Finite Group Databasebeta

← C2×#11749289 #14423470

Subgroups — C2×#11749289 #14423470

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×#6821C211yesmaximal, characteristic, complemented
2C22×C5×#215C211yesmaximal, characteristic, complemented
3C2×#91466C211yesmaximal, characteristic, complemented
4C22×#6654C211yesmaximal, characteristic, complemented
5C2×C3×#3967C211yesmaximal, characteristic, complemented
6#11749289C218yesmaximal, direct product factor
7C2×#90968C211yesmaximal, characteristic, complemented
8C2×#90957C211yesmaximal, characteristic, complemented
9C2×#65461—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×#6821—24no—
12C2×#6821—24no—
13C2×#6821—22no—
14C2×#6821C2214yescomplemented
15C22×D60—21no—
16C22×D60C2211yescharacteristic
17C22×C4×D15—21no—
18C22×C4×D15C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C22×#1203—21no—
21C2×C5×#215—24no—
22C2×C5×#215C2214yescomplemented
23C22×C5×C3⋊C8C2211yescharacteristic
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C22×C3×#168C2211yescharacteristic
26C2×(C2×D3)⋊Dic5—21no—
27#91466—22no—
28#91466C2214yescomplemented
29C2×#6654—24no—
30C2×#6654C2214yescomplemented
31C3×#3967C2214yescomplemented
32#90968C2214yescomplemented
33#90957C2214yescomplemented
34C2×#4810—51nomaximal, Hall
35C22×#713—31no—
36C22×C5×SD16—31no—
37C2×#4084—31no—
38C22×#686—31no—
39C2×#3967D311yescharacteristic, complemented
40#65461—38no—
41C2×#3953—31no—
42C2×#3952—31no—
43C23×D15—21no—
44C23×D15D411yescharacteristic
45C23×C5×D3—21no—
46C2×C3×C5×Q8—22no—
47C2×C3×C5×Q8—21no—
48C2×C3×C5×Q8D414yescomplemented
49C2×C3×C5×Q8C2312yes—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5C2311yescharacteristic
52C22×Dic15D411yescharacteristic
53#6821—216no—
54#6821—28no—
55#6821—28no—
56C2×D60—28no—
57C2×D60—24no—
58C2×D60—21no—
59C2×D60—22no—
60C2×D60D414yescomplemented
61C2×D60C2312yes—
62C2×C4×D15—28no—
63C2×C4×D15—22no—
64C2×C4×D15—22no—
65C2×C4×D15—24no—
66C2×C4×D15D412yes—
67C2×C4×D15C2312yes—
68C2×C5×D12—22no—
69C2×C5×D12—22no—
70C2×C5×D12—21no—
71C2×C5×D12C2312yes—
72C22×C3×Dic5—21no—
73C2×#1203—24no—
74C2×#1203—44no—
75C5×#215—28no—
76C2×C5×C3⋊C8—22no—
77C2×C5×C3⋊C8C2312yes—
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5C2312yes—
80C2×C3×#168—22no—
81C2×C3×#168C2312yes—
82(C2×D3)⋊Dic5—24no—
83#6654—28no—
84C22×#239—51no—
85C22×#215D511yescharacteristic, complemented
86C22×D24—51no—
87C2×#895—51no—
88C2×C3×#103—51no—
89C2×(C2×D3)⋊C8—51no—
90C2×#809—51no—
91#4810—58no—
92C22×C5×Q8C2×D311yescharacteristic
93C22×C5×D4—31no—
94C22×C22⋊D5—61no—
95C2×#713—34no—
96C2×#713—62no—
97C2×#713—64no—
98C2×#713—64no—
99C22×D20—31no—
100C22×D20—61no—
101C22×C4×D5—31no—
102C22×C4×D5—61no—
103C2×C5×SD16—34no—
104C2×C5×SD16—64no—
105C22×C5×C8—31no—
106C2×C22⋊Dic5—61no—
107#4084—34no—
108#4084—62no—
109C2×#686—34no—
110C2×#686—64no—
111C2×C4⋊Dic5C2×D311yescharacteristic
112C22×#168C2×D311yescharacteristic
113#3967C2×D314yescomplemented
114#3953—34no—
115#3952—34no—
116C2×#449—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×D15—22no—
119C22×D15—24no—
120C22×D15—22no—
121C22×D15—22no—
122C22×D15—22no—
123C22×D15—42no—
124C22×D15—42no—
