Finite Group Databasebeta

← #581565

Subgroups — #581565

Order 512.

6004 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#535C211yesmaximal, characteristic
2C2×#2333C211yesmaximal, characteristic, complemented
3C2×#2325C211yesmaximal, characteristic, complemented
4#14659C211yesmaximal, characteristic, complemented
5#14421C212yesmaximal, complemented
6#14419C212yesmaximal, complemented
7#14418C212yesmaximal, complemented
8#14417C212yesmaximal, complemented
9#14358C212yesmaximal, complemented
10#14357C212yesmaximal, complemented
11#14152C211yesmaximal, characteristic, complemented
12#14098C212yesmaximal, complemented
13#14025C212yesmaximal, complemented
14#13995C212yesmaximal, complemented
15#13967C212yesmaximal, complemented
16#13956C211yesmaximal, characteristic, complemented
17#13944C212yesmaximal, complemented
18#13937C211yesmaximal, characteristic, complemented
19#13867C212yesmaximal, complemented
20C23×#41C2211yescharacteristic
21C24×D4C2211yescharacteristic
22C2×#535—28no—
23C2×#535—28no—
24C2×#535C4116yescomplemented
25C22×#127C2212yes—
26C22×#124C2212yes—
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×#121C2211yescharacteristic
31C22×#120C2212yes—
32C22×#120C2212yes—
33C22×C4×D4C2212yescomplemented
34C22×#117C2211yescharacteristic
35C23×C22⋊C4C2212yes—
36#2333—28no—
37#2325—28no—
38C2×#391C2211yescharacteristic, complemented
39C2×#391C2211yescharacteristic, complemented
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2212yescomplemented
43C2×#390C2212yescomplemented
44C2×#390C2212yescomplemented
45C2×#388C2212yescomplemented
46C2×#388C2212yescomplemented
47C2×#387C2212yescomplemented
48C2×#387C2212yescomplemented
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#386C2211yescharacteristic
53C2×#386C2212yes—
54C2×#386C2211yescharacteristic
55C2×#386C2212yescomplemented
56C2×#386C2212yescomplemented
57C2×#386C2212yescomplemented
58C2×#386C2212yescomplemented
59C2×#386C2212yescomplemented
60C2×#386C2212yescomplemented
61C2×#386C2211yescharacteristic, complemented
62C2×#386C2211yescharacteristic, complemented
63C2×#385C2212yescomplemented
64C2×#381C2211yescharacteristic, complemented
65C2×#380C2211yescharacteristic, complemented
66C2×#379C2212yes—
67C2×#379C2212yes—
68C2×#379C2212yes—
69C2×C4×C22⋊C4C2212yescomplemented
70C2×C4×C22⋊C4C2211yescharacteristic, complemented
71C22×#95C2211yescharacteristic, complemented
72#1446C2212yescomplemented
73#1445C2212yescomplemented
74#1445C2212yescomplemented
75#1440C2212yescomplemented
76#1440C2212yescomplemented
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yescomplemented
80#1439C2212yescomplemented
81#1439C2212yescomplemented
82#1439C2212yescomplemented
83#1438C2212yes—
84#1438C2212yes—
85#1438C2212yes—
86#1438C2212yes—
87#1438C2212yes—
88#1438C2212yes—
89#1438C2212yescomplemented
90#1438C2212yescomplemented
91#1438C2212yescomplemented
92#1438C2212yescomplemented
93#1438C2212yescomplemented
94#1438C2212yescomplemented
95#1438C2212yescomplemented
96#1437C2212yes—
97#1437C2212yes—
98#1437C2212yescomplemented
99#1437C2212yescomplemented
100#1437C2212yescomplemented
101#1437C2212yescomplemented
102C4⋊#95C2212yescomplemented
103#1434C2212yescomplemented
104#1434C2212yescomplemented
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yescomplemented
108C22⋊#95C2212yescomplemented
109C22⋊#95C2212yescomplemented
110C22⋊#95C2212yescomplemented
111C4×#95C2212yescomplemented
112C26C2312yes—
113C22×#41—24no—
114C22×#41—24no—
115C22×#41—42no—
116C22×#41—42no—
117C22×#41—42no—
118C22×#41—42no—
119C22×#41C2×C418yescomplemented
120C23×Q8C2311yescharacteristic
121C23×D4—24no—
122C23×D4—24no—
