Finite Group Databasebeta

← C2×#20241877 #26183370

Subgroups — C2×#20241877 #26183370

Order 12032.

1606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2C22×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
3#20241877C218yesmaximal, direct product factor
4C2×#15688859C212yesmaximal, complemented
5C2×#15688856C212yesmaximal, complemented
6C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
7C22×#10625350C411yescharacteristic, complemented
8C23×C47⋊C8—21no—
9#15689634—22no—
10#15689634—22no—
11#15689634C414yescomplemented
12#15689634C2214yes—
13C2×#13094007—21no—
14C2×#13094003C411yescharacteristic, complemented
15C2×#13094003C2211yescharacteristic
16C2×#13093998C411yescharacteristic, complemented
17C2×#13093998C2211yescharacteristic
18C2×#13093993—21no—
19C2×C4×C22⋊D47—21no—
20C2×C4×C22⋊D47—21no—
21C2×#13093983C411yescharacteristic, complemented
22C2×C22⋊(C47⋊C8)—21no—
23C2×C22⋊(C47⋊C8)—22no—
24C2×C22⋊(C47⋊C8)C2212yes—
25C2×C22⋊(C47⋊C8)C2214yescomplemented
26#15688859C2218yescomplemented
27#15688856C2218yescomplemented
28C24×C4×C47C2211yescharacteristic
29C22×C22⋊C4×C47—21no—
30C22×C42×C47—21no—
31C4×C22⋊C4×C47—22no—
32C4×C22⋊C4×C47C2214yescomplemented
33C2×#95×C47C2212yes—
34C2×#10625350—22no—
35C2×#10625350—44no—
36C2×#10625350C2×C414yescomplemented
37C22×Dic94C2×C411yescharacteristic
38C22×D188C2×C411yescharacteristic
39C22×C22⋊D47—21no—
40C22×C22⋊D47—21no—
41C22×C22⋊D47—21no—
42C22×C4×D47—21no—
43C22×C47⋊C8—22no—
44C22×C47⋊C8—24no—
45C22×C47⋊C8—44no—
46#13094007—24no—
47#13094007—24no—
48#13094003—22no—
49#13094003—21no—
50#13094003—21no—
51#13094003C2×C412yes—
52#13094003C2×C414yescomplemented
53#13094003C2312yes—
54#13093998—22no—
55#13093998—21no—
56#13093998—21no—
57#13093998C2×C412yes—
58#13093998C2×C414yescomplemented
59#13093998C2312yes—
60#13093993—24no—
61#13093993—24no—
62C4×C22⋊D47—24no—
63C4×C22⋊D47—24no—
64C4×C22⋊D47—24no—
65C4×C22⋊D47—24no—
66#13093983—22no—
67#13093983C2×C414yescomplemented
68C2×C4⋊Dic47C2×C411yescharacteristic
69C2×C4⋊Dic47C2×C411yescharacteristic
70C2×Dic47⋊C4—21no—
71C2×Dic47⋊C4—21no—
72C2×C22⋊Dic47—21no—
73C2×C22⋊Dic47—21no—
74C2×C22⋊Dic47—21no—
75C2×(C2×D47)⋊C4—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×C4×Dic47—21no—
78C22⋊(C47⋊C8)—22no—
79C22⋊(C47⋊C8)—24no—
80C22⋊(C47⋊C8)C2314yes—
81C25×C47D411yescharacteristic
82C23×C4×C47—22no—
83C23×C4×C47—44no—
84C23×C4×C47C2×C411yescharacteristic
85C23×C4×C47C2×C411yescharacteristic
86C23×C4×C47C2×C412yes—
87C23×C4×C47D411yescharacteristic
88C23×C4×C47D411yescharacteristic
89C23×C4×C47D412yes—
90C23×C4×C47D411yescharacteristic
91C23×C4×C47D412yes—
92C23×C4×C47C2311yescharacteristic
93C23×C4×C47C2312yes—
94C2×C22⋊C4×C47—28no—
