Finite Group Databasebeta

← #741977

Subgroups — #741977

Order 512.

4818 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#551C211yesmaximal, characteristic, complemented
2C2×#2544C211yesmaximal, characteristic, complemented
3C2×#2598C211yesmaximal, characteristic, complemented
4C2×#2392C211yesmaximal, characteristic, complemented
5#16658C212yesmaximal, complemented
6#16256C212yesmaximal, complemented
7#15466C211yesmaximal, characteristic, complemented
8#15465C211yesmaximal, characteristic, complemented
9#15464C211yesmaximal, characteristic, complemented
10#15283C211yesmaximal, characteristic, complemented
11#15264C211yesmaximal, characteristic, complemented
12#15264C211yesmaximal, characteristic, complemented
13#15261C211yesmaximal, characteristic, complemented
14#15258C211yesmaximal, characteristic
15#14917C212yesmaximal, complemented
16#14806C212yesmaximal, complemented
17#14725C212yesmaximal, complemented
18#14721C212yesmaximal, complemented
19#14288C211yesmaximal, characteristic, complemented
20#14175C212yesmaximal, complemented
21#13967C212yesmaximal, complemented
22#13938C211yesmaximal, characteristic, complemented
23#13777C211yesmaximal, characteristic, complemented
24C2×#551—28no—
25C2×#551—28no—
26C2×#551—28no—
27C22×#127C2211yescharacteristic
28C22×#126C2211yescharacteristic
29C22×#126C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C22×#124C2211yescharacteristic, complemented
32C22×#123C2211yescharacteristic
33C22×#123C2211yescharacteristic
34C22×#123C2211yescharacteristic
35C22×C22⋊Q8C2211yescharacteristic
36C22×C22⋊Q8C2211yescharacteristic
37C22×#120C2211yescharacteristic
38C22×#120C2212yes—
39C22×C4×D4C2211yescharacteristic
40C22×C4×D4C2211yescharacteristic
41C22×C4×D4C2212yes—
42C22×C4×D4C2211yescharacteristic, complemented
43C22×#117C2211yescharacteristic
44C22×#117C2211yescharacteristic
45C23×C22⋊C4C2211yescharacteristic
46C23×C22⋊C4C2211yescharacteristic
47#2598—28no—
48#2544—28no—
49C2×#400C2211yescharacteristic, complemented
50C2×#399C2211yescharacteristic
51#2392—28no—
52C2×#398C2211yescharacteristic, complemented
53C2×#397C2211yescharacteristic
54C2×#396C2212yescomplemented
55C2×#394C2212yes—
56C2×#394C2212yes—
57C2×#394C2212yes—
58C2×#394C2211yescharacteristic, complemented
59C2×#394C2212yescomplemented
60C2×#394C2211yescharacteristic, complemented
61C2×#392C2211yescharacteristic
62C2×#392C2212yes—
63C2×#392C2211yescharacteristic
64C2×#392C2212yes—
65C2×#391C2211yescharacteristic, complemented
66C2×#390C2211yescharacteristic
67C2×#388C2212yescomplemented
68C2×#386C2212yes—
69C2×#386C2212yes—
70C2×#386C2212yes—
71C2×#386C2212yes—
72C2×#386C2212yes—
73C2×#386C2212yescomplemented
74C2×#386C2212yescomplemented
75C2×#385C2212yescomplemented
76C2×#383C2211yescharacteristic, complemented
77C2×#380C2212yes—
78C2×#379C2212yes—
79C2×C4×C4⋊C4C2211yescharacteristic, complemented
80C2×C4×C4⋊C4C2211yescharacteristic, complemented
81C2×C4×C22⋊C4C2212yescomplemented
82#1446C2211yescharacteristic, complemented
83#1446C2211yescharacteristic, complemented
84#1444C2212yescomplemented
85#1442C2212yescomplemented
86#1442C2212yescomplemented
87#1441C2212yescomplemented
88#1441C2212yescomplemented
89#1440C2212yes—
90#1440C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2211yescharacteristic
107#1438C2212yes—
108#1438C2212yes—
109#1438C2211yescharacteristic
110#1438C2212yescomplemented
111#1437C2212yes—
112#1437C2212yes—
113#1437C2211yescharacteristic
114#1437C2211yescharacteristic
115#1437C2211yescharacteristic
116#1437C2211yescharacteristic
117#1437C2212yescomplemented
118#1436C2212yescomplemented
119#1436C2211yescharacteristic, complemented
120#1436C2211yescharacteristic, complemented
121#1436C2211yescharacteristic, complemented
122#1436C2211yescharacteristic, complemented
123C4⋊#95C2212yescomplemented
124#1434C2212yescomplemented
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C22⋊#95C2212yes—
128C22⋊#95C2212yescomplemented
129C26C2311yescharacteristic
