Finite Group Databasebeta

← C2×#20255025 #27091414

Subgroups — C2×#20255025 #27091414

Order 12032.

2902 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094053C211yesmaximal, characteristic, complemented
2C22×#13094048C211yesmaximal, characteristic, complemented
3C2×#15689781C211yesmaximal, characteristic, complemented
4C2×#15689768C211yesmaximal, characteristic, complemented
5#20255025C2116yesmaximal, direct product factor
6C2×#15689505C211yesmaximal, characteristic, complemented
7C2×#15689380C211yesmaximal, characteristic, complemented
8C2×#15689375C211yesmaximal, characteristic, complemented
9C2×#15689346C211yesmaximal, characteristic, complemented
10C2×#15689286C211yesmaximal, characteristic, complemented
11C2×#15689265C211yesmaximal, characteristic, complemented
12C2×#15689263C211yesmaximal, characteristic, complemented
13C2×#15689272C211yesmaximal, characteristic, complemented
14C2×C4×#10625335C211yesmaximal, characteristic, complemented
15C2×#15689200C211yesmaximal, characteristic, complemented
16C2×C47×#463C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×#10625352C2211yescharacteristic
19C22×Q8×D47C2211yescharacteristic, complemented
20C22×D4×D47C2211yescharacteristic
21C2×#13094053—28no—
22C2×#13094053C2218yescomplemented
23C2×#13094048—28no—
24C2×#13094048C2218yescomplemented
25C22×Dic188C2211yescharacteristic, complemented
26C22×#10625337C2211yescharacteristic, complemented
27C22×#10625325C2211yescharacteristic
28C22×#10625335C2211yescharacteristic
29C22×#10625335C2211yescharacteristic, complemented
30C22×#10625336C2211yescharacteristic
31C22×#10625334C2211yescharacteristic
32C22×#10625324C2211yescharacteristic
33C22×#10625324C2211yescharacteristic, complemented
34#15689781—24no—
35#15689781C2218yescomplemented
36#15689768—24no—
37#15689768C2218yescomplemented
38C2×#13094012C2211yescharacteristic
39C2×#13094010—21no—
40C2×#13094008—21no—
41C2×#13094004C2211yescharacteristic
42C2×#13094001—21no—
43C2×#13094000C2211yescharacteristic
44C2×#13093999C2211yescharacteristic
45C2×#13093998—21no—
46C2×#13093997—21no—
47C2×#13093995C2211yescharacteristic, complemented
48C2×#13093994—21no—
49C2×C4×Dic94C2211yescharacteristic, complemented
50C2×C4×D188C2211yescharacteristic
51C2×(C22⋊D47)⋊C4—21no—
52C22×(C2×D47)⋊C4—21no—
53#15689505C2218yescomplemented
54#15689380C2218yescomplemented
55#15689375C2218yescomplemented
56#15689346C2218yescomplemented
57#15689286C2218yescomplemented
58#15689272C2218yescomplemented
59#15689265C2218yescomplemented
60#15689263C2218yescomplemented
61C4×#10625335C2218yescomplemented
62#15689200C2218yescomplemented
63C2×#13093955C2211yescharacteristic, complemented
64C2×#13093949C2211yescharacteristic, complemented
65C2×#13093947C2211yescharacteristic, complemented
