Finite Group Databasebeta

← #14810441

Subgroups — #14810441

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×#10622410C212yesmaximal, complemented
3#13076965C211yesmaximal, characteristic
4#13069758C211yesmaximal, characteristic, complemented
5#13069757C211yesmaximal, characteristic, complemented
6#13069754C211yesmaximal, characteristic, complemented
7#13069583C212yesmaximal, complemented
8#13068927C212yesmaximal
9#13068925C212yesmaximal
10#13068377C211yesmaximal, characteristic
11C11×#2024C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999—21no—
14C2×#66999C2211yescharacteristic
15C2×Q8×Dic11—21no—
16C2×#66997C2211yescharacteristic
17#10623259—28no—
18C2×#66950—21no—
19C2×#66950C2211yescharacteristic
20C2×#66945C2212yes—
21C2×#66943C2212yes—
22C2×#66940—21no—
23C2×C42×D11C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C11×#103C2212yes—
26C11×#391C2211yescharacteristic
27C2×#66899C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29C2×#66880C2212yes—
30C2×#66879C2212yes—
31#10622589C2211yescharacteristic
32C2×#66874C2212yes—
33#10622542C2211yescharacteristic
34#10622410—28no—
35#10622280—21no—
36#10622280—21no—
37#10622260—21no—
38#10622260—21no—
39C11×#340C2212yes—
40C11×#336C2211yescharacteristic
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622162C2211yescharacteristic
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×C4×D11D411yescharacteristic
48C22×C4×D11D411yescharacteristic
49C22×C4×D11C2311yescharacteristic
50C22×Dic22—21no—
51C22×Dic22C2311yescharacteristic
52C22×C8×C11C2312yes—
53C11×C4⋊Q8—24no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11C2311yescharacteristic
58#66999—28no—
59#66999—24no—
60Q8×Dic11—28no—
61#66997—24no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C22×C11⋊C8C2312yes—
81#66950—28no—
82#66950—24no—
83#66945—24no—
84#66945—24no—
85#66943—24no—
86#66943D418yes—
87#66940—28no—
88C42×D11—24no—
89#66922—24no—
90C11×#103—24no—
91C11×#95—21no—
92C11×#95—21no—
93#66899—24no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96(C2×D11)⋊C8—24no—
97#66880—24no—
98#66879—24no—
99#66874—24no—
100#25910—111nomaximal, Sylow
101C23×D11C2×D411yescharacteristic
102C2×Q8×C11—24no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—22no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11C2×D411yescharacteristic
119C22×Dic11C2×D411yescharacteristic
120C22×Dic11C2×D411yescharacteristic
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—21no—
127C2×C4×D11—21no—
128C2×C4×D11—41no—
129C2×C4×D11—41no—
130C2×C4×D11#4114yes—
131C2×Dic22—24no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×Dic22—21no—
135C2×Dic22—21no—
136C2×Dic22—42no—
137C2×Dic22—42no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4C2×D414yes—
145C42×C11—22no—
146(C2×D11)⋊C4—28no—
147(C2×D11)⋊C4—42no—
148(C2×D11)⋊C4—42no—
149C4⋊Dic11—24no—
150C4⋊Dic11—28no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—42no—
154C4⋊Dic11C2×D414yes—
155Dic11⋊C4—28no—
156Dic11⋊C4—42no—
157Dic11⋊C4—42no—
158Dic11⋊C4—42no—
159Dic11⋊C4—42no—
160Dic11⋊C4—42no—
161C4×Dic11—28no—
162C4×Dic11—22no—
163C4×Dic11—22no—
164C4×Dic11C2×D414yes—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×#533—111no—
169C2×#491—112no—
170#2857—111no—
