Finite Group Databasebeta

← C2×#11747512 #14423468

Subgroups — C2×#11747512 #14423468

Order 1920.

1624 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6773C211yesmaximal, characteristic, complemented
2C2×C3×#4041C211yesmaximal, characteristic, complemented
3C22×#6655C211yesmaximal, characteristic, complemented
4C22×#6653C211yesmaximal, characteristic, complemented
5C2×#91093C211yesmaximal, characteristic, complemented
6C2×C5×#810C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic, complemented
8#11747512C218yesmaximal, direct product factor
9C2×#65100—31nomaximal, Hall
10C22×D60C2211yescharacteristic
11C22×C5×Dic6C2211yescharacteristic
12C22×C3×D20—21no—
13C22×C3×D20C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×#1202—21no—
16C22×#1200—21no—
17C2×#6773—24no—
18C2×#6773—24no—
19C2×#6773—22no—
20C2×#6773C2214yescomplemented
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C22×C3⋊#168C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C2×C3×#685—21no—
25C3×#4041—22no—
26C3×#4041C2214yescomplemented
27C2×#6655—24no—
28C2×#6655C2214yescomplemented
29C2×#6653—24no—
30C2×#6653C2214yescomplemented
31#91093C2214yescomplemented
32C5×#810C2214yescomplemented
33#90955C2214yescomplemented
34C2×#5037—51nomaximal, Hall
35C22×#713—31no—
36C22×#688—31no—
37C22×D40—31no—
38C2×#4041D311yescharacteristic, complemented
39C2×C5×#103—31no—
40C2×#3952—31no—
41C2×#3941—31no—
42#65100—38no—
43C23×D15—21no—
44C23×C3×D5—21no—
45C23×C3×D5D411yescharacteristic
46C22×C3×C4×C5—21no—
47C22×C3×C4×C5C2311yescharacteristic
48C2×D60—21no—
49C2×D60—22no—
50C2×D60D414yescomplemented
51C2×D60C2312yes—
52C22×C5×Dic3—21no—
53C2×C5×Dic6—21no—
54C2×C5×Dic6—22no—
55C2×C5×Dic6D414yescomplemented
56C2×C5×Dic6C2312yes—
57C22×C3×Dic5D411yescharacteristic
58C2×C3×D20—22no—
59C2×C3×D20—22no—
60C2×C3×D20—24no—
61C2×C3×D20—21no—
62C2×C3×D20—44no—
63C2×C3×D20C2312yes—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5D412yes—
67C2×C3×C4×D5C2312yes—
68C2×#1202—28no—
69C2×#1202—24no—
70C2×#1200—28no—
71C2×#1200—24no—
72#6773—216no—
73#6773—28no—
74#6773—28no—
75C3×C5×C4⋊C4—21no—
76C3×C5×C4⋊C4C2312yes—
77C2×C3⋊#168—22no—
78C2×C3⋊#168C2312yes—
79C2×C5×C3⋊C8—22no—
80C2×C5×C3⋊C8C2312yes—
81C3×#685—24no—
82#6655—28no—
83#6653—28no—
84C22×#235—51no—
85C2×C3×#121—51no—
86C22×#214—51no—
87C22×#213—51no—
88C2×#830—51no—
89#5037—58no—
90C2×#810D511yescharacteristic, complemented
91C2×#809—51no—
92C22×C5×Q8—31no—
93C2×#713—34no—
94C2×#713—64no—
95C2×#713—64no—
96C2×#713—62no—
97C22×D20—21no—
98C22×D20—31no—
99C22×D20—61no—
100C22×D20C2×D311yescharacteristic
101C22×C4×D5—61no—
102C22×C4×D5C2×D311yescharacteristic
103C22×C5×C8—31no—
104C2×C5×C4⋊C4C2×D311yescharacteristic
105C2×#688—34no—
106C2×#688—64no—
107C2×#685—21no—
108C22×#168—31no—
109C2×D40—34no—
110C2×D40—64no—
111#4041—22no—
112#4041C2×D314yescomplemented
113C5×#103—34no—
114#3952—34no—
115#3941—34no—
116C2×#449—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×D15—24no—
119C22×D15—22no—
120C22×D15—42no—
121C22×D15—42no—
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5—22no—
125C22×C3×D5—22no—
126C22×C3×D5—42no—
127C22×C3×D5—42no—
128C22×C3×D5—42no—
