Finite Group Databasebeta

← #839410

Subgroups — #839410

Order 512.

4774 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2404C211yesmaximal, characteristic, complemented
2C2×#2397C211yesmaximal, characteristic, complemented
3C2×#2358C211yesmaximal, characteristic, complemented
4C2×#2339C211yesmaximal, characteristic, complemented
5#16814C211yesmaximal, characteristic, complemented
6#16392C211yesmaximal, characteristic, complemented
7#15399C212yesmaximal, complemented
8#15369C212yesmaximal, complemented
9#15327C212yesmaximal, complemented
10#15257C212yesmaximal, complemented
11#15161C211yesmaximal, characteristic, complemented
12#15123C211yesmaximal, characteristic, complemented
13#14902C211yesmaximal, characteristic, complemented
14#14885C211yesmaximal, characteristic, complemented
15#14865C211yesmaximal, characteristic, complemented
16#14796C211yesmaximal, characteristic, complemented
17#14734C211yesmaximal, characteristic, complemented
18#14175C211yesmaximal, characteristic, complemented
19#14171C212yesmaximal, complemented
20#14023C212yesmaximal, complemented
21#13975C212yesmaximal, complemented
22#13967C212yesmaximal, complemented
23#13895C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C22×#121C2212yes—
26C22×#120C2211yescharacteristic
27C22×#120C2212yes—
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2212yes—
31C22×C4×D4C2211yescharacteristic, complemented
32C22×C4×D4C2211yescharacteristic, complemented
33C22×C4×D4C2212yescomplemented
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2404—28no—
37#2397—28no—
38C2×#399C2211yescharacteristic
39C2×#399C2211yescharacteristic
40C2×#399C2211yescharacteristic, complemented
41C2×#399C2212yescomplemented
42C2×#393C2211yescharacteristic
43C2×#393C2211yescharacteristic
44C2×#393C2211yescharacteristic, complemented
45C2×#392C2212yes—
46C2×#392C2211yescharacteristic
47C2×#392C2212yes—
48C2×#392C2211yescharacteristic
49C2×#392C2211yescharacteristic, complemented
50#2358—28no—
51#2339—28no—
52C2×#391C2211yescharacteristic, complemented
53C2×#391C2211yescharacteristic, complemented
54C2×#390C2211yescharacteristic
55C2×#388C2211yescharacteristic
56C2×#388C2211yescharacteristic
57C2×#386C2211yescharacteristic
58C2×#386C2211yescharacteristic
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2211yescharacteristic
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#386C2212yescomplemented
69C2×#385C2211yescharacteristic
70C2×#385C2211yescharacteristic
71C2×#385C2212yes—
72C2×#385C2212yescomplemented
73C2×#381C2211yescharacteristic
74C2×#381C2212yescomplemented
75C2×#380C2211yescharacteristic
76C2×#380C2212yescomplemented
77C2×#379C2212yes—
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×#376C2211yescharacteristic, complemented
81C22×#95C2212yescomplemented
82#1446C2211yescharacteristic, complemented
83#1445C2211yescharacteristic, complemented
84#1444C2212yescomplemented
85#1443C2212yescomplemented
86#1443C2212yescomplemented
87#1442C2212yescomplemented
88#1442C2211yescharacteristic, complemented
89#1442C2212yescomplemented
90#1441C2212yescomplemented
91#1440C2212yes—
92#1440C2212yescomplemented
93#1439C2212yes—
94#1439C2212yes—
95#1439C2211yescharacteristic
96#1439C2211yescharacteristic
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1439C2211yescharacteristic, complemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1438C2212yescomplemented
111#1438C2211yescharacteristic, complemented
112#1437C2212yes—
113#1437C2212yes—
114#1437C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118C4⋊#95C2211yescharacteristic, complemented
119#1434C2211yescharacteristic, complemented
120#1434C2211yescharacteristic, complemented
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C22×#41—24no—
129C22×#41—28no—
130C22×#41—24no—
131C22×#41—44no—
132C22×#41—42no—
133C23×Q8C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2311yescharacteristic
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C24×C4C2312yes—
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C2×#121—28no—
151C2×#121—44no—
152C2×#121—44no—
153C2×#120—24no—
154C2×#120—28no—
155C2×#120—28no—
156C2×#120—24no—
157C2×#120—24no—
158C2×#120—44no—
159C2×C4×D4—28no—
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4—24no—