95C2×C22⋊C4×C47—24no—
96C2×C42×C47—24no—
97C2×C42×C47—44no—
98#95×C47—22no—
99#95×C47C2314yes—
100C24×C47—24no—
101C24×C47—24no—
102C24×C47—42no—
103C24×C47C22⋊C411yescharacteristic
104C24×C47C22⋊C412yes—
105C24×C47C22⋊C411yescharacteristic
106C24×C47C2×D412yes—
107C24×C47C2×D411yescharacteristic
108C23×D47—21no—
109C22×C4×C47—24no—
110C22×C4×C47—24no—
111C22×C4×C47—24no—
112C22×C4×C47—28no—
113C22×C4×C47—24no—
114C22×C4×C47—44no—
115C22×C4×C47—44no—
116C22×C4×C47—44no—
117C22×C4×C47—44no—
118C22×C4×C47—42no—
119C22×C4×C47—42no—
120C22×C4×C47—42no—
121C22×C4×C47—44no—
122C22×C4×C47—44no—
123C22×C4×C47C22⋊C411yescharacteristic
124C22×C4×C47C22⋊C412yes—
125C22×C4×C47C22⋊C412yes—
126C22×C4×C47C22⋊C412yes—
127C22×C4×C47C22⋊C412yes—
128C22×C4×C47C22⋊C412yes—
129C22×C4×C47C22⋊C411yescharacteristic
130C22×C4×C47C22×C411yescharacteristic
131C22×C4×C47C22×C412yes—
132C22×C4×C47C22×C411yescharacteristic
133C22×C4×C47C22×C412yes—
134C22×C4×C47C2×D412yes—
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D412yes—
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D412yes—
140C22×C4×C47C2411yescharacteristic
141C2×C22⋊D47—22no—
142C2×C22⋊D47—24no—
143C2×C22⋊D47—24no—
144C2×C22⋊D47—22no—
145C2×C22⋊D47—44no—
146C2×C22⋊D47—44no—
147C2×C22⋊D47—44no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151#10625350—48no—
152#10625350—48no—
153C2×D188—21no—
154C2×D188—42no—
155C2×D188C22×C412yes—
156C2×C4×D47—24no—
157C2×C4×D47—44no—
158C2×Dic94—21no—
159C2×Dic94—42no—
160C2×Dic94C22×C412yes—
161C22⋊C4×C47—216no—
162C42×C47—48no—
163C22⋊Dic47—24no—
164C22⋊Dic47—22no—
165C22⋊Dic47—24no—
166C22⋊Dic47—22no—
167(C2×D47)⋊C4—22no—
168(C2×D47)⋊C4—24no—
169(C2×D47)⋊C4—22no—
170C4⋊Dic47—21no—
171C4⋊Dic47—21no—
172C4⋊Dic47C22×C412yes—
173C4⋊Dic47C22×C412yes—
174Dic47⋊C4—22no—
175Dic47⋊C4—24no—
176Dic47⋊C4—22no—
177C4×Dic47—24no—
178C2×C47⋊C8—24no—
179C2×C47⋊C8—44no—
180C2×C47⋊C8—48no—
181C23×C47—22no—
182C23×C47—22no—
183C23×C47—22no—
184C23×C47—22no—
185C23×C47—24no—
186C23×C47—22no—
187C23×C47—24no—
188C23×C47—22no—
189C23×C47—24no—
190C23×C47—24no—
191C23×C47—22no—
192C23×C47—42no—
193C23×C47—42no—
194C23×C47—416no—
195C23×C47#10414yes—
196C23×C47C2×C22⋊C412yes—
197C23×C47C2×C22⋊C411yescharacteristic
198C23×C47C2×C22⋊C412yes—
199C23×C47C2×C22⋊C411yescharacteristic
200C23×C47#13514yes—
201C23×C47C22×D411yescharacteristic
202C22×D47—22no—
203C22×D47—42no—
204C22×D47—42no—
205C22×D47—42no—
206C2×C4×C47—22no—
207C2×C4×C47—22no—
208C2×C4×C47—22no—
209C2×C4×C47—24no—
210C2×C4×C47—24no—
211C2×C4×C47—24no—
212C2×C4×C47—24no—
213C2×C4×C47—24no—
214C2×C4×C47—24no—
215C2×C4×C47—28no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47—41no—
219C2×C4×C47—42no—
