Finite Group Databasebeta

← #532452

Subgroups — #532452

Order 512.

7278 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2403C211yesmaximal, characteristic
2C2×#2358C212yesmaximal, complemented
3C2×D4×C22⋊C4C212yesmaximal, complemented
4C22×#386C212yesmaximal, complemented
5#14572C211yesmaximal, characteristic, complemented
6#14521C211yesmaximal, characteristic, complemented
7#14519C212yesmaximal, complemented
8#14228C211yesmaximal, characteristic, complemented
9#14207C212yesmaximal, complemented
10#14175C211yesmaximal, characteristic, complemented
11#14140C212yesmaximal, complemented
12#14134C212yesmaximal, complemented
13#14127C211yesmaximal, characteristic, complemented
14#13999C212yesmaximal, complemented
15#13995C212yesmaximal, complemented
16#13975C212yesmaximal, complemented
17#13967C212yesmaximal, complemented
18#13813C212yesmaximal, complemented
19C4×#379C211yesmaximal, characteristic, complemented
20C24×D4C2212yes—
21C25×C4C2211yescharacteristic
22C22×#120C2212yes—
23C22×#120C2212yes—
24C22×C4×D4C2212yes—
25C22×C4×D4C2212yes—
26C22×C4×D4C2211yescharacteristic, complemented
27C23×C22⋊C4C2212yes—
28C23×C22⋊C4C2212yescomplemented
29C23×C22⋊C4C2212yescomplemented
30C23×C22⋊C4C2212yescomplemented
31#2403C4116yescomplemented
32C2×#392C2211yescharacteristic
33C2×#392C2212yes—
34C2×#392C2211yescharacteristic
35#2358—216no—
36D4×C22⋊C4—216no—
37C2×#390C2212yescomplemented
38C2×#390C2212yescomplemented
39C2×#390C2212yescomplemented
40C2×#390C2211yescharacteristic, complemented
41C2×#388C2212yescomplemented
42C2×#388C2212yescomplemented
43C2×#386—216no—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#386C2212yescomplemented
53C2×#386C2212yescomplemented
54C2×#386C2212yescomplemented
55C2×#386C2212yescomplemented
56C2×#386C2212yescomplemented
57C2×#386C2212yescomplemented
58C2×#386C2212yescomplemented
59C2×#386C2212yescomplemented
60C2×#386C2212yescomplemented
61C2×#385C2212yescomplemented
62C2×#385C2212yescomplemented
63C2×#385C2212yescomplemented
64C2×#380C2212yescomplemented
65C2×#379C2211yescharacteristic
66C2×#379C2211yescharacteristic
67C2×#379C2212yescomplemented
68C2×C4×C22⋊C4C2212yescomplemented
69C2×C4×C22⋊C4C2212yescomplemented
70C2×C4×C22⋊C4C2212yescomplemented
71C2×C4×C22⋊C4C2211yescharacteristic, complemented
72C2×C4×C22⋊C4C2211yescharacteristic, complemented
73C2×C4×C22⋊C4C2212yescomplemented
74C22×#95C2212yescomplemented
75C22×#95C2212yescomplemented
76#1444C2211yescharacteristic, complemented
77#1443C2212yescomplemented
78#1442C2211yescharacteristic, complemented
79#1442C2212yescomplemented
80#1440C2212yescomplemented
81#1440C2212yescomplemented
82#1439C2211yescharacteristic, complemented
83#1439C2212yescomplemented
84#1439C2211yescharacteristic, complemented
85#1439C2212yescomplemented
86#1439C2212yescomplemented
87#1439C2212yescomplemented
88#1439C2212yescomplemented
89#1438C2211yescharacteristic, complemented
90#1438C2212yescomplemented
91#1438C2211yescharacteristic, complemented
92#1438C2212yescomplemented
93#1437C2212yescomplemented
94#1437C2212yescomplemented
95#1437C2212yescomplemented
96#1437C2212yescomplemented
97#1436C2212yescomplemented
98#1436C2212yescomplemented
99#1436C2212yescomplemented
100#1434C2212yescomplemented
101#1434C2211yescharacteristic, complemented
102C22⋊#95C2212yescomplemented
