Finite Group Databasebeta

← C2×#20244543 #26243637

Subgroups — C2×#20244543 #26243637

Order 12032.

1454 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689751C211yesmaximal, characteristic, complemented
2C2×#15689129C211yesmaximal, characteristic
3C2×#15689127C211yesmaximal, characteristic
4C2×#15689025C211yesmaximal, characteristic
5#20244543C218yesmaximal, direct product factor
6C2×#15688891C211yesmaximal, characteristic, complemented
7C2×#15688883C211yesmaximal, characteristic, complemented
8C2×C47×#339C211yesmaximal, characteristic, complemented
9C23×D188C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11#15689751—22no—
12#15689751—22no—
13#15689751—22no—
14#15689751C2214yescomplemented
15C2×#13094024—21no—
16C2×#13094023—21no—
17C2×#13094016—21no—
18C2×#13094015—21no—
19C2×#13094001—22no—
20C2×#13093983C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22C22×(C2×D47)⋊C4—22no—
23#15689129—22no—
24#15689129C2214yes—
25#15689127—22no—
26#15689127C2214yes—
27C2×#13093946—21no—
28C2×#13093946—21no—
29C2×#13093944—21no—
30C2×#13093944—21no—
31#15689025—22no—
32#15689025C2214yes—
33#15688891C2214yescomplemented
34#15688883C2214yescomplemented
35C22×M16×C47C2211yescharacteristic
36C2×#117×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C47×#339C2214yescomplemented
39C24×D47—21no—
40C22×Dic94—22no—
41C22×D188—21no—
42C22×D188—21no—
43C22×D188—21no—
44C22×D188—21no—
45C22×D188—22no—
46C22×D188—22no—
47C22×D188—21no—
48C22×D188—22no—
49C22×D188Q814yescomplemented
50C22×D188C2312yes—
51C23×Dic47D412yes—
52C2×#10625329—21no—
53C2×#10625329—22no—
54C2×#10625329—22no—
55C2×#10625329C2312yes—
56C22×C47⋊C8—21no—
57#13094024—24no—
58#13094024—24no—
59#13094023—24no—
60#13094023—24no—
61#13094016—24no—
62#13094016—24no—
63#13094015—24no—
64#13094015—24no—
65#13094001—28no—
66#13094001—28no—
67#13093983—21no—
68#13093983—21no—
69#13093983D412yes—
70#13093983C2312yes—
71C2×C4⋊Dic47—22no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47D412yes—
77C2×C4⋊Dic47D411yescharacteristic
78C2×C4⋊Dic47D411yescharacteristic
79C2×C4⋊Dic47C2312yes—
80C2×Dic47⋊C4—22no—
81C2×Dic47⋊C4—22no—
82C2×C22⋊Dic47—21no—
83C2×(C2×D47)⋊C4—28no—
84C2×(C2×D47)⋊C4—48no—
85C2×C4×Dic47—21no—
86#13093946—24no—
87#13093946—24no—
88#13093944—24no—
89#13093944—24no—
90C23×C4×C47—21no—
91C23×C4×C47C2311yescharacteristic
92C2×M16×C47—21no—
93C2×M16×C47—22no—
94C2×M16×C47—22no—
95C2×M16×C47C2312yes—
96C22×C8×C47—21no—
97#117×C47—21no—
98#117×C47—21no—
99#117×C47D412yes—
100#117×C47C2312yes—
101C2×C4⋊C4×C47D411yescharacteristic
102C2×C4⋊C4×C47D411yescharacteristic
103C2×C22⋊C4×C47—21no—
104C2×C42×C47—21no—
105C2×C42×C47—22no—
106C2×C42×C47—22no—
107C2×C42×C47—21no—
108C2×C42×C47C2312yes—
109C24×C47C2×D411yescharacteristic
110C23×D47—24no—
111C23×D47—22no—
112C23×D47—44no—
113C23×D47—44no—
114C23×D47—41no—
115C23×D47—41no—
116C23×D47—42no—
117C22×C4×C47—24no—
118C22×C4×C47—21no—
119C22×C4×C47—21no—
120C22×C4×C47—22no—
121C22×C4×C47—42no—
122C22×C4×C47—42no—
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×Q812yes—
129C22×C4×C47#4112yes—
130C22×C4×C47#4112yes—
131C22×C4×C47#4112yes—
132C22×C4×C47C2411yescharacteristic
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—44no—
138C22×Dic47C2×D414yes—
139C2×D188—24no—
140C2×D188—24no—
