Finite Group Databasebeta

← #1259545

Subgroups — #1259545

Order 512.

4352 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2564C211yesmaximal, characteristic, complemented
2C2×#2404C211yesmaximal, characteristic, complemented
3C2×#2407C211yesmaximal, characteristic, complemented
4C2×#2358C211yesmaximal, characteristic, complemented
5#17023C211yesmaximal, characteristic, complemented
6#16809C211yesmaximal, characteristic, complemented
7#16600C211yesmaximal, characteristic, complemented
8#16394C211yesmaximal, characteristic, complemented
9#15979C212yesmaximal, complemented
10#15961C212yesmaximal, complemented
11#15376C212yesmaximal, complemented
12#15257C212yesmaximal, complemented
13#14977C211yesmaximal, characteristic, complemented
14#14889C211yesmaximal, characteristic, complemented
15#14757C211yesmaximal, characteristic, complemented
16#14749C212yesmaximal, complemented
17#14734C211yesmaximal, characteristic, complemented
18#14722C211yesmaximal, characteristic, complemented
19#14718C212yesmaximal, complemented
20#14572C212yesmaximal, complemented
21#14361C212yesmaximal, complemented
22#14319C211yesmaximal, characteristic, complemented
23#13894C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic, complemented
26C22×#121C2212yes—
27C22×#121C2211yescharacteristic, complemented
28C22×#120C2211yescharacteristic
29C22×#120C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34#2564—28no—
35#2407—28no—
36#2404—28no—
37C2×#400C2211yescharacteristic, complemented
38C2×#399C2211yescharacteristic
39C2×#399C2211yescharacteristic
40C2×#395C2211yescharacteristic, complemented
41C2×#394C2212yes—
42C2×#394C2212yes—
43C2×#394C2211yescharacteristic, complemented
44C2×#393C2211yescharacteristic
45C2×#393C2211yescharacteristic
46C2×#392C2212yes—
47C2×#392C2211yescharacteristic
48C2×#392C2212yes—
49C2×#392C2211yescharacteristic
50#2358—28no—
51C2×#391C2211yescharacteristic, complemented
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic, complemented
54C2×#388C2211yescharacteristic
55C2×#388C2211yescharacteristic
56C2×#388C2212yescomplemented
57C2×#387C2212yescomplemented
58C2×#386C2212yes—
59C2×#386C2211yescharacteristic
60C2×#386C2212yes—
61C2×#386C2212yes—
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#386C2212yescomplemented
69C2×#386C2212yescomplemented
70C2×#385C2211yescharacteristic
71C2×#385C2212yes—
72C2×#385C2211yescharacteristic
73C2×#385C2212yes—
74C2×#385C2212yescomplemented
75C2×#385C2212yescomplemented
76C2×#381C2211yescharacteristic
77C2×#380C2211yescharacteristic
78C2×#380C2212yescomplemented
79C2×#379C2212yes—
80C2×C4×C22⋊C4C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic
82C22×#95C2211yescharacteristic, complemented
83#1446C2211yescharacteristic, complemented
84#1445C2211yescharacteristic, complemented
85#1445C2212yescomplemented
86#1444C2211yescharacteristic, complemented
87#1443C2212yescomplemented
88#1443C2212yescomplemented
89#1443C2212yescomplemented
90#1442C2212yescomplemented
91#1441C2212yescomplemented
92#1441C2211yescharacteristic, complemented
93#1441C2212yescomplemented
94#1440C2212yes—
95#1440C2212yes—
96#1440C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yes—
102#1439C2212yes—
103#1439C2211yescharacteristic
104#1439C2211yescharacteristic
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1438C2212yes—
111#1438C2212yes—
112#1438C2212yes—
113#1438C2212yes—
114#1438C2212yes—
115#1438C2212yes—
116#1438C2212yescomplemented
117#1438C2211yescharacteristic, complemented
118#1437C2212yescomplemented
119#1436C2212yescomplemented
120#1434C2211yescharacteristic, complemented
121#1434C2211yescharacteristic, complemented
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2212yes—
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2211yescharacteristic, complemented
127C26C2311yescharacteristic
128C22×#41—24no—
129C22×#41—24no—
130C22×#41—44no—
131C22×#41—44no—
132C22×#41—42no—
