no—
252#388—44no—
253#386—24no—
254#386—24no—
255#386—42no—
256#385—42no—
257#381—24no—
258#381—24no—
259#381—24no—
260#381—42no—
261#381—42no—
262#381—42no—
263#380—42no—
264#379—24no—
265#379—24no—
266#379—24no—
267#379—42no—
268#379—42no—
269#379D418yes—
270C4×C22⋊C4—24no—
271C4×C22⋊C4—24no—
272C2×#95—24no—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2312yes—
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
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—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—42no—
318C25—42no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25C2×D414yes—
326C25C2×D414yes—
327C25C2411yescharacteristic
328C25C2412yes—
329C25C2411yescharacteristic
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—41no—
335C22×Q8—42no—
336C22×Q8—42no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—24no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—416no—
364C22×D4—416no—
365C22×D4—416no—
366C22×D4—41no—
367C22×D4—41no—
368C22×D4—42no—
369C22×D4—42no—
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—416no—
379C22×D4—416no—
380C22×D4—416no—
381C22×D4—416no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—24no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4C2×D414yes—
409C23×C4C2×D414yes—
410C23×C4#4114yes—
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2411yescharacteristic
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2411yescharacteristic
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429#124—416no—
430#123—416no—
431#123—416no—
432C22⋊Q8—416no—
433#120—416no—
434#120—416no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—41no—
451C2×C4⋊C4—41no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—416no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
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—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—416no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—41no—
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—416no—
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—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⋊C4C2×D414yes—
571C2×C22⋊C4C2×D414yes—
572C2×C22⋊C4C2×D414yes—
573C2×C22⋊C4C2×D414yes—
574C2×C22⋊C4C2×D414yes—
575C2×C22⋊C4C2×D414yes—
576C2×C22⋊C4C2×D418yes—
577C2×C22⋊C4C2×D418yes—
578C2×C42—22no—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—22no—
582C2×C42—42no—
583C2×C42—42no—
584C2×C42—42no—
585#95—24no—
586#95—24no—
587#95—22no—
588#95—24no—
589#95—22no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—24no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
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—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—28no—
622C24—28no—
623C24—22no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—22no—
638C24—22no—
639C24—21no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—21no—
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—28no—
658C24—28no—
659C24—28no—
660C24—28no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—22no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—44no—
673C24—44no—
674C24—44no—
675C24—44no—
676C24—48no—
677C24—48no—
678C24—44no—
679C24—44no—
680C24—44no—
681C24—44no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—44no—
689C24—44no—
690C24—44no—
691C24—44no—
692C24—44no—
693C24—44no—
694C24—44no—
695C24—44no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24—84no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24C22×D412yes—
713C24C22×D412yes—
714C24C22×D414yes—
715C24C22×D412yes—
716C24C22×D412yes—
717C24C2×#4112yes—
718C24H(5,𝔽2)12yes—
719C24H(5,𝔽2)12yes—
720C24H(5,𝔽2)12yes—
721C24H(5,𝔽2)12yes—
722C24C2511yescharacteristic
723C2×Q8—44no—
724C2×Q8—44no—
725C2×Q8—82no—
726C2×Q8—84no—
727C2×Q8—84no—
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—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—4128no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—84no—
756C2×D4—84no—
757C2×D4—82no—
758C2×D4—82no—
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—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
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—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—22no—
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—21no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—48no—
874C22×C4—48no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4—84no—
892C22×C4—84no—
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C22×D414yes—
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D412yes—
899C22×C4C22×D412yes—
900C22×C4C2×#4114yes—
901C22×C4H(5,𝔽2)14yes—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—84no—
910C4⋊C4—84no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—84no—
941C22⋊C4—82no—
942C22⋊C4—82no—
943C22⋊C4—84no—
944C22⋊C4—82no—
945C22⋊C4—82no—
946C22⋊C4—84no—
947C22⋊C4—84no—
948C22⋊C4—84no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C42—44no—
953C42—82no—
954C42—84no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—24no—
976C23—22no—
977C23—22no—
978C23—24no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—24no—
989C23—22no—
