Finite Group Databasebeta

← #14471942

Subgroups — #14471942

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752545C211yesmaximal, characteristic
2#11752472C211yesmaximal, characteristic, complemented
3C4×#6706C211yesmaximal, characteristic, complemented
4C5×C8×Dic6C211yesmaximal, characteristic, complemented
5C3×#64983C211yesmaximal, characteristic, complemented
6#11748004C212yesmaximal, complemented
7#11748003C212yesmaximal, complemented
8#11747781C212yesmaximal, complemented
9#11747739C212yesmaximal, complemented
10#11747083C211yesmaximal, characteristic, complemented
11#11746942C211yesmaximal, characteristic, complemented
12#10611663—31nomaximal, Hall
13C2×#6766—21no—
14C2×#6706C2211yescharacteristic
15C4×D60C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C3×#4020C2211yescharacteristic
19C3×#4015C2211yescharacteristic
20#91470—21no—
21#91469C2212yes—
22#91465—21no—
23#91458C2212yes—
24Dic3×D20C2212yes—
25#91409—22no—
26#91344—21no—
27#91340C2212yes—
28#91327—22no—
29C2×#6657C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91105C2211yescharacteristic
32#91101C2211yescharacteristic
33#91100C2211yescharacteristic
34C5×Dic3⋊C8C2212yes—
35C5×C8×Dic3C2212yes—
36C5×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×#3953C2212yes—
38C3×#3953C2212yes—
39#90987C2212yes—
40#90968C2212yes—
41#90965C2212yes—
42#81588—51nomaximal, Hall
43#65911—31no—
44Q8×Dic10—31no—
45C5×C8×Q8—31no—
46#65137—31no—
47#65137—32no—
48#65131—31no—
49#65131—32no—
50#64983—32no—
51#64983D311yescharacteristic, complemented
52C4×#677—31no—
53C4×#677—32no—
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30C2311yescharacteristic
57C2×C5×Dic6D411yescharacteristic
58C2×C3×D20—21no—
59C2×C3×D20—21no—
60C2×C3×D20C2312yes—
61C2×C3×Dic10—21no—
62C2×#1204—22no—
63C2×#1202—22no—
64C2×#1202—22no—
65C2×D5×Dic3—22no—
66#6766—44no—
67C2×C3×C5×C8C2311yescharacteristic
68C2×C3×C5×C8C2311yescharacteristic
69C3×C42×C5C2311yescharacteristic
70#6714—21no—
71C4⋊Dic15C2311yescharacteristic
72C4⋊Dic15C2311yescharacteristic
73#6712—21no—
74C4×Dic15—21no—
75#6706—22no—
76C5×C4⋊Dic3D411yescharacteristic
77C5×Dic3⋊C4D412yes—
78C4×C5×Dic3C2312yes—
79C2×C5×C3⋊C8C2312yes—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2312yes—
82Dic3⋊Dic5—22no—
83#6669—22no—
84#6665—22no—
85Dic3×Dic5—22no—
86#6657—24no—
87#5722—51no—
88#5718—51no—
89C3×#486—51no—
90#5084—51no—
91#5075—51no—
92#4762—52no—
93#4761—52no—
94#4760—52no—
95#4758—52no—
96C4×#204—51no—
97C8×Dic6D511yescharacteristic, complemented
98C2×#713—61no—
99C4×C5×Q8—31no—
100Q8×Dic5—61no—
101C2×#677—32no—
102C2×#677—31no—
103#4041—62no—
104#4041—61no—
105#4034—61no—
106#4034—62no—
107#4020—32no—
108#4020C2×D311yescharacteristic