103C22⋊#95C2212yescomplemented
104C22⋊#95C2212yescomplemented
105C22⋊#95C2212yescomplemented
106C22⋊#95C2212yescomplemented
107C22⋊#95C2212yescomplemented
108C22⋊#95C2211yescharacteristic, complemented
109C22⋊#95C2211yescharacteristic, complemented
110C4×#95C2211yescharacteristic, complemented
111C26C2312yes—
112C26C2311yescharacteristic
113C23×D4—28no—
114C23×D4—28no—
115C23×D4—28no—
116C23×D4—28no—
117C23×D4—44no—
118C23×D4—44no—
119C23×D4C2×C4116yescomplemented
120C23×D4C2312yes—
121C23×D4C2312yes—
122C23×D4C2312yes—
123C23×D4C2311yescharacteristic
124C23×D4C2312yes—
125C23×D4C2312yes—
126C23×D4C2311yescharacteristic
127C24×C4—24no—
128C24×C4—28no—
129C24×C4—42no—
130C24×C4—42no—
131C24×C4—44no—
132C24×C4C2312yes—
133C24×C4C2311yescharacteristic
134C24×C4C2312yes—
135C24×C4C2312yes—
136C24×C4C2312yes—
137C24×C4C2312yes—
138C24×C4C2311yescharacteristic
139C24×C4C2312yes—
140C24×C4C2312yes—
141C2×#120—28no—
142C2×#120—28no—
143C2×#120—44no—
144C2×#120—44no—
145C2×#120C2×C4116yescomplemented
146C2×#120C2×C4116yescomplemented
147C2×C4×D4—28no—
148C2×C4×D4—28no—
149C2×C4×D4—28no—
150C2×C4×D4—28no—
151C2×C4×D4—28no—
152C2×C4×D4—42no—
153C2×C4×D4—44no—
154C2×C4×D4—44no—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2311yescharacteristic
160C22×C22⋊C4—28no—
161C22×C22⋊C4—28no—
162C22×C22⋊C4—28no—
163C22×C22⋊C4—28no—
164C22×C22⋊C4—28no—
165C22×C22⋊C4—28no—
166C22×C22⋊C4—28no—
167C22×C22⋊C4—44no—
168C22×C22⋊C4—44no—
169C22×C22⋊C4—44no—
170C22×C22⋊C4—44no—
171C22×C22⋊C4—44no—
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⋊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⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C42C2311yescharacteristic
203C22×C42C2312yes—
204C22×C42C2312yes—
205C22×C42C2311yescharacteristic
206C22×C42C2312yes—
207#392C2×C418yescomplemented
208#392C2×C4116yescomplemented
209#392C2×C418yescomplemented
210#390—28no—
211#390—28no—
212#390—28no—
213#390—42no—
214#388—28no—
215#388—28no—
216#386—28no—
217#386—28no—
218#386—28no—
219#386—28no—
220#386—28no—
221#386—28no—
222#386—28no—
223#386—28no—
224#386—28no—
225#386—28no—
226#386—28no—
227#386—28no—
228#386—28no—
229#386—44no—
230#386C2×C4116yescomplemented
231#386C2×C4116yescomplemented
232#386D4116yescomplemented
233#385—28no—
234#385—28no—
235#385—44no—
236#380—28no—
237#379—28no—
238#379C2×C418yescomplemented
239#379D418yescomplemented
240C4×C22⋊C4—28no—
241C4×C22⋊C4—28no—
242C4×C22⋊C4—28no—
243C4×C22⋊C4—42no—
244C4×C22⋊C4—42no—
245C4×C22⋊C4—44no—
246C2×#95—28no—
247C2×#95—28no—
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×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2311yescharacteristic
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2311yescharacteristic
271C2×#95C2312yes—
272C2×#95C2311yescharacteristic
273C2×#95C2312yes—
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2312yes—
277C25—24no—
278C25—24no—
279C25—24no—
280C25—24no—
281C25—24no—
282C25—24no—
283C25—24no—
284C25—24no—
285C25—24no—
286C25—24no—
287C25—24no—
288C25—24no—
289C25—41no—
290C25—41no—
291C25—41no—
292C25—41no—
293C25—42no—
294C25—42no—
295C25—42no—
296C25—42no—
297C25—42no—
298C25—42no—
299C25C22×C418yes—
300C25C22×C414yes—
301C25C2×D414yes—
302C25#4114yes—
303C25C2412yes—
304C25C2412yes—
305C25C2411yescharacteristic
306C25C2412yes—
