Finite Group Databasebeta

← C2×#20255097 #27091508

Subgroups — C2×#20255097 #27091508

Order 12032.

2934 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×#13094045C211yesmaximal, characteristic, complemented
2C22×SD16×D47C211yesmaximal, characteristic, complemented
3C2×#15689785C211yesmaximal, characteristic, complemented
4C2×#15689768C211yesmaximal, characteristic, complemented
5#20255097C2116yesmaximal, direct product factor
6C2×#15689507C211yesmaximal, characteristic, complemented
7C2×#15689353C211yesmaximal, characteristic, complemented
8C2×#15689353C211yesmaximal, characteristic, complemented
9C2×#15689345C211yesmaximal, characteristic, complemented
10C2×#15689338C211yesmaximal, characteristic, complemented
11C2×#15689286C211yesmaximal, characteristic, complemented
12C2×#15689271C211yesmaximal, characteristic, complemented
13C2×#15689280C211yesmaximal, characteristic, complemented
14C2×#15689258C211yesmaximal, characteristic, complemented
15C2×C8×D188C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic, complemented
18C22×#10625352C2211yescharacteristic
19C22×Q8×D47C2211yescharacteristic
20C22×D4×D47C2211yescharacteristic
21C2×#13094045—28no—
22C2×#13094045C2218yescomplemented
23C22×Dic188C2211yescharacteristic, complemented
24C22×#10625337C2211yescharacteristic, complemented
25C22×#10625325C2211yescharacteristic
26C22×#10625325C2211yescharacteristic, complemented
27C22×#10625335C2211yescharacteristic
28C22×#10625336C2211yescharacteristic
29C2×SD16×D47—28no—
30C2×SD16×D47C2218yescomplemented
31C22×D376C2211yescharacteristic
32C22×#10625334C2211yescharacteristic
33C22×C8×D47C2211yescharacteristic
34C22×C8×D47C2211yescharacteristic, complemented
35#15689785—24no—
36#15689785C2218yescomplemented
37#15689768—24no—
38#15689768C2218yescomplemented
39C2×#13094012—21no—
40C2×#13094012C2211yescharacteristic
41C2×#13094012C2211yescharacteristic, complemented
42C2×#13094008—21no—
43C2×#13094004—21no—
44C2×#13094004C2211yescharacteristic
45C2×#13094004C2211yescharacteristic, complemented
46C2×#13093999—21no—
47C2×#13093999C2211yescharacteristic
48C2×#13093999C2211yescharacteristic
49C2×#13093998—21no—
50C2×#13093994—21no—
51C2×C4×D188—21no—
52C2×C4×D188C2211yescharacteristic
53C22×(C2×D47)⋊C4—21no—
54#15689507C2218yescomplemented
55#15689353C2218yescomplemented
56#15689353C2218yescomplemented
57#15689345C2218yescomplemented
58#15689338C2218yescomplemented
59#15689286C2218yescomplemented
60#15689280C2218yescomplemented
61#15689271C2218yescomplemented
62#15689258C2218yescomplemented
63C8×D188C2218yescomplemented
64C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
65C2×#13093947C2211yescharacteristic, complemented
66C2×#13093947C2211yescharacteristic, complemented
67C2×#13093944C2211yescharacteristic
68C2×#13093944C2211yescharacteristic, complemented
69C2×(C2×D47)⋊C8C2211yescharacteristic
70C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
71C22×SD16×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic, complemented
