Finite Group Databasebeta

← #760170

Subgroups — #760170

Order 512.

4628 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic, complemented
2C2×#2417C211yesmaximal, characteristic, complemented
3C2×#2416C211yesmaximal, characteristic
4C2×C4×#123C211yesmaximal, characteristic, complemented
5#16659C212yesmaximal, complemented
6#16658C212yesmaximal, complemented
7#15218C211yesmaximal, characteristic, complemented
8#15217C211yesmaximal, characteristic, complemented
9#15216C211yesmaximal, characteristic, complemented
10#15215C211yesmaximal, characteristic, complemented
11#14927C212yesmaximal, complemented
12#14926C212yesmaximal, complemented
13#14891C212yesmaximal, complemented
14#14890C212yesmaximal, complemented
15#14139C211yesmaximal, characteristic, complemented
16#14137C211yesmaximal, characteristic, complemented
17#14023C212yesmaximal, complemented
18#14018C211yesmaximal, characteristic, complemented
19#14017C211yesmaximal, characteristic, complemented
20#13975C212yesmaximal, complemented
21#13970C211yesmaximal, characteristic, complemented
22#13969C211yesmaximal, characteristic, complemented
23C2×C4⋊#95C211yesmaximal, characteristic, complemented
24C2×#529—28no—
25C2×#529—28no—
26C2×#529—28no—
27C22×#126C2212yes—
28C22×#125C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×#123C2211yescharacteristic
31C22×#123C2212yes—
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×#121C2212yes—
35C22×#121C2211yescharacteristic
36C22×#121C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38C22×C4×D4C2211yescharacteristic
39C22×C4×D4C2211yescharacteristic
40C22×C4×D4C2212yes—
41C22×#117C2212yes—
42C23×C4⋊C4C2211yescharacteristic
43C23×C4⋊C4C2211yescharacteristic
44C23×C42C2211yescharacteristic
45#2417—28no—
46#2416—28no—
47C2×#398C2212yes—
48C2×#396C2212yes—
49C2×#396C2212yes—
50C2×#394C2212yes—
51C4×#123—28no—
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#388C2211yescharacteristic
61C2×#388C2211yescharacteristic
62C2×#387C2211yescharacteristic
63C2×#387C2211yescharacteristic
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2211yescharacteristic
68C2×#386C2212yes—
69C2×#386C2212yes—
70C2×#385C2211yescharacteristic
71C2×#385C2212yes—
72C2×#381C2211yescharacteristic
73C2×#380C2212yes—
74C2×#380C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C22×#95C2212yes—
82C22×#95C2212yes—
83#1444C2212yes—
84#1444C2212yes—
85#1444C2212yes—
86#1442C2212yes—
87#1442C2212yes—
88#1442C2212yes—
89#1441C2212yes—
90#1441C2212yes—
91#1441C2212yes—
92#1441C2212yes—
93#1441C2212yes—
94#1440C2212yes—
95#1440C2212yes—
96#1440C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1438C2212yes—
111#1437C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114#1436C2212yes—
115C4⋊#95C2212yes—
116C4⋊#95C2212yes—
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120C4⋊#95C2211yescharacteristic
121C4⋊#95C2211yescharacteristic
122C4⋊#95C2211yescharacteristic
123C4⋊#95C2211yescharacteristic
124C4⋊#95C2211yescharacteristic
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C22⋊#95C2212yes—
128C22⋊#95C2212yes—
129C23×Q8C2311yescharacteristic
130C23×D4C2312yes—
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C23×D4C2312yes—
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2312yes—
137C24×C4C2312yes—
138C24×C4C2312yes—
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141#529—2128no—
142C2×#126—28no—
143C2×#126—28no—
144C2×#126—28no—
145C2×#125—24no—
146C2×#125—24no—
147C2×#125—24no—
148C2×#124—24no—
149C2×#124—24no—
150C2×#124—24no—
151C2×#123—28no—
152C2×#123—24no—
153C2×#123—28no—
154C2×#123—24no—
155C2×#123—28no—
156C2×#123—24no—
157C2×C22⋊Q8—24no—
158C2×C22⋊Q8—24no—
159C2×C22⋊Q8—24no—
160C2×C22⋊Q8—24no—
161C2×C22⋊Q8—42no—
162C2×C22⋊Q8D418yescomplemented
163C2×#121—24no—
164C2×#121—24no—
165C2×#121—24no—
166C2×#121—28no—
167C2×#121—28no—
168C2×#121—24no—
169C2×#121—42no—
170C2×#121—44no—
171C2×#121D418yes—