220C2×C4×C47—41no—
221C2×C4×C47—42no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—44no—
225C2×C4×C47—416no—
226C2×C4×C47—44no—
227C2×C4×C47#9914yes—
228C2×C4×C47C2×C22⋊C411yescharacteristic
229C2×C4×C47C2×C22⋊C412yes—
230C2×C4×C47C2×C22⋊C411yescharacteristic
231C2×C4×C47C2×C22⋊C412yes—
232C2×C4×C47C23×C411yescharacteristic
233C2×C4×C47C22×D411yescharacteristic
234C22⋊D47—48no—
235C22⋊D47—44no—
236C22⋊D47—44no—
237C22⋊D47—48no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—42no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244D188—42no—
245D188—42no—
246C4×D47—48no—
247Dic94—42no—
248Dic94—42no—
249C47⋊C8—44no—
250C2×#1501—471nomaximal, Sylow
251C22×C47—21no—
252C22×C47—21no—
253C22×C47—22no—
254C22×C47—22no—
255C22×C47—21no—
256C22×C47—21no—
257C22×C47—28no—
258C22×C47—28no—
259C22×C47—22no—
260C22×C47—22no—
261C22×C47—22no—
262C22×C47—48no—
263C22×C47—48no—
264C22×C47—44no—
265C22×C47C2×#9912yes—
266C22×C47#41612yes—
267C22×C47#41612yes—
268C22×C47C2×#10414yes—
269C22×C47C2×#10412yes—
270C22×C47C22×C22⋊C411yescharacteristic
271C22×C47C2×#13512yes—
272C2×D47—42no—
273C2×D47—42no—
274C2×D47—42no—
275C2×D47—84no—
276C4×C47—21no—
277C4×C47—21no—
278C4×C47—21no—
279C4×C47—21no—
280C4×C47—22no—
281C4×C47—48no—
282C4×C47C2×#9914yes—
283Dic47—42no—
284Dic47—42no—
285Dic47—42no—
286C2×#525—471no—
287C22×C22⋊C8—471no—
288C2×C4×C22⋊C4D4711yescharacteristic, complemented
289#1501—478no—
290C2×#328—472no—
291C2×#327—472no—
292C2×C47—22no—
293C2×C47—22no—
294C2×C47—24no—
295C2×C47—42no—
296C2×C47#150114yescomplemented
297C2×C47C22×#9911yescharacteristic
298C2×C47C2×#41611yescharacteristic
299C2×C47C22×#10411yescharacteristic
300D47—82no—
301C22×#41—471no—
302C24×C4C2×D4711yescharacteristic
303C23×C8—941no—
304#525—474no—
305#525—474no—
306#525—942no—
307#525—942no—
308C2×#123—941no—
309C2×C22⋊Q8—471no—
310C2×C22⋊Q8—471no—
311C2×#121—471no—
312C2×#121—471no—
313C2×#120—941no—
314C2×C4×D4—941no—
315C2×C4×D4—941no—
316C2×#117—471no—
317C22×C22⋊C4—21no—
318C22×C42—21no—
319C2×C22⋊C8—472no—
320C2×C22⋊C8—474no—
321C2×C22⋊C8—941no—
322C2×C22⋊C8—942no—
323C4×C22⋊C4—22no—
324C4×C22⋊C4C2×D4714yescomplemented
325C2×#95C2×D4712yes—
326#328—478no—
327#327—478no—
328C47C2×#150111yescharacteristic, complemented, Sylow
329C25C22⋊D4711yescharacteristic
330C2×#41—474no—
331C2×#41—942no—
332C2×#41—1884no—
333C22×Q8—471no—
334C22×D4—471no—
335C22×D4—941no—
336C22×D4—941no—
337C22×D4—941no—
338C23×C4—22no—
339C23×C4—44no—
340C23×C4—941no—
341C23×C4C4×D4711yescharacteristic
342C23×C4C4×D4711yescharacteristic
343C23×C4C4×D4712yes—
344C23×C4D18811yescharacteristic
345C23×C4D18811yescharacteristic
346C23×C4D18812yes—
347C23×C4C22⋊D4711yescharacteristic