123C23×D4—42no—
124C23×D4—42no—
125C23×D4—42no—
126C23×D4—42no—
127C23×D4C2×C418yescomplemented
128C23×D4C2312yes—
129C23×D4C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C23×D4C2312yes—
134C23×D4C2312yes—
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2312yes—
141C24×C4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145#535—2128no—
146C2×#127—28no—
147C2×#127—28no—
148C2×#127C2×C4116yescomplemented
149C2×#124—28no—
150C2×#124—28no—
151C2×#124C2×C4116yescomplemented
152C2×#121—24no—
153C2×#121—24no—
154C2×#121—24no—
155C2×#121—24no—
156C2×#121—24no—
157C2×#121—24no—
158C2×#121C2×C418yes—
159C2×#121C2×C418yescomplemented
160C2×#121C2×C418yescomplemented
161C2×#121C2×C418yescomplemented
162C2×#121D418yes—
163C2×#121D418yes—
164C2×#120—28no—
165C2×#120—28no—
166C2×#120—28no—
167C2×#120—28no—
168C2×#120C2×C4116yescomplemented
169C2×#120C2×C4116yescomplemented
170C2×C4×D4—28no—
171C2×C4×D4—44no—
172C2×C4×D4—44no—
173C2×#117—24no—
174C2×#117—24no—
175C2×#117C2×C418yescomplemented
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C22⋊C4—44no—
183C22×C22⋊C4—44no—
184C22×C22⋊C4—44no—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C42C2312yes—
217C22×C42C2312yes—
218C22×C42C2312yes—
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221#391—42no—
222#391—42no—
223#390—28no—
224#390—44no—
225#390—44no—
226#390—42no—
227#390—42no—
228#388—28no—
229#388—28no—
230#387—28no—
231#387—28no—
232#386—28no—
233#386—28no—
234#386—28no—
235#386—28no—
236#386—44no—
237#386—44no—
238#386—42no—
239#386—42no—
240#386—44no—
241#386—44no—
242#386—44no—
243#386—44no—
244#386—42no—
245#386—42no—
246#385—28no—
247#381—24no—
248#380—24no—
249#379—44no—
250#379—44no—
251#379—44no—
252C4×C22⋊C4—24no—
253C4×C22⋊C4—28no—
254C2×#95—24no—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
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×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C25—24no—
282C25—24no—
283C25—24no—
284C25—24no—
285C25—42no—
286C25—42no—
287C25—42no—
288C25—42no—
289C25—42no—
290C25—42no—
291C25—42no—
292C25—42no—
293C25—42no—
294C25—42no—
295C25C22×C418yes—
296C25C2412yes—
297C25C2411yescharacteristic
298C25C2412yes—
299C25C2411yescharacteristic
300C25C2411yescharacteristic
301C2×#41—232no—
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—41no—
313C22×Q8—41no—
314C22×Q8C22×C414yes—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—24no—
318C22×D4—24no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—232no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—416no—
341C22×D4—42no—
342C22×D4—42no—
343C22×D4—416no—
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—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—41no—
357C22×D4—41no—
358C22×D4—41no—
359C22×D4—41no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4—416no—
363C22×D4—416no—
364C22×D4—416no—
365C22×D4—416no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4C22×C414yes—
379C22×D4C22×C414yes—
380C22×D4C22×C418yes—
381C22×D4C22×C414yes—
382C22×D4C22×C418yes—
383C22×D4C22×C418yes—
384C22×D4C22×C418yes—
385C22×D4C22×C414yes—
386C22×D4C22×C414yes—
387C22×D4C22×C418yes—
388C22×D4C2×D414yes—
389C22×D4C2×D414yes—
390C22×D4C2×D418yes—
391C22×D4C2×D418yes—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—22no—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—41no—
408C23×C4—41no—
409C23×C4—41no—
410C23×C4—41no—
411C23×C4—41no—
412C23×C4—41no—
413C23×C4—41no—
414C23×C4—41no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—41no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4—41no—
429C23×C4—41no—
430C23×C4—42no—
431C23×C4—41no—
