Finite Group Databasebeta

← C2×#20244851 #26245218

Subgroups — C2×#20244851 #26245218

Order 12032.

1006 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689171C211yesmaximal, characteristic, complemented
2C2×#15689129C211yesmaximal, characteristic
3C2×#15689127C211yesmaximal, characteristic
4C22×#13093940C211yesmaximal, characteristic
5#20244851C218yesmaximal, direct product factor
6C2×#15688895C211yesmaximal, characteristic, complemented
7C2×#15688879C211yesmaximal, characteristic, complemented
8C2×C47×#344C211yesmaximal, characteristic, complemented
9C23×D188C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12C2×#13093983C2211yescharacteristic
13#15689171—22no—
14#15689171C2214yescomplemented
15C2×#13093959—22no—
16#15689129—22no—
17#15689129C2214yes—
18#15689127—22no—
19#15689127C2214yes—
20C2×#13093946—22no—
21C2×#13093944—22no—
22C2×#13093940—22no—
23C2×#13093940—22no—
24C2×#13093940C2214yes—
25#15688895C2214yescomplemented
26#15688879C2214yescomplemented
27C22×M16×C47C2211yescharacteristic
28C22×M16×C47C2211yescharacteristic
29C2×#117×C47C2211yescharacteristic
30C47×#344C2214yescomplemented
31C24×D47—21no—
32C22×D188—21no—
33C22×D188—21no—
34C22×D188—21no—
35C22×D188—21no—
36C22×D188—21no—
37C22×D188—21no—
38C22×D188—21no—
39C22×D188—21no—
40C22×D188—21no—
41C22×D188—21no—
42C22×D188—21no—
43C22×D188D412yes—
44C22×D188D412yes—
45C22×D188C2312yes—
46C2×#10625329—21no—
47C2×#10625329—21no—
48C2×#10625329—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329D412yes—
56C2×#10625329C2312yes—
57C2×#10625329C2312yes—
58C22×C47⋊C8—21no—
59C22×C47⋊C8D412yes—
60#13093983—21no—
61#13093983—21no—
62#13093983—21no—
63#13093983C2312yes—
64C2×C4⋊Dic47—21no—
65C2×C22⋊Dic47—21no—
66C2×C4×Dic47—21no—
67#13093959—28no—
68#13093946—28no—
69#13093944—28no—
70#13093940—28no—
71C23×C4×C47C2311yescharacteristic
72C2×M16×C47—21no—
73C2×M16×C47—21no—
74C2×M16×C47—21no—
75C2×M16×C47—21no—
76C2×M16×C47—21no—
77C2×M16×C47—21no—
78C2×M16×C47—21no—
79C2×M16×C47—21no—
80C2×M16×C47—21no—
81C2×M16×C47—21no—
82C2×M16×C47C2312yes—
83C2×M16×C47C2312yes—
84C22×C8×C47—21no—
85C22×C8×C47—21no—
86#117×C47—21no—
87#117×C47—21no—
88#117×C47—21no—
89#117×C47C2312yes—
90C2×C4⋊C4×C47—21no—
91C2×C22⋊C4×C47—21no—
92C2×C42×C47—21no—
93C24×C47#4111yescharacteristic
94C23×D47—22no—
95C23×D47—22no—
96C23×D47—22no—
97C23×D47—41no—
98C23×D47—41no—
99C23×D47—41no—
100C23×D47—41no—
101C23×D47—84no—
102C22×C4×C47—41no—
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47C2×D411yescharacteristic
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C22×C4×C47#4111yescharacteristic
111C22×C4×C47#4111yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C22×C4×C47#4111yescharacteristic
114C22×C4×C47#4111yescharacteristic
115C22×C4×C47#4111yescharacteristic
116C22×C4×C47C2411yescharacteristic
117C22×Dic47—41no—
118C2×D188—22no—
119C2×D188—22no—
120C2×D188—22no—
121C2×D188—22no—
122C2×D188—22no—
123C2×D188—22no—
124C2×D188—22no—
125C2×D188—22no—
126C2×D188—22no—
127C2×D188—22no—
128C2×D188—22no—
129C2×D188—22no—
130C2×D188—22no—
131C2×D188—22no—
132C2×D188—22no—
133C2×D188—41no—
134C2×D188—41no—
135C2×D188—41no—
136C2×D188—41no—
137C2×D188—41no—
138C2×D188—41no—
139C2×D188—41no—
140C2×D188—41no—
141C2×D188—41no—
142C2×D188—41no—
143C2×D188—41no—
144C2×D188—41no—
145C2×D188C2×D414yes—
146M16×C47—22no—
147M16×C47—22no—
148M16×C47—22no—
149M16×C47—22no—
150M16×C47—41no—