348C23×C4C22⋊D4712yes—
349C23×C4C22×D4711yescharacteristic
350C23×C4C22×D4712yes—
351C22×C8—942no—
352C22×C8—944no—
353C22×C8—1884no—
354#123—944no—
355#123—944no—
356C22⋊Q8—472no—
357C22⋊Q8—474no—
358C22⋊Q8—472no—
359C22⋊Q8—942no—
360C22⋊Q8—941no—
361C22⋊Q8—941no—
362#121—472no—
363#121—474no—
364#121—472no—
365#121—942no—
366#121—941no—
367#121—941no—
368#120—944no—
369#120—944no—
370C4×D4—944no—
371C4×D4—944no—
372C4×D4—944no—
373C4×D4—944no—
374#117—474no—
375#117—942no—
376C2×C4⋊C4—471no—
377C2×C4⋊C4—471no—
378C2×C4⋊C4—941no—
379C2×C4⋊C4—941no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—941no—
383C2×C22⋊C4—941no—
384C2×C22⋊C4—941no—
385C2×C22⋊C4—941no—
386C2×C22⋊C4—941no—
387C2×C42—24no—
388C2×C42—44no—
389C2×C42—941no—
390C22⋊C8—474no—
391C22⋊C8—942no—
392C22⋊C8—944no—
393#95—22no—
394#95C22×D4714yes—
395C24—24no—
396C24—24no—
397C24—42no—
398C24—941no—
399C24(C2×D47)⋊C411yescharacteristic
400C24(C2×D47)⋊C412yes—
401C24(C2×D47)⋊C411yescharacteristic
402C24C2×C22⋊D4712yes—
403C24C2×C22⋊D4711yescharacteristic
404#41—1888no—
405#41—1888no—
406C2×Q8—472no—
407C2×Q8—941no—
408C2×Q8—1882no—
409C2×D4—472no—
410C2×D4—942no—
411C2×D4—944no—
412C2×D4—944no—
413C2×D4—942no—
414C2×D4—941no—
415C2×D4—1882no—
416C2×D4—1884no—
417C2×D4—1884no—
418C2×D4—1884no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—28no—
423C22×C4—24no—
424C22×C4—44no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—941no—
434C22×C4—941no—
435C22×C4—941no—
436C22×C4—944no—
437C22×C4—1884no—
438C22×C4(C2×D47)⋊C411yescharacteristic
439C22×C4(C2×D47)⋊C412yes—
440C22×C4(C2×D47)⋊C412yes—
441C22×C4(C2×D47)⋊C412yes—
442C22×C4(C2×D47)⋊C412yes—
443C22×C4(C2×D47)⋊C412yes—
444C22×C4(C2×D47)⋊C411yescharacteristic
445C22×C4C2×C4×D4711yescharacteristic
446C22×C4C2×C4×D4712yes—
447C22×C4C2×C4×D4711yescharacteristic
448C22×C4C2×C4×D4712yes—
449C22×C4C2×D18811yescharacteristic
450C22×C4C2×D18812yes—
451C22×C4C2×D18811yescharacteristic
452C22×C4C2×D18812yes—
453C22×C4C2×C22⋊D4712yes—
454C22×C4C2×C22⋊D4711yescharacteristic
455C22×C4C23×D4711yescharacteristic
456C2×C8—944no—
457C2×C8—1884no—
458C2×C8—1888no—
459C4⋊C4—472no—
460C4⋊C4—472no—
461C4⋊C4—942no—
462C4⋊C4—944no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C4⋊C4—942no—
466C22⋊C4—216no—
467C22⋊C4—944no—
468C22⋊C4—942no—
469C22⋊C4—944no—
470C22⋊C4—942no—
471C22⋊C4—942no—
472C22⋊C4—944no—
473C22⋊C4—942no—
474C42—48no—
475C42—944no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—24no—
482C23—22no—
483C23—24no—
484C23—24no—
485C23—24no—
486C23—22no—
487C23—42no—
488C23—42no—
489C23—416no—
490C23—942no—
491C23—1882no—
492C23—1882no—
493C23—1882no—
494C23#1309395214yes—
495C23C2×(C2×D47)⋊C412yes—
