Finite Group Databasebeta

← #537732

Subgroups — #537732

Order 512.

6036 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2403C211yesmaximal, characteristic
2C2×D4×C22⋊C4C212yesmaximal, complemented
3C2×#2321C212yesmaximal, complemented
4#14534C212yesmaximal, complemented
5#14521C212yesmaximal, complemented
6#14520C212yesmaximal, complemented
7#14410C211yesmaximal, characteristic, complemented
8#14358C211yesmaximal, characteristic, complemented
9#14228C212yesmaximal, complemented
10#14145C211yesmaximal, characteristic, complemented
11#14134C211yesmaximal, characteristic, complemented
12#14012C212yesmaximal, complemented
13#13995C212yesmaximal, complemented
14#13975C212yesmaximal, complemented
15#13971C212yesmaximal, complemented
16#13967C212yesmaximal, complemented
17#13902C211yesmaximal, characteristic, complemented
18C2×#1438C211yesmaximal, characteristic, complemented
19#13813C212yesmaximal, complemented
20C24×D4C2211yescharacteristic
21C24×D4C2211yescharacteristic
22C22×#120C2212yes—
23C22×#120C2211yescharacteristic
24C22×#120C2211yescharacteristic
25C22×C4×D4C2212yes—
26C22×C4×D4C2212yes—
27C23×C22⋊C4C2212yes—
28C23×C22⋊C4C2211yescharacteristic, complemented
29C23×C22⋊C4C2212yescomplemented
30C23×C22⋊C4C2211yescharacteristic, complemented
31#2403C4116yescomplemented
32C2×#392C2212yes—
33C2×#392C2212yes—
34D4×C22⋊C4—216no—
35#2321—216no—
36C2×#390C2212yes—
37C2×#390C2212yescomplemented
38C2×#390C2212yescomplemented
39C2×#390C2212yescomplemented
40C2×#390C2212yescomplemented
41C2×#390C2212yescomplemented
42C2×#388C2212yescomplemented
43C2×#388C2212yescomplemented
44C2×#388C2212yescomplemented
45C2×#388C2212yescomplemented
46C2×#388C2212yescomplemented
47C2×#388C2212yescomplemented
48C2×#386C2212yes—
49C2×#386C2211yescharacteristic
50C2×#386C2212yes—
51C2×#386C2211yescharacteristic
52C2×#386C2212yes—
53C2×#386C2212yescomplemented
54C2×#386C2212yescomplemented
55C2×#386C2212yescomplemented
56C2×#386C2212yescomplemented
57C2×#386C2212yescomplemented
58C2×#386C2212yescomplemented
59C2×#385C2212yescomplemented
60C2×#385C2212yescomplemented
61C2×#380C2212yescomplemented
62C2×#380C2211yescharacteristic, complemented
63C2×#379C2212yes—
64C2×#379C2211yescharacteristic
65C2×#379C2212yescomplemented
66C2×#379C2212yescomplemented
67C2×C4×C22⋊C4C2212yescomplemented
68C2×C4×C22⋊C4C2212yescomplemented
69C2×C4×C22⋊C4C2211yescharacteristic, complemented
70C2×C4×C22⋊C4C2212yescomplemented
71C22×#95C2212yescomplemented
72#1444C2212yescomplemented
73#1442C2212yescomplemented
74#1440C2212yescomplemented
75#1440C2212yescomplemented
76#1439C2212yescomplemented
77#1439C2212yescomplemented
78#1439C2212yescomplemented
79#1439C2212yescomplemented
80#1439C2212yescomplemented
81#1439C2212yescomplemented
82#1438C2211yescharacteristic
83#1438C2211yescharacteristic
84#1438C2212yes—
85#1438C2211yescharacteristic
86#1438C2211yescharacteristic
87#1438C2211yescharacteristic, complemented
88#1438C2212yescomplemented
89#1438C2211yescharacteristic, complemented
90#1438C2212yescomplemented
91#1438C2211yescharacteristic, complemented
92#1438C2211yescharacteristic, complemented