125C22×D15C2×D412yes—
126C22×C5×D3—22no—
127C22×C5×D3—42no—
128C22×C5×D3—42no—
129C22×C5×D3—42no—
130C3×C5×Q8—24no—
131C3×C5×Q8—22no—
132C3×C5×Q8C2×D414yescomplemented
133C2×C3×C4×C5—24no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2×D412yes—
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—22no—
140C2×Dic15C2×D412yes—
141D60—216no—
142D60—24no—
143D60—22no—
144D60C2×D414yescomplemented
145C4×D15—216no—
146C4×D15—24no—
147C4×D15—22no—
148C4×D15—22no—
149C5×D12—22no—
150C5×D12—22no—
151C5×D12—42no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—42no—
154#1203—48no—
155C3×#168—22no—
156C5×C3⋊C8—22no—
157C22×C3×Q8C2×D511yescharacteristic
158C2×#239—54no—
159C2×#239—102no—
160C2×#239—104no—
161C2×#239—104no—
162C22×D12—51no—
163C22×D12—101no—
164C22×D12—101no—
165C22×D12C2×D511yescharacteristic
166C22×C4×D3—51no—
167C22×C4×D3—101no—
168C22×C3×C8—51no—
169C2×C3×C4⋊C4—51no—
170C2×#215—24no—
171C2×#215C2×D514yescomplemented
172C2×(C2×D3)⋊C4—101no—
173C22×C3⋊C8C2×D511yescharacteristic
174C2×D24—54no—
175C2×D24—104no—
176#895—54no—
177#895—102no—
178C3×#103—54no—
179(C2×D3)⋊C8—54no—
180#809—54no—
181C24×C5—61no—
182C23×D5—31no—
183C23×D5—61no—
184C2×C5×Q8—22no—
185C2×C5×Q8—21no—
186C2×C5×Q8D1214yescomplemented
187C2×C5×Q8C22×D312yes—
188C2×C5×D4—32no—
189C2×C5×D4—62no—
190C2×C5×D4—62no—
191C2×C5×D4—61no—
192C22×C4×C5—21no—
193C22×C4×C5C22×D311yescharacteristic
194C2×C22⋊D5—64no—
195C2×C22⋊D5—124no—
196C22×Dic5—21no—
197C22×Dic5—31no—
198#713—68no—
199#713—616no—
200#713—68no—
201C2×D20—34no—
202C2×D20—32no—
203C2×D20—64no—
204C2×D20—68no—
205C2×D20—62no—
206C2×D20—61no—
207C2×C4×D5—32no—
208C2×C4×D5—32no—
209C2×C4×D5—64no—
210C2×C4×D5—68no—
211C2×C4×D5—62no—
212C2×C4×D5—62no—
213C5×SD16—68no—
214C2×C5×C8—32no—
215C2×C5×C8—62no—
216C22⋊Dic5—64no—
217#686—68no—
218C4⋊Dic5—21no—
219C4⋊Dic5C22×D312yes—
220C2×#168—22no—
221C2×#168C22×D312yes—
222C22×#41—151no—
223C22×SD16—31no—
224C22×D8—151no—
225C2×#121—151no—
226#449—158no—
227C2×#103—51no—
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—22no—
235C2×D15—24no—
236C2×D15—22no—
237C2×D15—22no—
238C2×D15—42no—
239C2×D15—42no—
240C2×D15—44no—
241C2×D15—48no—
242C2×C5×D3—42no—
243C2×C5×D3—42no—
244C2×C5×D3—42no—
245C2×C5×D3—84no—
246C3×C4×C5—24no—
247C3×C4×C5#12012yes—
248C3×C4×C5C22×D411yescharacteristic
249C3×C4×C5C22×D411yescharacteristic
250Dic15—22no—
251C3×Dic5—42no—
252C23×D3—21no—
253C23×D3—51no—
254C23×D3—101no—
255C2×C3×Q8—21no—
256C2×C3×Q8—22no—
257C2×C3×Q8C22⋊D514yescomplemented
258C2×C3×Q8C22×D512yes—
259C22×C3×C4—21no—
260C22×C3×C4—101no—
261C22×C3×C4C22×D511yescharacteristic
262C22×Dic3—51no—
263#239—108no—
264#239—1016no—
265#239—108no—
266C2×D12—22no—
267C2×D12—22no—
268C2×D12—21no—
269C2×D12—54no—
270C2×D12—52no—
271C2×D12—104no—
272C2×D12—108no—
273C2×D12—101no—
274C2×D12—102no—
275C2×D12—104no—
276C2×D12—204no—
277C2×D12C22×D512yes—
278C2×C4×D3—52no—
279C2×C4×D3—52no—
280C2×C4×D3—104no—
281C2×C4×D3—108no—
282C2×C4×D3—102no—
283C2×C4×D3—102no—
284C2×C3×C8—52no—
285C2×C3×C8—102no—
286C3×C4⋊C4—52no—
287C3×C4⋊C4—101no—
288#215—28no—
289(C2×D3)⋊C4—104no—
290C2×C3⋊C8—22no—
291C2×C3⋊C8C22×D512yes—
