Finite Group Databasebeta

← #1006049

Subgroups — #1006049

Order 512.

3660 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2415C211yesmaximal, characteristic, complemented
2C2×#2414C211yesmaximal, characteristic, complemented
3C2×#2407C211yesmaximal, characteristic, complemented
4C2×#2407C211yesmaximal, characteristic, complemented
5#17086C212yesmaximal, complemented
6#16537C212yesmaximal, complemented
7#16530C212yesmaximal, complemented
8#16268C212yesmaximal, complemented
9#15777C212yesmaximal, complemented
10#15405C212yesmaximal, complemented
11#15344C212yesmaximal, complemented
12#15236C211yesmaximal, characteristic, complemented
13#15223C211yesmaximal, characteristic, complemented
14#15219C211yesmaximal, characteristic, complemented
15#15186C211yesmaximal, characteristic, complemented
16#15138C211yesmaximal, characteristic, complemented
17#14526C212yesmaximal, complemented
18#14138C211yesmaximal, characteristic, complemented
19#14136C211yesmaximal, characteristic, complemented
20#13937C211yesmaximal, characteristic, complemented
21#13871C211yesmaximal, characteristic, complemented
22#13871C211yesmaximal, 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
33C22×#117C2211yescharacteristic
34#2415—28no—
35#2414—28no—
36#2407—28no—
37#2407—28no—
38C2×#397C2212yes—
39C2×#397C2212yes—
40C2×#394C2212yes—
41C2×#394C2212yes—
42C2×#394C2212yes—
43C2×#394C2212yes—
44C2×#392C2211yescharacteristic
45C2×#392C2212yes—
46C2×#392C2212yes—
47C2×#392C2212yes—
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2212yes—
56C2×#390C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#389C2212yes—
60C2×#388C2212yes—
61C2×#388C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#385C2212yes—
65C2×#385C2212yes—
66C2×#382C2211yescharacteristic
67C2×#380C2211yescharacteristic
68C2×#380C2211yescharacteristic
69C2×#380C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75#1445C2212yes—
76#1445C2212yes—
77#1445C2212yes—
78#1444C2211yescharacteristic
79#1443C2212yes—
80#1443C2212yes—
81#1442C2212yes—
82#1442C2212yes—
83#1442C2212yes—
84#1440C2212yes—
85#1440C2212yes—
86#1440C2212yes—
87#1440C2212yes—
88#1440C2212yes—
89#1440C2212yes—
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yes—
93#1440C2212yes—
94#1439C2211yescharacteristic
95#1439C2211yescharacteristic
96#1439C2211yescharacteristic
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1438C2211yescharacteristic
101#1438C2211yescharacteristic
102#1438C2211yescharacteristic
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1438C2212yes—
111#1437C2212yes—
112#1437C2212yes—
113#1437C2212yes—
114#1437C2212yes—
115#1436C2212yes—
116#1436C2212yes—
117#1436C2212yes—
118#1436C2212yes—
119C4⋊#95C2211yescharacteristic
120C4⋊#95C2211yescharacteristic
121C4⋊#95C2211yescharacteristic
122C4⋊#95C2211yescharacteristic
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—42no—
155C2×#121—42no—
156C2×#121—42no—
157C2×#121D418yescomplemented
158C2×C4×D4—24no—
159C2×C4×D4—24no—
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4—24no—
163C2×C4×D4—24no—
164C2×C4×D4—42no—
165C2×C4×D4—42no—
166C2×C4×D4—42no—
167C2×#117—24no—
168C2×#117—24no—
169C2×#117—42no—
170C2×#117—42no—
171C2×#117—42no—
172C2×#117—42no—
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2312yes—
223#397—28no—
224#397—28no—
225#394—28no—
226#394—28no—
227#394—28no—
228#394—28no—
229#392—28no—
230#392—28no—
231#392—28no—
232#392—24no—
233#391—24no—
234#391—24no—
235#391—24no—
236#391—42no—
237#390—24no—
238#390—28no—
239#390—24no—
240#390—24no—
241#390—42no—
242#389—24no—
243#389—28no—
244#389—24no—
245#388—28no—
246#388—28no—
247#386—28no—
248#386—28no—
249#385—28no—
250#385—28no—
251#382—42no—
252#380—24no—
253#380—24no—
254#380—24no—
255#380—24no—
256#380—42no—
257C4×C22⋊C4—42no—
258C4×C22⋊C4—42no—
259C4×C22⋊C4—42no—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C25C2411yescharacteristic
298C25C2412yes—
299C25C2411yescharacteristic
300C25C2411yescharacteristic
301C2×#41—416no—
302C2×#41—416no—
303C2×#41—416no—
304C2×#41—416no—
305C2×#41—416no—
306C2×#41—416no—
307C2×#41—416no—
308C22×Q8—22no—
309C22×Q8—22no—
310C22×Q8—22no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8C2×D414yes—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—24no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—22no—
326C22×D4—24no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—41no—
336C22×D4—41no—
337C22×D4—41no—
338C22×D4—41no—
339C22×D4—41no—
340C22×D4—41no—
341C22×D4—41no—
342C22×D4—41no—
343C22×D4—41no—
344C22×D4—41no—
345C22×D4—41no—
346C22×D4—41no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4C2×D414yes—
363C22×D4C2×D418yes—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
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—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4C2×D414yes—
390C23×C4C2×D414yes—
391C23×C4#4114yes—
392C23×C4C2412yes—
393C23×C4C2411yescharacteristic
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2412yes—
