Finite Group Databasebeta

← #570827

Subgroups — #570827

Order 512.

5012 conjugacy classes of subgroups.

The subgroup lattice has 1365 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2433C211yesmaximal, characteristic
2C2×#2366C211yesmaximal, characteristic, complemented
3C2×#2308C211yesmaximal, characteristic, complemented
4#14520C212yesmaximal, complemented
5#14519C212yesmaximal, complemented
6#14486C211yesmaximal, characteristic, complemented
7#14419C212yesmaximal, complemented
8#14419C211yesmaximal, characteristic, complemented
9#14363C212yesmaximal, complemented
10#14358C212yesmaximal, complemented
11#14299C212yesmaximal, complemented
12#14175C212yesmaximal, complemented
13#14036C212yesmaximal, complemented
14#13995C212yesmaximal, complemented
15#13967C212yesmaximal, complemented
16#13967C212yesmaximal, complemented
17#13887C212yesmaximal, complemented
18#13867C211yesmaximal, characteristic, complemented
19#13832C211yesmaximal, characteristic, complemented
20C24×D4C2211yescharacteristic
21C22×#127C2211yescharacteristic
22C22×#127C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#120C2212yes—
25C22×#120C2212yes—
26C22×C4×D4C2212yescomplemented
27C22×C4×D4C2212yescomplemented
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31#2433C4116yescomplemented
32C2×#392C2212yes—
33C2×#392C2212yes—
34#2366—28no—
35#2308—28no—
36C2×#390C2212yes—
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2212yescomplemented
40C2×#390C2212yescomplemented
41C2×#388C2212yescomplemented
42C2×#388C2212yescomplemented
43C2×#386C2211yescharacteristic
44C2×#386C2211yescharacteristic
45C2×#386C2211yescharacteristic
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2211yescharacteristic
49C2×#386C2211yescharacteristic
50C2×#386C2212yes—
51C2×#386C2211yescharacteristic
52C2×#386C2211yescharacteristic
53C2×#386C2211yescharacteristic
54C2×#386C2212yescomplemented
55C2×#386C2212yescomplemented
56C2×#386C2212yescomplemented
57C2×#386C2212yescomplemented
58C2×#386C2212yescomplemented
59C2×#386C2212yescomplemented
60C2×#386C2212yescomplemented
61C2×#385C2212yescomplemented
62C2×#381C2212yes—
63C2×#379C2212yes—
64C2×#379C2211yescharacteristic
65C2×#379C2212yes—
66C2×C4×C4⋊C4C2212yescomplemented
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2212yescomplemented
69#1442C2212yescomplemented
70#1442C2212yescomplemented
71#1441C2212yescomplemented
72#1440C2212yescomplemented
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yescomplemented
76#1439C2212yescomplemented
77#1439C2212yescomplemented
78#1439C2212yescomplemented
79#1439C2212yescomplemented
80#1438C2212yes—
81#1438C2212yes—
82#1438C2212yes—
83#1438C2212yes—
84#1438C2212yescomplemented
85#1438C2212yescomplemented
86#1438C2212yescomplemented
87#1438C2212yescomplemented
88#1438C2212yescomplemented
89#1438C2212yescomplemented
90#1438C2212yescomplemented
91#1437C2212yes—
92#1437C2212yes—
93#1437C2212yescomplemented
94#1437C2212yescomplemented
95#1437C2212yescomplemented
96#1437C2212yescomplemented
97#1437C2212yescomplemented
98#1436C2212yescomplemented
99#1434C2212yescomplemented
100#1434C2212yescomplemented
101#1434C2212yescomplemented
102#1434C2212yescomplemented
103#1434C2212yescomplemented
104C22⋊#95C2212yes—
105C22⋊#95C2212yescomplemented
106C22⋊#95C2212yescomplemented
107C22⋊#95C2212yescomplemented
108C22⋊#95C2212yescomplemented
109C22⋊#95C2212yescomplemented
110C26C2311yescharacteristic
111C26C2311yescharacteristic
112C23×D4—24no—
113C23×D4—24no—
114C23×D4—42no—
115C23×D4—42no—
116C23×D4—42no—
117C23×D4—42no—
118C23×D4C2×C418yescomplemented
119C23×D4C2311yescharacteristic
120C23×D4C2311yescharacteristic
121C23×D4C2312yes—
122C23×D4C2312yes—
