Finite Group Databasebeta

← #523585

Subgroups — #523585

Order 512.

5182 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2405C211yesmaximal, characteristic
2C2×#2342C211yesmaximal, characteristic, complemented
3C22×#386C211yesmaximal, characteristic
4#14693C211yesmaximal, characteristic, complemented
5#14571C212yesmaximal, complemented
6#14517C212yesmaximal, complemented
7#14375C212yesmaximal, complemented
8#14359C212yesmaximal, complemented
9#14265C211yesmaximal, characteristic, complemented
10#14262C211yesmaximal, characteristic, complemented
11#14224C212yesmaximal, complemented
12#14182C212yesmaximal, complemented
13#14096C212yesmaximal, complemented
14#14064C212yesmaximal, complemented
15#14044C211yesmaximal, characteristic, complemented
16#14040C211yesmaximal, characteristic, complemented
17#13991C211yesmaximal, characteristic, complemented
18#13971C211yesmaximal, characteristic, complemented
19#13867C211yesmaximal, characteristic
20C22⋊C42C211yesmaximal, characteristic, complemented
21#13794C211yesmaximal, characteristic, complemented
22#13782C211yesmaximal, characteristic, complemented
23C4×#379C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#123C2212yes—
27C22×#117C2211yescharacteristic, complemented
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33#2405C4116yescomplemented
34C2×#394C2212yes—
35C2×#394C2212yes—
36#2342—28no—
37C2×#388C2211yescharacteristic, complemented
38C2×#388C2211yescharacteristic, complemented
39C2×#388C2211yescharacteristic, complemented
40C2×#388C2211yescharacteristic, complemented
41C2×#388C2212yescomplemented
42C2×#388C2212yescomplemented
43C2×#386—28no—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#385C2211yescharacteristic
52C2×#385C2211yescharacteristic
53C2×#385C2211yescharacteristic
54C2×#385C2211yescharacteristic
55C2×#385C2211yescharacteristic
56C2×#385C2211yescharacteristic
57C2×#385C2212yescomplemented
58C2×#385C2212yescomplemented
59C2×#381C2211yescharacteristic, complemented
60C2×#380C2211yescharacteristic, complemented
61C2×#379C2211yescharacteristic
62C2×#379C2211yescharacteristic
63C2×#379C2211yescharacteristic
64C2×#379C2211yescharacteristic
65C2×#379C2211yescharacteristic
66C2×#379C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×C4×C22⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic, complemented
72C2×C4×C22⋊C4C2212yescomplemented
73C2×C4×C22⋊C4C2212yescomplemented
74C2×C4×C22⋊C4C2212yescomplemented
75C22×#95C2211yescharacteristic
76C22×#95C2211yescharacteristic
77#1445C2212yescomplemented
78#1445C2212yescomplemented
79#1443C2212yescomplemented
80#1443C2212yescomplemented
81#1442C2212yescomplemented
82#1442C2212yescomplemented
83#1441C2212yescomplemented
84#1441C2212yescomplemented
85#1440C2212yescomplemented
86#1440C2212yescomplemented
87#1439C2212yescomplemented
88#1439C2212yescomplemented
89#1439C2212yescomplemented
90#1439C2212yescomplemented
91#1439C2212yescomplemented
92#1439C2212yescomplemented
93#1438C2212yes—
94#1438C2212yes—
95#1437C2212yescomplemented
96#1437C2212yescomplemented
97#1437C2212yescomplemented
98#1437C2212yescomplemented
99#1436C2212yescomplemented
100#1436C2212yescomplemented
101#1436C2212yescomplemented
102#1436C2212yescomplemented
103C4⋊#95C2212yescomplemented
104C4⋊#95C2212yescomplemented
105#1434C2212yescomplemented
106#1434C2212yescomplemented
107C22⋊#95C2211yescharacteristic
108C22⋊#95C2211yescharacteristic
109C22⋊#95C2211yescharacteristic
110C22⋊#95C2211yescharacteristic
111C22⋊#95C2211yescharacteristic
112C22⋊#95C2211yescharacteristic
113C22⋊#95C2211yescharacteristic
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2212yescomplemented
118C22⋊#95C2212yescomplemented
119C22⋊#95C2212yescomplemented
120C22⋊#95C2212yescomplemented
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C26C2311yescharacteristic
