Finite Group Databasebeta

← #988821

Subgroups — #988821

Order 512.

3676 conjugacy classes of subgroups.

The subgroup lattice has 1378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2485C211yesmaximal, characteristic, complemented
2C2×#2415C211yesmaximal, characteristic, complemented
3C2×#2407C211yesmaximal, characteristic, complemented
4C2×#2407C211yesmaximal, characteristic, complemented
5#17091C212yesmaximal, complemented
6#16841C212yesmaximal, complemented
7#16333C212yesmaximal, complemented
8#16310C212yesmaximal, complemented
9#15979C212yesmaximal, complemented
10#15655C212yesmaximal, complemented
11#15496C212yesmaximal, complemented
12#15186C211yesmaximal, characteristic, complemented
13#15179C211yesmaximal, characteristic, complemented
14#15141C211yesmaximal, characteristic, complemented
15#15129C211yesmaximal, characteristic, complemented
16#15123C211yesmaximal, characteristic, complemented
17#14549C212yesmaximal, complemented
18#14136C211yesmaximal, characteristic, complemented
19#13998C211yesmaximal, characteristic, complemented
20#13997C211yesmaximal, characteristic, complemented
21#13993C211yesmaximal, characteristic, complemented
22#13937C211yesmaximal, characteristic, complemented
23C4×#392C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×#117C2211yescharacteristic
33#2485—28no—
34#2415—28no—
35#2407—28no—
36#2407—28no—
37C2×#397C2212yes—
38C2×#397C2212yes—
39C2×#396C2212yes—
40C2×#394C2212yes—
41C2×#394C2212yes—
42C2×#394C2212yes—
43C2×#394C2212yes—
44C2×#394C2212yes—
45C2×#392C2211yescharacteristic
46C2×#392C2212yes—
47C2×#392C2212yes—
48C2×#392C2212yes—
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#390C2212yes—
57C2×#390C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#389C2212yes—
62C2×#389C2211yescharacteristic
63C2×#388C2212yes—
64C2×#388C2212yes—
65C2×#387C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#385C2212yes—
69C2×#385C2212yes—
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic
73C2×#380C2211yescharacteristic
74C2×#380C2211yescharacteristic
75C2×#380C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80#1445C2212yes—
81#1445C2212yes—
82#1444C2211yescharacteristic
83#1443C2212yes—
84#1443C2212yes—
85#1443C2212yes—
86#1442C2212yes—
87#1442C2212yes—
88#1441C2212yes—
89#1441C2212yes—
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yes—
93#1439C2212yes—
94#1439C2211yescharacteristic
95#1439C2211yescharacteristic
96#1439C2211yescharacteristic
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2211yescharacteristic
107#1438C2211yescharacteristic
108#1438C2211yescharacteristic
109#1438C2212yes—
110#1438C2212yes—
111#1438C2212yes—
112#1438C2212yes—
113#1438C2212yes—
114#1437C2212yes—
115#1437C2212yes—
116#1437C2212yes—
117#1437C2212yes—
118#1437C2212yes—
119#1436C2212yes—
120C4⋊#95C2211yescharacteristic
121C4⋊#95C2211yescharacteristic
122C4⋊#95C2212yes—
123C4⋊#95C2211yescharacteristic
124C22⋊#95C2212yes—
125C22⋊#95C2212yes—
126C4×#95C2211yescharacteristic
127C22×#41—24no—
128C22×#41—24no—
129C22×#41—24no—
130C22×#41—42no—
131C22×#41—42no—
132C22×#41—42no—
133C22×#41—42no—
134C23×Q8C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C2×C22⋊Q8—24no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—42no—
149C2×C22⋊Q8—42no—
150C2×C22⋊Q8—42no—
151C2×C22⋊Q8D418yescomplemented
152C2×#121—24no—
153C2×#121—24no—
154C2×#121—24no—
155C2×#121—24no—
156C2×#121—42no—
157C2×#121—42no—
158C2×C4×D4—24no—
159C2×C4×D4—24no—
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4—42no—
163C2×C4×D4—42no—
164C2×C4×D4—42no—
165C2×C4×D4—42no—
166C2×C4×D4—42no—
167C2×#117—24no—
168C2×#117—24no—
169C2×#117—42no—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2312yes—
221C22×C42C2312yes—
222#397—28no—
223#397—28no—
224#396—28no—
225#394—28no—
226#394—28no—
227#394—28no—
228#394—28no—
229#394—44no—
230#392—28no—
231#392—28no—
232#392—24no—
233#392—44no—
234#391—24no—
235#391—24no—
236#391—24no—
237#391—42no—
238#390—24no—
239#390—24no—
240#390—42no—
241#390—42no—
242#390—44no—
243#389—28no—
244#389—24no—
245#389—24no—
246#389—24no—
247#389—42no—
248#388—28no—
249#388—28no—
250#387—28no—
251#386—28no—
252#386—28no—
253#385—28no—
254#385—28no—
255#380—24no—
256#380—24no—
257#380—24no—
258#380—24no—
259#380—42no—
260#380D418yescomplemented
261C4×C4⋊C4—42no—
262C4×C22⋊C4—42no—
263C4×C22⋊C4—42no—
264C4×C22⋊C4—42no—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2311yescharacteristic
298C2×#95C2312yes—
299C2×#95C2311yescharacteristic
300C25C2411yescharacteristic
301C25C2411yescharacteristic
302C25C2412yes—
303C25C2411yescharacteristic
304C2×#41—416no—
305C2×#41—416no—
306C2×#41—416no—
307C2×#41—416no—
308C2×#41—416no—
309C2×#41—416no—
310C2×#41—416no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8C2×D414yes—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—41no—
