Finite Group Databasebeta

← C2×#11749286 #14423326

Subgroups — C2×#11749286 #14423326

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×#688C211yesmaximal, characteristic, complemented
3C2×#91465C211yesmaximal, characteristic
4C22×#6657C211yesmaximal, characteristic, complemented
5C2×C5×#835C211yesmaximal, characteristic, complemented
6#11749286C218yesmaximal, direct product factor
7C2×#90975C211yesmaximal, characteristic, complemented
8C2×#90957C211yesmaximal, characteristic, complemented
9C2×#65095—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×Q8×D15—24no—
12C2×Q8×D15—22no—
13C2×Q8×D15—24no—
14C2×Q8×D15C2214yescomplemented
15C22×C4×D15—21no—
16C22×C4×D15C2211yescharacteristic
17C22×Dic30—21no—
18C22×Dic30C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×#1202—21no—
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C2×C3×#688—24no—
24C2×C3×#688C2214yescomplemented
25C22×C3×#168C2211yescharacteristic
26C2×#6665—21no—
27#91465—22no—
28#91465C2214yes—
29C2×#6657—24no—
30C2×#6657C2214yescomplemented
31C5×#835C2214yescomplemented
32#90975C2214yescomplemented
33#90957C2214yescomplemented
34C2×#5170—51nomaximal, Hall
35C22×Q8×D5—31no—
36C22×#688D311yescharacteristic, complemented
37C22×#677—31no—
38C2×#4041—31no—
39C2×C5×#103—31no—
40C2×#3952—31no—
41C2×#3942—31no—
42#65095—38no—
43C23×D15D411yescharacteristic
44C23×C3×D5—21no—
45C2×C3×C5×Q8—22no—
46C2×C3×C5×Q8—21no—
47C2×C3×C5×Q8D414yescomplemented
48C2×C3×C5×Q8C2312yes—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5C2311yescharacteristic
51C22×Dic15—21no—
52C22×Dic15D411yescharacteristic
53Q8×D15—216no—
54Q8×D15—28no—
55Q8×D15—28no—
56C2×C4×D15—28no—
57C2×C4×D15—24no—
58C2×C4×D15—22no—
59C2×C4×D15—22no—
60C2×C4×D15D412yes—
61C2×C4×D15C2312yes—
62C2×Dic30—28no—
63C2×Dic30—21no—
64C2×Dic30—22no—
65C2×Dic30—24no—
66C2×Dic30D414yescomplemented
67C2×Dic30C2312yes—
68C22×C5×Dic3—21no—
69C2×C3×D20—22no—
70C2×C3×D20—22no—
71C2×C3×D20—21no—
72C2×C3×D20C2312yes—
73C2×#1202—24no—
74C2×#1202—44no—
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3C2312yes—
77C2×C5×C3⋊C8—22no—
78C2×C5×C3⋊C8C2312yes—
79C3×#688—28no—
80C2×C3×#168—22no—
81C2×C3×#168C2312yes—
82#6665—24no—
83#6657—28no—
84C22×D3×Q8—51no—
85C22×C3×SD16—51no—
86C2×#938—51no—
87C22×#214—51no—
88C2×#835D511yescharacteristic, complemented
89#5170—58no—
90C2×(C2×D3)⋊C8—51no—
91C2×#816—51no—
92C22×C5×Q8C2×D311yescharacteristic
93C2×Q8×D5—34no—
94C2×Q8×D5—64no—
95C2×Q8×D5—62no—
96C2×Q8×D5—64no—
97C22×D20—61no—
98C22×D20C2×D311yescharacteristic
99C22×C4×D5—31no—
100C22×C4×D5—61no—
101C22×Dic10—31no—
102C22×Dic10—61no—
103C22×C5×C8—31no—
104C2×C5×C4⋊C4—31no—
105C2×#688—24no—
106C2×#688C2×D314yescomplemented
107C2×#685—61no—
108C22×#168C2×D311yescharacteristic
109C2×#677—34no—
110C2×#677—64no—
111#4041—34no—
112#4041—62no—
113C5×#103—34no—
114#3952—34no—
115#3942—34no—
116C2×#448—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×D15—22no—
119C22×D15—22no—
120C22×D15SD1614yescomplemented
121C22×D15C2×D412yes—
122C22×C3×D5—22no—
123C22×C3×D5—42no—
