Finite Group Databasebeta

← C2×#11748149 #14423459

Subgroups — C2×#11748149 #14423459

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×#6765C211yesmaximal, characteristic, complemented
2C22×C3×D40C211yesmaximal, characteristic, complemented
3C2×#91456C211yesmaximal, characteristic, complemented
4C22×#6657C211yesmaximal, characteristic, complemented
5C2×#91100C211yesmaximal, characteristic, complemented
6C2×C5×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C2×#90965C211yesmaximal, characteristic, complemented
8#11748149C218yesmaximal, direct product factor
9C2×#65023—31nomaximal, Hall
10C22×Dic30C2211yescharacteristic
11C22×C4×C5×D3C2211yescharacteristic
12C22×C3×D20C2211yescharacteristic
13C22×C3×D20C2211yescharacteristic
14C22×#1201—21no—
15C22×#1201—21no—
16C22×D5×Dic3—21no—
17C2×#6765—24no—
18C2×#6765—22no—
19C2×#6765—24no—
20C2×#6765C2214yescomplemented
21C22×C3×C5×C8C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C2×C3×D40—24no—
25C2×C3×D40C2214yescomplemented
26C2×#6665—21no—
27#91456—22no—
28#91456C2214yescomplemented
29C2×#6657—24no—
30C2×#6657C2214yescomplemented
31#91100C2214yescomplemented
32C5×(C2×D3)⋊C8C2214yescomplemented
33#90965C2214yescomplemented
34C2×#5158—51nomaximal, Hall
35C22×#709—31no—
36C2×#4076—31no—
37C22×D40D311yescharacteristic, complemented
38C22×#677—31no—
39C2×C5×C22⋊C8—31no—
40C2×#3953—31no—
41C2×#3948—31no—
42#65023—38no—
43C23×C5×D3D411yescharacteristic
44C23×C3×D5—21no—
45C23×C3×D5—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C22×Dic15—21no—
48C22×Dic15—21no—
49C2×Dic30—21no—
50C2×Dic30—22no—
51C2×Dic30D414yescomplemented
52C2×Dic30C2312yes—
53C22×C5×Dic3D411yescharacteristic
54C2×C4×C5×D3—22no—
55C2×C4×C5×D3—22no—
56C2×C4×C5×D3D412yes—
57C2×C4×C5×D3C2312yes—
58C2×C3×D20—21no—
59C2×C3×D20—22no—
60C2×C3×D20—22no—
61C2×C3×D20—22no—
62C2×C3×D20—21no—
63C2×C3×D20D414yescomplemented
64C2×C3×D20C2312yes—
65C2×C3×D20C2312yes—
66C2×#1201—28no—
67C2×#1201—24no—
68C2×#1201—24no—
69C2×#1201—44no—
70C2×D5×Dic3—28no—
71C2×D5×Dic3—24no—
72#6765—216no—
73#6765—28no—
74#6765—28no—
75C2×C3×C5×C8—22no—
76C2×C3×C5×C8C2312yes—
77C4⋊Dic15—21no—
78C4⋊Dic15C2312yes—
79C2×C5×C3⋊C8—22no—
80C2×C5×C3⋊C8C2312yes—
81C3×D40—28no—
82#6665—24no—
83#6657—28no—
84C22×#237—51no—
85C22×C3×D8—51no—
86C2×#938—51no—
87C22×#214—51no—
88C2×#832—51no—
89#5158—58no—
90C2×(C2×D3)⋊C8D511yescharacteristic, complemented
91C2×#816—51no—
92C23×C4×C5—31no—
93C22×C22⋊D5—61no—
94C22×C22⋊D5—61no—
95C2×#709—34no—
96C2×#709—64no—
97C2×#709—62no—
98C2×#709—64no—
99C22×D20C2×D311yescharacteristic
100C22×D20C2×D311yescharacteristic