342C22×D4—41no—
343C22×D4—41no—
344C22×D4—41no—
345C22×D4—41no—
346C22×D4—41no—
347C22×D4—41no—
348C22×D4—41no—
349C22×D4—41no—
350C22×D4—41no—
351C22×D4—41no—
352C22×D4—41no—
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×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4#4114yes—
367C23×C4—22no—
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—22no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4C2×D414yes—
394C23×C4C2×D414yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2412yes—
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2412yes—
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C22⋊Q8—416no—
415C22⋊Q8—416no—
416#121—416no—
417#121—416no—
418C4×D4—416no—
419C4×D4—416no—
420C4×D4—416no—
421#117—416no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—41no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—41no—
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⋊C4C2×D414yes—
464C2×C4⋊C4C2×D414yes—
465C2×C4⋊C4C2×D414yes—
466C2×C4⋊C4C2×D418yes—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—41no—
510C2×C22⋊C4—41no—
511C2×C22⋊C4—41no—
512C2×C22⋊C4—41no—
513C2×C22⋊C4—41no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—41no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—41no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4—41no—
520C2×C22⋊C4—41no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—41no—
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—41no—
532C2×C22⋊C4—41no—
533C2×C22⋊C4—41no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—41no—
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⋊C4C2×D418yes—
559C2×C22⋊C4C2×D418yes—
560C2×C42—24no—
561C2×C42—24no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—42no—
575C2×C42—42no—
576C2×C42—42no—
577C2×C42—42no—
578#95—24no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—42no—
592#95—42no—
593#95—42no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—42no—
598#95—41no—
599#95—41no—
600#95—41no—
601#95—41no—
602#95—41no—
603#95—41no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95C2×D418yes—
612#95#4114yescomplemented
613C24—21no—
614C24—21no—
615C24—21no—
616C24—22no—
617C24—22no—
618C24—21no—
619C24—22no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—22no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—22no—
637C24—22no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—22no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24C22×D412yes—
670C24C22×D412yes—
671C24C2×#4114yes—
672C24H(5,𝔽2)12yes—
673C24C2511yescharacteristic
674#41—4128no—
675C2×Q8—28no—
676C2×Q8—28no—
677C2×Q8—28no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—44no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—48no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—84no—
723C2×D4—84no—
724C2×D4—84no—
725C2×D4—84no—
726C2×D4—84no—
727C2×D4—84no—
728C2×D4—84no—
729C2×D4—84no—
730C2×D4—84no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
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—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—28no—
796C22×C4—28no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4C22×D414yes—
876C22×C4C22×D414yes—
877C22×C4C22×D414yes—
878C22×C4C22×D412yes—
879C22×C4C22×D414yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C2×#4112yes—
884C22×C4C2×#4112yes—
885C22×C4C2×#4112yes—
886C22×C4C2×#4112yes—
887C22×C4H(5,𝔽2)12yes—
888C22×C4H(5,𝔽2)12yes—
889C22×C4H(5,𝔽2)12yes—
890C22×C4H(5,𝔽2)12yes—
891C22×C42−1+412yes—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—84no—
906C4⋊C4—84no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C42—48no—
939C42—44no—
940C42—44no—
941C42—44no—
942C42—44no—
943C42—84no—
944C23—22no—
945C23—22no—
946C23—24no—
947C23—22no—
948C23—22no—
949C23—24no—
950C23—24no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—24no—
966C23—22no—
967C23—24no—
968C23—24no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—41no—
973C23—42no—
974C23—41no—
975C23—41no—
976C23—42no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—42no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—42no—
988C23—42no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—42no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—42no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—41no—
1025C23—41no—
1026C23—42no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—42no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—42no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—42no—
1047C23—42no—
1048C23—41no—
1049C23—41no—
1050C23—42no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—42no—
1061C23—42no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—42no—
1066C23—42no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—42no—
1071C23—41no—
1072C23—42no—
1073C23—41no—
1074C23—41no—
1075C23—42no—