292D24—108no—
293C23×C5—62no—
294C23×C5—122no—
295C23×C5—122no—
296C23×C5—122no—
297C23×C5D3×D411yescharacteristic
298C22×D5—32no—
299C22×D5—64no—
300C22×D5—62no—
301C22×D5—62no—
302C22×D5—62no—
303C22×D5—62no—
304C22×D5—122no—
305C22×D5—122no—
306C5×Q8—24no—
307C5×Q8—22no—
308C5×Q8C2×D1214yescomplemented
309C5×D4—62no—
310C5×D4—62no—
311C5×D4—122no—
312C2×C4×C5—24no—
313C2×C4×C5—22no—
314C2×C4×C5C2×D1212yes—
315C2×C4×C5D3×D411yescharacteristic
316C2×C4×C5D3×D412yes—
317C2×C4×C5C23×D311yescharacteristic
318C22⋊D5—128no—
319C2×Dic5—22no—
320C2×Dic5—32no—
321C2×Dic5—42no—
322C2×Dic5—62no—
323D20—34no—
324D20—616no—
325D20—64no—
326D20—62no—
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×Q8D3×D511yescharacteristic
338C22×D4—31no—
339C22×D4—151no—
340C22×D4—301no—
341C22×D4—301no—
342C23×C4—151no—
343C23×C4—301no—
344C2×SD16—34no—
345C2×SD16—64no—
346C2×D8—154no—
347C2×D8—304no—
348C22×C8—31no—
349C22×C8—51no—
350#121—154no—
351#121—302no—
352C2×C4⋊C4—51no—
353C2×C22⋊C4—301no—
354#103—54no—
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—42no—
362D15—44no—
363C5×D3—82no—
364C23×C3D4×D511yescharacteristic
365C22×D3—22no—
366C22×D3—42no—
367C22×D3—42no—
368C22×D3—42no—
369C22×D3—52no—
370C22×D3—102no—
371C22×D3—102no—
372C22×D3—102no—
373C22×D3—104no—
374C22×D3—102no—
375C22×D3—202no—
376C22×D3—202no—
377C3×Q8—22no—
378C3×Q8—24no—
379C3×Q8C2×C22⋊D514yescomplemented
380C2×C3×C4—22no—
381C2×C3×C4—24no—
382C2×C3×C4—102no—
383C2×C3×C4—202no—
384C2×C3×C4D4×D512yes—
385C2×C3×C4D4×D511yescharacteristic
386C2×C3×C4C2×C22⋊D512yes—
387C2×C3×C4C23×D511yescharacteristic
388C2×Dic3—52no—
389C2×Dic3—102no—
390D12—22no—
391D12—22no—
392D12—42no—
393D12—54no—
394D12—1016no—
395D12—102no—
396D12—104no—
397D12—208no—
398C4×D3—1016no—
399C4×D3—102no—
400C4×D3—102no—
401C4×D3—104no—
402C3×C8—102no—
403C3⋊C8—22no—
404C22×C5—122no—
405C22×C5—122no—
406C22×C5—122no—
407C22×C5—244no—
408C22×C5#88212yes—
409C22×C5#91412yes—
410C22×C5#91912yes—
411C22×C5C2×D3×D411yescharacteristic
412C2×D5—64no—
413C2×D5—62no—
414C2×D5—62no—
415C2×D5—62no—
416C2×D5—122no—
417C2×D5—122no—
418C2×D5—124no—
419C2×D5—128no—
420C4×C5—24no—
421C4×C5#88212yes—
422C4×C5C22×D1211yescharacteristic
423C4×C5C2×D3×D411yescharacteristic
424Dic5—42no—
425Dic5—62no—
426C24—61no—
427C24—151no—
428C24—301no—
429#41—308no—
430#41—3016no—
431#41—308no—
432C2×Q8—21no—
433C2×Q8—22no—
434C2×Q8#120314yescomplemented
435C2×Q8C2×D3×D512yes—
436C2×D4—32no—
437C2×D4—62no—
438C2×D4—62no—
439C2×D4—61no—
440C2×D4—154no—
441C2×D4—152no—
442C2×D4—304no—
443C2×D4—308no—
444C2×D4—304no—
445C2×D4—302no—
446C2×D4—301no—
447C2×D4—604no—
448C22×C4—21no—
449C22×C4—101no—
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—68no—
459D8—308no—
460C2×C8—32no—
461C2×C8—52no—
462C2×C8—62no—
463C2×C8—102no—
464C4⋊C4—52no—
465C4⋊C4—101no—
466C22⋊C4—304no—
467C3×C5C2×#44911yescharacteristic, complemented, Hall
468C22×C3#406012yes—
469C22×C3#406212yes—
470C22×C3#408312yes—
471C22×C3C2×D4×D511yescharacteristic
472C2×D3—42no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3—84no—
476C2×D3—102no—
477C2×D3—102no—
478C2×D3—104no—
479C2×D3—102no—
