Finite Group Databasebeta

← #14796441

Subgroups — #14796441

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622455C211yesmaximal, characteristic
2C2×C4×#4325C211yesmaximal, characteristic
3#13073821C211yesmaximal, characteristic, complemented
4#13071516C211yesmaximal, characteristic
5#13070096C212yesmaximal, complemented
6#13069995C212yesmaximal, complemented
7#13069576C211yesmaximal, characteristic, complemented
8#13069332C211yesmaximal, characteristic, complemented
9#13068947C212yesmaximal
10#13068615C212yesmaximal
11C11×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C22×#4325C2211yescharacteristic
14C2×#66946C2212yes—
15C2×C4⋊C4×D11—21no—
16C2×C4×D44C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103C2212yes—
20C11×#384C2211yescharacteristic
21#10622843C2212yes—
22C2×#66899C2211yescharacteristic
23C2×#66885C2212yes—
24C2×#66881C2212yes—
25C2×Dic11⋊C8C2212yes—
26C4×#4325—24no—
27#10622602—22no—
28#10622600—21no—
29#10622592—22no—
30#10622589C2212yes—
31#10622586C2212yes—
32C2×#66873C2211yescharacteristic
33C2×#66872C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35#10622541—21no—
36#10622541—21no—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622455—24no—
39C11×#340C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×C4×D11—22no—
47C22×Dic22—21no—
48C22×C8×C11C2312yes—
49C4×Q8×C11—22no—
50C4×Q8×C11—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2312yes—
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58C2×#4325—22no—
59C2×#4325—22no—
60C2×#4325Q814yescomplemented
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11C2312yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74#66946—24no—
75#66946—42no—
76C4⋊C4×D11—44no—
77C4×D44—22no—
78C4×D44D414yes—
79#66922—22no—
80#66922—22no—
81C11×C4⋊C8—22no—
82C11×#103—42no—
83#66899—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95D412yes—
88#66885—24no—
89#66881—24no—
90Dic11⋊C8—42no—
91#66873—22no—
92#66872—22no—
93C4×C11⋊C8—22no—
94#24815—111nomaximal, Sylow
95C23×D11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11C2×Q812yes—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—22no—
110C22×Dic11C2×D412yes—
111C22×Dic11C2×D412yes—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44C2×D412yes—
116C2×D44C2×Q812yes—
117C2×D44#4112yes—
118C2×C4×D11—24no—
119C2×C4×D11—44no—
120C2×C4×D11—44no—
121C2×C4×D11—42no—
122C2×C4×D11—42no—
123C2×C4×D11—82no—
124C2×Dic22—42no—
125C2×Dic22—81no—
126C2×Dic22—81no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—81no—
137C42×C11—42no—
138C42×C11C2×D412yes—
139C42×C11#4112yes—
140#4325—28no—
141(C2×D11)⋊C4—24no—
142(C2×D11)⋊C4—44no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—42no—
148C4⋊Dic11SD1614yescomplemented
149C4⋊Dic11C2×D412yes—
150Dic11⋊C4—44no—
151Dic11⋊C4—82no—
152Dic11⋊C4—82no—
153C4×Dic11—22no—
154C4×Dic11—22no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8C2×Q812yes—
161C2×#476—111no—
162C2×C4×SD16—111no—
163#2567—111no—
164D4×C4⋊C4—111no—
165#2084—112no—
166#2066—112no—
167#1990—111no—
168#1939—111no—
169#1877—112no—
170#1803D1111yescharacteristic, complemented
171#1802—112no—
172C23×C11C22×D411yescharacteristic
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180Q8×C11—22no—
181Q8×C11—22no—
182Q8×C11—41no—
183Q8×C11—41no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11#12112yes—
196C2×C4×C11#12112yes—
197C2×C4×C11C2×SD1612yes—
198C2×C4×C11#13712yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×Q811yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11H(5,𝔽2)11yescharacteristic
204C2×C4×C112−1+411yescharacteristic
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11C2×SD1614yes—
217D44—22no—
218D44—22no—
219D44—22no—
220D44C22⋊Q814yes—
221C4×D11—48no—
222C4×D11—88no—
223Dic22—84no—
224C8×C11—42no—
225C11⋊C8—22no—
226C11⋊C8—41no—
227C22×SD16—111no—
228C2×C4⋊Q8—111no—
229C2×C4×Q8C2×D1111yescharacteristic
230C2×C4×D4—112no—
231C2×C4×D4—111no—
232C22×C4⋊C4—221no—
233#476—224no—
234C4×SD16—224no—
235C2×#106—112no—
236C2×#106—111no—
237C2×C4⋊C8—112no—
238C2×C4⋊C8C2×D1111yescharacteristic
239C2×#103—111no—
240C2×#103C2×D1112yes—
241C2×#102—112no—
242C2×#102—111no—
243C2×C4×C8—111no—
244#395—222no—
245#391—112no—
246#389—112no—
247#389—221no—
248#389—221no—
249#385—222no—
250#384—112no—
251#384C2×D1111yescharacteristic
252#380—221no—
253C4×C4⋊C4—111no—
254#340—112no—
255#340—112no—
256#340C2×D1112yes—
257#336—112no—
258C22×C11C2×#12111yescharacteristic
259C22×C11#54611yescharacteristic
260C22×C11D4×Q811yescharacteristic
261C22×C11C22×SD1611yescharacteristic
262C22×C11C2×#13711yescharacteristic
263C22×C11#57611yescharacteristic
264C22×C11#57711yescharacteristic
265C2×D11—24no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—42no—
270C2×D11—42no—
271C2×D11—42no—