172C2×C4×Q8—24no—
173C2×C4×Q8—24no—
174C2×C4×Q8—24no—
175C2×C4×D4—28no—
176C2×C4×D4—24no—
177C2×C4×D4—28no—
178C2×C4×D4—24no—
179C2×C4×D4—24no—
180C2×C4×D4—24no—
181C2×C4×D4—24no—
182C2×C4×D4—28no—
183C2×C4×D4—24no—
184C2×#117—28no—
185C2×#117—28no—
186C2×#117—28no—
187C22×C4⋊C4—24no—
188C22×C4⋊C4—24no—
189C22×C4⋊C4—24no—
190C22×C4⋊C4—24no—
191C22×C4⋊C4—42no—
192C22×C4⋊C4—42no—
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2312yes—
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2312yes—
236C22×C42—24no—
237C22×C42—24no—
238C22×C42D418yescomplemented
239C22×C42C2312yes—
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247#398—28no—
248#396—28no—
249#396—28no—
250#394—28no—
251#391—24no—
252#391—24no—
253#391—42no—
254#390—24no—
255#390—24no—
256#390—42no—
257#389—24no—
258#389—24no—
259#388—24no—
260#388—24no—
261#387—24no—
262#387—24no—
263#386—28no—
264#386—24no—
265#386—28no—
266#386—28no—
267#386—44no—
268#386—44no—
269#385—24no—
270#385—44no—
271#381—24no—
272#380—24no—
273#380—24no—
274#380—28no—
275C4×C4⋊C4—24no—
276C4×C4⋊C4—24no—
277C4×C22⋊C4—24no—
278C4×C22⋊C4—24no—
279C4×C22⋊C4—24no—
280C2×#95—44no—
281C2×#95—44no—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C25C2412yes—
319C25C2411yescharacteristic
320C25C2411yescharacteristic
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8C2×D414yes—
328C22×D4—22no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—24no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—22no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4C2×D418yes—
354C22×D4C2×D414yes—
355C22×D4#4114yes—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—24no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—22no—
390C23×C4—42no—
391C23×C4—41no—
392C23×C4—41no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4C2×D414yes—
401C23×C4C2×D414yes—
402C23×C4C2×D414yes—
403C23×C4C2×D414yes—
404C23×C4C2×D414yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2412yes—
410C23×C4C2412yes—
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425#126—264no—
426#125—232no—
427#124—232no—
428#123—232no—
429#123—264no—
430C22⋊Q8—232no—
431C22⋊Q8—416no—
432#121—232no—
433#121—416no—
434#121—432no—
435C4×Q8—232no—
436C4×D4—264no—
437C4×D4—232no—
438C4×D4—416no—
439#117—264no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
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—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—416no—
488C2×C4⋊C4—416no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—41no—
492C2×C4⋊C4—41no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4C2×D418yes—
498C2×C4⋊C4C2×D414yes—
499C2×C4⋊C4C2×D414yes—
500C2×C4⋊C4#4114yes—
501C2×C4⋊C4#4114yes—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
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—24no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4—41no—
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⋊C4C2×D418yes—
569C2×C22⋊C4C2×D418yes—
570C2×C22⋊C4#4114yes—
571C2×C42—232no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—24no—
575C2×C42—24no—
576C2×C42—24no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—22no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—22no—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42C2×D414yes—
593C2×C42C2×D414yes—
594C2×C42C2×D414yes—
595C2×C42C2×D414yes—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—24no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—24no—
614#95—24no—
615#95—24no—
616#95—24no—
617#95—24no—
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#95—42no—
628#95—42no—
629#95—42no—
630#95—42no—
631#95—42no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—22no—
643C24—22no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—21no—
652C24—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—22no—
660C24—21no—
661C24—22no—
662C24—22no—
663C24—21no—
664C24—21no—
665C24—22no—
666C24—22no—
667C24—21no—
