Finite Group Databasebeta

← #14471949

Subgroups — #14471949

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
1Q8×Dic30C211yesmaximal, characteristic, complemented
2#11752680C211yesmaximal, characteristic
3C5×#5027C211yesmaximal, characteristic, complemented
4C3×C4×#688C211yesmaximal, characteristic, complemented
5#11749346C212yesmaximal, complemented
6#11749240C212yesmaximal, complemented
7#11747407C212yesmaximal, complemented
8#11747256C212yesmaximal, complemented
9#11746906C211yesmaximal, characteristic, complemented
10#11746881C211yesmaximal, characteristic, complemented
11#11746851C211yesmaximal, characteristic, complemented
12#10612100—31nomaximal, Hall
13C2×#6772—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15Q8×Dic15C2212yes—
16#91777—22no—
17#91777C2212yes—
18#91758—21no—
19#91758C2211yescharacteristic
20C4×Dic30—21no—
21C4×Dic30C2211yescharacteristic
22C2×C5×#215C2212yes—
23C5×#874C2211yescharacteristic
24C2×C3×#688C2211yescharacteristic
25C3×C4×D20C2211yescharacteristic
26#91463C2212yes—
27#91453—22no—
28#91449—21no—
29#91435C2212yes—
30C5×#809C2212yes—
31C5×C4⋊(C3⋊C8)C2211yescharacteristic
32C3×#3967C2211yescharacteristic
33C3×#3941C2211yescharacteristic
34C3×#3940C2211yescharacteristic
35C3×C4×#168C2211yescharacteristic
36#90987C2212yes—
37#90983C2212yes—
38#90967C2212yes—
39#90967C2212yes—
40#90965C2212yes—
41#90951C2212yes—
42#79622—51nomaximal, Hall
43#66052—31no—
44Q8×Dic10—31no—
45C5×#460—31no—
46#65452—32no—
47SD16×Dic5—32no—
48#65359—31no—
49C4×#688D311yescharacteristic, complemented
50#65131—31no—
51#65119—31no—
52#65050—32no—
53#65049—32no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×Dic30—21no—
56C2×Dic30—22no—
57C2×Dic30D411yescharacteristic
58C2×C5×D12—21no—
59C2×C5×D12—21no—
60C2×C5×D12C2312yes—
61C2×C3×D20C2311yescharacteristic
62C2×C3×C4×D5—21no—
63C2×#1201—22no—
64C2×#1201—22no—
65C2×D3×Dic5—22no—
66#6772—44no—
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4C2311yescharacteristic
69C3×C42×C5—21no—
70C3×C42×C5C2311yescharacteristic
71C4⋊Dic15—21no—
72C4⋊Dic15—22no—
73C4⋊Dic15D411yescharacteristic
74C4⋊Dic15C2312yes—
75#6712—22no—
76#6712D412yes—
77C4×Dic15—22no—
78C4×Dic15C2312yes—
79C5×#215—24no—
80C2×C5×C3⋊C8C2312yes—
81C3×#688—22no—
82C3×#685—21no—
83C3×C4⋊Dic5C2311yescharacteristic
84C2×C3×#168C2311yescharacteristic
85C2×C3×#168C2311yescharacteristic
86(C2×D3)⋊Dic5—22no—
87Q8×Dic6—51no—
88#5553—51no—
89C3×C4×SD16—51no—
90#5163—52no—
91#5027D511yescharacteristic, complemented
92#5008—51no—
93#4870—52no—
94#4788—52no—
95#4760—52no—
96#4694—51no—
97C8×Dic6—51no—
98C2×#711—61no—
99C2×C5×SD16—32no—
100C5×#127—31no—
101C4×C5×Q8C2×D311yescharacteristic
102Q8×Dic5—32no—
103C2×#688C2×D311yescharacteristic
104#4086—32no—
105#4085—62no—
106#4084—61no—
107D4×Dic5—32no—
108#4034—32no—
109#4034—62no—
110C4×D20C2×D311yescharacteristic
111#4015—31no—
112#4015—61no—
113C4×Dic10—31no—
114C4×Dic10—61no—
115C5×C4⋊C8—31no—
116C5×#102—32no—
117#3967C2×D311yescharacteristic
118#3964—32no—
119#3964—32no—
120#3953—32no—
121#3949—32no—
122#3946—32no—
123C8×Dic5—32no—
124#3941C2×D311yescharacteristic
125#3940C2×D311yescharacteristic
126C4×#168C2×D311yescharacteristic
127#3362—151noSylow
128C22×C5×D3—22no—
129C22×C3×D5—21no—
130C3×C5×Q8—21no—
131C3×C5×Q8#4112yescomplemented
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—22no—
138C2×Dic15C2×D412yes—
139C2×Dic15C2×D412yes—
140Dic30—82no—
141Dic30—81no—
142Dic30SD1614yescomplemented
143C5×D12—22no—
144C5×D12—22no—
145C5×D12—42no—
146C5×D12—81no—
147C2×C3×Dic5—21no—
148C3×D20—21no—
149C3×D20—21no—
150C3×C4×D5—42no—
151#1201—44no—
152#1201—82no—
153D3×Dic5—44no—
154C3×#168—21no—