101C22×C4×D5—61no—
102C22×Dic10—31no—
103C22×C5×C8—31no—
104C22×C5×C8C2×D311yescharacteristic
105#4076—34no—
106#4076—62no—
107C2×#685—61no—
108C2×C4⋊Dic5—31no—
109C2×D40—24no—
110C2×D40C2×D314yescomplemented
111C2×#677—34no—
112C2×#677—64no—
113C5×C22⋊C8—34no—
114#3953—34no—
115#3948—34no—
116C2×#449—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×C5×D3—22no—
119C22×C5×D3—22no—
120C22×C5×D3—22no—
121C22×C5×D3C2×D412yes—
122C22×C3×D5—24no—
123C22×C3×D5—22no—
124C22×C3×D5—22no—
125C22×C3×D5—42no—
126C22×C3×D5—42no—
127C22×C3×D5—42no—
128C22×C3×D5—42no—
129C22×C3×D5—42no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D412yes—
132C2×C3×C4×C5C2×D412yes—
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—24no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—42no—
138Dic30—24no—
139Dic30—22no—
140Dic30C2×D414yescomplemented
141C2×C5×Dic3—22no—
142C2×C5×Dic3C2×D412yes—
143C4×C5×D3—24no—
144C4×C5×D3—22no—
145C4×C5×D3—22no—
146C3×D20—24no—
147C3×D20—22no—
148C3×D20—22no—
149C3×D20—22no—
150C3×D20—42no—
151C3×D20C2×D414yescomplemented
152#1201—216no—
153#1201—48no—
154D5×Dic3—216no—
155C3×C5×C8—22no—
156C5×C3⋊C8—22no—
157C22×C3×D4—51no—
158C22×C3×D4—51no—
159C22×#67—101no—
160C22×#67—101no—
161C23×Dic3—101no—
162C2×#237—54no—
163C2×#237—104no—
164C2×#237—104no—
165C2×#237—102no—
166C22×C4×D3C2×D511yescharacteristic
167C22×Dic6—51no—
168C2×C3×D8—54no—
169C2×C3×D8—104no—
170C22×C3×C8C2×D511yescharacteristic
171C2×#217—101no—
172#938—54no—
173#938—102no—
174C2×#214—54no—
175C2×#214—104no—
176C2×C4⋊Dic3—51no—
177C22×C3⋊C8C2×D511yescharacteristic
178#832—54no—
179(C2×D3)⋊C8C2×D514yescomplemented
180#816—54no—
181C24×C5—31no—
182C23×D5—21no—
183C23×D5—21no—
184C22×C4×C5—31no—
185C22×C4×C5—32no—
186C22×C4×C5—32no—
187C22×C4×C5—62no—
188C22×C4×C5—62no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—64no—
191C2×C22⋊D5—68no—
192C2×C22⋊D5—64no—
193C2×C22⋊D5—124no—
194C22×Dic5—61no—
195C22×Dic5—61no—
196#709—68no—
197#709—616no—
198#709—68no—
199C2×D20—21no—
200C2×D20—22no—
201C2×D20—22no—
202C2×D20—22no—
203C2×D20—21no—
204C2×D20#6714yescomplemented
205C2×D20C22×D312yes—
206C2×D20C22×D312yes—
207C2×C4×D5—64no—
208C2×C4×D5—68no—
209C2×Dic10—34no—
210C2×Dic10—32no—
211C2×Dic10—61no—
212C2×Dic10—62no—
213C2×C5×C8—22no—
214C2×C5×C8—32no—
215C2×C5×C8—62no—
216C2×C5×C8C22×D312yes—
217#685—64no—
218C4⋊Dic5—32no—
219C4⋊Dic5—61no—
220D40—28no—
221#677—68no—
222C22×#41—151no—
223C22×SD16—151no—
224C22×D8—51no—
225C2×#121—151no—
226#449—158no—
227C2×#103—151no—
228C2×#102—151no—
229C2×C22⋊C8—31no—
230C22×C3×C5#12012yes—