123C23×D4C2311yescharacteristic
124C23×D4C2312yes—
125C23×D4C2312yes—
126C23×D4C2311yescharacteristic
127C23×D4C2312yes—
128C23×D4C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C24×C4C2311yescharacteristic
131C24×C4C2312yes—
132C24×C4C2312yes—
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C2×#127—24no—
137C2×#127—24no—
138C2×#127—42no—
139C2×#127—42no—
140C2×#127C2×C418yescomplemented
141C2×#127C2×C418yescomplemented
142C2×#121—42no—
143C2×#121—42no—
144C2×#121C2×C418yescomplemented
145C2×#120—44no—
146C2×#120—44no—
147C2×#120—44no—
148C2×#120—44no—
149C2×#120C2×C4116yescomplemented
150C2×#120C2×C4116yescomplemented
151C2×C4×D4—28no—
152C2×C4×D4—28no—
153C2×C4×D4—44no—
154C2×C4×D4—44no—
155C2×C4×D4—44no—
156C2×C4×D4—44no—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C22⋊C4—24no—
162C22×C22⋊C4—24no—
163C22×C22⋊C4—44no—
164C22×C22⋊C4—42no—
165C22×C22⋊C4—42no—
166C22×C22⋊C4—42no—
167C22×C22⋊C4—42no—
168C22×C22⋊C4—42no—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C42C2312yes—
202C22×C42C2312yes—
203C22×C42C2311yescharacteristic
204C22×C42C2312yes—
205C22×C42C2311yescharacteristic
206#392C2×C4116yescomplemented
207#392C2×C4116yescomplemented
208#390—28no—
209#390—28no—
210#390—44no—
211#390C2×C418yescomplemented
212#390C2×C418yescomplemented
213#388—44no—
214#388—44no—
215#386—24no—
216#386—24no—
217#386—24no—
218#386—24no—
219#386—28no—
220#386—24no—
221#386—28no—
222#386—28no—
223#386—44no—
224#386—44no—
225#386—44no—
226#386—44no—
227#386—44no—
228#386—42no—
229#386—42no—
230#386—44no—
231#386—44no—
232#386D418yescomplemented
233#385—44no—
234#381—28no—
235#379—28no—
236#379—44no—
237#379—42no—
238C4×C4⋊C4—28no—
239C4×C22⋊C4—44no—
240C4×C22⋊C4C2×C418yescomplemented
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
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—
268C25—22no—
269C25—22no—
270C25—22no—
271C25—22no—
272C25—22no—
273C25—22no—
274C25—22no—
275C25—22no—
276C25—22no—
277C25—22no—
278C25—42no—
279C25—41no—
280C25—41no—
281C25—42no—
282C25—42no—
283C25—42no—
284C25—42no—
285C25—42no—
286C25—42no—
287C25—42no—
288C25C22×C414yes—
289C25C22×C414yes—
290C25C2411yescharacteristic
291C25C2412yes—
292C25C2411yescharacteristic
293C25C2411yescharacteristic
294C25C2411yescharacteristic
295C25C2411yescharacteristic
296C22×D4—24no—
297C22×D4—24no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—24no—
301C22×D4—24no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—24no—
312C22×D4—232no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—24no—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—42no—
322C22×D4—42no—
323C22×D4—416no—
324C22×D4—41no—
325C22×D4—41no—
326C22×D4—41no—
327C22×D4—41no—
328C22×D4—41no—
329C22×D4—41no—
330C22×D4—41no—
331C22×D4—41no—
332C22×D4—41no—
333C22×D4—41no—
334C22×D4—41no—
335C22×D4—41no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4—42no—
343C22×D4—42no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—41no—
347C22×D4—41no—
348C22×D4—41no—
349C22×D4—41no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—416no—
357C22×D4—416no—
358C22×D4—416no—
359C22×D4—416no—
360C22×D4—416no—
361C22×D4C22×C418yes—
362C22×D4C22×C418yes—
363C22×D4C22×C414yes—
364C22×D4C22×C414yes—
365C22×D4C22×C418yes—
366C22×D4C22×C418yes—
367C22×D4C22×C414yes—
368C22×D4C22×C414yes—
369C22×D4C22×C418yes—
370C22×D4C22×C414yes—
371C22×D4C2×D414yes—
372C22×D4#4114yes—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—24no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—41no—
386C23×C4—41no—
387C23×C4—41no—
388C23×C4—41no—
389C23×C4—41no—
390C23×C4—42no—
391C23×C4—41no—
392C23×C4—41no—
393C23×C4—41no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—41no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—41no—
