Finite Group Databasebeta

← C2×#20255857 #27094840

Subgroups — C2×#20255857 #27094840

Order 12032.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689826C211yesmaximal, characteristic, complemented
2C2×#15689776C211yesmaximal, characteristic, complemented
3#20255857C2116yesmaximal, direct product factor
4C2×#15689443C211yesmaximal, characteristic, complemented
5C2×#15689443C211yesmaximal, characteristic, complemented
6C2×#15689450C211yesmaximal, characteristic, complemented
7C2×#15689438C211yesmaximal, characteristic, complemented
8C2×#15689420C211yesmaximal, characteristic, complemented
9C2×#15689410C211yesmaximal, characteristic, complemented
10C2×#15689377C211yesmaximal, characteristic, complemented
11C2×#15689360C211yesmaximal, characteristic, complemented
12C2×#15689236C211yesmaximal, characteristic, complemented
13C2×#15689196C211yesmaximal, characteristic, complemented
14C2×#15689164C211yesmaximal, characteristic, complemented
15C2×#106×D47C211yesmaximal, characteristic, complemented
16C2×C47×#501C211yesmaximal, characteristic, complemented
17C22×#10625354—21no—
18C22×D376C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689826—24no—
22#15689826C2218yescomplemented
23#15689776—24no—
24#15689776C2218yescomplemented
25C2×#13094019—21no—
26C2×#13094009—21no—
27C2×#13094009—21no—
28C2×#13094009—21no—
29C2×#13094000—21no—
30C2×#13093999—21no—
31C2×#13093999C2211yescharacteristic
32C2×#13093999C2211yescharacteristic
33C2×#13093999C2211yescharacteristic
34C2×#13093999C2211yescharacteristic
35C2×C4×D188C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37C2×C4×D188C2211yescharacteristic
38C2×#13093986—21no—
39C2×#13093982C2211yescharacteristic
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689450C2218yescomplemented
44#15689443C2218yescomplemented
45#15689443C2218yescomplemented
46#15689438C2218yescomplemented
47#15689420C2218yescomplemented
48#15689410C2218yescomplemented
49#15689377C2218yescomplemented
50#15689360C2218yescomplemented
51#15689236C2218yescomplemented
52#15689196C2218yescomplemented
53#15689164C2218yescomplemented
54C2×#13093957C2211yescharacteristic
55C2×#13093956C2211yescharacteristic
56C2×#13093955C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59#106×D47C2218yescomplemented
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C2×C4⋊Q8×C47C2211yescharacteristic
70C2×#125×C47C2211yescharacteristic
71C47×#501C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#107×C47C2211yescharacteristic
74C2×#106×C47C2211yescharacteristic
75C2×#106×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C2×#10625354—28no—
78C2×#10625354—48no—
79C22×D188—21no—
80C22×D188—21no—
81C22×D188—21no—
82C22×D188—21no—
83C22×D188D411yescharacteristic
84C22×D188C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C22×C4×D47—21no—
91C22×C4×D47C2311yescharacteristic
92C22×C4×D47C2311yescharacteristic
93C2×D376—24no—
94C2×D376C2314yes—
95C2×#10625324—24no—
96C2×#10625324C2314yes—
97C22×C47⋊C8C2311yescharacteristic
98C22×C47⋊C8C2311yescharacteristic
99C2×C8×D47—24no—
100C2×C8×D47C2314yes—
101#13094019—28no—
102#13094009—28no—
103#13094009—28no—
104#13094009—28no—
105#13094000—28no—
106#13093999—28no—
107#13093999—22no—
108#13093999—22no—
109#13093999—22no—
110#13093999—22no—
111#13093999C2314yes—