93#1438C2212yescomplemented
94#1437C2212yescomplemented
95#1437C2212yescomplemented
96#1437C2212yescomplemented
97#1437C2212yescomplemented
98#1437C2212yescomplemented
99#1437C2212yescomplemented
100#1436C2212yescomplemented
101#1436C2212yescomplemented
102#1436C2212yescomplemented
103#1436C2212yescomplemented
104#1434C2212yescomplemented
105C22⋊#95C2212yescomplemented
106C22⋊#95C2212yescomplemented
107C22⋊#95C2212yescomplemented
108C22⋊#95C2212yescomplemented
109C4×#95C2212yescomplemented
110C26C2311yescharacteristic
111C26C2311yescharacteristic
112C26C2311yescharacteristic
113C23×D4—28no—
114C23×D4—28no—
115C23×D4—44no—
116C23×D4—42no—
117C23×D4—42no—
118C23×D4—42no—
119C23×D4—42no—
120C23×D4—44no—
121C23×D4C2×C418yes—
122C23×D4C2×C418yescomplemented
123C23×D4C2312yes—
124C23×D4C2311yescharacteristic
125C23×D4C2312yes—
126C23×D4C2311yescharacteristic
127C23×D4C2311yescharacteristic
128C23×D4C2312yes—
129C23×D4C2312yes—
130C23×D4C2311yescharacteristic
131C24×C4C2312yes—
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2312yes—
135C24×C4C2312yes—
136C24×C4C2312yes—
137C2×#120—28no—
138C2×#120—28no—
139C2×#120—44no—
140C2×#120—44no—
141C2×#120C2×C4116yescomplemented
142C2×#120C2×C418yescomplemented
143C2×#120C2×C418yescomplemented
144C2×C4×D4—28no—
145C2×C4×D4—28no—
146C2×C4×D4—28no—
147C2×C4×D4—28no—
148C2×C4×D4—44no—
149C2×C4×D4—44no—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C22⋊C4—28no—
156C22×C22⋊C4—28no—
157C22×C22⋊C4—28no—
158C22×C22⋊C4—44no—
159C22×C22⋊C4—44no—
160C22×C22⋊C4—44no—
161C22×C22⋊C4—44no—
162C22×C22⋊C4—44no—
163C22×C22⋊C4—42no—
164C22×C22⋊C4—42no—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2311yescharacteristic
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2311yescharacteristic
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C42C2312yes—
200C22×C42C2312yes—
201C22×C42C2312yes—
202C22×C42C2312yes—
203C22×C42C2312yes—
204#392C2×C4116yescomplemented
205#392C2×C4116yescomplemented
206#390—28no—
207#390—28no—
208#390—28no—
209#390—28no—
210#390—44no—
211#390—44no—
212#388—28no—
213#388—28no—
214#388—28no—
215#388—28no—
216#388—44no—
217#388—44no—
218#386—28no—
219#386—28no—
220#386—28no—
221#386—28no—
222#386—28no—
223#386—44no—
224#386—44no—
225#386C2×C418yescomplemented
226#386C2×C4116yescomplemented
227#386C2×C418yescomplemented
228#386D4116yescomplemented
229#385—28no—
230#385—44no—
231#380—28no—
232#380—42no—
233#379—28no—
234#379—28no—
235#379—28no—
236#379C2×C418yescomplemented
237C4×C22⋊C4—28no—
238C4×C22⋊C4—28no—
239C4×C22⋊C4—44no—
240C4×C22⋊C4—42no—
241C2×#95—44no—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2311yescharacteristic
254C2×#95C2312yes—
255C2×#95C2311yescharacteristic
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C25—24no—
269C25—22no—
270C25—22no—
271C25—24no—
272C25—24no—
273C25—24no—
274C25—24no—
275C25—24no—
276C25—22no—
277C25—22no—
278C25—24no—
279C25—24no—
280C25—42no—
281C25—42no—
282C25—42no—
283C25—42no—
284C25—42no—
285C25—42no—
286C25—41no—
287C25—41no—
288C25—42no—
289C25—42no—
290C25—42no—
291C25—42no—
292C25C22×C414yes—
293C25C22×C414yes—
294C25C22×C414yes—
