Finite Group Databasebeta

← C2×#11748513 #14423456

Subgroups — C2×#11748513 #14423456

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×C3×#709C211yesmaximal, characteristic, complemented
2C2×#91819C211yesmaximal, characteristic, complemented
3C22×#6658C211yesmaximal, characteristic, complemented
4C22×#6653C211yesmaximal, characteristic, complemented
5C2×C5×#830C211yesmaximal, characteristic, complemented
6#11748513C218yesmaximal, direct product factor
7C2×#90971C211yesmaximal, characteristic, complemented
8C2×#90965C211yesmaximal, characteristic, complemented
9C2×#65023—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×#1220—21no—
12C22×D60C2211yescharacteristic
13C22×C3×C22⋊D5—21no—
14C2×C3×#709—22no—
15C2×C3×#709—24no—
16C2×C3×#709—24no—
17C2×C3×#709C2214yescomplemented
18C22×C3×D20C2211yescharacteristic
19C22×C3×C4×D5—21no—
20C22×C3×Dic10C2211yescharacteristic
21#91819—22no—
22#91819C2214yescomplemented
23C2×#6714—21no—
24C2×C4⋊Dic15C2211yescharacteristic
25C22×C5×C3⋊C8C2211yescharacteristic
26C22×C5×C3⋊C8C2211yescharacteristic
27C2×#6658—24no—
28C2×#6658C2214yescomplemented
29C2×#6653—24no—
30C2×#6653C2214yescomplemented
31C5×#830C2214yescomplemented
32#90971C2214yescomplemented
33#90965C2214yescomplemented
34C2×#5238—51nomaximal, Hall
35C22×#709D311yescharacteristic, complemented
36C2×#4076—31no—
37C22×D40—31no—
38C22×#677—31no—
39C2×C5×C22⋊C8—31no—
40C2×#3953—31no—
41C2×#3948—31no—
42#65023—38no—
43C24×C3×C5D411yescharacteristic
44C23×D15—21no—
45C23×C3×D5—21no—
46C22×C3×C4×C5—22no—
47C22×C3×C4×C5—22no—
48C22×C3×C4×C5D411yescharacteristic
49C22×C3×C4×C5D412yes—
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C2×#1220—24no—
53C2×#1220—44no—
54C22×Dic15—21no—
55C2×D60—22no—
56C2×D60—22no—
57C2×D60—21no—
58C2×D60C2312yes—
59C2×C3×C22⋊D5—28no—
60C2×C3×C22⋊D5—24no—
61C22×C3×Dic5—21no—
62C3×#709—216no—
63C3×#709—28no—
64C3×#709—28no—
65C2×C3×D20—21no—
66C2×C3×D20—22no—
67C2×C3×D20D414yescomplemented
68C2×C3×D20C2312yes—
69C2×C3×C4×D5—28no—
70C2×C3×C4×D5—24no—
71C2×C3×Dic10—21no—
72C2×C3×Dic10—22no—
73C2×C3×Dic10D414yescomplemented
74C2×C3×Dic10C2312yes—
75#6714—24no—
76C4⋊Dic15—21no—
77C4⋊Dic15C2312yes—
78C2×C5×C3⋊C8—22no—
79C2×C5×C3⋊C8—22no—
80C2×C5×C3⋊C8C2312yes—
81C2×C5×C3⋊C8C2312yes—
82#6658—28no—
83#6653—28no—
84C22×C3×#41—51no—
85C22×#215—51no—
86C22×#213—51no—
87C2×#930—51no—
88#5238—58no—
89C2×#835—51no—
90C2×#832—51no—
91C2×#830D511yescharacteristic, complemented
92C23×C4×C5C2×D311yescharacteristic
93C22×C22⋊D5—21no—
94C22×C22⋊D5—61no—
95C2×#709—22no—
96C2×#709—24no—
97C2×#709—24no—
98C2×#709C2×D314yescomplemented
99C22×D20—31no—
100C22×D20C2×D311yescharacteristic
101C22×C4×D5—21no—
102C22×Dic10C2×D311yescharacteristic
103C22×C5×C8—31no—
104C22×C5×C8—31no—
105#4076—34no—
106#4076—62no—
107C2×#685—61no—
108C2×C4⋊Dic5—31no—
109C2×D40—34no—
110C2×D40—64no—
111C2×#677—34no—
112C2×#677—64no—
113C5×C22⋊C8—34no—
114#3953—34no—
115#3948—34no—
116C2×#449—151noSylow
117C23×C3×C5—22no—
118C23×C3×C5—22no—
119C23×C3×C5—22no—
120C23×C3×C5C2×D412yes—
121C23×C3×C5C2×D411yescharacteristic
122C22×D15—22no—
123C22×D15—42no—
124C22×D15—42no—
125C22×D15—42no—
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—24no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2×D412yes—