130C23×Q8C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2312yes—
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2312yes—
145#551—2128no—
146C2×#127—24no—
147C2×#127—44no—
148C2×#126—24no—
149C2×#126—24no—
150C2×#126—24no—
151C2×#126—24no—
152C2×#126—24no—
153C2×#126—24no—
154C2×#124—24no—
155C2×#124—24no—
156C2×#124—24no—
157C2×#124—44no—
158C2×#124D418yescomplemented
159C2×#123—24no—
160C2×#123—24no—
161C2×#123—24no—
162C2×#123—24no—
163C2×#123—24no—
164C2×#123—24no—
165C2×#123—24no—
166C2×#123—24no—
167C2×#123—24no—
168C2×C22⋊Q8—24no—
169C2×C22⋊Q8—24no—
170C2×C22⋊Q8—24no—
171C2×C22⋊Q8—24no—
172C2×C22⋊Q8—24no—
173C2×C22⋊Q8—24no—
174C2×#120—24no—
175C2×#120—24no—
176C2×#120—24no—
177C2×#120—28no—
178C2×#120—44no—
179C2×#120—44no—
180C2×C4×D4—28no—
181C2×C4×D4—24no—
182C2×C4×D4—24no—
183C2×C4×D4—24no—
184C2×C4×D4—24no—
185C2×C4×D4—24no—
186C2×C4×D4—24no—
187C2×C4×D4—24no—
188C2×C4×D4—24no—
189C2×C4×D4—24no—
190C2×C4×D4—44no—
191C2×C4×D4—44no—
192C2×#117—24no—
193C2×#117—24no—
194C2×#117—24no—
195C2×#117—24no—
196C2×#117D418yescomplemented
197C2×#117D418yescomplemented
198C22×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2312yes—
210C22×C4⋊C4C2312yes—
211C22×C22⋊C4—24no—
212C22×C22⋊C4—24no—
213C22×C22⋊C4—24no—
214C22×C22⋊C4—24no—
215C22×C22⋊C4—24no—
216C22×C22⋊C4—24no—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2311yescharacteristic
237C22×C22⋊C4C2311yescharacteristic
238C22×C22⋊C4C2311yescharacteristic
239C22×C22⋊C4C2312yes—
240C22×C22⋊C4C2312yes—
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2312yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2312yes—
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2312yes—
250C22×C22⋊C4C2312yes—
251C22×C22⋊C4C2312yes—
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254C22×C42C2312yes—
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258#400—24no—
259#399—24no—
260#398—24no—
261#397—24no—
262#396—28no—
263#394—24no—
264#394—24no—
265#394—28no—
266#394—28no—
267#394—28no—
268#394—44no—
269#392—24no—
270#392—24no—
271#392—28no—
272#392—44no—
273#391—24no—
274#390—24no—
275#388—28no—
276#386—28no—
277#386—28no—
278#386—28no—
279#386—28no—
280#386—44no—
281#386—44no—
282#386—44no—
283#385—28no—
284#383—24no—
285#380—28no—
286#379—44no—
287C4×C4⋊C4—24no—
288C4×C4⋊C4—24no—
289C4×C22⋊C4—28no—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
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—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—24no—
323C25—24no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25C2411yescharacteristic
329C25C2411yescharacteristic
330C25C2412yes—
331C25C2411yescharacteristic
332C25C2411yescharacteristic
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—42no—
336C22×Q8—42no—
337C22×Q8C2×D414yes—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4C2×D414yes—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
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—24no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4C2×D414yes—
417C23×C4C2×D414yes—
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436#127—416no—
437#126—232no—
438#126—232no—
439#124—232no—
440#124—416no—
441#123—232no—
442#123—232no—
443#123—232no—
444C22⋊Q8—232no—
445C22⋊Q8—232no—
446#120—232no—
447#120—432no—
448C4×D4—232no—
449C4×D4—232no—
450C4×D4—432no—
451C4×D4—416no—
452#117—232no—
453#117—232no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
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—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4C2×D414yes—
490C2×C4⋊C4C2×D414yes—
491C2×C4⋊C4C2×D414yes—
492C2×C4⋊C4C2×D414yes—
493C2×C22⋊C4—232no—
494C2×C22⋊C4—232no—
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—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
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—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
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—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