295C25C2411yescharacteristic
296C25C2411yescharacteristic
297C25C2411yescharacteristic
298C25C2412yes—
299C25C2411yescharacteristic
300C25C2411yescharacteristic
301C22×D4—24no—
302C22×D4—24no—
303C22×D4—24no—
304C22×D4—24no—
305C22×D4—24no—
306C22×D4—24no—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—24no—
312C22×D4—24no—
313C22×D4—264no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—24no—
317C22×D4—24no—
318C22×D4—416no—
319C22×D4—416no—
320C22×D4—41no—
321C22×D4—41no—
322C22×D4—42no—
323C22×D4—42no—
324C22×D4—42no—
325C22×D4—41no—
326C22×D4—41no—
327C22×D4—42no—
328C22×D4—41no—
329C22×D4—41no—
330C22×D4—42no—
331C22×D4—41no—
332C22×D4—41no—
333C22×D4—42no—
334C22×D4—42no—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4—416no—
343C22×D4—416no—
344C22×D4—416no—
345C22×D4—432no—
346C22×D4—416no—
347C22×D4—432no—
348C22×D4—432no—
349C22×D4C22×C414yes—
350C22×D4C22×C418yes—
351C22×D4C22×C418yes—
352C22×D4C22×C418yes—
353C22×D4C22×C418yes—
354C22×D4C22×C414yes—
355C22×D4C22×C414yes—
356C22×D4C22×C414yes—
357C22×D4C2×D418yes—
358C22×D4#4118yes—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—41no—
376C23×C4—41no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4C22×C414yes—
395C23×C4C22×C414yes—
396C23×C4C2×D418yes—
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2412yes—
400C23×C4C2412yes—
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2412yes—
408C23×C4C2412yes—
409C23×C4C2411yescharacteristic
410#120—264no—
411#120—416no—
412#120—416no—
413C4×D4—432no—
414C4×D4—432no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
429C2×C4⋊C4—42no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
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—24no—
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—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—432no—
476C2×C22⋊C4—432no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—41no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—41no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—41no—
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—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—416no—
504C2×C22⋊C4—416no—
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—42no—
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⋊C4C22×C418yes—
520C2×C22⋊C4C22×C414yes—
521C2×C22⋊C4C22×C418yes—
522C2×C22⋊C4C22×C418yes—
523C2×C22⋊C4C22×C418yes—
524C2×C22⋊C4C22×C414yes—
525C2×C22⋊C4C22×C418yes—
526C2×C22⋊C4C22×C418yes—
527C2×C22⋊C4C2×D418yes—
528C2×C22⋊C4C2×D418yescomplemented
529C2×C22⋊C4C2×D418yescomplemented
530C2×C42—24no—
531C2×C42—24no—
532C2×C42—24no—
533C2×C42—24no—
534C2×C42—24no—
535C2×C42—24no—
536C2×C42—24no—
537C2×C42—42no—
538C2×C42—42no—
539C2×C42—42no—
540C2×C42—42no—
541C2×C42—42no—
542C2×C42—42no—
543C2×C42—42no—
544C2×C42—42no—
545#95—24no—
546#95—24no—
547#95—24no—
548#95—24no—
549#95—24no—
550#95—24no—
551#95—24no—
552#95—24no—
553#95—24no—
554#95—24no—
555#95—42no—
556#95—42no—
557#95—42no—
558#95—41no—
559#95—41no—
560#95—41no—
561#95—41no—
562#95—42no—
563#95—42no—
564#95—42no—
565#95—42no—
566#95—42no—
567#95C22×C418yes—
568#95C22×C418yes—