73C2×C4×D4×C47C2211yescharacteristic
74C4×SD16×C47C2218yescomplemented
75C2×#106×C47C2211yescharacteristic, complemented
76C2×#103×C47C2211yescharacteristic, complemented
77C2×#102×C47C2211yescharacteristic
78C2×C4×C8×C47C2211yescharacteristic, complemented
79C24×D47—21no—
80C2×#10625354—22no—
81C2×#10625354—24no—
82C2×#10625354—42no—
83C2×#10625354C2314yescomplemented
84C2×#10625352—24no—
85C2×#10625352—22no—
86C2×#10625352—42no—
87C2×#10625352C2314yes—
88C22×Dic94—21no—
89C22×Dic94C2311yescharacteristic
90C22×Dic94C2311yescharacteristic
91C2×Q8×D47—22no—
92C2×Q8×D47—24no—
93C2×Q8×D47—42no—
94C2×Q8×D47C2314yes—
95C22×D188—21no—
96C22×D188—21no—
97C22×D188—21no—
98C22×D188D411yescharacteristic
99C22×D188C2311yescharacteristic
100C22×D188C2311yescharacteristic
101C22×C22⋊D47—21no—
102C22×C22⋊D47—21no—
103C2×D4×D47—24no—
104C2×D4×D47—22no—
105C2×D4×D47—42no—
106C2×D4×D47C2314yes—
107C23×Dic47—21no—
108C22×C4×D47—21no—
109C22×C4×D47—21no—
110C22×C4×D47C2311yescharacteristic
111C22×C4×D47C2311yescharacteristic
112#13094045—232no—
113C2×Dic188—42no—
114C2×Dic188C2314yescomplemented
115C2×#10625337—24no—
116C2×#10625337C2314yescomplemented
117C2×#10625325—24no—
118C2×#10625325—24no—
119C2×#10625325C2314yes—
120C2×#10625325C2314yescomplemented
121C2×#10625335—24no—
122C2×#10625335C2314yes—
123C2×#10625336—24no—
124C2×#10625336C2314yes—
125SD16×D47—232no—
126C2×D376—42no—
127C2×D376C2314yes—
128C2×#10625334—24no—
129C2×#10625334C2314yes—
130C22×C47⋊C8C2311yescharacteristic
131C22×C47⋊C8C2311yescharacteristic
132C2×C8×D47—24no—
133C2×C8×D47—24no—
134C2×C8×D47C2314yes—
135C2×C8×D47C2314yescomplemented
136#13094012—22no—
137#13094012—22no—
138#13094012—28no—
139#13094012C2314yes—
140#13094012C2314yescomplemented
141#13094008—28no—
142#13094004—22no—
143#13094004—22no—
144#13094004—28no—
145#13094004C2314yes—
146#13094004C2314yescomplemented
147#13093999—28no—
148#13093999—22no—
149#13093999—22no—
150#13093999C2314yes—
151#13093999C2314yes—
152#13093998—28no—
153#13093994—28no—
154C4×D188—28no—
155C4×D188D414yes—
156C4×D188C2314yes—
157C2×C4⋊Dic47—21no—
158C2×C4⋊Dic47—21no—
159C2×C4⋊Dic47D411yescharacteristic
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—21no—
166C2×(C2×D47)⋊C4—21no—
167C2×(C2×D47)⋊C4—21no—
168C2×(C2×D47)⋊C4—28no—
169C2×(C2×D47)⋊C4D411yescharacteristic
170C2×(C2×D47)⋊C4D411yescharacteristic
171C4⋊(C47⋊C8)C2314yescomplemented
172#13093947C2314yescomplemented
173#13093947C2314yescomplemented
174#13093944C2314yes—
175#13093944C2314yescomplemented
176(C2×D47)⋊C8C2314yes—
177(C2×D47)⋊C8C2314yescomplemented
178C22×Q8×C47C2311yescharacteristic
179C22×D4×C47C2311yescharacteristic
180C23×C4×C47—21no—
181C2×SD16×C47D418yescomplemented
182C2×SD16×C47C2314yes—
183C22×C8×C47C2311yescharacteristic
184C22×C8×C47C2311yescharacteristic
185C4×Q8×C47—22no—
186C4×Q8×C47C2314yescomplemented
187C4×D4×C47—22no—
188C4×D4×C47C2314yes—
189C2×C4⋊C4×C47—21no—
190C2×C4⋊C4×C47C2311yescharacteristic