412C23×C4C22×C414yes—
413C23×C4C2×D414yes—
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2412yes—
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2412yes—
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427#127—232no—
428#127—416no—
429#121—416no—
430#120—432no—
431#120—432no—
432C4×D4—432no—
433C4×D4—432no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—41no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4C22×C414yes—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—41no—
479C2×C22⋊C4—41no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—41no—
487C2×C22⋊C4—41no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—416no—
502C2×C22⋊C4—416no—
503C2×C22⋊C4—416no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—41no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—41no—
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—41no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—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⋊C4C22×C418yes—
538C2×C22⋊C4C22×C418yes—
539C2×C22⋊C4C22×C418yes—
540C2×C22⋊C4C22×C418yes—
541C2×C22⋊C4C22×C418yes—
542C2×C22⋊C4C22×C418yes—
543C2×C22⋊C4C2×D414yes—
544C2×C22⋊C4C2×D418yes—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—24no—
548C2×C42—24no—
549C2×C42—24no—
550C2×C42—24no—
551C2×C42—42no—
552C2×C42—42no—
553C2×C42—41no—
554C2×C42—41no—
555C2×C42—42no—
556C2×C42—42no—
557C2×C42—42no—
558C2×C42C22×C414yes—
559C2×C42C22×C414yes—
560#95—24no—
561#95—24no—
562#95—24no—
563#95—24no—
564#95—24no—
565#95—24no—
566#95—24no—
567#95—24no—
568#95—24no—
569#95—24no—
570#95—42no—
571#95—42no—
572#95—42no—
573#95—42no—
574#95—42no—
575#95—42no—
576#95—42no—
577#95—42no—
578#95—42no—
579#95—42no—
580#95—42no—
581#95—42no—
582#95—42no—
583#95—42no—
584#95—42no—
585#95C22×C418yes—
586#95C2×D418yes—
587C24—28no—
588C24—28no—
589C24—28no—
590C24—28no—
591C24—21no—
592C24—21no—
593C24—21no—
594C24—21no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—22no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—28no—
624C24—28no—
625C24—28no—
626C24—21no—
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—22no—
640C24—21no—
641C24—21no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—21no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—28no—
651C24—28no—
652C24—44no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24—48no—
657C24—44no—
658C24—44no—
659C24—44no—
660C24—44no—
661C24—44no—
662C24—44no—
663C24—48no—
664C24—84no—
665C24—84no—
666C24—84no—
667C24—84no—
668C24—84no—
669C24—84no—
670C24—84no—
671C24—84no—
672C24—82no—
673C24—82no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—82no—
679C24—84no—
680C24—82no—
681C24—82no—
682C24—82no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24C23×C412yes—
690C24C23×C414yes—
691C24C23×C412yes—
692C24C23×C412yes—
693C24C23×C412yes—
694C24C23×C412yes—
695C24C22×D412yes—
696C24C22×D412yes—
697C24C2×#4112yes—
698C24C2×#4112yes—
699C24H(5,𝔽2)12yes—
700C24H(5,𝔽2)12yes—
701C24H(5,𝔽2)12yes—
702C24H(5,𝔽2)12yes—
703C24C2511yescharacteristic
704C2×D4—216no—
705C2×D4—216no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—216no—
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—216no—
715C2×D4—216no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—4128no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—82no—
759C2×D4—82no—
760C2×D4—82no—
761C2×D4—82no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—84no—
769C2×D4—84no—
770C2×D4—84no—
771C2×D4—84no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4C4×D4116yes—
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—28no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—28no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