496C23C2×(C2×D47)⋊C411yescharacteristic
497C23C2×(C2×D47)⋊C412yes—
498C23C2×(C2×D47)⋊C411yescharacteristic
499C23#1309404414yes—
500C23C22×C22⋊D4711yescharacteristic
501Q8—1882no—
502Q8—1882no—
503D4—1882no—
504D4—1882no—
505D4—1888no—
506D4—1884no—
507D4—1884no—
508D4—1888no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—28no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—44no—
528C2×C4—416no—
529C2×C4—44no—
530C2×C4—942no—
531C2×C4—942no—
532C2×C4—942no—
533C2×C4—1882no—
534C2×C4—1882no—
535C2×C4—1882no—
536C2×C4—1888no—
537C2×C4#1309393814yes—
538C2×C4C2×(C2×D47)⋊C412yes—
539C2×C4C2×(C2×D47)⋊C411yescharacteristic
540C2×C4C2×(C2×D47)⋊C411yescharacteristic
541C2×C4C2×(C2×D47)⋊C412yes—
542C2×C4C22×C4×D4711yescharacteristic
543C2×C4C22×D18811yescharacteristic
544C8—1884no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—22no—
550C22—28no—
551C22—28no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—48no—
557C22—48no—
558C22—44no—
559C22—3764no—
560C22—1882no—
561C22—1882no—
562C22—1882no—
563C22C2×#1309393812yes—
564C22#1568911712yes—
565C22#1568911712yes—
566C22C2×#1309395214yes—
567C22C2×#1309395212yes—
568C22C22×(C2×D47)⋊C411yescharacteristic
569C22C2×#1309404412yes—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—22no—
574C4—21no—
575C4—48no—
576C4—1882no—
577C4—1882no—
578C4—1882no—
579C4C2×#1309393814yes—
580C2—22no—
581C2—22no—
582C2—24no—
583C2—42no—
584C2—3762no—
585C2#2024187714yesdirect product factor
586C2C22×#1309393811yescharacteristic
587C2C2×#1568911711yescharacteristic
588C2C22×#1309395211yescharacteristic
subgroupG/H
centerC22×C4(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C4×C22⋊C4×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#15689634C2
cosocleC22×C4×C47C24
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C2×#1501
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊(C47⋊C8)C2semidirect
3. #20241877C2direct (N × H)
4. C2×#15688859C2semidirect
5. C2×#15688856C2semidirect
6. C2×C4×C22⋊C4×C47C2semidirect
7. C22×#10625350C4semidirect
11. #15689634C4semidirect
14. C2×#13094003C4semidirect
16. C2×#13093998C4semidirect
21. C2×#13093983C4semidirect
25. C2×C22⋊(C47⋊C8)C22semidirect
26. #15688859C22semidirect
27. #15688856C22semidirect
32. C4×C22⋊C4×C47C22semidirect
36. C2×#10625350C2×C4semidirect
52. #13094003C2×C4semidirect
58. #13093998C2×C4semidirect
67. #13093983C2×C4semidirect
288. C2×C4×C22⋊C4D47semidirect
296. C2×C47#1501semidirect
324. C4×C22⋊C4C2×D47semidirect
328. C47C2×#1501semidirect
585. C2#20241877direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896342
C22×C22⋊(C47⋊C8)2
#202418772
C2×#156888592
C2×#156888562
C2×C4×C22⋊C4×C472
C2×#150147