Finite Group Databasebeta

← #557552

Subgroups — #557552

Order 512.

5944 conjugacy classes of subgroups.

The subgroup lattice has 1393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2403C211yesmaximal, characteristic
2C2×#2375C211yesmaximal, characteristic, complemented
3C22×#386C211yesmaximal, characteristic, complemented
4#14694C212yesmaximal, complemented
5#14621C212yesmaximal, complemented
6#14521C212yesmaximal, complemented
7#14520C212yesmaximal, complemented
8#14520C212yesmaximal, complemented
9#14513C211yesmaximal, characteristic, complemented
10#14427C212yesmaximal, complemented
11#14357C212yesmaximal, complemented
12#14357C211yesmaximal, characteristic, complemented
13#14140C212yesmaximal, complemented
14#13999C212yesmaximal, complemented
15#13995C212yesmaximal, complemented
16#13971C212yesmaximal, complemented
17#13902C211yesmaximal, characteristic, complemented
18#13867C212yesmaximal, complemented
19#13832C211yesmaximal, characteristic, complemented
20C24×D4C2211yescharacteristic
21C24×D4C2211yescharacteristic
22C25×C4C2211yescharacteristic, complemented
23C22×#120C2211yescharacteristic
24C22×#120C2212yes—
25C22×#120C2211yescharacteristic
26C23×C22⋊C4C2212yes—
27C23×C22⋊C4C2211yescharacteristic, complemented
28#2403C4116yescomplemented
29C2×#392C2212yes—
30C2×#392C2212yes—
31#2375—28no—
32C2×#390C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#390C2212yescomplemented
35C2×#390C2212yescomplemented
36C2×#390C2211yescharacteristic, complemented
37C2×#390C2211yescharacteristic, complemented
38C2×#388C2212yescomplemented
39C2×#388C2212yescomplemented
40C2×#388C2212yescomplemented
41C2×#388C2212yescomplemented
42C2×#386—28no—
43C2×#386C2212yes—
44C2×#386C2211yescharacteristic
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2211yescharacteristic
50C2×#386C2212yes—
51C2×#386C2211yescharacteristic
52C2×#386C2211yescharacteristic
53C2×#386C2211yescharacteristic, complemented
54C2×#386C2212yescomplemented
55C2×#386C2211yescharacteristic, complemented
56C2×#386C2212yescomplemented
57C2×#386C2212yescomplemented
58C2×#386C2212yescomplemented
59C2×#386C2212yescomplemented
60C2×#385C2212yescomplemented
61C2×#380C2211yescharacteristic, complemented
62C2×#379C2212yes—
63C2×#379C2211yescharacteristic
64C2×#379C2212yescomplemented
65C2×#379C2212yescomplemented
66C2×#379C2212yescomplemented
67C2×C4×C22⋊C4C2211yescharacteristic, complemented
68C2×C4×C22⋊C4C2212yescomplemented
69C22×#95C2212yescomplemented
70#1443C2212yescomplemented
71#1443C2212yescomplemented
72#1442C2212yescomplemented
73#1442C2212yescomplemented
74#1440C2212yescomplemented
75#1440C2212yescomplemented
76#1440C2212yescomplemented
77#1440C2212yescomplemented
78#1439C2212yescomplemented
79#1439C2212yescomplemented
80#1439C2212yescomplemented
81#1439C2212yescomplemented
82#1439C2212yescomplemented
83#1439C2212yescomplemented
84#1438C2212yes—
85#1438C2212yescomplemented
86#1438C2212yescomplemented
87#1438C2212yescomplemented
88#1438C2212yescomplemented
89#1438C2212yescomplemented
90#1438C2212yescomplemented
91#1438C2212yescomplemented
92#1437C2212yescomplemented
93#1437C2212yescomplemented
94#1437C2212yescomplemented
95#1437C2212yescomplemented
96#1437C2212yescomplemented
97#1437C2212yescomplemented
98#1436C2212yescomplemented
99#1436C2212yescomplemented
100#1434C2212yescomplemented
101#1434C2212yescomplemented
102C22⋊#95C2212yescomplemented
103C22⋊#95C2212yescomplemented