171#2024—111no—
172#2024—111no—
173#2024—111no—
174#2024D1111yescharacteristic, complemented
175#1992—112no—
176#1873—112no—
177#1873—112no—
178#1749—111no—
179C23×C11C22×D411yescharacteristic
180C22×D11—21no—
181C22×D11—21no—
182C22×D11—21no—
183C22×D11—21no—
184C22×D11—21no—
185C22×D11—21no—
186C22×D11#12412yes—
187Q8×C11—48no—
188Q8×C11—42no—
189Q8×C11—42no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—24no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11#13712yes—
204C2×C4×C11#13712yes—
205C2×C4×C11C22×D412yes—
206C2×C4×C11C2×#4112yes—
207C2×C4×C112−1+411yescharacteristic
208C2×C4×C112−1+411yescharacteristic
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—24no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11#12012yes—
225C2×Dic11#12012yes—
226C2×Dic11#12412yes—
227C4×D11—24no—
228C4×D11—24no—
229C4×D11—44no—
230C4×D11—44no—
231Dic22—48no—
232Dic22—42no—
233Dic22—42no—
234C8×C11—42no—
235C11⋊C8—42no—
236#533—228no—
237C2×C4⋊Q8—111no—
238C2×C4⋊Q8—111no—
239C2×C4⋊Q8C2×D1111yescharacteristic
240C2×#125—112no—
241C2×C22⋊Q8—111no—
242C2×C22⋊Q8—111no—
243C2×C22⋊Q8—221no—
244C2×C22⋊Q8—221no—
245C2×C4×Q8—221no—
246C2×C4×Q8—221no—
247C2×#117—112no—
248C22×C42—111no—
249#491—228no—
250C2×#103—112no—
251C2×#103—112no—
252C2×#103—112no—
253C2×#103C2×D1112yes—
254C2×C22⋊C8—112no—
255C2×#97—112no—
256#391—111no—
257#391C2×D1111yescharacteristic
258#389—221no—
259#389—221no—
260#384—111no—
261#380—221no—
262#380—221no—
263#340—112no—
264#340—112no—
265#340—112no—
266#340C2×D1112yes—
267#336—111no—
268#336C2×D1111yescharacteristic
269C22×C11C2×#12011yescharacteristic
270C22×C11C2×#12411yescharacteristic
271C22×C11#53611yescharacteristic
272C22×C11C2×#13711yescharacteristic
273C22×C11C2×#13711yescharacteristic
274C22×C11#57511yescharacteristic
275C22×C11#57511yescharacteristic
276C2×D11—22no—
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—41no—
280C2×D11—41no—
281C2×D11—41no—
282C2×D11—41no—
283C4×C11—22no—
284C4×C11—22no—
285C4×C11—44no—
286C4×C11—81no—
287C4×C11—81no—
288C4×C11#54812yes—
289C4×C11#54812yes—
290Dic11—22no—
291Dic11—22no—
292Dic11—22no—
293Dic11—44no—
294Dic11—81no—
295Dic11—81no—
296C22×Q8—21no—
297C22×Q8—111no—
298C22×Q8—221no—
299C22×Q8C22×D1111yescharacteristic
300C23×C4—111no—
301C23×C4—111no—
302C23×C4—111no—
303C22×C8—112no—
304C22×C8C22×D1112yes—
305C4⋊Q8—24no—
306C4⋊Q8—224no—
307C4⋊Q8—224no—
308#125—118no—
309#125—224no—
310C22⋊Q8—228no—
311C22⋊Q8—228no—
312C22⋊Q8—224no—
313C22⋊Q8—224no—
314C4×Q8—228no—
315C4×Q8—228no—
316#117—224no—
317#117—224no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—112no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—222no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4C22×D1111yescharacteristic
331C2×C4⋊C4C22×D1112yes—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—221no—
334C2×C22⋊C4—221no—
335C2×C42—111no—
336C2×C42—111no—
337C2×C42—111no—
338C2×C42—224no—
339C2×C42—222no—
340C2×C42C22×D1111yescharacteristic
341#103—24no—
342#103—224no—
343#103—224no—
344#103—224no—
345C22⋊C8—224no—
346#97—224no—
347#95—21no—
348#95—21no—
349#95—221no—
350#95—221no—
351C2×C11#243611yescharacteristic
352C2×C11#300711yescharacteristic
353C2×C11#300711yescharacteristic
