Finite Group Databasebeta

← #14439377

Subgroups — #14439377

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×C3×C5×SD16C211yesmaximal, characteristic, complemented
2#11756575C211yesmaximal, characteristic, complemented
3C2×#91831C211yesmaximal, characteristic, complemented
4#11756564C211yesmaximal, characteristic, complemented
5C2×#91821C211yesmaximal, characteristic, complemented
6C2×#91793C211yesmaximal, characteristic, complemented
7#11751277C212yesmaximal, complemented
8#11751276C212yesmaximal, complemented
9#11751269C212yesmaximal, complemented
10#11751268C212yesmaximal, complemented
11#11751202C211yesmaximal, characteristic, complemented
12#10615585—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C22×C3×C5×D4C2211yescharacteristic
15C2×#6817C2211yescharacteristic
16C2×#6817C2211yescharacteristic
17C2×C3×C5×SD16—24no—
18C2×C3×C5×SD16C2212yes—
19C2×C3×C5×SD16C2212yes—
20C22×C3×C5×C8C2211yescharacteristic
21#91842—22no—
22#91836C2212yescomplemented
23#91835—22no—
24#91833C2212yescomplemented
25C2×#6718C2212yescomplemented
26#91831—24no—
27C2×#6717C2212yescomplemented
28#91829C2212yes—
29#91827—22no—
30#91825C2212yes—
31C2×#6716C2212yes—
32#91821—24no—
33C2×#6715C2212yes—
34#91818—22no—
35#91815C2211yescharacteristic
36C2×#6710C2211yescharacteristic
37C2×Dic60C2211yescharacteristic, complemented
38#91793—24no—
39C2×D120C2211yescharacteristic, complemented
40C2×#6706C2211yescharacteristic, complemented
41C2×#6706C2211yescharacteristic, complemented
42#91099C2212yescomplemented
43C8×Dic15C2212yescomplemented
44#83854—51nomaximal, Hall
45C22×C5×SD16D311yescharacteristic, complemented
46#66150—31no—
47C2×#4088—31no—
48#66139—31no—
49C2×#4078—31no—
50C2×#4050—31no—
51#65465—32no—
52#65464—32no—
53#65457—32no—
54#65456—32no—
55#65390—31no—
56C24×C3×C5—21no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8—22no—
59C2×C3×C5×Q8—22no—
60C2×C3×C5×Q8C2312yes—
61C2×C3×C5×D4—22no—
62C2×C3×C5×D4—22no—
63C2×C3×C5×D4—21no—
64C2×C3×C5×D4C2312yes—
65C22×C3×C4×C5—21no—
66C22×C3×C4×C5C2311yescharacteristic
67C2×#1220—21no—
68C2×#1220—21no—
69C2×#1220—24no—
70#6817—22no—
71#6817—22no—
72#6817—22no—
73#6817—22no—
74C2×D60C2311yescharacteristic
75C2×D60C2311yescharacteristic
76C2×C4×D15—21no—
77C2×C4×D15—21no—
78C2×Dic30C2311yescharacteristic
79C2×Dic30C2311yescharacteristic
80C3×C5×SD16—24no—
81C3×C5×SD16—24no—
82C2×C3×C5×C8D414yescomplemented
83C2×C3×C5×C8C2311yescharacteristic
84C2×C3×C5×C8C2311yescharacteristic
85#6719—24no—
86#6719D412yes—
87#6718—24no—
88#6717—24no—
89#6716—24no—
90#6715—24no—
91#6714—24no—
92C4⋊Dic15D412yes—
93#6712—24no—
94C4×Dic15C2312yes—
95#6710D414yescomplemented
96C2×C3⋊#168C2312yes—
97Dic60—22no—
98D120—22no—
99#6706—22no—
100#6706—22no—
101C22×C3×SD16D511yescharacteristic, complemented
102#5816—51no—
103C2×#942—51no—
104#5805—51no—
105C2×#932—51no—
106C2×#904—51no—
107#5176—52no—
108#5175—52no—
109#5168—52no—
110#5167—52no—
111#5101—51no—
112C22×C5×Q8C2×D311yescharacteristic
113C22×C5×D4C2×D311yescharacteristic
114C2×#709—31no—
115C2×#709—31no—
116C2×C5×SD16—24no—
117C2×C5×SD16C2×D312yes—
118C2×C5×SD16C2×D312yes—
119C22×C5×C8C2×D311yescharacteristic
120#4099—62no—
121#4093—32no—
122#4092—62no—
123#4090—32no—
124C2×#689—32no—
125#4088—64no—
126C2×#688—32no—