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⋊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⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—42no—
587C2×C22⋊C4—42no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4C2×D414yes—
592C2×C22⋊C4C2×D414yes—
593C2×C22⋊C4C2×D414yes—
594C2×C22⋊C4C2×D414yes—
595C2×C22⋊C4C2×D414yes—
596C2×C22⋊C4C2×D414yes—
597C2×C22⋊C4C2×D414yes—
598C2×C22⋊C4C2×D414yes—
599C2×C22⋊C4#4118yes—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—24no—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—42no—
608C2×C42—42no—
609C2×C42—42no—
610C2×C42—42no—
611C2×C42C2×D414yes—
612C2×C42C2×D414yes—
613C2×C42C2×D414yes—
614C2×C42C2×D414yes—
615C2×C42C2×D414yes—
616#95—24no—
617#95—24no—
618#95—24no—
619#95—22no—
620#95—22no—
621#95—24no—
622#95—24no—
623#95—22no—
624#95—22no—
625#95—24no—
626#95—24no—
627#95—24no—
628#95—24no—
629#95—24no—
630#95—24no—
631#95—24no—
632#95—42no—
633#95—42no—
634#95—42no—
635#95—42no—
636#95—42no—
637#95—42no—
638#95—42no—
639#95—42no—
640#95—42no—
641#95—42no—
642#95—42no—
643#95—42no—
644#95—42no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—28no—
660C24—21no—
661C24—21no—
662C24—22no—
663C24—22no—
664C24—21no—
665C24—21no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24—82no—
707C24—82no—
708C24—84no—
709C24—84no—
710C24C22×D412yes—
711C24C22×D412yes—
712C24C22×D412yes—
713C24C22×D412yes—
714C24C2×#4114yes—
715C24H(5,𝔽2)14yes—
716C24H(5,𝔽2)14yes—
717C24C2511yescharacteristic
718C2×Q8—28no—
719C2×Q8—44no—
720C2×Q8—44no—
721C2×Q8—84no—
722C2×Q8—84no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—216no—
726C2×D4—28no—
727C2×D4—28no—
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—44no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—48no—
748C2×D4—44no—
749C2×D4—48no—
750C2×D4—44no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—44no—
758C2×D4—84no—
759C2×D4—84no—
760C2×D4—84no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—84no—
769C2×D4—84no—
770C2×D4—84no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
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—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
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—28no—
826C22×C4—28no—
827C22×C4—28no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
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—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
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—44no—
864C22×C4—44no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—84no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4—82no—
877C22×C4—82no—
878C22×C4—82no—
879C22×C4—82no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—84no—
884C22×C4—82no—
885C22×C4—82no—
886C22×C4—84no—
887C22×C4—84no—
888C22×C4C22×D412yes—
889C22×C4C22×D412yes—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C22×D412yes—
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C22×D412yes—
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D412yes—
899C22×C4C22×D412yes—
900C22×C4C22×D412yes—
901C22×C4C22×D412yes—
902C22×C4C22×D412yes—
903C22×C4C22×D412yes—
904C22×C4C22×D412yes—
905C22×C4C2×#4114yes—
906C22×C4C2×#4114yes—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—28no—
911C4⋊C4—28no—
912C4⋊C4—28no—
913C4⋊C4—28no—
914C4⋊C4—28no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—44no—
919C4⋊C4—84no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—84no—
947C22⋊C4—84no—
948C22⋊C4—84no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C42—28no—
956C42—28no—
957C42—48no—
958C42—44no—
959C42—44no—
960C42#120116yescomplemented
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—22no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—416no—
999C23—416no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—42no—
1005C23—41no—
1006C23—41no—
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—41no—
1023C23—41no—
1024C23—42no—
1025C23—41no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—816no—