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2412yes—
405C23×C4C2412yes—
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C22⋊Q8—416no—
412C22⋊Q8—416no—
413#121—416no—
414#121—416no—
415C4×D4—416no—
416C4×D4—416no—
417C4×D4—416no—
418#117—416no—
419#117—416no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
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—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—41no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4—41no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4C2×D414yes—
457C2×C4⋊C4C2×D414yes—
458C2×C4⋊C4C2×D418yes—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
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—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
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—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—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—41no—
497C2×C22⋊C4—41no—
498C2×C22⋊C4—41no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—41no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—41no—
512C2×C22⋊C4—41no—
513C2×C22⋊C4—41no—
514C2×C22⋊C4—41no—
515C2×C22⋊C4—41no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—41no—
525C2×C22⋊C4—41no—
526C2×C22⋊C4—41no—
527C2×C22⋊C4—41no—
528C2×C22⋊C4—41no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
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⋊C4C2×D418yes—
551C2×C22⋊C4C2×D418yes—
552C2×C42—24no—
553C2×C42—24no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—42no—
567C2×C42—42no—
568C2×C42—42no—
569C2×C42—42no—
570#95—24no—
571#95—24no—
572#95—24no—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—42no—
585#95—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—41no—
590#95—41no—
591#95—42no—
592#95—41no—
593#95—42no—
594#95—42no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—41no—
599#95—41no—
600#95—41no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95#4114yescomplemented
607C24—21no—
608C24—21no—
609C24—22no—
610C24—21no—
611C24—21no—
612C24—22no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—22no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—22no—
641C24—22no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—22no—
649C24—22no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—22no—
654C24—22no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24C22×D412yes—
664C24C22×D414yes—
665C24C22×D412yes—
666C24C2×#4112yes—
667C24C2511yescharacteristic
668#41—4128no—
669C2×Q8—28no—
670C2×Q8—28no—
671C2×Q8—28no—
672C2×Q8—44no—
673C2×Q8—44no—
674C2×Q8—44no—
675C2×Q8—44no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—48no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—84no—
717C2×D4—84no—
718C2×D4—84no—
719C2×D4—84no—
720C2×D4—84no—
721C2×D4—84no—
722C2×D4—84no—
723C2×D4—84no—
724C2×D4—84no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—22no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—44no—
859C22×C4—44no—
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×C4C22×D414yes—
871C22×C4C22×D414yes—
872C22×C4C22×D414yes—
873C22×C4C22×D412yes—
874C22×C4C22×D412yes—
875C22×C4C22×D412yes—
876C22×C4C22×D412yes—
877C22×C4C2×#4112yes—
878C22×C4C2×#4112yes—
879C22×C4C2×#4112yes—
880C22×C4C2×#4112yes—
881C22×C4C2×#4112yes—
882C22×C4H(5,𝔽2)12yes—
883C22×C4H(5,𝔽2)12yes—
884C22×C4H(5,𝔽2)12yes—
885C22×C4H(5,𝔽2)12yes—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—48no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—84no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—84no—
922C22⋊C4—84no—
923C22⋊C4—84no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C42—48no—
931C42—48no—
932C42—44no—
933C42—44no—
934C42—44no—
935C42—44no—
936C23—22no—
937C23—24no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—24no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—24no—
948C23—24no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—24no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—22no—
963C23—22no—
964C23—41no—
965C23—41no—
966C23—42no—
967C23—41no—
968C23—41no—
969C23—42no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—42no—
974C23—41no—
975C23—41no—
976C23—42no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—42no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—42no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—42no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—42no—
998C23—42no—
999C23—41no—
1000C23—41no—
1001C23—42no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—41no—
1018C23—42no—
1019C23—41no—
1020C23—42no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—42no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—42no—
1033C23—41no—
1034C23—42no—
1035C23—41no—
1036C23—42no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—42no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—42no—
1049C23—42no—
1050C23—41no—
1051C23—41no—
1052C23—42no—
1053C23—41no—
1054C23—41no—
1055C23—42no—