124C22×C3×D5—42no—
125C22×C3×D5—42no—
126C3×C5×Q8—24no—
127C3×C5×Q8—22no—
128C3×C5×Q8C2×D414yescomplemented
129C2×C3×C4×C5—24no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D412yes—
133C2×C3×C4×C5C2×D412yes—
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—22no—
136C2×Dic15—24no—
137C2×Dic15—22no—
138C2×Dic15C2×D412yes—
139C4×D15—216no—
140C4×D15—24no—
141C4×D15—22no—
142C4×D15—22no—
143Dic30—216no—
144Dic30—24no—
145Dic30—22no—
146Dic30C2×D414yescomplemented
147C2×C5×Dic3—22no—
148C2×C5×Dic3—42no—
149C3×D20—22no—
150C3×D20—22no—
151C3×D20—42no—
152#1202—48no—
153C3×#168—22no—
154C5×C3⋊C8—22no—
155C22×C3×Q8C2×D511yescharacteristic
156C22×C3×D4—51no—
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—54no—
167C2×C3×SD16—104no—
168C22×C3×C8—51no—
169C2×#217—101no—
170#938—54no—
171#938—102no—
172C2×#214—54no—
173C2×#214—104no—
174C2×C4⋊Dic3C2×D511yescharacteristic
175C22×C3⋊C8C2×D511yescharacteristic
176#835C2×D514yescomplemented
177(C2×D3)⋊C8—54no—
178#816—54no—
179C23×D5—21no—
180C23×D5—31no—
181C2×C5×Q8—22no—
182C2×C5×Q8—21no—
183C2×C5×Q8#6714yescomplemented
184C2×C5×Q8C22×D312yes—
185C22×C4×C5—21no—
186C22×C4×C5—61no—
187C22×C4×C5C22×D311yescharacteristic
188C22×Dic5—31no—
189C22×Dic5—61no—
190Q8×D5—68no—
191Q8×D5—616no—
192Q8×D5—68no—
193C2×D20—22no—
194C2×D20—22no—
195C2×D20—21no—
196C2×D20—64no—
197C2×D20—124no—
198C2×D20C22×D312yes—
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—
211C2×C5×C8—32no—
212C2×C5×C8—62no—
213C5×C4⋊C4—32no—
214C5×C4⋊C4—61no—
215#688—28no—
216#685—64no—
217C2×#168—22no—
218C2×#168C22×D312yes—
219#677—68no—
220C23×Q8—151no—
221C22×SD16—51no—
222C22×SD16—151no—
223C2×#121—151no—
224#448—158no—
225C2×#103—31no—
226C2×#103—151no—
227C2×C22⋊C8—151no—
228C22×C3×C5#12012yes—
229C22×C3×C5C2×SD1612yes—
230C22×C3×C5#13712yes—
231C22×C3×C5C22×D411yescharacteristic
232C2×D15—22no—
233C2×D15—22no—
234C2×D15—28no—
235C2×D15C2×SD1614yescomplemented
236C2×C3×D5—42no—
237C2×C3×D5—42no—
238C2×C3×D5—42no—
239C2×C3×D5—84no—
240C3×C4×C5—24no—
241C3×C4×C5#12012yes—
242C3×C4×C5C22×D411yescharacteristic
243C3×C4×C5C22×D411yescharacteristic
244Dic15—22no—
245Dic15—24no—
246C5×Dic3—42no—
247C24×C3—101no—
248C23×D3—51no—
249C2×C3×Q8—21no—
250C2×C3×Q8—22no—
251C2×C3×Q8D2014yescomplemented
252C2×C3×Q8C22×D512yes—
253C2×C3×D4—52no—
254C2×C3×D4—102no—
255C2×C3×D4—102no—
256C2×C3×D4—101no—
257C22×C3×C4—21no—
258C22×C3×C4C22×D511yescharacteristic
259C2×#67—104no—
260C2×#67—204no—
261C22×Dic3—21no—
262C22×Dic3—51no—
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—102no—
278C2×Dic6—101no—
279C3×SD16—108no—
280C2×C3×C8—52no—
281C2×C3×C8—102no—
282#217—104no—
283#214—108no—
284C4⋊Dic3—21no—
285C4⋊Dic3C22×D512yes—
286C2×C3⋊C8—22no—
287C2×C3⋊C8C22×D512yes—
288C23×C5D3×D411yescharacteristic
289C22×D5—22no—
290C22×D5—34no—
291C22×D5—32no—
292C22×D5—42no—
293C22×D5—42no—
294C22×D5—42no—
295C22×D5—62no—
296C22×D5—62no—
297C5×Q8—24no—
298C5×Q8—22no—
299C5×Q8C2×#6714yescomplemented
300C2×C4×C5—24no—
301C2×C4×C5—22no—
302C2×C4×C5—62no—
303C2×C4×C5—122no—