668C24C22×D414yes—
669C24C22×D412yes—
670C24C22×D412yes—
671C24C22×D412yes—
672C24C2×#4112yes—
673C24C2×#4112yes—
674C24C2×#4112yes—
675C24H(5,𝔽2)12yes—
676C242−1+412yes—
677C24C2511yescharacteristic
678C2×Q8—28no—
679C2×Q8—28no—
680C2×Q8—28no—
681C2×Q8—44no—
682C2×Q8—44no—
683C2×Q8—44no—
684C2×Q8—44no—
685C2×D4—216no—
686C2×D4—28no—
687C2×D4—28no—
688C2×D4—216no—
689C2×D4—216no—
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—28no—
693C2×D4—28no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—44no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—44no—
704C2×D4—48no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—84no—
710C2×D4—84no—
711C2×D4—84no—
712C2×D4—84no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—28no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—28no—
726C22×C4—28no—
727C22×C4—216no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—22no—
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—22no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—28no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—44no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—48no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—84no—
872C22×C4—84no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4#120116yes—
878C22×C4C22×D414yes—
879C22×C4C22×D414yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D414yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C22×D412yes—
888C22×C4C22×D412yes—
889C22×C4C22×D412yes—
890C22×C4C22×D412yes—
891C22×C4C2×#4112yes—
892C22×C4C2×#4112yes—
893C22×C4C2×#4114yes—
894C22×C4C2×#4114yes—
895C22×C4C2×#4112yes—
896C22×C4C2×#4112yes—
897C22×C4C2×#4112yes—
898C22×C4H(5,𝔽2)12yes—
899C22×C4H(5,𝔽2)12yes—
900C22×C42−1+412yes—
901C22×C42−1+412yes—
902C4⋊C4—216no—
903C4⋊C4—216no—
904C4⋊C4—216no—
905C4⋊C4—28no—
906C4⋊C4—28no—
907C4⋊C4—216no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—28no—
911C4⋊C4—28no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—84no—
922C22⋊C4—216no—
923C22⋊C4—216no—
924C22⋊C4—216no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—216no—
928C22⋊C4—28no—
929C22⋊C4—216no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C42—216no—
946C42—28no—
947C42—28no—
948C42—28no—
949C42—28no—
950C42—44no—
951C42—44no—
952C42—44no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—24no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—24no—
992C23—24no—
993C23—22no—
994C23—22no—
995C23—41no—
996C23—42no—
997C23—41no—
998C23—42no—
999C23—41no—
1000C23—41no—
1001C23—42no—
1002C23—41no—
1003C23—42no—
1004C23—42no—
1005C23—41no—
1006C23—42no—
1007C23—41no—
1008C23—41no—
1009C23—42no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—42no—
1014C23—42no—
1015C23—41no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—41no—
1020C23—41no—
1021C23—42no—
1022C23—42no—
1023C23—41no—
1024C23—42no—
1025C23—41no—
1026C23—42no—
1027C23—41no—
1028C23—41no—
1029C23—42no—
1030C23—41no—
1031C23—42no—
1032C23—41no—
1033C23—42no—
1034C23—42no—
1035C23—41no—
1036C23—41no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—41no—
1042C23—41no—
1043C23—42no—
1044C23—41no—
1045C23—42no—
1046C23—41no—
1047C23—42no—
1048C23—42no—
1049C23—41no—
1050C23—41no—
1051C23C2×#12014yes—
1052C23#52514yes—
1053C23#53714yes—
1054C23#54614yes—
1055C23#54714yes—
1056C23#54814yes—
1057C23#55014yes—
1058C23C23×D411yescharacteristic
1059C23C23×D411yescharacteristic
1060C23C23×D411yescharacteristic
1061C23C22×#4111yescharacteristic
1062C23C22×#4111yescharacteristic
1063C23C22×#4111yescharacteristic
1064C23C22×#4111yescharacteristic
1065C23C2×H(5,𝔽2)11yescharacteristic
1066C23C2×H(5,𝔽2)11yescharacteristic
1067C23C2×H(5,𝔽2)11yescharacteristic
1068C23C2×2−1+411yescharacteristic
1069C23C2×2−1+411yescharacteristic
1070C23C2×2−1+411yescharacteristic
1071C23#58511yescharacteristic
1072C23#58511yescharacteristic
1073Q8—416no—
1074D4—432no—
1075D4—416no—
1076D4—416no—