104C22⋊#95C2212yescomplemented
105C22⋊#95C2212yescomplemented
106C22⋊#95C2212yescomplemented
107C22⋊#95C2212yescomplemented
108C22⋊#95C2212yescomplemented
109C22⋊#95C2212yescomplemented
110C26C2311yescharacteristic
111C26C2311yescharacteristic
112C26C2311yescharacteristic
113C23×D4—24no—
114C23×D4—24no—
115C23×D4—42no—
116C23×D4—42no—
117C23×D4—44no—
118C23×D4—44no—
119C23×D4—42no—
120C23×D4—42no—
121C23×D4—42no—
122C23×D4—42no—
123C23×D4C2×C418yes—
124C23×D4C2×C418yescomplemented
125C23×D4C2312yes—
126C23×D4C2311yescharacteristic
127C23×D4C2311yescharacteristic
128C23×D4C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2312yes—
131C23×D4C2312yes—
132C23×D4C2311yescharacteristic
133C24×C4—24no—
134C24×C4—44no—
135C24×C4—44no—
136C24×C4—42no—
137C24×C4—42no—
138C24×C4C2312yes—
139C24×C4C2312yes—
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C2×#120—24no—
146C2×#120—24no—
147C2×#120—44no—
148C2×#120—44no—
149C2×#120—42no—
150C2×#120—42no—
151C2×#120C2×C4116yes—
152C2×#120C2×C418yescomplemented
153C2×#120C2×C418yescomplemented
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2312yes—
158C22×C22⋊C4—28no—
159C22×C22⋊C4—24no—
160C22×C22⋊C4—44no—
161C22×C22⋊C4—42no—
162C22×C22⋊C4—44no—
163C22×C22⋊C4—42no—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C42C2311yescharacteristic
198C22×C42C2312yes—
199C22×C42C2311yescharacteristic
200C22×C42C2312yes—
201#392C2×C4116yescomplemented
202#392C2×C4116yescomplemented
203#390—24no—
204#390—24no—
205#390—28no—
206#390—44no—
207#390—42no—
208#390—42no—
209#388—28no—
210#388—28no—
211#388—28no—
212#388—44no—
213#386—24no—
214#386—28no—
215#386—24no—
216#386—28no—
217#386—24no—
218#386—28no—
219#386—44no—
220#386—44no—
221#386—44no—
222#386—44no—
223#386—44no—
224#386—44no—
225#386—44no—
226#386C2×C418yescomplemented
227#386C2×C418yescomplemented
228#386C2×C4116yescomplemented
229#386D418yescomplemented
230#385—44no—
231#380—42no—
232#379—28no—
233#379—44no—
234#379—44no—
235#379—44no—
236#379C2×C418yescomplemented
237C4×C22⋊C4—44no—
238C4×C22⋊C4—42no—
239C2×#95—28no—
240C2×#95C2312yes—
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—24no—
277C25—24no—
278C25—24no—
279C25—22no—
280C25—22no—
281C25—24no—
282C25—22no—
283C25—22no—
284C25—42no—
285C25—42no—
286C25—42no—
287C25—41no—
288C25—41no—
289C25—42no—
290C25—42no—
291C25—41no—
292C25—41no—
293C25—42no—
294C25—41no—
295C25—41no—
296C25—42no—
297C25—42no—
298C25C22×C414yes—
299C25C22×C414yes—
300C25C22×C414yescomplemented
301C25C2412yes—
302C25C2411yescharacteristic
303C25C2411yescharacteristic
304C25C2411yescharacteristic
305C25C2411yescharacteristic
306C25C2411yescharacteristic
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—24no—
317C22×D4—24no—
318C22×D4—24no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—232no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—416no—
329C22×D4—41no—
330C22×D4—41no—
331C22×D4—41no—
332C22×D4—41no—
333C22×D4—41no—
334C22×D4—41no—
335C22×D4—41no—
336C22×D4—41no—
337C22×D4—41no—
338C22×D4—41no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4—42no—
343C22×D4—41no—
344C22×D4—41no—
345C22×D4—42no—
346C22×D4—42no—
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—416no—
356C22×D4—432no—
357C22×D4—416no—
358C22×D4—416no—
359C22×D4—416no—
360C22×D4—416no—
361C22×D4—416no—
362C22×D4—416no—
363C22×D4—432no—
364C22×D4—416no—
365C22×D4C22×C418yes—
366C22×D4C22×C414yes—
367C22×D4C22×C414yes—