191C2×C4⋊C4×C47C2311yescharacteristic
192C2×C22⋊C4×C47—21no—
193C2×C42×C47—21no—
194C2×C42×C47C2311yescharacteristic
195#106×C47C2314yescomplemented
196#103×C47C2314yescomplemented
197#102×C47C2314yes—
198C4×C8×C47C2314yescomplemented
199C24×C47—21no—
200C23×D47—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×C47C2×D414yes—
211C2×Q8×C47C2412yes—
212C2×D4×C47—21no—
213C2×D4×C47—22no—
214C2×D4×C47C2×D414yes—
215C2×D4×C47C2412yes—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—24no—
220C22×C4×C47—82no—
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2411yescharacteristic
224C2×C22⋊D47—24no—
225C2×C22⋊D47—24no—
226C2×C22⋊D47—44no—
227C2×C22⋊D47—44no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47—24no—
231C22×Dic47—44no—
232C22×Dic47C2×D411yescharacteristic
233C22×Dic47C2×D411yescharacteristic
234#10625354—28no—
235#10625354—44no—
236#10625354—48no—
237Q8×D47—28no—
238Q8×D47—44no—
239Q8×D47—48no—
240#10625352—28no—
241#10625352—44no—
242#10625352—48no—
243D4×D47—28no—
244D4×D47—44no—
245D4×D47—48no—
246C2×D188—24no—
247C2×D188—22no—
248C2×D188—22no—
249C2×D188—22no—
250C2×D188—22no—
251C2×D188—24no—
252C2×D188—24no—
253C2×D188—21no—
254C2×D188—21no—
255C2×D188—24no—
256C2×D188—44no—
257C2×D188—44no—
258C2×D188—82no—
259C2×D188C2×D414yes—
260C2×D188C2412yes—
261C2×D188C2412yes—
262C2×C4×D47—22no—
263C2×C4×D47—22no—
264C2×C4×D47—22no—
265C2×C4×D47—22no—
266C2×C4×D47—24no—
267C2×C4×D47—24no—
268C2×C4×D47—44no—
269C2×C4×D47—44no—
270C2×C4×D47C2×D412yes—
271C2×C4×D47C2×D412yes—
272C2×C4×D47C2412yes—
273C2×C4×D47C2412yes—
274C2×Dic94—22no—
275C2×Dic94—22no—
276C2×Dic94—22no—
277C2×Dic94—22no—
278C2×Dic94—21no—
279C2×Dic94—21no—
280C2×Dic94—24no—
281C2×Dic94—44no—
282C2×Dic94C2412yes—
283C2×Dic94C2412yes—
284SD16×C47C2×D4116yescomplemented
285C2×C8×C47—22no—
286C2×C8×C47C2×D414yes—
287C2×C8×C47C2412yes—
288C2×C8×C47C2412yes—
289C4⋊C4×C47—24no—
290C4⋊C4×C47—21no—
291C4⋊C4×C47—21no—
292C4⋊C4×C47C2412yes—
293C4⋊C4×C47C2412yes—
294C22⋊C4×C47—24no—
295C42×C47—24no—
296C42×C47C2×D412yes—
297C42×C47C2412yes—
298#10625337—28no—
299#10625336—28no—
300#10625335—28no—
301#10625334—28no—
302(C2×D47)⋊C4—24no—
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)⋊C4—24no—
309(C2×D47)⋊C4—24no—
310(C2×D47)⋊C4C2×D414yes—
311(C2×D47)⋊C4C2×D414yes—
312C4⋊Dic47—24no—
313C4⋊Dic47—24no—
314C4⋊Dic47C2×D414yes—
315C2×C47⋊C8—22no—
316C2×C47⋊C8—22no—
317C2×C47⋊C8C2412yes—
318C2×C47⋊C8C2412yes—
319Dic188—44no—
320D376—44no—
321#10625325—28no—
322#10625325—28no—
323C8×D47—28no—
324C8×D47—28no—
325C23×C47—24no—
326C23×C47—22no—
327C23×C47—42no—
328C23×C47—42no—
329C23×C47C22×D411yescharacteristic
330C22×D47—22no—
331C22×D47—22no—
332C22×D47—22no—
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—22no—
337C22×D47—48no—
338C22×D47—42no—
339C22×D47—42no—
340C22×D47—42no—
341C22×D47—42no—
342C22×D47—42no—
343C22×D47—42no—
344C22×D47—48no—
345C22×D47—84no—
346C22×D47—816no—
347C22×D47#13514yescomplemented
348C22×D47C22×D412yes—
