Finite Group Databasebeta

← C2×#11751270 #14423234

Subgroups — C2×#11751270 #14423234

Order 1920.

1992 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D15C211yesmaximal, characteristic
2C22×C3×C5×SD16C211yesmaximal, characteristic, complemented
3C2×#91835C211yesmaximal, characteristic, complemented
4C22×#6717C211yesmaximal, characteristic, complemented
5C2×#91116C211yesmaximal, characteristic, complemented
6#11751270C218yesmaximal, direct product factor
7C2×#91105C211yesmaximal, characteristic, complemented
8C2×#91104C211yesmaximal, characteristic, complemented
9C2×#65458—31nomaximal, Hall
10C24×D15—21no—
11C22×C3×C5×Q8C2211yescharacteristic, complemented
12C22×C3×C5×D4C2211yescharacteristic
13C22×#1220—21no—
14C2×D4×D15—24no—
15C2×D4×D15—24no—
16C2×D4×D15—22no—
17C2×D4×D15C2214yes—
18C22×D60C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C2×C3×C5×SD16—24no—
21C2×C3×C5×SD16C2214yescomplemented
22C22×C3×C5×C8C2211yescharacteristic, complemented
23#91835—22no—
24#91835C2214yescomplemented
25C2×#6717—24no—
26C2×#6717C2214yescomplemented
27C2×#6714—21no—
28C2×C4⋊Dic15C2211yescharacteristic, complemented
29C2×#6712—21no—
30C22×C3⋊#168C2211yescharacteristic, complemented
31#91116C2214yescomplemented
32#91105C2214yescomplemented
33#91104C2214yescomplemented
34C2×#5169—51nomaximal, Hall
35C22×D4×D5—31no—
36C22×C5×SD16D311yescharacteristic, complemented
37C2×#4092—31no—
38C22×#688—31no—
39C2×#3964—31no—
40#65458—38no—
41C2×#3953—31no—
42C2×#3952—31no—
43C24×C3×C5—21no—
44C23×D15—28no—
45C23×D15—21no—
46C23×D15—24no—
47C23×D15—44no—
48C23×D15—44no—
49C23×D15D411yescharacteristic
50C2×C3×C5×Q8—21no—
51C2×C3×C5×Q8—22no—
52C2×C3×C5×Q8—22no—
53C2×C3×C5×Q8C2312yescomplemented
54C2×C3×C5×D4—21no—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4D414yes—
57C2×C3×C5×D4C2312yes—
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5C2311yescharacteristic
60C2×#1220—28no—
61C2×#1220—24no—
62C22×Dic15—21no—
63C22×Dic15D411yescharacteristic
64D4×D15—216no—
65D4×D15—28no—
66D4×D15—28no—
67C2×D60—21no—
68C2×D60—22no—
69C2×D60D414yes—
70C2×D60C2312yes—
71C2×C4×D15—22no—
72C2×C4×D15—22no—
73C2×C4×D15D412yes—
74C2×C4×D15C2312yes—
75C3×C5×SD16—28no—
76C2×C3×C5×C8—22no—
77C2×C3×C5×C8C2312yescomplemented
78#6717—28no—
79#6714—24no—
80C4⋊Dic15—21no—
81C4⋊Dic15C2312yescomplemented
82#6712—24no—
83C2×C3⋊#168—22no—
84C2×C3⋊#168C2312yescomplemented
85C22×D3×D4—51no—
86C22×C3×SD16D511yescharacteristic, complemented
87C2×#946—51no—
88C22×#215—51no—
89C2×#832—51no—
90#5169—58no—
91C2×#821—51no—
92C2×(C2×D3)⋊C8—51no—
93C24×D5—61no—
94C22×C5×Q8C2×D311yescharacteristic, complemented
95C22×C5×D4C2×D311yescharacteristic
96C22×C22⋊D5—61no—
97C2×D4×D5—34no—
98C2×D4×D5—62no—
99C2×D4×D5—64no—
100C2×D4×D5—64no—
101C22×D20—31no—
102C22×C4×D5—31no—
103C2×C5×SD16—24no—
104C2×C5×SD16C2×D314yescomplemented