66C2×#13093946C2211yescharacteristic
67C2×#13093945C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
70C2×C4×C47⋊C8C2211yescharacteristic, complemented
71C22×SD16×C47C2211yescharacteristic
72C22×D8×C47C2211yescharacteristic
73C2×#124×C47C2211yescharacteristic, complemented
74C2×C4×D4×C47C2211yescharacteristic
75C47×#463C2218yescomplemented
76C2×C4⋊C8×C47C2211yescharacteristic, complemented
77C2×#103×C47C2211yescharacteristic, complemented
78C2×#102×C47C2211yescharacteristic, complemented
79C24×D47—21no—
80C2×#10625352—24no—
81C2×#10625352—22no—
82C2×#10625352—22no—
83C2×#10625352—24no—
84C2×#10625352—42no—
85C2×#10625352—42no—
86C2×#10625352C2314yes—
87C2×#10625352C2314yes—
88C22×Dic94—21no—
89C22×Dic94C2311yescharacteristic
90C22×Dic94C2311yescharacteristic
91C2×Q8×D47—22no—
92C2×Q8×D47—24no—
93C2×Q8×D47—42no—
94C2×Q8×D47C2314yescomplemented
95C22×D188—21no—
96C22×D188D411yescharacteristic
97C22×D188C2311yescharacteristic
98C22×C22⋊D47—21no—
99C22×C22⋊D47—21no—
100C22×C22⋊D47—21no—
101C22×C22⋊D47—21no—
102C2×D4×D47—24no—
103C2×D4×D47—22no—
104C2×D4×D47—42no—
105C2×D4×D47C2314yes—
106C23×Dic47—21no—
107C23×Dic47—21no—
108C22×C4×D47—21no—
109C22×C4×D47C2311yescharacteristic
110C22×C4×D47C2311yescharacteristic
111#13094053—232no—
112#13094048—232no—
113C2×Dic188—24no—
114C2×Dic188C2314yescomplemented
115C2×#10625337—24no—
116C2×#10625337C2314yescomplemented
117C2×#10625325—24no—
118C2×#10625325C2314yes—
119C2×#10625335—42no—
120C2×#10625335D418yescomplemented
121C2×#10625335C2314yes—
122C2×#10625335C2314yescomplemented
123C2×#10625336—42no—
124C2×#10625336C2314yes—
125C2×#10625334—24no—
126C2×#10625334C2314yes—
127C2×#10625324—24no—
128C2×#10625324—24no—
129C2×#10625324C2314yes—
130C2×#10625324C2314yescomplemented
131C22×C47⋊C8C2311yescharacteristic
132C22×C47⋊C8C2311yescharacteristic
133#13094012—22no—
134#13094012C2314yes—
135#13094010—28no—
136#13094008—28no—
137#13094004—22no—
138#13094004C2314yes—
139#13094001—28no—
140#13094000—22no—
141#13094000C2314yes—
142#13093999—22no—
143#13093999C2314yes—
144#13093998—28no—
145#13093997—28no—
146#13093995—22no—
147#13093995C2314yescomplemented
148#13093994—28no—
149C4×Dic94—22no—
150C4×Dic94C2314yescomplemented
151C4×D188D414yes—
152C4×D188C2314yes—
153(C22⋊D47)⋊C4—28no—
154C2×C4⋊Dic47—21no—
155C2×C4⋊Dic47D411yescharacteristic
156C2×C4⋊Dic47C2311yescharacteristic
157C2×Dic47⋊C4—21no—
158C2×Dic47⋊C4—21no—
159C2×C22⋊Dic47—21no—
160C2×(C2×D47)⋊C4—21no—
161C2×(C2×D47)⋊C4—21no—
162C2×(C2×D47)⋊C4—21no—
163C2×(C2×D47)⋊C4—21no—
164C2×(C2×D47)⋊C4—21no—
165C2×(C2×D47)⋊C4—28no—
166C2×(C2×D47)⋊C4D411yescharacteristic
167C2×(C2×D47)⋊C4D411yescharacteristic
168C2×C4×Dic47—21no—
169#13093955C2314yescomplemented
170#13093949C2314yescomplemented