1076C23—42no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23C23×D411yescharacteristic
1085C23C23×D411yescharacteristic
1086C23C22×#4111yescharacteristic
1087C23C22×#4111yescharacteristic
1088C23C2×H(5,𝔽2)11yescharacteristic
1089C23C2×H(5,𝔽2)11yescharacteristic
1090C23C2×H(5,𝔽2)11yescharacteristic
1091C23C2×H(5,𝔽2)11yescharacteristic
1092C23C2×H(5,𝔽2)11yescharacteristic
1093C23C2×2−1+411yescharacteristic
1094C23#58511yescharacteristic
1095C23#58511yescharacteristic
1096C23#58511yescharacteristic
1097C23#58511yescharacteristic
1098C23#58511yescharacteristic
1099Q8—416no—
1100D4—416no—
1101D4—416no—
1102D4—416no—
1103D4—432no—
1104D4—416no—
1105D4—816no—
1106D4—816no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—432no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—416no—
1179C2×C4—416no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—42no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—42no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—42no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—42no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—42no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—42no—
1236C2×C4—88no—
1237C2×C4#53414yes—
1238C2×C4#53514yes—
1239C2×C4#53814yes—
1240C2×C4D4214yes—
1241C2×C4#54614yes—
1242C2×C4#54614yes—
1243C2×C4#56014yes—
1244C22—44no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—44no—
1250C22—42no—
1251C22—42no—
1252C22—44no—
1253C22—42no—
1254C22—42no—
1255C22—44no—
1256C22—44no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—44no—
1268C22—42no—
1269C22—42no—
1270C22—44no—
1271C22—42no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—82no—
1277C22—81no—
1278C22—82no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—82no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—82no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—82no—
1294C22—81no—
1295C22—82no—
1296C22—82no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—82no—
1304C22C2×#53411yescharacteristic
1305C22C2×#53511yescharacteristic
1306C22C2×#53811yescharacteristic
1307C22C2×D4211yescharacteristic
1308C22C2×#54611yescharacteristic
1309C22C2×#54611yescharacteristic
1310C22D4×#4111yescharacteristic
1311C22D4×#4111yescharacteristic
1312C22#348211yescharacteristic
1313C22#348511yescharacteristic
1314C22#348711yescharacteristic
1315C22#348811yescharacteristic
1316C22#348811yescharacteristic
1317C22#349711yescharacteristic
1318C22#349711yescharacteristic
1319C22#350611yescharacteristic
1320C22#350611yescharacteristic
1321C22#350611yescharacteristic
1322C22#351311yescharacteristic
1323C22#351911yescharacteristic
1324C22#352111yescharacteristic
1325C22#352111yescharacteristic
1326C22C2×#56011yescharacteristic
1327C22#353611yescharacteristic
1328C22#353911yescharacteristic
1329C22#353911yescharacteristic
1330C22#354011yescharacteristic
1331C22#354111yescharacteristic
1332C22#354111yescharacteristic
1333C22#354211yescharacteristic
1334C22#354211yescharacteristic
1335C22#354711yescharacteristic
1336C22#355111yescharacteristic
1337C22#355111yescharacteristic
1338C22#355111yescharacteristic
1339C4—42no—
1340C4—44no—
1341C4—42no—
1342C4—42no—
1343C4—42no—
1344C4—44no—
1345C4—44no—
1346C4—42no—
1347C4—42no—
1348C4—44no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—82no—
1354C4—82no—
1355C4—82no—
1356C4—81no—
1357C4#267818yes—
1358C2—84no—
1359C2—82no—
1360C2—82no—
1361C2—82no—
1362C2#3986111yescharacteristic
1363C2#3988611yescharacteristic
1364C2#4006811yescharacteristic
1365C2#4264311yescharacteristic
1366C2#4276011yescharacteristic
1367C2#4279611yescharacteristic
1368C2#4501011yescharacteristic
1369C2#4502311yescharacteristic
1370C2#4524411yescharacteristic
1371C2#4633311yescharacteristic
1372C2C2×#267811yescharacteristic
1373C2#5309811yescharacteristic
1374C2#5899911yescharacteristic
1375C2#5981111yescharacteristic
1376C2#5981111yescharacteristic
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×#2485C2semidirect
2. C2×#2415C2semidirect
3. C2×#2407C2semidirect
4. C2×#2407C2semidirect
5. #17091C2semidirect
6. #16841C2semidirect
7. #16333C2semidirect
8. #16310C2semidirect
9. #15979C2semidirect
10. #15655C2semidirect
11. #15496C2semidirect
12. #15186C2semidirect
13. #15179C2semidirect
14. #15141C2semidirect
15. #15129C2semidirect
16. #15123C2semidirect
17. #14549C2semidirect
18. #14136C2semidirect
19. #13998C2semidirect
20. #13997C2semidirect
21. #13993C2semidirect
22. #13937C2semidirect
23. C4×#392C2semidirect
151. C2×C22⋊Q8D4semidirect
260. #380D4semidirect
612. #95#41semidirect

Maximal subgroups

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

subgroupindex
C2×#24852
C2×#24152
C2×#24072
#170912
#168412
#163332
#163102
#159792
#156552
#154962
#151862
#151792
#151412
#151292
#151232
#145492
#141362
#139982
#139972
#139932
#139372
C4×#3922