Finite Group Databasebeta

← C2×#11747518 #14423467

Subgroups — C2×#11747518 #14423467

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×#6766C211yesmaximal, characteristic, complemented
2C2×#91784C211yesmaximal, characteristic, complemented
3C22×#6660C211yesmaximal, characteristic, complemented
4C22×#6653C211yesmaximal, characteristic, complemented
5C2×C5×#810C211yesmaximal, characteristic, complemented
6C2×C3×#3941C211yesmaximal, characteristic, complemented
7C2×#90957C211yesmaximal, characteristic, complemented
8#11747518C218yesmaximal, direct product factor
9C2×#65100—31nomaximal, Hall
10C22×D60—21no—
11C22×D60C2211yescharacteristic
12C22×C4×D15C2211yescharacteristic
13C22×C5×Dic6C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×#1202—21no—
16C22×D5×Dic3—21no—
17C2×#6766—22no—
18C2×#6766—24no—
19C2×#6766—24no—
20C2×#6766C2214yescomplemented
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×#6714—21no—
23#91784—22no—
24#91784C2214yescomplemented
25C22×C5×C3⋊C8C2211yescharacteristic
26C22×C3×#168C2211yescharacteristic
27C2×#6660—24no—
28C2×#6660C2214yescomplemented
29C2×#6653—24no—
30C2×#6653C2214yescomplemented
31C5×#810C2214yescomplemented
32C3×#3941C2214yescomplemented
33#90957C2214yescomplemented
34C2×#4781—51nomaximal, Hall
35C22×#713—31no—
36C22×#688—31no—
37C22×D40—31no—
38C2×#4041—31no—
39C2×C5×#103—31no—
40C2×#3952—31no—
41C2×#3941D311yescharacteristic, complemented
42#65100—38no—
43C23×D15—21no—
44C23×D15D411yescharacteristic
45C23×C3×D5—21no—
46C22×C3×C4×C5—21no—
47C22×C3×C4×C5C2311yescharacteristic
48C22×Dic15D411yescharacteristic
49C2×D60—22no—
50C2×D60—22no—
51C2×D60—24no—
52C2×D60—21no—
53C2×D60—44no—
54C2×D60C2312yes—
55C2×C4×D15—22no—
56C2×C4×D15—22no—
57C2×C4×D15D412yes—
58C2×C4×D15C2312yes—
59C22×C5×Dic3—21no—
60C2×C5×Dic6—21no—
61C2×C5×Dic6—22no—
62C2×C5×Dic6D414yescomplemented
63C2×C5×Dic6C2312yes—
64C2×C3×D20—21no—
65C2×C3×D20—22no—
66C2×C3×D20D414yescomplemented
67C2×C3×D20C2312yes—
68C2×#1202—28no—
69C2×#1202—24no—
70C2×D5×Dic3—28no—
71C2×D5×Dic3—24no—
72#6766—216no—
73#6766—28no—
74#6766—28no—
75C3×C5×C4⋊C4—21no—
76C3×C5×C4⋊C4C2312yes—
77#6714—24no—
78C2×C5×C3⋊C8—22no—
79C2×C5×C3⋊C8C2312yes—
80C2×C3×#168—22no—
81C2×C3×#168C2312yes—
82#6660—28no—
83#6653—28no—
84C22×#237—51no—
85C22×#213—51no—
86C22×#204—51no—
87C2×#895—51no—
88C2×C3×#102—51no—
89C2×(C2×D3)⋊C8—51no—
90C2×#810D511yescharacteristic, complemented
91#4781—58no—
92C22×C5×Q8—31no—
93C2×#713—34no—
94C2×#713—62no—
95C2×#713—64no—
96C2×#713—64no—
97C22×D20—31no—
98C22×D20—61no—
99C22×D20—61no—
100C22×D20C2×D311yescharacteristic
101C22×C4×D5—31no—
102C22×C4×D5—61no—
103C22×C5×C8—31no—
104C2×C5×C4⋊C4C2×D311yescharacteristic
105C2×#688—34no—
106C2×#688—64no—
107C2×#685—61no—
108C22×#168C2×D311yescharacteristic
109C2×D40—34no—
110C2×D40—64no—
111#4041—34no—
112#4041—62no—
113C5×#103—34no—
114#3952—34no—
115#3941C2×D314yescomplemented
116C2×#449—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×D15—22no—
119C22×D15—22no—
120C22×D15—22no—
121C22×D15—22no—
122C22×D15—42no—
123C22×D15—42no—
124C22×D15—42no—
125C22×D15C2×D412yes—