109C4×D20—32no—
110C4×D20—31no—
111#4015—32no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—32no—
115C5×C4⋊C8—32no—
116C5×C4⋊C8—31no—
117C4×C5×C8—32no—
118C4×C5×C8C2×D311yescharacteristic
119#3953—32no—
120#3953—31no—
121#3953—32no—
122#3953C2×D312yes—
123#3953C2×D312yes—
124#3949—31no—
125#3949—32no—
126#3948—31no—
127#3362—151noSylow
128C22×D15—21no—
129C22×C3×D5—22no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2411yescharacteristic
133C2×Dic15—21no—
134C2×Dic15—21no—
135C2×Dic15—21no—
136D60—21no—
137D60—21no—
138C4×D15—42no—
139Dic30—21no—
140Dic30#4112yescomplemented
141C2×C5×Dic3C2×D412yes—
142C2×C5×Dic3C2×D412yes—
143C5×Dic6SD1614yescomplemented
144C2×C3×Dic5—22no—
145C3×D20—22no—
146C3×D20—22no—
147C3×D20—42no—
148C3×D20—81no—
149C3×Dic10—81no—
150#1204—82no—
151#1202—44no—
152#1202—82no—
153D5×Dic3—44no—
154C3×C5×C8—21no—
155C3×C5×C8—21no—
156C5×C3⋊C8—22no—
157C2×#237—101no—
158C3×C4⋊Q8—51no—
159C3×#127—51no—
160#944—102no—
161#940—52no—
162#939—102no—
163#938—101no—
164D4×Dic3—52no—
165C2×#214—52no—
166C2×#204—51no—
167#888—52no—
168#888—101no—
169#887—52no—
170#887—101no—
171C4×D12—51no—
172C4×Dic6—51no—
173C4×Dic6C2×D511yescharacteristic
174C3×#102—52no—
175C3×#102—52no—
176C3×C4×C8C2×D511yescharacteristic
177#832—52no—
178#821—51no—
179#817—51no—
180#816—51no—
181Dic3⋊C8C2×D512yes—
182C8×Dic3C2×D512yes—
183#809—52no—
184#808—52no—
185C4⋊(C3⋊C8)C2×D511yescharacteristic
186C2×C5×Q8—31no—
187#713—124no—
188C2×D20—21no—
189C2×D20—21no—
190C2×D20—31no—
191C2×D20—62no—
192C2×D20—62no—
193C2×D20C22×D312yes—
194C2×C4×D5—62no—
195C2×C4×D5—61no—
196C2×Dic10—21no—
197C2×Dic10—31no—
198C2×Dic10—62no—
199C2×C5×C8—32no—
200C2×C5×C8C22×D311yescharacteristic
201C2×C5×C8C22×D311yescharacteristic
202C5×C4⋊C4—32no—
203C5×C4⋊C4—31no—
204C42×C5—32no—
205C42×C5C22×D311yescharacteristic
206#685—62no—
207#685—61no—
208C4⋊Dic5—21no—
209C4⋊Dic5—31no—
210C4⋊Dic5—31no—
211C4⋊Dic5—62no—
212C4⋊Dic5C22×D312yes—
213#683—62no—
214#683—61no—
215C4×Dic5—62no—
216C4×Dic5—61no—
217#677—62no—
218#677—64no—
219Q82—151no—
220#550—151no—
221#486—51no—
222#486—152no—
223#476—152no—
224#476—151no—
225#460—152no—
226#460—151no—
227C8×Q8—31no—
228C4×SD16—152no—
229C4×SD16—151no—
230C22×C3×C5C22×D411yescharacteristic
231C2×D15—41no—
232C2×D15—41no—
233C2×D15—41no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—42no—
237C3×C4×C5—21no—
238C3×C4×C5C2×SD1612yes—
239C3×C4×C5C2×#4111yescharacteristic
240C3×C4×C52−1+411yescharacteristic
241Dic15—22no—
242Dic15—41no—
243Dic15—41no—
244C3×Dic5—42no—
245C5×Dic3—22no—
246C5×Dic3C2×SD1614yes—
247C2×C3×Q8—101no—
248C2×C3×D4—52no—
249C2×C3×D4—101no—
250C2×C3×D4—101no—
251C2×#67—102no—
252C2×#67—102no—
253C22×Dic3—102no—