432C23×C4C22×C414yes—
433C23×C4C22×C414yes—
434C23×C4C22×C414yes—
435C23×C4C2×D414yes—
436C23×C4C2×D414yes—
437C23×C4C2412yes—
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2412yes—
441C23×C4C2412yes—
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2412yes—
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2411yescharacteristic
448C23×C4C2412yes—
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451#127—264no—
452#124—264no—
453#121—232no—
454#121—232no—
455#121—232no—
456#121C22⋊C4164yescomplemented
457#120—264no—
458#120—264no—
459C4×D4—432no—
460#117—232no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4—41no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4C22×C414yes—
476C2×C4⋊C4C22×C414yes—
477C2×C4⋊C4C2×D414yes—
478C2×C4⋊C4C2×D414yes—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
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—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—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
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—432no—
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—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⋊C4—41no—
551C2×C22⋊C4—41no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—41no—
554C2×C22⋊C4—41no—
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⋊C4C22×C418yes—
567C2×C22⋊C4C22×C418yes—
568C2×C22⋊C4C22×C418yes—
569C2×C22⋊C4C22×C418yes—
570C2×C22⋊C4C22×C418yes—
571C2×C22⋊C4C2×D418yes—
572C2×C22⋊C4C2×D418yes—
573C2×C42—24no—
574C2×C42—24no—
575C2×C42—24no—
576C2×C42—24no—
577C2×C42—22no—
578C2×C42—24no—
579C2×C42—22no—
580C2×C42—42no—
581C2×C42—42no—
582C2×C42—41no—
583C2×C42—41no—
584C2×C42—41no—
585C2×C42—41no—
586C2×C42—42no—
587C2×C42C22×C418yes—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—24no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
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#95—42no—
614C24—21no—
615C24—21no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—21no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—216no—
667C24—216no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24C23×C414yes—
702C24C23×C412yes—
703C24C23×C414yes—
704C24C23×C412yes—
705C24C23×C412yes—
706C24C22×D414yes—
707C24C22×D414yes—
708C24C22×D412yes—
709C24C22×D412yes—
710C24H(5,𝔽2)12yes—
711C24H(5,𝔽2)12yes—
712C24C2511yescharacteristic
713#41—4128no—
714C2×Q8—28no—
715C2×Q8—28no—
716C2×Q8—44no—
717C2×Q8—44no—
718C2×Q8—44no—
719C2×Q8—44no—
720C2×Q8—44no—
721C2×D4—28no—
722C2×D4—216no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—216no—
727C2×D4—216no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—216no—
731C2×D4—216no—
732C2×D4—28no—
733C2×D4—48no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—48no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—4128no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—84no—
779C2×D4—84no—
780C2×D4—84no—
781C2×D4—84no—
782C2×D4—84no—
783C2×D4—84no—
784C2×D4—84no—
785C2×D4—84no—
786C2×D4—84no—
787C2×D4—84no—
788C2×D4—84no—
789C2×D4—84no—
790C2×D4C2×C22⋊C4116yes—
791C2×D4C2×C22⋊C4132yescomplemented
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—28no—
796C22×C4—28no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—28no—
840C22×C4—28no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—48no—
898C22×C4—48no—
899C22×C4—44no—
900C22×C4—84no—
901C22×C4—84no—
902C22×C4—84no—
903C22×C4—84no—
904C22×C4—84no—
905C22×C4—82no—
906C22×C4—84no—
907C22×C4—84no—
908C22×C4—82no—
909C22×C4—84no—
910C22×C4—82no—
911C22×C4—82no—
912C22×C4—84no—
913C22×C4—84no—
914C22×C4—84no—
915C22×C4—84no—
916C22×C4—84no—
917C22×C4—84no—