105C22×C5×C8C2×D311yescharacteristic, complemented
106#4092—34no—
107#4092—62no—
108C2×#688—34no—
109C2×#688—64no—
110C2×#685—61no—
111C2×C4⋊Dic5—31no—
112C2×#683—61no—
113C22×#168—31no—
114#3964—34no—
115#3953—34no—
116#3952—34no—
117C2×#450—151noSylow
118C23×C3×C5—24no—
119C23×C3×C5—22no—
120C23×C3×C5—42no—
121C23×C3×C5—42no—
122C23×C3×C5C2×D411yescharacteristic
123C22×D15—22no—
124C22×D15—22no—
125C22×D15—216no—
126C22×D15—24no—
127C22×D15—22no—
128C22×D15—48no—
129C22×D15—432no—
130C22×D15—42no—
131C22×D15—42no—
132C22×D15—48no—
133C22×D15SD1614yescomplemented
134C22×D15C2×D412yes—
135C3×C5×Q8—22no—
136C3×C5×Q8—22no—
137C3×C5×Q8—42no—
138C3×C5×D4—24no—
139C3×C5×D4—22no—
140C3×C5×D4C2×D414yes—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—42no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2411yescharacteristic
147#1220—216no—
148C2×Dic15—22no—
149C2×Dic15—22no—
150C2×Dic15—42no—
151C2×Dic15C2×D412yes—
152D60—24no—
153D60—22no—
154D60C2×D414yes—
155C4×D15—24no—
156C4×D15—22no—
157C4×D15—22no—
158C3×C5×C8—22no—
159C3⋊#168—22no—
160C24×D3—101no—
161C22×C3×Q8C2×D511yescharacteristic, complemented
162C22×C3×D4C2×D511yescharacteristic
163C22×#67—101no—
164C2×D3×D4—54no—
165C2×D3×D4—102no—
166C2×D3×D4—104no—
167C2×D3×D4—104no—
168C22×D12—51no—
169C22×C4×D3—51no—
170C2×C3×SD16—24no—
171C2×C3×SD16C2×D514yescomplemented
172C22×C3×C8C2×D511yescharacteristic, complemented
173#946—54no—
174#946—102no—
175C2×#215—54no—
176C2×#215—104no—
177C2×(C2×D3)⋊C4—101no—
178C2×C4⋊Dic3—51no—
179C2×Dic3⋊C4—101no—
180C22×C3⋊C8—51no—
181#832—54no—
182#821—54no—
183(C2×D3)⋊C8—54no—
184C24×C5—21no—
185C23×D5—31no—
186C23×D5—64no—
187C23×D5—68no—
188C23×D5—61no—
189C23×D5—124no—
190C23×D5—124no—
191C2×C5×Q8—21no—
192C2×C5×Q8—22no—
193C2×C5×Q8—22no—
194C2×C5×Q8C22×D312yescomplemented
195C2×C5×D4—21no—
196C2×C5×D4—22no—
197C2×C5×D4#6714yes—
198C2×C5×D4C22×D312yes—
199C22×C4×C5—21no—
200C22×C4×C5C22×D311yescharacteristic
201C2×C22⋊D5—64no—
202C2×C22⋊D5—68no—
203C22×Dic5—31no—
204C22×Dic5—61no—
205D4×D5—68no—
206D4×D5—616no—
207D4×D5—68no—
208C2×D20—34no—
209C2×D20—32no—
210C2×D20—61no—
211C2×D20—62no—
212C2×C4×D5—32no—
213C2×C4×D5—32no—
214C2×C4×D5—62no—
215C2×C4×D5—62no—
216C5×SD16—28no—
217C2×C5×C8—22no—
218C2×C5×C8C22×D312yescomplemented
219#688—68no—
220#685—64no—
221C4⋊Dic5—32no—
222C4⋊Dic5—61no—
223#683—64no—
224C2×#168—32no—
225C2×#168—62no—
226C23×D4—151no—
227C22×SD16—151no—
228C22×SD16D1511yescharacteristic, complemented
229C2×C22⋊Q8—151no—
230#450—158no—
231C2×#102—151no—
232C2×#102—151no—
233C2×C22⋊C8—151no—
234C22×C3×C5—24no—
235C22×C3×C5—42no—
236C22×C3×C5—42no—
237C22×C3×C5—48no—
238C22×C3×C5#12012yes—
239C22×C3×C5C2×SD1612yes—
240C22×C3×C5AGL(1,ℤ/8)12yes—
241C22×C3×C5C22×D411yescharacteristic
242C2×D15—22no—
243C2×D15—22no—
244C2×D15—28no—
245C2×D15—24no—