307C22×D4—24no—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—264no—
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—24no—
317C22×D4—24no—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—264no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—41no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4—42no—
335C22×D4—42no—
336C22×D4—41no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4—41no—
342C22×D4—42no—
343C22×D4—42no—
344C22×D4—41no—
345C22×D4—432no—
346C22×D4—432no—
347C22×D4—432no—
348C22×D4—432no—
349C22×D4—432no—
350C22×D4C22×C418yes—
351C22×D4C22×C418yes—
352C22×D4C22×C418yes—
353C22×D4C22×C418yes—
354C22×D4C22×C414yescomplemented
355C22×D4C22×C418yescomplemented
356C22×D4C22×C414yescomplemented
357C22×D4C2×D418yes—
358C22×D4#4118yes—
359C23×C4—24no—
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—22no—
372C23×C4—22no—
373C23×C4—24no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—24no—
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—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—41no—
399C23×C4—41no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—416no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—432no—
418C23×C4—432no—
419C23×C4—416no—
420C23×C4—416no—
421C23×C4C22×C418yes—
422C23×C4C2×D418yes—
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2412yes—
432C23×C4C2411yescharacteristic
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437C23×C4C2411yescharacteristic
438#120—264no—
439#120—432no—
440C4×D4—416no—
441C4×D4—432no—
442C4×D4—432no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—41no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—41no—
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—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—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—24no—
501C2×C22⋊C4—432no—
502C2×C22⋊C4—432no—
503C2×C22⋊C4—432no—
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—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—41no—
518C2×C22⋊C4—41no—
519C2×C22⋊C4—41no—
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—41no—
527C2×C22⋊C4—41no—
528C2×C22⋊C4—41no—
529C2×C22⋊C4—41no—
530C2×C22⋊C4—432no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4C22×C418yes—
536C2×C22⋊C4C22×C418yes—
537C2×C22⋊C4C22×C414yes—
538C2×C22⋊C4C22×C414yes—
539C2×C22⋊C4C22×C418yescomplemented
540C2×C22⋊C4C22×C418yescomplemented
541C2×C22⋊C4C22×C418yescomplemented
542C2×C22⋊C4C22×C418yescomplemented
543C2×C22⋊C4C2×D418yes—
544C2×C22⋊C4C2×D418yes—
545C2×C22⋊C4C2×D418yes—
546C2×C22⋊C4C2×D414yes—
547C2×C22⋊C4C2×D414yes—
548C2×C22⋊C4C2×D418yescomplemented
549C2×C22⋊C4C2×D418yescomplemented
550C2×C42—24no—
551C2×C42—24no—
552C2×C42—24no—
553C2×C42—24no—
554C2×C42—24no—
555C2×C42—22no—
556C2×C42—24no—
557C2×C42—22no—
558C2×C42—42no—
559C2×C42—42no—
560C2×C42—42no—
561C2×C42—42no—
562C2×C42—42no—
563#95—24no—
564#95—24no—
565#95—24no—
566#95—24no—
567#95—24no—
568#95—24no—
569#95—24no—
570#95—24no—
571#95—24no—
572#95—24no—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—41no—
579#95—41no—
580#95—41no—
581#95—41no—
582#95—42no—
583#95—42no—
584#95—42no—
585#95—42no—
586#95—42no—
587#95C22×C414yescomplemented
588#95C22×C418yescomplemented
589#95C22×C414yescomplemented
590#95C2×D418yescomplemented
591#95C2×D418yescomplemented