127C26C2311yescharacteristic
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—44no—
131C23×D4—44no—
132C23×D4C2×C418yes—
133C23×D4C2312yes—
134C23×D4C2312yes—
135C24×C4—24no—
136C24×C4—24no—
137C24×C4—44no—
138C24×C4—42no—
139C24×C4—44no—
140C24×C4C2312yes—
141C24×C4C2311yescharacteristic
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C2×#123—44no—
151C2×#123—44no—
152C2×#123C2×C4116yescomplemented
153C2×#117—24no—
154C2×#117—44no—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C22⋊C4—24no—
164C22×C22⋊C4—24no—
165C22×C22⋊C4—24no—
166C22×C22⋊C4—24no—
167C22×C22⋊C4—24no—
168C22×C22⋊C4—24no—
169C22×C22⋊C4—24no—
170C22×C22⋊C4—44no—
171C22×C22⋊C4—42no—
172C22×C22⋊C4—44no—
173C22×C22⋊C4—42no—
174C22×C22⋊C4C2×C418yescomplemented
175C22×C22⋊C4D418yes—
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2312yes—
212C22×C42C2312yes—
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215#394C2×C4116yescomplemented
216#394C2×C4116yescomplemented
217#388—24no—
218#388—24no—
219#388—24no—
220#388—24no—
221#388—44no—
222#388—44no—
223#386—28no—
224#386—28no—
225#386—28no—
226#386—28no—
227#386—44no—
228#386—44no—
229#386C2×C4116yescomplemented
230#385—24no—
231#385—24no—
232#385—24no—
233#385—44no—
234#385—42no—
235#385—44no—
236#385C2×C418yescomplemented
237#385C2×C418yescomplemented
238#381—24no—
239#380—24no—
240#379—24no—
241#379—24no—
242#379—42no—
243#379C2×C418yescomplemented
244#379C2×C418yescomplemented
245#379C2×C418yescomplemented
246C4×C22⋊C4—24no—
247C4×C22⋊C4—24no—
248C4×C22⋊C4—24no—
249C4×C22⋊C4—24no—
250C4×C22⋊C4—44no—
251C4×C22⋊C4—44no—
252C4×C22⋊C4—42no—
253C4×C22⋊C4—44no—
254C2×#95—24no—
255C2×#95—24no—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2311yescharacteristic
259C2×#95C2311yescharacteristic
260C2×#95C2311yescharacteristic
261C2×#95C2311yescharacteristic
262C2×#95C2312yes—
263C2×#95C2311yescharacteristic
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2311yescharacteristic
267C2×#95C2312yes—
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
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—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C25—22no—
295C25—22no—
296C25—24no—
297C25—24no—
298C25—22no—
299C25—22no—
300C25—22no—
301C25—22no—
302C25—22no—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—42no—
307C25—42no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25—42no—
312C25C22×C414yes—
313C25C22×C414yes—
314C25C2×D414yes—
315C25#4114yes—
316C25C2411yescharacteristic
317C25C2411yescharacteristic
318C25C2412yes—
319C25C2411yescharacteristic
320C22×D4—232no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—42no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4—432no—
334C22×D4—416no—
335C22×D4—416no—
336C22×D4—432no—
337C22×D4C22×C418yes—
338C22×D4C22×C418yes—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—24no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—24no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—22no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4—42no—
368C23×C4—42no—
369C23×C4—42no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4—42no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4—416no—
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—432no—
391C23×C4—416no—
392C23×C4—416no—
393C23×C4—432no—
394C23×C4C22×C414yes—
395C23×C4C22×C414yescomplemented
396C23×C4C22×C414yescomplemented
397C23×C4C2×D414yes—
398C23×C4C2×D414yes—
399C23×C4#4114yes—
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2412yes—
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2412yes—
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2412yes—
417C23×C4C2412yes—
418C23×C4C2411yescharacteristic
419#123—432no—
420#117—416no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—42no—