231C22×C3×C5#13512yes—
232C22×C3×C5AGL(1,ℤ/8)12yes—
233C22×C3×C5C22×D411yescharacteristic
234C2×C5×D3—22no—
235C2×C5×D3—22no—
236C2×C5×D3—22no—
237C2×C5×D3—44no—
238C2×C3×D5—24no—
239C2×C3×D5—42no—
240C2×C3×D5—42no—
241C2×C3×D5—48no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—42no—
245C2×C3×D5—84no—
246C3×C4×C5#12012yes—
247C3×C4×C5C22×D411yescharacteristic
248C3×C4×C5C22×D411yescharacteristic
249Dic15—24no—
250Dic15—42no—
251C5×Dic3—22no—
252C24×C3—101no—
253C24×C3—101no—
254C23×D3D2011yescharacteristic
255C2×C3×D4—54no—
256C2×C3×D4—52no—
257C2×C3×D4—52no—
258C2×C3×D4—101no—
259C2×C3×D4—101no—
260C2×C3×D4—102no—
261C2×C3×D4—102no—
262C2×C3×D4—102no—
263C22×C3×C4C22×D511yescharacteristic
264C2×#67—108no—
265C2×#67—104no—
266C2×#67—104no—
267C2×#67—204no—
268C22×Dic3—108no—
269C22×Dic3—101no—
270C22×Dic3—104no—
271C22×Dic3—101no—
272C22×Dic3D2011yescharacteristic
273#237—108no—
274#237—108no—
275#237—1016no—
276C2×C4×D3—22no—
277C2×C4×D3—22no—
278C2×C4×D3D2012yes—
279C2×C4×D3C22×D512yes—
280C2×Dic6—54no—
281C2×Dic6—52no—
282C2×Dic6—101no—
283C2×Dic6—102no—
284C3×D8—108no—
285C2×C3×C8—22no—
286C2×C3×C8C22×D512yes—
287#217—104no—
288#214—108no—
289C4⋊Dic3—52no—
290C4⋊Dic3—101no—
291C2×C3⋊C8—22no—
292C2×C3⋊C8C22×D512yes—
293C23×C5—32no—
294C23×C5—62no—
295C23×C5—62no—
296C23×C5—62no—
297C23×C5D3×D411yescharacteristic
298C22×D5—24no—
299C22×D5—22no—
300C22×D5—22no—
301C22×D5—42no—
302C22×D5—42no—
303C22×D5—42no—
304C22×D5—42no—
305C22×D5—42no—
306C2×C4×C5—32no—
307C2×C4×C5—62no—
308C2×C4×C5—64no—
309C2×C4×C5—62no—
310C2×C4×C5—62no—
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5D3×D412yes—
313C2×C4×C5C2×#6712yes—
314C2×C4×C5C23×D311yescharacteristic
315C22⋊D5—616no—
316C22⋊D5—128no—
317C2×Dic5—64no—
318C2×Dic5—62no—
319C2×Dic5—62no—
320C2×Dic5—122no—
321D20—24no—
322D20—22no—
323D20—22no—
324D20—22no—
325D20—42no—
326D20C2×#6714yescomplemented
327C4×D5—616no—
328Dic10—34no—
329Dic10—64no—
330Dic10—62no—
331C5×C8—22no—
332C5×C8—62no—
333C2×#41—154no—
334C2×#41—302no—
335C2×#41—304no—
336C2×#41—304no—
337C22×Q8—151no—
338C22×D4—51no—
339C22×D4—51no—
340C22×D4—301no—
341C22×D4—301no—
342C23×C4—31no—
343C23×C4—301no—
344C2×SD16—154no—
345C2×SD16—304no—
346C2×D8—54no—
347C2×D8—104no—
348C22×C8—31no—
349C22×C8D3×D511yescharacteristic
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#44914yescomplemented
358C2×C3×C5C2×#12011yescharacteristic
359C2×C3×C5C2×#13511yescharacteristic
360C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
361C3×D5—44no—
362C3×D5—82no—
363C5×D3—42no—
364C23×C3—102no—
365C23×C3—104no—