171#13093947C2314yescomplemented
172#13093946C2314yes—
173#13093945C2314yes—
174(C2×D47)⋊C8C2314yes—
175(C2×D47)⋊C8C2314yescomplemented
176C4×C47⋊C8C2314yescomplemented
177C22×Q8×C47C2311yescharacteristic
178C22×D4×C47C2311yescharacteristic
179C22×D4×C47C2311yescharacteristic
180C23×C4×C47—21no—
181C2×SD16×C47—24no—
182C2×SD16×C47C2314yes—
183C2×D8×C47—24no—
184C2×D8×C47C2314yes—
185C22×C8×C47C2311yescharacteristic
186C22×C8×C47C2311yescharacteristic
187#124×C47—22no—
188#124×C47C2314yescomplemented
189C4×D4×C47—22no—
190C4×D4×C47C2314yes—
191C2×C4⋊C4×C47C2311yescharacteristic
192C2×C22⋊C4×C47—21no—
193C2×C22⋊C4×C47—21no—
194C2×C22⋊C4×C47—21no—
195C2×C42×C47C2311yescharacteristic
196C4⋊C8×C47C2314yescomplemented
197#103×C47C2314yescomplemented
198#102×C47C2314yescomplemented
199C24×C47—21no—
200C24×C47—21no—
201C23×D47—21no—
202C23×D47—24no—
203C23×D47—44no—
204C23×D47—44no—
205C23×D47—82no—
206C23×D47C2×D411yescharacteristic
207C23×D47C2×D411yescharacteristic
208C2×Q8×C47—21no—
209C2×Q8×C47—22no—
210C2×Q8×C47—22no—
211C2×Q8×C47C2412yes—
212C2×D4×C47—21no—
213C2×D4×C47—22no—
214C2×D4×C47—21no—
215C2×D4×C47—22no—
216C2×D4×C47—22no—
217C2×D4×C47C2×D414yes—
218C2×D4×C47C2412yes—
219C2×D4×C47C2412yes—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—24no—
223C22×C4×C47—82no—
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2411yescharacteristic
227C2×C22⋊D47—24no—
228C2×C22⋊D47—24no—
229C2×C22⋊D47—24no—
230C2×C22⋊D47—24no—
231C2×C22⋊D47—44no—
232C2×C22⋊D47—44no—
233C2×C22⋊D47—44no—
234C2×C22⋊D47—44no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—24no—
239C22×Dic47—24no—
240C22×Dic47—44no—
241C22×Dic47—44no—
242C22×Dic47C2×D411yescharacteristic
243C22×Dic47C2×D411yescharacteristic
244Q8×D47—28no—
245Q8×D47—44no—
246Q8×D47—48no—
247#10625352—28no—
248#10625352—28no—
249#10625352—44no—
250#10625352—44no—
251#10625352—48no—
252#10625352—48no—
253D4×D47—28no—
254D4×D47—44no—
255D4×D47—48no—
256C2×D188—22no—
257C2×D188—22no—
258C2×D188—21no—
259C2×D188—24no—
260C2×D188—42no—
261C2×D188—82no—
262C2×D188C2×D414yes—
263C2×D188C2412yes—
264C2×C4×D47—22no—
265C2×C4×D47—22no—
266C2×C4×D47—22no—
267C2×C4×D47—22no—
268C2×C4×D47—24no—
269C2×C4×D47—44no—
270C2×C4×D47C2×D412yes—
271C2×C4×D47C2×D412yes—
272C2×C4×D47C2412yes—
273C2×C4×D47C2412yes—
274C2×Dic94—21no—
275C2×Dic94—22no—
276C2×Dic94—22no—
277C2×Dic94—22no—
278C2×Dic94—21no—
279C2×Dic94—24no—
280C2×Dic94—44no—
281C2×Dic94C2×D414yes—
282C2×Dic94C2412yes—
283C2×Dic94C2412yes—
284SD16×C47—28no—
285D8×C47—28no—
286C2×C8×C47—22no—
287C2×C8×C47—22no—
288C2×C8×C47C2412yes—
289C2×C8×C47C2412yes—
290C4⋊C4×C47—21no—
291C4⋊C4×C47C2412yes—
292C22⋊C4×C47—24no—
293C22⋊C4×C47—24no—
294C22⋊C4×C47—24no—
295C42×C47C2×D412yes—
296C42×C47C2412yes—