155C3×#168—21no—
156C5×C3⋊C8—22no—
157C2×#235—101no—
158C2×C3×SD16—51no—
159C3×C4×Q8C2×D511yescharacteristic
160C3×C4×D4—51no—
161Q8×Dic3—52no—
162C2×#215C2×D512yes—
163#940—52no—
164#930—101no—
165#893—52no—
166#888—52no—
167#888—102no—
168#884—102no—
169#874C2×D511yescharacteristic
170#869—51no—
171#869—101no—
172C4×Dic6—51no—
173C4×Dic6—101no—
174C3×#106—51no—
175C3×#103—51no—
176C3×#102—51no—
177C3×C4×C8—51no—
178#832—52no—
179#821—52no—
180#821—52no—
181Dic3⋊C8—52no—
182C8×Dic3—52no—
183#809C2×D512yes—
184#808—52no—
185C4⋊(C3⋊C8)C2×D511yescharacteristic
186C2×C5×Q8C22×D311yescharacteristic
187C2×C5×D4—32no—
188C2×C5×D4—61no—
189C2×C5×D4—61no—
190C2×C22⋊D5—62no—
191C2×C22⋊D5—62no—
192C22×Dic5—62no—
193#711—124no—
194C2×D20C22×D311yescharacteristic
195C2×C4×D5—21no—
196C2×Dic10—31no—
197C2×Dic10—62no—
198C2×Dic10—61no—
199C5×SD16—64no—
200C2×C5×C8—32no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4C22×D311yescharacteristic
203C42×C5—21no—
204C42×C5C22×D311yescharacteristic
205C22⋊Dic5—62no—
206#688—22no—
207#685—21no—
208C4⋊Dic5—31no—
209C4⋊Dic5—32no—
210C4⋊Dic5—62no—
211C4⋊Dic5—61no—
212C4⋊Dic5C22×D311yescharacteristic
213#683—32no—
214#683—62no—
215C4×Dic5—32no—
216C4×Dic5—62no—
217C2×#168C22×D311yescharacteristic
218C2×#168C22×D311yescharacteristic
219Q82—151no—
220#550—151no—
221#486—151no—
222#486—152no—
223#476—152no—
224#476—151no—
225#460—31no—
226#460—152no—
227C8×Q8—151no—
228C4×SD16—51no—
229C4×SD16—152no—
230C22×C3×C5C22×D411yescharacteristic
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C2×C5×D3—42no—
234C2×C3×D5—41no—
235C2×C3×D5—41no—
236C2×C3×D5—41no—
237C3×C4×C5—22no—
238C3×C4×C5—21no—
239C3×C4×C5—41no—
240C3×C4×C5C2×SD1612yes—
241C3×C4×C5C2×#4111yescharacteristic
242C3×C4×C52−1+411yescharacteristic
243Dic15—22no—
244Dic15—42no—
245Dic15C2×SD1614yes—
246C3×Dic5—41no—
247C2×C3×Q8C22×D511yescharacteristic
248C2×C3×D4—51no—
249C22×C3×C4—101no—
250C2×#67—102no—
251C2×#67—102no—
252#235—204no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12C22×D512yes—
256C2×C4×D3—102no—
257C2×Dic6—51no—
258C2×Dic6—102no—
259C2×Dic6—101no—
260C3×SD16—102no—
261C2×C3×C8—51no—
262C2×C3×C8—51no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—51no—
265C3×C4⋊C4C22×D511yescharacteristic
266C3×C22⋊C4—101no—
267C3×C42—21no—
268C3×C42C22×D511yescharacteristic
269#215—24no—
270(C2×D3)⋊C4—102no—
271C4⋊Dic3—51no—
272C4⋊Dic3—52no—
273C4⋊Dic3—102no—
274C4⋊Dic3—101no—
275Dic3⋊C4—52no—
276Dic3⋊C4—102no—
277C4×Dic3—52no—
278C4×Dic3—102no—
279C2×C3⋊C8C22×D512yes—
280C23×C5—62no—
281C22×D5—21no—
282C5×Q8—21no—
283C5×Q8#23512yescomplemented
284C5×D4—62no—
285C5×D4—62no—
286C5×D4—122no—
287C5×D4—241no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C22⋊D5—242no—
295C2×Dic5—21no—
296C2×Dic5—32no—
297C2×Dic5—32no—
298C2×Dic5—62no—
299C2×Dic5—124no—
300D20—21no—
301D20—21no—
302C4×D5—42no—
303Dic10—34no—
304Dic10—242no—
305Dic10—241no—
306C5×C8—62no—
307#168—21no—
308#168—21no—
309C2×#41—301no—
310C2×SD16—32no—
311C2×SD16—51no—
312C4⋊Q8—152no—
313C4⋊Q8—151no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—31no—
317#127—152no—
318#121—302no—
319#121—301no—
320C4×Q8—151no—
321C4×Q8—152no—
322C4×Q8—301no—
323C4×Q8D3×D511yescharacteristic
324C4×D4—51no—
325C4×D4—152no—
326#106—51no—
327#106—152no—
328C4⋊C8—31no—
329C4⋊C8—152no—
330#103—51no—
331#102—32no—
332#102—51no—
333#102—152no—
334#102—152no—
335#102—152no—
336C4×C8—51no—
337C4×C8—152no—
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341C3×D5—81no—
342C5×D3—82no—
343C23×C3—101no—
344C22×D3—22no—
345C3×Q8—21no—
346C3×Q8#71112yescomplemented
347C3×D4—101no—
348C3×D4—101no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—101no—