304C2×C4×C5D3×D411yescharacteristic
305C2×C4×C5D3×D412yes—
306C2×C4×C5C2×#6712yes—
307C2×C4×C5C23×D311yescharacteristic
308C2×Dic5—32no—
309C2×Dic5—64no—
310C2×Dic5—62no—
311C2×Dic5—62no—
312D20—22no—
313D20—22no—
314D20—42no—
315D20—128no—
316C4×D5—616no—
317C4×D5—64no—
318C4×D5—62no—
319C4×D5—62no—
320Dic10—34no—
321Dic10—616no—
322Dic10—64no—
323Dic10—62no—
324C5×C8—62no—
325#168—22no—
326C22×Q8—154no—
327C22×Q8—151no—
328C22×Q8—301no—
329C22×Q8—302no—
330C22×Q8—304no—
331C22×Q8—304no—
332C22×Q8D3×D511yescharacteristic
333C22×D4—51no—
334C22×D4—301no—
335C23×C4—151no—
336C23×C4—301no—
337C2×SD16—54no—
338C2×SD16—104no—
339C2×SD16—154no—
340C2×SD16—304no—
341C22×C8—31no—
342C22×C8—51no—
343#121—154no—
344#121—302no—
345C2×C4⋊C4—31no—
346C2×C22⋊C4—301no—
347#103—34no—
348#103—154no—
349C22⋊C8—154no—
350C2×C3×C5#44814yescomplemented
351C2×C3×C5C2×#12011yescharacteristic
352C2×C3×C5C22×SD1611yescharacteristic
353C2×C3×C5C2×#13711yescharacteristic
354D15—24no—
355C3×D5—82no—
356C23×C3—102no—
357C23×C3—202no—
358C23×C3—202no—
359C23×C3—202no—
360C23×C3D4×D511yescharacteristic
361C22×D3—52no—
362C22×D3—54no—
363C22×D3—102no—
364C22×D3—102no—
365C3×Q8—22no—
366C3×Q8—24no—
367C3×Q8C2×D2014yescomplemented
368C3×D4—102no—
369C3×D4—102no—
370C3×D4—202no—
371C2×C3×C4—22no—
372C2×C3×C4—24no—
373C2×C3×C4C2×D2012yes—
374C2×C3×C4D4×D512yes—
375C2×C3×C4D4×D511yescharacteristic
376C2×C3×C4C23×D511yescharacteristic
377#67—208no—
378C2×Dic3—22no—
379C2×Dic3—42no—
380C2×Dic3—52no—
381C2×Dic3—102no—
382C2×Dic3—104no—
383C2×Dic3—102no—
384C4×D3—1016no—
385C4×D3—102no—
386C4×D3—102no—
387C4×D3—104no—
388Dic6—54no—
389Dic6—1016no—
390Dic6—102no—
391Dic6—104no—
392C3×C8—102no—
393C3⋊C8—22no—
394C22×C5D3×SD1612yes—
395C22×C5#91512yes—
396C22×C5#93712yes—
397C22×C5C2×D3×D411yescharacteristic
398C2×D5—34no—
399C2×D5—42no—
400C2×D5—42no—
401C2×D5—42no—
402C2×D5—68no—
403C2×D5—62no—
404C2×D5—62no—
405C2×D5—84no—
406C4×C5—24no—
407C4×C5—122no—
408C4×C5#93712yes—
409C4×C5C2×D3×D411yescharacteristic
410C4×C5C22×#6711yescharacteristic
411Dic5—64no—
412Dic5—62no—
413C24—101no—
414C24—151no—
415C2×Q8—21no—
416C2×Q8—22no—
417C2×Q8—154no—
418C2×Q8—152no—
419C2×Q8—304no—
420C2×Q8—308no—
421C2×Q8—308no—
422C2×Q8—3016no—
423C2×Q8—308no—
424C2×Q8—302no—
425C2×Q8—301no—
426C2×Q8#120214yescomplemented
427C2×Q8C2×D3×D512yes—
428C2×D4—52no—
429C2×D4—102no—
430C2×D4—102no—
431C2×D4—101no—
432C2×D4—304no—
433C2×D4—604no—
434C22×C4—21no—
435C22×C4—61no—
436C22×C4—151no—
437C22×C4—152no—
438C22×C4—152no—
439C22×C4—304no—
440C22×C4—308no—
441C22×C4—301no—
442C22×C4—302no—
443C22×C4—302no—
444C22×C4C2×D3×D511yescharacteristic
445SD16—108no—
446SD16—308no—
447C2×C8—32no—
448C2×C8—52no—
449C2×C8—62no—
450C2×C8—102no—
451C4⋊C4—32no—
452C4⋊C4—61no—
453C22⋊C4—304no—
454C3×C5C2×#44811yescharacteristic, complemented, Hall
455C22×C3—202no—
456C22×C3—202no—
457C22×C3—202no—
458C22×C3—404no—
459C22×C3#402812yes—
460C22×C3D5×SD1612yes—
461C22×C3#406412yes—
462C22×C3C2×D4×D511yescharacteristic
463C2×D3—54no—
464C2×D3—102no—
465C2×D3—102no—
466C2×D3—108no—