126C22×C3×D5—24no—
127C22×C3×D5—22no—
128C22×C3×D5—42no—
129C22×C3×D5—42no—
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
136C2×Dic15—22no—
137C2×Dic15C2×D412yes—
138D60—22no—
139D60—22no—
140D60—48no—
141D60—42no—
142C4×D15—24no—
143C4×D15—22no—
144C4×D15—22no—
145C2×C5×Dic3—24no—
146C2×C5×Dic3—22no—
147C5×Dic6—24no—
148C5×Dic6—22no—
149C5×Dic6C2×D414yescomplemented
150C3×D20—24no—
151C3×D20—22no—
152C3×D20C2×D414yescomplemented
153#1202—216no—
154D5×Dic3—216no—
155C3×#168—22no—
156C5×C3⋊C8—22no—
157C22×C3×D4—51no—
158C22×#67—101no—
159C23×Dic3—101no—
160C2×#237—54no—
161C2×#237—102no—
162C2×#237—104no—
163C2×#237—104no—
164C22×D12—51no—
165C22×D12—101no—
166C22×C4×D3—51no—
167C22×Dic6C2×D511yescharacteristic
168C22×C3×C8—51no—
169C2×C3×C4⋊C4C2×D511yescharacteristic
170C2×#213—54no—
171C2×#213—104no—
172C2×(C2×D3)⋊C4—101no—
173C22×C3⋊C8C2×D511yescharacteristic
174C2×#204—54no—
175C2×#204—104no—
176#895—54no—
177#895—102no—
178C3×#102—54no—
179(C2×D3)⋊C8—54no—
180#810C2×D514yescomplemented
181C23×D5—21no—
182C23×D5—31no—
183C23×D5—61no—
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—31no—
192#713—68no—
193#713—616no—
194#713—68no—
195C2×D20—22no—
196C2×D20—21no—
197C2×D20—32no—
198C2×D20—64no—
199C2×D20—68no—
200C2×D20—62no—
201C2×D20—62no—
202C2×D20—64no—
203C2×D20—61no—
204C2×D20—124no—
205C2×D20D1214yescomplemented
206C2×D20C22×D312yes—
207C2×C4×D5—32no—
208C2×C4×D5—32no—
209C2×C4×D5—64no—
210C2×C4×D5—68no—
211C2×C4×D5—62no—
212C2×C4×D5—62no—
213C2×C5×C8—32no—
214C2×C5×C8—62no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4C22×D312yes—
217#688—68no—
218#685—64no—
219C2×#168—22no—
220C2×#168C22×D312yes—
221D40—68no—
222C22×#41—151no—
223C22×SD16—151no—
224C22×D8—151no—
225C2×#121—151no—
226#449—158no—
227C2×#103—31no—
228C2×#102—51no—
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—22no—
235C2×D15—22no—
236C2×D15—22no—
237C2×D15—44no—
238C2×D15—42no—
239C2×D15—42no—
240C2×D15—42no—
241C2×D15—84no—
242C2×C3×D5—24no—
243C2×C3×D5—42no—
244C2×C3×D5—42no—
245C2×C3×D5—48no—
246C3×C4×C5—42no—
247C3×C4×C5#12012yes—
248C3×C4×C5C22×D411yescharacteristic
249C3×C4×C5C22×D411yescharacteristic
250Dic15—22no—
251C5×Dic3—24no—
252C24×C3—101no—
253C23×D3—51no—
254C23×D3—101no—
255C2×C3×D4—54no—
256C2×C3×D4—52no—
257C2×C3×D4—102no—
258C2×C3×D4—101no—
259C22×C3×C4—21no—
260C22×C3×C4C22×D511yescharacteristic
261C2×#67—104no—
262C2×#67—108no—
263C22×Dic3—21no—
264C22×Dic3—51no—
265C22×Dic3—104no—
266C22×Dic3—108no—
267#237—108no—
268#237—1016no—
269#237—108no—
270C2×D12—52no—
271C2×D12—102no—
272C2×D12—102no—
273C2×D12—104no—
274C2×D12—101no—
275C2×D12—204no—
276C2×C4×D3—52no—
277C2×C4×D3—52no—
278C2×C4×D3—102no—
279C2×C4×D3—102no—
280C2×Dic6—22no—
281C2×Dic6—21no—
282C2×Dic6D2014yescomplemented
283C2×Dic6C22×D512yes—
284C2×C3×C8—52no—
285C2×C3×C8—102no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4C22×D512yes—
288#213—108no—
289(C2×D3)⋊C4—104no—
290C2×C3⋊C8—22no—
291C2×C3⋊C8C22×D512yes—
292#204—108no—
293C23×C5D3×D411yescharacteristic
294C22×D5—24no—
295C22×D5—22no—
296C22×D5—32no—
297C22×D5—42no—
298C22×D5—42no—
