Finite Group Databasebeta

← #557236

Subgroups — #557236

Order 512.

3970 conjugacy classes of subgroups.

The subgroup lattice has 1397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2847C211yesmaximal, characteristic
2#14680C211yesmaximal, characteristic, complemented
3#14666C212yesmaximal, complemented
4#14516C212yesmaximal, complemented
5#14513C212yesmaximal, complemented
6#14428C212yesmaximal, complemented
7#14427C212yesmaximal, complemented
8#14358C212yesmaximal, complemented
9#14357C212yesmaximal, complemented
10#13998C211yesmaximal, characteristic, complemented
11#13998C211yesmaximal, characteristic, complemented
12#13998C211yesmaximal, characteristic, complemented
13#13994C211yesmaximal, characteristic, complemented
14#13993C211yesmaximal, characteristic, complemented
15#13993C211yesmaximal, characteristic, complemented
16#13974C211yesmaximal, characteristic, complemented
17#13973C211yesmaximal, characteristic, complemented
18#13973C211yesmaximal, characteristic, complemented
19#13970C211yesmaximal, characteristic, complemented
20#13970C211yesmaximal, characteristic, complemented
21#13970C211yesmaximal, characteristic, complemented
22#13832C212yesmaximal, complemented
23C4×#379C211yesmaximal, characteristic, complemented
24C25×C4C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#120C2212yes—
29C22×C4×D4C2211yescharacteristic, complemented
30#2847C4116yescomplemented
31C2×#390C2212yes—
32C2×#390C2212yes—
33C2×#390C2212yes—
34C2×#390C2211yescharacteristic, complemented
35C2×#390C2211yescharacteristic, complemented
36C2×#390C2211yescharacteristic, complemented
37C2×#389C2211yescharacteristic, complemented
38C2×#389C2211yescharacteristic, complemented
39C2×#389C2211yescharacteristic, complemented
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#379C2211yescharacteristic
58C2×#379C2211yescharacteristic
59C2×#379C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic, complemented
61C2×C4×C4⋊C4C2211yescharacteristic, complemented
62C2×C4×C4⋊C4C2211yescharacteristic, complemented
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69#1443C2212yescomplemented
70#1443C2212yescomplemented
71#1443C2212yescomplemented
72#1442C2212yescomplemented
73#1442C2212yescomplemented
74#1442C2212yescomplemented
75#1440C2212yes—
76#1440C2212yes—
77#1440C2212yescomplemented
78#1440C2212yescomplemented
79#1440C2212yescomplemented
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yescomplemented
85#1439C2212yescomplemented
86#1439C2212yescomplemented
87#1438C2212yes—
88#1438C2212yes—
89#1438C2212yes—
90#1438C2212yes—
91#1438C2212yes—
92#1438C2212yes—
93#1437C2212yes—
94#1437C2212yes—
95#1437C2212yes—
96#1437C2212yes—
97#1437C2212yescomplemented
98#1437C2212yescomplemented
99#1437C2212yescomplemented
100#1436C2212yescomplemented
101#1436C2212yescomplemented
102#1436C2212yescomplemented
103C4⋊#95C2211yescharacteristic, complemented
104C4⋊#95C2211yescharacteristic, complemented
105C4⋊#95C2211yescharacteristic, complemented
106C4⋊#95C2211yescharacteristic, complemented
107C4⋊#95C2211yescharacteristic, complemented
108C4⋊#95C2211yescharacteristic, complemented
109#1434C2212yescomplemented
110#1434C2212yescomplemented
111#1434C2212yescomplemented
112C22⋊#95C2211yescharacteristic
113C22⋊#95C2212yes—
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2212yes—
116C22⋊#95C2212yes—
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C26C2311yescharacteristic
