Finite Group Databasebeta

← C2×#20254577 #27088382

Subgroups — C2×#20254577 #27088382

Order 12032.

2050 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689668C211yesmaximal, characteristic
2C22×#13094015C211yesmaximal, characteristic, complemented
3#20254577C2116yesmaximal, direct product factor
4C2×#15689530C212yesmaximal, complemented
5C2×#15689486C212yesmaximal, complemented
6C2×#15689441C211yesmaximal, characteristic, complemented
7C2×#15689437C211yesmaximal, characteristic, complemented
8C2×#15689434C211yesmaximal, characteristic, complemented
9C2×#15689422C212yesmaximal, complemented
10C2×#15689421C212yesmaximal, complemented
11C2×#15689177C211yesmaximal, characteristic, complemented
12C2×C47×#481C211yesmaximal, characteristic, complemented
13C22×#10625352—21no—
14#15689668—24no—
15#15689668C2218yes—
16C2×#13094023C2211yescharacteristic
17C2×#13094020C2211yescharacteristic
18C2×#13094015—21no—
19C2×#13094015—21no—
20C2×#13094015—24no—
21C2×#13094015C2212yes—
22C2×#13094015C2212yes—
23C2×#13094015C2218yescomplemented
24C2×#13094010—21no—
25C2×#13093998C2211yescharacteristic
26C2×#13093996—21no—
27C2×D4×Dic47C2211yescharacteristic
28C2×#13093986C2211yescharacteristic
29C2×(C22⋊D47)⋊C4—21no—
30C22×C4⋊Dic47—21no—
31C22×C4⋊Dic47C2211yescharacteristic
32C22×Dic47⋊C4—21no—
33C22×C4×Dic47C2211yescharacteristic
34#15689530C22116yescomplemented
35#15689486C22116yescomplemented
36#15689441C2218yescomplemented
37#15689437C2218yescomplemented
38#15689434C2218yescomplemented
39#15689422C22116yescomplemented
40#15689421C22116yescomplemented
41#15689177C2218yescomplemented
42C2×#13093958C2212yes—
43C2×#13093957C2212yes—
44C2×#13093955C2212yes—
45C2×Dic47⋊C8C2212yes—
46C2×#13093946C2212yes—
47C2×#13093945C2212yes—
48C2×#13093944C2212yes—
49C2×C22⋊(C47⋊C8)C2211yescharacteristic
50C2×#13093934C2212yes—
51C2×#121×C47C2211yescharacteristic
52C22×C4⋊C4×C47C2211yescharacteristic
53C47×#481C2218yescomplemented
54C2×#106×C47C2212yes—
55C2×#102×C47C2212yes—
56C2×C22⋊C8×C47C2211yescharacteristic
57C2×#10625352—28no—
58C2×#10625352—48no—
59C22×Dic94—21no—
60C22×D188C2311yescharacteristic
61C22×C22⋊D47—21no—
62C22×C22⋊D47—21no—
63C22×C22⋊D47—21no—
64C23×Dic47—21no—
65C23×Dic47—21no—
66C23×Dic47D411yescharacteristic
67C23×Dic47D411yescharacteristic
68C22×C4×D47—21no—
69C22×C47⋊C8C2312yes—
70#13094023—22no—
71#13094023C2314yes—
72#13094020—22no—
73#13094020C2314yes—
74#13094015—24no—
75#13094015—24no—
76#13094015—28no—
77#13094015—28no—
78#13094015C2318yes—
79#13094015C2318yes—
80#13094010—28no—
81#13093998—22no—
82#13093998C2314yes—
83#13093996—28no—
84D4×Dic47—22no—
85D4×Dic47C2314yes—
86#13093986—22no—
87#13093986C2314yes—
88(C22⋊D47)⋊C4—28no—
89C2×C4⋊Dic47—21no—
90C2×C4⋊Dic47—22no—
91C2×C4⋊Dic47—22no—