349C22×D47C22×D412yes—
350Q8×C47—24no—
351Q8×C47—22no—
352Q8×C47C22×D414yes—
353D4×C47—24no—
354D4×C47—22no—
355D4×C47C22×D414yes—
356C2×C4×C47—24no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—42no—
363C2×C4×C47—42no—
364C2×C4×C47—84no—
365C2×C4×C47C22×D412yes—
366C2×C4×C47C22×D412yes—
367C2×C4×C47C22×D411yescharacteristic
368C2×C4×C47C22×D412yes—
369C2×C4×C47H(5,𝔽2)12yes—
370C2×C4×C47C2511yescharacteristic
371C22⋊D47—48no—
372C22⋊D47—48no—
373C2×Dic47—22no—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—48no—
378C2×Dic47—42no—
379C2×Dic47—42no—
380C2×Dic47C22×D412yes—
381C2×Dic47C22×D412yes—
382D188—28no—
383D188—22no—
384D188—22no—
385D188—22no—
386D188—22no—
387D188—48no—
388D188—48no—
389D188—42no—
390D188—42no—
391D188—84no—
392C4×D47—24no—
393C4×D47—24no—
394C4×D47—22no—
395C4×D47—22no—
396C4×D47—22no—
397C4×D47—22no—
398C4×D47—48no—
399C4×D47—48no—
400Dic94—22no—
401Dic94—22no—
402Dic94—22no—
403Dic94—22no—
404Dic94—48no—
405Dic94—42no—
406Dic94—42no—
407C8×C47—22no—
408C8×C47C22×D414yes—
409C47⋊C8—22no—
410C47⋊C8—22no—
411C2×#3282—471nomaximal, Sylow
412C22×C47—24no—
413C22×C47—48no—
414C22×C47—42no—
415C22×C47—42no—
416C22×C47D4212yes—
417C22×C47C2×#13512yes—
418C22×C47#57712yes—
419C22×C47C23×D411yescharacteristic
420C2×D47—22no—
421C2×D47—28no—
422C2×D47—22no—
423C2×D47—22no—
424C2×D47—22no—
425C2×D47—22no—
426C2×D47—44no—
427C2×D47—42no—
428C2×D47—42no—
429C2×D47—42no—
430C2×D47—42no—
431C2×D47—42no—
432C2×D47—42no—
433C2×D47—816no—
434C2×D47—84no—
435C2×D47—84no—
436C2×D47C2×#13514yescomplemented
437C4×C47—24no—
438C4×C47—22no—
439C4×C47—22no—
440C4×C47—42no—
441C4×C47—42no—
442C4×C47D4212yes—
443C4×C47C23×D411yescharacteristic
444C4×C47C2×H(5,𝔽2)11yescharacteristic
445Dic47—22no—
446Dic47—22no—
447Dic47—42no—
448Dic47—42no—
449C22×#135—471no—
450C23×SD16—471no—
451C2×#548—471no—
452C2×#546—471no—
453#3282—4716no—
454C2×#495—471no—
455C2×#465—471no—
456C2×#465—471no—
457C2×#464—471no—
458C2×#463—471no—
459C2×#452—471no—
460C2×#449—471no—
461C2×#451—471no—
462C2×#447—471no—
463C2×C4×SD16D4711yescharacteristic, complemented
464C2×C8×D4—471no—
465C2×C47—44no—
466C2×C47#328214yescomplemented
467C2×C47C2×D4211yescharacteristic
468C2×C47C22×#13511yescharacteristic
469C2×C47C2×#57711yescharacteristic
470D47—24no—
471D47—42no—
472D47—82no—
473D47—82no—
474C22×#41—471no—
475C22×#41—471no—
476C23×Q8—471no—
477C23×D4—471no—
478C2×#135—478no—
479C2×#135—948no—
480C22×Q16—471no—
481C22×Q16—471no—
482C22×SD16—471no—
483C22×SD16—471no—
484C22×SD16—478no—
485C22×SD16—471no—
486C22×SD16—471no—
487C22×SD16—948no—
488C22×SD16C2×D4711yescharacteristic
489C22×D8—471no—
490C22×D8—471no—
491C23×C8—471no—
492C23×C8—471no—
493#548—478no—
494#548—944no—
495#546—478no—
496#546—944no—
497C2×#124—471no—
498C2×#124—471no—
499C2×#124—941no—
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×Q8C2×D4711yescharacteristic, complemented
510C2×C4×D4—471no—
511C2×C4×D4—941no—
512C2×C4×D4C2×D4711yescharacteristic
