Finite Group Databasebeta

← C2×#11751273 #14423411

Subgroups — C2×#11751273 #14423411

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×C3×C5×SD16C211yesmaximal, characteristic, complemented
3C2×#91827C211yesmaximal, characteristic, complemented
4C22×#6715C211yesmaximal, characteristic, complemented
5C2×#91119C211yesmaximal, characteristic, complemented
6#11751273C218yesmaximal, direct product factor
7C2×#91105C211yesmaximal, characteristic, complemented
8C2×#91104C211yesmaximal, characteristic, complemented
9C2×#65461—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C5×D4C2211yescharacteristic
12C22×#1220—21no—
13C2×#6821—24no—
14C2×#6821—24no—
15C2×#6821—22no—
16C2×#6821C2214yescomplemented
17C22×D60—21no—
18C22×D60C2211yescharacteristic
19C22×C4×D15—21no—
20C22×C4×D15C2211yescharacteristic
21C2×C3×C5×SD16—24no—
22C2×C3×C5×SD16C2214yescomplemented
23C22×C3×C5×C8C2211yescharacteristic
24C2×#6719—21no—
25#91827—22no—
26#91827C2214yescomplemented
27C2×#6715—24no—
28C2×#6715C2214yescomplemented
29C2×C4⋊Dic15C2211yescharacteristic
30C22×C3⋊#168C2211yescharacteristic
31#91119C2214yescomplemented
32#91105C2214yescomplemented
33#91104C2214yescomplemented
34C2×#5172—51nomaximal, Hall
35C22×#713—31no—
36C22×C5×SD16D311yescharacteristic, complemented
37C2×#4084—31no—
38C22×#686—31no—
39C2×#3967—31no—
40#65461—38no—
41C2×#3953—31no—
42C2×#3952—31no—
43C24×C3×C5—21no—
44C23×D15—21no—
45C23×D15D411yescharacteristic
46C2×C3×C5×Q8—22no—
47C2×C3×C5×Q8—21no—
48C2×C3×C5×Q8D414yescomplemented
49C2×C3×C5×Q8C2312yes—
50C2×C3×C5×D4—22no—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4—21no—
53C2×C3×C5×D4C2312yes—
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—24no—
57C2×#1220—44no—
58C22×Dic15—21no—
59C22×Dic15D411yescharacteristic
60#6821—216no—
61#6821—28no—
62#6821—28no—
63C2×D60—28no—
64C2×D60—24no—
65C2×D60—21no—
66C2×D60—22no—
67C2×D60D414yescomplemented
68C2×D60C2312yes—
69C2×C4×D15—28no—
70C2×C4×D15—22no—
71C2×C4×D15—22no—
72C2×C4×D15—24no—
73C2×C4×D15D412yes—
74C2×C4×D15C2312yes—
75C3×C5×SD16—28no—
76C2×C3×C5×C8—22no—
77C2×C3×C5×C8C2312yes—
78#6719—24no—
79#6715—28no—
80C4⋊Dic15—21no—
81C4⋊Dic15C2312yes—
82C2×C3⋊#168—22no—
83C2×C3⋊#168C2312yes—
84C22×#239—51no—
85C22×C3×SD16D511yescharacteristic, complemented
86C2×#938—51no—
87C22×#213—51no—
88C2×#835—51no—
89#5172—58no—
90C2×#821—51no—
91C2×(C2×D3)⋊C8—51no—
92C22×C5×Q8C2×D311yescharacteristic
93C22×C5×D4C2×D311yescharacteristic
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—24no—
104C2×C5×SD16C2×D314yescomplemented
105C22×C5×C8C2×D311yescharacteristic
106C2×C22⋊Dic5—61no—
107#4084—34no—
108#4084—62no—
109C2×#686—34no—
110C2×#686—64no—
111C2×C4⋊Dic5—31no—
112C22×#168—31no—
113#3967—34no—
114#3953—34no—
115#3952—34no—
116C2×#449—151noSylow
117C23×C3×C5—22no—
118C23×C3×C5—42no—
119C23×C3×C5—42no—
120C23×C3×C5—42no—
121C23×C3×C5C2×D411yescharacteristic
122C22×D15—22no—
123C22×D15—24no—
124C22×D15—22no—
125C22×D15—22no—
126C22×D15—22no—
127C22×D15—42no—
128C22×D15—42no—
129C22×D15C2×D412yes—
130C3×C5×Q8—24no—
131C3×C5×Q8—22no—
132C3×C5×Q8C2×D414yescomplemented
133C3×C5×D4—22no—
134C3×C5×D4—22no—
135C3×C5×D4—42no—