138C2×C3×C4×C5C2411yescharacteristic
139#1220—48no—
140C2×Dic15—22no—
141C2×Dic15—42no—
142D60—22no—
143D60—22no—
144D60—42no—
145C3×C22⋊D5—216no—
146C2×C3×Dic5—24no—
147C2×C3×Dic5—22no—
148C3×D20—24no—
149C3×D20—22no—
150C3×D20C2×D414yescomplemented
151C3×C4×D5—216no—
152C3×Dic10—24no—
153C3×Dic10—22no—
154C3×Dic10C2×D414yescomplemented
155C5×C3⋊C8—22no—
156C5×C3⋊C8—22no—
157C2×C3×#41—54no—
158C2×C3×#41—104no—
159C2×C3×#41—104no—
160C2×C3×#41—102no—
161C22×C3×Q8—51no—
162C22×C3×D4—51no—
163C22×C3×D4—101no—
164C23×C3×C4—101no—
165C23×C3×C4C2×D511yescharacteristic
166C22×#67—101no—
167C22×D12—51no—
168C2×#215—54no—
169C2×#215—104no—
170C2×#213—54no—
171C2×#213—104no—
172#930—54no—
173#930—102no—
174C2×(C2×D3)⋊C4—101no—
175C2×C4⋊Dic3—51no—
176C22×C3⋊C8C2×D511yescharacteristic
177C22×C3⋊C8C2×D511yescharacteristic
178#835—54no—
179#832—54no—
180#830C2×D514yescomplemented
181C24×C5#6711yescharacteristic
182C23×D5—21no—
183C23×D5—61no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5#6711yescharacteristic
187C22×C4×C5#6712yes—
188C22×C4×C5C22×D312yes—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—28no—
191C2×C22⋊D5—24no—
192C2×C22⋊D5—64no—
193C2×C22⋊D5—124no—
194C22×Dic5—21no—
195C22×Dic5—61no—
196#709—216no—
197#709—28no—
198#709—28no—
199C2×D20—21no—
200C2×D20—22no—
201C2×D20—32no—
202C2×D20—62no—
203C2×D20—62no—
204C2×D20—61no—
205C2×D20#6714yescomplemented
206C2×D20C22×D312yes—
207C2×C4×D5—28no—
208C2×C4×D5—24no—
209C2×Dic10—21no—
210C2×Dic10—22no—
211C2×Dic10#6714yescomplemented
212C2×Dic10C22×D312yes—
213C2×C5×C8—32no—
214C2×C5×C8—32no—
215C2×C5×C8—62no—
216C2×C5×C8—62no—
217#685—64no—
218C4⋊Dic5—32no—
219C4⋊Dic5—61no—
220D40—68no—
221#677—68no—
222C22×#41—51no—
223C22×SD16—151no—
224C22×D8—151no—
225C2×#121—151no—
226#449—158no—
227C2×#103—151no—
228C2×#102—151no—
229C2×C22⋊C8—31no—
230C22×C3×C5—22no—
231C22×C3×C5—22no—
232C22×C3×C5—22no—
233C22×C3×C5—44no—
234C22×C3×C5#12012yes—
235C22×C3×C5#13512yes—
236C22×C3×C5AGL(1,ℤ/8)12yes—
237C22×C3×C5C22×D411yescharacteristic
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—22no—
247C3×C4×C5#12012yes—
248C3×C4×C5C22×D411yescharacteristic
249C3×C4×C5C22×D411yescharacteristic
250Dic15—42no—
251C3×Dic5—24no—
252C24×C3—101no—
253C24×C3D2011yescharacteristic
254C23×D3—101no—
255C3×#41—108no—
256C3×#41—108no—
257C3×#41—1016no—
258C2×C3×Q8—54no—
259C2×C3×Q8—52no—
260C2×C3×Q8—101no—
261C2×C3×Q8—102no—
262C2×C3×D4—54no—
263C2×C3×D4—52no—
264C2×C3×D4—108no—
265C2×C3×D4—104no—
266C2×C3×D4—101no—
267C2×C3×D4—102no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—108no—
271C22×C3×C4—101no—
272C22×C3×C4—104no—
273C22×C3×C4D2011yescharacteristic
274C22×C3×C4D2012yes—
275C22×C3×C4C22×D512yes—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—104no—
278C2×#67—204no—
279C22×Dic3—101no—
280C2×D12—52no—
281C2×D12—102no—
282C2×D12—102no—
283C2×D12—101no—
284#215—108no—
285#213—108no—
286(C2×D3)⋊C4—104no—
287C4⋊Dic3—52no—
288C4⋊Dic3—101no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8—22no—
291C2×C3⋊C8C22×D512yes—
292C2×C3⋊C8C22×D512yes—
293C23×C5—22no—
294C23×C5—22no—
295C23×C5—22no—
296C23×C5C2×#6712yes—
297C23×C5C2×#6711yescharacteristic
298C22×D5—24no—
299C22×D5—22no—
300C22×D5—42no—
301C22×D5—42no—