125C23×D4C2311yescharacteristic
126C23×D4C2312yes—
127C23×D4C2312yes—
128C23×D4C2312yes—
129C24×C4—42no—
130C24×C4—42no—
131C24×C4—42no—
132C24×C4—42no—
133C24×C4—42no—
134C24×C4—42no—
135C24×C4C2×C418yescomplemented
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2312yes—
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C2×#121—42no—
144C2×#121—42no—
145C2×#121—42no—
146C2×#121—42no—
147C2×#121—42no—
148C2×#121—42no—
149C2×#121C2×C418yes—
150C2×#121C2×C418yes—
151C2×#121C2×C418yes—
152C2×#120—44no—
153C2×#120—44no—
154C2×#120C2×C4116yescomplemented
155C2×C4×D4—42no—
156C2×C4×D4—42no—
157C2×C4×D4—42no—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C22⋊C4C2311yescharacteristic
169C22×C22⋊C4C2311yescharacteristic
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2311yescharacteristic
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2311yescharacteristic
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C42C2311yescharacteristic
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
202C22×C42C2311yescharacteristic
203C22×C42C2312yes—
204C22×C42C2312yes—
205C22×C42C2312yes—
206#390—28no—
207#390—42no—
208#390—42no—
209#390—42no—
210#390—44no—
211#390—44no—
212#389—42no—
213#389—42no—
214#389—42no—
215#388—44no—
216#388—44no—
217#386—28no—
218#386—44no—
219#386—44no—
220#386C2×C4116yescomplemented
221#386C2×C4116yescomplemented
222#386C2×C4116yescomplemented
223#380—42no—
224#380—42no—
225#380—42no—
226#380—42no—
227#380—42no—
228#380—42no—
229#380C2×C418yescomplemented
230#380C2×C418yescomplemented
231#380C2×C418yescomplemented
232#379—24no—
233#379—24no—
234#379—44no—
235C4×C4⋊C4—42no—
236C4×C4⋊C4—42no—
237C4×C4⋊C4—42no—
238C4×C22⋊C4—42no—
239C4×C22⋊C4—42no—
240C4×C22⋊C4—42no—
241C4×C22⋊C4—42no—
242C4×C22⋊C4—42no—
243C4×C22⋊C4—42no—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2311yescharacteristic
247C2×#95C2311yescharacteristic
248C2×#95C2311yescharacteristic
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2311yescharacteristic
253C2×#95C2311yescharacteristic
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2311yescharacteristic
257C2×#95C2311yescharacteristic
258C2×#95C2312yes—
259C2×#95C2311yescharacteristic
260C2×#95C2311yescharacteristic
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C25—22no—
284C25—22no—
285C25—22no—
286C25—22no—
287C25—22no—
288C25—22no—
289C25—41no—
290C25—41no—
291C25—41no—
292C25—41no—
293C25—41no—
294C25—41no—
295C25—41no—
296C25—41no—
297C25C22×C414yes—
298C25C2412yes—
299C25C2411yescharacteristic
300C25C2411yescharacteristic
301C25C2411yescharacteristic
302C22×D4—24no—
303C22×D4—24no—
304C22×D4—24no—
305C22×D4—24no—
306C22×D4—24no—
307C22×D4—24no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—42no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4—42no—
318C22×D4—42no—
319C22×D4—42no—
320C22×D4—42no—
321C22×D4—42no—
322C22×D4—42no—
323C22×D4—42no—
324C22×D4—42no—
325C22×D4—42no—
326C22×D4C22×C414yes—
327C22×D4C22×C418yes—
328C22×D4C22×C418yes—
329C22×D4C22×C418yes—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—24no—
349C23×C4—416no—
350C23×C4—416no—
351C23×C4—416no—
352C23×C4—41no—
353C23×C4—41no—
354C23×C4—41no—
355C23×C4—41no—
356C23×C4—41no—
357C23×C4—41no—
358C23×C4—41no—
359C23×C4—41no—
360C23×C4—41no—
361C23×C4—41no—
362C23×C4—41no—
363C23×C4—41no—
364C23×C4—41no—
365C23×C4—41no—
366C23×C4—41no—
