Finite Group Databasebeta

← #14439474

Subgroups — #14439474

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6717C211yesmaximal, characteristic, complemented
2C5×#5816C211yesmaximal, characteristic, complemented
3C2×C3×#4088C211yesmaximal, characteristic, complemented
4#11754609C211yesmaximal, characteristic, complemented
5C2×#91305C211yesmaximal, characteristic, complemented
6C2×#91297C211yesmaximal, characteristic, complemented
7#11749344C212yesmaximal, complemented
8#11749342C212yesmaximal, complemented
9#11749324C212yesmaximal, complemented
10#11749323C212yesmaximal, complemented
11#11748327C211yesmaximal, characteristic, complemented
12#10615133—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17C2×#6717—24no—
18C2×#6717C2212yes—
19C2×#6717C2212yes—
20C22×C3⋊#168C2211yescharacteristic
21C5×#947C2212yescomplemented
22C5×#946—22no—
23C5×#944C2212yescomplemented
24C5×#929—22no—
25C5×#926C2211yescharacteristic
26C2×C3×#689C2212yescomplemented
27C3×#4088—24no—
28C2×C3×#688C2212yescomplemented
29C2×C3×#681C2211yescharacteristic
30#91572—22no—
31#91458C2212yes—
32#91450—22no—
33#91374C2212yes—
34C2×#6661C2211yescharacteristic, complemented
35C2×#6660C2212yes—
36C2×#6656C2211yescharacteristic, complemented
37C2×#6655C2211yescharacteristic, complemented
38#91305—24no—
39C2×#6654C2212yes—
40#91297—24no—
41C2×#6652C2211yescharacteristic, complemented
42#90953C2212yescomplemented
43Dic3×#168C2212yescomplemented
44#83974—51nomaximal, Hall
45C5×#536—31no—
46C2×#4096—31no—
47C2×#4095—31no—
48C2×#4088D311yescharacteristic, complemented
49C22×#688—31no—
50#65859—31no—
51#65375—32no—
52#65374—32no—
53#65348—32no—
54#65347—32no—
55#65286—31no—
56C23×D15—21no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8—22no—
59C2×C3×C5×Q8—22no—
60C2×C3×C5×Q8C2312yes—
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×D60—22no—
64C2×D60—22no—
65C2×D60—21no—
66C2×D60C2312yes—
67C2×C5×#67—21no—
68C5×#235—22no—
69C5×#235—22no—
70C2×C5×D12C2311yescharacteristic
71C2×C4×C5×D3—21no—
72C2×C5×Dic6C2311yescharacteristic
73C2×C3×C22⋊D5—21no—
74C3×#709—22no—
75C3×#709—22no—
76C2×C3×D20C2311yescharacteristic
77C2×C3×C4×D5—21no—
78C2×C3×Dic10C2311yescharacteristic
79C2×#1202—24no—
80#6717—24no—
81#6717—24no—
82C2×C3⋊#168D414yescomplemented
83C2×C3⋊#168C2311yescharacteristic
84C2×C3⋊#168C2311yescharacteristic
85C5×#217D412yes—
86C5×(C2×D3)⋊C4—24no—
87C5×C4⋊Dic3D412yes—
88C5×Dic3⋊C4—24no—
89C4×C5×Dic3C2312yes—
90C3×#689—24no—
91C3×#688—24no—
92C3×#681D414yescomplemented
93C2×C3×#168C2312yes—
94#6667—24no—
95#6661—22no—
96#6660—24no—
97#6656—22no—
98#6655—22no—
99#6654—24no—
100#6652—22no—
101C2×C3×#137—51no—
102#5830—51no—
103C2×#950—51no—
104#5816D511yescharacteristic, complemented
105C22×#215—51no—
106C2×#908—51no—
107#5191—52no—
108#5190—52no—
109#5176—52no—
110#5175—52no—
111#5122—51no—
112C2×C5×#41—31no—
113C22×C5×Q8C2×D311yescharacteristic
114C2×#709C2×D311yescharacteristic
115C22×D20—31no—
116C5×C4⋊Q8—32no—
117C5×#124—32no—
118C5×#123—62no—
119C5×C22⋊Q8—62no—
120C5×#117—31no—
121#4096—64no—
122#4095—64no—
123C2×#689—31no—
124C2×#689C2×D312yescomplemented
125#4088—24no—
126C2×#688—32no—
127C2×#688—32no—
128C2×#688—31no—
129C2×#688—32no—
130C2×#688—64no—