133C23×Q8C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2312yes—
144C24×C4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—24no—
151C2×C22⋊Q8—42no—
152C2×#121—28no—
153C2×#121—24no—
154C2×#121—44no—
155C2×#121—44no—
156C2×#121—44no—
157C2×#120—24no—
158C2×#120—24no—
159C2×#120—24no—
160C2×#120—28no—
161C2×#120—44no—
162C2×#120—44no—
163C2×C4×D4—24no—
164C2×C4×D4—24no—
165C2×C4×D4—42no—
166C2×C4×D4—44no—
167C2×C4×D4D418yescomplemented
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—42no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220#400—24no—
221#399—24no—
222#399—42no—
223#395—24no—
224#394—28no—
225#394—42no—
226#394—44no—
227#393—24no—
228#393D418yescomplemented
229#392—28no—
230#392—28no—
231#392—24no—
232#392—24no—
233#391—24no—
234#390—24no—
235#390—24no—
236#388—24no—
237#388—24no—
238#388—44no—
239#387—28no—
240#386—24no—
241#386—24no—
242#386—28no—
243#386—24no—
244#386—28no—
245#386—28no—
246#386—28no—
247#386—28no—
248#386—44no—
249#386—44no—
250#386—44no—
251#386—44no—
252#385—24no—
253#385—24no—
254#385—28no—
255#385—28no—
256#385—44no—
257#385—44no—
258#381—24no—
259#380—24no—
260#380—28no—
261#379—44no—
262C4×C22⋊C4—24no—
263C4×C22⋊C4—24no—
264C2×#95—24no—
265C2×#95C2311yescharacteristic
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2311yescharacteristic
299C2×#95C2312yes—
300C25—22no—
301C25—22no—
302C25—22no—
303C25—22no—
304C25—24no—
305C25—22no—
306C25—41no—
307C25—41no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25C2411yescharacteristic
312C25C2412yes—
313C25C2411yescharacteristic
314C25C2411yescharacteristic
315C25C2411yescharacteristic
316C2×#41—416no—
317C2×#41—416no—
318C2×#41—416no—
319C2×#41—432no—
320C2×#41—432no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—42no—
324C22×Q8—42no—
325C22×Q8C2×D414yes—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
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—22no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—22no—
355C22×D4—41no—
356C22×D4—42no—
357C22×D4—41no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4C2×D414yes—
374C22×D4#4114yescomplemented
375C22×D4#4114yescomplemented
376C23×C4—24no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—24no—
382C23×C4—22no—
383C23×C4—24no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—22no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—41no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—41no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—41no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4C2×D414yes—
414C23×C4C2×D414yes—
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2411yescharacteristic
433C22⋊Q8—416no—
434#121—432no—
435#121—416no—
436#120—232no—
437#120—432no—
438C4×D4—416no—
439C4×D4—416no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4C2×D414yes—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
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—416no—
520C2×C22⋊C4—416no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—41no—
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—41no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
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—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⋊C4—42no—
561C2×C22⋊C4C2×D414yes—
562C2×C22⋊C4C2×D414yes—
563C2×C22⋊C4C2×D414yes—
564C2×C22⋊C4C2×D418yes—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—42no—
569C2×C42—41no—
570C2×C42—42no—
571C2×C42C2×D414yes—
572#95—24no—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—22no—
578#95—24no—
579#95—24no—
580#95—24no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—22no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95C2×D414yes—
606#95C2×D418yes—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—22no—
614C24—21no—
615C24—22no—
616C24—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—21no—