367C23×C4—41no—
368C23×C4—41no—
369C23×C4—41no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4—42no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—416no—
377C23×C4—416no—
378C23×C4—416no—
379C23×C4—416no—
380C23×C4C22×C414yes—
381C23×C4C22×C414yes—
382C23×C4C22×C414yes—
383C23×C4C22×C414yes—
384C23×C4C22×C414yes—
385C23×C4C22×C414yes—
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2412yes—
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405#121—416no—
406#121—416no—
407#121—416no—
408#120—432no—
409C4×D4—416no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—42no—
437C2×C4⋊C4C22×C414yes—
438C2×C4⋊C4C22×C414yes—
439C2×C4⋊C4C22×C414yes—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
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—41no—
470C2×C22⋊C4—41no—
471C2×C22⋊C4—41no—
472C2×C22⋊C4—41no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
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—41no—
489C2×C22⋊C4—41no—
490C2×C22⋊C4—41no—
491C2×C22⋊C4—41no—
492C2×C22⋊C4—41no—
493C2×C22⋊C4—41no—
494C2×C22⋊C4—41no—
495C2×C22⋊C4—41no—
496C2×C22⋊C4—41no—
497C2×C22⋊C4—41no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
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—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⋊C4C22×C418yes—
526C2×C22⋊C4C22×C418yes—
527C2×C22⋊C4C22×C418yes—
528C2×C22⋊C4C22×C418yes—
529C2×C22⋊C4C22×C418yes—
530C2×C22⋊C4C22×C418yes—
531C2×C22⋊C4#4114yes—
532C2×C22⋊C4#4114yes—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—24no—
546C2×C42—42no—
547C2×C42—42no—
548C2×C42—42no—
549C2×C42—42no—
550C2×C42—42no—
551C2×C42—42no—
552C2×C42—42no—
553C2×C42—42no—
554#95—24no—
555#95—24no—
556#95—42no—
557#95—42no—
558#95—41no—
559#95—41no—
560#95—41no—
561#95—41no—
562#95—41no—
563#95—41no—
564#95—41no—
565#95—41no—
566#95—41no—
567#95—41no—
568#95—41no—
569#95—41no—
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#95—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95C22×C418yes—
591#95C22×C418yes—
592#95C22×C418yes—
593C24—21no—
594C24—21no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—28no—
630C24—28no—
631C24—28no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—44no—
647C24—44no—
648C24—44no—
649C24—44no—
650C24—44no—
651C24—44no—
652C24—44no—
653C24—44no—
654C24—44no—
655C24—44no—
656C24—44no—
657C24—44no—
658C24—44no—
659C24—44no—
660C24—44no—
661C24—44no—
662C24—44no—
663C24—44no—
664C24—44no—
665C24—44no—
666C24—44no—
667C24—44no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—44no—
672C24—44no—
673C24—44no—
674C24—44no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24C23×C414yes—
679C24C23×C412yes—
680C24C23×C412yes—
681C24C23×C412yes—
682C24C2×#4112yes—
683C24C2×#4112yes—
684C24H(5,𝔽2)12yes—
685C24H(5,𝔽2)12yes—
686C24H(5,𝔽2)12yes—
687C242−1+412yes—
688C24C2511yescharacteristic
689C2×D4—216no—
690C2×D4—216no—
691C2×D4—216no—
692C2×D4—28no—
693C2×D4—28no—
694C2×D4—28no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—84no—
706C2×D4—84no—
707C2×D4—84no—
708C2×D4—84no—
709C2×D4—84no—
710C2×D4—84no—
711C2×D4—84no—
712C2×D4—84no—
713C2×D4—84no—
714C2×D4—84no—
715C2×D4—84no—
716C2×D4—84no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—22no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
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—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—4128no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—48no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4C23×C414yes—