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⋊C4—42no—
438C2×C4⋊C4—42no—
439C2×C4⋊C4C22×C418yescomplemented
440C2×C4⋊C4C22×C418yescomplemented
441C2×C22⋊C4—232no—
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—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
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—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—22no—
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—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—416no—
492C2×C22⋊C4—416no—
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—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—416no—
513C2×C22⋊C4—416no—
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⋊C4C22×C414yes—
521C2×C22⋊C4C22×C414yes—
522C2×C22⋊C4C22×C418yes—
523C2×C22⋊C4C22×C418yes—
524C2×C22⋊C4C22×C414yes—
525C2×C22⋊C4C22×C414yes—
526C2×C22⋊C4C22×C418yes—
527C2×C22⋊C4C22×C418yes—
528C2×C22⋊C4C22×C414yescomplemented
529C2×C22⋊C4C22×C414yescomplemented
530C2×C22⋊C4C22×C418yescomplemented
531C2×C22⋊C4C22×C418yescomplemented
532C2×C22⋊C4C2×D414yes—
533C2×C22⋊C4C2×D414yes—
534C2×C22⋊C4C2×D414yes—
535C2×C22⋊C4C2×D414yes—
536C2×C22⋊C4#4114yes—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—24no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—24no—
543C2×C42—24no—
544C2×C42—42no—
545C2×C42—42no—
546C2×C42—42no—
547C2×C42—42no—
548C2×C42—42no—
549C2×C42—42no—
550C2×C42—42no—
551#95—24no—
552#95—24no—
553#95—24no—
554#95—24no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563#95—24no—
564#95—24no—
565#95—24no—
566#95—42no—
567#95—42no—
568#95—42no—
569#95—42no—
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#95C22×C418yescomplemented
588#95C22×C418yescomplemented
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—28no—
594C24—28no—
595C24—216no—
596C24—28no—
597C24—216no—
598C24—22no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—22no—
603C24—21no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—21no—
609C24—22no—
610C24—22no—
611C24—21no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—21no—
620C24—21no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—28no—
627C24—28no—
628C24—28no—
629C24—28no—
630C24—28no—
631C24—28no—
632C24—28no—
633C24—28no—
634C24—48no—
635C24—44no—
636C24—48no—
637C24—44no—
638C24—44no—
639C24—48no—
640C24—48no—
641C24—44no—
642C24—48no—
643C24—48no—
644C24—48no—
645C24—48no—
646C24—48no—
647C24—48no—
648C24—48no—
649C24—48no—
650C24—48no—
651C24—44no—
652C24—44no—
653C24—48no—
654C24—44no—
655C24—44no—
656C24—44no—
657C24—44no—
658C24—84no—
659C24—84no—
660C24—84no—
661C24—84no—
662C24—84no—
663C24—84no—
664C24—84no—
665C24—84no—
666C24C4×D4116yes—
667C24C23×C412yes—
668C24C23×C412yes—
669C24C23×C414yes—
670C24C23×C412yes—
671C24C22×D412yes—
672C24C22×D412yes—
673C24C22×D412yes—
674C24C2×#4112yes—
675C24C2×#4112yes—
676C24C2×#4112yes—
677C24C2×#4112yes—
678C24C2×#4112yes—
679C24H(5,𝔽2)14yes—
680C24H(5,𝔽2)14yes—
681C24H(5,𝔽2)12yes—
682C242−1+412yes—
683C24C2511yescharacteristic
684C2×D4—216no—
685C2×D4—216no—
686C2×D4—216no—
687C2×D4—216no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—4128no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—22no—
702C22×C4—216no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—22no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—22no—
722C22×C4—21no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—21no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
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—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—21no—
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—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—44no—
803C22×C4—48no—
804C22×C4—48no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—48no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—48no—