513C22×C22⋊C4—941no—
514#495—478no—
515#465—478no—
516#465—478no—
517#464—478no—
518#463—478no—
519#452—478no—
520#451—478no—
521#449—478no—
522#447—478no—
523C4×SD16C2×D4718yescomplemented
524C8×D4—478no—
525C2×#106C2×D4711yescharacteristic, complemented
526C2×C4⋊C8—471no—
527C2×#103—471no—
528C2×#103—471no—
529C2×#103C2×D4711yescharacteristic, complemented
530C2×#102—471no—
531C2×#102—471no—
532C2×#102C2×D4711yescharacteristic
533C2×C22⋊C8—471no—
534C2×C22⋊C8—471no—
535C2×C4×C8C2×D4711yescharacteristic, complemented
536C47C2×#328211yescharacteristic, 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—471no—
558C22×D4—941no—
559C22×D4—941no—
560C22×D4—941no—
561C22×D4—942no—
562C22×D4—941no—
563C22×D4—944no—
564C22×D4—941no—
565C22×D4—1882no—
566C22×D4C22×D4711yescharacteristic
567C23×C4—21no—
568C23×C4—471no—
569C23×C4—471no—
570C23×C4—941no—
571C23×C4—941no—
572C23×C4—941no—
573#135—9432no—
574C2×Q16—474no—
575C2×Q16—474no—
576C2×Q16—944no—
577C2×Q16—1882no—
578C2×SD16—474no—
579C2×SD16—474no—
580C2×SD16—474no—
581C2×SD16—474no—
582C2×SD16—944no—
583C2×SD16—944no—
584C2×SD16—9432no—
585C2×SD16—944no—
586C2×SD16—944no—
587C2×SD16D18818yescomplemented
588C2×SD16C22×D4714yes—
589C2×D8—474no—
590C2×D8—474no—
591C2×D8—944no—
592C2×D8—1882no—
593C22×C8—471no—
594C22×C8—471no—
595C22×C8—474no—
596C22×C8—474no—
597C22×C8—944no—
598C22×C8—944no—
599C22×C8C22×D4711yescharacteristic
600C22×C8C22×D4711yescharacteristic
601#124—474no—
602#124—474no—
603#124—948no—
604#124—942no—
605#124—942no—
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—942no—
616#121—942no—
617#121—948no—
618#120—948no—
619C4×Q8—22no—
620C4×Q8C22×D4714yescomplemented
621C4×D4—22no—
622C4×D4—474no—
623C4×D4—474no—
624C4×D4—948no—
625C4×D4C22×D4714yes—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—471no—
628C2×C4⋊C4—941no—
629C2×C4⋊C4—941no—
630C2×C4⋊C4C22×D4711yescharacteristic
631C2×C4⋊C4C22×D4711yescharacteristic
632C2×C22⋊C4—21no—
633C2×C22⋊C4—471no—
634C2×C22⋊C4—471no—
635C2×C22⋊C4—948no—
636C2×C22⋊C4—941no—
637C2×C22⋊C4—941no—
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—21no—
645C2×C42C22×D4711yescharacteristic
646#106C22×D4714yescomplemented
647C4⋊C8—474no—
648#103—474no—
649#103—474no—
650#103C22×D4714yescomplemented
651#102—474no—
652#102—474no—
653#102C22×D4714yes—
654C22⋊C8—474no—
655C22⋊C8—474no—
656C4×C8C22×D4714yescomplemented
657C24—21no—
658C24—471no—
659C24—471no—
660C24—944no—
661C24—941no—
662C24—941no—
663C24—3762no—
664C24—1884no—
665C24—1884no—
666#41—948no—
667#41—948no—
668#41—1884no—
669#41—1888no—
670#41—1884no—
671#41—1888no—
672C2×Q8—21no—
673C2×Q8—22no—
674C2×Q8—472no—
675C2×Q8—472no—
676C2×Q8—944no—
677C2×Q8—941no—
678C2×Q8—941no—
679C2×Q8—948no—
680C2×Q8—942no—
681C2×Q8—942no—
682C2×Q8—942no—
683C2×Q8—942no—
684C2×Q8—1884no—
685C2×Q8—1884no—
686C2×Q8—1888no—
687C2×Q8C2×D18814yes—
688C2×Q8C23×D4712yes—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—474no—
692C2×D4—472no—
693C2×D4—472no—
