Finite Group Databasebeta

← C2×#20241929 #26183531

Subgroups — C2×#20241929 #26183531

Order 12032.

1510 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2C2×#15689087C211yesmaximal, characteristic, complemented
3#20241929C218yesmaximal, direct product factor
4C2×#15688859C212yesmaximal, complemented
5C2×#15688856C212yesmaximal, complemented
6C2×C47×#380C211yesmaximal, characteristic, complemented
7C22×#10625350C411yescharacteristic, complemented
8C22×#10625329—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
22#15689087—22no—
23#15689087C2214yescomplemented
24C2×C22⋊(C47⋊C8)—21no—
25C2×C22⋊(C47⋊C8)C2212yes—
26#15688859C2218yescomplemented
27#15688856C2218yescomplemented
28C24×C4×C47C2211yescharacteristic
29C22×C4⋊C4×C47—21no—
30C22×C22⋊C4×C47—21no—
31C47×#380—22no—
32C47×#380C2214yescomplemented
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—
43C2×#10625329—24no—
44C2×#10625329—44no—
45C22×C47⋊C8—22no—
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)—24no—
79C22⋊(C47⋊C8)—22no—
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×C4⋊C4×C47—24no—
95C2×C4⋊C4×C47—44no—
96C2×C22⋊C4×C47—24no—
97C2×C22⋊C4×C47—44no—
98#95×C47—22no—
99#95×C47C2314yes—
100C24×C47—22no—
101C24×C47—22no—
102C24×C47—42no—
103C24×C47—42no—
104C24×C47C22⋊C411yescharacteristic
105C24×C47C22⋊C411yescharacteristic
106C24×C47C22⋊C412yes—
107C24×C47C2×D411yescharacteristic
108C24×C47C2×D412yes—
109C23×D47—21no—
110C22×C4×C47—24no—
111C22×C4×C47—24no—
112C22×C4×C47—24no—
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×C47—44no—
124C22×C4×C47C22⋊C411yescharacteristic
125C22×C4×C47C22⋊C412yes—
126C22×C4×C47C22⋊C412yes—
127C22×C4×C47C22⋊C412yes—
128C22×C4×C47C22⋊C412yes—
129C22×C4×C47C22⋊C412yes—
130C22×C4×C47C22⋊C411yescharacteristic
131C22×C4×C47C22×C411yescharacteristic
132C22×C4×C47C22×C412yes—
133C22×C4×C47C22×C411yescharacteristic
134C22×C4×C47C22×C412yes—
135C22×C4×C47C2×D412yes—
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D412yes—
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D412yes—
141C22×C4×C47C2411yescharacteristic
142C2×C22⋊D47—22no—
143C2×C22⋊D47—24no—
144C2×C22⋊D47—24no—
145C2×C22⋊D47—22no—
146C2×C22⋊D47—44no—
147C2×C22⋊D47—44no—
148C2×C22⋊D47—42no—
149C2×C22⋊D47—42no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153#10625350—48no—
154#10625350—48no—
155C2×D188—21no—
156C2×D188—42no—
157C2×D188C22×C412yes—
158C2×C4×D47—24no—
159C2×C4×D47—44no—
160C2×Dic94—21no—
161C2×Dic94—42no—
162C2×Dic94C22×C412yes—
163C4⋊C4×C47—48no—
164C22⋊C4×C47—48no—
165C22⋊Dic47—24no—
166C22⋊Dic47—22no—
167C22⋊Dic47—24no—
168C22⋊Dic47—22no—
169(C2×D47)⋊C4—22no—
170(C2×D47)⋊C4—24no—
171(C2×D47)⋊C4—22no—
172C4⋊Dic47—21no—
173C4⋊Dic47—21no—
174C4⋊Dic47C22×C412yes—
175C4⋊Dic47C22×C412yes—
176Dic47⋊C4—22no—
177Dic47⋊C4—24no—
178Dic47⋊C4—22no—
179C4×Dic47—24no—
180#10625329—48no—
181C2×C47⋊C8—24no—
182C2×C47⋊C8—44no—
183C23×C47—22no—