272C4×C11—22no—
273C4×C11—42no—
274C4×C11—82no—
275C4×C11—81no—
276C4×C11#46114yes—
277C4×C11C2×C22⋊Q811yescharacteristic
278C4×C11#53711yescharacteristic
279C4×C11#55211yescharacteristic
280C4×C11#55411yescharacteristic
281Dic11—24no—
282Dic11—42no—
283Dic11—42no—
284Dic11—82no—
285C22×Q8—221no—
286C22×Q8C22×D1111yescharacteristic
287C22×D4—111no—
288C23×C4—222no—
289C23×C4—221no—
290C2×SD16—114no—
291C2×SD16—222no—
292C2×SD16—222no—
293C22×C8—111no—
294C22×C8—111no—
295C22×C8C22×D1112yes—
296C4⋊Q8—222no—
297C4⋊Q8—222no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×D4—114no—
301C4×D4—224no—
302C4×D4—222no—
303C4×D4—442no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—444no—
316C2×C4⋊C4C22×D1112yes—
317C2×C4⋊C4C22×D1111yescharacteristic
318C2×C22⋊C4—221no—
319C2×C22⋊C4—222no—
320C2×C42—21no—
321C2×C42—112no—
322C2×C42C22×D1111yescharacteristic
323#106—222no—
324#106—224no—
325C4⋊C8—22no—
326C4⋊C8—442no—
327#103—42no—
328#103—222no—
329#102—222no—
330#102—224no—
331C4×C8—222no—
332#95—112no—
333#95—222no—
334#95—222no—
335#95—222no—
336C2×C11#241711yescharacteristic
337C2×C11C2×#46111yescharacteristic
338C2×C11#304511yescharacteristic
339C2×C11#329511yescharacteristic
340C2×C11#333111yescharacteristic
341C2×C11Q8×SD1611yescharacteristic
342C2×C11#338511yescharacteristic
343D11—44no—
344C24—221no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—442no—
351C2×Q8—881no—
352C2×Q8—881no—
353C2×Q8Q8×D1112yes—
354C2×D4—112no—
355C2×D4—112no—
356C2×D4—112no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—221no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—112no—
364C22×C4—112no—
365C22×C4—221no—
366C22×C4—224no—
367C22×C4—222no—
368C22×C4—444no—
369C22×C4—444no—
370C22×C4—442no—
371C22×C4—442no—
372C22×C4—882no—
373C22×C4D4×D1111yescharacteristic
374C22×C4D4×D1111yescharacteristic
375C22×C4C23×D1111yescharacteristic
376SD16—228no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—112no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—221no—
384C2×C8—221no—
385C2×C8—221no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C4⋊C4—81no—
393C4⋊C4—114no—
394C4⋊C4—112no—
395C4⋊C4—222no—
396C4⋊C4—221no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C4⋊C4—444no—
400C4⋊C4—442no—
401C4⋊C4—882no—
402C4⋊C4—882no—
403C22⋊C4—224no—
404C22⋊C4—444no—
405C42—42no—
406C42—222no—
407C42—222no—
408C42#433912yes—
409C42D4×D1112yes—
410C11#2481511yescharacteristic, complemented, Sylow
411C23—222no—
412C23—222no—
413C23—222no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23—441no—
418C23C2×D4×D1111yescharacteristic
419Q8—22no—
420Q8—22no—
421Q8—41no—
422Q8—41no—
423Q8—884no—
424D4—114no—
425D4—222no—
426D4—222no—
427D4—222no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—114no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—222no—
445C2×C4—222no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—448no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—888no—
453C2×C4#6693712yes—
454C2×C4#6693712yes—
455C2×C4SD16×D1112yes—
456C2×C4#6697112yes—
457C2×C4C2×#433911yescharacteristic
458C2×C4C2×D4×D1111yescharacteristic
459C2×C4#6703711yescharacteristic
460C2×C4C2×Q8×D1111yescharacteristic
461C2×C4#41×D1111yescharacteristic
462C2×C4#6704311yescharacteristic
463C8—42no—
464C8—222no—
465C8—441no—
466C22—224no—
467C22—442no—
468C22—442no—
469C22—442no—
470C22—442no—
471C22—442no—
472C22—442no—
473C22C2×#6693711yescharacteristic
474C22#1062314311yescharacteristic
475C22#1062316311yescharacteristic
476C22C2×SD16×D1111yescharacteristic
477C22C2×#6697111yescharacteristic
478C22#1062330511yescharacteristic
479C22#1062330911yescharacteristic
480C4—22no—
481C4—42no—
482C4—82no—
483C4—81no—
484C4—224no—
485C4—442no—
486C4—442no—
487C4—882no—
488C4#1062243114yes—
489C4#1062304211yescharacteristic
490C4#1062306011yescharacteristic
491C4#1062313911yescharacteristic
492C4D11×C22⋊Q811yescharacteristic
493C2—444no—
494C2#1307206911yescharacteristic
495C2C2×#1062243111yescharacteristic
496C2#1307815411yescharacteristic
497C2#1308044311yescharacteristic
498C2#1308093511yescharacteristic
499C2#1308147511yescharacteristic
500C2#1308152511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1803D11
hypocenterC11#24815
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
3. #13073821C2semidirect
5. #13070096C2semidirect
6. #13069995C2semidirect
7. #13069576C2semidirect
8. #13069332C2semidirect
11. C11×#1803C2semidirect
60. C2×#4325Q8semidirect
148. C4⋊Dic11SD16semidirect
170. #1803D11semidirect
410. C11#24815semidirect

Maximal subgroups

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

subgroupindex
C2×#106224552
C2×C4×#43252
#130738212
#130715162
#130700962
#130699952
#130695762
#130693322
#130689472
#130686152
C11×#18032
#2481511