302C22×D5—62no—
303C22×D5—122no—
304C22×D5—122no—
305C22×D5—122no—
306C2×C4×C5—22no—
307C2×C4×C5—24no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5C2×#6712yes—
311C2×C4×C5C2×#6711yescharacteristic
312C2×C4×C5C2×#6712yes—
313C2×C4×C5C2×#6712yes—
314C2×C4×C5C23×D311yescharacteristic
315C22⋊D5—216no—
316C22⋊D5—128no—
317C2×Dic5—24no—
318C2×Dic5—22no—
319C2×Dic5—62no—
320C2×Dic5—122no—
321D20—24no—
322D20—22no—
323D20—62no—
324D20—62no—
325D20—122no—
326D20C2×#6714yescomplemented
327C4×D5—216no—
328Dic10—24no—
329Dic10—22no—
330Dic10C2×#6714yescomplemented
331C5×C8—62no—
332C5×C8—62no—
333C2×#41—54no—
334C2×#41—104no—
335C2×#41—104no—
336C2×#41—102no—
337C22×Q8—51no—
338C22×D4—51no—
339C22×D4—101no—
340C22×D4—151no—
341C22×D4—301no—
342C23×C4—101no—
343C23×C4D3×D511yescharacteristic
344C2×SD16—154no—
345C2×SD16—304no—
346C2×D8—154no—
347C2×D8—304no—
348C22×C8—31no—
349C22×C8—31no—
350#121—154no—
351#121—302no—
352C2×C4⋊C4—151no—
353C2×C22⋊C4—301no—
354#103—154no—
355#102—154no—
356C22⋊C8—34no—
357C2×C3×C5—42no—
358C2×C3×C5#44914yescomplemented
359C2×C3×C5C2×#12011yescharacteristic
360C2×C3×C5C2×#13511yescharacteristic
361C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
362D15—82no—
363C3×D5—44no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—102no—
368C23×C3—104no—
369C23×C3—202no—
370C23×C3—202no—
371C23×C3C2×D2012yes—
372C23×C3C2×D2011yescharacteristic
373C22×D3—102no—
374C22×D3—202no—
375C22×D3—202no—
376C22×D3—202no—
377C3×Q8—54no—
378C3×Q8—102no—
379C3×Q8—104no—
380C3×D4—54no—
381C3×D4—1016no—
382C3×D4—102no—
383C3×D4—104no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—24no—
388C2×C3×C4—1016no—
389C2×C3×C4—102no—
390C2×C3×C4—104no—
391C2×C3×C4C2×D2012yes—
392C2×C3×C4C2×D2011yescharacteristic
393C2×C3×C4D4×D512yes—
394C2×C3×C4D4×D512yes—
395C2×C3×C4C23×D511yescharacteristic
396#67—208no—
397C2×Dic3—102no—
398C2×Dic3—202no—
399D12—102no—
400D12—102no—
401D12—202no—
402C3⋊C8—22no—
403C3⋊C8—22no—
404C22×C5—22no—
405C22×C5—22no—
406C22×C5—22no—
407C22×C5—44no—
408C22×C5#94912yes—
409C22×C5#95012yes—
410C22×C5#95312yes—
411C22×C5C22×#6711yescharacteristic
412C2×D5—24no—
413C2×D5—48no—
414C2×D5—42no—
415C2×D5—42no—
416C2×D5—122no—
417C2×D5—122no—
418C2×D5—122no—
419C2×D5—244no—
420C4×C5—22no—
421C4×C5#95312yes—
422C4×C5C22×#6711yescharacteristic
423C4×C5C22×#6711yescharacteristic
424Dic5—24no—
425Dic5—122no—
426C24—101no—
427C24—301no—
428C24#120211yescharacteristic
429#41—108no—
430#41—108no—
431#41—1016no—
432C2×Q8—54no—
433C2×Q8—52no—
434C2×Q8—101no—
435C2×Q8—102no—
436C2×D4—54no—
437C2×D4—52no—
438C2×D4—108no—
439C2×D4—104no—
440C2×D4—101no—
441C2×D4—102no—
442C2×D4—152no—
443C2×D4—304no—
444C2×D4—301no—
445C2×D4—302no—
446C2×D4—302no—
447C2×D4—604no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—108no—
451C22×C4—101no—
452C22×C4—104no—
453C22×C4—301no—
454C22×C4#120212yes—
455C22×C4#120211yescharacteristic
456C22×C4C2×D3×D512yes—
457C22×C4C2×D3×D511yescharacteristic
458SD16—308no—
459D8—308no—
460C2×C8—32no—
461C2×C8—32no—
462C2×C8—62no—
463C2×C8—62no—
464C4⋊C4—152no—
465C4⋊C4—301no—
466C22⋊C4—304no—
467C3×C5C2×#44911yescharacteristic, complemented, Hall
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—44no—
472C22×C3—104no—
473C22×C3—202no—