163C2×C4×D4—28no—
164C2×C4×D4—24no—
165C2×C4×D4—24no—
166C2×C4×D4—24no—
167C2×C4×D4—42no—
168C2×C4×D4—44no—
169C2×C4×D4—44no—
170C2×C4×D4—42no—
171C2×C4×D4—44no—
172C2×C4×D4—44no—
173C2×C4×D4—44no—
174C2×C4×D4—44no—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C22⋊C4—24no—
185C22×C22⋊C4—24no—
186C22×C22⋊C4—24no—
187C22×C22⋊C4—44no—
188C22×C22⋊C4—42no—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226#399—24no—
227#399—28no—
228#399—24no—
229#399—42no—
230#393—24no—
231#393—24no—
232#393—42no—
233#392—28no—
234#392—24no—
235#392—24no—
236#392—28no—
237#392D418yescomplemented
238#391—24no—
239#391—24no—
240#390—24no—
241#388—24no—
242#388—24no—
243#386—28no—
244#386—24no—
245#386—28no—
246#386—28no—
247#386—28no—
248#386—28no—
249#386—28no—
250#386—24no—
251#386—24no—
252#386—44no—
253#386—44no—
254#386—44no—
255#385—24no—
256#385—24no—
257#385—44no—
258#385—44no—
259#381—28no—
260#381—24no—
261#380—24no—
262#380—44no—
263#379—44no—
264C4×C22⋊C4—24no—
265C4×C22⋊C4D418yescomplemented
266#376—24no—
267C2×#95—28no—
268C2×#95C2311yescharacteristic
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2311yescharacteristic
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C25—22no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—24no—
308C25—22no—
309C25—42no—
310C25—41no—
311C25—41no—
312C25—42no—
313C25—42no—
314C25C2411yescharacteristic
315C25C2411yescharacteristic
316C25C2411yescharacteristic
317C25C2412yes—
318C25C2411yescharacteristic
319C2×#41—232no—
320C2×#41—416no—
321C2×#41—432no—
322C2×#41—416no—
323C2×#41—432no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—24no—
327C22×Q8—22no—
328C22×Q8—42no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—22no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—24no—
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—22no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—24no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—41no—
365C22×D4—42no—
366C22×D4—41no—
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×D4C2×D414yes—
376C22×D4C2×D418yes—
377C22×D4#4118yes—
378C22×D4#4114yescomplemented
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—22no—
385C23×C4—24no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—24no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—22no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—41no—
410C23×C4—42no—
411C23×C4—41no—
412C23×C4—41no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—41no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4C2×D414yes—
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2412yes—
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2412yes—
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443#121—432no—
444#120—232no—
445#120—432no—
446C4×D4—416no—
447C4×D4—416no—
448C4×D4—432no—
449C4×D4—432no—
450C4×D4—416no—
451C4×D4—416no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
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—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—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
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—22no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—416no—
530C2×C22⋊C4—416no—
531C2×C22⋊C4—41no—
532C2×C22⋊C4—41no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—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⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4C2×D414yes—
567C2×C22⋊C4C2×D414yes—
568C2×C22⋊C4C2×D414yes—
569C2×C22⋊C4C2×D418yes—
570C2×C22⋊C4#4114yescomplemented
571C2×C42—24no—
572C2×C42—22no—
573C2×C42—24no—
574C2×C42—24no—
575C2×C42—22no—
576C2×C42—22no—
577C2×C42—42no—
578C2×C42—42no—
579C2×C42C2×D414yes—
580C2×C42C2×D414yes—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—24no—
600#95—24no—
601#95—22no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95C2×D414yes—
614#95C2×D414yes—
615#95C2×D414yes—
616C24—21no—
617C24—22no—
618C24—21no—
619C24—22no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—21no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—21no—
640C24—22no—
641C24—21no—
642C24—21no—
643C24—22no—
644C24—21no—
645C24—28no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—22no—
651C24—21no—
652C24—22no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—44no—