1081C23—816no—
1082C23—88no—
1083C23—816no—
1084C23—816no—
1085C23—816no—
1086C23—816no—
1087C23#53214yes—
1088C23#53514yes—
1089C23C23×D411yescharacteristic
1090C23C23×D411yescharacteristic
1091C23C23×D411yescharacteristic
1092C23C22×#4112yes—
1093C23C2×H(5,𝔽2)12yes—
1094C23C2×H(5,𝔽2)12yes—
1095C23#58512yes—
1096C23#58512yes—
1097C23#58512yes—
1098Q8—88no—
1099D4—416no—
1100D4—416no—
1101D4—416no—
1102D4—432no—
1103D4—88no—
1104D4—816no—
1105D4—816no—
1106D4—816no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—416no—
1146C2×C4—416no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
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—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—816no—
1211C2×C4—88no—
1212C2×C4—88no—
1213C2×C4—88no—
1214C2×C4C2×#12014yes—
1215C2×C4C2×#12014yes—
1216C2×C4C2×#12014yes—
1217C22—28no—
1218C22—24no—
1219C22—24no—
1220C22—28no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—44no—
1245C22—42no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—832no—
1253C22—82no—
1254C22—82no—
1255C22—82no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22—82no—
1263C22—82no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22C22×#12011yescharacteristic
1270C22C2×#53211yescharacteristic
1271C22C2×#53511yescharacteristic
1272C22#344911yescharacteristic
1273C22#344911yescharacteristic
1274C22D4×#4112yes—
1275C22D4×#4112yes—
1276C22#348411yescharacteristic
1277C22#348511yescharacteristic
1278C22#348812yes—
1279C22#348812yes—
1280C22#348812yes—
1281C22#348812yes—
1282C22#349012yes—
1283C22#351012yes—
1284C22#351312yes—
1285C22#351312yes—
1286C22#353312yes—
1287C22#353412yes—
1288C22#356012yes—
1289C22#356612yes—
1290C4—24no—
1291C4—24no—
1292C4—24no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—44no—
1302C4—44no—
1303C4—82no—
1304C4—82no—
1305C4—82no—
1306C4—82no—
1307C4—82no—
1308C2—44no—
1309C2—44no—
1310C2—84no—
1311C2—82no—
1312C2—82no—
1313C2#3473811yescharacteristic
1314C2#3525011yescharacteristic
1315C2#3551211yescharacteristic
1316C2#3573212yes—
1317C2#3836612yes—
1318C2#3987212yes—
1319C2#4199512yes—
1320C2#4423112yes—
1321C2#4440112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#15258C2
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×#551C2semidirect
2. C2×#2544C2semidirect
3. C2×#2598C2semidirect
4. C2×#2392C2semidirect
5. #16658C2semidirect
6. #16256C2semidirect
7. #15466C2semidirect
8. #15465C2semidirect
9. #15464C2semidirect
10. #15283C2semidirect
11. #15264C2semidirect
12. #15264C2semidirect
13. #15261C2semidirect
15. #14917C2semidirect
16. #14806C2semidirect
17. #14725C2semidirect
18. #14721C2semidirect
19. #14288C2semidirect
20. #14175C2semidirect
21. #13967C2semidirect
22. #13938C2semidirect
23. #13777C2semidirect
31. C22×#124C22semidirect
42. C22×C4×D4C22semidirect
49. C2×#400C22semidirect
52. C2×#398C22semidirect
54. C2×#396C22semidirect
58. C2×#394C22semidirect
59. C2×#394C22semidirect
60. C2×#394C22semidirect
65. C2×#391C22semidirect
67. C2×#388C22semidirect
73. C2×#386C22semidirect
74. C2×#386C22semidirect
75. C2×#385C22semidirect
76. C2×#383C22semidirect
79. C2×C4×C4⋊C4C22semidirect
80. C2×C4×C4⋊C4C22semidirect
81. C2×C4×C22⋊C4C22semidirect
82. #1446C22semidirect
83. #1446C22semidirect
84. #1444C22semidirect
85. #1442C22semidirect
86. #1442C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
110. #1438C22semidirect
117. #1437C22semidirect
118. #1436C22semidirect
119. #1436C22semidirect
120. #1436C22semidirect
121. #1436C22semidirect
122. #1436C22semidirect
123. C4⋊#95C22semidirect
124. #1434C22semidirect
128. C22⋊#95C22semidirect
158. C2×#124D4semidirect
196. C2×#117D4semidirect
197. C2×#117D4semidirect
960. C42#120semidirect

Maximal subgroups

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

subgroupindex
C22×#5512
C2×#25442
C2×#25982
C2×#23922
#166582
#162562
#154662
#154652
#154642
#152832
#152642
#152612
#152582
#149172
#148062
#147252
#147212
#142882
#141752
#139672
#139382
#137772