474C22×C3—202no—
475C22×C3—208no—
476C22×C3#402812yes—
477C22×C3#405012yes—
478C22×C3#405412yes—
479C22×C3C22×D2011yescharacteristic
480C2×D3—202no—
481C2×D3—202no—
482C2×D3—202no—
483C2×D3—404no—
484C3×C4—22no—
485C3×C4—104no—
486C3×C4#402812yes—
487C3×C4C2×D4×D511yescharacteristic
488C3×C4C2×D4×D511yescharacteristic
489Dic3—202no—
490C2×C5—42no—
491C2×C5#523814yescomplemented
492C2×C5C2×#94911yescharacteristic
493C2×C5C2×#95011yescharacteristic
494C2×C5C2×#95311yescharacteristic
495D5—44no—
496D5—242no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—102no—
501C23—104no—
502C23—202no—
503C23—202no—
504C23—302no—
505C23—602no—
506C23—602no—
507C23—602no—
508C23C2×#120212yes—
509C23C2×#120211yescharacteristic
510Q8—54no—
511Q8—102no—
512Q8—104no—
513D4—54no—
514D4—1016no—
515D4—102no—
516D4—104no—
517D4—302no—
518D4—302no—
519D4—608no—
520D4—602no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—1016no—
526C2×C4—102no—
527C2×C4—104no—
528C2×C4—302no—
529C2×C4—602no—
530C2×C4C2×#120212yes—
531C2×C4C2×#120211yescharacteristic
532C2×C4D5×#6712yes—
533C2×C4D5×#6712yes—
534C2×C4C22×D3×D511yescharacteristic
535C8—62no—
536C8—62no—
537C2×C3—42no—
538C2×C3—204no—
539C2×C3#6502314yescomplemented
540C2×C3C2×#402811yescharacteristic
541C2×C3C2×#405011yescharacteristic
542C2×C3C2×#405411yescharacteristic
543D3—402no—
544C5C2×#523811yescharacteristic, complemented, Sylow
545C22—22no—
546C22—22no—
547C22—22no—
548C22—44no—
549C22—104no—
550C22—202no—
551C22—208no—
552C22—202no—
553C22—602no—
554C22—602no—
555C22—602no—
556C22—1204no—
557C22#9130112yes—
558C22#9131112yes—
559C22#9156412yes—
560C22C22×#120211yescharacteristic
561C4—22no—
562C4—104no—
563C4—602no—
564C4#9156412yes—
565C4C2×D5×#6711yescharacteristic
566C4C2×D5×#6711yescharacteristic
567C3C2×#6502311yescharacteristic, complemented, Sylow
568C2—42no—
569C2—204no—
570C2—1202no—
571C2#1174851314yesdirect product factor
572C2C2×#9130111yescharacteristic
573C2C2×#9131111yescharacteristic
574C2C2×#9156411yescharacteristic
subgroupG/H
centerC23C2×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C2×D4
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#449
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#709C2semidirect
2. C2×#91819C2semidirect
3. C22×#6658C2semidirect
4. C22×#6653C2semidirect
5. C2×C5×#830C2semidirect
6. #11748513C2direct (N × H)
7. C2×#90971C2semidirect
8. C2×#90965C2semidirect
17. C2×C3×#709C22semidirect
22. #91819C22semidirect
28. C2×#6658C22semidirect
30. C2×#6653C22semidirect
31. C5×#830C22semidirect
32. #90971C22semidirect
33. #90965C22semidirect
35. C22×#709D3semidirect
67. C2×C3×D20D4semidirect
73. C2×C3×Dic10D4semidirect
91. C2×#830D5semidirect
98. C2×#709C2×D3semidirect
150. C3×D20C2×D4semidirect
154. C3×Dic10C2×D4semidirect
180. #830C2×D5semidirect
205. C2×D20#67semidirect
211. C2×Dic10#67semidirect
326. D20C2×#67semidirect
330. Dic10C2×#67semidirect
358. C2×C3×C5#449semidirect
467. C3×C5C2×#449semidirect
491. C2×C5#5238semidirect
539. C2×C3#65023semidirect
544. C5C2×#5238semidirect
567. C3C2×#65023semidirect
571. C2#11748513direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7092
C2×#918192
C22×#66582
C22×#66532
C2×C5×#8302
#117485132
C2×#909712
C2×#909652
C2×#650233
C2×#52385