667C24—44no—
668C24—48no—
669C24—48no—
670C24—44no—
671C24—44no—
672C24—48no—
673C24—48no—
674C24—44no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24—84no—
679C24—82no—
680C24—84no—
681C24—82no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24C22×D412yes—
689C24C22×D414yes—
690C24C22×D412yes—
691C24C2×#4112yes—
692C24C2×#4112yes—
693C24C2×#4114yes—
694C24C2×#4114yes—
695C24C2×#4112yes—
696C24H(5,𝔽2)14yes—
697C242−1+412yes—
698C24C2511yescharacteristic
699#41—4128no—
700C2×Q8—28no—
701C2×Q8—48no—
702C2×Q8—48no—
703C2×Q8—44no—
704C2×Q8—44no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—216no—
708C2×D4—216no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—216no—
712C2×D4—216no—
713C2×D4—216no—
714C2×D4—216no—
715C2×D4—216no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—44no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—44no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—44no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—44no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—48no—
742C2×D4—44no—
743C2×D4—48no—
744C2×D4—44no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—82no—
750C2×D4—82no—
751C2×D4—84no—
752C2×D4—84no—
753C2×D4—84no—
754C2×D4—84no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—216no—
763C22×C4—28no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—28no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—21no—
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—21no—
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—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—44no—
849C22×C4—44no—
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—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—44no—
871C22×C4—48no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—48no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—82no—
878C22×C4—84no—
879C22×C4—82no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4—82no—
886C22×C4—84no—
887C22×C4—82no—
888C22×C4—84no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4C22×D412yes—
892C22×C4C22×D414yes—
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C22×D412yes—
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D412yes—
899C22×C4C22×D412yes—
900C22×C4C2×#4112yes—
901C22×C4C2×#4114yes—
902C22×C4C2×#4112yes—
903C22×C4C2×#4112yes—
904C22×C4H(5,𝔽2)14yes—
905C22×C4H(5,𝔽2)14yes—
906C22×C4H(5,𝔽2)12yes—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—82no—
915C4⋊C4—84no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—48no—
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—44no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—82no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C22⋊C4—84no—
948C22⋊C4—84no—
949C42—216no—
950C42—28no—
951C42—44no—
952C42—44no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—22no—
957C23—22no—
958C23—24no—
959C23—22no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—22no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—22no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—22no—
1004C23—22no—
1005C23—416no—
1006C23—416no—
1007C23—42no—
1008C23—41no—
1009C23—41no—
1010C23—42no—
1011C23—41no—
1012C23—41no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—41no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—41no—
1025C23—42no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—41no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—42no—
1050C23—42no—
1051C23—41no—
1052C23—41no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—41no—
1057C23—41no—
1058C23—42no—
1059C23—41no—
1060C23—41no—
1061C23—42no—
1062C23—42no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
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—88no—
1080C23—88no—
1081C23—816no—
1082C23—88no—
1083C23—816no—
1084C23—816no—
1085C23—88no—
1086C23—816no—
1087C23—88no—
1088C23#52514yes—
1089C23#54618yes—
1090C23#54714yes—
1091C23C23×D411yescharacteristic
1092C23C23×D411yescharacteristic
1093C23C22×#4112yes—
1094C23C22×#4111yescharacteristic
1095C23C22×#4111yescharacteristic
1096C23C2×H(5,𝔽2)12yes—
1097C23C2×H(5,𝔽2)11yescharacteristic
1098C23C2×H(5,𝔽2)12yes—
1099C23C2×H(5,𝔽2)12yes—
1100C23C2×2−1+411yescharacteristic
1101C23#58511yescharacteristic