92C2×C4⋊Dic47—22no—
93C2×C4⋊Dic47—28no—
94C2×C4⋊Dic47C2312yes—
95C2×C4⋊Dic47C2314yes—
96C2×C4⋊Dic47C2311yescharacteristic
97C2×Dic47⋊C4—22no—
98C2×Dic47⋊C4—22no—
99C2×Dic47⋊C4—28no—
100C2×Dic47⋊C4—21no—
101C2×C22⋊Dic47—21no—
102C2×(C2×D47)⋊C4—21no—
103C2×(C2×D47)⋊C4—21no—
104C2×C4×Dic47D411yescharacteristic
105C2×C4×Dic47D411yescharacteristic
106C2×C4×Dic47D414yes—
107C2×C4×Dic47C2311yescharacteristic
108C2×C4×Dic47C2311yescharacteristic
109C2×C4×Dic47C2314yes—
110#13093958C2318yes—
111#13093957C2318yes—
112#13093955C2318yes—
113Dic47⋊C8C2318yes—
114#13093946C2318yes—
115#13093945C2318yes—
116#13093944C2318yes—
117C22⋊(C47⋊C8)C2314yes—
118#13093934C2318yes—
119C22×D4×C47—21no—
120C22×D4×C47C2311yescharacteristic
121C23×C4×C47—21no—
122C23×C4×C47C2311yescharacteristic
123C22×C8×C47C2312yes—
124#121×C47—22no—
125#121×C47C2314yes—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—22no—
128C2×C4⋊C4×C47C2314yes—
129C2×C4⋊C4×C47C2312yes—
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C22⋊C4×C47—21no—
132#106×C47C2318yes—
133#102×C47C2318yes—
134C22⋊C8×C47C2314yes—
135C24×C47—21no—
136C24×C47C2×D411yescharacteristic
137C23×D47—21no—
138C2×D4×C47—24no—
139C2×D4×C47—21no—
140C2×D4×C47—24no—
141C2×D4×C47—44no—
142C2×D4×C47C2412yes—
143C22×C4×C47—24no—
144C22×C4×C47—21no—
145C22×C4×C47—24no—
146C22×C4×C47—22no—
147C22×C4×C47—44no—
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D412yes—
150C22×C4×C47C2412yes—
151C22×C4×C47C2411yescharacteristic
152C2×C22⋊D47—24no—
153C2×C22⋊D47—24no—
154C2×C22⋊D47—24no—
155C2×C22⋊D47—44no—
156C2×C22⋊D47—44no—
157C2×C22⋊D47—44no—
158C22×Dic47—24no—
159C22×Dic47—21no—
160C22×Dic47—24no—
161C22×Dic47—22no—
162C22×Dic47—24no—
163C22×Dic47—42no—
164C22×Dic47—44no—
165C22×Dic47—44no—
166C22×Dic47C2×D411yescharacteristic
167C22×Dic47C2×D411yescharacteristic
168C22×Dic47C2×D411yescharacteristic
169C22×Dic47C2×D411yescharacteristic
170C22×Dic47C2×D414yes—
171C22×Dic47C2×D414yes—
172#10625352—432no—
173C2×D188—24no—
174C2×D188—21no—
175C2×D188C2412yes—
176C2×C4×D47—24no—
177C2×C4×D47—44no—
178C2×Dic94—24no—
179C2×Dic94—44no—
180C2×C8×C47—24no—
181C2×C8×C47C2414yes—
182C4⋊C4×C47—24no—
183C4⋊C4×C47—22no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47C2412yes—
186C4⋊C4×C47C2414yes—
187C22⋊C4×C47—24no—
188C22⋊Dic47—24no—
189(C2×D47)⋊C4—24no—
190(C2×D47)⋊C4—24no—
191C4⋊Dic47—24no—
192C4⋊Dic47—22no—
193C4⋊Dic47—21no—
194C4⋊Dic47—28no—
195C4⋊Dic47—28no—
196C4⋊Dic47C2414yes—
197C4⋊Dic47C2412yes—
198Dic47⋊C4—28no—
199Dic47⋊C4—28no—
200Dic47⋊C4—24no—
201C4×Dic47C2×D414yes—
202C4×Dic47C2×D412yes—
203C4×Dic47C2×D414yes—
204C4×Dic47C2×D412yes—
205C4×Dic47C2412yes—
206C4×Dic47C2412yes—
207C2×C47⋊C8—24no—
208C2×C47⋊C8C2414yes—
209C23×C47—22no—
210C23×C47—22no—