368C22×D4C22×C418yes—
369C22×D4C22×C418yes—
370C22×D4C22×C414yes—
371C22×D4C22×C414yes—
372C22×D4C22×C418yescomplemented
373C22×D4C2×D414yes—
374C22×D4#4114yes—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—24no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—24no—
382C23×C4—22no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—41no—
394C23×C4—41no—
395C23×C4—41no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—41no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—41no—
407C23×C4—41no—
408C23×C4—41no—
409C23×C4—41no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—432no—
416C23×C4—416no—
417C23×C4—416no—
418C23×C4—432no—
419C23×C4—416no—
420C23×C4C22×C414yes—
421C23×C4C22×C414yescomplemented
422C23×C4C2×D414yescomplemented
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2412yes—
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2411yescharacteristic
436#120—232no—
437#120—432no—
438#120—416no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—41no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4—42no—
451C2×C22⋊C4—22no—
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—22no—
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—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—41no—
486C2×C22⋊C4—41no—
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—41no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—41no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—41no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—432no—
505C2×C22⋊C4—416no—
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⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
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⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4C22×C418yes—
543C2×C22⋊C4C22×C418yes—
544C2×C22⋊C4C22×C418yes—
545C2×C22⋊C4C22×C414yescomplemented
546C2×C22⋊C4C22×C418yescomplemented
547C2×C22⋊C4C22×C414yescomplemented
548C2×C22⋊C4C22×C418yescomplemented
549C2×C22⋊C4C22×C418yescomplemented
550C2×C22⋊C4C2×D418yes—
551C2×C22⋊C4C2×D414yescomplemented
552C2×C42—24no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—41no—
556C2×C42—41no—
557C2×C42—42no—
558C2×C42—42no—
559C2×C42—42no—
560C2×C42—41no—
561C2×C42—41no—
562C2×C42—42no—
563C2×C42—42no—
564#95—24no—
565#95—24no—
566#95—24no—
567#95—24no—
568#95—24no—
569#95—24no—
570#95—24no—
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#95—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95C22×C418yescomplemented
590#95C22×C418yescomplemented
591#95C2×D418yescomplemented
592C24—21no—
593C24—21no—
594C24—22no—
595C24—21no—
596C24—21no—
597C24—22no—
598C24—28no—
599C24—28no—
600C24—28no—
601C24—28no—
602C24—28no—
603C24—28no—
604C24—28no—
605C24—21no—
606C24—21no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—28no—
630C24—216no—
631C24—22no—
632C24—21no—
633C24—22no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—21no—
651C24—21no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—28no—
656C24—216no—
657C24—28no—
658C24—48no—
659C24—44no—
660C24—44no—
661C24—48no—
662C24—48no—
663C24—44no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—44no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—44no—
682C24—44no—
683C24—48no—
684C24—44no—
685C24—48no—
686C24—44no—
687C24—48no—
688C24—44no—
689C24—44no—
690C24—44no—
691C24—48no—
692C24—44no—
693C24—84no—
694C24—82no—
695C24—82no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—82no—