918C22×C4C2×C22⋊C4116yescomplemented
919C22×C4C23×C414yes—
920C22×C4C23×C412yes—
921C22×C4C23×C414yes—
922C22×C4C23×C412yes—
923C22×C4C23×C412yes—
924C22×C4C23×C412yes—
925C22×C4C22×D412yes—
926C22×C4C22×D412yes—
927C22×C4C22×D412yes—
928C22×C4C22×D414yes—
929C22×C4C22×D414yes—
930C22×C4C22×D412yes—
931C22×C4H(5,𝔽2)14yes—
932C22×C4H(5,𝔽2)14yes—
933C22×C4H(5,𝔽2)12yes—
934C22×C4H(5,𝔽2)12yes—
935C4⋊C4—28no—
936C4⋊C4—48no—
937C4⋊C4—82no—
938C4⋊C4—82no—
939C4⋊C4—84no—
940C4⋊C4C2×C22⋊C4116yescomplemented
941C22⋊C4—216no—
942C22⋊C4—216no—
943C22⋊C4—216no—
944C22⋊C4—216no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C22⋊C4—84no—
958C22⋊C4—82no—
959C22⋊C4—84no—
960C22⋊C4—82no—
961C22⋊C4—84no—
962C22⋊C4—84no—
963C22⋊C4—84no—
964C22⋊C4—84no—
965C22⋊C4—84no—
966C22⋊C4—84no—
967C22⋊C4—84no—
968C22⋊C4—84no—
969C22⋊C4—84no—
970C22⋊C4—84no—
971C22⋊C4C2×C22⋊C4132yescomplemented
972C42—216no—
973C42—48no—
974C42—82no—
975C42—82no—
976C42—84no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—22no—
992C23—24no—
993C23—22no—
994C23—22no—
995C23—24no—
996C23—24no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—24no—
1004C23—24no—
1005C23—22no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—22no—
1015C23—22no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—432no—
1034C23—432no—
1035C23—41no—
1036C23—41no—
1037C23—42no—
1038C23—42no—
1039C23—41no—
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—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—41no—
1078C23—42no—
1079C23—41no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—41no—
1088C23—42no—
1089C23—41no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—42no—
1103C23—42no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—42no—
1110C23—42no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—816no—
1116C23—816no—
1117C23—816no—
1118C23—816no—
1119C23—816no—
1120C23—816no—
1121C23—816no—
1122C23—816no—
1123C23—816no—
1124C23—816no—
1125C23—816no—
1126C23—816no—
1127C23—816no—
1128C23C22×C22⋊C418yes—
1129C23C22×C22⋊C414yes—
1130C23#51814yes—
1131C23C24×C411yescharacteristic
1132C23C23×D411yescharacteristic
1133C23C23×D411yescharacteristic
1134C23C2×H(5,𝔽2)11yescharacteristic
1135C23C2×H(5,𝔽2)11yescharacteristic
1136C23C2×H(5,𝔽2)11yescharacteristic
1137C23C2×H(5,𝔽2)11yescharacteristic
1138C23C2×H(5,𝔽2)12yes—
1139C23C2×H(5,𝔽2)12yes—
1140C23#58512yes—
1141C23#58512yes—
1142Q8—416no—
1143D4—416no—
1144D4—432no—
1145D4—432no—
1146D4—416no—
1147D4—416no—
1148D4—416no—
1149D4—416no—
1150D4—816no—
1151D4—816no—
1152D4—816no—
1153C2×C4—232no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—416no—
1191C2×C4—416no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—88no—
1251C2×C4—816no—
1252C2×C4—816no—
1253C2×C4—88no—
1254C2×C4C22×C22⋊C418yes—
1255C2×C4C22×C22⋊C414yes—
1256C2×C4C22×C22⋊C414yes—
1257C2×C4#51814yes—
1258C22—28no—
1259C22—24no—
1260C22—24no—
1261C22—28no—
1262C22—24no—
1263C22—28no—
1264C22—24no—
1265C22—28no—
1266C22—42no—
1267C22—44no—
1268C22—42no—
1269C22—42no—
1270C22—44no—
1271C22—42no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22—42no—
1281C22—44no—
1282C22—42no—
1283C22—42no—
1284C22—44no—
1285C22—42no—
1286C22—44no—
1287C22—44no—
1288C22—44no—
1289C22—44no—
1290C22—44no—
1291C22—44no—
1292C22—44no—
1293C22—42no—
1294C22—42no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—42no—
1299C22—44no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—42no—
1304C22—44no—
1305C22—42no—
1306C22—44no—
1307C22—864no—
1308C22—81no—
1309C22—82no—
1310C22—81no—
1311C22—82no—
1312C22—82no—
1313C22—82no—
1314C22—82no—
1315C22—82no—
1316C22—82no—
1317C22—82no—