211C23×C47—22no—
212C23×C47—42no—
213C23×C47—42no—
214C23×C47—42no—
215C23×C47AGL(1,ℤ/8)14yes—
216C23×C47C22×D412yes—
217C23×C47C22×D411yescharacteristic
218C22×D47—22no—
219C22×D47—42no—
220C22×D47—42no—
221C22×D47—42no—
222D4×C47—24no—
223D4×C47—48no—
224D4×C47—42no—
225C2×C4×C47—22no—
226C2×C4×C47—24no—
227C2×C4×C47—24no—
228C2×C4×C47—24no—
229C2×C4×C47—22no—
230C2×C4×C47—48no—
231C2×C4×C47—42no—
232C2×C4×C47—44no—
233C2×C4×C47C22×D412yes—
234C2×C4×C47C22×D411yescharacteristic
235C2×C4×C472−1+414yes—
236C2×C4×C47C2511yescharacteristic
237C22⋊D47—48no—
238C22⋊D47—48no—
239C22⋊D47—48no—
240C2×Dic47—22no—
241C2×Dic47—22no—
242C2×Dic47—28no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—24no—
246C2×Dic47—22no—
247C2×Dic47—44no—
248C2×Dic47—48no—
249C2×Dic47—42no—
250C2×Dic47—48no—
251C2×Dic47—44no—
252C2×Dic47C22×D412yes—
253C2×Dic47C22×D412yes—
254C2×Dic47C22×D412yes—
255C2×Dic47C22×D412yes—
256D188—24no—
257D188—42no—
258C4×D47—48no—
259Dic94—48no—
260C8×C47—24no—
261C47⋊C8—24no—
262C2×#3234—471nomaximal, Sylow
263C22×C47—22no—
264C22×C47—28no—
265C22×C47—22no—
266C22×C47—42no—
267C22×C47—42no—
268C22×C47—42no—
269C22×C47—84no—
270C22×C47#53612yes—
271C22×C47C2×AGL(1,ℤ/8)14yes—
272C22×C47C2×AGL(1,ℤ/8)12yes—
273C22×C47#57512yes—
274C22×C47C23×D411yescharacteristic
275C2×D47—42no—
276C2×D47—42no—
277C2×D47—42no—
278C2×D47—84no—
279C4×C47—22no—
280C4×C47—42no—
281C4×C47—44no—
282C4×C47#53612yes—
283C4×C47C2×2−1+412yes—
284Dic47—22no—
285Dic47—22no—
286Dic47—22no—
287Dic47—22no—
288Dic47—42no—
289Dic47—44no—
290C2×#532—471no—
291C22×#125—471no—
292#3234—4716no—
293C2×#501—472no—
294C2×#490—472no—
295C2×#481—471no—
296C2×#481D4711yescharacteristic, complemented
297C2×#480—471no—
298C2×#480—471no—
299C2×#478—472no—
300C2×#478—472no—
301C2×#432—471no—
302C2×C47—24no—
303C2×C47—82no—
304C2×C47#323414yescomplemented
305C2×C47C2×#53611yescharacteristic
306C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
307C2×C47C2×#57511yescharacteristic
308D47—82no—
309C22×#41—941no—
310#532—478no—
311#532—944no—
312C2×C4⋊Q8—471no—
313C2×#127—471no—
314C2×#125—472no—
315C2×#125—472no—
316C2×#125—478no—
317C2×#125—941no—
318C2×#125—941no—
319C2×#125—944no—
320C2×#124—941no—
321C2×#121—471no—
322C2×#121—941no—
323C2×#121C2×D4711yescharacteristic
324C2×C4×D4—471no—
325C2×C4×D4—471no—
326C2×C4×D4—941no—
327C22×C4⋊C4—471no—
328C22×C4⋊C4—941no—
329C22×C4⋊C4—941no—
330C22×C4⋊C4C2×D4711yescharacteristic
331C22×C42—471no—
332#501—4716no—
333#490—4716no—
334#481—478no—
335#481C2×D4718yescomplemented
336#480—478no—
337#480—478no—
338#478—4716no—
339#478—4716no—
340#432—478no—
341C2×#107—472no—
342C2×#107—472no—
343C2×#106—472no—
344C2×#106C2×D4712yes—
345C2×C4⋊C8—472no—
346C2×#102—472no—