112#13093999C2314yes—
113#13093999C2314yes—
114#13093999C2314yes—
115C4×D188—22no—
116C4×D188—22no—
117C4×D188D414yes—
118C4×D188C2314yes—
119C4×D188C2314yes—
120C4×D188C2314yes—
121#13093986—28no—
122#13093982—22no—
123#13093982C2314yes—
124C2×C4⋊Dic47D411yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C4⋊C4×D47—22no—
131C4⋊C4×D47—22no—
132C4⋊C4×D47—22no—
133C4⋊C4×D47C2314yes—
134C4⋊C4×D47C2314yes—
135C4⋊C4×D47C2314yes—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4D411yescharacteristic
144C2×(C2×D47)⋊C4D411yescharacteristic
145C2×C4×Dic47—21no—
146#13093957C2314yes—
147#13093956C2314yes—
148#13093955C2314yes—
149#13093955C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152#13093946C2314yes—
153#13093946C2314yes—
154#13093944C2314yes—
155#13093944C2314yes—
156#13093944C2314yes—
157#13093944C2314yes—
158(C2×D47)⋊C8C2314yes—
159(C2×D47)⋊C8C2314yes—
160C22×Q8×C47—21no—
161C22×C8×C47C2311yescharacteristic
162C22×C8×C47C2311yescharacteristic
163C4⋊Q8×C47—22no—
164C4⋊Q8×C47C2314yes—
165#125×C47—22no—
166#125×C47C2314yes—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C42×C47C2311yescharacteristic
175#107×C47C2314yes—
176#107×C47C2314yes—
177#106×C47C2314yes—
178#106×C47C2314yes—
179#97×C47C2314yes—
180C23×D47—21no—
181C23×D47—21no—
182C23×D47C2×D411yescharacteristic
183C23×D47C2×D411yescharacteristic
184C2×Q8×C47—24no—
185C2×Q8×C47—44no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2411yescharacteristic
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47C2×D411yescharacteristic
196C22×Dic47C2×D411yescharacteristic
197#10625354—432no—
198C2×D188—24no—
199C2×D188—22no—
200C2×D188—22no—
201C2×D188—22no—
202C2×D188—22no—
203C2×D188—24no—
204C2×D188—24no—
205C2×D188—24no—
206C2×D188—21no—
207C2×D188—21no—
208C2×D188—24no—
209C2×D188—44no—
210C2×D188—44no—
211C2×D188—44no—
212C2×D188—82no—
213C2×D188C2×D414yes—
214C2×D188C2412yes—
215C2×D188C2412yes—
216C2×C4×D47—22no—
217C2×C4×D47—22no—
218C2×C4×D47—22no—
219C2×C4×D47—22no—
220C2×C4×D47—24no—
221C2×C4×D47—24no—
222C2×C4×D47—24no—
223C2×C4×D47—24no—
224C2×C4×D47—24no—
225C2×C4×D47—44no—
226C2×C4×D47—44no—
227C2×C4×D47—44no—
228C2×C4×D47—82no—
229C2×C4×D47—82no—
230C2×C4×D47C2×D412yes—
231C2×C4×D47C2×D412yes—
232C2×C4×D47C2412yes—
233C2×C4×D47C2412yes—
234C2×C8×C47—22no—
235C2×C8×C47#4114yescomplemented
236C2×C8×C47C2412yes—
237C2×C8×C47C2412yes—
238C4⋊C4×C47—24no—
239C4⋊C4×C47—24no—
240C4⋊C4×C47—24no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47C2412yes—
246C4⋊C4×C47C2412yes—
247C4⋊C4×C47C2412yes—
248C4⋊C4×C47C2412yes—
249C42×C47C2×D412yes—
250C42×C47C2412yes—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4C2×D414yes—
259(C2×D47)⋊C4C2×D414yes—
260C4⋊Dic47—21no—
261C4⋊Dic47—21no—
262C4⋊Dic47C2×D414yes—
263C4⋊Dic47C2412yes—
264C4⋊Dic47C2412yes—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268C4×Dic47—24no—
269C2×C47⋊C8—22no—
270C2×C47⋊C8—22no—
271C2×C47⋊C8C2412yes—
272C2×C47⋊C8C2412yes—
273D376—28no—
274#10625324—28no—
275C8×D47—28no—
276C23×C47C22×D411yescharacteristic
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—42no—
285C22×D47—42no—
286C22×D47—42no—
287C22×D47—42no—
288C22×D47—42no—
289C22×D47—42no—
290C22×D47AGL(1,ℤ/8)14yes—
291C22×D47C22×D412yes—
292C22×D47C22×D412yes—