884C22×C4C23×C414yes—
885C22×C4C23×C414yes—
886C22×C4C23×C412yes—
887C22×C4C23×C412yes—
888C22×C4C23×C412yes—
889C22×C4C23×C412yes—
890C22×C4C2×#4112yes—
891C22×C4C2×#4112yes—
892C22×C4C2×#4112yes—
893C22×C4C2×#4112yes—
894C22×C4H(5,𝔽2)12yes—
895C22×C4H(5,𝔽2)12yes—
896C22×C4H(5,𝔽2)12yes—
897C22×C4H(5,𝔽2)12yes—
898C22×C4H(5,𝔽2)12yes—
899C22×C4H(5,𝔽2)12yes—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—84no—
908C4⋊C4—84no—
909C4⋊C4—84no—
910C22⋊C4—216no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—48no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C42—44no—
942C42—44no—
943C42—44no—
944C42—44no—
945C42—84no—
946C42—84no—
947C42—84no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—416no—
1010C23—416no—
1011C23—416no—
1012C23—416no—
1013C23—416no—
1014C23—416no—
1015C23—416no—
1016C23—416no—
1017C23—416no—
1018C23—416no—
1019C23—416no—
1020C23—416no—
1021C23—416no—
1022C23—416no—
1023C23—416no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
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—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23C4×#4114yes—
1101C23#51814yes—
1102C23#52014yes—
1103C23C24×C411yescharacteristic
1104C23C22×#4111yescharacteristic
1105C23C22×#4111yescharacteristic
1106C23C2×H(5,𝔽2)11yescharacteristic
1107C23C2×H(5,𝔽2)11yescharacteristic
1108C23C2×H(5,𝔽2)11yescharacteristic
1109C23C2×H(5,𝔽2)11yescharacteristic
1110C23C2×H(5,𝔽2)11yescharacteristic
1111C23C2×H(5,𝔽2)11yescharacteristic
1112C23C2×H(5,𝔽2)11yescharacteristic
1113C23C2×H(5,𝔽2)11yescharacteristic
1114C23C2×H(5,𝔽2)11yescharacteristic
1115C23C2×2−1+411yescharacteristic
1116C23#58511yescharacteristic
1117C23#58511yescharacteristic
1118D4—416no—
1119D4—816no—
1120D4—816no—
1121D4—816no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—416no—
1153C2×C4—416no—
1154C2×C4—416no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—416no—
1196C2×C4—416no—
1197C2×C4—416no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—41no—
1229C2×C4—42no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—41no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—41no—
1249C2×C4—42no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—42no—
1254C2×C4—816no—
1255C2×C4#51814yes—
1256C2×C4#51814yes—
1257C2×C4#51814yes—
1258C2×C4#56014yes—
1259C2×C4#56014yes—
1260C2×C4#56014yes—
1261C2×C4H(3,𝔽4)14yes—
1262C22—24no—
1263C22—24no—
1264C22—24no—
1265C22—24no—
1266C22—24no—
1267C22—24no—
1268C22—24no—
1269C22—24no—
1270C22—24no—
1271C22—464no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
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—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—44no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—44no—
1315C22—82no—
1316C22—82no—
1317C22—82no—
1318C22—82no—
1319C22—82no—
1320C22—82no—
1321C22—82no—
1322C22—82no—
1323C22C2×C4×#4111yescharacteristic
1324C22C2×#51811yescharacteristic
1325C22C2×#51811yescharacteristic
1326C22C2×#51811yescharacteristic
1327C22C2×#51811yescharacteristic
1328C22C2×#52011yescharacteristic
1329C22#342811yescharacteristic
1330C22#350511yescharacteristic
1331C22#350511yescharacteristic
1332C22#350611yescharacteristic
1333C22#350611yescharacteristic
1334C22#351911yescharacteristic
1335C22#351911yescharacteristic
1336C22#351911yescharacteristic