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—22no—
840C22×C4—22no—
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—44no—
857C22×C4—44no—
858C22×C4—48no—
859C22×C4—44no—
860C22×C4—48no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—44no—
869C22×C4—48no—
870C22×C4—44no—
871C22×C4—84no—
872C22×C4—84no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—82no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4—82no—
881C22×C4—84no—
882C22×C4—82no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4—82no—
888C22×C4—82no—
889C22×C4—84no—
890C22×C4—82no—
891C22×C4—82no—
892C22×C4—84no—
893C22×C4—82no—
894C22×C4—84no—
895C22×C4C23×C412yes—
896C22×C4C23×C414yes—
897C22×C4C23×C414yes—
898C22×C4C23×C412yes—
899C22×C4C23×C414yes—
900C22×C4C22×D414yes—
901C22×C4C22×D414yes—
902C22×C4C22×D412yes—
903C22×C4C2×#4112yes—
904C22×C4H(5,𝔽2)14yes—
905C22×C4H(5,𝔽2)14yes—
906C22×C4H(5,𝔽2)14yes—
907C4⋊C4—216no—
908C4⋊C4—44no—
909C4⋊C4—48no—
910C4⋊C4—84no—
911C22⋊C4—216no—
912C22⋊C4—216no—
913C22⋊C4—216no—
914C22⋊C4—44no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—82no—
933C22⋊C4—84no—
934C22⋊C4—82no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C42—28no—
944C42—44no—
945C42—48no—
946C42—48no—
947C42—84no—
948C23—232no—
949C23—22no—
950C23—22no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—22no—
990C23—22no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—22no—
996C23—24no—
997C23—22no—
998C23—24no—
999C23—24no—
1000C23—22no—
1001C23—24no—
1002C23—24no—
1003C23—22no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—22no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—416no—
1012C23—416no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—41no—
1037C23—42no—
1038C23—41no—
1039C23—42no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—41no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—41no—
1057C23—41no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—41no—
1062C23—41no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—41no—
1072C23—42no—
1073C23—42no—
1074C23—41no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—41no—
1093C23—41no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—88no—
1098C23—88no—
1099C23—88no—
1100C23—816no—
1101C23—816no—
1102C23—816no—
1103C23—88no—
1104C23—816no—
1105C23—88no—
1106C23—88no—
1107C23—88no—
1108C23—816no—
1109C23—816no—
1110C23—88no—
1111C23—816no—
1112C23—88no—
1113C23—88no—
1114C23—88no—
1115C23—816no—
1116C23C2×C4×D414yes—
1117C23C2×C4×D414yes—
1118C23#51814yes—
1119C23#51814yes—
1120C23C24×C411yescharacteristic
1121C23C23×D411yescharacteristic
1122C23C22×#4111yescharacteristic
1123C23C2×H(5,𝔽2)11yescharacteristic
1124C23C2×H(5,𝔽2)11yescharacteristic
1125C23C2×H(5,𝔽2)11yescharacteristic
1126C23C2×H(5,𝔽2)11yescharacteristic
1127C23C2×H(5,𝔽2)12yes—
1128C23C2×H(5,𝔽2)12yes—
1129C23C2×H(5,𝔽2)12yes—
1130C23#58512yes—
1131D4—416no—
1132D4—432no—
1133D4—432no—
1134D4—416no—
1135D4—416no—
1136D4—416no—
1137D4—88no—
1138D4—816no—
1139D4—816no—
1140D4—816no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—416no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
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—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—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—88no—
1232C2×C4—88no—
1233C2×C4—816no—
1234C2×C4—816no—
1235C2×C4—88no—
1236C2×C4—88no—
1237C2×C4C2×C4×D414yes—
1238C2×C4#51818yes—
1239C22—24no—
1240C22—24no—
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—24no—
1245C22—28no—
1246C22—28no—
1247C22—28no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—42no—
1285C22—44no—
