Finite Group Databasebeta

← C2×#11751271 #14423291

Subgroups — C2×#11751271 #14423291

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×D15C211yesmaximal, characteristic, complemented
2C22×C3×C5×SD16C211yesmaximal, characteristic, complemented
3C2×#91827C211yesmaximal, characteristic
4C22×#6716C211yesmaximal, characteristic, complemented
5C2×#91119C211yesmaximal, characteristic, complemented
6#11751271C218yesmaximal, direct product factor
7C2×#91104C211yesmaximal, characteristic, complemented
8C2×#91100C211yesmaximal, characteristic, complemented
9C2×#65459—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C5×D4C2211yescharacteristic
12C22×#1220—21no—
13C2×Q8×D15—24no—
14C2×Q8×D15—22no—
15C2×Q8×D15—24no—
16C2×Q8×D15C2214yescomplemented
17C22×C4×D15—21no—
18C22×C4×D15C2211yescharacteristic
19C22×Dic30—21no—
20C22×Dic30C2211yescharacteristic
21C2×C3×C5×SD16—24no—
22C2×C3×C5×SD16C2214yescomplemented
23C22×C3×C5×C8C2211yescharacteristic
24C2×#6719—21no—
25#91827—22no—
26#91827C2214yes—
27C2×#6716—24no—
28C2×#6716C2214yescomplemented
29C2×C4⋊Dic15C2211yescharacteristic
30C22×C3⋊#168C2211yescharacteristic
31#91119C2214yescomplemented
32#91104C2214yescomplemented
33#91100C2214yescomplemented
34C2×#5170—51nomaximal, Hall
35C22×Q8×D5—31no—
36C22×C5×SD16D311yescharacteristic, complemented
37C2×#4084—31no—
38C22×#687—31no—
39C2×#3967—31no—
40#65459—38no—
41C2×#3952—31no—
42C2×#3948—31no—
43C24×C3×C5—21no—
44C23×D15D411yescharacteristic
45C2×C3×C5×Q8—22no—
46C2×C3×C5×Q8—21no—
47C2×C3×C5×Q8D414yescomplemented
48C2×C3×C5×Q8C2312yes—
49C2×C3×C5×D4—22no—
50C2×C3×C5×D4—22no—
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4C2312yes—
53C22×C3×C4×C5—21no—
54C22×C3×C4×C5C2311yescharacteristic
55C2×#1220—24no—
56C2×#1220—44no—
57C22×Dic15—21no—
58C22×Dic15—21no—
59C22×Dic15D411yescharacteristic
60Q8×D15—216no—
61Q8×D15—28no—
62Q8×D15—28no—
63C2×C4×D15—28no—
64C2×C4×D15—24no—
65C2×C4×D15—22no—
66C2×C4×D15—22no—
67C2×C4×D15D412yes—
68C2×C4×D15C2312yes—
69C2×Dic30—28no—
70C2×Dic30—21no—
71C2×Dic30—22no—
72C2×Dic30—24no—
73C2×Dic30D414yescomplemented
74C2×Dic30C2312yes—
75C3×C5×SD16—28no—
76C2×C3×C5×C8—22no—
77C2×C3×C5×C8C2312yes—
78#6719—24no—
79#6716—28no—
80C4⋊Dic15—21no—
81C4⋊Dic15C2312yes—
82C2×C3⋊#168—22no—
83C2×C3⋊#168C2312yes—
84C22×D3×Q8—51no—
85C22×C3×SD16D511yescharacteristic, complemented
86C2×#938—51no—
87C22×#214—51no—
88C2×#835—51no—
89#5170—58no—
90C2×(C2×D3)⋊C8—51no—
91C2×#816—51no—
92C22×C5×Q8C2×D311yescharacteristic
93C22×C5×D4C2×D311yescharacteristic
94C22×C22⋊D5—61no—
95C2×Q8×D5—34no—
96C2×Q8×D5—64no—
97C2×Q8×D5—62no—