828C22×C4—48no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—48no—
832C22×C4—4128no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—44no—
836C22×C4—48no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—84no—
840C22×C4—84no—
841C22×C4—82no—
842C22×C4—82no—
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×C4C23×C412yes—
852C22×C4C23×C412yes—
853C22×C4C23×C414yes—
854C22×C4C23×C414yes—
855C22×C4C23×C414yes—
856C22×C4C23×C412yes—
857C22×C4C23×C412yes—
858C22×C4C22×D412yes—
859C22×C4C22×D412yes—
860C22×C4C22×D412yes—
861C22×C4C22×D412yes—
862C22×C4C2×#4114yes—
863C22×C4C2×#4114yes—
864C22×C4H(5,𝔽2)14yes—
865C4⋊C4—48no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—82no—
870C4⋊C4—82no—
871C4⋊C4—84no—
872C4⋊C4—84no—
873C22⋊C4—28no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—216no—
879C22⋊C4—216no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—82no—
903C22⋊C4—82no—
904C22⋊C4—84no—
905C22⋊C4—84no—
906C42—44no—
907C42—44no—
908C42—82no—
909C42—84no—
910C42—82no—
911C42—84no—
912C23—24no—
913C23—24no—
914C23—22no—
915C23—22no—
916C23—24no—
917C23—22no—
918C23—22no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—232no—
929C23—24no—
930C23—22no—
931C23—22no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—22no—
937C23—22no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—24no—
948C23—24no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—24no—
958C23—22no—
959C23—22no—
960C23—24no—
961C23—22no—
962C23—22no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—232no—
976C23—416no—
977C23—416no—
978C23—432no—
979C23—432no—
980C23—416no—
981C23—416no—
982C23—416no—
983C23—416no—
984C23—432no—
985C23—432no—
986C23—416no—
987C23—416no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—88no—
1021C23—88no—
1022C23—816no—
1023C23—816no—
1024C23—816no—
1025C23—88no—
1026C23—88no—
1027C23—816no—
1028C23C2×C4×D414yes—
1029C23C2×C4×D414yes—
1030C23C2×C4×D414yes—
1031C23C4×#4114yes—
1032C23#51818yes—
1033C23#52014yes—
1034C23#54614yes—
1035C23#54714yes—
1036C23#55114yes—
1037C23#55214yes—
1038C23C24×C411yescharacteristic
1039C23C23×D411yescharacteristic
1040C23C22×#4111yescharacteristic
1041C23C22×#4111yescharacteristic
1042C23C22×#4111yescharacteristic
1043C23C2×H(5,𝔽2)12yes—
1044C23C2×H(5,𝔽2)12yes—
1045C23C2×H(5,𝔽2)11yescharacteristic
1046C23C2×H(5,𝔽2)12yes—
1047C23C2×2−1+411yescharacteristic
1048C23#58512yes—
1049D4—432no—
1050D4—432no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—416no—
1088C2×C4—432no—
1089C2×C4—416no—
1090C2×C4—416no—
1091C2×C4—416no—
1092C2×C4—432no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—42no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—42no—
1099C2×C4—42no—
1100C2×C4—42no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—42no—
1106C2×C4—42no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—42no—
1110C2×C4—42no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—41no—
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—88no—
1166C2×C4—88no—
1167C2×C4—816no—
1168C2×C4—88no—
1169C2×C4#53414yes—
1170C22—24no—
1171C22—24no—
1172C22—24no—
1173C22—28no—
1174C22—28no—
1175C22—24no—
1176C22—28no—
1177C22—24no—
1178C22—24no—
1179C22—28no—
1180C22—24no—
1181C22—24no—
1182C22—24no—
1183C22—24no—
1184C22—24no—
1185C22—28no—
1186C22—24no—
1187C22—28no—
1188C22—28no—
1189C22—464no—
1190C22—44no—
1191C22—42no—
1192C22—42no—
1193C22—44no—
1194C22—42no—
1195C22—42no—
1196C22—44no—
1197C22—44no—
1198C22—44no—
1199C22—44no—
1200C22—44no—
1201C22—44no—
1202C22—44no—
1203C22—44no—
1204C22—44no—
1205C22—44no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—44no—
1210C22—42no—
1211C22—42no—
1212C22—44no—
1213C22—42no—
1214C22—42no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—832no—