141C2×D188—24no—
142C2×D188—24no—
143C2×D188—22no—
144C2×D188—22no—
145C2×D188—22no—
146C2×D188—22no—
147C2×D188—24no—
148C2×D188—22no—
149C2×D188—41no—
150C2×D188—41no—
151C2×D188—42no—
152C2×D188—42no—
153C2×D188—42no—
154C2×D188—42no—
155C2×D188—42no—
156C2×D188C2×Q814yescomplemented
157C2×Dic94—28no—
158C2×Dic94—84no—
159M16×C47—22no—
160M16×C47—22no—
161M16×C47—42no—
162C2×C8×C47—22no—
163C2×C8×C47—42no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47C2×D412yes—
167C4⋊C4×C47C2×D412yes—
168C22⋊C4×C47—22no—
169C22⋊C4×C47—22no—
170C42×C47—22no—
171C42×C47—22no—
172C42×C47—22no—
173C42×C47—22no—
174C42×C47—42no—
175C22⋊Dic47—22no—
176C22⋊Dic47—22no—
177(C2×D47)⋊C4—416no—
178C4⋊Dic47—28no—
179C4⋊Dic47—22no—
180C4⋊Dic47—22no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—22no—
184C4⋊Dic47—22no—
185C4⋊Dic47C2×D412yes—
186C4⋊Dic47C2×D412yes—
187Dic47⋊C4—28no—
188Dic47⋊C4—28no—
189C4×Dic47—22no—
190C4×Dic47—22no—
191#10625329—22no—
192#10625329—22no—
193#10625329—42no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8—42no—
196C23×C47—22no—
197C23×C47—22no—
198C23×C47#12011yescharacteristic
199C23×C47#12011yescharacteristic
200C23×C47C22⋊Q812yes—
201C23×C47#12412yes—
202C23×C47C22×D411yescharacteristic
203C22×D47—24no—
204C22×D47—44no—
205C22×D47—44no—
206C22×D47—416no—
207C22×D47—42no—
208C22×D47—42no—
209C22×D47—44no—
210C22×D47—44no—
211C22×D47—82no—
212C22×D47—82no—
213C22×D47—88no—
214C22×D47—82no—
215C22×D47—82no—
216C2×C4×C47—24no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—42no—
220C2×C4×C47—48no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47#12011yescharacteristic
225C2×C4×C47#12011yescharacteristic
226C2×C4×C47C22⋊Q812yes—
227C2×C4×C47C22⋊Q812yes—
228C2×C4×C47C22⋊Q812yes—
229C2×C4×C47C22⋊Q812yes—
230C2×C4×C47C22⋊Q812yes—
231C2×C4×C47#12412yes—
232C2×C4×C47#12412yes—
233C2×C4×C47#12412yes—
234C2×C4×C47#12412yes—
235C2×C4×C47#12412yes—
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C22×Q811yescharacteristic
239C2×C4×C47C2×#4111yescharacteristic
240C2×C4×C47C2×#4111yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—24no—
245C2×Dic47—42no—
246C2×Dic47—44no—
247C2×Dic47—42no—
248C2×Dic47—44no—
249C2×Dic47—82no—
250D188—24no—
251D188—24no—
252D188—42no—
253D188—42no—
254D188—44no—
255D188—44no—
256Dic94—88no—
257C8×C47—42no—
258C47⋊C8—42no—
259C2×#2027—471nomaximal, Sylow
260C22×C47—21no—
261C22×C47—21no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47—24no—
265C22×C47—24no—
266C22×C47#39312yes—
267C22×C47#39312yes—
268C22×C47#45312yes—
269C22×C47#45412yes—
270C22×C47C2×#12011yescharacteristic
271C22×C47C2×C22⋊Q811yescharacteristic
272C22×C47C2×#12411yescharacteristic
273C2×D47—48no—
274C2×D47—44no—
275C2×D47—84no—
276C2×D47—88no—
277C2×D47—82no—
278C2×D47—82no—
279C2×D47—88no—
280C4×C47—44no—
281C4×C47—42no—
282C4×C47—42no—
283C4×C47#39312yes—
284C4×C47#39312yes—
285C4×C47C2×C22⋊Q811yescharacteristic
286C4×C47C2×C22⋊Q811yescharacteristic
287C4×C47C2×#12411yescharacteristic
288C4×C47C2×#12411yescharacteristic
289Dic47—42no—
290Dic47—44no—
291Dic47—42no—
292C2×#544—471no—
293C2×#418—471no—
294C2×#418—471no—
295C2×#390—471no—
296#2027—478no—
297C2×#343—471no—
298C2×#339—471no—
299C2×#339D4711yescharacteristic, complemented
300C2×C47—21no—
301C2×C47—21no—