297C22⋊Dic47—24no—
298#10625337—28no—
299#10625336—44no—
300#10625335—44no—
301#10625335C2×D4116yescomplemented
302#10625334—28no—
303(C2×D47)⋊C4—24no—
304(C2×D47)⋊C4—24no—
305(C2×D47)⋊C4—24no—
306(C2×D47)⋊C4—24no—
307(C2×D47)⋊C4—24no—
308(C2×D47)⋊C4C2×D414yes—
309(C2×D47)⋊C4C2×D414yes—
310C4⋊Dic47—21no—
311C4⋊Dic47—24no—
312C4⋊Dic47C2×D414yes—
313C4⋊Dic47C2412yes—
314Dic47⋊C4—24no—
315Dic47⋊C4—24no—
316C4×Dic47—24no—
317C2×C47⋊C8—22no—
318C2×C47⋊C8C2×D414yes—
319C2×C47⋊C8C2412yes—
320C2×C47⋊C8C2412yes—
321Dic188—28no—
322#10625325—28no—
323#10625324—28no—
324#10625324—28no—
325C23×C47—24no—
326C23×C47—22no—
327C23×C47—22no—
328C23×C47—42no—
329C23×C47—42no—
330C23×C47—42no—
331C23×C47—42no—
332C23×C47—42no—
333C23×C47C22×D411yescharacteristic
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—48no—
342C22×D47—48no—
343C22×D47—42no—
344C22×D47—42no—
345C22×D47—42no—
346C22×D47—84no—
347C22×D47—816no—
348C22×D47C22×D412yes—
349C22×D47C22×D412yes—
350Q8×C47—22no—
351Q8×C47—22no—
352Q8×C47—42no—
353D4×C47—24no—
354D4×C47—22no—
355D4×C47—22no—
356D4×C47—22no—
357D4×C47—42no—
358D4×C47C22×D414yes—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—42no—
364C2×C4×C47—42no—
365C2×C4×C47—84no—
366C2×C4×C47C22×D412yes—
367C2×C4×C47C22×D412yes—
368C2×C4×C47C22×D411yescharacteristic
369C2×C4×C47C22×D412yes—
370C2×C4×C47H(5,𝔽2)12yes—
371C2×C4×C47C2511yescharacteristic
372C22⋊D47—48no—
373C22⋊D47—48no—
374C22⋊D47—48no—
375C22⋊D47—48no—
376C2×Dic47—24no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—48no—
383C2×Dic47—48no—
384C2×Dic47—42no—
385C2×Dic47—42no—
386C2×Dic47C22×D412yes—
387C2×Dic47C22×D412yes—
388D188—22no—
389D188—22no—
390D188—44no—
391D188—42no—
392D188—84no—
393C4×D47—24no—
394C4×D47—24no—
395C4×D47—22no—
396C4×D47—22no—
397C4×D47—22no—
398C4×D47—22no—
399C4×D47—48no—
400Dic94—24no—
401Dic94—22no—
402Dic94—22no—
403Dic94—22no—
404Dic94—48no—
405Dic94—42no—
406Dic94C22×D414yes—
407C8×C47—22no—
408C8×C47—22no—
409C47⋊C8—22no—
410C47⋊C8C22×D414yes—
411C2×#3275—471nomaximal, Sylow
412C22×C47—24no—
413C22×C47—48no—
414C22×C47—42no—
415C22×C47—42no—
416C22×C47—42no—
417C22×C47—42no—
418C22×C47—42no—
419C22×C47—84no—
420C22×C47D4212yes—
421C22×C47#57512yes—
422C22×C47#57712yes—
423C22×C47C23×D411yescharacteristic
424C2×D47—22no—
425C2×D47—22no—
426C2×D47—22no—
427C2×D47—22no—
428C2×D47—22no—
429C2×D47—22no—
430C2×D47—44no—
431C2×D47—44no—
432C2×D47—42no—
433C2×D47—42no—
434C2×D47—42no—
435C2×D47—816no—
436C2×D47—84no—
437C4×C47—22no—
438C4×C47—22no—
439C4×C47—42no—
440C4×C47—42no—
441C4×C47D4212yes—
442C4×C47C23×D411yescharacteristic
443C4×C47C2×H(5,𝔽2)11yescharacteristic
444Dic47—24no—
445Dic47—22no—
446Dic47—22no—
447Dic47—42no—
448Dic47—42no—
449C22×#137—471no—
450C22×AGL(1,ℤ/8)—471no—