1219C22#235918yes—
1220C22C22×C4×D411yescharacteristic
1221C22C2×C4×#4111yescharacteristic
1222C22C2×#51812yes—
1223C22C2×#52011yescharacteristic
1224C22C4×H(5,𝔽2)12yes—
1225C22C2×#53411yescharacteristic
1226C22#344911yescharacteristic
1227C22#345912yes—
1228C22C2×#54611yescharacteristic
1229C22C2×#54711yescharacteristic
1230C22C2×#55111yescharacteristic
1231C22C2×#55211yescharacteristic
1232C22#348411yescharacteristic
1233C22#348411yescharacteristic
1234C22#349012yes—
1235C22#349012yes—
1236C22#349412yes—
1237C22#351312yes—
1238C22#351912yes—
1239C22#353212yes—
1240C22#353412yes—
1241C22#353512yes—
1242C22#353612yes—
1243C4—24no—
1244C4—42no—
1245C4—42no—
1246C4—42no—
1247C4—42no—
1248C4—44no—
1249C4—44no—
1250C4—42no—
1251C4—42no—
1252C4—44no—
1253C4—42no—
1254C4—44no—
1255C4—44no—
1256C4—81no—
1257C4—81no—
1258C4—82no—
1259C4—81no—
1260C4—81no—
1261C4—82no—
1262C2—28no—
1263C2—48no—
1264C2—44no—
1265C2—44no—
1266C2C4×#53411yescharacteristic
1267C2C2×#235911yescharacteristic
1268C2#3419811yescharacteristic
1269C2#3430212yes—
1270C2#3445612yes—
1271C2#3783211yescharacteristic
1272C2#3784011yescharacteristic
1273C2#3793212yes—
1274C2#3891211yescharacteristic
1275C2#3891611yescharacteristic
1276C2#3903612yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC24×D4C22
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×#2342C2semidirect
4. #14693C2semidirect
5. #14571C2semidirect
6. #14517C2semidirect
7. #14375C2semidirect
8. #14359C2semidirect
9. #14265C2semidirect
10. #14262C2semidirect
11. #14224C2semidirect
12. #14182C2semidirect
13. #14096C2semidirect
14. #14064C2semidirect
15. #14044C2semidirect
16. #14040C2semidirect
17. #13991C2semidirect
18. #13971C2semidirect
20. C22⋊C42C2semidirect
21. #13794C2semidirect
22. #13782C2semidirect
23. C4×#379C2semidirect
27. C22×#117C22semidirect
33. #2405C4semidirect
37. C2×#388C22semidirect
38. C2×#388C22semidirect
39. C2×#388C22semidirect
40. C2×#388C22semidirect
41. C2×#388C22semidirect
42. C2×#388C22semidirect
57. C2×#385C22semidirect
58. C2×#385C22semidirect
59. C2×#381C22semidirect
60. C2×#380C22semidirect
71. C2×C4×C22⋊C4C22semidirect
72. C2×C4×C22⋊C4C22semidirect
73. C2×C4×C22⋊C4C22semidirect
74. C2×C4×C22⋊C4C22semidirect
77. #1445C22semidirect
78. #1445C22semidirect
79. #1443C22semidirect
80. #1443C22semidirect
81. #1442C22semidirect
82. #1442C22semidirect
83. #1441C22semidirect
84. #1441C22semidirect
85. #1440C22semidirect
86. #1440C22semidirect
87. #1439C22semidirect
88. #1439C22semidirect
89. #1439C22semidirect
90. #1439C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
95. #1437C22semidirect
96. #1437C22semidirect
97. #1437C22semidirect
98. #1437C22semidirect
99. #1436C22semidirect
100. #1436C22semidirect
101. #1436C22semidirect
102. #1436C22semidirect
103. C4⋊#95C22semidirect
104. C4⋊#95C22semidirect
105. #1434C22semidirect
106. #1434C22semidirect
117. C22⋊#95C22semidirect
118. C22⋊#95C22semidirect
119. C22⋊#95C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
152. C2×#123C2×C4semidirect
174. C22×C22⋊C4C2×C4semidirect
215. #394C2×C4semidirect
216. #394C2×C4semidirect
229. #386C2×C4semidirect
236. #385C2×C4semidirect
237. #385C2×C4semidirect
243. #379C2×C4semidirect
244. #379C2×C4semidirect
245. #379C2×C4semidirect
395. C23×C4C22×C4semidirect
396. C23×C4C22×C4semidirect
439. C2×C4⋊C4C22×C4semidirect
440. C2×C4⋊C4C22×C4semidirect
528. C2×C22⋊C4C22×C4semidirect
529. C2×C22⋊C4C22×C4semidirect
530. C2×C22⋊C4C22×C4semidirect
531. C2×C22⋊C4C22×C4semidirect
587. #95C22×C4semidirect
588. #95C22×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24052
C2×#23422
C22×#3862
#146932
#145712
#145172
#143752
#143592
#142652
#142622
#142242
#141822
#140962
#140642
#140442
#140402
#139912
#139712
#138672
C22⋊C422
#137942
#137822
C4×#3792