302C2×C47—22no—
303C2×C47#202714yescomplemented
304C2×C47C2×#39311yescharacteristic
305C2×C47C2×#45311yescharacteristic
306C2×C47C2×#45411yescharacteristic
307D47—84no—
308C23×D4—471no—
309C22×M16—471no—
310C22×M16C2×D4711yescharacteristic
311#544—474no—
312#544—942no—
313#544—942no—
314#544—942no—
315C2×C4⋊Q8—941no—
316C2×C4⋊Q8—941no—
317C2×#125—941no—
318C2×#125—941no—
319C2×C22⋊Q8—942no—
320C2×#117—471no—
321C2×#117C2×D4711yescharacteristic
322C22×C4⋊C4—471no—
323C22×C22⋊C4—942no—
324C22×C42C2×D4711yescharacteristic
325#418—474no—
326#418—474no—
327#418—942no—
328#418—942no—
329C2×#102—941no—
330C2×#102—941no—
331C2×#102—941no—
332C2×#102—941no—
333#390—474no—
334#390—942no—
335#343—474no—
336#339—474no—
337#339C2×D4714yescomplemented
338C47C2×#202711yescharacteristic, complemented, Sylow
339C25—941no—
340C22×Q8—942no—
341C22×D4—474no—
342C22×D4—472no—
343C22×D4—941no—
344C22×D4—941no—
345C22×D4—942no—
346C22×D4—942no—
347C22×D4—941no—
348C22×D4—941no—
349C22×D4—941no—
350C22×D4—942no—
351C23×C4—21no—
352C23×C4—472no—
353C23×C4C22×D4711yescharacteristic
354C2×M16—21no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—472no—
358C2×M16—941no—
359C2×M16—942no—
360C2×M16—942no—
361C2×M16C22×D4712yes—
362C22×C8—21no—
363C22×C8—941no—
364C4⋊Q8—944no—
365C4⋊Q8—944no—
366C4⋊Q8—944no—
367C4⋊Q8—944no—
368#125—944no—
369#125—944no—
370#125—944no—
371#125—944no—
372C22⋊Q8—948no—
373C22⋊Q8—948no—
374#117—21no—
375#117—21no—
376#117—472no—
377#117—472no—
378#117—941no—
379#117—941no—
380#117D18812yes—
381#117C22×D4712yes—
382C2×C4⋊C4—471no—
383C2×C4⋊C4—471no—
384C2×C4⋊C4—472no—
385C2×C4⋊C4—472no—
386C2×C4⋊C4—942no—
387C2×C4⋊C4—942no—
388C2×C4⋊C4—942no—
389C2×C4⋊C4—941no—
390C2×C4⋊C4—941no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4—941no—
393C2×C4⋊C4D18811yescharacteristic
394C2×C4⋊C4D18811yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—941no—
397C2×C22⋊C4—948no—
398C2×C22⋊C4—1888no—
399C2×C42—21no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—21no—
403C2×C42—941no—
404C2×C42C22×D4712yes—
405#102—944no—
406#102—944no—
407#102—944no—
408#102—944no—
409C24—944no—
410C24—942no—
411C24—1884no—
412C24—1884no—
413C24—1881no—
414C24—1881no—
415C24—1882no—
416C24D4×D4711yescharacteristic
417C2×Q8—948no—
418C2×Q8—3764no—
419C2×D4—474no—
420C2×D4—944no—
421C2×D4—944no—
422C2×D4—944no—
423C2×D4—944no—
424C2×D4—944no—
425C2×D4—942no—
426C2×D4—942no—
427C2×D4—942no—
428C2×D4—942no—
429C2×D4—942no—
430C2×D4—1881no—
431C2×D4—1881no—
432C2×D4—1882no—
433C2×D4—1882no—
434C2×D4—1882no—
435C2×D4—1882no—
436C2×D4—1882no—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—474no—
444C22×C4—942no—
445C22×C4—941no—
446C22×C4—941no—
447C22×C4—942no—
448C22×C4—1884no—
449C22×C4C2×D18811yescharacteristic
450C22×C4C2×D18811yescharacteristic
451C22×C4#1062535012yes—
452C22×C4#1062535012yes—
453C22×C4D4×D4711yescharacteristic
454C22×C4D4×D4711yescharacteristic
455C22×C4D4×D4711yescharacteristic
456C22×C4#1062535212yes—
457C22×C4Q8×D4712yes—
458C22×C4C23×D4711yescharacteristic
459M16—22no—
460M16—22no—
461M16—42no—
462M16—942no—
463M16—942no—
464M16—1882no—
465C2×C8—22no—
466C2×C8—42no—
467C2×C8—942no—
468C2×C8—1882no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—472no—
472C4⋊C4—472no—
473C4⋊C4—948no—