702C24—82no—
703C24—84no—
704C24—82no—
705C24—82no—
706C24—84no—
707C24—84no—
708C24—82no—
709C24—84no—
710C24—82no—
711C24—84no—
712C24—84no—
713C24—84no—
714C24—84no—
715C24C23×C414yes—
716C24C23×C412yes—
717C24C23×C412yes—
718C24C23×C412yes—
719C24C23×C412yes—
720C24C23×C412yes—
721C24C22×D412yes—
722C24C22×D412yes—
723C24C2×#4112yes—
724C24C2×#4112yes—
725C24H(5,𝔽2)12yes—
726C24H(5,𝔽2)12yes—
727C24H(5,𝔽2)14yes—
728C24H(5,𝔽2)12yes—
729C24H(5,𝔽2)14yes—
730C24H(5,𝔽2)12yes—
731C24C2511yescharacteristic
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—216no—
736C2×D4—28no—
737C2×D4—216no—
738C2×D4—216no—
739C2×D4—216no—
740C2×D4—216no—
741C2×D4—28no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—4128no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—4128no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—48no—
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×D4C4×D4116yes—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—216no—
795C22×C4—28no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
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—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—28no—
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—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—48no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—48no—
878C22×C4—44no—
879C22×C4—48no—
880C22×C4—44no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—48no—
886C22×C4—48no—
887C22×C4—48no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
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—44no—
900C22×C4—48no—
901C22×C4—4128no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—48no—
905C22×C4—44no—
906C22×C4—48no—
907C22×C4—48no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—48no—
911C22×C4—48no—
912C22×C4—84no—
913C22×C4—84no—
914C22×C4—84no—
915C22×C4C23×C414yes—
916C22×C4C23×C412yes—
917C22×C4C23×C414yes—
918C22×C4C23×C414yes—
919C22×C4C23×C412yes—
920C22×C4C22×D414yes—
921C22×C4C22×D414yes—
922C22×C4C22×D412yes—
923C22×C4C2×#4112yes—
924C22×C4H(5,𝔽2)14yes—
925C4⋊C4—82no—
926C4⋊C4—82no—
927C4⋊C4—84no—
928C4⋊C4—84no—
929C22⋊C4—28no—
930C22⋊C4—216no—
931C22⋊C4—216no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—84no—
947C22⋊C4—84no—
948C22⋊C4—84no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C22⋊C4—84no—
958C22⋊C4—84no—
959C22⋊C4—84no—
960C22⋊C4—84no—
961C22⋊C4—84no—
962C42—82no—
963C42—82no—
964C42—84no—
965C42—84no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—22no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—22no—
978C23—24no—
979C23—22no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—232no—
985C23—22no—
986C23—22no—
987C23—24no—
988C23—24no—
989C23—22no—
990C23—24no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—22no—
998C23—22no—
999C23—24no—
1000C23—22no—
1001C23—22no—
1002C23—24no—
1003C23—22no—
1004C23—22no—
1005C23—24no—
1006C23—24no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—22no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—22no—
1028C23—22no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—432no—
1034C23—432no—
1035C23—416no—
1036C23—432no—
1037C23—416no—
1038C23—416no—
1039C23—416no—
1040C23—432no—
1041C23—416no—
1042C23—416no—
1043C23—432no—
1044C23—416no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—41no—
1051C23—42no—
1052C23—42no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—42no—