151M16×C47—41no—
152M16×C47—41no—
153M16×C47—41no—
154C2×C8×C47—22no—
155C2×C8×C47—22no—
156C2×C8×C47—41no—
157C2×C8×C47—41no—
158C2×C8×C47—41no—
159C2×C8×C47—41no—
160C4⋊C4×C47—22no—
161C4⋊C4×C47—41no—
162C22⋊C4×C47—22no—
163C22⋊C4×C47—41no—
164C42×C47—22no—
165C42×C47—41no—
166C22⋊Dic47—22no—
167C22⋊Dic47—41no—
168C4⋊Dic47—22no—
169C4⋊Dic47—41no—
170C4×Dic47—22no—
171C4×Dic47—41no—
172#10625329—22no—
173#10625329—22no—
174#10625329—22no—
175#10625329—22no—
176#10625329—22no—
177#10625329—22no—
178#10625329—41no—
179#10625329—41no—
180C2×C47⋊C8—22no—
181C2×C47⋊C8—22no—
182C2×C47⋊C8—22no—
183C2×C47⋊C8—41no—
184C2×C47⋊C8—41no—
185C2×C47⋊C8C2×D414yes—
186C23×C47—42no—
187C23×C47#12311yescharacteristic
188C23×C47#12311yescharacteristic
189C23×C47#12411yescharacteristic
190C23×C47#12411yescharacteristic
191C23×C47#12611yescharacteristic
192C23×C47#12611yescharacteristic
193C23×C47C2×#4111yescharacteristic
194C22×D47—24no—
195C22×D47—42no—
196C22×D47—42no—
197C22×D47—42no—
198C22×D47—42no—
199C22×D47—42no—
200C22×D47—42no—
201C22×D47—84no—
202C22×D47—84no—
203C22×D47—84no—
204C22×D47—84no—
205C22×D47—84no—
206C22×D47—84no—
207C22×D47—84no—
208C2×C4×C47—42no—
209C2×C4×C47—82no—
210C2×C4×C47#12111yescharacteristic
211C2×C4×C47#12111yescharacteristic
212C2×C4×C47#12111yescharacteristic
213C2×C4×C47#12111yescharacteristic
214C2×C4×C47#12311yescharacteristic
215C2×C4×C47#12311yescharacteristic
216C2×C4×C47#12311yescharacteristic
217C2×C4×C47#12311yescharacteristic
218C2×C4×C47#12311yescharacteristic
219C2×C4×C47#12311yescharacteristic
220C2×C4×C47#12311yescharacteristic
221C2×C4×C47#12311yescharacteristic
222C2×C4×C47#12311yescharacteristic
223C2×C4×C47#12311yescharacteristic
224C2×C4×C47#12411yescharacteristic
225C2×C4×C47#12411yescharacteristic
226C2×C4×C47#12611yescharacteristic
227C2×C4×C47#12611yescharacteristic
228C2×C4×C47#12611yescharacteristic
229C2×C4×C47#12611yescharacteristic
230C2×C4×C47#12611yescharacteristic
231C2×C4×C47#12611yescharacteristic
232C2×C4×C47C22×D411yescharacteristic
233C2×C4×C47C22×D411yescharacteristic
234C2×C4×C47C2×#4111yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C2×Dic47—42no—
239C2×Dic47—82no—
240D188—24no—
241D188—24no—
242D188—42no—
243D188—42no—
244D188—42no—
245D188—42no—
246D188—42no—
247D188—42no—
248C8×C47—42no—
249C8×C47—42no—
250C47⋊C8—24no—
251C47⋊C8—42no—
252C2×#2081—471nomaximal, Sylow
253C22×C47—22no—
254C22×C47—22no—
255C22×C47—22no—
256C22×C47—41no—
257C22×C47—41no—
258C22×C47—41no—
259C22×C47—41no—
260C22×C47#39711yescharacteristic
261C22×C47#39711yescharacteristic
262C22×C47#39711yescharacteristic
263C22×C47#39711yescharacteristic
264C22×C47C2×#12311yescharacteristic
265C22×C47C2×#12411yescharacteristic
266C22×C47C2×#12611yescharacteristic
267C2×D47—44no—
268C2×D47—84no—
269C2×D47—84no—
270C2×D47—84no—
271C2×D47—84no—
272C2×D47—84no—
273C2×D47—84no—
274C2×D47—84no—
275C4×C47—82no—
276C4×C47#39711yescharacteristic
277C4×C47#39711yescharacteristic
278C4×C47#39711yescharacteristic
279C4×C47#39711yescharacteristic
280C4×C47C2×#12111yescharacteristic
281C4×C47C2×#12311yescharacteristic
282C4×C47C2×#12311yescharacteristic
283C4×C47C2×#12611yescharacteristic
284Dic47—82no—
285C2×#430—471no—
286C2×#418—471no—
287C2×#418—471no—
288C22×#100—471no—
289#2081—478no—
290C2×#344—471no—
291C2×#344D4711yescharacteristic, complemented
292C2×H(3,ℤ/4)—471no—
293C2×C47—21no—
294C2×C47—21no—
295C2×C47—21no—
