Finite Group Databasebeta

← #650726

Subgroups — #650726

Order 512.

4704 conjugacy classes of subgroups.

The subgroup lattice has 1348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic, complemented
2C2×#2544C211yesmaximal, characteristic, complemented
3C2×#2445C211yesmaximal, characteristic, complemented
4C2×#2428C211yesmaximal, characteristic
5#15908C212yesmaximal, complemented
6#15908C212yesmaximal, complemented
7#15270C212yesmaximal, complemented
8#15260C212yesmaximal, complemented
9#15229C211yesmaximal, characteristic, complemented
10#15218C211yesmaximal, characteristic, complemented
11#15215C211yesmaximal, characteristic, complemented
12#15179C211yesmaximal, characteristic, complemented
13#14888C212yesmaximal, complemented
14#14721C212yesmaximal, complemented
15#14698C211yesmaximal, characteristic, complemented
16#14135C212yesmaximal, complemented
17#14027C211yesmaximal, characteristic, complemented
18#14026C211yesmaximal, characteristic, complemented
19#14023C212yesmaximal, complemented
20#14017C211yesmaximal, characteristic, complemented
21#13970C211yesmaximal, characteristic, complemented
22D4×#95C211yesmaximal, characteristic, complemented
23C4×#385C211yesmaximal, characteristic, complemented
24C22×#127C2211yescharacteristic
25C2×#529—28no—
26C2×#529—28no—
27C2×#529—28no—
28C22×#126C2212yes—
29C22×#125C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C22×#123C2212yes—
33C22×#123C2212yes—
34C22×C22⋊Q8C2211yescharacteristic
35C22×#121C2211yescharacteristic
36C22×#121C2212yes—
37C22×#121C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39C22×C4×D4C2212yes—
40C22×C4×D4C2211yescharacteristic
41C22×C4×D4C2211yescharacteristic
42C22×C4×D4C2211yescharacteristic
43C22×#117C2212yes—
44C23×C42C2211yescharacteristic
45#2544—28no—
46#2445—28no—
47#2428—28no—
48C2×#394C2212yes—
49C2×#394C2212yes—
50C2×#394C2212yes—
51C2×#394C2212yes—
52C2×#394C2212yes—
53C2×#392C2212yes—
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#390C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#390C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#389C2211yescharacteristic
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#386C2212yes—
69C2×#386C2212yes—
70C2×#386C2212yes—
71C2×#385C2211yescharacteristic
72C2×#385C2211yescharacteristic
73C2×#380C2211yescharacteristic
74C2×C4×C4⋊C4C2211yescharacteristic
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C22×#95C2212yes—
79#1444C2212yes—
80#1444C2212yes—
81#1444C2212yes—
82#1442C2212yes—
83#1442C2212yes—
84#1441C2212yes—
85#1441C2212yes—
86#1441C2212yes—
87#1440C2212yes—
88#1440C2212yes—
89#1440C2212yes—
90#1440C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1437C2212yes—
104#1437C2212yes—
105#1437C2212yes—
106#1437C2212yes—
107#1436C2211yescharacteristic
108#1436C2211yescharacteristic
109#1436C2211yescharacteristic
110#1436C2212yes—
111#1436C2211yescharacteristic
112#1436C2212yes—
113C4⋊#95C2211yescharacteristic
114C4⋊#95C2211yescharacteristic
115C4⋊#95C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C22⋊#95C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C4×#95C2211yescharacteristic
128C4×#95C2211yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C23×D4C2312yes—
133C23×D4C2312yes—
134C23×D4C2312yes—
135C23×D4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2312yes—
140C24×C4C2312yes—
141C24×C4C2312yes—
142C2×#127—24no—
143C2×#127—24no—
144C2×#127—24no—
145#529—2128no—
146C2×#126—28no—
147C2×#126—28no—
148C2×#126—28no—
149C2×#125—24no—
150C2×#125—24no—
151C2×#125—24no—
152C2×#124—24no—
153C2×#124—24no—
154C2×#124—24no—
155C2×#124—24no—
156C2×#124—42no—
157C2×#124D418yescomplemented