347C2×#102—472no—
348C2×#102—472no—
349C2×#102C2×D4712yes—
350C2×C22⋊C8—471no—
351C2×C22⋊C8C2×D4711yescharacteristic
352C2×#97—472no—
353C47C2×#323411yescharacteristic, complemented, Sylow
354C2×#41—948no—
355C2×#41—1888no—
356C22×Q8—941no—
357C22×D4—21no—
358C22×D4—471no—
359C22×D4—941no—
360C22×D4—941no—
361C22×D4—941no—
362C22×D4C22×D4711yescharacteristic
363C23×C4—21no—
364C23×C4—471no—
365C23×C4—471no—
366C23×C4—941no—
367C23×C4—941no—
368C23×C4—941no—
369C23×C4C22×D4711yescharacteristic
370C22×C8—472no—
371C22×C8C22×D4712yes—
372C4⋊Q8—474no—
373C4⋊Q8—942no—
374#127—474no—
375#127—942no—
376#125—478no—
377#125—478no—
378#125—944no—
379#125—948no—
380#125—948no—
381#125—944no—
382#124—948no—
383#121—22no—
384#121—474no—
385#121—948no—
386#121—942no—
387#121C22×D4714yes—
388C4×D4—474no—
389C4×D4—474no—
390C4×D4—948no—
391C4×D4—942no—
392C4×D4—942no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—472no—
396C2×C4⋊C4—474no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4—948no—
399C2×C4⋊C4—942no—
400C2×C4⋊C4—942no—
401C2×C4⋊C4—948no—
402C2×C4⋊C4—942no—
403C2×C4⋊C4—942no—
404C2×C4⋊C4—941no—
405C2×C4⋊C4—942no—
406C2×C4⋊C4—941no—
407C2×C4⋊C4C22×D4712yes—
408C2×C4⋊C4C22×D4714yes—
409C2×C4⋊C4C22×D4711yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—941no—
412C2×C22⋊C4—941no—
413C2×C22⋊C4—941no—
414C2×C42—471no—
415C2×C42—471no—
416C2×C42—474no—
417C2×C42—471no—
418C2×C42—471no—
419C2×C42—474no—
420#107—478no—
421#107—478no—
422#106—478no—
423#106C22×D4718yes—
424C4⋊C8—478no—
425#102—478no—
426#102—478no—
427#102—478no—
428#102C22×D4718yes—
429C22⋊C8—474no—
430C22⋊C8C22×D4714yes—
431#97—478no—
432C24—21no—
433C24—941no—
434C24D4×D4711yescharacteristic
435#41—18832no—
436C2×Q8—944no—
437C2×Q8—1884no—
438C2×D4—24no—
439C2×D4—21no—
440C2×D4—24no—
441C2×D4—44no—
442C2×D4—472no—
443C2×D4—944no—
444C2×D4—944no—
445C2×D4—944no—
446C2×D4—941no—
447C2×D4—944no—
448C2×D4—1884no—
449C2×D4—1884no—
450C2×D4—1884no—
451C2×D4C23×D4712yes—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—44no—
457C22×C4—474no—
458C22×C4—471no—
459C22×C4—471no—
460C22×C4—471no—
461C22×C4—471no—
462C22×C4—474no—
463C22×C4—944no—
464C22×C4—944no—
465C22×C4—944no—
466C22×C4—944no—
467C22×C4—941no—
468C22×C4—942no—
469C22×C4—1884no—
470C22×C4—1882no—
471C22×C4—1884no—
472C22×C4—1884no—
473C22×C4D4×D4712yes—
474C22×C4D4×D4711yescharacteristic
475C22×C4C23×D4712yes—
476C22×C4C23×D4711yescharacteristic
477C2×C8—24no—
478C2×C8—474no—
479C2×C8—944no—
480C2×C8C23×D4714yes—
481C4⋊C4—24no—
482C4⋊C4—22no—
483C4⋊C4—21no—
484C4⋊C4—474no—
485C4⋊C4—472no—
486C4⋊C4—948no—
487C4⋊C4—948no—
488C4⋊C4—944no—
489C4⋊C4—948no—
490C4⋊C4—948no—
491C4⋊C4—944no—
492C4⋊C4—942no—
493C4⋊C4—941no—
494C4⋊C4C23×D4714yes—
495C4⋊C4C23×D4712yes—