296C2×C47—21no—
297C2×C47—21no—
298C2×C47—21no—
299C2×C47#208112yescomplemented
300C2×C47C2×#39711yescharacteristic
301D47—84no—
302C23×D4—471no—
303C22×M16—471no—
304C22×M16—471no—
305C22×M16C2×D4711yescharacteristic
306C22×M16C2×D4711yescharacteristic
307C2×#117—471no—
308C2×#117C2×D4711yescharacteristic
309#430—474no—
310#430—942no—
311C2×#108—942no—
312#418—474no—
313#418—474no—
314#418—942no—
315#418—942no—
316C2×#102—942no—
317C2×#102—942no—
318C2×#100—474no—
319C2×#100—942no—
320C2×#100—942no—
321#344—474no—
322#344C2×D4714yescomplemented
323H(3,ℤ/4)—474no—
324C47C2×#208111yescharacteristic, complemented, Sylow
325C25—941no—
326C22×D4—472no—
327C22×D4—472no—
328C22×D4—472no—
329C22×D4—941no—
330C22×D4—941no—
331C22×D4—941no—
332C22×D4—941no—
333C22×D4—941no—
334C22×D4—941no—
335C22×D4—941no—
336C22×D4—941no—
337C22×D4—941no—
338C22×D4—941no—
339C22×D4—941no—
340C23×C4C22×D4711yescharacteristic
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—472no—
352C2×M16—472no—
353C2×M16—472no—
354C2×M16—941no—
355C2×M16—941no—
356C2×M16—941no—
357C2×M16—941no—
358C2×M16—941no—
359C2×M16—941no—
360C2×M16—941no—
361C2×M16—941no—
362C2×M16—941no—
363C2×M16C22×D4712yes—
364C2×M16C22×D4712yes—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—472no—
368C22×C8—941no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—472no—
373#117—941no—
374#117—941no—
375#117—941no—
376#117C22×D4712yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—941no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—941no—
381C2×C42—21no—
382C2×C42—941no—
383#108—948no—
384#102—948no—
385#102—948no—
386#100—948no—
387C24—942no—
388C24—942no—
389C24—942no—
390C24—3764no—
391C24—1881no—
392C24—1881no—
393C24—1881no—
394C24—1881no—
395C24#1062535011yescharacteristic
396C2×D4—474no—
397C2×D4—942no—
398C2×D4—942no—
399C2×D4—942no—
400C2×D4—942no—
401C2×D4—942no—
402C2×D4—942no—
403C2×D4—942no—
404C2×D4—942no—
405C2×D4—942no—
406C2×D4—942no—
407C2×D4—942no—
408C2×D4—942no—
409C2×D4—942no—
410C2×D4—942no—
411C2×D4—942no—
412C2×D4—1881no—
413C2×D4—1881no—
414C2×D4—1881no—
415C2×D4—1881no—
416C2×D4—1881no—
417C2×D4—1881no—
418C2×D4—1881no—
419C2×D4—1881no—
420C2×D4—1881no—
421C2×D4—1881no—
422C2×D4—1881no—
423C2×D4—1881no—
424C22×C4—41no—
425C22×C4—1881no—
426C22×C4#1062535011yescharacteristic
427C22×C4#1062535011yescharacteristic
428C22×C4#1062535011yescharacteristic
429C22×C4#1062535011yescharacteristic
430C22×C4#1062535011yescharacteristic
431C22×C4D4×D4711yescharacteristic
432C22×C4D4×D4711yescharacteristic
433C22×C4D4×D4711yescharacteristic
434C22×C4D4×D4711yescharacteristic
435C22×C4#1062535211yescharacteristic
436C22×C4#1062535211yescharacteristic
437C22×C4#1062535411yescharacteristic
438C22×C4#1062535411yescharacteristic
439C22×C4C23×D4711yescharacteristic
440M16—22no—
441M16—22no—
442M16—22no—
443M16—22no—
444M16—41no—
445M16—41no—
446M16—41no—
447M16—41no—
448M16—942no—
449M16—942no—
450M16—942no—
451M16—942no—
452M16—942no—
453M16—942no—
454M16—1881no—
455M16—1881no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—41no—
459C2×C8—41no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—474no—
463C2×C8—942no—
464C2×C8—942no—
465C2×C8—942no—
466C2×C8—1881no—
467C2×C8—1881no—
468C4⋊C4—22no—
469C4⋊C4—41no—
470C4⋊C4—942no—
471C4⋊C4—1881no—
472C22⋊C4—22no—
473C22⋊C4—41no—
474C22⋊C4—942no—
475C22⋊C4—1881no—
476C42—22no—
477C42—41no—
478C42—942no—
479C42—1881no—