694C2×D4—944no—
695C2×D4—944no—
696C2×D4—944no—
697C2×D4—944no—
698C2×D4—944no—
699C2×D4—948no—
700C2×D4—944no—
701C2×D4—941no—
702C2×D4—941no—
703C2×D4—942no—
704C2×D4—942no—
705C2×D4—942no—
706C2×D4—942no—
707C2×D4—3762no—
708C2×D4—1884no—
709C2×D4—1884no—
710C2×D4—1884no—
711C2×D4—1888no—
712C2×D4—1884no—
713C2×D4—1884no—
714C2×D4C2×D18814yes—
715C2×D4C23×D4712yes—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—24no—
720C22×C4—82no—
721C22×C4—471no—
722C22×C4—471no—
723C22×C4—472no—
724C22×C4—472no—
725C22×C4—472no—
726C22×C4—472no—
727C22×C4—944no—
728C22×C4—944no—
729C22×C4—944no—
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—1884no—
744SD16—948no—
745SD16—948no—
746SD16—948no—
747SD16—948no—
748SD16C2×D188116yescomplemented
749D8—948no—
750D8—1884no—
751C2×C8—22no—
752C2×C8—472no—
753C2×C8—472no—
754C2×C8—942no—
755C2×C8—942no—
756C2×C8—948no—
757C2×C8—948no—
758C2×C8C2×D18814yes—
759C2×C8C23×D4712yes—
760C2×C8C23×D4712yes—
761C4⋊C4—24no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—474no—
765C4⋊C4—944no—
766C4⋊C4—944no—
767C4⋊C4C23×D4712yes—
768C4⋊C4C23×D4712yes—
769C22⋊C4—24no—
770C22⋊C4—474no—
771C22⋊C4—474no—
772C22⋊C4—944no—
773C22⋊C4—944no—
774C22⋊C4—944no—
775C22⋊C4—944no—
776C22⋊C4—944no—
777C22⋊C4—944no—
778C22⋊C4—944no—
779C22⋊C4—944no—
780C42—24no—
781C42D4×D4712yes—
782C42C23×D4712yes—
783C23—24no—
784C23—22no—
785C23—42no—
786C23—42no—
787C23—474no—
788C23—472no—
789C23—472no—
790C23—942no—
791C23—942no—
792C23—942no—
793C23—942no—
794C23—942no—
795C23—942no—
796C23—942no—
797C23—37616no—
798C23—3764no—
799C23—1888no—
800C23—1888no—
801C23—1882no—
802C23—1882no—
803C23—1882no—
804C23—1882no—
805C23—1882no—
806C23—1882no—
807C23C2×D4×D4711yescharacteristic
808Q8—24no—
809Q8—22no—
810Q8—942no—
811Q8—942no—
812Q8—942no—
813Q8—942no—
814Q8—1888no—
815Q8—1882no—
816Q8—1882no—
817Q8C22×D18814yes—
818D4—24no—
819D4—22no—
820D4—948no—
821D4—942no—
822D4—942no—
823D4—942no—
824D4—942no—
825D4—3764no—
826D4—1888no—
827D4—1888no—
828D4—1888no—
829D4—1888no—
830D4—1882no—
831D4—1882no—
832D4C22×D18814yes—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—84no—
842C2×C4—472no—
843C2×C4—472no—
844C2×C4—942no—
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×C4C22×D18812yes—
863C2×C4#1309407012yes—
864C2×C4C24×D4711yescharacteristic
865C8—22no—
866C8—942no—
867C8—942no—
868C8C22×D18814yes—
869C22—24no—
870C22—42no—
871C22—42no—
872C22—48no—
873C22—474no—
874C22—942no—
875C22—942no—
876C22—948no—
877C22—942no—
878C22—942no—
879C22—942no—
880C22—37616no—
881C22—3764no—
882C22—3764no—
883C22—1882no—
884C22—1882no—
885C22—1882no—
886C22—1882no—
887C22—1882no—
888C22—1882no—
889C22—1884no—
890C22D4×D18812yes—
891C22#135×D4712yes—
892C22#1568992912yes—
893C22C22×D4×D4711yescharacteristic
894C4—24no—
895C4—22no—
896C4—22no—
897C4—42no—
898C4—42no—
899C4—942no—
900C4—942no—
901C4—1882no—
902C4—1882no—
903C4D4×D18812yes—
904C4C23×D18811yescharacteristic
905C4C2×#1309407011yescharacteristic