474C4⋊C4—948no—
475C4⋊C4—948no—
476C4⋊C4—942no—
477C4⋊C4—942no—
478C4⋊C4—941no—
479C4⋊C4—941no—
480C4⋊C4—942no—
481C4⋊C4—942no—
482C4⋊C4C2×D18812yes—
483C4⋊C4C2×D18812yes—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—942no—
487C22⋊C4—942no—
488C22⋊C4—18816no—
489C42—22no—
490C42—22no—
491C42—22no—
492C42—22no—
493C42—42no—
494C42—942no—
495C42—942no—
496C23—22no—
497C23—22no—
498C23—944no—
499C23—3762no—
500C23—3762no—
501C23—3768no—
502C23—3762no—
503C23—3762no—
504C23—1884no—
505C23—1884no—
506C23—18816no—
507C23—1884no—
508C23—1884no—
509C23—1882no—
510C23—1882no—
511C23#1309399411yescharacteristic
512C23#1309399411yescharacteristic
513C23#1309400212yes—
514C23#1309401012yes—
515C23C2×D4×D4711yescharacteristic
516Q8—3768no—
517D4—944no—
518D4—944no—
519D4—1884no—
520D4—1884no—
521D4—1882no—
522D4—1882no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—42no—
527C2×C4—48no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—942no—
532C2×C4—942no—
533C2×C4—944no—
534C2×C4—3762no—
535C2×C4—1884no—
536C2×C4—1882no—
537C2×C4—1882no—
538C2×C4—1884no—
539C2×C4#1309399411yescharacteristic
540C2×C4#1309399411yescharacteristic
541C2×C4#1309400212yes—
542C2×C4#1309400212yes—
543C2×C4#1309400212yes—
544C2×C4#1309400412yes—
545C2×C4#1309400412yes—
546C2×C4#1309401012yes—
547C2×C4#1309401012yes—
548C2×C4#1309401012yes—
549C2×C4#1309401212yes—
550C2×C4#1309401212yes—
551C2×C4C2×D4×D4711yescharacteristic
552C2×C4C22×D18811yescharacteristic
553C2×C4C2×Q8×D4711yescharacteristic
554C2×C4C2×#1062535211yescharacteristic
555C2×C4C2×#1062535011yescharacteristic
556C2×C4C2×#1062535011yescharacteristic
557C8—42no—
558C8—1882no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—24no—
564C22—24no—
565C22—3764no—
566C22—3768no—
567C22—3762no—
568C22—3762no—
569C22—3768no—
570C22—1888no—
571C22—1884no—
572C22#1568903612yes—
573C22#1568903612yes—
574C22#1568929212yes—
575C22#1568929712yes—
576C22C2×#1309399411yescharacteristic
577C22C2×#1309400211yescharacteristic
578C22C2×#1309401011yescharacteristic
579C4—44no—
580C4—42no—
581C4—42no—
582C4—1884no—
583C4—1882no—
584C4—1882no—
585C4#1568903612yes—
586C4#1568903612yes—
587C4C2×#1309400211yescharacteristic
588C4C2×#1309400411yescharacteristic
589C4C2×#1309401011yescharacteristic
590C4C2×#1309401211yescharacteristic
591C2—21no—
592C2—22no—
593C2—21no—
594C2—3764no—
595C2#2024454314yesdirect product factor
596C2C2×#1568903611yescharacteristic
597C2C2×#1568929211yescharacteristic
598C2C2×#1568929711yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#339C2
socleC23×C47#120
prime radicalC23×D188C22
hypercenterC2×#339D47
hypocenterC47C2×#2027
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C2×#15689751C2semidirect
5. #20244543C2direct (N × H)
6. C2×#15688891C2semidirect
7. C2×#15688883C2semidirect
8. C2×C47×#339C2semidirect
14. #15689751C22semidirect
33. #15688891C22semidirect
34. #15688883C22semidirect
38. C47×#339C22semidirect
49. C22×D188Q8semidirect
156. C2×D188C2×Q8semidirect
299. C2×#339D47semidirect
303. C2×C47#2027semidirect
337. #339C2×D47semidirect
338. C47C2×#2027semidirect
595. C2#20244543direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897512
C2×#156891292
C2×#156891272
C2×#156890252
#202445432
C2×#156888912
C2×#156888832
C2×C47×#3392
C2×#202747