98C2×Q8×D5—64no—
99C22×C4×D5—31no—
100C22×C4×D5—61no—
101C22×Dic10—31no—
102C22×Dic10—61no—
103C2×C5×SD16—24no—
104C2×C5×SD16C2×D314yescomplemented
105C22×C5×C8C2×D311yescharacteristic
106C2×C22⋊Dic5—61no—
107#4084—34no—
108#4084—62no—
109C2×#687—34no—
110C2×#687—64no—
111C2×C4⋊Dic5—31no—
112C22×#168—31no—
113#3967—34no—
114#3952—34no—
115#3948—34no—
116C2×#448—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—22no—
124C22×D15SD1614yescomplemented
125C22×D15C2×D412yes—
126C3×C5×Q8—24no—
127C3×C5×Q8—22no—
128C3×C5×Q8C2×D414yescomplemented
129C3×C5×D4—22no—
130C3×C5×D4—22no—
131C3×C5×D4—42no—
132C2×C3×C4×C5—24no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2411yescharacteristic
138#1220—48no—
139C2×Dic15—22no—
140C2×Dic15—24no—
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15—42no—
144C2×Dic15C2×D412yes—
145C4×D15—216no—
146C4×D15—24no—
147C4×D15—22no—
148C4×D15—22no—
149Dic30—216no—
150Dic30—24no—
151Dic30—22no—
152Dic30C2×D414yescomplemented
153C3×C5×C8—22no—
154C3⋊#168—22no—
155C22×C3×Q8C2×D511yescharacteristic
156C22×C3×D4C2×D511yescharacteristic
157C22×#67—101no—
158C2×D3×Q8—54no—
159C2×D3×Q8—104no—
160C2×D3×Q8—102no—
161C2×D3×Q8—104no—
162C22×C4×D3—51no—
163C22×C4×D3—101no—
164C22×Dic6—51no—
165C22×Dic6—101no—
166C2×C3×SD16—24no—
167C2×C3×SD16C2×D514yescomplemented
168C22×C3×C8C2×D511yescharacteristic
169C2×#217—101no—
170#938—54no—
171#938—102no—
172C2×#214—54no—
173C2×#214—104no—
174C2×C4⋊Dic3—51no—
175C22×C3⋊C8—51no—
176#835—54no—
177(C2×D3)⋊C8—54no—
178#816—54no—
179C24×C5—21no—
180C23×D5—31no—
181C2×C5×Q8—22no—
182C2×C5×Q8—21no—
183C2×C5×Q8#6714yescomplemented
184C2×C5×Q8C22×D312yes—
185C2×C5×D4—22no—
186C2×C5×D4—21no—
187C2×C5×D4—22no—
188C2×C5×D4C22×D312yes—
189C22×C4×C5—21no—
190C22×C4×C5C22×D311yescharacteristic
191C2×C22⋊D5—64no—
192C2×C22⋊D5—124no—
193C22×Dic5—31no—
194C22×Dic5—61no—
195C22×Dic5—61no—
196Q8×D5—68no—
197Q8×D5—616no—
198Q8×D5—68no—
199C2×C4×D5—32no—
200C2×C4×D5—32no—
201C2×C4×D5—64no—
202C2×C4×D5—68no—
203C2×C4×D5—62no—
204C2×C4×D5—62no—
205C2×Dic10—34no—
206C2×Dic10—32no—
207C2×Dic10—64no—
208C2×Dic10—68no—
209C2×Dic10—61no—
210C2×Dic10—62no—
211C5×SD16—28no—
212C2×C5×C8—22no—
213C2×C5×C8C22×D312yes—
214C22⋊Dic5—64no—
215#687—68no—
216C4⋊Dic5—32no—
217C4⋊Dic5—61no—
218C2×#168—32no—
219C2×#168—62no—
220C23×Q8—151no—
221C22×SD16—151no—
222C22×SD16D1511yescharacteristic, complemented
223C2×#121—151no—
224#448—158no—
225C2×#103—151no—
226C2×#103—151no—
227C2×C22⋊C8—151no—
228C22×C3×C5—42no—
229C22×C3×C5—42no—
230C22×C3×C5—42no—
231C22×C3×C5—84no—
232C22×C3×C5#12012yes—