293Q8×C47—48no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47—42no—
304C2×C4×C47C22×D412yes—
305C2×C4×C47C22×D412yes—
306C2×C4×C47C22×D411yescharacteristic
307C2×C4×C47C2×#4112yes—
308C2×C4×C472−1+412yes—
309C2×C4×C47C2511yescharacteristic
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47C22×D412yes—
317C2×Dic47C22×D412yes—
318D188—28no—
319D188—22no—
320D188—22no—
321D188—22no—
322D188—22no—
323D188—48no—
324D188—48no—
325D188—48no—
326D188—42no—
327D188—42no—
328D188—84no—
329C4×D47—24no—
330C4×D47—24no—
331C4×D47—22no—
332C4×D47—22no—
333C4×D47—22no—
334C4×D47—22no—
335C4×D47—48no—
336C4×D47—48no—
337C4×D47—48no—
338C4×D47—84no—
339C4×D47—84no—
340C8×C47—22no—
341C8×C47C2×#4114yescomplemented
342C47⋊C8—22no—
343C47⋊C8—22no—
344C2×#3345—471nomaximal, Sylow
345C22×C47#54712yes—
346C22×C47C2×AGL(1,ℤ/8)12yes—
347C22×C47#57712yes—
348C22×C47C23×D411yescharacteristic
349C2×D47—28no—
350C2×D47—22no—
351C2×D47—22no—
352C2×D47—22no—
353C2×D47—22no—
354C2×D47—22no—
355C2×D47—44no—
356C2×D47—42no—
357C2×D47—42no—
358C2×D47—42no—
359C2×D47—42no—
360C2×D47—42no—
361C2×D47—42no—
362C2×D47—84no—
363C2×D47—84no—
364C2×D47C2×AGL(1,ℤ/8)14yes—
365C4×C47—22no—
366C4×C47—22no—
367C4×C47—42no—
368C4×C47—42no—
369C4×C47—42no—
370C4×C47—42no—
371C4×C47#54712yes—
372C4×C47C22×#4111yescharacteristic
373C4×C47C2×2−1+411yescharacteristic
374Dic47—22no—
375Dic47—22no—
376Dic47—42no—
377Dic47—42no—
378C2×#553—471no—
379C2×#547—471no—
380#3345—4716no—
381C2×#501D4711yescharacteristic, complemented
382C2×#481—471no—
383C2×#481—471no—
384C2×#482—471no—
385C2×#480—471no—
386C2×#478—471no—
387C2×#476—471no—
388C2×#469—471no—
389C2×#466—471no—
390C2×#442—471no—
391C2×#435—471no—
392C2×#428—471no—
393C22×#106—471no—
394C2×C47#334514yescomplemented
395C2×C47C2×#54711yescharacteristic
396C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
397C2×C47C2×#57711yescharacteristic
398D47—24no—
399D47—42no—
400D47—82no—
401D47—82no—
402C22×#41—941no—
403C22×D8—471no—
404C22×M16—471no—
405C23×C8—471no—
406#553—478no—
407#553—944no—
408#547—478no—
409#547—944no—
410C2×C4⋊Q8C2×D4711yescharacteristic
411C2×#126—941no—
412C2×#125C2×D4711yescharacteristic
413C2×#123—941no—
414C2×#123—941no—
415C2×#123—941no—
416C2×C22⋊Q8—941no—
417C2×#121—471no—
418C2×#121—471no—
419C2×#121—471no—
420C2×#121—471no—
421C2×#121—941no—
422C2×C4×D4—471no—
423C2×C4×D4—471no—
424C2×C4×D4—471no—
425C2×C4×D4—941no—
426C2×#117—471no—
427C22×C4⋊C4—471no—
428C22×C4⋊C4—471no—
429C22×C4⋊C4—471no—
430#501C2×D4718yescomplemented
431#482—478no—
432#481—478no—
433#481—478no—
434#480—478no—
435#478—478no—
436#476—478no—
437#469—478no—
438#466—478no—
439#442—478no—
440#435—478no—
441#428—478no—
442C2×#107—471no—
443C2×#107C2×D4711yescharacteristic
444C2×#107C2×D4711yescharacteristic
445C2×#106—471no—
446C2×#106—471no—
447C2×#106—471no—
448C2×#106—471no—
449C2×#106—478no—
450C2×#106C2×D4711yescharacteristic
451C2×#106C2×D4711yescharacteristic
452C2×C4⋊C8—471no—
453C2×#102—471no—
454C2×#102—471no—
455C2×#102—471no—
456C2×#102—471no—
457C2×#102—471no—
458C2×#102—471no—
459C2×C22⋊C8—471no—
460C2×C22⋊C8—471no—
461C2×#97C2×D4711yescharacteristic
462C47C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—948no—
464C2×#41—1888no—
465C22×Q8—21no—
466C22×D4—471no—
467C22×D4—471no—
468C22×D4—471no—