451C2×#548—471no—
452C2×#546—471no—
453#3275—4716no—
454C2×#495—471no—
455C2×#470—471no—
456C2×#469—471no—
457C2×#464—471no—
458C2×#463D4711yescharacteristic, complemented
459C2×#452—471no—
460C2×#449—471no—
461C2×#448—471no—
462C2×#450—471no—
463C2×C4×SD16—471no—
464C2×#436—471no—
465C2×C47—44no—
466C2×C47—82no—
467C2×C47#327514yescomplemented
468C2×C47C2×D4211yescharacteristic
469C2×C47C2×#57511yescharacteristic
470C2×C47C2×#57711yescharacteristic
471D47—42no—
472D47—42no—
473D47—82no—
474C22×#41—471no—
475C22×#41—471no—
476C23×Q8—471no—
477C23×D4—471no—
478C2×#137—478no—
479C2×#137—948no—
480C2×AGL(1,ℤ/8)—478no—
481C2×AGL(1,ℤ/8)—948no—
482C22×Q16—471no—
483C22×Q16—471no—
484C22×SD16—471no—
485C22×SD16—471no—
486C22×SD16—471no—
487C22×SD16—471no—
488C22×SD16C2×D4711yescharacteristic
489C22×D8—471no—
490C22×D8C2×D4711yescharacteristic
491C22×M16—471no—
492C22×M16—471no—
493#548—478no—
494#548—944no—
495#546—478no—
496#546—944no—
497C2×#124—471no—
498C2×#124—941no—
499C2×#124C2×D4711yescharacteristic, complemented
500C2×#123—941no—
501C2×C22⋊Q8—471no—
502C2×C22⋊Q8—471no—
503C2×C22⋊Q8—941no—
504C2×#121—471no—
505C2×#121—471no—
506C2×#121—941no—
507C2×#121—941no—
508C2×#120—941no—
509C2×C4×Q8—471no—
510C2×C4×D4—471no—
511C2×C4×D4—941no—
512C2×C4×D4C2×D4711yescharacteristic
513C22×C22⋊C4—941no—
514#495—478no—
515#470—478no—
516#469—478no—
517#464—478no—
518#463C2×D4718yescomplemented
519#452—478no—
520#450—478no—
521#449—478no—
522#448—478no—
523C4×SD16—478no—
524#436—478no—
525C2×#106—471no—
526C2×C4⋊C8C2×D4711yescharacteristic, complemented
527C2×#103—471no—
528C2×#103—471no—
529C2×#103C2×D4711yescharacteristic, complemented
530C2×#102—471no—
531C2×#102—471no—
532C2×#102C2×D4711yescharacteristic, complemented
533C2×C22⋊C8—471no—
534C2×C22⋊C8—471no—
535C2×C4×C8—471no—
536C47C2×#327511yescharacteristic, complemented, Sylow
537C25—941no—
538C2×#41—474no—
539C2×#41—474no—
540C2×#41—942no—
541C2×#41—942no—
542C2×#41—944no—
543C2×#41—944no—
544C2×#41—1882no—
545C2×#41—1882no—
546C22×Q8—474no—
547C22×Q8—471no—
548C22×Q8—471no—
549C22×Q8—941no—
550C22×Q8—942no—
551C22×Q8—944no—
552C22×Q8—1882no—
553C22×Q8C22×D4711yescharacteristic
554C22×D4—474no—
555C22×D4—471no—
556C22×D4—471no—
557C22×D4—941no—
558C22×D4—942no—
559C22×D4—941no—
560C22×D4—944no—
561C22×D4—941no—
562C22×D4—941no—
563C22×D4—941no—
564C22×D4—1882no—
565C22×D4C22×D4711yescharacteristic
566C22×D4C22×D4711yescharacteristic
567C23×C4—21no—
568C23×C4—471no—
569C23×C4—471no—
570C23×C4—941no—
571C23×C4—941no—
572C23×C4—941no—
573#137—9432no—
574AGL(1,ℤ/8)—9432no—
575C2×Q16—474no—
576C2×Q16—474no—
577C2×Q16—944no—
578C2×Q16—944no—
579C2×SD16—24no—
580C2×SD16—478no—
581C2×SD16—474no—
582C2×SD16—474no—
583C2×SD16—474no—
584C2×SD16—474no—