127#4086—32no—
128#4084—62no—
129#4082—32no—
130C2×#687—32no—
131#4078—64no—
132C2×#686—32no—
133#4075—62no—
134#4072—31no—
135C2×#681—31no—
136C2×Dic20—31no—
137#4050—64no—
138C2×D40—31no—
139C2×#677—31no—
140C2×#677—31no—
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5—22no—
145C23×C3×C5—42no—
146C23×C3×C5—82no—
147C23×C3×C5C2×D411yescharacteristic
148C22×D15—21no—
149C22×D15—21no—
150C3×C5×Q8—22no—
151C3×C5×Q8—22no—
152C3×C5×Q8—42no—
153C3×C5×D4—22no—
154C3×C5×D4—22no—
155C3×C5×D4—42no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—42no—
158C2×C3×C4×C5C2×D411yescharacteristic
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5C2×D412yes—
161C2×C3×C4×C5C2411yescharacteristic
162#1220—42no—
163#1220—42no—
164#1220—84no—
165C2×Dic15—21no—
166C2×Dic15—21no—
167C2×Dic15C2×D414yes—
168D60—21no—
169D60—21no—
170D60—21no—
171D60—21no—
172C4×D15—42no—
173C4×D15—42no—
174Dic30—21no—
175Dic30—21no—
176Dic30—21no—
177Dic30—21no—
178C3×C5×C8C2×D412yes—
179C3×C5×C8C2×D412yes—
180C3⋊#168C2×D414yes—
181C22×C3×Q8C2×D511yescharacteristic
182C22×C3×D4C2×D511yescharacteristic
183C2×#235—51no—
184C2×#235—51no—
185C2×C3×SD16—24no—
186C2×C3×SD16C2×D512yes—
187C2×C3×SD16C2×D512yes—
188C22×C3×C8C2×D511yescharacteristic
189#953—102no—
190#947—52no—
191#946—102no—
192#944—52no—
193C2×#216—52no—
194#942—104no—
195C2×#215—52no—
196#940—52no—
197#938—102no—
198#936—52no—
199C2×#214—52no—
200#932—104no—
201C2×#213—52no—
202#929—102no—
203#926—51no—
204C2×#208—51no—
205C2×Dic12—51no—
206#904—104no—
207C2×D24—51no—
208C2×#204—51no—
209C2×#204—51no—
210#815—52no—
211C8×Dic3—52no—
212C24×C5—21no—
213C2×C5×Q8—21no—
214C2×C5×Q8—22no—
215C2×C5×Q8—22no—
216C2×C5×Q8C22×D312yes—
217C2×C5×D4—22no—
218C2×C5×D4—21no—
219C2×C5×D4—22no—
220C2×C5×D4C22×D312yes—
221C22×C4×C5—21no—
222C22×C4×C5C22×D311yescharacteristic
223C2×C22⋊D5—64no—
224C2×C22⋊D5—61no—
225C2×C22⋊D5—61no—
226#709—62no—
227#709—62no—
228#709—62no—
229#709—62no—
230C2×D20—31no—
231C2×D20—31no—
232C2×C4×D5—61no—
233C2×C4×D5—61no—
234C2×Dic10—31no—
235C2×Dic10—31no—
236C5×SD16—24no—
237C5×SD16—24no—
238C2×C5×C8#6714yescomplemented
239C2×C5×C8C22×D311yescharacteristic
240C2×C5×C8C22×D311yescharacteristic
241C22⋊Dic5—32no—
242C22⋊Dic5—64no—
243#689—64no—
244#688—64no—
245#687—64no—
246#686—64no—
247#685—64no—
248C4⋊Dic5—32no—
249#683—64no—
250C4×Dic5—32no—
251#681—34no—
252C2×#168—32no—
253Dic20—62no—
254D40—62no—
255#677—62no—
256#677—62no—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—151no—
260C22×SD16D1511yescharacteristic, complemented
261#536—151no—
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—42no—
270C22×C3×C5—44no—
271C22×C3×C5—84no—
272C22×C3×C5#12712yes—
273C22×C3×C5C22×D411yescharacteristic
274C2×D15—41no—
275C2×D15—41no—
276C2×D15—42no—
277C2×D15—42no—
278C3×C4×C5—42no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—24no—
283Dic15—41no—
284Dic15—41no—
285C24×C3—21no—
286C2×C3×Q8—21no—
287C2×C3×Q8—22no—
288C2×C3×Q8—22no—
289C2×C3×Q8C22×D512yes—
290C2×C3×D4—22no—
291C2×C3×D4—21no—
292C2×C3×D4—22no—
293C2×C3×D4C22×D512yes—
294C22×C3×C4—21no—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—104no—
297C2×#67—101no—
298C2×#67—101no—
299#235—102no—
300#235—102no—
301#235—102no—
302#235—102no—
303C2×D12—51no—
304C2×D12—51no—