184C23×C47—22no—
185C23×C47—22no—
186C23×C47—22no—
187C23×C47—22no—
188C23×C47—22no—
189C23×C47—24no—
190C23×C47—22no—
191C23×C47—22no—
192C23×C47—22no—
193C23×C47—22no—
194C23×C47—42no—
195C23×C47—42no—
196C23×C47—42no—
197C23×C47—42no—
198C23×C47—48no—
199C23×C47—48no—
200C23×C47C2×C22⋊C412yes—
201C23×C47C2×C22⋊C412yes—
202C23×C47C2×C22⋊C411yescharacteristic
203C23×C47C2×C22⋊C411yescharacteristic
204C23×C47AGL(1,ℤ/8)12yes—
205C23×C47#13712yes—
206C23×C47C22×D411yescharacteristic
207C22×D47—22no—
208C22×D47—42no—
209C22×D47—42no—
210C22×D47—42no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—24no—
215C2×C4×C47—24no—
216C2×C4×C47—24no—
217C2×C4×C47—24no—
218C2×C4×C47—24no—
219C2×C4×C47—24no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—41no—
223C2×C4×C47—42no—
224C2×C4×C47—41no—
225C2×C4×C47—42no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—44no—
229C2×C4×C47—44no—
230C2×C4×C47—44no—
231C2×C4×C47—88no—
232C2×C4×C47#9914yes—
233C2×C4×C47C2×C22⋊C411yescharacteristic
234C2×C4×C47C2×C22⋊C412yes—
235C2×C4×C47C2×C22⋊C411yescharacteristic
236C2×C4×C47C2×C22⋊C412yes—
237C2×C4×C47C23×C411yescharacteristic
238C2×C4×C47C22×D411yescharacteristic
239C22⋊D47—48no—
240C22⋊D47—48no—
241C22⋊D47—42no—
242C22⋊D47—42no—
243C22⋊D47—44no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—42no—
248C2×Dic47—42no—
249C2×Dic47—42no—
250D188—42no—
251D188—42no—
252C4×D47—48no—
253Dic94—42no—
254Dic94—42no—
255C47⋊C8—44no—
256C2×#1513—471nomaximal, Sylow
257C22×C47—21no—
258C22×C47—21no—
259C22×C47—21no—
260C22×C47—21no—
261C22×C47—24no—
262C22×C47—24no—
263C22×C47—22no—
264C22×C47—22no—
265C22×C47—22no—
266C22×C47—22no—
267C22×C47—22no—
268C22×C47—22no—
269C22×C47—44no—
270C22×C47—44no—
271C22×C47—48no—
272C22×C47—44no—
273C22×C47—44no—
274C22×C47C2×#9912yes—
275C22×C47#41712yes—
276C22×C47#41712yes—
277C22×C47#42112yes—
278C22×C47C22×C22⋊C411yescharacteristic
279C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
280C22×C47C2×#13711yescharacteristic
281C2×D47—42no—
282C2×D47—42no—
283C2×D47—42no—
284C2×D47—84no—
285C4×C47—21no—
286C4×C47—21no—
287C4×C47—21no—
288C4×C47—21no—
289C4×C47—22no—
290C4×C47—84no—
291C4×C47C2×#9914yes—
292Dic47—42no—
293Dic47—42no—
294Dic47—42no—
295C2×#525—471no—
296C2×#407—471no—
297C2×#380D4711yescharacteristic, complemented
298#1513—478no—
299C2×#328—472no—
300C2×#327—472no—
301C2×C47—21no—
302C2×C47—21no—
303C2×C47—22no—
304C2×C47—42no—
305C2×C47—42no—
306C2×C47#151314yescomplemented
307C2×C47C22×#9911yescharacteristic
308C2×C47C2×#41711yescharacteristic
309C2×C47C2×#42111yescharacteristic
310D47—82no—
311C22×#41—471no—
312C24×C4C2×D4711yescharacteristic
313C22×M16—941no—
314#525—474no—
315#525—474no—
316#525—942no—
317#525—942no—
318C2×#123—941no—
319C2×C22⋊Q8—471no—
320C2×C22⋊Q8—471no—
321C2×#121—471no—
322C2×#121—471no—
323C2×#120—941no—
324C2×C4×D4—941no—
325C2×C4×D4—941no—
326C2×#117—471no—