354C2×C11#313511yescharacteristic
355C2×C11#313911yescharacteristic
356C2×C11#323711yescharacteristic
357C2×C11#323711yescharacteristic
358D11—42no—
359C24—111no—
360C2×Q8—24no—
361C2×Q8—22no—
362C2×Q8—21no—
363C2×Q8—22no—
364C2×Q8—21no—
365C2×Q8—42no—
366C2×Q8—42no—
367C2×Q8—224no—
368C2×Q8—222no—
369C2×Q8—221no—
370C2×Q8—222no—
371C2×Q8—221no—
372C2×Q8—442no—
373C2×Q8—442no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—111no—
378C22×C4—111no—
379C22×C4—111no—
380C22×C4—114no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—221no—
390C22×C4—221no—
391C22×C4—441no—
392C22×C4—441no—
393C22×C4D4×D1111yescharacteristic
394C22×C4D4×D1111yescharacteristic
395C22×C4C23×D1111yescharacteristic
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—222no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—114no—
406C4⋊C4—228no—
407C4⋊C4—228no—
408C4⋊C4—224no—
409C4⋊C4—222no—
410C4⋊C4—222no—
411C4⋊C4—442no—
412C4⋊C4—442no—
413C4⋊C4—442no—
414C4⋊C4—442no—
415C4⋊C4—442no—
416C4⋊C4—442no—
417C4⋊C4D4×D1114yes—
418C22⋊C4—228no—
419C22⋊C4—442no—
420C22⋊C4—442no—
421C42—22no—
422C42—114no—
423C42—222no—
424C42—222no—
425C42—228no—
426C11#2591011yescharacteristic, complemented, Sylow
427C23—112no—
428C23—221no—
429C23—221no—
430C23—221no—
431C23—221no—
432C23—221no—
433C23—221no—
434C23C2×D4×D1111yescharacteristic
435Q8—48no—
436Q8—42no—
437Q8—42no—
438Q8—448no—
439Q8—442no—
440Q8—442no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—24no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—112no—
455C2×C4—112no—
456C2×C4—112no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—221no—
463C2×C4—224no—
464C2×C4—224no—
465C2×C4—224no—
466C2×C4—444no—
467C2×C4—444no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4#6696812yes—
477C2×C4#6697112yes—
478C2×C4C2×D4×D1112yes—
479C2×C4#6704011yescharacteristic
480C2×C4#41×D1112yes—
481C2×C4#6704311yescharacteristic
482C8—42no—
483C8—442no—
484C22—222no—
485C22—222no—
486C22—222no—
487C22—441no—
488C22—441no—
489C22—441no—
490C22—441no—
491C22D11×#12011yescharacteristic
492C22#1062315911yescharacteristic
493C22D11×#12411yescharacteristic
494C22C2×#6696811yescharacteristic
495C22C2×#6697111yescharacteristic
496C22#1062330411yescharacteristic
497C22#1062330811yescharacteristic
498C4—22no—
499C4—22no—
500C4—44no—
501C4—81no—
502C4—81no—
503C4—222no—
504C4—222no—
505C4—222no—
506C4—444no—
507C4—881no—
508C4—881no—
509C4#1062316412yes—
510C4#1062320812yes—
511C2—442no—
512C2#1307226911yescharacteristic
513C2#1307787111yescharacteristic
514C2#1307787511yescharacteristic
515C2#1307895811yescharacteristic
516C2#1307899311yescharacteristic
517C2#1307982811yescharacteristic
518C2#1307982911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2024C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2024D11
hypocenterC11#25910
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
2. C2×#10622410C2semidirect
4. #13069758C2semidirect
5. #13069757C2semidirect
6. #13069754C2semidirect
7. #13069583C2semidirect
11. C11×#2024C2semidirect
174. #2024D11semidirect
426. C11#25910semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106224102
#130769652
#130697582
#130697572
#130697542
#130695832
#130689272
#130689252
#130683772
C11×#20242
#2591011