254#237—204no—
255C2×D12—51no—
256C2×C4×D3—101no—
257C2×Dic6—51no—
258C2×Dic6—102no—
259C2×Dic6D2011yescharacteristic
260C2×C3×C8C22×D511yescharacteristic
261C2×C3×C8C22×D511yescharacteristic
262C3×C4⋊C4—52no—
263C3×C4⋊C4—101no—
264C3×C42C22×D511yescharacteristic
265#217—102no—
266#214—104no—
267(C2×D3)⋊C4—101no—
268C4⋊Dic3—51no—
269C4⋊Dic3—51no—
270C4⋊Dic3D2011yescharacteristic
271Dic3⋊C4—101no—
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274Dic3⋊C4D2012yes—
275C4×Dic3—101no—
276C4×Dic3—102no—
277C4×Dic3C22×D512yes—
278C2×C3⋊C8C22×D512yes—
279#204—102no—
280C22×D5—22no—
281C22×D5—61no—
282C5×Q8—34no—
283C2×C4×C5—32no—
284C2×C4×C5—32no—
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—22no—
289C2×Dic5—61no—
290C2×Dic5—61no—
291C2×Dic5—61no—
292D20—22no—
293D20—22no—
294D20—42no—
295D20—61no—
296D20—61no—
297D20—81no—
298D20—124no—
299D20—242no—
300C4×D5—124no—
301C4×D5—122no—
302Dic10—32no—
303Dic10—61no—
304Dic10—81no—
305Dic10—242no—
306C5×C8—21no—
307C5×C8—21no—
308C5×C8—62no—
309C2×#41—301no—
310C2×SD16—152no—
311C2×SD16—151no—
312C4⋊Q8—51no—
313C4⋊Q8—152no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—51no—
317#127—152no—
318#121—301no—
319#121—302no—
320C4×Q8—31no—
321C4×Q8—152no—
322C4×Q8—151no—
323C4×Q8—301no—
324C4×D4—152no—
325C4×D4—151no—
326#106—152no—
327#106—151no—
328C4⋊C8—32no—
329C4⋊C8—31no—
330#103—151no—
331#102—52no—
332#102—52no—
333#102—152no—
334#102—152no—
335#102—151no—
336C4×C8—32no—
337C4×C8D3×D511yescharacteristic
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341D15—81no—
342C3×D5—82no—
343C23×C3—102no—
344C22×D3—101no—
345C3×Q8—401no—
346C3×D4—102no—
347C3×D4—102no—
348C3×D4—202no—
349C3×D4—401no—
350C2×C3×C4—102no—
351C2×C3×C4C2×D2011yescharacteristic
352C2×C3×C4C2×D2011yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355#67—402no—
356C2×Dic3—101no—
357C2×Dic3—101no—
358C2×Dic3—101no—
359C2×Dic3—204no—
360C2×Dic3C2×D2012yes—
361C2×Dic3C2×D2012yes—
362D12—101no—
363D12—101no—
364C4×D3—202no—
365Dic6—52no—
366Dic6—101no—
367Dic6—402no—
368Dic6#67714yescomplemented
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—22no—
372C22×C5C2×D3×D411yescharacteristic
373C2×D5—42no—
374C2×D5—42no—
375C2×D5—42no—
376C2×D5—121no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—21no—
380C4×C5—34no—
381C4×C5—62no—
382C4×C5D3×SD1612yes—
383C4×C5D3×#4111yescharacteristic
384C4×C5#101011yescharacteristic
385Dic5—42no—
386Dic5—62no—
387Dic5—121no—
388Dic5—121no—
389#41—604no—
390C2×Q8—31no—
391C2×Q8—101no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—52no—
395C2×D4—101no—
396C2×D4—101no—
397C2×D4—151no—
398C2×D4—302no—
399C2×D4—302no—
400C22×C4—302no—
401C22×C4—301no—
402SD16—302no—
403SD16—304no—