1318C22—81no—
1319C22—82no—
1320C22—81no—
1321C22—82no—
1322C22C23×C22⋊C411yescharacteristic
1323C22C2×#51811yescharacteristic
1324C22C2×#51811yescharacteristic
1325C22C4×H(5,𝔽2)12yes—
1326C22C4×H(5,𝔽2)12yes—
1327C22#348411yescharacteristic
1328C22#348411yescharacteristic
1329C22#348411yescharacteristic
1330C22#348411yescharacteristic
1331C22#348411yescharacteristic
1332C22#348511yescharacteristic
1333C22#348812yes—
1334C22#349612yes—
1335C22#349811yescharacteristic
1336C22#350011yescharacteristic
1337C22#353212yes—
1338C22#353312yes—
1339C22#354212yes—
1340C22#354212yes—
1341C22#354312yes—
1342C22#354612yes—
1343C22#355812yes—
1344C22#356212yes—
1345C4—24no—
1346C4—24no—
1347C4—24no—
1348C4—28no—
1349C4—44no—
1350C4—44no—
1351C4—42no—
1352C4—44no—
1353C4—82no—
1354C4—82no—
1355C4—82no—
1356C4—82no—
1357C4—82no—
1358C4—82no—
1359C2—44no—
1360C2—48no—
1361C2—44no—
1362C2—82no—
1363C2—84no—
1364C2#3417111yescharacteristic
1365C2#3425611yescharacteristic
1366C2#3425811yescharacteristic
1367C2#3440612yes—
1368C2#3443812yes—
1369C2#4635511yescharacteristic
1370C2#4635911yescharacteristic
1371C2#4636712yes—
1372C2#4641612yes—
1373C2#4642411yescharacteristic
1374C2#4642811yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#535C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2333C2semidirect
3. C2×#2325C2semidirect
4. #14659C2semidirect
5. #14421C2semidirect
6. #14419C2semidirect
7. #14418C2semidirect
8. #14417C2semidirect
9. #14358C2semidirect
10. #14357C2semidirect
11. #14152C2semidirect
12. #14098C2semidirect
13. #14025C2semidirect
14. #13995C2semidirect
15. #13967C2semidirect
16. #13956C2semidirect
17. #13944C2semidirect
18. #13937C2semidirect
19. #13867C2semidirect
24. C2×#535C4semidirect
33. C22×C4×D4C22semidirect
38. C2×#391C22semidirect
39. C2×#391C22semidirect
42. C2×#390C22semidirect
43. C2×#390C22semidirect
44. C2×#390C22semidirect
45. C2×#388C22semidirect
46. C2×#388C22semidirect
47. C2×#387C22semidirect
48. C2×#387C22semidirect
55. C2×#386C22semidirect
56. C2×#386C22semidirect
57. C2×#386C22semidirect
58. C2×#386C22semidirect
59. C2×#386C22semidirect
60. C2×#386C22semidirect
61. C2×#386C22semidirect
62. C2×#386C22semidirect
63. C2×#385C22semidirect
64. C2×#381C22semidirect
65. C2×#380C22semidirect
69. C2×C4×C22⋊C4C22semidirect
70. C2×C4×C22⋊C4C22semidirect
71. C22×#95C22semidirect
72. #1446C22semidirect
73. #1445C22semidirect
74. #1445C22semidirect
75. #1440C22semidirect
76. #1440C22semidirect
79. #1439C22semidirect
80. #1439C22semidirect
81. #1439C22semidirect
82. #1439C22semidirect
89. #1438C22semidirect
90. #1438C22semidirect
91. #1438C22semidirect
92. #1438C22semidirect
93. #1438C22semidirect
94. #1438C22semidirect
95. #1438C22semidirect
98. #1437C22semidirect
99. #1437C22semidirect
100. #1437C22semidirect
101. #1437C22semidirect
102. C4⋊#95C22semidirect
103. #1434C22semidirect
104. #1434C22semidirect
107. C22⋊#95C22semidirect
108. C22⋊#95C22semidirect
109. C22⋊#95C22semidirect
110. C22⋊#95C22semidirect
111. C4×#95C22semidirect
119. C22×#41C2×C4semidirect
127. C23×D4C2×C4semidirect
148. C2×#127C2×C4semidirect
151. C2×#124C2×C4semidirect
159. C2×#121C2×C4semidirect
160. C2×#121C2×C4semidirect
161. C2×#121C2×C4semidirect
168. C2×#120C2×C4semidirect
169. C2×#120C2×C4semidirect
175. C2×#117C2×C4semidirect
456. #121C22⋊C4semidirect
791. C2×D4C2×C22⋊C4semidirect
918. C22×C4C2×C22⋊C4semidirect
940. C4⋊C4C2×C22⋊C4semidirect
971. C22⋊C4C2×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#5352
C2×#23332
C2×#23252
#146592
#144212
#144192
#144182
#144172
#143582
#143572
#141522
#140982
#140252
#139952
#139672
#139562
#139442
#139372
#138672