299C22×D5—62no—
300C22×D5—62no—
301C22×D5—62no—
302C22×D5—62no—
303C22×D5—122no—
304C22×D5—122no—
305C22×D5—122no—
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×C5C2×D1212yes—
314C2×C4×C5D3×D412yes—
315C2×C4×C5D3×D411yescharacteristic
316C2×C4×C5C23×D311yescharacteristic
317C2×Dic5—32no—
318C2×Dic5—62no—
319D20—24no—
320D20—22no—
321D20—616no—
322D20—62no—
323D20—62no—
324D20—128no—
325D20—122no—
326D20C2×D1214yescomplemented
327C4×D5—616no—
328C4×D5—64no—
329C4×D5—62no—
330C4×D5—62no—
331C5×C8—62no—
332#168—22no—
333C2×#41—154no—
334C2×#41—302no—
335C2×#41—304no—
336C2×#41—304no—
337C22×Q8—31no—
338C22×D4—51no—
339C22×D4—151no—
340C22×D4—301no—
341C22×D4—301no—
342C23×C4—151no—
343C23×C4—301no—
344C2×SD16—154no—
345C2×SD16—304no—
346C2×D8—154no—
347C2×D8—304no—
348C22×C8—31no—
349C22×C8—51no—
350#121—154no—
351#121—302no—
352C2×C4⋊C4D3×D511yescharacteristic
353C2×C22⋊C4—301no—
354#103—34no—
355#102—54no—
356C22⋊C8—154no—
357C2×C3×C5#44914yescomplemented
358C2×C3×C5C2×#12011yescharacteristic
359C2×C3×C5C2×#13511yescharacteristic
360C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
361D15—42no—
362D15—82no—
363C3×D5—44no—
364C23×C3—102no—
365C23×C3—104no—
366C23×C3—202no—
367C23×C3—202no—
368C23×C3D4×D511yescharacteristic
369C22×D3—52no—
370C22×D3—102no—
371C22×D3—102no—
372C22×D3—102no—
373C22×D3—102no—
374C22×D3—202no—
375C22×D3—202no—
376C22×D3—202no—
377C3×D4—54no—
378C3×D4—102no—
379C3×D4—104no—
380C2×C3×C4—22no—
381C2×C3×C4—42no—
382C2×C3×C4C2×D2012yes—
383C2×C3×C4D4×D512yes—
384C2×C3×C4D4×D511yescharacteristic
385C2×C3×C4C23×D511yescharacteristic
386#67—1016no—
387C2×Dic3—22no—
388C2×Dic3—24no—
389C2×Dic3—52no—
390C2×Dic3—1016no—
391C2×Dic3—102no—
392D12—102no—
393D12—102no—
394D12—208no—
395D12—202no—
396C4×D3—102no—
397C4×D3—102no—
398C4×D3—104no—
399Dic6—22no—
400Dic6—24no—
401Dic6C2×D2014yescomplemented
402C3×C8—102no—
403C3⋊C8—22no—
404C22×C5#88212yes—
405C22×C5#91112yes—
406C22×C5#91612yes—
407C22×C5C2×D3×D411yescharacteristic
408C2×D5—24no—
409C2×D5—42no—
410C2×D5—42no—
411C2×D5—48no—
412C2×D5—62no—
413C2×D5—62no—
414C2×D5—62no—
415C2×D5—124no—
416C2×D5—122no—
417C2×D5—122no—
418C2×D5—122no—
419C2×D5—244no—
420C4×C5—42no—
421C4×C5—64no—
422C4×C5#88212yes—
423C4×C5C22×D1211yescharacteristic
424C4×C5C2×D3×D411yescharacteristic
425Dic5—62no—
426C24—101no—
427C24—151no—
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—54no—
437C2×D4—52no—
438C2×D4—102no—
439C2×D4—101no—
440C2×D4—152no—
441C2×D4—304no—
442C2×D4—304no—
443C2×D4—308no—
444C2×D4—302no—
445C2×D4—302no—
446C2×D4—301no—
447C2×D4—604no—
448C22×C4—21no—
449C22×C4—61no—
450C22×C4—151no—
451C22×C4—152no—
452C22×C4—152no—
453C22×C4—304no—
454C22×C4—308no—
455C22×C4—302no—
456C22×C4—302no—
457C22×C4C2×D3×D511yescharacteristic
458SD16—308no—
459D8—308no—
460C2×C8—32no—
461C2×C8—52no—
462C2×C8—62no—
463C2×C8—102no—
464C4⋊C4—21no—
465C4⋊C4C2×D3×D512yes—
466C22⋊C4—304no—
467C3×C5C2×#44911yescharacteristic, complemented, Hall
468C22×C3—104no—
469C22×C3—202no—
470C22×C3—202no—
471C22×C3—208no—
472C22×C3#402812yes—
473C22×C3#406012yes—
474C22×C3#406512yes—