246C2×D15—432no—
247C2×D15—42no—
248C2×D15—42no—
249C2×D15—48no—
250C2×D15C2×SD1614yescomplemented
251C3×C4×C5—42no—
252C3×C4×C5#12012yes—
253C3×C4×C5C22×D411yescharacteristic
254C3×C4×C5C22×D411yescharacteristic
255Dic15—22no—
256Dic15—42no—
257C24×C3—21no—
258C23×D3—51no—
259C23×D3—104no—
260C23×D3—108no—
261C23×D3—101no—
262C23×D3—204no—
263C23×D3—204no—
264C2×C3×Q8—21no—
265C2×C3×Q8—22no—
266C2×C3×Q8—22no—
267C2×C3×Q8C22×D512yescomplemented
268C2×C3×D4—22no—
269C2×C3×D4—21no—
270C2×C3×D4C22⋊D514yes—
271C2×C3×D4C22×D512yes—
272C22×C3×C4—21no—
273C22×C3×C4C22×D511yescharacteristic
274C2×#67—104no—
275C2×#67—108no—
276C22×Dic3—51no—
277C22×Dic3—101no—
278D3×D4—108no—
279D3×D4—1016no—
280D3×D4—108no—
281C2×D12—54no—
282C2×D12—52no—
283C2×D12—101no—
284C2×D12—102no—
285C2×C4×D3—52no—
286C2×C4×D3—52no—
287C2×C4×D3—102no—
288C2×C4×D3—102no—
289C3×SD16—28no—
290C2×C3×C8—22no—
291C2×C3×C8C22×D512yescomplemented
292#215—108no—
293(C2×D3)⋊C4—104no—
294C4⋊Dic3—52no—
295C4⋊Dic3—101no—
296Dic3⋊C4—104no—
297C2×C3⋊C8—52no—
298C2×C3⋊C8—102no—
299C23×C5—24no—
300C23×C5—22no—
301C23×C5—42no—
302C23×C5—42no—
303C23×C5D3×D411yescharacteristic
304C22×D5—34no—
305C22×D5—32no—
306C22×D5—62no—
307C22×D5—62no—
308C22×D5—616no—
309C22×D5—64no—
310C22×D5—62no—
311C22×D5—128no—
312C22×D5—1232no—
313C22×D5—128no—
314C22×D5—122no—
315C22×D5—122no—
316C5×Q8—22no—
317C5×Q8—22no—
318C5×Q8—42no—
319C5×D4—24no—
320C5×D4—22no—
321C5×D4C2×#6714yes—
322C2×C4×C5—22no—
323C2×C4×C5—42no—
324C2×C4×C5D3×D411yescharacteristic
325C2×C4×C5D3×D412yes—
326C2×C4×C5C2×#6712yes—
327C2×C4×C5C23×D311yescharacteristic
328C22⋊D5—616no—
329C2×Dic5—32no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—122no—
333D20—34no—
334D20—64no—
335D20—62no—
336C4×D5—64no—
337C4×D5—62no—
338C4×D5—62no—
339C5×C8—22no—
340#168—62no—
341C25—301no—
342C22×Q8C2×D1511yescharacteristic, complemented
343C22×D4—154no—
344C22×D4—151no—
345C22×D4—302no—
346C22×D4—301no—
347C22×D4—304no—
348C22×D4—304no—
349C22×D4C2×D1511yescharacteristic
350C23×C4—151no—
351C2×SD16—24no—
352C2×SD16—154no—
353C2×SD16—304no—
354C2×SD16C2×D1514yescomplemented
355C22×C8—151no—
356C22×C8C2×D1511yescharacteristic, complemented
357C22⋊Q8—154no—
358C22⋊Q8—302no—
359C2×C4⋊C4—151no—
360C2×C4⋊C4—301no—
361C2×C22⋊C4—301no—
362#102—154no—
363#102—154no—
364C22⋊C8—154no—
365C2×C3×C5—44no—
366C2×C3×C5#45014yescomplemented
367C2×C3×C5C2×#12011yescharacteristic
368C2×C3×C5C22×SD1611yescharacteristic
369C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
370D15—24no—
371D15—44no—
372C23×C3—22no—
373C23×C3—24no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3D4×D511yescharacteristic
377C22×D3—52no—
378C22×D3—54no—
379C22×D3—102no—
380C22×D3—102no—
381C22×D3—1016no—
382C22×D3—102no—
383C22×D3—104no—
384C22×D3—208no—
385C22×D3—208no—
386C22×D3—2032no—
387C22×D3—202no—