131C2×#688C2×D312yescomplemented
132C2×#687—31no—
133C2×#686—31no—
134C2×#686—32no—
135C2×#681C2×D311yescharacteristic
136C22×#168—31no—
137#4041—62no—
138#4028—62no—
139#4021—32no—
140#4020—32no—
141#3935—32no—
142C4×#168—32no—
143#3154—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—22no—
146C22×D15—42no—
147C22×D15—82no—
148C22×C5×D3—21no—
149C22×C3×D5—21no—
150C3×C5×Q8—22no—
151C3×C5×Q8—22no—
152C3×C5×Q8—42no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—42no—
155C2×C3×C4×C5C2×D411yescharacteristic
156C2×C3×C4×C5C2×D412yes—
157C2×C3×C4×C5C2×D412yes—
158C2×C3×C4×C5C2411yescharacteristic
159D60—22no—
160D60—22no—
161D60—42no—
162C5×#67—42no—
163C2×C5×Dic3—21no—
164C2×C5×Dic3C2×D414yes—
165C5×D12—21no—
166C5×D12—21no—
167C4×C5×D3—42no—
168C5×Dic6—21no—
169C5×Dic6—21no—
170C3×C22⋊D5—42no—
171C2×C3×Dic5—21no—
172C3×D20—21no—
173C3×D20—21no—
174C3×C4×D5—42no—
175C3×Dic10—21no—
176C3×Dic10—21no—
177#1202—84no—
178C3⋊#168C2×D412yes—
179C3⋊#168C2×D412yes—
180C3×#168C2×D414yes—
181C2×C3×#41—51no—
182C22×C3×Q8C2×D511yescharacteristic
183C2×#235C2×D511yescharacteristic
184C22×D12—51no—
185C3×#137—104no—
186C2×C3×Q16—52no—
187C2×C3×SD16—52no—
188C2×C3×M16—51no—
189#950—104no—
190#947—52no—
191#947C2×D512yescomplemented
192#946—22no—
193#944C2×D512yescomplemented
194C2×#216—51no—
195C2×#215—52no—
196C2×#215—52no—
197C2×#215—51no—
198C2×#215—104no—
199#940—52no—
200#937—102no—
201C2×#214—51no—
202C2×#213—51no—
203#930—102no—
204#929—22no—
205#926C2×D511yescharacteristic
206C22×C3⋊C8—51no—
207#908—104no—
208C2×D24—52no—
209C2×#204—52no—
210#815—52no—
211C8×Dic3—52no—
212C23×D5—61no—
213C5×#41—62no—
214C5×#41—62no—
215C2×C5×Q8—21no—
216C2×C5×Q8—22no—
217C2×C5×Q8—22no—
218C2×C5×Q8—31no—
219C2×C5×Q8C22×D312yes—
220C2×C5×D4—31no—
221C2×C5×D4—61no—
222C22×C4×C5—21no—
223C22×C4×C5—61no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—21no—
226#709—22no—
227#709—22no—
228C2×D20—32no—
229C2×D20—62no—
230C2×D20—62no—
231C2×D20—61no—
232C2×D20—64no—
233C2×D20C22×D311yescharacteristic
234C2×C4×D5—21no—
235C2×Dic10C22×D311yescharacteristic
236C5×C4⋊C4—32no—
237C5×C4⋊C4—64no—
238C5×C22⋊C4—32no—
239C5×C22⋊C4—64no—
240C42×C5—32no—
241#689—24no—
242#689—62no—
243#688—24no—
244#688—62no—
245#688—64no—
246#688—64no—
247#688—64no—
248#687—62no—
249#686—62no—
250#686—64no—
251#685—64no—
252#681#6714yescomplemented
253C2×#168—34no—
254C2×#168—31no—
255C2×#168—31no—
256C2×#168C22×D312yes—
257C2×#137—51no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—151no—
260C22×SD16—151no—
261#536—31no—
262#535—151no—
263#497—152no—
264#496—152no—
265#495—152no—
266#492—152no—
267#405—151no—
268C22×C3×C5—22no—
269C22×C3×C5#12712yes—
270C22×C3×C5C22×D411yescharacteristic
271C2×D15—42no—
272C2×D15—44no—
273C2×D15—84no—
274C2×C5×D3—41no—
275C2×C5×D3—42no—
276C2×C3×D5—41no—
277C2×C3×D5—42no—
278C3×C4×C5—42no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282C3×Dic5—41no—
283C5×Dic3—24no—
284C5×Dic3—41no—
285C23×D3—101no—
286C3×#41—102no—
287C3×#41—102no—
288C2×C3×Q8—21no—
289C2×C3×Q8—22no—
290C2×C3×Q8—22no—
291C2×C3×Q8—51no—
292C2×C3×Q8C22×D512yes—
293C2×C3×D4—51no—
294C2×C3×D4—101no—
295C22×C3×C4—21no—
296C22×C3×C4—101no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—21no—