1056C23—42no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—42no—
1068C23—42no—
1069C23—41no—
1070C23—42no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23C23×D411yescharacteristic
1077C23C23×D411yescharacteristic
1078C23C22×#4111yescharacteristic
1079C23C22×#4111yescharacteristic
1080C23C2×H(5,𝔽2)11yescharacteristic
1081C23C2×H(5,𝔽2)11yescharacteristic
1082C23C2×H(5,𝔽2)11yescharacteristic
1083C23C2×H(5,𝔽2)11yescharacteristic
1084C23#58511yescharacteristic
1085C23#58511yescharacteristic
1086C23#58511yescharacteristic
1087C23#58511yescharacteristic
1088C23#58511yescharacteristic
1089C23#58511yescharacteristic
1090C23#58511yescharacteristic
1091Q8—416no—
1092D4—416no—
1093D4—416no—
1094D4—416no—
1095D4—432no—
1096D4—416no—
1097D4—816no—
1098D4—816no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—432no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—42no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—42no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—416no—
1164C2×C4—416no—
1165C2×C4—416no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—42no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—42no—
1216C2×C4—41no—
1217C2×C4—42no—
1218C2×C4—41no—
1219C2×C4—42no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4#53414yes—
1230C2×C4#53414yes—
1231C2×C4#53814yes—
1232C2×C4D4214yes—
1233C2×C4#54614yes—
1234C2×C4#54614yes—
1235C2×C4#56014yes—
1236C22—42no—
1237C22—44no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—44no—
1242C22—42no—
1243C22—44no—
1244C22—42no—
1245C22—42no—
1246C22—44no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—44no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—44no—
1259C22—42no—
1260C22—44no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—81no—
1265C22—82no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—82no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—82no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—82no—
1281C22—81no—
1282C22—82no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—82no—
1288C22—81no—
1289C22—82no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—82no—
1296C22C2×#53411yescharacteristic
1297C22C2×#53411yescharacteristic
1298C22C2×#53811yescharacteristic
1299C22C2×D4211yescharacteristic
1300C22C2×#54611yescharacteristic
1301C22C2×#54611yescharacteristic
1302C22D4×#4111yescharacteristic
1303C22D4×#4111yescharacteristic
1304C22#347511yescharacteristic
1305C22#348511yescharacteristic
1306C22#348511yescharacteristic
1307C22#348711yescharacteristic
1308C22#348711yescharacteristic
1309C22#349311yescharacteristic
1310C22#349311yescharacteristic
1311C22#350011yescharacteristic
1312C22#350011yescharacteristic
1313C22#350611yescharacteristic
1314C22#350611yescharacteristic
1315C22#350611yescharacteristic
1316C22#351211yescharacteristic
1317C22#351711yescharacteristic
1318C22C2×#56011yescharacteristic
1319C22#353911yescharacteristic
1320C22#353911yescharacteristic
1321C22#353911yescharacteristic
1322C22#354011yescharacteristic
1323C22#354011yescharacteristic
1324C22#354011yescharacteristic
1325C22#355111yescharacteristic
1326C22#355111yescharacteristic
1327C22#355111yescharacteristic
1328C22#356211yescharacteristic
1329C22#356211yescharacteristic
1330C22#356211yescharacteristic
1331C4—44no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—44no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—44no—
1340C4—82no—
1341C4—81no—
1342C4—81no—
1343C4—82no—
1344C4—81no—
1345C4—82no—
1346C4—82no—
1347C4—81no—
1348C4—81no—
1349C4#266818yes—
1350C2—84no—
1351C2—82no—
1352C2—82no—
1353C2—82no—
1354C2#3996111yescharacteristic
1355C2#3996111yescharacteristic
1356C2#4000911yescharacteristic
1357C2#4267311yescharacteristic
1358C2#4268511yescharacteristic
1359C2#4288311yescharacteristic
1360C2#4509211yescharacteristic
1361C2#4509311yescharacteristic
1362C2#4523611yescharacteristic
1363C2#4633311yescharacteristic
1364C2C2×#266811yescharacteristic
1365C2#5307811yescharacteristic
1366C2#5899911yescharacteristic
1367C2#5901711yescharacteristic
1368C2#5901811yescharacteristic
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×#2415C2semidirect
2. C2×#2414C2semidirect
3. C2×#2407C2semidirect
4. C2×#2407C2semidirect
5. #17086C2semidirect
6. #16537C2semidirect
7. #16530C2semidirect
8. #16268C2semidirect
9. #15777C2semidirect
10. #15405C2semidirect
11. #15344C2semidirect
12. #15236C2semidirect
13. #15223C2semidirect
14. #15219C2semidirect
15. #15186C2semidirect
16. #15138C2semidirect
17. #14526C2semidirect
18. #14138C2semidirect
19. #14136C2semidirect
20. #13937C2semidirect
21. #13871C2semidirect
22. #13871C2semidirect
23. C4×#392C2semidirect
151. C2×C22⋊Q8D4semidirect
157. C2×#121D4semidirect
606. #95#41semidirect

Maximal subgroups

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

subgroupindex
C2×#24152
C2×#24142
C2×#24072
#170862
#165372
#165302
#162682
#157772
#154052
#153442
#152362
#152232
#152192
#151862
#151382
#145262
#141382
#141362
#139372
#138712
C4×#3922