467C3×C4—24no—
468C3×C4#402812yes—
469C3×C4C22×D2011yescharacteristic
470C3×C4C2×D4×D511yescharacteristic
471Dic3—42no—
472Dic3—104no—
473Dic3—102no—
474C2×C5#517014yescomplemented
475C2×C5C2×D3×SD1611yescharacteristic
476C2×C5C2×#91511yescharacteristic
477C2×C5C2×#93711yescharacteristic
478D5—64no—
479D5—82no—
480C23—102no—
481C23—154no—
482C23—152no—
483C23—202no—
484C23—202no—
485C23—202no—
486C23—302no—
487C23—302no—
488C23#679011yescharacteristic
489Q8—22no—
490Q8—24no—
491Q8—154no—
492Q8—3016no—
493Q8—302no—
494Q8—304no—
495Q8C2×#120214yescomplemented
496D4—102no—
497D4—102no—
498D4—202no—
499D4—608no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—62no—
503C2×C4—122no—
504C2×C4—152no—
505C2×C4—3016no—
506C2×C4—302no—
507C2×C4—302no—
508C2×C4—304no—
509C2×C4—302no—
510C2×C4—302no—
511C2×C4—304no—
512C2×C4C2×#120212yes—
513C2×C4#679012yes—
514C2×C4#679011yescharacteristic
515C2×C4C22×D3×D511yescharacteristic
516C8—62no—
517C8—102no—
518C2×C3—402no—
519C2×C3#6509514yescomplemented
520C2×C3C2×#402811yescharacteristic
521C2×C3C2×D5×SD1611yescharacteristic
522C2×C3C2×#406411yescharacteristic
523D3—104no—
524C5C2×#517011yescharacteristic, complemented, Sylow
525C22—154no—
526C22—202no—
527C22—202no—
528C22—202no—
529C22—302no—
530C22—302no—
531C22—308no—
532C22—404no—
533C22#9150512yes—
534C22#9152212yes—
535C22#9157212yes—
536C22C2×#679011yescharacteristic
537C4—24no—
538C4—122no—
539C4—302no—
540C4—304no—
541C4#9157212yes—
542C4C22×#120211yescharacteristic
543C4C2×#679011yescharacteristic
544C3C2×#6509511yescharacteristic, complemented, Sylow
545C2—304no—
546C2—402no—
547C2#1174928614yesdirect product factor
548C2C2×#9150511yescharacteristic
549C2C2×#9152211yescharacteristic
550C2C2×#9157211yescharacteristic
subgroupG/H
centerC23#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC2×#91465C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#448
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D15C2semidirect
2. C22×C3×#688C2semidirect
4. C22×#6657C2semidirect
5. C2×C5×#835C2semidirect
6. #11749286C2direct (N × H)
7. C2×#90975C2semidirect
8. C2×#90957C2semidirect
14. C2×Q8×D15C22semidirect
24. C2×C3×#688C22semidirect
30. C2×#6657C22semidirect
31. C5×#835C22semidirect
32. #90975C22semidirect
33. #90957C22semidirect
36. C22×#688D3semidirect
47. C2×C3×C5×Q8D4semidirect
66. C2×Dic30D4semidirect
88. C2×#835D5semidirect
106. C2×#688C2×D3semidirect
120. C22×D15SD16semidirect
128. C3×C5×Q8C2×D4semidirect
146. Dic30C2×D4semidirect
176. #835C2×D5semidirect
183. C2×C5×Q8#67semidirect
235. C2×D15C2×SD16semidirect
251. C2×C3×Q8D20semidirect
299. C5×Q8C2×#67semidirect
350. C2×C3×C5#448semidirect
367. C3×Q8C2×D20semidirect
426. C2×Q8#1202semidirect
454. C3×C5C2×#448semidirect
474. C2×C5#5170semidirect
495. Q8C2×#1202semidirect
519. C2×C3#65095semidirect
524. C5C2×#5170semidirect
544. C3C2×#65095semidirect
547. C2#11749286direct (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×#6882
C2×#914652
C22×#66572
C2×C5×#8352
#117492862
C2×#909752
C2×#909572
C2×#650953
C2×#51705