585C2×SD16—944no—
586C2×SD16—1882no—
587C2×SD16—1882no—
588C2×SD16C22×D4714yes—
589C2×D8—24no—
590C2×D8—474no—
591C2×D8—944no—
592C2×D8C22×D4714yes—
593C2×M16—474no—
594C2×M16—474no—
595C2×M16—944no—
596C2×M16—944no—
597C22×C8—471no—
598C22×C8—471no—
599C22×C8C22×D4711yescharacteristic
600C22×C8C22×D4711yescharacteristic
601#124—22no—
602#124—474no—
603#124—948no—
604#124—942no—
605#124C22×D4714yescomplemented
606#123—948no—
607C22⋊Q8—474no—
608C22⋊Q8—474no—
609C22⋊Q8—948no—
610C22⋊Q8—942no—
611C22⋊Q8—942no—
612#121—474no—
613#121—474no—
614#121—948no—
615#121—948no—
616#121—942no—
617#121—942no—
618#120—948no—
619C4×Q8—474no—
620C4×Q8—942no—
621C4×D4—22no—
622C4×D4—474no—
623C4×D4—474no—
624C4×D4—948no—
625C4×D4C22×D4714yes—
626C2×C4⋊C4—471no—
627C2×C4⋊C4—471no—
628C2×C4⋊C4—941no—
629C2×C4⋊C4—941no—
630C2×C4⋊C4—941no—
631C2×C4⋊C4C22×D4711yescharacteristic
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—471no—
636C2×C22⋊C4—471no—
637C2×C22⋊C4—948no—
638C2×C22⋊C4—941no—
639C2×C22⋊C4—941no—
640C2×C22⋊C4—941no—
641C2×C22⋊C4—941no—
642C2×C22⋊C4—941no—
643C2×C22⋊C4—941no—
644C2×C42—941no—
645C2×C42C22×D4711yescharacteristic
646#106—474no—
647C4⋊C8C22×D4714yescomplemented
648#103—474no—
649#103—474no—
650#103C22×D4714yescomplemented
651#102—474no—
652#102—474no—
653#102C22×D4714yescomplemented
654C22⋊C8—474no—
655C22⋊C8—474no—
656C4×C8—474no—
657C24—21no—
658C24—21no—
659C24—471no—
660C24—471no—
661C24—944no—
662C24—941no—
663C24—3762no—
664C24—1884no—
665C24—1884no—
666#41—948no—
667#41—948no—
668#41—1884no—
669#41—1884no—
670#41—1888no—
671#41—1888no—
672C2×Q8—21no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—474no—
676C2×Q8—472no—
677C2×Q8—472no—
678C2×Q8—944no—
679C2×Q8—941no—
680C2×Q8—941no—
681C2×Q8—942no—
682C2×Q8—948no—
683C2×Q8—942no—
684C2×Q8—942no—
685C2×Q8—1884no—
686C2×Q8—1884no—
687C2×Q8—1888no—
688C2×Q8C23×D4712yes—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—21no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—474no—
695C2×D4—472no—
696C2×D4—944no—
697C2×D4—944no—
698C2×D4—948no—
699C2×D4—944no—
700C2×D4—944no—
701C2×D4—944no—
702C2×D4—942no—
703C2×D4—941no—
704C2×D4—942no—
705C2×D4—3762no—
706C2×D4—1882no—
707C2×D4—1884no—
708C2×D4—1888no—
709C2×D4—1884no—
710C2×D4—1884no—
711C2×D4—1884no—
712C2×D4—1884no—
713C2×D4D4×D4714yes—
714C2×D4C23×D4712yes—
715C2×D4C23×D4712yes—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—82no—
720C22×C4—471no—
721C22×C4—471no—
722C22×C4—472no—
723C22×C4—472no—
724C22×C4—472no—
725C22×C4—472no—
726C22×C4—944no—
727C22×C4—944no—
728C22×C4—944no—
729C22×C4—941no—
730C22×C4—942no—
731C22×C4—942no—
732C22×C4—942no—
733C22×C4—942no—
734C22×C4—941no—
735C22×C4—941no—
736C22×C4—1884no—
737C22×C4—1884no—
738C22×C4—1884no—