990C23—24no—
991C23—24no—
992C23—416no—
993C23—416no—
994C23—416no—
995C23—416no—
996C23—416no—
997C23—416no—
998C23—42no—
999C23—42no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—41no—
1004C23—41no—
1005C23—42no—
1006C23—42no—
1007C23—41no—
1008C23—41no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—41no—
1024C23—41no—
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—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—41no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—88no—
1082C23—88no—
1083C23—816no—
1084C23—816no—
1085C23—88no—
1086C23—88no—
1087C23—88no—
1088C23—88no—
1089C23—816no—
1090C23—88no—
1091C23—816no—
1092C23—816no—
1093C23—816no—
1094C23—88no—
1095C23—816no—
1096C23—816no—
1097C23#53514yes—
1098C23#53514yes—
1099C23#53814yes—
1100C23D4214yes—
1101C23#54614yes—
1102C23#54614yes—
1103C23H(3,𝔽4)14yes—
1104C23C23×D411yescharacteristic
1105C23C23×D411yescharacteristic
1106C23C22×#4111yescharacteristic
1107C23C2×H(5,𝔽2)12yes—
1108C23C2×H(5,𝔽2)11yescharacteristic
1109C23C2×H(5,𝔽2)11yescharacteristic
1110C23C2×H(5,𝔽2)11yescharacteristic
1111C23C2×H(5,𝔽2)11yescharacteristic
1112C23#58512yes—
1113C23#58512yes—
1114C23#58512yes—
1115Q8—88no—
1116D4—432no—
1117D4—432no—
1118D4—88no—
1119D4—88no—
1120D4—816no—
1121D4—88no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—416no—
1146C2×C4—416no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
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—88no—
1230C2×C4—88no—
1231C2×C4—88no—
1232C2×C4#53414yes—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—28no—
1237C22—24no—
1238C22—28no—
1239C22—28no—
1240C22—24no—
1241C22—24no—
1242C22—28no—
1243C22—42no—
1244C22—44no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—44no—
1251C22—44no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—42no—
1260C22—44no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—832no—
1265C22—832no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—82no—
1274C22—82no—
1275C22—82no—
1276C22—82no—
1277C22—82no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—82no—
1286C22—81no—
1287C22—81no—
1288C22—82no—
1289C22—82no—
1290C22—81no—
1291C22—81no—
1292C22—82no—
1293C22#267018yes—
1294C22C2×#53411yescharacteristic
1295C22C2×#53511yescharacteristic
1296C22C2×#53511yescharacteristic
1297C22#344911yescharacteristic
1298C22C2×#53811yescharacteristic
1299C22C2×D4211yescharacteristic
1300C22C2×#54611yescharacteristic
1301C22C2×#54611yescharacteristic
1302C22#348512yes—
1303C22#348511yescharacteristic
1304C22#348511yescharacteristic
1305C22#349412yes—
1306C22#349612yes—
1307C22#351012yes—
1308C22C2×H(3,𝔽4)11yescharacteristic
1309C22#353312yes—
1310C22#353312yes—
1311C22#353312yes—
1312C22#353412yes—
1313C22#354212yes—
1314C22#354212yes—
1315C22#354212yes—
1316C22#354512yes—
1317C4—24no—
1318C4—42no—
1319C4—44no—
1320C4—44no—
1321C4—42no—
1322C4—42no—
1323C4—42no—
1324C4—42no—
1325C4—81no—
1326C4—81no—
1327C4—82no—
1328C4—82no—
1329C4—82no—
1330C4—81no—
1331C4—82no—
1332C4—81no—
1333C4—82no—
1334C4—81no—
1335C2—28no—
1336C2—82no—
1337C2—84no—
1338C2—82no—
1339C2—161no—
1340C2#3695611yescharacteristic
1341C2#3743711yescharacteristic
1342C2#3765411yescharacteristic
1343C2#3783411yescharacteristic
1344C2#3933811yescharacteristic
1345C2#3946111yescharacteristic
1346C2#4050912yes—
1347C2#4196312yes—
1348C2#4390512yes—
1349C2C2×#267011yescharacteristic
1350C2#5236712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2613C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#2561C2semidirect
2. C2×#2472C2semidirect
4. C22×#394C2semidirect
5. #17107C2semidirect
6. #17090C2semidirect
7. #16537C2semidirect
8. #16504C2semidirect
9. #16438C2semidirect
10. #16438C2semidirect
11. #15780C2semidirect
12. #15655C2semidirect
13. #15069C2semidirect
14. #14934C2semidirect
15. #14918C2semidirect
16. #14911C2semidirect
17. #14911C2semidirect
18. #14725C2semidirect
19. #14335C2semidirect
20. #13996C2semidirect
21. #13991C2semidirect
22. #13904C2semidirect
23. #13873C2semidirect
25. C22×#124C22semidirect
39. C2×#397C22semidirect
40. C2×#397C22semidirect
48. C2×#394C22semidirect
49. C2×#394C22semidirect
50. C2×#394C22semidirect
51. C2×#393C22semidirect
52. C2×#393C22semidirect
55. C2×#390C22semidirect
56. C2×#388C22semidirect
57. C2×#388C22semidirect
58. C2×#388C22semidirect
59. C2×#388C22semidirect
60. C2×#388C22semidirect
61. C2×#388C22semidirect
82. #1446C22semidirect
83. #1445C22semidirect
84. #1445C22semidirect
85. #1445C22semidirect
86. #1444C22semidirect
87. #1444C22semidirect
88. #1442C22semidirect
89. #1442C22semidirect
90. #1442C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1439C22semidirect
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. #1438C22semidirect
115. #1438C22semidirect
116. #1438C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1437C22semidirect
120. C4⋊#95C22semidirect
121. C4⋊#95C22semidirect
122. C4⋊#95C22semidirect
186. C22×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25612
C2×#24722
C2×#26132
C22×#3942
#171072
#170902
#165372
#165042
#164382
#157802
#156552
#150692
#149342
#149182
#149112
#147252
#143352
#139962
#139912
#139042
#138732