569#95C2×D418yescomplemented
570#95C2×D418yescomplemented
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—21no—
590C24—21no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—28no—
595C24—28no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—21no—
616C24—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—216no—
621C24—216no—
622C24—28no—
623C24—28no—
624C24—216no—
625C24—44no—
626C24—44no—
627C24—44no—
628C24—44no—
629C24—48no—
630C24—48no—
631C24—48no—
632C24—44no—
633C24—48no—
634C24—48no—
635C24—48no—
636C24—48no—
637C24—44no—
638C24—48no—
639C24—44no—
640C24—48no—
641C24—48no—
642C24—48no—
643C24—48no—
644C24—48no—
645C24—48no—
646C24—44no—
647C24—48no—
648C24—48no—
649C24—44no—
650C24—48no—
651C24—44no—
652C24—44no—
653C24—48no—
654C24—48no—
655C24—44no—
656C24—44no—
657C24—84no—
658C24—84no—
659C24—84no—
660C24—84no—
661C24—84no—
662C24—84no—
663C24—84no—
664C24—84no—
665C24—84no—
666C24—84no—
667C24—84no—
668C24—84no—
669C24—82no—
670C24—82no—
671C24—84no—
672C24—84no—
673C24—84no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—82no—
679C24—82no—
680C24—84no—
681C24C23×C412yes—
682C24C23×C412yes—
683C24C23×C412yes—
684C24C23×C414yes—
685C24C23×C412yes—
686C24C23×C412yes—
687C24C22×D414yes—
688C24C22×D414yes—
689C24C2×#4114yes—
690C24C2×#4114yes—
691C24H(5,𝔽2)14yes—
692C24H(5,𝔽2)12yes—
693C24H(5,𝔽2)12yes—
694C24C2511yescharacteristic
695C2×D4—216no—
696C2×D4—216no—
697C2×D4—216no—
698C2×D4—216no—
699C2×D4—216no—
700C2×D4—216no—
701C2×D4—216no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—216no—
705C2×D4—216no—
706C2×D4—216no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—48no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—4128no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—4128no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—84no—
737C2×D4—84no—
738C2×D4—84no—
739C2×D4—84no—
740C2×D4—84no—
741C2×D4—84no—
742C2×D4—84no—
743C2×D4—84no—
744C2×D4C4×D4132yes—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—28no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—216no—
800C22×C4—216no—
801C22×C4—28no—
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—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—48no—
827C22×C4—44no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—84no—
842C22×C4—84no—
843C22×C4—84no—
844C22×C4—84no—
845C22×C4—84no—
846C22×C4—84no—
847C22×C4—84no—
848C22×C4—84no—
849C22×C4—84no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—84no—
853C22×C4—84no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4C23×C412yes—
858C22×C4C23×C414yes—
859C22×C4C23×C414yes—
860C22×C4C23×C414yes—
861C22×C4C23×C412yes—
862C22×C4C22×D414yes—
863C22×C4C22×D414yes—
864C22×C4C22×D414yes—
865C22×C4C22×D414yes—
866C22×C4C22×D414yes—
867C22×C4C2×#4114yes—
868C22×C4H(5,𝔽2)14yes—
869C22×C4H(5,𝔽2)14yes—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—84no—
873C4⋊C4—84no—
874C4⋊C4—84no—
875C22⋊C4—216no—
876C22⋊C4—216no—
877C22⋊C4—28no—
878C22⋊C4—216no—
879C22⋊C4—216no—
880C22⋊C4—216no—
881C22⋊C4—216no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—44no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—44no—
