Finite Group Databasebeta

← #14471826

Subgroups — #14471826

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756338C211yesmaximal, characteristic, complemented
2C3×#65919C211yesmaximal, characteristic, complemented
3C5×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4C4×#6658C211yesmaximal, characteristic, complemented
5#11747044C212yesmaximal, complemented
6#11747043C211yesmaximal, characteristic
7C4×#6653C212yesmaximal, complemented
8#11746916C211yesmaximal, characteristic, complemented
9#11746891C212yesmaximal, complemented
10#11746890C211yesmaximal, characteristic, complemented
11#11746888C212yesmaximal, complemented
12#10611658—31nomaximal, Hall
13C3×C4×C5×Q8C2211yescharacteristic
14#91835—21no—
15#91785—22no—
16C4⋊C4×D15—21no—
17C4×D60C2212yes—
18C4×D60C2211yescharacteristic
19#91759C2212yes—
20#91758C2211yescharacteristic
21C3×#4093—21no—
22C3×#4040—22no—
23C3×#4039—21no—
24C3×#4021C2212yes—
25C3×#4020C2211yescharacteristic
26C3×C4×D20C2212yes—
27C3×C4×Dic10C2211yescharacteristic
28C2×#6658C2211yescharacteristic
29C2×#6653C2212yes—
30C5×C4⋊(C3⋊C8)C2212yes—
31C5×C4⋊(C3⋊C8)C2211yescharacteristic
32C4×C5×C3⋊C8C2211yescharacteristic
33C4×C5×C3⋊C8C2212yes—
34#90990C2212yes—
35#90987C2211yescharacteristic
36#90971C2211yescharacteristic
37#90971C2212yes—
38#90968C2211yescharacteristic
39#90965C2212yes—
40#90965C2212yes—
41#90965C2212yes—
42#83713—51nomaximal, Hall
43#65919D311yescharacteristic, complemented
44#65913—31no—
45C5×C8×Q8—31no—
46#65139—31no—
47#65136—32no—
48#65133—32no—
49#65132—31no—
50#64986—32no—
51#64983—31no—
52C4×D40—32no—
53C4×#677—31no—
54C2×C3×C5×Q8D411yescharacteristic
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C4×D15—22no—
58C2×Dic30—21no—
59C2×C3×D20—21no—
60C2×C3×D20—21no—
61C2×C3×D20C2312yes—
62C2×C3×C4×D5—22no—
63C2×C3×Dic10C2311yescharacteristic
64C3×C5×C4⋊C4D411yescharacteristic
65C3×C5×C4⋊C4D412yes—
66C3×C42×C5C2311yescharacteristic
67C3×C42×C5C2312yes—
68#6714—21no—
69#6714—22no—
70C4⋊Dic15—21no—
71C4⋊Dic15C2311yescharacteristic
72C4⋊Dic15C2312yes—
73#6712—22no—
74#6712—22no—
75C2×C5×C3⋊C8C2311yescharacteristic
76C2×C5×C3⋊C8C2311yescharacteristic
77C2×C5×C3⋊C8C2312yes—
78C3×#685—22no—
79C3×#685—22no—
80C3×#685—22no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×#683—21no—
83C3×C4×Dic5—21no—
84#6658—22no—
85#6653—24no—
86C3×#559—51no—
87#5579—51no—
88#5072—51no—
89#5070—51no—
90#5057—52no—
91#5056—52no—
92C4×#215—51no—
93Q8×C3⋊C8D511yescharacteristic, complemented
94#5021—51no—
95C4×#213—52no—
96#5009—52no—
97C4×C5×Q8C2×D311yescharacteristic
98#4093—21no—
99#4092—61no—
100C2×D40—32no—
101C2×#677—31no—
102#4042—62no—