136C2×C3×C4×C5—24no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2411yescharacteristic
142#1220—48no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—42no—
146C2×Dic15C2×D412yes—
147D60—216no—
148D60—24no—
149D60—22no—
150D60C2×D414yescomplemented
151C4×D15—216no—
152C4×D15—24no—
153C4×D15—22no—
154C4×D15—22no—
155C3×C5×C8—22no—
156C3⋊#168—22no—
157C22×C3×Q8C2×D511yescharacteristic
158C22×C3×D4C2×D511yescharacteristic
159C22×#67—101no—
160C2×#239—54no—
161C2×#239—102no—
162C2×#239—104no—
163C2×#239—104no—
164C22×D12—51no—
165C22×D12—101no—
166C22×C4×D3—51no—
167C22×C4×D3—101no—
168C2×C3×SD16—24no—
169C2×C3×SD16C2×D514yescomplemented
170C22×C3×C8C2×D511yescharacteristic
171C2×#217—101no—
172#938—54no—
173#938—102no—
174C2×#213—54no—
175C2×#213—104no—
176C2×C4⋊Dic3—51no—
177C22×C3⋊C8—51no—
178#835—54no—
179#821—54no—
180(C2×D3)⋊C8—54no—
181C24×C5—21no—
182C23×D5—31no—
183C23×D5—61no—
184C2×C5×Q8—22no—
185C2×C5×Q8—21no—
186C2×C5×Q8#6714yescomplemented
187C2×C5×Q8C22×D312yes—
188C2×C5×D4—22no—
189C2×C5×D4—21no—
190C2×C5×D4—22no—
191C2×C5×D4C22×D312yes—
192C22×C4×C5—21no—
193C22×C4×C5C22×D311yescharacteristic
194C2×C22⋊D5—64no—
195C2×C22⋊D5—124no—
196C22×Dic5—31no—
197C22×Dic5—61no—
198#713—68no—
199#713—616no—
200#713—68no—
201C2×D20—34no—
202C2×D20—32no—
203C2×D20—64no—
204C2×D20—68no—
205C2×D20—61no—
206C2×D20—62no—
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—28no—
214C2×C5×C8—22no—
215C2×C5×C8C22×D312yes—
216C22⋊Dic5—64no—
217#686—68no—
218C4⋊Dic5—32no—
219C4⋊Dic5—61no—
220C2×#168—32no—
221C2×#168—62no—
222C22×#41—151no—
223C22×SD16D1511yescharacteristic, complemented
224C22×D8—151no—
225C2×#121—151no—
226#449—158no—
227C2×#103—151no—
228C2×#102—151no—
229C2×C22⋊C8—151no—
230C22×C3×C5—42no—
231C22×C3×C5—42no—
232C22×C3×C5—42no—
233C22×C3×C5—84no—
234C22×C3×C5#12012yes—
235C22×C3×C5#13512yes—
236C22×C3×C5AGL(1,ℤ/8)12yes—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—22no—
239C2×D15—24no—
240C2×D15—22no—
241C2×D15—22no—
242C2×D15—42no—
243C2×D15—42no—
244C2×D15—44no—
245C2×D15—48no—
246C3×C4×C5—24no—
247C3×C4×C5#12012yes—
248C3×C4×C5C22×D411yescharacteristic
249C3×C4×C5C22×D411yescharacteristic
250Dic15—22no—
251Dic15—42no—
252C24×C3—21no—
253C23×D3—51no—
254C23×D3—101no—
255C2×C3×Q8—21no—
256C2×C3×Q8—22no—
257C2×C3×Q8C22⋊D514yescomplemented
258C2×C3×Q8C22×D512yes—
259C2×C3×D4—22no—
260C2×C3×D4—21no—
261C2×C3×D4—22no—
262C2×C3×D4C22×D512yes—
263C22×C3×C4—21no—
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—104no—
266C2×#67—204no—
267C22×Dic3—51no—
268C22×Dic3—101no—
269#239—108no—
270#239—1016no—
271#239—108no—
272C2×D12—54no—
273C2×D12—52no—
274C2×D12—104no—
275C2×D12—108no—
276C2×D12—101no—
277C2×D12—102no—
278C2×C4×D3—52no—
279C2×C4×D3—52no—
280C2×C4×D3—104no—
281C2×C4×D3—108no—
282C2×C4×D3—102no—
283C2×C4×D3—102no—
284C3×SD16—28no—
285C2×C3×C8—22no—
286C2×C3×C8C22×D512yes—
287#217—104no—
288#213—108no—
289C4⋊Dic3—52no—
290C4⋊Dic3—101no—
291C2×C3⋊C8—52no—
292C2×C3⋊C8—102no—
293C23×C5—22no—
294C23×C5—42no—
295C23×C5—42no—
296C23×C5—42no—
297C23×C5D3×D411yescharacteristic
298C22×D5—32no—
299C22×D5—62no—
300C22×D5—62no—
301C22×D5—64no—
302C22×D5—62no—
303C22×D5—62no—
304C22×D5—122no—
305C22×D5—122no—
306C5×Q8—24no—