305C2×C4×D3—101no—
306C2×C4×D3—101no—
307C2×Dic6—51no—
308C2×Dic6—51no—
309C3×SD16—24no—
310C3×SD16—24no—
311C2×C3×C8C22⋊D514yescomplemented
312C2×C3×C8C22×D511yescharacteristic
313C2×C3×C8C22×D511yescharacteristic
314#217—52no—
315#217—104no—
316#216—104no—
317#215—104no—
318#214—104no—
319#213—104no—
320(C2×D3)⋊C4—104no—
321C4⋊Dic3—52no—
322Dic3⋊C4—104no—
323C4×Dic3—52no—
324#208—54no—
325C2×C3⋊C8—52no—
326Dic12—102no—
327D24—102no—
328#204—102no—
329#204—102no—
330C23×C5—22no—
331C23×C5—42no—
332C23×C5—82no—
333C23×C5D3×D411yescharacteristic
334C22×D5—61no—
335C22×D5—61no—
336C5×Q8—22no—
337C5×Q8—22no—
338C5×Q8—42no—
339C5×D4—22no—
340C5×D4—22no—
341C5×D4—42no—
342C2×C4×C5—22no—
343C2×C4×C5—42no—
344C2×C4×C5D3×D411yescharacteristic
345C2×C4×C5D3×D412yes—
346C2×C4×C5C2×#6712yes—
347C2×C4×C5C23×D311yescharacteristic
348C22⋊D5—122no—
349C22⋊D5—122no—
350C22⋊D5—244no—
351C2×Dic5—34no—
352C2×Dic5—61no—
353C2×Dic5—61no—
354D20—61no—
355D20—61no—
356D20—61no—
357D20—61no—
358C4×D5—122no—
359C4×D5—122no—
360Dic10—61no—
361Dic10—61no—
362Dic10—61no—
363Dic10—61no—
364C5×C8C2×#6712yes—
365C5×C8C2×#6712yes—
366#168—34no—
367C2×#41—151no—
368C2×#41—151no—
369C22×Q8C2×D1511yescharacteristic
370C22×D4C2×D1511yescharacteristic
371#137—304no—
372AGL(1,ℤ/8)—304no—
373#135—304no—
374C2×Q16—152no—
375C2×Q16—151no—
376C2×SD16—24no—
377C2×SD16—152no—
378C2×SD16—152no—
379C2×SD16—151no—
380C2×SD16—151no—
381C2×SD16C2×D1512yes—
382C2×SD16C2×D1512yes—
383C2×D8—152no—
384C2×D8—151no—
385C2×M16—151no—
386C22×C8C2×D1511yescharacteristic
387C4⋊Q8—152no—
388#127—152no—
389#124—152no—
390#124—152no—
391#123—302no—
392C22⋊Q8—302no—
393#121—302no—
394#120—302no—
395#117—151no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5—82no—
400C2×C3×C5C2×#12711yescharacteristic
401C2×C3×C5#57712yes—
402D15—81no—
403D15—81no—
404C23×C3—22no—
405C23×C3—42no—
406C23×C3—82no—
407C23×C3D4×D511yescharacteristic
408C22×D3—101no—
409C22×D3—101no—
410C3×Q8—22no—
411C3×Q8—22no—
412C3×Q8—42no—
413C3×D4—22no—
414C3×D4—22no—
415C3×D4—42no—
416C2×C3×C4—22no—
417C2×C3×C4—42no—
418C2×C3×C4D4×D512yes—
419C2×C3×C4D4×D511yescharacteristic
420C2×C3×C4C2×C22⋊D512yes—
421C2×C3×C4C23×D511yescharacteristic
422#67—202no—
423#67—202no—
424#67—404no—
425C2×Dic3—54no—
426C2×Dic3—101no—
427C2×Dic3—101no—
428D12—101no—
429D12—101no—
430D12—101no—
431D12—101no—
432C4×D3—202no—
433C4×D3—202no—
434Dic6—101no—
435Dic6—101no—
436Dic6—101no—
437Dic6—101no—
438C3×C8C2×C22⋊D512yes—
439C3×C8C2×C22⋊D512yes—
440C3⋊C8—54no—
441C22×C5—22no—
442C22×C5—44no—
443C22×C5—42no—
444C22×C5—84no—
445C22×C5#94012yes—
446C22×C5C2×D3×D411yescharacteristic
447C2×D5—122no—
448C2×D5—122no—
449C2×D5—121no—
450C2×D5—121no—
451C4×C5—42no—
452C4×C5#94012yes—
453C4×C5C2×D3×D411yescharacteristic
454C4×C5C22×#6711yescharacteristic
455Dic5—64no—
456Dic5—121no—
457Dic5—121no—
458C24—21no—
459#41—302no—
460#41—302no—
461#41—302no—
462#41—302no—
463C2×Q8—21no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—151no—
467C2×Q8—151no—
468C2×Q8C22×D1512yes—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—22no—
472C2×D4—151no—
473C2×D4—151no—
474C2×D4—304no—
475C2×D4—301no—
476C2×D4—301no—
477C2×D4C22×D1512yes—
478C22×C4—21no—
479C22×C4—301no—
480C22×C4—301no—