158C2×#123—28no—
159C2×#123—28no—
160C2×#123—28no—
161C2×#123—28no—
162C2×#123—28no—
163C2×#123—44no—
164C2×C22⋊Q8—24no—
165C2×C22⋊Q8—24no—
166C2×C22⋊Q8—24no—
167C2×#121—24no—
168C2×#121—24no—
169C2×#121—28no—
170C2×#121—24no—
171C2×#121—24no—
172C2×#121—28no—
173C2×#121—44no—
174C2×#121—42no—
175C2×#121D418yes—
176C2×C4×Q8—24no—
177C2×C4×Q8—24no—
178C2×C4×Q8—24no—
179C2×C4×D4—28no—
180C2×C4×D4—24no—
181C2×C4×D4—24no—
182C2×C4×D4—28no—
183C2×C4×D4—24no—
184C2×C4×D4—24no—
185C2×C4×D4—24no—
186C2×C4×D4—28no—
187C2×C4×D4—24no—
188C2×C4×D4—42no—
189C2×C4×D4—42no—
190C2×C4×D4D418yescomplemented
191C2×#117—28no—
192C2×#117—28no—
193C2×#117—28no—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C42—24no—
235C22×C42—24no—
236C22×C42—24no—
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2312yes—
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246#394—28no—
247#394—28no—
248#394—28no—
249#394—28no—
250#394—28no—
251#392—28no—
252#391—24no—
253#391—24no—
254#391—42no—
255#390—24no—
256#390—24no—
257#390—24no—
258#390—24no—
259#390—24no—
260#389—24no—
261#389—24no—
262#386—28no—
263#386—28no—
264#386—28no—
265#386—28no—
266#386—44no—
267#386—44no—
268#386—44no—
269#385—24no—
270#385—24no—
271#380—42no—
272C4×C4⋊C4—24no—
273C4×C4⋊C4—24no—
274C4×C22⋊C4—24no—
275C4×C22⋊C4—24no—
276C2×#95—44no—
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C25C2412yes—
315C25C2412yes—
316C25C2411yescharacteristic
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8C2×D414yes—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4C2×D418yes—
363C22×D4C2×D414yes—
364C22×D4C2×D414yes—
365C22×D4C2×D414yes—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—41no—
394C23×C4—41no—
395C23×C4—41no—
396C23×C4—41no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4C2×D414yes—
407C23×C4C2×D418yes—
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2412yes—
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428#127—416no—
429#126—264no—
430#125—232no—
431#124—232no—
432#124—416no—
433#123—264no—
434#123—432no—
435C22⋊Q8—232no—
436#121—232no—
437#121—432no—
438#121—416no—
439C4×Q8—232no—
440C4×D4—264no—
441C4×D4—232no—
442C4×D4—416no—
443C4×D4—416no—
444#117—264no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—22no—
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—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—41no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4C2×D414yes—
487C2×C4⋊C4C2×D414yes—
488C2×C4⋊C4#4114yes—
489C2×C4⋊C4#4114yes—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
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—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
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—41no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4C2×D418yes—
561C2×C22⋊C4C2×D418yes—
562C2×C22⋊C4C2×D418yes—
563C2×C22⋊C4C2×D418yes—
564C2×C22⋊C4#4114yes—
565C2×C42—232no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—24no—
570C2×C42—24no—
571C2×C42—24no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—22no—
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×C42C2×D414yes—
591C2×C42C2×D414yes—
592C2×C42#4114yes—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—24no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—24no—
610#95—24no—
611#95—22no—
612#95—24no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95—42no—
619#95—41no—
620#95—41no—
621#95—41no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95—42no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—21no—
638C24—22no—
639C24—21no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—21no—