307C5×Q8—22no—
308C5×Q8C2×#6714yescomplemented
309C5×D4—22no—
310C5×D4—22no—
311C5×D4—42no—
312C2×C4×C5—24no—
313C2×C4×C5—22no—
314C2×C4×C5D3×D411yescharacteristic
315C2×C4×C5D3×D412yes—
316C2×C4×C5C2×#6712yes—
317C2×C4×C5C23×D311yescharacteristic
318C22⋊D5—128no—
319C2×Dic5—32no—
320C2×Dic5—62no—
321C2×Dic5—62no—
322C2×Dic5—122no—
323D20—34no—
324D20—616no—
325D20—64no—
326D20—62no—
327C4×D5—616no—
328C4×D5—64no—
329C4×D5—62no—
330C4×D5—62no—
331C5×C8—22no—
332#168—62no—
333C2×#41—154no—
334C2×#41—302no—
335C2×#41—304no—
336C2×#41—304no—
337C22×Q8C2×D1511yescharacteristic
338C22×D4—151no—
339C22×D4—301no—
340C22×D4—301no—
341C22×D4C2×D1511yescharacteristic
342C23×C4—151no—
343C23×C4—301no—
344C2×SD16—24no—
345C2×SD16C2×D1514yescomplemented
346C2×D8—154no—
347C2×D8—304no—
348C22×C8—151no—
349C22×C8C2×D1511yescharacteristic
350#121—154no—
351#121—302no—
352C2×C4⋊C4—151no—
353C2×C22⋊C4—301no—
354#103—154no—
355#102—154no—
356C22⋊C8—154no—
357C2×C3×C5—82no—
358C2×C3×C5#44914yescomplemented
359C2×C3×C5C2×#12011yescharacteristic
360C2×C3×C5C2×#13511yescharacteristic
361C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
362D15—42no—
363D15—44no—
364C23×C3—22no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3D4×D511yescharacteristic
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
380C3×D4—22no—
381C3×D4—22no—
382C3×D4—42no—
383C2×C3×C4—22no—
384C2×C3×C4—24no—
385C2×C3×C4D4×D512yes—
386C2×C3×C4D4×D511yescharacteristic
387C2×C3×C4C2×C22⋊D512yes—
388C2×C3×C4C23×D511yescharacteristic
389#67—208no—
390C2×Dic3—52no—
391C2×Dic3—102no—
392C2×Dic3—102no—
393C2×Dic3—202no—
394D12—54no—
395D12—1016no—
396D12—102no—
397D12—104no—
398C4×D3—1016no—
399C4×D3—102no—
400C4×D3—102no—
401C4×D3—104no—
402C3×C8—22no—
403C3⋊C8—102no—
404C22×C5—42no—
405C22×C5—42no—
406C22×C5—42no—
407C22×C5—84no—
408C22×C5#91412yes—
409C22×C5#91612yes—
410C22×C5#93712yes—
411C22×C5C2×D3×D411yescharacteristic
412C2×D5—62no—
413C2×D5—62no—
414C2×D5—64no—
415C2×D5—62no—
416C2×D5—124no—
417C2×D5—128no—
418C2×D5—122no—
419C2×D5—122no—
420C4×C5—24no—
421C4×C5#93712yes—
422C4×C5C2×D3×D411yescharacteristic
423C4×C5C22×#6711yescharacteristic
424Dic5—62no—
425Dic5—122no—
426C24—21no—
427C24—151no—
428C24—301no—
429#41—308no—
430#41—3016no—
431#41—308no—
432C2×Q8—22no—
433C2×Q8—21no—
434C2×Q8#122014yescomplemented
435C2×Q8C22×D1512yes—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—22no—
439C2×D4—154no—
440C2×D4—152no—
441C2×D4—304no—
442C2×D4—308no—
443C2×D4—304no—
444C2×D4—301no—
445C2×D4—302no—
446C2×D4—604no—
447C2×D4C22×D1512yes—
448C22×C4—21no—
449C22×C4—151no—
450C22×C4—152no—
451C22×C4—152no—
452C22×C4—304no—
453C22×C4—308no—
454C22×C4—302no—
455C22×C4—302no—
456C22×C4—301no—
457C22×C4C22×D1511yescharacteristic
458SD16—28no—
459D8—308no—
460C2×C8—22no—
461C2×C8—152no—
462C2×C8—302no—
463C2×C8C22×D1512yes—
464C4⋊C4—152no—
465C4⋊C4—301no—
466C22⋊C4—304no—
467C3×C5C2×#44911yescharacteristic, complemented, Hall
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—84no—
472C22×C3#406012yes—
473C22×C3#406212yes—
474C22×C3#408312yes—
475C22×C3C2×D4×D511yescharacteristic
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#408312yes—