480C23—42no—
481C23—944no—
482C23—3764no—
483C23—3764no—
484C23—3764no—
485C23—3764no—
486C23—3764no—
487C23—3764no—
488C23—3764no—
489C23—1882no—
490C23—1882no—
491C23—1882no—
492C23—1882no—
493C23—1882no—
494C23—1882no—
495C23#1309400911yescharacteristic
496C23#1309400911yescharacteristic
497C23#1309401011yescharacteristic
498C23#1309401011yescharacteristic
499C23#1309401811yescharacteristic
500C23#1309401811yescharacteristic
501C23C2×#1062535011yescharacteristic
502D4—944no—
503D4—944no—
504D4—1882no—
505D4—1882no—
506D4—1882no—
507D4—1882no—
508D4—1882no—
509D4—1882no—
510C2×C4—42no—
511C2×C4—82no—
512C2×C4—3762no—
513C2×C4—1882no—
514C2×C4#1309399711yescharacteristic
515C2×C4#1309399711yescharacteristic
516C2×C4#1309399711yescharacteristic
517C2×C4#1309399711yescharacteristic
518C2×C4#1309400611yescharacteristic
519C2×C4#1309400611yescharacteristic
520C2×C4#1309400611yescharacteristic
521C2×C4#1309400611yescharacteristic
522C2×C4#1309400911yescharacteristic
523C2×C4#1309400911yescharacteristic
524C2×C4#1309400911yescharacteristic
525C2×C4#1309400911yescharacteristic
526C2×C4#1309400911yescharacteristic
527C2×C4#1309400911yescharacteristic
528C2×C4#1309401011yescharacteristic
529C2×C4#1309401011yescharacteristic
530C2×C4#1309401811yescharacteristic
531C2×C4#1309401811yescharacteristic
532C2×C4#1309401911yescharacteristic
533C2×C4#1309401911yescharacteristic
534C2×C4#1309401911yescharacteristic
535C2×C4#1309401911yescharacteristic
536C2×C4C2×D4×D4711yescharacteristic
537C2×C4C2×D4×D4711yescharacteristic
538C2×C4C2×#1062535211yescharacteristic
539C2×C4C2×#1062535011yescharacteristic
540C2×C4C2×#1062535011yescharacteristic
541C2×C4C2×#1062535411yescharacteristic
542C8—42no—
543C8—42no—
544C8—944no—
545C8—1882no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—3764no—
554C22—3764no—
555C22—3764no—
556C22—3764no—
557C22—3764no—
558C22—3764no—
559C22—3764no—
560C22—1884no—
561C22#1568905211yescharacteristic
562C22#1568905211yescharacteristic
563C22#1568905211yescharacteristic
564C22#1568905211yescharacteristic
565C22C2×#1309400911yescharacteristic
566C22C2×#1309401011yescharacteristic
567C22C2×#1309401811yescharacteristic
568C4—82no—
569C4—3762no—
570C4#1568905211yescharacteristic
571C4#1568905211yescharacteristic
572C4#1568905211yescharacteristic
573C4#1568905211yescharacteristic
574C4C2×#1309399711yescharacteristic
575C4C2×#1309400611yescharacteristic
576C4C2×#1309400911yescharacteristic
577C4C2×#1309401911yescharacteristic
578C2—21no—
579C2—21no—
580C2—21no—
581C2—21no—
582C2—21no—
583C2—21no—
584C2—3764no—
585C2#2024485112yesdirect product factor
586C2C2×#1568905211yescharacteristic
subgroupG/H
centerC22#15689052
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#344C2
socleC22×C47#397
prime radicalC23×D188C22
hypercenterC2×#344D47
hypocenterC47C2×#2081
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#15689171C2semidirect
5. #20244851C2direct (N × H)
6. C2×#15688895C2semidirect
7. C2×#15688879C2semidirect
8. C2×C47×#344C2semidirect
14. #15689171C22semidirect
25. #15688895C22semidirect
26. #15688879C22semidirect
30. C47×#344C22semidirect
291. C2×#344D47semidirect
299. C2×C47#2081semidirect
322. #344C2×D47semidirect
324. C47C2×#2081semidirect
585. C2#20244851direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156891712
C2×#156891292
C2×#156891272
C22×#130939402
#202448512
C2×#156888952
C2×#156888792
C2×C47×#3442
C2×#208147