233C22×C3×C5C2×SD1612yes—
234C22×C3×C5#13712yes—
235C22×C3×C5C22×D411yescharacteristic
236C2×D15—22no—
237C2×D15—22no—
238C2×D15—28no—
239C2×D15C2×SD1614yescomplemented
240C3×C4×C5—24no—
241C3×C4×C5#12012yes—
242C3×C4×C5C22×D411yescharacteristic
243C3×C4×C5C22×D411yescharacteristic
244Dic15—22no—
245Dic15—24no—
246Dic15—42no—
247C24×C3—21no—
248C23×D3—51no—
249C2×C3×Q8—21no—
250C2×C3×Q8—22no—
251C2×C3×Q8C22⋊D514yescomplemented
252C2×C3×Q8C22×D512yes—
253C2×C3×D4—22no—
254C2×C3×D4—21no—
255C2×C3×D4—22no—
256C2×C3×D4C22×D512yes—
257C22×C3×C4—21no—
258C22×C3×C4C22×D511yescharacteristic
259C2×#67—104no—
260C2×#67—204no—
261C22×Dic3—51no—
262C22×Dic3—101no—
263C22×Dic3—101no—
264D3×Q8—108no—
265D3×Q8—1016no—
266D3×Q8—108no—
267C2×C4×D3—52no—
268C2×C4×D3—52no—
269C2×C4×D3—104no—
270C2×C4×D3—108no—
271C2×C4×D3—102no—
272C2×C4×D3—102no—
273C2×Dic6—54no—
274C2×Dic6—52no—
275C2×Dic6—104no—
276C2×Dic6—108no—
277C2×Dic6—101no—
278C2×Dic6—102no—
279C3×SD16—28no—
280C2×C3×C8—22no—
281C2×C3×C8C22×D512yes—
282#217—104no—
283#214—108no—
284C4⋊Dic3—52no—
285C4⋊Dic3—101no—
286C2×C3⋊C8—52no—
287C2×C3⋊C8—102no—
288C23×C5—22no—
289C23×C5—42no—
290C23×C5—42no—
291C23×C5—42no—
292C23×C5D3×D411yescharacteristic
293C22×D5—34no—
294C22×D5—32no—
295C22×D5—62no—
296C22×D5—62no—
297C5×Q8—24no—
298C5×Q8—22no—
299C5×Q8C2×#6714yescomplemented
300C5×D4—22no—
301C5×D4—22no—
302C5×D4—42no—
303C2×C4×C5—24no—
304C2×C4×C5—22no—
305C2×C4×C5D3×D411yescharacteristic
306C2×C4×C5D3×D412yes—
307C2×C4×C5C2×#6712yes—
308C2×C4×C5C23×D311yescharacteristic
309C22⋊D5—128no—
310C2×Dic5—32no—
311C2×Dic5—64no—
312C2×Dic5—62no—
313C2×Dic5—62no—
314C2×Dic5—62no—
315C2×Dic5—122no—
316C4×D5—616no—
317C4×D5—64no—
318C4×D5—62no—
319C4×D5—62no—
320Dic10—34no—
321Dic10—616no—
322Dic10—64no—
323Dic10—62no—
324C5×C8—22no—
325#168—62no—
326C22×Q8—154no—
327C22×Q8—151no—
328C22×Q8—301no—
329C22×Q8—302no—
330C22×Q8—304no—
331C22×Q8—304no—
332C22×Q8C2×D1511yescharacteristic
333C22×D4—301no—
334C22×D4C2×D1511yescharacteristic
335C23×C4—151no—
336C23×C4—301no—
337C2×SD16—24no—
338C2×SD16—154no—
339C2×SD16—304no—
340C2×SD16C2×D1514yescomplemented
341C22×C8—151no—
342C22×C8C2×D1511yescharacteristic
343#121—154no—
344#121—302no—
345C2×C4⋊C4—151no—
346C2×C22⋊C4—301no—
347#103—154no—
348#103—154no—
349C22⋊C8—154no—
350C2×C3×C5—82no—
351C2×C3×C5#44814yescomplemented
352C2×C3×C5C2×#12011yescharacteristic
353C2×C3×C5C22×SD1611yescharacteristic
354C2×C3×C5C2×#13711yescharacteristic
355D15—24no—
356C23×C3—22no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3D4×D511yescharacteristic
361C22×D3—52no—