486C3×C4C2×D4×D511yescharacteristic
487C3×C4C22×C22⋊D511yescharacteristic
488Dic3—102no—
489Dic3—202no—
490C2×C5—82no—
491C2×C5#517214yescomplemented
492C2×C5C2×#91411yescharacteristic
493C2×C5C2×#91611yescharacteristic
494C2×C5C2×#93711yescharacteristic
495D5—122no—
496D5—124no—
497C23—22no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—152no—
502C23—302no—
503C23—302no—
504C23—304no—
505C23—302no—
506C23—302no—
507C23—602no—
508C23—602no—
509C23D4×D1511yescharacteristic
510Q8—24no—
511Q8—22no—
512Q8C2×#122014yescomplemented
513D4—22no—
514D4—22no—
515D4—42no—
516D4—154no—
517D4—3016no—
518D4—304no—
519D4—302no—
520D4—608no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—152no—
524C2×C4—3016no—
525C2×C4—302no—
526C2×C4—304no—
527C2×C4—302no—
528C2×C4—302no—
529C2×C4—302no—
530C2×C4—602no—
531C2×C4D4×D1511yescharacteristic
532C2×C4D4×D1512yes—
533C2×C4C2×#122012yes—
534C2×C4C23×D1511yescharacteristic
535C8—22no—
536C8—302no—
537C2×C3—82no—
538C2×C3#6546114yescomplemented
539C2×C3C2×#406011yescharacteristic
540C2×C3C2×#406211yescharacteristic
541C2×C3C2×#408311yescharacteristic
542D3—202no—
543D3—204no—
544C5C2×#517211yescharacteristic, complemented, Sylow
545C22—42no—
546C22—42no—
547C22—42no—
548C22—84no—
549C22—304no—
550C22—302no—
551C22—302no—
552C22—302no—
553C22—604no—
554C22—608no—
555C22—602no—
556C22—602no—
557C22#9180312yes—
558C22#9180512yes—
559C22#9182612yes—
560C22C2×D4×D1511yescharacteristic
561C4—24no—
562C4—302no—
563C4—602no—
564C4#9182612yes—
565C4C2×D4×D1511yescharacteristic
566C4C22×#122011yescharacteristic
567C3C2×#6546111yescharacteristic, complemented, Sylow
568C2—82no—
569C2—602no—
570C2—604no—
571C2#1175127314yesdirect product factor
572C2C2×#9180311yescharacteristic
573C2C2×#9180511yescharacteristic
574C2C2×#9182611yescharacteristic
subgroupG/H
centerC23D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC22×C3×C5×SD16C2
socleC23×C3×C5C2×D4
hypercenterC22×SD16D15
hypocenterC3×C5C2×#449
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#6821C2semidirect
2. C22×C3×C5×SD16C2semidirect
3. C2×#91827C2semidirect
4. C22×#6715C2semidirect
5. C2×#91119C2semidirect
6. #11751273C2direct (N × H)
7. C2×#91105C2semidirect
8. C2×#91104C2semidirect
16. C2×#6821C22semidirect
22. C2×C3×C5×SD16C22semidirect
26. #91827C22semidirect
28. C2×#6715C22semidirect
31. #91119C22semidirect
32. #91105C22semidirect
33. #91104C22semidirect
36. C22×C5×SD16D3semidirect
48. C2×C3×C5×Q8D4semidirect
67. C2×D60D4semidirect
85. C22×C3×SD16D5semidirect
104. C2×C5×SD16C2×D3semidirect
132. C3×C5×Q8C2×D4semidirect
150. D60C2×D4semidirect
169. C2×C3×SD16C2×D5semidirect
186. C2×C5×Q8#67semidirect
223. C22×SD16D15semidirect
257. C2×C3×Q8C22⋊D5semidirect
308. C5×Q8C2×#67semidirect
345. C2×SD16C2×D15semidirect
358. C2×C3×C5#449semidirect
379. C3×Q8C2×C22⋊D5semidirect
434. C2×Q8#1220semidirect
467. C3×C5C2×#449semidirect
491. C2×C5#5172semidirect
512. Q8C2×#1220semidirect
538. C2×C3#65461semidirect
544. C5C2×#5172semidirect
567. C3C2×#65461semidirect
571. C2#11751273direct (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×C3×C5×SD162
C2×#918272
C22×#67152
C2×#911192
#117512732
C2×#911052
C2×#911042
C2×#654613
C2×#51725