129C22×C3×D5C2×D412yes—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—42no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D412yes—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2411yescharacteristic
136D60—24no—
137D60—22no—
138D60C2×D414yescomplemented
139C2×C5×Dic3—24no—
140C2×C5×Dic3—22no—
141C5×Dic6—24no—
142C5×Dic6—22no—
143C5×Dic6C2×D414yescomplemented
144C2×C3×Dic5—22no—
145C2×C3×Dic5C2×D412yes—
146C3×D20—22no—
147C3×D20—22no—
148C3×D20—48no—
149C3×D20—42no—
150C3×C4×D5—24no—
151C3×C4×D5—22no—
152C3×C4×D5—22no—
153#1202—216no—
154#1200—216no—
155C3⋊#168—22no—
156C5×C3⋊C8—22no—
157C22×C3×D4—51no—
158C22×C3×D4—101no—
159C23×C3×C4—51no—
160C22×#67—101no—
161C2×#235—54no—
162C2×#235—104no—
163C2×#235—102no—
164C2×#235—104no—
165C22×D12—51no—
166C22×C4×D3—101no—
167C22×Dic6C2×D511yescharacteristic
168C3×#121—54no—
169C3×#121—102no—
170C2×C3×C4⋊C4C2×D511yescharacteristic
171C2×C3×C22⋊C4—101no—
172C2×#214—54no—
173C2×#214—104no—
174C2×#213—54no—
175C2×#213—104no—
176C22×C3⋊C8—51no—
177C22×C3⋊C8C2×D511yescharacteristic
178#830—54no—
179#810C2×D514yescomplemented
180#809—54no—
181C23×D5—21no—
182C23×D5—61no—
183C23×D5#6711yescharacteristic
184C2×C5×Q8—34no—
185C2×C5×Q8—32no—
186C2×C5×Q8—62no—
187C2×C5×Q8—61no—
188C22×C4×C5—21no—
189C22×C4×C5—61no—
190C22×C4×C5C22×D311yescharacteristic
191C22×Dic5#6711yescharacteristic
192#713—68no—
193#713—68no—
194#713—616no—
195C2×D20—22no—
196C2×D20—22no—
197C2×D20—24no—
198C2×D20—21no—
199C2×D20—34no—
200C2×D20—32no—
201C2×D20—44no—
202C2×D20—68no—
203C2×D20—64no—
204C2×D20—62no—
205C2×D20—61no—
206C2×D20C22×D312yes—
207C2×C4×D5—22no—
208C2×C4×D5—22no—
209C2×C4×D5—68no—
210C2×C4×D5—64no—
211C2×C4×D5#6712yes—
212C2×C4×D5C22×D312yes—
213C2×C5×C8—32no—
214C2×C5×C8—62no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4C22×D312yes—
217#688—68no—
218#685—24no—
219C2×#168—32no—
220C2×#168—62no—
221D40—68no—
222C22×#41—151no—
223C22×SD16—151no—
224C22×D8—151no—
225C2×#121—51no—
226#449—158no—
227C2×#103—31no—
228C2×#102—151no—
229C2×C22⋊C8—151no—
230C22×C3×C5#12012yes—
231C22×C3×C5#13512yes—
232C22×C3×C5AGL(1,ℤ/8)12yes—
233C22×C3×C5C22×D411yescharacteristic
234C2×D15—24no—
235C2×D15—42no—
236C2×D15—42no—
237C2×D15—48no—
238C2×C3×D5—22no—
239C2×C3×D5—22no—
240C2×C3×D5—22no—
241C2×C3×D5—44no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—42no—
245C2×C3×D5—84no—
246C3×C4×C5—42no—
247C3×C4×C5#12012yes—
248C3×C4×C5C22×D411yescharacteristic
249C3×C4×C5C22×D411yescharacteristic
250C3×Dic5—22no—
251C5×Dic3—24no—
252C24×C3—51no—
253C24×C3—101no—
254C23×D3—101no—
255C2×C3×D4—52no—
256C2×C3×D4—104no—
257C2×C3×D4—102no—
258C2×C3×D4—102no—
259C2×C3×D4—101no—
260C2×C3×D4—204no—
261C22×C3×C4—21no—
262C22×C3×C4—51no—
263C22×C3×C4—52no—
264C22×C3×C4—52no—
265C22×C3×C4—102no—
266C22×C3×C4—102no—
267C22×C3×C4C22×D511yescharacteristic
268C2×#67—104no—
269C2×#67—108no—
270C22×Dic3—21no—
271#235—108no—
272#235—1016no—
273#235—108no—
274C2×D12—54no—
275C2×D12—52no—
276C2×D12—102no—
277C2×D12—101no—
278C2×C4×D3—104no—
279C2×C4×D3—108no—
280C2×Dic6—22no—
281C2×Dic6—21no—
282C2×Dic6D2014yescomplemented
283C2×Dic6C22×D512yes—
284C3×C4⋊C4—21no—
285C3×C4⋊C4C22×D512yes—
286C3×C22⋊C4—104no—
287#214—108no—
288#213—108no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8—52no—
291C2×C3⋊C8—102no—