645C24—22no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—21no—
651C24—21no—
652C24—22no—
653C24—21no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24C22×D414yes—
670C24C22×D414yes—
671C24C22×D414yes—
672C24C22×D412yes—
673C24C2×#4112yes—
674C24H(5,𝔽2)12yes—
675C24C2511yescharacteristic
676C2×Q8—28no—
677C2×Q8—28no—
678C2×Q8—28no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—44no—
682C2×Q8—44no—
683C2×D4—216no—
684C2×D4—216no—
685C2×D4—28no—
686C2×D4—28no—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—28no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4—84no—
718C2×D4—84no—
719C2×D4—84no—
720C2×D4—84no—
721C2×D4—84no—
722C2×D4—84no—
723C2×D4—84no—
724C2×D4#120116yes—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—216no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—216no—
819C22×C4—28no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—48no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—44no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4C22×D412yes—
884C22×C4C22×D414yes—
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C22×D412yes—
888C22×C4C22×D414yes—
889C22×C4C22×D414yes—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C22×D412yes—
893C22×C4C22×D412yes—
894C22×C4C2×#4112yes—
895C22×C4C2×#4114yes—
896C22×C4C2×#4112yes—
897C22×C4C2×#4112yes—
898C22×C4C2×#4112yes—
899C22×C4C2×#4112yes—
900C22×C4C2×#4112yes—
901C22×C4C2×#4112yes—
902C22×C4C2×#4112yes—
903C22×C4C2×#4112yes—
904C22×C4H(5,𝔽2)12yes—
905C22×C4H(5,𝔽2)12yes—
906C22×C42−1+412yes—
907C4⋊C4—216no—
908C4⋊C4—216no—
909C4⋊C4—216no—
910C4⋊C4—216no—
911C4⋊C4—28no—
912C4⋊C4—28no—
913C4⋊C4—28no—
914C4⋊C4—28no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C22⋊C4—28no—
923C22⋊C4—216no—
924C22⋊C4—216no—
925C22⋊C4—216no—
926C22⋊C4—216no—
927C22⋊C4—216no—
928C22⋊C4—28no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C42—28no—
948C42—28no—
949C42—216no—
950C42—28no—
951C42—28no—
952C42—28no—
953C42—44no—
954C42—44no—
955C42—44no—
956C23—22no—
957C23—24no—
958C23—22no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—22no—
964C23—24no—
965C23—22no—
966C23—24no—
967C23—24no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—22no—
976C23—22no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—24no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—41no—
993C23—42no—
994C23—41no—
995C23—42no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—41no—
1005C23—41no—
1006C23—42no—
1007C23—42no—
1008C23—41no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—41no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—41no—
1017C23—42no—
1018C23—41no—
1019C23—42no—
1020C23—41no—
1021C23—42no—
1022C23—42no—
1023C23—41no—
1024C23—42no—
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—
1059C23C2×#12018yes—
1060C23#54614yes—
1061C23C23×D411yescharacteristic
1062C23C23×D411yescharacteristic
1063C23C23×D411yescharacteristic
1064C23C22×#4111yescharacteristic
1065C23C22×#4111yescharacteristic
1066C23C22×#4111yescharacteristic
1067C23C22×#4111yescharacteristic
1068C23C2×H(5,𝔽2)11yescharacteristic
1069C23C2×H(5,𝔽2)11yescharacteristic
1070C23C2×H(5,𝔽2)11yescharacteristic
1071C23C2×2−1+411yescharacteristic
1072C23#58511yescharacteristic
1073C23#58511yescharacteristic
1074C23#58511yescharacteristic
1075C23#58511yescharacteristic
1076Q8—416no—
1077D4—232no—
1078D4—432no—
1079D4—816no—
1080D4—816no—
1081D4—816no—
1082D4—88no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—432no—
1132C2×C4—416no—
1133C2×C4—416no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—41no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—42no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—41no—