327C22×C4⋊C4—21no—
328C22×C22⋊C4—21no—
329#407—474no—
330#407—942no—
331C2×C22⋊C8—472no—
332C2×C22⋊C8—941no—
333#380—22no—
334#380C2×D4714yescomplemented
335C2×#95C2×D4712yes—
336#328—478no—
337#327—478no—
338C47C2×#151311yescharacteristic, complemented, Sylow
339C25C22⋊D4711yescharacteristic
340C2×#41—474no—
341C2×#41—942no—
342C2×#41—1884no—
343C22×Q8—471no—
344C22×D4—471no—
345C22×D4—941no—
346C22×D4—941no—
347C22×D4—941no—
348C23×C4—22no—
349C23×C4—44no—
350C23×C4—941no—
351C23×C4C4×D4711yescharacteristic
352C23×C4C4×D4711yescharacteristic
353C23×C4C4×D4712yes—
354C23×C4D18811yescharacteristic
355C23×C4D18811yescharacteristic
356C23×C4D18812yes—
357C23×C4C22⋊D4711yescharacteristic
358C23×C4C22⋊D4712yes—
359C23×C4C22×D4711yescharacteristic
360C23×C4C22×D4712yes—
361C2×M16—944no—
362C2×M16—1884no—
363C22×C8—942no—
364#123—944no—
365#123—944no—
366C22⋊Q8—472no—
367C22⋊Q8—474no—
368C22⋊Q8—472no—
369C22⋊Q8—942no—
370C22⋊Q8—941no—
371C22⋊Q8—941no—
372#121—472no—
373#121—474no—
374#121—472no—
375#121—942no—
376#121—941no—
377#121—941no—
378#120—944no—
379#120—944no—
380C4×D4—944no—
381C4×D4—944no—
382C4×D4—944no—
383C4×D4—944no—
384#117—474no—
385#117—942no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—471no—
389C2×C4⋊C4—471no—
390C2×C4⋊C4—941no—
391C2×C4⋊C4—941no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—941no—
395C2×C22⋊C4—941no—
396C2×C22⋊C4—941no—
397C2×C22⋊C4—941no—
398C2×C22⋊C4—941no—
399C2×C42—941no—
400C22⋊C8—474no—
401C22⋊C8—942no—
402C22⋊C8—944no—
403#95—22no—
404#95C22×D4714yes—
405C24—22no—
406C24—22no—
407C24—42no—
408C24—42no—
409C24—941no—
410C24(C2×D47)⋊C411yescharacteristic
411C24(C2×D47)⋊C411yescharacteristic
412C24(C2×D47)⋊C412yes—
413C24C2×C22⋊D4711yescharacteristic
414C24C2×C22⋊D4712yes—
415#41—1888no—
416#41—1888no—
417C2×Q8—472no—
418C2×Q8—941no—
419C2×Q8—1882no—
420C2×D4—472no—
421C2×D4—944no—
422C2×D4—942no—
423C2×D4—944no—
424C2×D4—942no—
425C2×D4—941no—
426C2×D4—1882no—
427C2×D4—1884no—
428C2×D4—1884no—
429C2×D4—1882no—
430C2×D4—1882no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—44no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4—941no—
446C22×C4—941no—
447C22×C4—941no—
448C22×C4—944no—
449C22×C4—1884no—
450C22×C4(C2×D47)⋊C412yes—
451C22×C4(C2×D47)⋊C412yes—
452C22×C4(C2×D47)⋊C412yes—
453C22×C4(C2×D47)⋊C411yescharacteristic
454C22×C4(C2×D47)⋊C412yes—
455C22×C4(C2×D47)⋊C412yes—
456C22×C4(C2×D47)⋊C411yescharacteristic
457C22×C4C2×C4×D4712yes—
458C22×C4C2×C4×D4711yescharacteristic
459C22×C4C2×C4×D4712yes—
460C22×C4C2×C4×D4711yescharacteristic
461C22×C4C2×D18812yes—
462C22×C4C2×D18811yescharacteristic
463C22×C4C2×D18811yescharacteristic
464C22×C4C2×D18812yes—
465C22×C4C2×C22⋊D4712yes—
466C22×C4C2×C22⋊D4711yescharacteristic
467C22×C4C23×D4711yescharacteristic
468M16—1888no—
469C2×C8—944no—
470C2×C8—1884no—
471C4⋊C4—48no—
472C4⋊C4—472no—
473C4⋊C4—472no—
474C4⋊C4—942no—