623C24—22no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—22no—
628C24—22no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—28no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—21no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—21no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—44no—
658C24—44no—
659C24—44no—
660C24—48no—
661C24—48no—
662C24—44no—
663C24—48no—
664C24—48no—
665C24—44no—
666C24—44no—
667C24—44no—
668C24—44no—
669C24—82no—
670C24—84no—
671C24—82no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24C22×D412yes—
680C24C22×D412yes—
681C24C22×D412yes—
682C24C2×#4112yes—
683C24C2×#4112yes—
684C24C2×#4112yes—
685C24C2×#4112yes—
686C24H(5,𝔽2)14yes—
687C24H(5,𝔽2)14yes—
688C242−1+412yes—
689C24C2511yescharacteristic
690#41—4128no—
691C2×Q8—28no—
692C2×Q8—48no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—48no—
696C2×D4—216no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—48no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—44no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—44no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—44no—
733C2×D4—84no—
734C2×D4—82no—
735C2×D4—82no—
736C2×D4—84no—
737C2×D4—84no—
738C2×D4—84no—
739C2×D4—84no—
740C2×D4—84no—
741C2×D4—84no—
742C2×D4—84no—
743C2×D4—84no—
744C2×D4—84no—
745C2×D4—84no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—28no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—21no—
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—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—44no—
843C22×C4—48no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—44no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4—82no—
866C22×C4—84no—
867C22×C4—84no—
868C22×C4—82no—
869C22×C4—84no—
870C22×C4—84no—
871C22×C4—82no—
872C22×C4—84no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4C22×D414yes—
879C22×C4C22×D412yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D414yes—
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C2×#4112yes—
888C22×C4C2×#4112yes—
889C22×C4H(5,𝔽2)14yes—
890C22×C4H(5,𝔽2)12yes—
891C4⋊C4—44no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—82no—
899C4⋊C4—84no—
900C4⋊C4—84no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—216no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4—82no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C42—44no—
936C42—44no—
937C42—82no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—24no—
950C23—24no—
951C23—22no—
952C23—22no—
953C23—24no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—24no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—22no—
970C23—22no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—22no—
977C23—22no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—22no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—416no—
989C23—416no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—42no—
995C23—41no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—41no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—41no—
1020C23—42no—
1021C23—42no—
1022C23—41no—
1023C23—41no—
1024C23—42no—
1025C23—42no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—41no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—41no—
1036C23—42no—
1037C23—42no—
1038C23—41no—
1039C23—42no—
1040C23—41no—
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—88no—
1065C23—816no—
1066C23—88no—
1067C23—88no—
1068C23—816no—
1069C23—816no—
1070C23—88no—
1071C23—88no—
1072C23—816no—
1073C23#52514yes—
1074C23#53414yes—
1075C23#54814yes—
1076C23C23×D411yescharacteristic
1077C23C23×D411yescharacteristic
1078C23C22×#4111yescharacteristic
1079C23C22×#4111yescharacteristic
1080C23C2×H(5,𝔽2)12yes—
1081C23C2×H(5,𝔽2)11yescharacteristic
1082C23C2×H(5,𝔽2)12yes—
1083C23C2×H(5,𝔽2)12yes—
1084C23C2×2−1+411yescharacteristic
1085C23#58512yes—
1086C23#58511yescharacteristic
1087Q8—416no—
1088D4—416no—
1089D4—416no—
1090D4—416no—
1091D4—432no—
1092D4—88no—
1093D4—816no—