1286C22—42no—
1287C22—42no—
1288C22—44no—
1289C22—44no—
1290C22—44no—
1291C22—44no—
1292C22—44no—
1293C22—44no—
1294C22—44no—
1295C22—832no—
1296C22—832no—
1297C22—82no—
1298C22—81no—
1299C22—82no—
1300C22—82no—
1301C22—82no—
1302C22—82no—
1303C22—81no—
1304C22—82no—
1305C22—81no—
1306C22—82no—
1307C22—81no—
1308C22—82no—
1309C22—82no—
1310C22—82no—
1311C22C22×C4×D411yescharacteristic
1312C22C2×#51811yescharacteristic
1313C22C2×#51812yes—
1314C22C2×#51811yescharacteristic
1315C22C4×H(5,𝔽2)12yes—
1316C22#348411yescharacteristic
1317C22#348411yescharacteristic
1318C22#348412yes—
1319C22#348812yes—
1320C22#349011yescharacteristic
1321C22#349011yescharacteristic
1322C22#351312yes—
1323C22#351912yes—
1324C22#353211yescharacteristic
1325C22#353311yescharacteristic
1326C22#353712yes—
1327C22#354212yes—
1328C22#354212yes—
1329C22#354311yescharacteristic
1330C22#354312yes—
1331C22#354312yes—
1332C22#354311yescharacteristic
1333C22#355812yes—
1334C4—24no—
1335C4—28no—
1336C4—44no—
1337C4—42no—
1338C4—44no—
1339C4—44no—
1340C4—44no—
1341C4—44no—
1342C4—82no—
1343C4—82no—
1344C4—82no—
1345C4—82no—
1346C4—82no—
1347C2—44no—
1348C2—44no—
1349C2—44no—
1350C2—44no—
1351C2—84no—
1352C2—82no—
1353C2#3419811yescharacteristic
1354C2#3429012yes—
1355C2#3436411yescharacteristic
1356C2#3440611yescharacteristic
1357C2#3447112yes—
1358C2#4782711yescharacteristic
1359C2#4783112yes—
1360C2#4805012yes—
1361C2#4805811yescharacteristic
1362C2#4814311yescharacteristic
1363C2#5063511yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2433C2
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×#2366C2semidirect
3. C2×#2308C2semidirect
4. #14520C2semidirect
5. #14519C2semidirect
6. #14486C2semidirect
7. #14419C2semidirect
8. #14419C2semidirect
9. #14363C2semidirect
10. #14358C2semidirect
11. #14299C2semidirect
12. #14175C2semidirect
13. #14036C2semidirect
14. #13995C2semidirect
15. #13967C2semidirect
16. #13967C2semidirect
17. #13887C2semidirect
18. #13867C2semidirect
19. #13832C2semidirect
26. C22×C4×D4C22semidirect
27. C22×C4×D4C22semidirect
31. #2433C4semidirect
39. C2×#390C22semidirect
40. C2×#390C22semidirect
41. C2×#388C22semidirect
42. C2×#388C22semidirect
54. C2×#386C22semidirect
55. C2×#386C22semidirect
56. C2×#386C22semidirect
57. C2×#386C22semidirect
58. C2×#386C22semidirect
59. C2×#386C22semidirect
60. C2×#386C22semidirect
61. C2×#385C22semidirect
66. C2×C4×C4⋊C4C22semidirect
68. C2×C4×C22⋊C4C22semidirect
69. #1442C22semidirect
70. #1442C22semidirect
71. #1441C22semidirect
72. #1440C22semidirect
75. #1439C22semidirect
76. #1439C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect
79. #1439C22semidirect
84. #1438C22semidirect
85. #1438C22semidirect
86. #1438C22semidirect
87. #1438C22semidirect
88. #1438C22semidirect
89. #1438C22semidirect
90. #1438C22semidirect
93. #1437C22semidirect
94. #1437C22semidirect
95. #1437C22semidirect
96. #1437C22semidirect
97. #1437C22semidirect
98. #1436C22semidirect
99. #1434C22semidirect
100. #1434C22semidirect
101. #1434C22semidirect
102. #1434C22semidirect
103. #1434C22semidirect
105. C22⋊#95C22semidirect
106. C22⋊#95C22semidirect
107. C22⋊#95C22semidirect
108. C22⋊#95C22semidirect
109. C22⋊#95C22semidirect
118. C23×D4C2×C4semidirect
140. C2×#127C2×C4semidirect
141. C2×#127C2×C4semidirect
144. C2×#121C2×C4semidirect
149. C2×#120C2×C4semidirect
150. C2×#120C2×C4semidirect
206. #392C2×C4semidirect
207. #392C2×C4semidirect
211. #390C2×C4semidirect
212. #390C2×C4semidirect
232. #386D4semidirect
240. C4×C22⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24332
C2×#23662
C2×#23082
#145202
#145192
#144862
#144192
#143632
#143582
#142992
#141752
#140362
#139952
#139672
#138872
#138672
#138322