475C4⋊C4—944no—
476C4⋊C4—941no—
477C4⋊C4—941no—
478C4⋊C4—942no—
479C22⋊C4—48no—
480C22⋊C4—944no—
481C22⋊C4—944no—
482C22⋊C4—942no—
483C22⋊C4—942no—
484C22⋊C4—942no—
485C22⋊C4—944no—
486C22⋊C4—942no—
487C42—944no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—48no—
504C23—48no—
505C23—942no—
506C23—1882no—
507C23—1882no—
508C23—1882no—
509C23C2×(C2×D47)⋊C412yes—
510C23C2×(C2×D47)⋊C412yes—
511C23C2×(C2×D47)⋊C411yescharacteristic
512C23C2×(C2×D47)⋊C411yescharacteristic
513C23#1309405012yes—
514C23#1309405512yes—
515C23C22×C22⋊D4711yescharacteristic
516Q8—1882no—
517Q8—1882no—
518D4—1882no—
519D4—1882no—
520D4—1888no—
521D4—1888no—
522D4—1884no—
523D4—1882no—
524D4—1882no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—88no—
546C2×C4—942no—
547C2×C4—942no—
548C2×C4—942no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4—1882no—
552C2×C4—1888no—
553C2×C4#1309393814yes—
554C2×C4C2×(C2×D47)⋊C411yescharacteristic
555C2×C4C2×(C2×D47)⋊C412yes—
556C2×C4C2×(C2×D47)⋊C411yescharacteristic
557C2×C4C2×(C2×D47)⋊C412yes—
558C2×C4C22×C4×D4711yescharacteristic
559C2×C4C22×D18811yescharacteristic
560C8—1884no—
561C22—24no—
562C22—24no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—44no—
574C22—48no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—3764no—
579C22—1882no—
580C22—1882no—
581C22—1882no—
582C22C2×#1309393812yes—
583C22#1568912212yes—
584C22#1568912212yes—
585C22#1568914112yes—
586C22C22×(C2×D47)⋊C411yescharacteristic
587C22C2×#1309405011yescharacteristic
588C22C2×#1309405511yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—22no—
593C4—21no—
594C4—84no—
595C4—1882no—
596C4—1882no—
597C4—1882no—
598C4C2×#1309393814yes—
599C2—21no—
600C2—22no—
601C2—21no—
602C2—42no—
603C2—42no—
604C2—3762no—
605C2#2024192914yesdirect product factor
606C2C22×#1309393811yescharacteristic
607C2C2×#1568912211yescharacteristic
608C2C2×#1568914111yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#380C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#15689634C2
cosocleC22×C4×C47C24
hypercenterC2×#380D47
hypocenterC47C2×#1513
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#15689087C2semidirect
3. #20241929C2direct (N × H)
4. C2×#15688859C2semidirect
5. C2×#15688856C2semidirect
6. C2×C47×#380C2semidirect
7. C22×#10625350C4semidirect
11. #15689634C4semidirect
14. C2×#13094003C4semidirect
16. C2×#13093998C4semidirect
21. C2×#13093983C4semidirect
23. #15689087C22semidirect
26. #15688859C22semidirect
27. #15688856C22semidirect
32. C47×#380C22semidirect
36. C2×#10625350C2×C4semidirect
52. #13094003C2×C4semidirect
58. #13093998C2×C4semidirect
67. #13093983C2×C4semidirect
297. C2×#380D47semidirect
306. C2×C47#1513semidirect
334. #380C2×D47semidirect
338. C47C2×#1513semidirect
605. C2#20241929direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896342
C2×#156890872
#202419292
C2×#156888592
C2×#156888562
C2×C47×#3802
C2×#151347