366C23×C3—102no—
367C23×C3—202no—
368C23×C3—202no—
369C23×C3—202no—
370C23×C3—202no—
371C23×C3—202no—
372C23×C3C2×D2011yescharacteristic
373C22×D3—22no—
374C22×D3—22no—
375C22×D3—22no—
376C22×D3C2×D2012yes—
377C3×D4—54no—
378C3×D4—102no—
379C3×D4—102no—
380C3×D4—102no—
381C3×D4—104no—
382C3×D4—202no—
383C2×C3×C4C2×D2011yescharacteristic
384C2×C3×C4D4×D512yes—
385C2×C3×C4D4×D512yes—
386C2×C3×C4C23×D511yescharacteristic
387#67—1016no—
388#67—208no—
389C2×Dic3—22no—
390C2×Dic3—1016no—
391C2×Dic3—102no—
392C2×Dic3—104no—
393C2×Dic3—102no—
394C2×Dic3—202no—
395C2×Dic3C2×D2012yes—
396C4×D3—22no—
397C4×D3—22no—
398C4×D3—24no—
399Dic6—54no—
400Dic6—102no—
401Dic6—104no—
402C3×C8—22no—
403C3⋊C8—22no—
404C22×C5—62no—
405C22×C5—62no—
406C22×C5—62no—
407C22×C5—124no—
408C22×C5#91112yes—
409C22×C5#91212yes—
410C22×C5#93712yes—
411C22×C5C2×D3×D411yescharacteristic
412C2×D5—24no—
413C2×D5—48no—
414C2×D5—42no—
415C2×D5—42no—
416C2×D5—42no—
417C2×D5—42no—
418C2×D5—42no—
419C2×D5—84no—
420C4×C5—62no—
421C4×C5#93712yes—
422C4×C5C2×D3×D411yescharacteristic
423C4×C5C22×#6711yescharacteristic
424Dic5—64no—
425Dic5—122no—
426C24—31no—
427C24—101no—
428C24—101no—
429#41—308no—
430#41—308no—
431#41—3016no—
432C2×Q8—154no—
433C2×Q8—152no—
434C2×Q8—301no—
435C2×Q8—302no—
436C2×D4—54no—
437C2×D4—52no—
438C2×D4—52no—
439C2×D4—101no—
440C2×D4—101no—
441C2×D4—102no—
442C2×D4—102no—
443C2×D4—102no—
444C2×D4—304no—
445C2×D4—308no—
446C2×D4—304no—
447C2×D4—604no—
448C22×C4—31no—
449C22×C4—32no—
450C22×C4—32no—
451C22×C4—62no—
452C22×C4—62no—
453C22×C4—304no—
454C22×C4—308no—
455C22×C4—301no—
456C22×C4—301no—
457C22×C4C2×D3×D511yescharacteristic
458SD16—308no—
459D8—108no—
460C2×C8—22no—
461C2×C8—32no—
462C2×C8—62no—
463C2×C8C2×D3×D512yes—
464C4⋊C4—152no—
465C4⋊C4—301no—
466C22⋊C4—304no—
467C3×C5C2×#44911yescharacteristic, complemented, Hall
468C22×C3—104no—
469C22×C3—202no—
470C22×C3—202no—
471C22×C3—208no—
472C22×C3—202no—
473C22×C3—202no—
474C22×C3—202no—
475C22×C3—404no—
476C22×C3#402812yes—
477C22×C3#405012yes—
478C22×C3#405412yes—
479C22×C3C22×D2011yescharacteristic
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—22no—
483C2×D3—44no—
484C3×C4#402812yes—
485C3×C4C2×D4×D511yescharacteristic
486C3×C4C2×D4×D511yescharacteristic
487Dic3—22no—
488Dic3—104no—
489Dic3—202no—
490C2×C5—122no—
491C2×C5#515814yescomplemented
492C2×C5C2×#91111yescharacteristic
493C2×C5C2×#91211yescharacteristic
494C2×C5C2×#93711yescharacteristic
495D5—44no—
496D5—82no—
497C23—32no—
498C23—62no—
499C23—62no—
500C23—62no—
501C23—104no—
502C23—102no—
503C23—102no—
504C23—202no—