1337C22#351911yescharacteristic
1338C22#351911yescharacteristic
1339C22#351911yescharacteristic
1340C22#352011yescharacteristic
1341C22#352011yescharacteristic
1342C22C2×#56011yescharacteristic
1343C22C2×#56011yescharacteristic
1344C22C2×#56011yescharacteristic
1345C22C2×H(3,𝔽4)11yescharacteristic
1346C22#353611yescharacteristic
1347C22#353611yescharacteristic
1348C22#353711yescharacteristic
1349C22#353711yescharacteristic
1350C22#354111yescharacteristic
1351C22#354111yescharacteristic
1352C22#354211yescharacteristic
1353C22#354211yescharacteristic
1354C22#354211yescharacteristic
1355C22#354211yescharacteristic
1356C22#354211yescharacteristic
1357C22#354211yescharacteristic
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—42no—
1364C4—44no—
1365C4—44no—
1366C4—42no—
1367C4—44no—
1368C4—82no—
1369C4—81no—
1370C4—81no—
1371C4—82no—
1372C4—82no—
1373C4—81no—
1374C4—82no—
1375C4—81no—
1376C4#237518yes—
1377C2—44no—
1378C2—44no—
1379C2—44no—
1380C2—84no—
1381C2#3422311yescharacteristic
1382C2#3423311yescharacteristic
1383C2#3424611yescharacteristic
1384C2C2×#237511yescharacteristic
1385C2#3436311yescharacteristic
1386C2#3437911yescharacteristic
1387C2#3440411yescharacteristic
1388C2#4559811yescharacteristic
1389C2#4559911yescharacteristic
1390C2#4560011yescharacteristic
1391C2#4560011yescharacteristic
1392C2#4560111yescharacteristic
1393C2#4562311yescharacteristic
1394C2#4564511yescharacteristic
1395C2#4564611yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2847C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14680C2semidirect
3. #14666C2semidirect
4. #14516C2semidirect
5. #14513C2semidirect
6. #14428C2semidirect
7. #14427C2semidirect
8. #14358C2semidirect
9. #14357C2semidirect
10. #13998C2semidirect
11. #13998C2semidirect
12. #13998C2semidirect
13. #13994C2semidirect
14. #13993C2semidirect
15. #13993C2semidirect
16. #13974C2semidirect
17. #13973C2semidirect
18. #13973C2semidirect
19. #13970C2semidirect
20. #13970C2semidirect
21. #13970C2semidirect
22. #13832C2semidirect
23. C4×#379C2semidirect
29. C22×C4×D4C22semidirect
30. #2847C4semidirect
34. C2×#390C22semidirect
35. C2×#390C22semidirect
36. C2×#390C22semidirect
37. C2×#389C22semidirect
38. C2×#389C22semidirect
39. C2×#389C22semidirect
60. C2×C4×C4⋊C4C22semidirect
61. C2×C4×C4⋊C4C22semidirect
62. C2×C4×C4⋊C4C22semidirect
69. #1443C22semidirect
70. #1443C22semidirect
71. #1443C22semidirect
72. #1442C22semidirect
73. #1442C22semidirect
74. #1442C22semidirect
77. #1440C22semidirect
78. #1440C22semidirect
79. #1440C22semidirect
84. #1439C22semidirect
85. #1439C22semidirect
86. #1439C22semidirect
97. #1437C22semidirect
98. #1437C22semidirect
99. #1437C22semidirect
100. #1436C22semidirect
101. #1436C22semidirect
102. #1436C22semidirect
103. C4⋊#95C22semidirect
104. C4⋊#95C22semidirect
105. C4⋊#95C22semidirect
106. C4⋊#95C22semidirect
107. C4⋊#95C22semidirect
108. C4⋊#95C22semidirect
109. #1434C22semidirect
110. #1434C22semidirect
111. #1434C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
135. C24×C4C2×C4semidirect
154. C2×#120C2×C4semidirect
220. #386C2×C4semidirect
221. #386C2×C4semidirect
222. #386C2×C4semidirect
229. #380C2×C4semidirect
230. #380C2×C4semidirect
231. #380C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#28472
#146802
#146662
#145162
#145132
#144282
#144272
#143582
#143572
#139982
#139942
#139932
#139742
#139732
#139702
#138322
C4×#3792