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—216no—
601C24—216no—
602C24—216no—
603C24—216no—
604C24—216no—
605C24—216no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—21no—
616C24—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—21no—
623C24—21no—
624C24—22no—
625C24—22no—
626C24—216no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—216no—
642C24—216no—
643C24—216no—
644C24—44no—
645C24—44no—
646C24—44no—
647C24—44no—
648C24—44no—
649C24—44no—
650C24—48no—
651C24—48no—
652C24—48no—
653C24—44no—
654C24—48no—
655C24—44no—
656C24—48no—
657C24—44no—
658C24—48no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—44no—
663C24—48no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24—84no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24C4×D4116yescomplemented
692C24C23×C414yes—
693C24C23×C412yes—
694C24C23×C414yes—
695C24C23×C414yes—
696C24C22×D412yes—
697C24C22×D414yes—
698C24C22×D414yes—
699C24C22×D414yes—
700C24C2×#4114yes—
701C24C2×#4112yes—
702C24C2×#4114yes—
703C24C2×#4114yes—
704C24H(5,𝔽2)14yes—
705C24H(5,𝔽2)14yes—
706C24C2511yescharacteristic
707C2×D4—216no—
708C2×D4—216no—
709C2×D4—216no—
710C2×D4—216no—
711C2×D4—216no—
712C2×D4—216no—
713C2×D4—216no—
714C2×D4—216no—
715C2×D4—216no—
716C2×D4—216no—
717C2×D4—216no—
718C2×D4—216no—
719C2×D4—216no—
720C2×D4—216no—
721C2×D4—216no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—44no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—44no—
733C2×D4—4256no—
734C2×D4—44no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—84no—
746C2×D4—84no—
747C2×D4—84no—
748C2×D4—84no—
749C2×D4—82no—
750C2×D4—84no—
751C2×D4—82no—
752C2×D4C4×D4132yescomplemented
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—216no—
761C22×C4—28no—
762C22×C4—216no—
763C22×C4—216no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
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—21no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
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—21no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—216no—
821C22×C4—216no—
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—48no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—44no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—44no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—44no—
870C22×C4—4128no—
871C22×C4—44no—
872C22×C4—48no—
873C22×C4—44no—
874C22×C4—48no—
875C22×C4—48no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4—84no—
888C22×C4—84no—
889C22×C4—84no—
890C22×C4C23×C414yes—
891C22×C4C23×C412yes—
892C22×C4C23×C414yes—
893C22×C4C23×C412yes—
894C22×C4C23×C414yes—
895C22×C4C22×D414yes—
896C22×C4C22×D414yes—
897C22×C4C22×D412yes—
898C22×C4C22×D414yes—
899C22×C4C22×D412yes—
900C22×C4C22×D414yes—
901C22×C4C22×D414yes—
902C22×C4C22×D414yes—
903C22×C4C2×#4114yes—
904C22×C4H(5,𝔽2)12yes—
905C22×C4H(5,𝔽2)12yes—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—44no—
909C4⋊C4—84no—
910C4⋊C4—82no—
911C22⋊C4—216no—
912C22⋊C4—216no—
913C22⋊C4—216no—
914C22⋊C4—216no—
915C22⋊C4—216no—
916C22⋊C4—216no—
917C22⋊C4—216no—
918C22⋊C4—216no—
919C22⋊C4—48no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C42—48no—
942C42—48no—
943C42—44no—
944C42—84no—
945C42—82no—