888C22⋊C4—48no—
889C22⋊C4—44no—
890C22⋊C4—48no—
891C22⋊C4—44no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—44no—
901C22⋊C4—48no—
902C22⋊C4—84no—
903C22⋊C4—84no—
904C22⋊C4—84no—
905C22⋊C4—84no—
906C22⋊C4—84no—
907C22⋊C4—84no—
908C22⋊C4—84no—
909C42—48no—
910C42—48no—
911C42—84no—
912C42—84no—
913C42—84no—
914C23—22no—
915C23—22no—
916C23—24no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—22no—
926C23—24no—
927C23—24no—
928C23—22no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—22no—
934C23—24no—
935C23—22no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—416no—
974C23—416no—
975C23—432no—
976C23—432no—
977C23—416no—
978C23—416no—
979C23—41no—
980C23—42no—
981C23—41no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—41no—
1000C23—42no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—416no—
1006C23—416no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—41no—
1041C23—41no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—816no—
1056C23—816no—
1057C23—88no—
1058C23—816no—
1059C23—816no—
1060C23—88no—
1061C23—816no—
1062C23—816no—
1063C23—816no—
1064C23—816no—
1065C23—816no—
1066C23—816no—
1067C23—816no—
1068C23—816no—
1069C23—816no—
1070C23—88no—
1071C23—816no—
1072C23—816no—
1073C23—816no—
1074C23C2×C4×D418yes—
1075C23C2×C4×D418yes—
1076C23#51814yes—
1077C23#51814yes—
1078C23D4214yes—
1079C23#54618yes—
1080C23#55114yes—
1081C23C24×C411yescharacteristic
1082C23C23×D412yes—
1083C23C22×#4112yes—
1084C23C2×H(5,𝔽2)11yescharacteristic
1085C23C2×H(5,𝔽2)11yescharacteristic
1086C23C2×H(5,𝔽2)12yes—
1087C23C2×H(5,𝔽2)12yes—
1088C23C2×H(5,𝔽2)12yes—
1089C23#58512yes—
1090D4—264no—
1091D4—416no—
1092D4—432no—
1093D4—416no—
1094D4—416no—
1095D4—416no—
1096D4—816no—
1097D4—816no—
1098C2×C4—24no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—416no—
1133C2×C4—416no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—816no—
1186C2×C4—816no—
1187C2×C4—816no—
1188C2×C4—816no—
1189C2×C4C2×C4×D418yes—
1190C2×C4#51814yes—
1191C22—28no—
1192C22—24no—
1193C22—28no—
1194C22—24no—
1195C22—28no—
1196C22—28no—
1197C22—28no—
1198C22—28no—
1199C22—28no—
1200C22—24no—
1201C22—28no—
1202C22—28no—
1203C22—28no—
1204C22—44no—
1205C22—44no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—44no—
1210C22—42no—
1211C22—44no—
1212C22—42no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—832no—
1239C22—832no—
1240C22—832no—
1241C22—82no—
1242C22—82no—
1243C22—82no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22—82no—
1252C22—82no—
1253C22#235818yes—
1254C22C22×C4×D412yes—
1255C22C2×#51811yescharacteristic
1256C22C2×#51811yescharacteristic
1257C22C2×#51811yescharacteristic
1258C22C4×H(5,𝔽2)12yes—
1259C22C2×D4211yescharacteristic
1260C22C2×#54612yes—
1261C22C2×#55111yescharacteristic
1262C22#348412yes—
1263C22#348812yes—
1264C22#349612yes—
1265C22#349812yes—
1266C22#351312yes—
1267C22#351412yes—
1268C22#351912yes—
1269C22#351912yes—
1270C22#353212yes—
1271C22#353212yes—
1272C22#353211yescharacteristic
1273C22#353311yescharacteristic
1274C22#354212yes—
1275C4—24no—
1276C4—28no—
1277C4—44no—
1278C4—42no—