1190C2×C4—416no—
1191C2×C4—41no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—41no—
1218C2×C4—42no—
1219C2×C4—816no—
1220C2×C4—816no—
1221C2×C4C2×#12014yes—
1222C2×C4#53214yes—
1223C2×C4#53714yes—
1224C2×C4#54614yes—
1225C2×C4#54614yes—
1226C2×C4#54614yes—
1227C2×C4#54714yes—
1228C2×C4#54714yes—
1229C22—24no—
1230C22—24no—
1231C22—28no—
1232C22—28no—
1233C22—24no—
1234C22—28no—
1235C22—44no—
1236C22—42no—
1237C22—44no—
1238C22—44no—
1239C22—42no—
1240C22—42no—
1241C22—44no—
1242C22—42no—
1243C22—44no—
1244C22—42no—
1245C22—44no—
1246C22—42no—
1247C22—44no—
1248C22—42no—
1249C22—44no—
1250C22—42no—
1251C22—44no—
1252C22—42no—
1253C22—44no—
1254C22—42no—
1255C22—44no—
1256C22—42no—
1257C22—44no—
1258C22—42no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22—82no—
1263C22—82no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—82no—
1274C22C22×#12011yescharacteristic
1275C22C2×#53211yescharacteristic
1276C22#344411yescharacteristic
1277C22C2×#53711yescharacteristic
1278C22#346011yescharacteristic
1279C22C2×#54611yescharacteristic
1280C22C2×#54611yescharacteristic
1281C22C2×#54611yescharacteristic
1282C22C2×#54611yescharacteristic
1283C22C2×#54711yescharacteristic
1284C22C2×#54711yescharacteristic
1285C22D4×#4111yescharacteristic
1286C22D4×#4111yescharacteristic
1287C22D4×#4111yescharacteristic
1288C22D4×#4111yescharacteristic
1289C22#348011yescharacteristic
1290C22#348111yescharacteristic
1291C22#348511yescharacteristic
1292C22#348511yescharacteristic
1293C22#348811yescharacteristic
1294C22#348811yescharacteristic
1295C22#348811yescharacteristic
1296C22#348811yescharacteristic
1297C22#349411yescharacteristic
1298C22#350711yescharacteristic
1299C22#351211yescharacteristic
1300C22#351311yescharacteristic
1301C22#351411yescharacteristic
1302C22#351711yescharacteristic
1303C22#352211yescharacteristic
1304C22#352411yescharacteristic
1305C22#354311yescharacteristic
1306C22#355411yescharacteristic
1307C22#355711yescharacteristic
1308C22#356211yescharacteristic
1309C4—24no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—44no—
1314C4—42no—
1315C4—42no—
1316C4—44no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—44no—
1322C4—42no—
1323C4—44no—
1324C4—82no—
1325C4—81no—
1326C4—81no—
1327C4—82no—
1328C4#243018yes—
1329C2—44no—
1330C2—48no—
1331C2—162no—
1332C2C2×#243011yescharacteristic
1333C2#3488911yescharacteristic
1334C2#3557011yescharacteristic
1335C2#3613911yescharacteristic
1336C2#3614111yescharacteristic
1337C2#3621211yescharacteristic
1338C2#3621211yescharacteristic
1339C2#3775111yescharacteristic
1340C2#3779811yescharacteristic
1341C2#3890911yescharacteristic
1342C2#3985711yescharacteristic
1343C2#5903011yescharacteristic
1344C2#5906811yescharacteristic
1345C2#5907211yescharacteristic
1346C2#5910111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2428C2
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×#2544C2semidirect
3. C2×#2445C2semidirect
5. #15908C2semidirect
6. #15908C2semidirect
7. #15270C2semidirect
8. #15260C2semidirect
9. #15229C2semidirect
10. #15218C2semidirect
11. #15215C2semidirect
12. #15179C2semidirect
13. #14888C2semidirect
14. #14721C2semidirect
15. #14698C2semidirect
16. #14135C2semidirect
17. #14027C2semidirect
18. #14026C2semidirect
19. #14023C2semidirect
20. #14017C2semidirect
21. #13970C2semidirect
22. D4×#95C2semidirect
23. C4×#385C2semidirect
157. C2×#124D4semidirect
190. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5292
C2×#25442
C2×#24452
C2×#24282
#159082
#152702
#152602
#152292
#152182
#152152
#151792
#148882
#147212
#146982
#141352
#140272
#140262
#140232
#140172
#139702
D4×#952
C4×#3852