103#4040—22no—
104#4039—21no—
105D5×C4⋊C4—61no—
106#4021C2×D312yes—
107#4020C2×D311yescharacteristic
108C4×D20—31no—
109C4×D20—32no—
110C4×D20C2×D312yes—
111#4016—32no—
112#4015—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×C4⋊C8—31no—
115C5×C4⋊C8—32no—
116C4×C5×C8—31no—
117C4×C5×C8—32no—
118#3953—32no—
119#3953—32no—
120#3953—32no—
121#3953—31no—
122#3950—32no—
123#3949—31no—
124#3948—32no—
125#3948—31no—
126#3361—151noSylow
127C22×D15—21no—
128C22×C3×D5—22no—
129C3×C5×Q8—22no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D412yes—
132C2×C3×C4×C5C2×D412yes—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136C2×Dic15—22no—
137D60—21no—
138D60#4112yes—
139C4×D15—42no—
140C4×D15—82no—
141Dic30—81no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—21no—
144C3×D20—22no—
145C3×D20—22no—
146C3×D20—42no—
147C3×D20—81no—
148C3×C4×D5—82no—
149C3×Dic10—21no—
150C3×Dic10—21no—
151C5×C3⋊C8—21no—
152C5×C3⋊C8—22no—
153C5×C3⋊C8—21no—
154C3×#127—51no—
155C3×#124—52no—
156C3×#124—101no—
157C3×#123—102no—
158C3×C4×Q8—51no—
159C3×C4×Q8C2×D511yescharacteristic
160C3×C4×D4—52no—
161C3×C4×D4—101no—
162#946—101no—
163C2×#215—51no—
164C2×#213—52no—
165#896—102no—
166D3×C4⋊C4—101no—
167C4×D12—52no—
168C4×D12—51no—
169#870—52no—
170#869—51no—
171#835—52no—
172#835—51no—
173#832—52no—
174#832—52no—
175#832—52no—
176#809—51no—
177#808—51no—
178#807—52no—
179C4⋊(C3⋊C8)C2×D512yes—
180C4⋊(C3⋊C8)C2×D511yescharacteristic
181C4×C3⋊C8C2×D512yes—
182C4×C3⋊C8C2×D511yescharacteristic
183C2×C5×Q8#6711yescharacteristic
184C2×D20—21no—
185C2×D20—21no—
186C2×D20—31no—
187C2×D20C22×D312yes—
188C2×C4×D5—22no—
189C2×C4×D5—61no—
190C2×C4×D5—62no—
191C2×Dic10—61no—
192C2×Dic10C22×D311yescharacteristic
193C2×C5×C8—32no—
194C2×C5×C8—31no—
195C2×C5×C8—31no—
196C5×C4⋊C4#6711yescharacteristic
197C5×C4⋊C4#6712yes—
198C42×C5C22×D311yescharacteristic
199C42×C5C22×D312yes—
200#685—22no—
201#685—22no—
202#685—22no—
203#685—61no—
204#685—62no—
205C4⋊Dic5—31no—
206C4⋊Dic5—32no—
207C4⋊Dic5—61no—
208C4⋊Dic5C22×D311yescharacteristic
209#683—21no—
210#683—62no—
211#683—62no—
212C4×Dic5—21no—
213D40—64no—
214#677—62no—
215#559—51no—
216#554—151no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—31no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C2×C3×D5—42no—
233C3×C4×C5—22no—
234C3×C4×C5—22no—
235C3×C4×C5—21no—
236C3×C4×C5#13512yes—
237C3×C4×C5C2×#4111yescharacteristic
238C3×C4×C52−1+411yescharacteristic
239Dic15—41no—
240Dic15—42no—
241C3×Dic5—41no—
242C3×Dic5—41no—
243C2×C3×Q8—51no—
244C2×C3×Q8D2011yescharacteristic
245C2×C3×D4—52no—
246C2×C3×D4—101no—
247C2×C3×D4—101no—
248C22×C3×C4—102no—
249C2×D12—51no—