292C2×C3⋊C8C22×D512yes—
293C23×C5C2×#6711yescharacteristic
294C22×D5—22no—
295C22×D5—22no—
296C22×D5—22no—
297C22×D5—22no—
298C22×D5—42no—
299C22×D5—42no—
300C22×D5—42no—
301C22×D5—64no—
302C22×D5—62no—
303C22×D5—122no—
304C22×D5—122no—
305C22×D5C2×#6712yes—
306C5×Q8—34no—
307C5×Q8—64no—
308C5×Q8—62no—
309C2×C4×C5—22no—
310C2×C4×C5—42no—
311C2×C4×C5—64no—
312C2×C4×C5—62no—
313C2×C4×C5D3×D412yes—
314C2×C4×C5D3×D412yes—
315C2×C4×C5C2×#6711yescharacteristic
316C2×C4×C5C23×D311yescharacteristic
317C2×Dic5—22no—
318C2×Dic5C2×#6712yes—
319D20—22no—
320D20—22no—
321D20—34no—
322D20—48no—
323D20—42no—
324D20—616no—
325D20—64no—
326D20—62no—
327C4×D5—24no—
328C4×D5—22no—
329C4×D5—22no—
330C4×D5—616no—
331C5×C8—62no—
332#168—62no—
333C2×#41—154no—
334C2×#41—302no—
335C2×#41—304no—
336C2×#41—304no—
337C22×Q8—31no—
338C22×D4—51no—
339C22×D4—101no—
340C22×D4—151no—
341C22×D4—301no—
342C23×C4—51no—
343C23×C4—301no—
344C2×SD16—154no—
345C2×SD16—304no—
346C2×D8—154no—
347C2×D8—304no—
348C22×C8—31no—
349C22×C8—151no—
350#121—54no—
351#121—102no—
352C2×C4⋊C4D3×D511yescharacteristic
353C2×C22⋊C4—101no—
354#103—34no—
355#102—154no—
356C22⋊C8—154no—
357C2×C3×C5#44914yescomplemented
358C2×C3×C5C2×#12011yescharacteristic
359C2×C3×C5C2×#13511yescharacteristic
360C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
361D15—44no—
362C3×D5—42no—
363C3×D5—82no—
364C23×C3—52no—
365C23×C3—102no—
366C23×C3—102no—
367C23×C3—102no—
368C23×C3—102no—
369C23×C3—202no—
370C23×C3—202no—
371C23×C3—202no—
372C23×C3D4×D511yescharacteristic
373C22×D3—102no—
374C22×D3—104no—
375C22×D3—202no—
376C22×D3—202no—
377C3×D4—102no—
378C3×D4—102no—
379C3×D4—208no—
380C3×D4—202no—
381C2×C3×C4—22no—
382C2×C3×C4—42no—
383C2×C3×C4—52no—
384C2×C3×C4—102no—
385C2×C3×C4—102no—
386C2×C3×C4—102no—
387C2×C3×C4—104no—
388C2×C3×C4C2×D2012yes—
389C2×C3×C4D4×D512yes—
390C2×C3×C4D4×D511yescharacteristic
391C2×C3×C4C23×D511yescharacteristic
392#67—1016no—
393C2×Dic3—22no—
394C2×Dic3—24no—
395D12—54no—
396D12—102no—
397D12—104no—
398C4×D3—1016no—
399Dic6—22no—
400Dic6—24no—
401Dic6C2×D2014yescomplemented
402C3⋊C8—22no—
403C3⋊C8—102no—
404C22×C5#93212yes—
405C22×C5#93712yes—
406C22×C5#95012yes—
407C22×C5C22×#6711yescharacteristic
408C2×D5—22no—
409C2×D5—22no—
410C2×D5—22no—
411C2×D5—44no—
412C2×D5—42no—
413C2×D5—42no—
414C2×D5—42no—
415C2×D5—64no—
416C2×D5—84no—
417C2×D5—122no—
418C2×D5—128no—
419C2×D5—122no—
420C4×C5—42no—
421C4×C5—64no—
422C4×C5#93712yes—
423C4×C5C2×D3×D411yescharacteristic
424C4×C5C2×D3×D411yescharacteristic
425Dic5—22no—
426C24—51no—
427C24—101no—
428C24—301no—
429#41—308no—
430#41—308no—
431#41—3016no—
432C2×Q8—34no—
433C2×Q8—32no—
434C2×Q8—62no—
435C2×Q8—61no—
436C2×D4—52no—
437C2×D4—104no—
438C2×D4—102no—
439C2×D4—102no—
440C2×D4—101no—
441C2×D4—154no—
442C2×D4—152no—
443C2×D4—204no—
444C2×D4—304no—
445C2×D4—308no—
446C2×D4—302no—
447C2×D4—301no—
448C22×C4—21no—
449C22×C4—51no—
450C22×C4—52no—
451C22×C4—52no—
452C22×C4—61no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—304no—
456C22×C4—308no—
457C22×C4C2×D3×D511yescharacteristic
458SD16—308no—
459D8—308no—
460C2×C8—32no—
461C2×C8—62no—
462C2×C8—152no—
463C2×C8—302no—
464C4⋊C4—21no—
465C4⋊C4C2×D3×D512yes—
466C22⋊C4—104no—