1061C23—41no—
1062C23—42no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—416no—
1076C23—416no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—41no—
1082C23—41no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—41no—
1088C23—41no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—41no—
1101C23—42no—
1102C23—41no—
1103C23—42no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—41no—
1108C23—42no—
1109C23—42no—
1110C23—41no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—42no—
1116C23—42no—
1117C23—42no—
1118C23—42no—
1119C23—42no—
1120C23—42no—
1121C23—42no—
1122C23—42no—
1123C23—88no—
1124C23—816no—
1125C23—88no—
1126C23—816no—
1127C23—88no—
1128C23—88no—
1129C23—816no—
1130C23—88no—
1131C23—88no—
1132C23—816no—
1133C23—88no—
1134C23—816no—
1135C23—88no—
1136C23—88no—
1137C23—816no—
1138C23—88no—
1139C23—88no—
1140C23—816no—
1141C23C2×C4×D414yes—
1142C23C2×C4×D414yes—
1143C23#51814yes—
1144C23#51818yes—
1145C23#51814yes—
1146C23#56014yes—
1147C23#56018yes—
1148C23H(3,𝔽4)14yes—
1149C23C24×C411yescharacteristic
1150C23C23×D411yescharacteristic
1151C23C22×#4111yescharacteristic
1152C23C2×H(5,𝔽2)11yescharacteristic
1153C23C2×H(5,𝔽2)11yescharacteristic
1154C23C2×H(5,𝔽2)11yescharacteristic
1155C23C2×H(5,𝔽2)11yescharacteristic
1156C23C2×H(5,𝔽2)12yes—
1157C23C2×H(5,𝔽2)12yes—
1158C23C2×H(5,𝔽2)12yes—
1159C23#58512yes—
1160D4—416no—
1161D4—416no—
1162D4—416no—
1163D4—416no—
1164D4—432no—
1165D4—432no—
1166D4—816no—
1167D4—816no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—24no—
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—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—416no—
1196C2×C4—432no—
1197C2×C4—416no—
1198C2×C4—432no—
1199C2×C4—416no—
1200C2×C4—416no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—41no—
1208C2×C4—41no—
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—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—42no—
1263C2×C4—42no—
1264C2×C4—816no—
1265C2×C4C2×C4×D414yes—
1266C22—24no—
1267C22—24no—
1268C22—24no—
1269C22—28no—
1270C22—24no—
1271C22—24no—
1272C22—24no—
1273C22—28no—
1274C22—28no—
1275C22—28no—
1276C22—24no—
1277C22—24no—
1278C22—24no—
1279C22—28no—
1280C22—28no—
1281C22—28no—
1282C22—464no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—44no—
1305C22—44no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22—42no—
1311C22—44no—
1312C22—44no—
1313C22—42no—
1314C22—42no—
1315C22—44no—
1316C22—44no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22—44no—
1322C22—832no—
1323C22—832no—
1324C22—81no—
1325C22—82no—
1326C22—81no—
1327C22—82no—
1328C22—82no—
1329C22—82no—
1330C22—82no—
1331C22—82no—
1332C22—81no—
1333C22—81no—
1334C22—82no—
1335C22—82no—
1336C22—82no—
1337C22—82no—
1338C22#237518yescomplemented
1339C22C22×C4×D411yescharacteristic
1340C22C2×#51811yescharacteristic
1341C22C2×#51812yes—
1342C22C2×#51811yescharacteristic
1343C22C4×H(5,𝔽2)12yes—
1344C22#348412yes—
1345C22#348411yescharacteristic
1346C22#348411yescharacteristic
1347C22#348812yes—
1348C22#349011yescharacteristic
1349C22#349011yescharacteristic
1350C22#351312yes—
1351C22#351912yes—
1352C22C2×#56012yes—
1353C22C2×#56011yescharacteristic
1354C22C2×H(3,𝔽4)11yescharacteristic
1355C22#353211yescharacteristic
1356C22#353212yes—
1357C22#353311yescharacteristic
1358C22#353412yes—
1359C22#353412yes—
1360C22#353712yes—
1361C22#354212yes—
1362C4—24no—
1363C4—44no—
1364C4—44no—
1365C4—44no—