250C2×C4×D3—101no—
251C2×C4×D3—102no—
252C2×Dic6—101no—
253C3×C4⋊C4—51no—
254C3×C4⋊C4—101no—
255C3×C4⋊C4D2011yescharacteristic
256C3×C4⋊C4D2012yes—
257C3×C22⋊C4—102no—
258C3×C22⋊C4—102no—
259C3×C22⋊C4—102no—
260C3×C42—101no—
261C3×C42C22×D511yescharacteristic
262C3×C42C22×D512yes—
263#215—102no—
264#213—104no—
265(C2×D3)⋊C4—101no—
266(C2×D3)⋊C4—102no—
267C4⋊Dic3—52no—
268C4⋊Dic3—51no—
269C4⋊Dic3—101no—
270Dic3⋊C4—102no—
271Dic3⋊C4—102no—
272C2×C3⋊C8C22×D511yescharacteristic
273C2×C3⋊C8C22×D512yes—
274C2×C3⋊C8C22×D511yescharacteristic
275C22×D5—22no—
276C22×D5—61no—
277C5×Q8—22no—
278C2×C4×C5C2×#6711yescharacteristic
279C2×C4×C5C2×#6712yes—
280C2×C4×C5C2×#6712yes—
281C2×C4×C5C2×#6711yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—21no—
284C2×Dic5—21no—
285C2×Dic5—61no—
286C2×Dic5—62no—
287D20—22no—
288D20—22no—
289D20—32no—
290D20—42no—
291D20—61no—
292D20—81no—
293C4×D5—82no—
294C4×D5—122no—
295C4×D5—242no—
296Dic10—21no—
297Dic10—21no—
298Dic10—241no—
299C5×C8—61no—
300C5×C8—62no—
301C5×C8—61no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8—151no—
305#127—51no—
306#125—152no—
307#124—52no—
308#124—101no—
309#123—102no—
310C22⋊Q8—301no—
311C22⋊Q8—302no—
312C4×Q8—51no—
313C4×Q8D3×D511yescharacteristic
314C4×D4—52no—
315C4×D4—101no—
316C4×D4—152no—
317C4×D4—151no—
318C2×C4⋊C4—301no—
319#107—152no—
320#106—151no—
321C4⋊C8—31no—
322C4⋊C8—32no—
323#103—151no—
324#103—152no—
325#102—151no—
326#102—152no—
327#102—152no—
328#102—152no—
329C4×C8—32no—
330C4×C8—31no—
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334D15—42no—
335C3×D5—82no—
336C23×C3—102no—
337C22×D3—101no—
338C3×Q8—22no—
339C3×Q8—101no—
340C3×Q8—101no—
341C3×D4—102no—
342C3×D4—102no—
343C3×D4—202no—
344C3×D4—401no—
345C2×C3×C4—101no—
346C2×C3×C4—101no—
347C2×C3×C4—402no—
348C2×C3×C4C2×D2012yes—
349C2×C3×C4C2×D2012yes—
350C2×C3×C4C2×D2011yescharacteristic
351C2×C3×C4C2×D2011yescharacteristic
352C2×C3×C4C23×D511yescharacteristic
353C2×Dic3—101no—
354C2×Dic3—102no—
355D12—52no—
356D12—101no—
357C4×D3—202no—
358C4×D3—402no—
359Dic6—401no—
360C3⋊C8—21no—
361C3⋊C8—22no—
362C3⋊C8—21no—
363C22×C5C22×#6711yescharacteristic
364C2×D5—42no—
365C2×D5—42no—
366C2×D5—42no—
367C2×D5—62no—
368C2×D5—121no—
369C2×D5—121no—
370C4×C5—22no—
371C4×C5—21no—
372C4×C5—22no—
373C4×C5#95012yes—
374C4×C5D3×#4111yescharacteristic
375C4×C5#101011yescharacteristic
376Dic5—41no—
377Dic5—41no—
378Dic5—121no—
379Dic5—122no—
380C2×Q8—51no—
381C2×Q8—301no—
382C2×Q8#120211yescharacteristic
383C2×D4—52no—
384C2×D4—101no—
385C2×D4—101no—
386C2×D4—151no—
387C22×C4—102no—
388C22×C4—301no—
389C22×C4—302no—
390SD16—302no—
391D8—304no—
392C2×C8—31no—