467C3×C5C2×#44911yescharacteristic, complemented, Hall
468C22×C3—102no—
469C22×C3—102no—
470C22×C3—102no—
471C22×C3—204no—
472C22×C3—202no—
473C22×C3—202no—
474C22×C3—202no—
475C22×C3—404no—
476C22×C3#402812yes—
477C22×C3#406012yes—
478C22×C3#406512yes—
479C22×C3C2×D4×D511yescharacteristic
480C2×D3—104no—
481C2×D3—202no—
482C2×D3—202no—
483C2×D3—208no—
484C3×C4—42no—
485C3×C4—102no—
486C3×C4#402812yes—
487C3×C4C22×D2011yescharacteristic
488C3×C4C2×D4×D511yescharacteristic
489Dic3—24no—
490C2×C5#503714yescomplemented
491C2×C5C2×#93211yescharacteristic
492C2×C5C2×#93711yescharacteristic
493C2×C5C2×#95011yescharacteristic
494D5—42no—
495D5—82no—
496D5—124no—
497C23—52no—
498C23—102no—
499C23—102no—
500C23—102no—
501C23—102no—
502C23—202no—
503C23—202no—
504C23—202no—
505C23—304no—
506C23—302no—
507C23—602no—
508C23—602no—
509C23D5×#6711yescharacteristic
510Q8—34no—
511Q8—64no—
512Q8—62no—
513D4—102no—
514D4—102no—
515D4—154no—
516D4—208no—
517D4—202no—
518D4—3016no—
519D4—304no—
520D4—302no—
521C2×C4—22no—
522C2×C4—42no—
523C2×C4—52no—
524C2×C4—64no—
525C2×C4—62no—
526C2×C4—102no—
527C2×C4—104no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—3016no—
531C2×C4D3×D2012yes—
532C2×C4#677712yes—
533C2×C4D5×#6711yescharacteristic
534C2×C4C22×D3×D511yescharacteristic
535C8—62no—
536C8—302no—
537C2×C3—202no—
538C2×C3—402no—
539C2×C3#6510014yescomplemented
540C2×C3C2×#402811yescharacteristic
541C2×C3C2×#406011yescharacteristic
542C2×C3C2×#406511yescharacteristic
543D3—204no—
544C5C2×#503711yescharacteristic, complemented, Sylow
545C22—102no—
546C22—102no—
547C22—102no—
548C22—204no—
549C22—202no—
550C22—202no—
551C22—202no—
552C22—304no—
553C22—404no—
554C22—602no—
555C22—608no—
556C22—602no—
557C22#9147412yes—
558C22#9149112yes—
559C22#9151612yes—
560C22C2×D5×#6711yescharacteristic
561C4—42no—
562C4—64no—
563C4—102no—
564C4#9147412yes—
565C4C2×D3×D2011yescharacteristic
566C4C2×#677711yescharacteristic
567C3C2×#6510011yescharacteristic, complemented, Sylow
568C2—202no—
569C2—402no—
570C2—604no—
571C2#1174751214yesdirect product factor
572C2C2×#9147411yescharacteristic
573C2C2×#9149111yescharacteristic
574C2C2×#9151611yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#449
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6773C2semidirect
2. C2×C3×#4041C2semidirect
3. C22×#6655C2semidirect
4. C22×#6653C2semidirect
5. C2×#91093C2semidirect
6. C2×C5×#810C2semidirect
7. C2×#90955C2semidirect
8. #11747512C2direct (N × H)
20. C2×#6773C22semidirect
26. C3×#4041C22semidirect
28. C2×#6655C22semidirect
30. C2×#6653C22semidirect
31. #91093C22semidirect
32. C5×#810C22semidirect
33. #90955C22semidirect
38. C2×#4041D3semidirect
50. C2×D60D4semidirect
55. C2×C5×Dic6D4semidirect
90. C2×#810D5semidirect
112. #4041C2×D3semidirect
138. D60C2×D4semidirect
143. C5×Dic6C2×D4semidirect
179. #810C2×D5semidirect
282. C2×Dic6D20semidirect
357. C2×C3×C5#449semidirect
401. Dic6C2×D20semidirect
467. C3×C5C2×#449semidirect
490. C2×C5#5037semidirect
539. C2×C3#65100semidirect
544. C5C2×#5037semidirect
567. C3C2×#65100semidirect
571. C2#11747512direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67732
C2×C3×#40412
C22×#66552
C22×#66532
C2×#910932
C2×C5×#8102
C2×#909552
#117475122
C2×#651003
C2×#50375