739C22×C4D4×D4711yescharacteristic
740C22×C4D4×D4711yescharacteristic
741C22×C4C23×D4711yescharacteristic
742Q16—948no—
743Q16—948no—
744SD16—28no—
745SD16—4716no—
746SD16—948no—
747SD16—1884no—
748SD16—1884no—
749D8—28no—
750D8—948no—
751M16—948no—
752M16—948no—
753C2×C8—22no—
754C2×C8—22no—
755C2×C8—474no—
756C2×C8—472no—
757C2×C8—472no—
758C2×C8—942no—
759C2×C8C23×D4712yes—
760C2×C8C23×D4712yes—
761C4⋊C4—21no—
762C4⋊C4—474no—
763C4⋊C4—472no—
764C4⋊C4—944no—
765C4⋊C4—944no—
766C4⋊C4—944no—
767C4⋊C4—941no—
768C4⋊C4C23×D4712yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—474no—
773C22⋊C4—474no—
774C22⋊C4—944no—
775C22⋊C4—944no—
776C22⋊C4—944no—
777C22⋊C4—944no—
778C22⋊C4—944no—
779C22⋊C4—944no—
780C42—944no—
781C42D4×D4712yes—
782C42C23×D4712yes—
783C23—24no—
784C23—22no—
785C23—22no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—472no—
792C23—472no—
793C23—942no—
794C23—942no—
795C23—942no—
796C23—942no—
797C23—942no—
798C23—942no—
799C23—942no—
800C23—3764no—
801C23—37616no—
802C23—1888no—
803C23—1888no—
804C23—1882no—
805C23—1882no—
806C23—1882no—
807C23C2×D4×D4711yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—42no—
811Q8—474no—
812Q8—944no—
813Q8—942no—
814Q8—942no—
815Q8—942no—
816Q8—1888no—
817Q8—1882no—
818D4—24no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—42no—
823D4—942no—
824D4—942no—
825D4—3764no—
826D4—1884no—
827D4—1888no—
828D4—1888no—
829D4—1888no—
830D4—1888no—
831D4—1882no—
832D4C2×D4×D4714yes—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—84no—
840C2×C4—472no—
841C2×C4—472no—
842C2×C4—942no—
843C2×C4—942no—
844C2×C4—944no—
845C2×C4—942no—
846C2×C4—944no—
847C2×C4—944no—
848C2×C4—942no—
849C2×C4—942no—
850C2×C4—942no—
851C2×C4—942no—
852C2×C4—942no—
853C2×C4—942no—
854C2×C4—1888no—
855C2×C4—1888no—
856C2×C4—1888no—
857C2×C4—1882no—
858C2×C4—1882no—
859C2×C4C2×D4×D4712yes—
860C2×C4C2×D4×D4712yes—
861C2×C4C2×D4×D4711yescharacteristic
862C2×C4C2×D4×D4712yes—
863C2×C4#1309407012yes—
864C2×C4C24×D4711yescharacteristic
865C8—22no—
866C8—22no—
867C8—474no—
868C8—942no—
869C22—24no—
870C22—48no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—84no—
877C22—942no—
878C22—942no—
879C22—942no—
880C22—942no—
881C22—942no—
882C22—942no—
883C22—37616no—
884C22—3764no—
885C22—1882no—
886C22—1882no—
887C22—1882no—
888C22—1884no—
889C22—1884no—
890C22#1568975712yes—
891C22#1568992012yes—
892C22#1568993312yes—
893C22C22×D4×D4711yescharacteristic
894C4—22no—
895C4—22no—
896C4—42no—
897C4—42no—
898C4—942no—
899C4—942no—
900C4—944no—
901C4—1882no—
902C4—1882no—
903C4#1568975712yes—
904C4C22×D4×D4711yescharacteristic
905C4C2×#1309407011yescharacteristic
906C2—44no—
907C2—82no—
908C2—3762no—
909C2—1882no—
910C2—1882no—
911C2#2025502514yesdirect product factor