393C2×C8—31no—
394C2×C8—32no—
395C4⋊C4—51no—
396C4⋊C4—101no—
397C4⋊C4—151no—
398C4⋊C4—152no—
399C4⋊C4—302no—
400C4⋊C4—301no—
401C4⋊C4—302no—
402C4⋊C4#120211yescharacteristic
403C4⋊C4#120212yes—
404C22⋊C4—102no—
405C22⋊C4—102no—
406C22⋊C4—102no—
407C22⋊C4—301no—
408C22⋊C4—302no—
409C42—101no—
410C42C2×D3×D512yes—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—202no—
414C22×C3—202no—
415C22×C3—202no—
416C22×C3C22×D2011yescharacteristic
417C2×D3—102no—
418C2×D3—201no—
419C2×D3—201no—
420C3×C4—22no—
421C3×C4—21no—
422C3×C4—22no—
423C3×C4—201no—
424C3×C4—201no—
425C3×C4#405012yes—
426C3×C4#414711yescharacteristic
427C3×C4D5×#4111yescharacteristic
428Dic3—201no—
429Dic3—202no—
430C2×C5C2×#95011yescharacteristic
431C2×C5#583111yescharacteristic
432C2×C5#583511yescharacteristic
433D5—82no—
434D5—122no—
435C23—102no—
436C23—301no—
437Q8—22no—
438Q8—101no—
439Q8—101no—
440Q8—1201no—
441D4—102no—
442D4—102no—
443D4—152no—
444D4—202no—
445D4—301no—
446D4—401no—
447C2×C4—101no—
448C2×C4—101no—
449C2×C4—301no—
450C2×C4—302no—
451C2×C4—402no—
452C2×C4—602no—
453C2×C4—1202no—
454C2×C4C2×#120212yes—
455C2×C4C2×#120212yes—
456C2×C4C2×#120211yescharacteristic
457C2×C4C2×#120211yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—61no—
460C8—62no—
461C8—61no—
462C2×C3—402no—
463C2×C3#6591011yescharacteristic
464C2×C3C2×#405011yescharacteristic
465C2×C3#6608611yescharacteristic
466D3—202no—
467C5#8371311yescharacteristic, complemented, Sylow
468C22—202no—
469C22—202no—
470C22—202no—
471C22—302no—
472C22—601no—
473C22—601no—
474C22C22×#120211yescharacteristic
475C4—22no—
476C4—21no—
477C4—22no—
478C4—201no—
479C4—201no—
480C4—602no—
481C4—601no—
482C4#9131112yes—
483C4#9202811yescharacteristic
484C4#9203411yescharacteristic
485C3#1061165811yescharacteristic, complemented, Sylow
486C2—402no—
487C2—602no—
488C2C2×#9131111yescharacteristic
489C2#1175525711yescharacteristic
490C2#1175531111yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11747043C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756338C2semidirect
2. C3×#65919C2semidirect
3. C5×Q8×C3⋊C8C2semidirect
4. C4×#6658C2semidirect
5. #11747044C2semidirect
7. C4×#6653C2semidirect
8. #11746916C2semidirect
9. #11746891C2semidirect
10. #11746890C2semidirect
11. #11746888C2semidirect
43. #65919D3semidirect
93. Q8×C3⋊C8D5semidirect
412. C3×C5#3361semidirect
467. C5#83713semidirect
485. C3#10611658semidirect

Maximal subgroups

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

subgroupindex
#117563382
C3×#659192
C5×Q8×C3⋊C82
C4×#66582
#117470442
#117470432
C4×#66532
#117469162
#117468912
#117468902
#117468882
#106116583
#837135