352C2×C3×C4—202no—
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4C23×D511yescharacteristic
356#67—204no—
357#67—402no—
358C2×Dic3—52no—
359C2×Dic3—52no—
360C2×Dic3—102no—
361D12—22no—
362D12—22no—
363D12—42no—
364D12—81no—
365C4×D3—204no—
366Dic6—54no—
367Dic6—402no—
368Dic6—401no—
369C3×C8—101no—
370C3×C8—101no—
371C3⋊C8—22no—
372C22×C5—122no—
373C22×C5—122no—
374C22×C5—122no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—41no—
377C2×D5—41no—
378C2×D5—41no—
379C4×C5—21no—
380C4×C5—22no—
381C4×C5—41no—
382C4×C5D3×SD1612yes—
383C4×C5C2×#23511yescharacteristic
384C4×C5#101011yescharacteristic
385Dic5—34no—
386Dic5—41no—
387Dic5—62no—
388Dic5—122no—
389#41—604no—
390C2×Q8—151no—
391C2×Q8—302no—
392C2×Q8—301no—
393C2×Q8C2×D3×D511yescharacteristic
394C2×D4—32no—
395C2×D4—51no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—302no—
399C2×D4—302no—
400C22×C4—101no—
401C22×C4—302no—
402SD16—64no—
403SD16—102no—
404C2×C8—32no—
405C2×C8—51no—
406C2×C8—51no—
407C4⋊C4—21no—
408C4⋊C4—51no—
409C4⋊C4—152no—
410C4⋊C4—151no—
411C4⋊C4—152no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4C2×D3×D511yescharacteristic
416C22⋊C4—101no—
417C22⋊C4—302no—
418C42—21no—
419C42—152no—
420C42—302no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—201no—
424C22×C3—201no—
425C22×C3—201no—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—42no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4—201no—
434C3×C4D5×SD1612yes—
435C3×C4C2×#71111yescharacteristic
436C3×C4#415011yescharacteristic
437Dic3—54no—
438Dic3—102no—
439Dic3—202no—
440C2×C5—242no—
441C2×C5#555211yescharacteristic
442C2×C5C2×D3×SD1611yescharacteristic
443C2×C5#576911yescharacteristic
444D5—81no—
445C23—62no—
446C23—101no—
447Q8—21no—
448Q8—154no—
449Q8—1201no—
450Q8—1202no—
451Q8#677212yescomplemented
452D4—62no—
453D4—62no—
454D4—101no—
455D4—101no—
456D4—122no—
457D4—241no—
458D4—604no—
459D4—1202no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—101no—
463C2×C4—152no—
464C2×C4—152no—
465C2×C4—202no—
466C2×C4—302no—
467C2×C4—604no—
468C2×C4#679011yescharacteristic
469C2×C4#679011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—62no—
472C8—101no—
473C8—101no—
474C2×C3—401no—
475C2×C3#6593211yescharacteristic
476C2×C3C2×D5×SD1611yescharacteristic
477C2×C3#6610811yescharacteristic
478D3—82no—
479C5#7962211yescharacteristic, complemented, Sylow
480C22—122no—
481C22—122no—
482C22—122no—
483C22—201no—
484C22—201no—
485C22—201no—
486C22C2×#679011yescharacteristic
487C4—22no—
488C4—21no—
489C4—41no—
490C4—154no—
491C4—201no—
492C4—302no—
493C4—602no—
494C4#9150512yes—
495C4#9200111yescharacteristic
496C4C2×#677211yescharacteristic
497C3#1061210011yescharacteristic, complemented, Sylow
498C2—242no—
499C2—401no—
500C2#1175455611yescharacteristic
501C2C2×#9150511yescharacteristic
502C2#1175533211yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11752680C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×Dic30C2semidirect
3. C5×#5027C2semidirect
4. C3×C4×#688C2semidirect
5. #11749346C2semidirect
6. #11749240C2semidirect
7. #11747407C2semidirect
8. #11747256C2semidirect
9. #11746906C2semidirect
10. #11746881C2semidirect
11. #11746851C2semidirect
49. C4×#688D3semidirect
91. #5027D5semidirect
131. C3×C5×Q8#41semidirect
142. Dic30SD16semidirect
283. C5×Q8#235semidirect
346. C3×Q8#711semidirect
422. C3×C5#3362semidirect
451. Q8#6772semidirect
479. C5#79622semidirect
497. C3#10612100semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic302
#117526802
C5×#50272
C3×C4×#6882
#117493462
#117492402
#117474072
#117472562
#117469062
#117468812
#117468512
#106121003
#796225