505C23—202no—
506C23—202no—
507C23—202no—
508C23—202no—
509C23D3×D2011yescharacteristic
510Q8—154no—
511Q8—304no—
512Q8—302no—
513D4—54no—
514D4—104no—
515D4—102no—
516D4—102no—
517D4—102no—
518D4—202no—
519D4—3016no—
520D4—608no—
521C2×C4—32no—
522C2×C4—62no—
523C2×C4—64no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—3016no—
527C2×C4—304no—
528C2×C4—302no—
529C2×C4—302no—
530C2×C4—602no—
531C2×C4D3×D2011yescharacteristic
532C2×C4#677712yes—
533C2×C4D5×#6712yes—
534C2×C4C22×D3×D511yescharacteristic
535C8—22no—
536C8—62no—
537C2×C3—204no—
538C2×C3—402no—
539C2×C3#6502314yescomplemented
540C2×C3C2×#402811yescharacteristic
541C2×C3C2×#405011yescharacteristic
542C2×C3C2×#405411yescharacteristic
543D3—42no—
544C5C2×#515811yescharacteristic, complemented, Sylow
545C22—62no—
546C22—62no—
547C22—62no—
548C22—104no—
549C22—124no—
550C22—202no—
551C22—208no—
552C22—202no—
553C22—202no—
554C22—202no—
555C22—202no—
556C22—404no—
557C22#9125412yes—
558C22#9127312yes—
559C22#9147412yes—
560C22C2×D3×D2011yescharacteristic
561C4—62no—
562C4—304no—
563C4—602no—
564C4#9147412yes—
565C4C2×#677711yescharacteristic
566C4C2×D5×#6711yescharacteristic
567C3C2×#6502311yescharacteristic, complemented, Sylow
568C2—122no—
569C2—204no—
570C2—402no—
571C2#1174814914yesdirect product factor
572C2C2×#9125411yescharacteristic
573C2C2×#9127311yescharacteristic
574C2C2×#9147411yescharacteristic
subgroupG/H
centerC23D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
hypercenterC22×C8D3×D5
hypocenterC3×C5C2×#449
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×#6765C2semidirect
2. C22×C3×D40C2semidirect
3. C2×#91456C2semidirect
4. C22×#6657C2semidirect
5. C2×#91100C2semidirect
6. C2×C5×(C2×D3)⋊C8C2semidirect
7. C2×#90965C2semidirect
8. #11748149C2direct (N × H)
20. C2×#6765C22semidirect
25. C2×C3×D40C22semidirect
28. #91456C22semidirect
30. C2×#6657C22semidirect
31. #91100C22semidirect
32. C5×(C2×D3)⋊C8C22semidirect
33. #90965C22semidirect
37. C22×D40D3semidirect
51. C2×Dic30D4semidirect
63. C2×C3×D20D4semidirect
90. C2×(C2×D3)⋊C8D5semidirect
110. C2×D40C2×D3semidirect
140. Dic30C2×D4semidirect
151. C3×D20C2×D4semidirect
179. (C2×D3)⋊C8C2×D5semidirect
204. C2×D20#67semidirect
326. D20C2×#67semidirect
357. C2×C3×C5#449semidirect
467. C3×C5C2×#449semidirect
491. C2×C5#5158semidirect
539. C2×C3#65023semidirect
544. C5C2×#5158semidirect
567. C3C2×#65023semidirect
571. C2#11748149direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67652
C22×C3×D402
C2×#914562
C22×#66572
C2×#911002
C2×C5×(C2×D3)⋊C82
C2×#909652
#117481492
C2×#650233
C2×#51585