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—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—264no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—22no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—416no—
1013C23—416no—
1014C23—416no—
1015C23—416no—
1016C23—432no—
1017C23—416no—
1018C23—416no—
1019C23—416no—
1020C23—432no—
1021C23—432no—
1022C23—432no—
1023C23—432no—
1024C23—432no—
1025C23—42no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—41no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—41no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—41no—
1051C23—432no—
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—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—816no—
1081C23—816no—
1082C23—816no—
1083C23—816no—
1084C23—816no—
1085C23—816no—
1086C23—816no—
1087C23—816no—
1088C23—816no—
1089C23—816no—
1090C23—816no—
1091C23C2×C4×D414yes—
1092C23C2×C4×D418yes—
1093C23C2×C4×D418yes—
1094C23C2×C4×D418yes—
1095C23#51818yes—
1096C23D4218yes—
1097C23#54618yes—
1098C23#54618yes—
1099C23#55118yes—
1100C23C24×C411yescharacteristic
1101C23C23×D411yescharacteristic
1102C23C23×D412yes—
1103C23C22×#4111yescharacteristic
1104C23C22×#4112yes—
1105C23C2×H(5,𝔽2)12yes—
1106C23C2×H(5,𝔽2)12yes—
1107C23C2×H(5,𝔽2)11yescharacteristic
1108C23C2×H(5,𝔽2)11yescharacteristic
1109C23#58511yescharacteristic
1110C23#58511yescharacteristic
1111D4—264no—
1112D4—432no—
1113D4—416no—
1114D4—432no—
1115D4—432no—
1116D4—816no—
1117D4—88no—
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—22no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—432no—
1157C2×C4—432no—
1158C2×C4—416no—
1159C2×C4—432no—
1160C2×C4—416no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
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—41no—
1175C2×C4—41no—
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—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—41no—
1198C2×C4—41no—
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—816no—
1215C2×C4—816no—
1216C2×C4—816no—
1217C2×C4—816no—
1218C2×C4C2×C4×D418yes—
1219C2×C4D4214yes—
1220C22—28no—
1221C22—28no—
1222C22—28no—
1223C22—28no—
1224C22—28no—
1225C22—28no—
1226C22—28no—
1227C22—28no—
1228C22—28no—
1229C22—28no—
1230C22—28no—
1231C22—28no—
1232C22—28no—
1233C22—28no—
1234C22—28no—
1235C22—28no—
1236C22—28no—
1237C22—24no—
1238C22—28no—
1239C22—464no—
1240C22—44no—
1241C22—42no—
1242C22—42no—
1243C22—44no—
1244C22—44no—
1245C22—42no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—42no—
1250C22—44no—
1251C22—42no—
1252C22—44no—
1253C22—42no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—864no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—82no—
1274C22—82no—
1275C22—82no—
1276C22—82no—
1277C22#2358116yescomplemented
1278C22C22×C4×D411yescharacteristic
1279C22C22×C4×D412yes—
1280C22C2×#51812yes—
1281C22C4×H(5,𝔽2)11yescharacteristic
1282C22C4×H(5,𝔽2)11yescharacteristic
1283C22C2×D4212yes—
1284C22C2×D4211yescharacteristic
1285C22C2×#54612yes—
1286C22C2×#54612yes—
1287C22D4×#4112yes—
1288C22C2×#55112yes—
1289C22#348111yescharacteristic
1290C22#348412yes—
1291C22#348812yes—
1292C22#349011yescharacteristic
1293C22#349111yescharacteristic
1294C22#349611yescharacteristic
1295C22#349611yescharacteristic
1296C22#351312yes—
1297C22#351912yes—
1298C22#353211yescharacteristic
1299C22#353412yes—
1300C22#353711yescharacteristic
1301C4—28no—