1102Q8—416no—
1103D4—232no—
1104D4—432no—
1105D4—432no—
1106D4—416no—
1107D4—416no—
1108D4—432no—
1109D4—88no—
1110D4—816no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—416no—
1146C2×C4—432no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—41no—
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—41no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—41no—
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—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—88no—
1217C2×C4—816no—
1218C2×C4—88no—
1219C2×C4—816no—
1220C2×C4—88no—
1221C2×C4—88no—
1222C2×C4#52514yes—
1223C2×C4#53514yes—
1224C2×C4D4214yes—
1225C22—28no—
1226C22—24no—
1227C22—24no—
1228C22—24no—
1229C22—28no—
1230C22—24no—
1231C22—28no—
1232C22—28no—
1233C22—42no—
1234C22—44no—
1235C22—42no—
1236C22—44no—
1237C22—42no—
1238C22—42no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—42no—
1245C22—42no—
1246C22—44no—
1247C22—42no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—42no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—42no—
1260C22—44no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—44no—
1265C22—44no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—44no—
1271C22—44no—
1272C22—832no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22—81no—
1284C22—81no—
1285C22C2×#52511yescharacteristic
1286C22C2×#52511yescharacteristic
1287C22C2×#53511yescharacteristic
1288C22C2×D4211yescharacteristic
1289C22C2×#54612yes—
1290C22C2×#54711yescharacteristic
1291C22D4×#4111yescharacteristic
1292C22#348112yes—
1293C22#348112yes—
1294C22#348411yescharacteristic
1295C22#348412yes—
1296C22#348911yescharacteristic
1297C22#349012yes—
1298C22#349012yes—
1299C22#349811yescharacteristic
1300C22#350611yescharacteristic
1301C22#351312yes—
1302C22#351912yes—
1303C22#352011yescharacteristic
1304C22#352012yes—
1305C22#353612yes—
1306C22#354212yes—
1307C22#354312yes—
1308C4—24no—
1309C4—24no—
1310C4—24no—
1311C4—42no—
1312C4—44no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—44no—
1317C4—44no—
1318C4—42no—
1319C4—81no—
1320C4—81no—
1321C4—82no—
1322C4—82no—
1323C4—82no—
1324C4—82no—
1325C4—81no—
1326C2—48no—
1327C2—44no—
1328C2—44no—
1329C2—82no—
1330C2—82no—
1331C2#3496311yescharacteristic
1332C2#3569211yescharacteristic
1333C2#3599011yescharacteristic
1334C2#3609811yescharacteristic
1335C2#3610011yescharacteristic
1336C2#3767411yescharacteristic
1337C2#4247811yescharacteristic
1338C2#4336012yes—
1339C2#4342012yes—
1340C2#5902912yes—
1341C2#5909012yes—
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×#2404C2semidirect
2. C2×#2397C2semidirect
3. C2×#2358C2semidirect
4. C2×#2339C2semidirect
5. #16814C2semidirect
6. #16392C2semidirect
7. #15399C2semidirect
8. #15369C2semidirect
9. #15327C2semidirect
10. #15257C2semidirect
11. #15161C2semidirect
12. #15123C2semidirect
13. #14902C2semidirect
14. #14885C2semidirect
15. #14865C2semidirect
16. #14796C2semidirect
17. #14734C2semidirect
18. #14175C2semidirect
19. #14171C2semidirect
20. #14023C2semidirect
21. #13975C2semidirect
22. #13967C2semidirect
23. #13895C2semidirect
31. C22×C4×D4C22semidirect
32. C22×C4×D4C22semidirect
33. C22×C4×D4C22semidirect
40. C2×#399C22semidirect
41. C2×#399C22semidirect
44. C2×#393C22semidirect
49. C2×#392C22semidirect
52. C2×#391C22semidirect
53. C2×#391C22semidirect
68. C2×#386C22semidirect
72. C2×#385C22semidirect
74. C2×#381C22semidirect
76. C2×#380C22semidirect
80. C2×#376C22semidirect
81. C22×#95C22semidirect
82. #1446C22semidirect
83. #1445C22semidirect
84. #1444C22semidirect
85. #1443C22semidirect
86. #1443C22semidirect
87. #1442C22semidirect
88. #1442C22semidirect
89. #1442C22semidirect
90. #1441C22semidirect
92. #1440C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
114. #1437C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. C4⋊#95C22semidirect
119. #1434C22semidirect
120. #1434C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
237. #392D4semidirect
265. C4×C22⋊C4D4semidirect
378. C22×D4#41semidirect
570. C2×C22⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#24042
C2×#23972
C2×#23582
C2×#23392
#168142
#163922
#153992
#153692
#153272
#152572
#151612
#151232
#149022
#148852
#148652
#147962
#147342
#141752
#141712
#140232
#139752
#139672
#138952