475C22×C3C2×D4×D511yescharacteristic
476C2×D3—102no—
477C2×D3—102no—
478C2×D3—102no—
479C2×D3—204no—
480C2×D3—202no—
481C2×D3—202no—
482C2×D3—202no—
483C2×D3—404no—
484C3×C4—42no—
485C3×C4#402812yes—
486C3×C4C22×D2011yescharacteristic
487C3×C4C2×D4×D511yescharacteristic
488Dic3—24no—
489Dic3—102no—
490C2×C5#478114yescomplemented
491C2×C5C2×#88211yescharacteristic
492C2×C5C2×#91111yescharacteristic
493C2×C5C2×#91611yescharacteristic
494D5—44no—
495D5—122no—
496D5—242no—
497C23—104no—
498C23—102no—
499C23—152no—
500C23—202no—
501C23—202no—
502C23—302no—
503C23—302no—
504C23—302no—
505C23—302no—
506C23—602no—
507C23—602no—
508C23—602no—
509C23#679011yescharacteristic
510Q8—34no—
511Q8—64no—
512Q8—62no—
513D4—54no—
514D4—104no—
515D4—102no—
516D4—3016no—
517D4—302no—
518D4—302no—
519D4—608no—
520D4—602no—
521C2×C4—22no—
522C2×C4—42no—
523C2×C4—64no—
524C2×C4—62no—
525C2×C4—152no—
526C2×C4—3016no—
527C2×C4—302no—
528C2×C4—304no—
529C2×C4—302no—
530C2×C4—302no—
531C2×C4D5×D1212yes—
532C2×C4D3×D2012yes—
533C2×C4#679011yescharacteristic
534C2×C4C22×D3×D511yescharacteristic
535C8—62no—
536C8—102no—
537C2×C3—204no—
538C2×C3#6510014yescomplemented
539C2×C3C2×#402811yescharacteristic
540C2×C3C2×#406011yescharacteristic
541C2×C3C2×#406511yescharacteristic
542D3—202no—
543D3—402no—
544C5C2×#478111yescharacteristic, complemented, Sylow
545C22—104no—
546C22—202no—
547C22—208no—
548C22—202no—
549C22—302no—
550C22—302no—
551C22—302no—
552C22—604no—
553C22—602no—
554C22—602no—
555C22—602no—
556C22—1204no—
557C22#9147612yes—
558C22#9149812yes—
559C22#9152112yes—
560C22C2×#679011yescharacteristic
561C4—42no—
562C4—64no—
563C4—302no—
564C4#9147612yes—
565C4C2×D5×D1211yescharacteristic
566C4C2×D3×D2011yescharacteristic
567C3C2×#6510011yescharacteristic, complemented, Sylow
568C2—204no—
569C2—602no—
570C2—1202no—
571C2#1174751814yesdirect product factor
572C2C2×#9147611yescharacteristic
573C2C2×#9149811yescharacteristic
574C2C2×#9152111yescharacteristic
subgroupG/H
centerC23#6790
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×#6766C2semidirect
2. C2×#91784C2semidirect
3. C22×#6660C2semidirect
4. C22×#6653C2semidirect
5. C2×C5×#810C2semidirect
6. C2×C3×#3941C2semidirect
7. C2×#90957C2semidirect
8. #11747518C2direct (N × H)
20. C2×#6766C22semidirect
24. #91784C22semidirect
28. C2×#6660C22semidirect
30. C2×#6653C22semidirect
31. C5×#810C22semidirect
32. C3×#3941C22semidirect
33. #90957C22semidirect
41. C2×#3941D3semidirect
62. C2×C5×Dic6D4semidirect
66. C2×C3×D20D4semidirect
90. C2×#810D5semidirect
115. #3941C2×D3semidirect
149. C5×Dic6C2×D4semidirect
152. C3×D20C2×D4semidirect
180. #810C2×D5semidirect
205. C2×D20D12semidirect
282. C2×Dic6D20semidirect
326. D20C2×D12semidirect
357. C2×C3×C5#449semidirect
401. Dic6C2×D20semidirect
467. C3×C5C2×#449semidirect
490. C2×C5#4781semidirect
538. C2×C3#65100semidirect
544. C5C2×#4781semidirect
567. C3C2×#65100semidirect
571. C2#11747518direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67662
C2×#917842
C22×#66602
C22×#66532
C2×C5×#8102
C2×C3×#39412
C2×#909572
#117475182
C2×#651003
C2×#47815