1366C4—44no—
1367C4—42no—
1368C4—44no—
1369C4—44no—
1370C4—82no—
1371C4—82no—
1372C4—82no—
1373C4—82no—
1374C4—82no—
1375C2—28no—
1376C2—44no—
1377C2—44no—
1378C2—44no—
1379C2—82no—
1380C2—84no—
1381C2#3419811yescharacteristic
1382C2#3429012yes—
1383C2C2×#237511yescharacteristic
1384C2#3440711yescharacteristic
1385C2#3446812yes—
1386C2#4543911yescharacteristic
1387C2#4544412yes—
1388C2#4545511yescharacteristic
1389C2#4556312yes—
1390C2#4556811yescharacteristic
1391C2#4572711yescharacteristic
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×#2375C2semidirect
3. C22×#386C2semidirect
4. #14694C2semidirect
5. #14621C2semidirect
6. #14521C2semidirect
7. #14520C2semidirect
8. #14520C2semidirect
9. #14513C2semidirect
10. #14427C2semidirect
11. #14357C2semidirect
12. #14357C2semidirect
13. #14140C2semidirect
14. #13999C2semidirect
15. #13995C2semidirect
16. #13971C2semidirect
17. #13902C2semidirect
18. #13867C2semidirect
19. #13832C2semidirect
22. C25×C4C22semidirect
27. C23×C22⋊C4C22semidirect
28. #2403C4semidirect
34. C2×#390C22semidirect
35. C2×#390C22semidirect
36. C2×#390C22semidirect
37. C2×#390C22semidirect
38. C2×#388C22semidirect
39. C2×#388C22semidirect
40. C2×#388C22semidirect
41. C2×#388C22semidirect
53. C2×#386C22semidirect
54. C2×#386C22semidirect
55. C2×#386C22semidirect
56. C2×#386C22semidirect
57. C2×#386C22semidirect
58. C2×#386C22semidirect
59. C2×#386C22semidirect
60. C2×#385C22semidirect
61. C2×#380C22semidirect
64. C2×#379C22semidirect
65. C2×#379C22semidirect
66. C2×#379C22semidirect
67. C2×C4×C22⋊C4C22semidirect
68. C2×C4×C22⋊C4C22semidirect
69. C22×#95C22semidirect
70. #1443C22semidirect
71. #1443C22semidirect
72. #1442C22semidirect
73. #1442C22semidirect
74. #1440C22semidirect
75. #1440C22semidirect
76. #1440C22semidirect
77. #1440C22semidirect
78. #1439C22semidirect
79. #1439C22semidirect
80. #1439C22semidirect
81. #1439C22semidirect
82. #1439C22semidirect
83. #1439C22semidirect
85. #1438C22semidirect
86. #1438C22semidirect
87. #1438C22semidirect
88. #1438C22semidirect
89. #1438C22semidirect
90. #1438C22semidirect
91. #1438C22semidirect
92. #1437C22semidirect
93. #1437C22semidirect
94. #1437C22semidirect
95. #1437C22semidirect
96. #1437C22semidirect
97. #1437C22semidirect
98. #1436C22semidirect
99. #1436C22semidirect
100. #1434C22semidirect
101. #1434C22semidirect
102. C22⋊#95C22semidirect
103. C22⋊#95C22semidirect
104. C22⋊#95C22semidirect
105. C22⋊#95C22semidirect
106. C22⋊#95C22semidirect
107. C22⋊#95C22semidirect
108. C22⋊#95C22semidirect
109. C22⋊#95C22semidirect
124. C23×D4C2×C4semidirect
152. C2×#120C2×C4semidirect
153. C2×#120C2×C4semidirect
201. #392C2×C4semidirect
202. #392C2×C4semidirect
226. #386C2×C4semidirect
227. #386C2×C4semidirect
228. #386C2×C4semidirect
229. #386D4semidirect
236. #379C2×C4semidirect
300. C25C22×C4semidirect
372. C22×D4C22×C4semidirect
421. C23×C4C22×C4semidirect
422. C23×C4C2×D4semidirect
545. C2×C22⋊C4C22×C4semidirect
546. C2×C22⋊C4C22×C4semidirect
547. C2×C22⋊C4C22×C4semidirect
548. C2×C22⋊C4C22×C4semidirect
549. C2×C22⋊C4C22×C4semidirect
551. C2×C22⋊C4C2×D4semidirect
589. #95C22×C4semidirect
590. #95C22×C4semidirect
591. #95C2×D4semidirect
1338. C22#2375semidirect

Maximal subgroups

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

subgroupindex
C2×#24032
C2×#23752
C22×#3862
#146942
#146212
#145212
#145202
#145132
#144272
#143572
#141402
#139992
#139952
#139712
#139022
#138672
#138322