388C22×D3—202no—
389C3×Q8—22no—
390C3×Q8—22no—
391C3×Q8—42no—
392C3×D4—22no—
393C3×D4—24no—
394C3×D4C2×C22⋊D514yes—
395C2×C3×C4—22no—
396C2×C3×C4—42no—
397C2×C3×C4D4×D512yes—
398C2×C3×C4D4×D511yescharacteristic
399C2×C3×C4C2×C22⋊D512yes—
400C2×C3×C4C23×D511yescharacteristic
401#67—1016no—
402C2×Dic3—52no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3—202no—
406D12—54no—
407D12—102no—
408D12—104no—
409C4×D3—102no—
410C4×D3—102no—
411C4×D3—104no—
412C3×C8—22no—
413C3⋊C8—102no—
414C22×C5—24no—
415C22×C5—48no—
416C22×C5—42no—
417C22×C5—42no—
418C22×C5D3×SD1612yes—
419C22×C5#91412yes—
420C22×C5#93712yes—
421C22×C5C2×D3×D411yescharacteristic
422C2×D5—34no—
423C2×D5—68no—
424C2×D5—62no—
425C2×D5—62no—
426C2×D5—64no—
427C2×D5—1232no—
428C2×D5—128no—
429C2×D5—122no—
430C2×D5—122no—
431C4×C5—42no—
432C4×C5#93712yes—
433C4×C5C2×D3×D411yescharacteristic
434C4×C5C22×#6711yescharacteristic
435Dic5—62no—
436Dic5—122no—
437C24—21no—
438C24—151no—
439C24—304no—
440C24—308no—
441C24—301no—
442C24—604no—
443C24—604no—
444C2×Q8—21no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8C22×D1512yescomplemented
448C2×D4—21no—
449C2×D4—22no—
450C2×D4—154no—
451C2×D4—152no—
452C2×D4—304no—
453C2×D4—308no—
454C2×D4—3016no—
455C2×D4—308no—
456C2×D4—308no—
457C2×D4—301no—
458C2×D4—302no—
459C2×D4#122014yes—
460C2×D4C22×D1512yes—
461C22×C4—21no—
462C22×C4—151no—
463C22×C4—152no—
464C22×C4—152no—
465C22×C4—302no—
466C22×C4—302no—
467C22×C4—301no—
468C22×C4C22×D1511yescharacteristic
469SD16—28no—
470SD16—308no—
471C2×C8—22no—
472C2×C8—152no—
473C2×C8—302no—
474C2×C8C22×D1512yescomplemented
475C4⋊C4—152no—
476C4⋊C4—304no—
477C4⋊C4—301no—
478C22⋊C4—304no—
479C3×C5C2×#45011yescharacteristic, complemented, Hall
480C22×C3—24no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—48no—
484C22×C3D5×SD1612yes—
485C22×C3#406012yes—
486C22×C3#408312yes—
487C22×C3C2×D4×D511yescharacteristic
488C2×D3—54no—
489C2×D3—102no—
490C2×D3—102no—
491C2×D3—108no—
492C2×D3—104no—
493C2×D3—2032no—
494C2×D3—202no—
495C2×D3—202no—
496C2×D3—208no—
497C3×C4—42no—
498C3×C4#408312yes—
499C3×C4C2×D4×D511yescharacteristic
500C3×C4C22×C22⋊D511yescharacteristic
501Dic3—102no—
502Dic3—202no—
503C2×C5—44no—
504C2×C5#516914yescomplemented
505C2×C5C2×D3×SD1611yescharacteristic
506C2×C5C2×#91411yescharacteristic
507C2×C5C2×#93711yescharacteristic
508D5—64no—
509D5—124no—
510C23—24no—
511C23—22no—
512C23—42no—
513C23—42no—
514C23—154no—
515C23—152no—
516C23—3016no—
517C23—302no—
518C23—302no—
519C23—304no—
520C23—302no—
521C23—608no—
522C23—6032no—
523C23—608no—
524C23—602no—
525C23—602no—
526C23D4×D1511yescharacteristic
527Q8—22no—
528Q8—22no—
529Q8—42no—
530D4—24no—
531D4—22no—
532D4—154no—
533D4—3016no—
534D4—304no—
535D4—302no—
536D4C2×#122014yes—
537C2×C4—22no—
538C2×C4—42no—
539C2×C4—152no—
540C2×C4—302no—