362C22×D3—54no—
363C22×D3—102no—
364C22×D3—102no—
365C3×Q8—22no—
366C3×Q8—24no—
367C3×Q8C2×C22⋊D514yescomplemented
368C3×D4—22no—
369C3×D4—22no—
370C3×D4—42no—
371C2×C3×C4—22no—
372C2×C3×C4—24no—
373C2×C3×C4D4×D512yes—
374C2×C3×C4D4×D511yescharacteristic
375C2×C3×C4C2×C22⋊D512yes—
376C2×C3×C4C23×D511yescharacteristic
377#67—208no—
378C2×Dic3—52no—
379C2×Dic3—102no—
380C2×Dic3—104no—
381C2×Dic3—102no—
382C2×Dic3—102no—
383C2×Dic3—202no—
384C4×D3—1016no—
385C4×D3—102no—
386C4×D3—102no—
387C4×D3—104no—
388Dic6—54no—
389Dic6—1016no—
390Dic6—102no—
391Dic6—104no—
392C3×C8—22no—
393C3⋊C8—102no—
394C22×C5—42no—
395C22×C5—42no—
396C22×C5—42no—
397C22×C5—84no—
398C22×C5D3×SD1612yes—
399C22×C5#91512yes—
400C22×C5#93712yes—
401C22×C5C2×D3×D411yescharacteristic
402C2×D5—34no—
403C2×D5—68no—
404C2×D5—62no—
405C2×D5—62no—
406C4×C5—24no—
407C4×C5#93712yes—
408C4×C5C2×D3×D411yescharacteristic
409C4×C5C22×#6711yescharacteristic
410Dic5—64no—
411Dic5—62no—
412Dic5—122no—
413C24—21no—
414C24—151no—
415C2×Q8—22no—
416C2×Q8—21no—
417C2×Q8—154no—
418C2×Q8—152no—
419C2×Q8—304no—
420C2×Q8—308no—
421C2×Q8—308no—
422C2×Q8—3016no—
423C2×Q8—308no—
424C2×Q8—301no—
425C2×Q8—302no—
426C2×Q8#122014yescomplemented
427C2×Q8C22×D1512yes—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—304no—
432C2×D4—604no—
433C2×D4C22×D1512yes—
434C22×C4—21no—
435C22×C4—151no—
436C22×C4—152no—
437C22×C4—152no—
438C22×C4—304no—
439C22×C4—308no—
440C22×C4—301no—
441C22×C4—302no—
442C22×C4—302no—
443C22×C4—301no—
444C22×C4C22×D1511yescharacteristic
445SD16—28no—
446SD16—308no—
447C2×C8—22no—
448C2×C8—152no—
449C2×C8—302no—
450C2×C8C22×D1512yes—
451C4⋊C4—152no—
452C4⋊C4—301no—
453C22⋊C4—304no—
454C3×C5C2×#44811yescharacteristic, complemented, Hall
455C22×C3—42no—
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—84no—
459C22×C3D5×SD1612yes—
460C22×C3#406112yes—
461C22×C3#408312yes—
462C22×C3C2×D4×D511yescharacteristic
463C2×D3—54no—
464C2×D3—102no—
465C2×D3—102no—
466C2×D3—108no—
467C3×C4—24no—
468C3×C4#408312yes—
469C3×C4C2×D4×D511yescharacteristic
470C3×C4C22×C22⋊D511yescharacteristic
471Dic3—104no—
472Dic3—102no—
473Dic3—202no—
474C2×C5—82no—
475C2×C5#517014yescomplemented
476C2×C5C2×D3×SD1611yescharacteristic
477C2×C5C2×#91511yescharacteristic
478C2×C5C2×#93711yescharacteristic
479D5—64no—
480C23—22no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—154no—
485C23—152no—
486C23—302no—
487C23—302no—
488C23D4×D1511yescharacteristic
489Q8—24no—
490Q8—22no—
491Q8—154no—
492Q8—3016no—
493Q8—304no—
494Q8—302no—
495Q8C2×#122014yescomplemented
496D4—22no—
497D4—22no—