906C2—44no—
907C2—944no—
908C2—3762no—
909C2—3762no—
910C2—1882no—
911C2#2025509714yesdirect product factor
912C2C2×D4×D18811yescharacteristic
913C2C2×#135×D4711yescharacteristic
914C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×SD16×C47C2
socleC23×C47C22×D4
hypercenterC2×C4×SD16D47
hypocenterC47C2×#3282
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#13094045C2semidirect
2. C22×SD16×D47C2semidirect
3. C2×#15689785C2semidirect
4. C2×#15689768C2semidirect
5. #20255097C2direct (N × H)
6. C2×#15689507C2semidirect
7. C2×#15689353C2semidirect
8. C2×#15689353C2semidirect
9. C2×#15689345C2semidirect
10. C2×#15689338C2semidirect
11. C2×#15689286C2semidirect
12. C2×#15689271C2semidirect
13. C2×#15689280C2semidirect
14. C2×#15689258C2semidirect
15. C2×C8×D188C2semidirect
16. C2×C4×SD16×C47C2semidirect
17. C22×#10625354C22semidirect
22. C2×#13094045C22semidirect
23. C22×Dic188C22semidirect
24. C22×#10625337C22semidirect
26. C22×#10625325C22semidirect
30. C2×SD16×D47C22semidirect
34. C22×C8×D47C22semidirect
36. #15689785C22semidirect
38. #15689768C22semidirect
41. C2×#13094012C22semidirect
45. C2×#13094004C22semidirect
54. #15689507C22semidirect
55. #15689353C22semidirect
56. #15689353C22semidirect
57. #15689345C22semidirect
58. #15689338C22semidirect
59. #15689286C22semidirect
60. #15689280C22semidirect
61. #15689271C22semidirect
62. #15689258C22semidirect
63. C8×D188C22semidirect
64. C2×C4⋊(C47⋊C8)C22semidirect
65. C2×#13093947C22semidirect
66. C2×#13093947C22semidirect
68. C2×#13093944C22semidirect
70. C2×(C2×D47)⋊C8C22semidirect
72. C2×C4×Q8×C47C22semidirect
74. C4×SD16×C47C22semidirect
75. C2×#106×C47C22semidirect
76. C2×#103×C47C22semidirect
78. C2×C4×C8×C47C22semidirect
83. C2×#10625354C23semidirect
114. C2×Dic188C23semidirect
116. C2×#10625337C23semidirect
120. C2×#10625325C23semidirect
135. C2×C8×D47C23semidirect
140. #13094012C23semidirect
146. #13094004C23semidirect
171. C4⋊(C47⋊C8)C23semidirect
172. #13093947C23semidirect
173. #13093947C23semidirect
175. #13093944C23semidirect
177. (C2×D47)⋊C8C23semidirect
181. C2×SD16×C47D4semidirect
186. C4×Q8×C47C23semidirect
195. #106×C47C23semidirect
196. #103×C47C23semidirect
198. C4×C8×C47C23semidirect
284. SD16×C47C2×D4semidirect
347. C22×D47#135semidirect
436. C2×D47C2×#135semidirect
463. C2×C4×SD16D47semidirect
466. C2×C47#3282semidirect
509. C2×C4×Q8C2×D47semidirect
523. C4×SD16C2×D47semidirect
525. C2×#106C2×D47semidirect
529. C2×#103C2×D47semidirect
535. C2×C4×C8C2×D47semidirect
536. C47C2×#3282semidirect
587. C2×SD16D188semidirect
620. C4×Q8C22×D47semidirect
646. #106C22×D47semidirect
650. #103C22×D47semidirect
656. C4×C8C22×D47semidirect
748. SD16C2×D188semidirect
911. C2#20255097direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940452
C22×SD16×D472
C2×#156897852
C2×#156897682
#202550972
C2×#156895072
C2×#156893532
C2×#156893452
C2×#156893382
C2×#156892862
C2×#156892712
C2×#156892802
C2×#156892582
C2×C8×D1882
C2×C4×SD16×C472
C2×#328247