541C2×C4—304no—
542C2×C4—302no—
543C2×C4—302no—
544C2×C4—302no—
545C2×C4—602no—
546C2×C4D4×D1511yescharacteristic
547C2×C4D4×D1512yes—
548C2×C4C2×#122012yes—
549C2×C4C23×D1511yescharacteristic
550C8—22no—
551C8—302no—
552C2×C3—44no—
553C2×C3#6545814yescomplemented
554C2×C3C2×D5×SD1611yescharacteristic
555C2×C3C2×#406011yescharacteristic
556C2×C3C2×#408311yescharacteristic
557D3—104no—
558D3—204no—
559C5C2×#516911yescharacteristic, complemented, Sylow
560C22—24no—
561C22—48no—
562C22—42no—
563C22—42no—
564C22—154no—
565C22—302no—
566C22—308no—
567C22—302no—
568C22—304no—
569C22—6032no—
570C22—608no—
571C22—602no—
572C22—602no—
573C22SD16×D1512yes—
574C22#9180312yes—
575C22#9182612yes—
576C22C2×D4×D1511yescharacteristic
577C4—42no—
578C4—302no—
579C4—602no—
580C4#9182612yes—
581C4C2×D4×D1511yescharacteristic
582C4C22×#122011yescharacteristic
583C3C2×#6545811yescharacteristic, complemented, Sylow
584C2—44no—
585C2—304no—
586C2—604no—
587C2#1175127014yesdirect product factor
588C2C2×SD16×D1511yescharacteristic
589C2C2×#9180311yescharacteristic
590C2C2×#9182611yescharacteristic
subgroupG/H
centerC23D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC22×C3×C5×SD16C2
socleC23×C3×C5C2×D4
prime radicalC22×D4×D15C2
hypercenterC22×SD16D15
hypocenterC3×C5C2×#450
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
2. C22×C3×C5×SD16C2semidirect
3. C2×#91835C2semidirect
4. C22×#6717C2semidirect
5. C2×#91116C2semidirect
6. #11751270C2direct (N × H)
7. C2×#91105C2semidirect
8. C2×#91104C2semidirect
11. C22×C3×C5×Q8C22semidirect
21. C2×C3×C5×SD16C22semidirect
22. C22×C3×C5×C8C22semidirect
24. #91835C22semidirect
26. C2×#6717C22semidirect
28. C2×C4⋊Dic15C22semidirect
30. C22×C3⋊#168C22semidirect
31. #91116C22semidirect
32. #91105C22semidirect
33. #91104C22semidirect
36. C22×C5×SD16D3semidirect
53. C2×C3×C5×Q8C23semidirect
77. C2×C3×C5×C8C23semidirect
81. C4⋊Dic15C23semidirect
84. C2×C3⋊#168C23semidirect
86. C22×C3×SD16D5semidirect
94. C22×C5×Q8C2×D3semidirect
104. C2×C5×SD16C2×D3semidirect
105. C22×C5×C8C2×D3semidirect
133. C22×D15SD16semidirect
161. C22×C3×Q8C2×D5semidirect
171. C2×C3×SD16C2×D5semidirect
172. C22×C3×C8C2×D5semidirect
194. C2×C5×Q8C22×D3semidirect
218. C2×C5×C8C22×D3semidirect
228. C22×SD16D15semidirect
250. C2×D15C2×SD16semidirect
267. C2×C3×Q8C22×D5semidirect
291. C2×C3×C8C22×D5semidirect
342. C22×Q8C2×D15semidirect
354. C2×SD16C2×D15semidirect
356. C22×C8C2×D15semidirect
366. C2×C3×C5#450semidirect
447. C2×Q8C22×D15semidirect
474. C2×C8C22×D15semidirect
479. C3×C5C2×#450semidirect
504. C2×C5#5169semidirect
553. C2×C3#65458semidirect
559. C5C2×#5169semidirect
583. C3C2×#65458semidirect
587. C2#11751270direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D152
C22×C3×C5×SD162
C2×#918352
C22×#67172
C2×#911162
#117512702
C2×#911052
C2×#911042
C2×#654583
C2×#51695