404C2×C8—32no—
405C2×C8C2×D3×D511yescharacteristic
406C2×C8C2×D3×D511yescharacteristic
407C4⋊C4—32no—
408C4⋊C4—31no—
409C4⋊C4—52no—
410C4⋊C4—101no—
411C4⋊C4—151no—
412C4⋊C4—151no—
413C4⋊C4—302no—
414C4⋊C4—302no—
415C4⋊C4—301no—
416C22⋊C4—302no—
417C22⋊C4—301no—
418C42—32no—
419C42—302no—
420C42—301no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—202no—
424C22×C3—202no—
425C22×C3—202no—
426C22×C3C22×D2011yescharacteristic
427C2×D3—201no—
428C2×D3—201no—
429C2×D3—201no—
430C3×C4—21no—
431C3×C4—202no—
432C3×C4C2×#67712yes—
433C3×C4#414711yescharacteristic
434C3×C4D5×#4111yescharacteristic
435Dic3—22no—
436Dic3—102no—
437Dic3—201no—
438Dic3—201no—
439Dic3C2×#67714yes—
440C2×C5#567711yescharacteristic
441C2×C5#575711yescharacteristic
442C2×C5C2×D3×SD1611yescharacteristic
443D5—82no—
444D5—241no—
445C23—102no—
446C23—301no—
447Q8—34no—
448Q8—152no—
449Q8—301no—
450Q8—401no—
451Q8—1202no—
452D4—102no—
453D4—102no—
454D4—202no—
455D4—301no—
456D4—301no—
457D4—401no—
458D4—604no—
459D4—1202no—
460C2×C4—32no—
461C2×C4—32no—
462C2×C4—102no—
463C2×C4—301no—
464C2×C4—301no—
465C2×C4—301no—
466C2×C4—604no—
467C2×C4—602no—
468C2×C4D3×D2011yescharacteristic
469C2×C4D3×D2011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—21no—
472C8—21no—
473C8—62no—
474C2×C3—402no—
475C2×C3#6591011yescharacteristic
476C2×C3C22×#67711yescharacteristic
477C2×C3#6608611yescharacteristic
478D3—401no—
479C5#8158811yescharacteristic, complemented, Sylow
480C22—202no—
481C22—202no—
482C22—202no—
483C22—601no—
484C22—601no—
485C22—601no—
486C22C2×D3×D2011yescharacteristic
487C4—21no—
488C4—34no—
489C4—62no—
490C4—202no—
491C4—302no—
492C4—601no—
493C4—601no—
494C4D3×#67712yes—
495C4#9200011yescharacteristic
496C4#9201611yescharacteristic
497C3#1061166311yescharacteristic, complemented, Sylow
498C2—402no—
499C2—1201no—
500C2#1175254611yescharacteristic
501C2C2×D3×#67711yescharacteristic
502C2#1175397111yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11752545C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #11752472C2semidirect
3. C4×#6706C2semidirect
4. C5×C8×Dic6C2semidirect
5. C3×#64983C2semidirect
6. #11748004C2semidirect
7. #11748003C2semidirect
8. #11747781C2semidirect
9. #11747739C2semidirect
10. #11747083C2semidirect
11. #11746942C2semidirect
51. #64983D3semidirect
97. C8×Dic6D5semidirect
140. Dic30#41semidirect
143. C5×Dic6SD16semidirect
368. Dic6#677semidirect
422. C3×C5#3362semidirect
479. C5#81588semidirect
497. C3#10611663semidirect

Maximal subgroups

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

subgroupindex
#117525452
#117524722
C4×#67062
C5×C8×Dic62
C3×#649832
#117480042
#117480032
#117477812
#117477392
#117470832
#117469422
#106116633
#815885