299C2×#67—104no—
300#235—22no—
301#235—22no—
302C2×D12—52no—
303C2×D12—102no—
304C2×D12—102no—
305C2×D12—101no—
306C2×D12C22×D511yescharacteristic
307C2×C4×D3—21no—
308C2×Dic6C22×D511yescharacteristic
309C3×Q16—104no—
310C3×SD16—104no—
311C3×M16—54no—
312C2×C3×C8—52no—
313#217C22⋊D512yes—
314#216—102no—
315#215—102no—
316#215—104no—
317#215—104no—
318#214—102no—
319#213—102no—
320(C2×D3)⋊C4—24no—
321(C2×D3)⋊C4—104no—
322C4⋊Dic3C22⋊D512yes—
323Dic3⋊C4—24no—
324C4×Dic3C22×D512yes—
325C2×C3⋊C8—54no—
326C2×C3⋊C8—51no—
327C2×C3⋊C8—51no—
328D24—104no—
329#204—104no—
330C23×C5—61no—
331C23×C5D3×D411yescharacteristic
332C22×D5—21no—
333C22×D5—62no—
334C22×D5—122no—
335C22×D5—242no—
336C5×Q8—22no—
337C5×Q8—22no—
338C5×Q8—42no—
339C5×Q8—61no—
340C5×Q8—61no—
341C5×D4—61no—
342C5×D4—61no—
343C5×D4—122no—
344C2×C4×C5—22no—
345C2×C4×C5—34no—
346C2×C4×C5—42no—
347C2×C4×C5—61no—
348C2×C4×C5—122no—
349C2×C4×C5D3×D411yescharacteristic
350C2×C4×C5D3×D412yes—
351C2×C4×C5C2×#6712yes—
352C2×C4×C5C23×D311yescharacteristic
353C22⋊D5—42no—
354C2×Dic5—21no—
355D20—21no—
356D20—21no—
357D20—62no—
358D20—62no—
359D20—122no—
360D20—244no—
361C4×D5—42no—
362Dic10—21no—
363Dic10—21no—
364#168—32no—
365#168—32no—
366#168C2×#6714yes—
367C2×#41—31no—
368C2×#41—51no—
369C22×Q8D3×D511yescharacteristic
370C22×D4—151no—
371#137—104no—
372AGL(1,ℤ/8)—304no—
373#135—304no—
374C2×Q16—52no—
375C2×Q16—151no—
376C2×SD16—52no—
377C2×SD16—152no—
378C2×SD16—151no—
379C2×SD16—151no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×SD16—304no—
383C2×D8—152no—
384C2×D8—151no—
385C2×M16—51no—
386C22×C8—151no—
387C4⋊Q8—32no—
388#127—152no—
389#124—32no—
390#124—152no—
391#123—62no—
392C22⋊Q8—62no—
393#121—302no—
394#120—302no—
395#117—31no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5C2×#12711yescharacteristic
400C2×C3×C5#57712yes—
401D15—82no—
402C3×D5—81no—
403C5×D3—81no—
404C23×C3—101no—
405C23×C3C2×C22⋊D511yescharacteristic
406C22×D3—21no—
407C22×D3—102no—
408C22×D3—202no—
409C22×D3—402no—
410C3×Q8—22no—
411C3×Q8—22no—
412C3×Q8—42no—
413C3×Q8—101no—
414C3×Q8—101no—
415C3×D4—101no—
416C3×D4—101no—
417C3×D4—202no—
418C2×C3×C4—22no—
419C2×C3×C4—42no—
420C2×C3×C4—101no—
421C2×C3×C4—202no—
422C2×C3×C4D4×D512yes—
423C2×C3×C4D4×D512yes—
424C2×C3×C4C2×C22⋊D511yescharacteristic
425C2×C3×C4C23×D511yescharacteristic
426#67—42no—
427#67—404no—
428C2×Dic3—21no—
429C2×Dic3C2×C22⋊D514yes—
430D12—21no—
431D12—21no—
432D12—102no—
433D12—102no—
434D12—202no—
435C4×D3—42no—
436Dic6—21no—
437Dic6—21no—
438C3×C8—54no—
439C3⋊C8—52no—
440C3⋊C8—52no—
441C22×C5—22no—
442C22×C5—122no—
443C22×C5—121no—
444C22×C5#94012yes—
445C22×C5C2×D3×D411yescharacteristic
446C2×D5—42no—
447C2×D5—41no—
448C2×D5—124no—
449C2×D5—122no—
450C2×D5—244no—
451C4×C5—42no—
452C4×C5—64no—
453C4×C5—121no—
454C4×C5#94012yes—
455C4×C5C2×D3×D411yescharacteristic
456C4×C5C22×#6711yescharacteristic
457Dic5—41no—
458C24—301no—
459#41—62no—
460#41—62no—
461#41—102no—
462#41—102no—
463C2×Q8—21no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—31no—
467C2×Q8—51no—
468C2×Q8C2×D3×D512yes—
469C2×D4—31no—
470C2×D4—51no—
471C2×D4—61no—
472C2×D4—101no—
473C2×D4—152no—
474C2×D4—304no—
475C2×D4—302no—
476C2×D4—301no—
477C2×D4—302no—