1302C4—24no—
1303C4—44no—
1304C4—42no—
1305C4—44no—
1306C4—42no—
1307C4—44no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—44no—
1312C4—44no—
1313C4—44no—
1314C4—82no—
1315C4—82no—
1316C2—216no—
1317C2—44no—
1318C2—48no—
1319C2—84no—
1320C2C2×#235812yes—
1321C2C4×D4211yescharacteristic
1322C2#3427311yescharacteristic
1323C2#3429012yes—
1324C2#3446811yescharacteristic
1325C2#5899111yescharacteristic
1326C2#5899711yescharacteristic
1327C2#5901112yes—
1328C2#5912312yes—
1329C2#5926711yescharacteristic
1330C2#5980311yescharacteristic
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×#2358C2semidirect
3. C2×D4×C22⋊C4C2semidirect
4. C22×#386C2semidirect
5. #14572C2semidirect
6. #14521C2semidirect
7. #14519C2semidirect
8. #14228C2semidirect
9. #14207C2semidirect
10. #14175C2semidirect
11. #14140C2semidirect
12. #14134C2semidirect
13. #14127C2semidirect
14. #13999C2semidirect
15. #13995C2semidirect
16. #13975C2semidirect
17. #13967C2semidirect
18. #13813C2semidirect
19. C4×#379C2semidirect
26. C22×C4×D4C22semidirect
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×#388C22semidirect
42. C2×#388C22semidirect
52. C2×#386C22semidirect
53. C2×#386C22semidirect
54. C2×#386C22semidirect
55. C2×#386C22semidirect
56. C2×#386C22semidirect
57. C2×#386C22semidirect
58. C2×#386C22semidirect
59. C2×#386C22semidirect
60. C2×#386C22semidirect
61. C2×#385C22semidirect
62. C2×#385C22semidirect
63. C2×#385C22semidirect
64. C2×#380C22semidirect
67. C2×#379C22semidirect
68. C2×C4×C22⋊C4C22semidirect
69. C2×C4×C22⋊C4C22semidirect
70. C2×C4×C22⋊C4C22semidirect
71. C2×C4×C22⋊C4C22semidirect
72. C2×C4×C22⋊C4C22semidirect
73. C2×C4×C22⋊C4C22semidirect
74. C22×#95C22semidirect
75. C22×#95C22semidirect
76. #1444C22semidirect
77. #1443C22semidirect
78. #1442C22semidirect
79. #1442C22semidirect
80. #1440C22semidirect
81. #1440C22semidirect
82. #1439C22semidirect
83. #1439C22semidirect
84. #1439C22semidirect
85. #1439C22semidirect
86. #1439C22semidirect
87. #1439C22semidirect
88. #1439C22semidirect
89. #1438C22semidirect
90. #1438C22semidirect
91. #1438C22semidirect
92. #1438C22semidirect
93. #1437C22semidirect
94. #1437C22semidirect
95. #1437C22semidirect
96. #1437C22semidirect
97. #1436C22semidirect
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
110. C4×#95C22semidirect
119. C23×D4C2×C4semidirect
145. C2×#120C2×C4semidirect
146. C2×#120C2×C4semidirect
207. #392C2×C4semidirect
208. #392C2×C4semidirect
209. #392C2×C4semidirect
230. #386C2×C4semidirect
231. #386C2×C4semidirect
232. #386D4semidirect
238. #379C2×C4semidirect
239. #379D4semidirect
354. C22×D4C22×C4semidirect
355. C22×D4C22×C4semidirect
356. C22×D4C22×C4semidirect
539. C2×C22⋊C4C22×C4semidirect
540. C2×C22⋊C4C22×C4semidirect
541. C2×C22⋊C4C22×C4semidirect
542. C2×C22⋊C4C22×C4semidirect
548. C2×C22⋊C4C2×D4semidirect
549. C2×C22⋊C4C2×D4semidirect
587. #95C22×C4semidirect
588. #95C22×C4semidirect
589. #95C22×C4semidirect
590. #95C2×D4semidirect
591. #95C2×D4semidirect
691. C24C4×D4semidirect
752. C2×D4C4×D4semidirect
1277. C22#2358semidirect

Maximal subgroups

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

subgroupindex
C2×#24032
C2×#23582
C2×D4×C22⋊C42
C22×#3862
#145722
#145212
#145192
#142282
#142072
#141752
#141402
#141342
#141272
#139992
#139952
#139752
#139672
#138132
C4×#3792