912C2C2×#1568975711yescharacteristic
913C2C2×#1568992011yescharacteristic
914C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#463C2
socleC23×C47C22×D4
hypercenterC2×#463D47
hypocenterC47C2×#3275
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C22×#13094053C2semidirect
2. C22×#13094048C2semidirect
3. C2×#15689781C2semidirect
4. C2×#15689768C2semidirect
5. #20255025C2direct (N × H)
6. C2×#15689505C2semidirect
7. C2×#15689380C2semidirect
8. C2×#15689375C2semidirect
9. C2×#15689346C2semidirect
10. C2×#15689286C2semidirect
11. C2×#15689265C2semidirect
12. C2×#15689263C2semidirect
13. C2×#15689272C2semidirect
14. C2×C4×#10625335C2semidirect
15. C2×#15689200C2semidirect
16. C2×C47×#463C2semidirect
19. C22×Q8×D47C22semidirect
22. C2×#13094053C22semidirect
24. C2×#13094048C22semidirect
25. C22×Dic188C22semidirect
26. C22×#10625337C22semidirect
29. C22×#10625335C22semidirect
33. C22×#10625324C22semidirect
35. #15689781C22semidirect
37. #15689768C22semidirect
47. C2×#13093995C22semidirect
49. C2×C4×Dic94C22semidirect
53. #15689505C22semidirect
54. #15689380C22semidirect
55. #15689375C22semidirect
56. #15689346C22semidirect
57. #15689286C22semidirect
58. #15689272C22semidirect
59. #15689265C22semidirect
60. #15689263C22semidirect
61. C4×#10625335C22semidirect
62. #15689200C22semidirect
63. C2×#13093955C22semidirect
64. C2×#13093949C22semidirect
65. C2×#13093947C22semidirect
69. C2×(C2×D47)⋊C8C22semidirect
70. C2×C4×C47⋊C8C22semidirect
73. C2×#124×C47C22semidirect
75. C47×#463C22semidirect
76. C2×C4⋊C8×C47C22semidirect
77. C2×#103×C47C22semidirect
78. C2×#102×C47C22semidirect
94. C2×Q8×D47C23semidirect
114. C2×Dic188C23semidirect
116. C2×#10625337C23semidirect
120. C2×#10625335D4semidirect
122. C2×#10625335C23semidirect
130. C2×#10625324C23semidirect
147. #13093995C23semidirect
150. C4×Dic94C23semidirect
169. #13093955C23semidirect
170. #13093949C23semidirect
171. #13093947C23semidirect
175. (C2×D47)⋊C8C23semidirect
176. C4×C47⋊C8C23semidirect
188. #124×C47C23semidirect
196. C4⋊C8×C47C23semidirect
197. #103×C47C23semidirect
198. #102×C47C23semidirect
301. #10625335C2×D4semidirect
458. C2×#463D47semidirect
467. C2×C47#3275semidirect
499. C2×#124C2×D47semidirect
518. #463C2×D47semidirect
526. C2×C4⋊C8C2×D47semidirect
529. C2×#103C2×D47semidirect
532. C2×#102C2×D47semidirect
536. C47C2×#3275semidirect
605. #124C22×D47semidirect
647. C4⋊C8C22×D47semidirect
650. #103C22×D47semidirect
653. #102C22×D47semidirect
911. C2#20255025direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940532
C22×#130940482
C2×#156897812
C2×#156897682
#202550252
C2×#156895052
C2×#156893802
C2×#156893752
C2×#156893462
C2×#156892862
C2×#156892652
C2×#156892632
C2×#156892722
C2×C4×#106253352
C2×#156892002
C2×C47×#4632
C2×#327547