1077D4—816no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—232no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—416no—
1125C2×C4—432no—
1126C2×C4—416no—
1127C2×C4—41no—
1128C2×C4—42no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—42no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—816no—
1214C2×C4—816no—
1215C2×C4—88no—
1216C2×C4C2×#12014yes—
1217C2×C4C2×#12014yes—
1218C2×C4#53214yes—
1219C2×C4#53714yes—
1220C2×C4#53714yes—
1221C2×C4#54614yes—
1222C2×C4#54614yes—
1223C2×C4#54714yes—
1224C2×C4#54714yes—
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—24no—
1229C22—24no—
1230C22—24no—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—42no—
1240C22—42no—
1241C22—44no—
1242C22—42no—
1243C22—42no—
1244C22—44no—
1245C22—42no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—42no—
1252C22—42no—
1253C22—82no—
1254C22—82no—
1255C22—81no—
1256C22—82no—
1257C22—81no—
1258C22—82no—
1259C22—81no—
1260C22—82no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—82no—
1266C22—82no—
1267C22—81no—
1268C22—82no—
1269C22#240718yes—
1270C22C22×#12011yescharacteristic
1271C22C2×#52511yescharacteristic
1272C22C2×#53211yescharacteristic
1273C22C2×#53711yescharacteristic
1274C22C2×#53711yescharacteristic
1275C22C2×#53711yescharacteristic
1276C22#344911yescharacteristic
1277C22C2×#54611yescharacteristic
1278C22C2×#54611yescharacteristic
1279C22C2×#54611yescharacteristic
1280C22C2×#54711yescharacteristic
1281C22C2×#54711yescharacteristic
1282C22C2×#54711yescharacteristic
1283C22C2×#54811yescharacteristic
1284C22C2×#55011yescharacteristic
1285C22#348111yescharacteristic
1286C22#348111yescharacteristic
1287C22#348211yescharacteristic
1288C22#348211yescharacteristic
1289C22#348811yescharacteristic
1290C22#348811yescharacteristic
1291C22#348911yescharacteristic
1292C22#348911yescharacteristic
1293C22#351311yescharacteristic
1294C22#351311yescharacteristic
1295C22#351411yescharacteristic
1296C22#351411yescharacteristic
1297C22#351511yescharacteristic
1298C22#351511yescharacteristic
1299C22#351611yescharacteristic
1300C22#351611yescharacteristic
1301C22#354311yescharacteristic
1302C22#354411yescharacteristic
1303C22#355211yescharacteristic
1304C22#355211yescharacteristic
1305C4—24no—
1306C4—24no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—44no—
1312C4—42no—
1313C4—44no—
1314C4—44no—
1315C4—44no—
1316C4—42no—
1317C4—44no—
1318C4—82no—
1319C4—81no—
1320C4—82no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4#243018yes—
1325C2—28no—
1326C2—82no—
1327C2—84no—
1328C2C2×#240711yescharacteristic
1329C2C2×#243011yescharacteristic
1330C2#3496411yescharacteristic
1331C2#3513011yescharacteristic
1332C2#3523411yescharacteristic
1333C2#3525111yescharacteristic
1334C2#3762011yescharacteristic
1335C2#5903011yescharacteristic
1336C2#5903111yescharacteristic
1337C2#5904611yescharacteristic
1338C2#5904711yescharacteristic
1339C2#5906111yescharacteristic
1340C2#5906211yescharacteristic
1341C2#5907511yescharacteristic
1342C2#5907611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2416C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#529C2semidirect
2. C2×#2417C2semidirect
4. C2×C4×#123C2semidirect
5. #16659C2semidirect
6. #16658C2semidirect
7. #15218C2semidirect
8. #15217C2semidirect
9. #15216C2semidirect
10. #15215C2semidirect
11. #14927C2semidirect
12. #14926C2semidirect
13. #14891C2semidirect
14. #14890C2semidirect
15. #14139C2semidirect
16. #14137C2semidirect
17. #14023C2semidirect
18. #14018C2semidirect
19. #14017C2semidirect
20. #13975C2semidirect
21. #13970C2semidirect
22. #13969C2semidirect
23. C2×C4⋊#95C2semidirect
162. C2×C22⋊Q8D4semidirect
238. C22×C42D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5292
C2×#24172
C2×#24162
C2×C4×#1232
#166592
#166582
#152182
#152172
#152162
#152152
#149272
#149262
#148912
#148902
#141392
#141372
#140232
#140182
#140172
#139752
#139702
#139692
C2×C4⋊#952