478C22×C4—21no—
479C22×C4—61no—
480C22×C4—101no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—104no—
483Q16—302no—
484SD16—104no—
485SD16—304no—
486SD16—302no—
487SD16—302no—
488SD16—304no—
489SD16—304no—
490D8—304no—
491D8—302no—
492M16—54no—
493C2×C8—52no—
494C2×C8—154no—
495C2×C8—151no—
496C2×C8—151no—
497C4⋊C4—32no—
498C4⋊C4—64no—
499C22⋊C4—32no—
500C22⋊C4—64no—
501C22⋊C4—304no—
502C42—32no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—201no—
506C22×C3—202no—
507C22×C3#408612yes—
508C22×C3C22×C22⋊D511yescharacteristic
509C2×D3—41no—
510C2×D3—42no—
511C2×D3—202no—
512C2×D3—204no—
513C2×D3—404no—
514C3×C4—42no—
515C3×C4—201no—
516C3×C4#408612yes—
517C3×C4C2×D4×D511yescharacteristic
518C3×C4C2×D4×D511yescharacteristic
519Dic3—24no—
520Dic3—41no—
521C2×C5—22no—
522C2×C5—241no—
523C2×C5#577812yes—
524C2×C5C2×#94011yescharacteristic
525D5—81no—
526D5—242no—
527C23—61no—
528C23—101no—
529C23—302no—
530C23—602no—
531C23—1202no—
532C23D3×C22⋊D511yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—42no—
536Q8—61no—
537Q8—61no—
538Q8—101no—
539Q8—101no—
540D4—61no—
541D4—61no—
542D4—101no—
543D4—101no—
544D4—122no—
545D4—202no—
546D4—302no—
547D4—302no—
548D4—602no—
549D4—1204no—
550C2×C4—22no—
551C2×C4—34no—
552C2×C4—42no—
553C2×C4—61no—
554C2×C4—101no—
555C2×C4—122no—
556C2×C4—202no—
557C2×C4D5×#6712yes—
558C2×C4D3×C22⋊D511yescharacteristic
559C2×C4#679012yes—
560C2×C4C22×D3×D511yescharacteristic
561C8—54no—
562C8—152no—
563C8—152no—
564C2×C3—22no—
565C2×C3—401no—
566C2×C3C2×#408611yescharacteristic
567C2×C3#6617112yes—
568D3—81no—
569D3—402no—
570C5#8397411yescharacteristic, complemented, Sylow
571C22—22no—
572C22—122no—
573C22—121no—
574C22—202no—
575C22—201no—
576C22—604no—
577C22—602no—
578C22—1204no—
579C22#9156712yes—
580C22C2×D3×C22⋊D511yescharacteristic
581C4—42no—
582C4—64no—
583C4—121no—
584C4—201no—
585C4#9156712yes—
586C4C2×D5×#6711yescharacteristic
587C4C2×#679011yescharacteristic
588C3#1061513311yescharacteristic, complemented, Sylow
589C2—22no—
590C2—241no—
591C2—401no—
592C2—1202no—
593C2#1175509212yes—
594C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#6717C2semidirect
2. C5×#5816C2semidirect
3. C2×C3×#4088C2semidirect
4. #11754609C2semidirect
5. C2×#91305C2semidirect
6. C2×#91297C2semidirect
7. #11749344C2semidirect
8. #11749342C2semidirect
9. #11749324C2semidirect
10. #11749323C2semidirect
11. #11748327C2semidirect
21. C5×#947C22semidirect
23. C5×#944C22semidirect
26. C2×C3×#689C22semidirect
28. C2×C3×#688C22semidirect
34. C2×#6661C22semidirect
36. C2×#6656C22semidirect
37. C2×#6655C22semidirect
41. C2×#6652C22semidirect
42. #90953C22semidirect
43. Dic3×#168C22semidirect
48. C2×#4088D3semidirect
82. C2×C3⋊#168D4semidirect
92. C3×#681D4semidirect
104. #5816D5semidirect
124. C2×#689C2×D3semidirect
131. C2×#688C2×D3semidirect
191. #947C2×D5semidirect
193. #944C2×D5semidirect
252. #681#67semidirect
503. C3×C5#3154semidirect
570. C5#83974semidirect
588. C3#10615133semidirect

Maximal subgroups

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

subgroupindex
C22×#67172
C5×#58162
C2×C3×#40882
#117546092
C2×#913052
C2×#912972
#117493442
#117493422
#117493242
#117493232
#117483272
#106151333
#839745