498D4—42no—
499D4—608no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—152no—
503C2×C4—3016no—
504C2×C4—302no—
505C2×C4—304no—
506C2×C4—302no—
507C2×C4—304no—
508C2×C4—302no—
509C2×C4—302no—
510C2×C4—302no—
511C2×C4—602no—
512C2×C4D4×D1511yescharacteristic
513C2×C4D4×D1512yes—
514C2×C4C2×#122012yes—
515C2×C4C23×D1511yescharacteristic
516C8—22no—
517C8—302no—
518C2×C3—82no—
519C2×C3#6545914yescomplemented
520C2×C3C2×D5×SD1611yescharacteristic
521C2×C3C2×#406111yescharacteristic
522C2×C3C2×#408311yescharacteristic
523D3—104no—
524C5C2×#517011yescharacteristic, complemented, Sylow
525C22—42no—
526C22—42no—
527C22—42no—
528C22—84no—
529C22—154no—
530C22—302no—
531C22—308no—
532C22—302no—
533C22SD16×D1512yes—
534C22#9180412yes—
535C22#9182612yes—
536C22C2×D4×D1511yescharacteristic
537C4—24no—
538C4—302no—
539C4—304no—
540C4—602no—
541C4#9182612yes—
542C4C2×D4×D1511yescharacteristic
543C4C22×#122011yescharacteristic
544C3C2×#6545911yescharacteristic, complemented, Sylow
545C2—82no—
546C2—304no—
547C2#1175127114yesdirect product factor
548C2C2×SD16×D1511yescharacteristic
549C2C2×#9180411yescharacteristic
550C2C2×#9182611yescharacteristic
subgroupG/H
centerC23D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC22×C3×C5×SD16C2
socleC23×C3×C5C2×D4
prime radicalC2×#91827C2
hypercenterC22×SD16D15
hypocenterC3×C5C2×#448
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×Q8×D15C2semidirect
2. C22×C3×C5×SD16C2semidirect
4. C22×#6716C2semidirect
5. C2×#91119C2semidirect
6. #11751271C2direct (N × H)
7. C2×#91104C2semidirect
8. C2×#91100C2semidirect
16. C2×Q8×D15C22semidirect
22. C2×C3×C5×SD16C22semidirect
28. C2×#6716C22semidirect
31. #91119C22semidirect
32. #91104C22semidirect
33. #91100C22semidirect
36. C22×C5×SD16D3semidirect
47. C2×C3×C5×Q8D4semidirect
73. C2×Dic30D4semidirect
85. C22×C3×SD16D5semidirect
104. C2×C5×SD16C2×D3semidirect
124. C22×D15SD16semidirect
128. C3×C5×Q8C2×D4semidirect
152. Dic30C2×D4semidirect
167. C2×C3×SD16C2×D5semidirect
183. C2×C5×Q8#67semidirect
222. C22×SD16D15semidirect
239. C2×D15C2×SD16semidirect
251. C2×C3×Q8C22⋊D5semidirect
299. C5×Q8C2×#67semidirect
340. C2×SD16C2×D15semidirect
351. C2×C3×C5#448semidirect
367. C3×Q8C2×C22⋊D5semidirect
426. C2×Q8#1220semidirect
454. C3×C5C2×#448semidirect
475. C2×C5#5170semidirect
495. Q8C2×#1220semidirect
519. C2×C3#65459semidirect
524. C5C2×#5170semidirect
544. C3C2×#65459semidirect
547. C2#11751271direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D152
C22×C3×C5×SD162
C2×#918272
C22×#67162
C2×#911192
#117512712
C2×#911042
C2×#911002
C2×#654593
C2×#51705