480C2×D3—202no—
481C2×D3—202no—
482C2×D3—204no—
483C2×D3—208no—
484C3×C4—24no—
485C3×C4—202no—
486C3×C4#408312yes—
487C3×C4C2×D4×D511yescharacteristic
488C3×C4C22×C22⋊D511yescharacteristic
489Dic3—102no—
490C2×C5—242no—
491C2×C5#481014yescomplemented
492C2×C5C2×#88211yescharacteristic
493C2×C5C2×#91411yescharacteristic
494C2×C5C2×#91911yescharacteristic
495D5—122no—
496D5—124no—
497C23—62no—
498C23—122no—
499C23—122no—
500C23—122no—
501C23—152no—
502C23—302no—
503C23—302no—
504C23—302no—
505C23—304no—
506C23—302no—
507C23—602no—
508C23—602no—
509C23#679011yescharacteristic
510Q8—22no—
511Q8—24no—
512Q8C2×#120314yescomplemented
513D4—62no—
514D4—62no—
515D4—122no—
516D4—154no—
517D4—3016no—
518D4—302no—
519D4—304no—
520D4—608no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—102no—
524C2×C4—152no—
525C2×C4—202no—
526C2×C4—3016no—
527C2×C4—302no—
528C2×C4—302no—
529C2×C4—302no—
530C2×C4—304no—
531C2×C4C2×#120312yes—
532C2×C4#679012yes—
533C2×C4#679011yescharacteristic
534C2×C4C22×D3×D511yescharacteristic
535C8—62no—
536C8—102no—
537C2×C3#6546114yescomplemented
538C2×C3C2×#406011yescharacteristic
539C2×C3C2×#406211yescharacteristic
540C2×C3C2×#408311yescharacteristic
541D3—82no—
542D3—202no—
543D3—204no—
544C5C2×#481011yescharacteristic, complemented, Sylow
545C22—122no—
546C22—122no—
547C22—122no—
548C22—244no—
549C22—302no—
550C22—302no—
551C22—304no—
552C22—302no—
553C22—602no—
554C22—602no—
555C22—604no—
556C22—608no—
557C22#9150612yes—
558C22#9152312yes—
559C22#9157312yes—
560C22C2×#679011yescharacteristic
561C4—24no—
562C4—202no—
563C4—302no—
564C4#9157312yes—
565C4C22×#120311yescharacteristic
566C4C2×#679011yescharacteristic
567C3C2×#6546111yescharacteristic, complemented, Sylow
568C2—242no—
569C2—602no—
570C2—604no—
571C2#1174928914yesdirect product factor
572C2C2×#9150611yescharacteristic
573C2C2×#9152311yescharacteristic
574C2C2×#9157311yescharacteristic
subgroupG/H
centerC23#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#449
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#6821C2semidirect
2. C22×C5×#215C2semidirect
3. C2×#91466C2semidirect
4. C22×#6654C2semidirect
5. C2×C3×#3967C2semidirect
6. #11749289C2direct (N × H)
7. C2×#90968C2semidirect
8. C2×#90957C2semidirect
14. C2×#6821C22semidirect
22. C2×C5×#215C22semidirect
28. #91466C22semidirect
30. C2×#6654C22semidirect
31. C3×#3967C22semidirect
32. #90968C22semidirect
33. #90957C22semidirect
39. C2×#3967D3semidirect
48. C2×C3×C5×Q8D4semidirect
60. C2×D60D4semidirect
85. C22×#215D5semidirect
113. #3967C2×D3semidirect
132. C3×C5×Q8C2×D4semidirect
144. D60C2×D4semidirect
171. C2×#215C2×D5semidirect
186. C2×C5×Q8D12semidirect
257. C2×C3×Q8C22⋊D5semidirect
308. C5×Q8C2×D12semidirect
357. C2×C3×C5#449semidirect
379. C3×Q8C2×C22⋊D5semidirect
434. C2×Q8#1203semidirect
467. C3×C5C2×#449semidirect
491. C2×C5#4810semidirect
512. Q8C2×#1203semidirect
537. C2×C3#65461semidirect
544. C5C2×#4810semidirect
567. C3C2×#65461semidirect
571. C2#11749289direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68212
C22×C5×#2152
C2×#914662
C22×#66542
C2×C3×#39672
#117492892
C2×#909682
C2×#909572
C2×#654613
C2×#48105