1094D4—816no—
1095D4—816no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—24no—
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—24no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—416no—
1129C2×C4—432no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—41no—
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—88no—
1204C2×C4—816no—
1205C2×C4—88no—
1206C2×C4—88no—
1207C2×C4—88no—
1208C2×C4D4214yes—
1209C22—24no—
1210C22—24no—
1211C22—24no—
1212C22—28no—
1213C22—24no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—44no—
1224C22—44no—
1225C22—42no—
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—44no—
1244C22—44no—
1245C22—44no—
1246C22—42no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—42no—
1254C22—832no—
1255C22—82no—
1256C22—81no—
1257C22—82no—
1258C22—81no—
1259C22—82no—
1260C22—82no—
1261C22—81no—
1262C22—82no—
1263C22—82no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—81no—
1268C22—82no—
1269C22C2×#52511yescharacteristic
1270C22C2×#53411yescharacteristic
1271C22#344911yescharacteristic
1272C22C2×D4211yescharacteristic
1273C22C2×#54811yescharacteristic
1274C22D4×#4111yescharacteristic
1275C22#348412yes—
1276C22#348411yescharacteristic
1277C22#348812yes—
1278C22#348911yescharacteristic
1279C22#349012yes—
1280C22#349811yescharacteristic
1281C22#350511yescharacteristic
1282C22#351312yes—
1283C22#351312yes—
1284C22#351912yes—
1285C22#352011yescharacteristic
1286C22#353212yes—
1287C22#353412yes—
1288C22#353512yes—
1289C22#353612yes—
1290C22#354612yes—
1291C22#356012yes—
1292C4—24no—
1293C4—42no—
1294C4—42no—
1295C4—44no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—44no—
1300C4—44no—
1301C4—42no—
1302C4—42no—
1303C4—81no—
1304C4—82no—
1305C4—81no—
1306C4—82no—
1307C4—82no—
1308C4—82no—
1309C4—81no—
1310C2—44no—
1311C2—44no—
1312C2—44no—
1313C2—84no—
1314C2—82no—
1315C2#3506311yescharacteristic
1316C2#3569211yescharacteristic
1317C2#3609711yescharacteristic
1318C2#3764411yescharacteristic
1319C2#3768111yescharacteristic
1320C2#4060411yescharacteristic
1321C2#4195211yescharacteristic
1322C2#4310312yes—
1323C2#4423112yes—
1324C2#4830912yes—
1325C2#5163712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2564C2semidirect
2. C2×#2404C2semidirect
3. C2×#2407C2semidirect
4. C2×#2358C2semidirect
5. #17023C2semidirect
6. #16809C2semidirect
7. #16600C2semidirect
8. #16394C2semidirect
9. #15979C2semidirect
10. #15961C2semidirect
11. #15376C2semidirect
12. #15257C2semidirect
13. #14977C2semidirect
14. #14889C2semidirect
15. #14757C2semidirect
16. #14749C2semidirect
17. #14734C2semidirect
18. #14722C2semidirect
19. #14718C2semidirect
20. #14572C2semidirect
21. #14361C2semidirect
22. #14319C2semidirect
23. #13894C2semidirect
25. C22×C22⋊Q8C22semidirect
27. C22×#121C22semidirect
37. C2×#400C22semidirect
40. C2×#395C22semidirect
43. C2×#394C22semidirect
51. C2×#391C22semidirect
53. C2×#390C22semidirect
56. C2×#388C22semidirect
57. C2×#387C22semidirect
68. C2×#386C22semidirect
69. C2×#386C22semidirect
74. C2×#385C22semidirect
75. C2×#385C22semidirect
78. C2×#380C22semidirect
82. C22×#95C22semidirect
83. #1446C22semidirect
84. #1445C22semidirect
85. #1445C22semidirect
86. #1444C22semidirect
87. #1443C22semidirect
88. #1443C22semidirect
89. #1443C22semidirect
90. #1442C22semidirect
91. #1441C22semidirect
92. #1441C22semidirect
93. #1441C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
116. #1438C22semidirect
117. #1438C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. #1434C22semidirect
121. #1434C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
167. C2×C4×D4D4semidirect
228. #393D4semidirect
374. C22×D4#41semidirect
375. C22×D4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#25642
C2×#24042
C2×#24072
C2×#23582
#170232
#168092
#166002
#163942
#159792
#159612
#153762
#152572
#149772
#148892
#147572
#147492
#147342
#147222
#147182
#145722
#143612
#143192
#138942