496C22⋊C4—24no—
497C22⋊C4—944no—
498C22⋊C4—944no—
499C22⋊C4—944no—
500C42—472no—
501C42—474no—
502C42—474no—
503C42—472no—
504C42—472no—
505C42—472no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—942no—
513C23—1882no—
514C23—1882no—
515C23—1882no—
516C23#1309405114yes—
517C23C2×D4×D4712yes—
518C23C2×D4×D4711yescharacteristic
519Q8—1888no—
520D4—24no—
521D4—48no—
522D4—42no—
523D4—944no—
524D4—1888no—
525D4—1888no—
526D4—1888no—
527D4—1882no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—48no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—472no—
537C2×C4—472no—
538C2×C4—472no—
539C2×C4—472no—
540C2×C4—942no—
541C2×C4—942no—
542C2×C4—948no—
543C2×C4—942no—
544C2×C4—942no—
545C2×C4—942no—
546C2×C4—944no—
547C2×C4—1888no—
548C2×C4—1884no—
549C2×C4—1888no—
550C2×C4—1888no—
551C2×C4—1884no—
552C2×C4—1882no—
553C2×C4C2×D4×D4712yes—
554C2×C4C2×D4×D4711yescharacteristic
555C2×C4#1309407114yes—
556C2×C4C24×D4711yescharacteristic
557C8—24no—
558C8—944no—
559C22—22no—
560C22—28no—
561C22—22no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—84no—
566C22—3764no—
567C22—1882no—
568C22—1882no—
569C22—1882no—
570C22#1568969512yes—
571C22C2×#1309405114yes—
572C22C2×#1309405112yes—
573C22#1568991912yes—
574C22C22×D4×D4711yescharacteristic
575C4—22no—
576C4—42no—
577C4—44no—
578C4—942no—
579C4—942no—
580C4—942no—
581C4—942no—
582C4—1882no—
583C4—1884no—
584C4#1568969512yes—
585C4C2×#1309407112yes—
586C2—24no—
587C2—82no—
588C2—3762no—
589C2#2025457714yesdirect product factor
590C2C2×#1568969511yescharacteristic
591C2C22×#1309405111yescharacteristic
592C2C2×#1568991911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#481C2
socleC23×C47C22×D4
prime radicalC2×#15689668C2
hypercenterC2×#481D47
hypocenterC47C2×#3234
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C22×#13094015C2semidirect
3. #20254577C2direct (N × H)
4. C2×#15689530C2semidirect
5. C2×#15689486C2semidirect
6. C2×#15689441C2semidirect
7. C2×#15689437C2semidirect
8. C2×#15689434C2semidirect
9. C2×#15689422C2semidirect
10. C2×#15689421C2semidirect
11. C2×#15689177C2semidirect
12. C2×C47×#481C2semidirect
23. C2×#13094015C22semidirect
34. #15689530C22semidirect
35. #15689486C22semidirect
36. #15689441C22semidirect
37. #15689437C22semidirect
38. #15689434C22semidirect
39. #15689422C22semidirect
40. #15689421C22semidirect
41. #15689177C22semidirect
53. C47×#481C22semidirect
296. C2×#481D47semidirect
304. C2×C47#3234semidirect
335. #481C2×D47semidirect
353. C47C2×#3234semidirect
589. C2#20254577direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896682
C22×#130940152
#202545772
C2×#156895302
C2×#156894862
C2×#156894412
C2×#156894372
C2×#156894342
C2×#156894222
C2×#156894212
C2×#156891772
C2×C47×#4812
C2×#323447