469C22×D4—941no—
470C22×D4—941no—
471C22×D4—941no—
472C22×D4—941no—
473C23×C4—471no—
474C23×C4—471no—
475C23×C4—941no—
476C23×C4—941no—
477C23×C4—941no—
478C23×C4—941no—
479C23×C4—941no—
480C2×D8—474no—
481C2×D8—944no—
482C2×M16—474no—
483C2×M16—944no—
484C22×C8—471no—
485C22×C8—471no—
486C22×C8—474no—
487C22×C8—944no—
488C22×C8C22×D4711yescharacteristic
489C22×C8C22×D4711yescharacteristic
490C4⋊Q8—22no—
491C4⋊Q8C22×D4714yes—
492#126—948no—
493#125—22no—
494#125C22×D4714yes—
495#123—948no—
496#123—948no—
497#123—948no—
498C22⋊Q8—948no—
499#121—474no—
500#121—474no—
501#121—474no—
502#121—474no—
503#121—942no—
504#121—942no—
505#121—942no—
506#121—942no—
507#121—948no—
508C4×D4—474no—
509C4×D4—474no—
510C4×D4—474no—
511C4×D4—474no—
512C4×D4—948no—
513C4×D4—942no—
514C4×D4—942no—
515#117—474no—
516#117—942no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—474no—
524C2×C4⋊C4—474no—
525C2×C4⋊C4—474no—
526C2×C4⋊C4—942no—
527C2×C4⋊C4—942no—
528C2×C4⋊C4—942no—
529C2×C4⋊C4—941no—
530C2×C4⋊C4—941no—
531C2×C4⋊C4—941no—
532C2×C4⋊C4C22×D4711yescharacteristic
533C2×C4⋊C4C22×D4711yescharacteristic
534C2×C4⋊C4C22×D4711yescharacteristic
535C2×C4⋊C4C22×D4711yescharacteristic
536C2×C22⋊C4—471no—
537C2×C22⋊C4—471no—
538C2×C22⋊C4—941no—
539C2×C22⋊C4—941no—
540C2×C22⋊C4—941no—
541C2×C22⋊C4—941no—
542C2×C22⋊C4—941no—
543C2×C22⋊C4—941no—
544C2×C22⋊C4—941no—
545C2×C42—941no—
546C2×C42C22×D4711yescharacteristic
547#107—474no—
548#107C22×D4714yes—
549#107C22×D4714yes—
550#106—474no—
551#106—474no—
552#106—474no—
553#106—474no—
554#106C22×D4714yes—
555#106C22×D4714yes—
556C4⋊C8—474no—
557#102—474no—
558#102—474no—
559#102—474no—
560#102—474no—
561#102—474no—
562#102—474no—
563C22⋊C8—474no—
564C22⋊C8—474no—
565#97C22×D4714yes—
566C24—471no—
567C24—471no—
568C24—941no—
569C24—941no—
570#41—18832no—
571C2×Q8—24no—
572C2×Q8—44no—
573C2×D4—474no—
574C2×D4—472no—
575C2×D4—472no—
576C2×D4—944no—
577C2×D4—944no—
578C2×D4—944no—
579C2×D4—944no—
580C2×D4—944no—
581C2×D4—941no—
582C2×D4—941no—
583C2×D4—942no—
584C2×D4—942no—
585C2×D4—942no—
586C2×D4—942no—
587C2×D4—3762no—
588C2×D4—1884no—
589C2×D4—1884no—
590C2×D4—1884no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—471no—
596C22×C4—471no—
597C22×C4—472no—
598C22×C4—472no—
599C22×C4—472no—
600C22×C4—472no—
601C22×C4—944no—
602C22×C4—944no—
603C22×C4—944no—
604C22×C4—942no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—944no—
611C22×C4—944no—
612C22×C4—3762no—
613C22×C4—3762no—
614C22×C4—1884no—
615C22×C4—1884no—
616C22×C4—1884no—
617C22×C4D4×D4711yescharacteristic
618C22×C4D4×D4711yescharacteristic
619C22×C4C23×D4711yescharacteristic
620D8—948no—
621M16—948no—
622C2×C8—22no—
623C2×C8—472no—
624C2×C8—472no—
625C2×C8—942no—
626C2×C8—942no—
627C2×C8—948no—
628C2×C8#1062535414yescomplemented
629C2×C8C23×D4712yes—
630C2×C8C23×D4712yes—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—474no—
639C4⋊C4—472no—
640C4⋊C4—472no—
641C4⋊C4—944no—
642C4⋊C4—944no—
643C4⋊C4—944no—
644C4⋊C4—941no—
645C4⋊C4—941no—
646C4⋊C4C23×D4712yes—
647C4⋊C4C23×D4712yes—
648C4⋊C4C23×D4712yes—
649C4⋊C4C23×D4712yes—
650C22⋊C4—474no—
651C22⋊C4—474no—
652C22⋊C4—944no—
653C22⋊C4—944no—
654C22⋊C4—944no—
655C22⋊C4—944no—
656C22⋊C4—944no—
657C22⋊C4—944no—
658C22⋊C4—944no—
659C42—944no—
660C42D4×D4712yes—
661C42C23×D4712yes—