1279C4—44no—
1280C4—44no—
1281C4—44no—
1282C4—44no—
1283C4—44no—
1284C4—44no—
1285C4—82no—
1286C4—82no—
1287C4—82no—
1288C2—28no—
1289C2—48no—
1290C2—44no—
1291C2—82no—
1292C2—82no—
1293C2—82no—
1294C2C2×#235811yescharacteristic
1295C2#3429012yes—
1296C2#3431012yes—
1297C2#3435611yescharacteristic
1298C2#3440711yescharacteristic
1299C2#4388612yes—
1300C2#4389312yes—
1301C2#4391012yes—
1302C2#4408412yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2403C2
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×D4×C22⋊C4C2semidirect
3. C2×#2321C2semidirect
4. #14534C2semidirect
5. #14521C2semidirect
6. #14520C2semidirect
7. #14410C2semidirect
8. #14358C2semidirect
9. #14228C2semidirect
10. #14145C2semidirect
11. #14134C2semidirect
12. #14012C2semidirect
13. #13995C2semidirect
14. #13975C2semidirect
15. #13971C2semidirect
16. #13967C2semidirect
17. #13902C2semidirect
18. C2×#1438C2semidirect
19. #13813C2semidirect
28. C23×C22⋊C4C22semidirect
29. C23×C22⋊C4C22semidirect
30. C23×C22⋊C4C22semidirect
31. #2403C4semidirect
37. C2×#390C22semidirect
38. C2×#390C22semidirect
39. C2×#390C22semidirect
40. C2×#390C22semidirect
41. C2×#390C22semidirect
42. C2×#388C22semidirect
43. C2×#388C22semidirect
44. C2×#388C22semidirect
45. C2×#388C22semidirect
46. C2×#388C22semidirect
47. C2×#388C22semidirect
53. C2×#386C22semidirect
54. C2×#386C22semidirect
55. C2×#386C22semidirect
56. C2×#386C22semidirect
57. C2×#386C22semidirect
58. C2×#386C22semidirect
59. C2×#385C22semidirect
60. C2×#385C22semidirect
61. C2×#380C22semidirect
62. C2×#380C22semidirect
65. C2×#379C22semidirect
66. C2×#379C22semidirect
67. C2×C4×C22⋊C4C22semidirect
68. C2×C4×C22⋊C4C22semidirect
69. C2×C4×C22⋊C4C22semidirect
70. C2×C4×C22⋊C4C22semidirect
71. C22×#95C22semidirect
72. #1444C22semidirect
73. #1442C22semidirect
74. #1440C22semidirect
75. #1440C22semidirect
76. #1439C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect
79. #1439C22semidirect
80. #1439C22semidirect
81. #1439C22semidirect
87. #1438C22semidirect
88. #1438C22semidirect
89. #1438C22semidirect
90. #1438C22semidirect
91. #1438C22semidirect
92. #1438C22semidirect
93. #1438C22semidirect
94. #1437C22semidirect
95. #1437C22semidirect
96. #1437C22semidirect
97. #1437C22semidirect
98. #1437C22semidirect
99. #1437C22semidirect
100. #1436C22semidirect
101. #1436C22semidirect
102. #1436C22semidirect
103. #1436C22semidirect
104. #1434C22semidirect
105. C22⋊#95C22semidirect
106. C22⋊#95C22semidirect
107. C22⋊#95C22semidirect
108. C22⋊#95C22semidirect
109. C4×#95C22semidirect
122. C23×D4C2×C4semidirect
141. C2×#120C2×C4semidirect
142. C2×#120C2×C4semidirect
143. C2×#120C2×C4semidirect
204. #392C2×C4semidirect
205. #392C2×C4semidirect
225. #386C2×C4semidirect
226. #386C2×C4semidirect
227. #386C2×C4semidirect
228. #386D4semidirect
236. #379C2×C4semidirect
528. C2×C22⋊C4C2×D4semidirect
529. C2×C22⋊C4C2×D4semidirect
569. #95C2×D4semidirect
570. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24032
C2×D4×C22⋊C42
C2×#23212
#145342
#145212
#145202
#144102
#143582
#142282
#141452
#141342
#140122
#139952
#139752
#139712
#139672
#139022
C2×#14382
#138132