481C22×C4C22×D1511yescharacteristic
482Q16—304no—
483Q16—302no—
484SD16—24no—
485SD16—24no—
486SD16—304no—
487SD16—304no—
488SD16—302no—
489SD16—302no—
490D8—304no—
491D8—302no—
492M16—154no—
493C2×C8—152no—
494C2×C8#122014yescomplemented
495C2×C8C22×D1511yescharacteristic
496C2×C8C22×D1511yescharacteristic
497C4⋊C4—152no—
498C4⋊C4—304no—
499C22⋊C4—152no—
500C22⋊C4—304no—
501C22⋊C4—304no—
502C42—152no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—44no—
506C22×C3—42no—
507C22×C3—84no—
508C22×C3#408612yes—
509C22×C3C2×D4×D511yescharacteristic
510C2×D3—202no—
511C2×D3—202no—
512C2×D3—201no—
513C2×D3—201no—
514C3×C4—42no—
515C3×C4#408612yes—
516C3×C4C2×D4×D511yescharacteristic
517C3×C4C22×C22⋊D511yescharacteristic
518Dic3—104no—
519Dic3—201no—
520Dic3—201no—
521C2×C5—22no—
522C2×C5—82no—
523C2×C5#576212yes—
524C2×C5C2×#94011yescharacteristic
525D5—241no—
526D5—241no—
527C23—22no—
528C23—42no—
529C23—82no—
530C23—301no—
531C23—301no—
532C23D4×D1511yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—42no—
536Q8—301no—
537Q8—301no—
538Q8—301no—
539Q8—301no—
540D4—22no—
541D4—22no—
542D4—42no—
543D4—301no—
544D4—301no—
545D4—301no—
546D4—301no—
547D4—602no—
548D4—602no—
549D4—1204no—
550C2×C4—22no—
551C2×C4—42no—
552C2×C4—154no—
553C2×C4—301no—
554C2×C4—301no—
555C2×C4—602no—
556C2×C4—602no—
557C2×C4D4×D1511yescharacteristic
558C2×C4D4×D1512yes—
559C2×C4C2×#122012yes—
560C2×C4C23×D1511yescharacteristic
561C8—154no—
562C8C2×#122012yes—
563C8C2×#122012yes—
564C2×C3—22no—
565C2×C3—82no—
566C2×C3#6609612yes—
567C2×C3C2×#408611yescharacteristic
568D3—401no—
569D3—401no—
570C5#8385411yescharacteristic, complemented, Sylow
571C22—22no—
572C22—42no—
573C22—44no—
574C22—84no—
575C22—601no—
576C22—601no—
577C22—602no—
578C22—602no—
579C22#9182912yes—
580C22C2×D4×D1511yescharacteristic
581C4—42no—
582C4—304no—
583C4—601no—
584C4—601no—
585C4#9182912yes—
586C4C2×D4×D1511yescharacteristic
587C4C22×#122011yescharacteristic
588C3#1061558511yescharacteristic, complemented, Sylow
589C2—22no—
590C2—82no—
591C2—1201no—
592C2—1201no—
593C2#1175652112yes—
594C2C2×#9182911yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC22×C3×C5×SD16C2
socleC22×C3×C5C22×D4
hypercenterC22×SD16D15
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×SD16C2semidirect
2. #11756575C2semidirect
3. C2×#91831C2semidirect
4. #11756564C2semidirect
5. C2×#91821C2semidirect
6. C2×#91793C2semidirect
7. #11751277C2semidirect
8. #11751276C2semidirect
9. #11751269C2semidirect
10. #11751268C2semidirect
11. #11751202C2semidirect
22. #91836C22semidirect
24. #91833C22semidirect
25. C2×#6718C22semidirect
27. C2×#6717C22semidirect
37. C2×Dic60C22semidirect
39. C2×D120C22semidirect
40. C2×#6706C22semidirect
41. C2×#6706C22semidirect
42. #91099C22semidirect
43. C8×Dic15C22semidirect
45. C22×C5×SD16D3semidirect
82. C2×C3×C5×C8D4semidirect
95. #6710D4semidirect
101. C22×C3×SD16D5semidirect
238. C2×C5×C8#67semidirect
260. C22×SD16D15semidirect
311. C2×C3×C8C22⋊D5semidirect
494. C2×C8#1220semidirect
503. C3×C5#3154semidirect
570. C5#83854semidirect
588. C3#10615585semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C5×SD162
#117565752
C2×#918312
#117565642
C2×#918212
C2×#917932
#117512772
#117512762
#117512692
#117512682
#117512022
#106155853
#838545