662C23—474no—
663C23—472no—
664C23—472no—
665C23—942no—
666C23—942no—
667C23—942no—
668C23—942no—
669C23—942no—
670C23—942no—
671C23—942no—
672C23—1882no—
673C23—1882no—
674C23—1882no—
675C23—1882no—
676C23—1882no—
677C23—1882no—
678C23C2×D4×D4711yescharacteristic
679Q8—48no—
680D4—948no—
681D4—942no—
682D4—942no—
683D4—942no—
684D4—942no—
685D4—3764no—
686D4—1888no—
687D4—1888no—
688D4—1888no—
689D4—1882no—
690D4—1882no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—472no—
702C2×C4—472no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—944no—
706C2×C4—944no—
707C2×C4—942no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—3764no—
714C2×C4—3764no—
715C2×C4—1888no—
716C2×C4—1888no—
717C2×C4—1888no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4C2×D4×D4712yes—
721C2×C4C2×D4×D4712yes—
722C2×C4C2×D4×D4711yescharacteristic
723C2×C4C2×#1062535412yes—
724C2×C4#1309407212yes—
725C2×C4C24×D4711yescharacteristic
726C8—22no—
727C8—942no—
728C8—942no—
729C8C2×#1062535414yescomplemented
730C22—474no—
731C22—942no—
732C22—942no—
733C22—948no—
734C22—942no—
735C22—942no—
736C22—942no—
737C22—3764no—
738C22—3764no—
739C22—1882no—
740C22—1882no—
741C22—1882no—
742C22—1882no—
743C22—1882no—
744C22—1882no—
745C22—1884no—
746C22#1568977612yes—
747C22AGL(1,ℤ/8)×D4712yes—
748C22#1568993212yes—
749C22C22×D4×D4711yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—942no—
757C4—942no—
758C4—1882no—
759C4—1882no—
760C4#1568977612yes—
761C4C22×#1062535411yescharacteristic
762C4C2×#1309407211yescharacteristic
763C2—944no—
764C2—3762no—
765C2—3762no—
766C2—1882no—
767C2#2025585714yesdirect product factor
768C2C2×#1568977611yescharacteristic
769C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
770C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#501C2
socleC23×C47C22×D4
hypercenterC2×#501D47
hypocenterC47C2×#3345
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#15689826C2semidirect
2. C2×#15689776C2semidirect
3. #20255857C2direct (N × H)
4. C2×#15689443C2semidirect
5. C2×#15689443C2semidirect
6. C2×#15689450C2semidirect
7. C2×#15689438C2semidirect
8. C2×#15689420C2semidirect
9. C2×#15689410C2semidirect
10. C2×#15689377C2semidirect
11. C2×#15689360C2semidirect
12. C2×#15689236C2semidirect
13. C2×#15689196C2semidirect
14. C2×#15689164C2semidirect
15. C2×#106×D47C2semidirect
16. C2×C47×#501C2semidirect
22. #15689826C22semidirect
24. #15689776C22semidirect
43. #15689450C22semidirect
44. #15689443C22semidirect
45. #15689443C22semidirect
46. #15689438C22semidirect
47. #15689420C22semidirect
48. #15689410C22semidirect
49. #15689377C22semidirect
50. #15689360C22semidirect
51. #15689236C22semidirect
52. #15689196C22semidirect
53. #15689164C22semidirect
59. #106×D47C22semidirect
71. C47×#501C22semidirect
235. C2×C8×C47#41semidirect
341. C8×C47C2×#41semidirect
381. C2×#501D47semidirect
394. C2×C47#3345semidirect
430. #501C2×D47semidirect
462. C47C2×#3345semidirect
628. C2×C8#10625354semidirect
729. C8C2×#10625354semidirect
767. C2#20255857direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898262
C2×#156897762
#202558572
C2×#156894432
C2×#156894502
C2×#156894382
C2×#156894202
C2×#156894102
C2×#156893772
C2×#156893602
C2×#156892362
C2×#156891962
C2×#156891642
C2×#106×D472
C2×C47×#5012
C2×#334547