Finite Group Databasebeta

← #14789919

Subgroups — #14789919

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×#10622470C212yesmaximal, complemented
3#13071146C211yesmaximal, characteristic
4#13069944C211yesmaximal, characteristic, complemented
5#13069758C211yesmaximal, characteristic, complemented
6#13069754C211yesmaximal, characteristic, complemented
7#13069570C212yesmaximal, complemented
8#13068927C212yesmaximal
9#13068814C212yesmaximal
10#13068595C211yesmaximal, characteristic
11C11×#2058C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999—21no—
14C2×Q8×Dic11—21no—
15#10623259—28no—
16C2×#66950—21no—
17C2×#66950C2211yescharacteristic
18C2×#66945C2212yes—
19C2×#66943C2212yes—
20C2×#66940—21no—
21C2×#66940C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×C11×#106C2212yes—
25C11×#389C2211yescharacteristic
26C2×(C2×D11)⋊C8C2212yes—
27C2×#66880C2212yes—
28C2×Dic11⋊C8C2212yes—
29#10622602—21no—
30#10622600C2211yescharacteristic
31C4⋊C4×Dic11—21no—
32C4⋊C4×Dic11C2211yescharacteristic
33C2×#66874C2212yes—
34C2×#66871C2212yes—
35#10622542C2211yescharacteristic
36#10622470—28no—
37#10622279—21no—
38#10622267—21no—
39C11×#340C2212yes—
40C11×#336C2211yescharacteristic
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622162C2211yescharacteristic
45C22×Q8×C11—21no—
46C22×C4×D11D411yescharacteristic
47C22×C4×D11D411yescharacteristic
48C22×C4×D11C2311yescharacteristic
49C22×Dic22—21no—
50C22×Dic22C2311yescharacteristic
51C22×C8×C11C2312yes—
52C11×C4⋊Q8—24no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C42×C11C2311yescharacteristic
59#66999—28no—
60Q8×Dic11—28no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—21no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C22×C11⋊C8C2312yes—
78#66950—28no—
79#66950—22no—
80#66950Q814yescomplemented
81#66945—24no—
82#66945—24no—
83#66943—24no—
84#66943D418yes—
85#66940—28no—
86#66940—24no—
87C42×D11—24no—
88#66922—24no—
89C11×#106—24no—
90C11×#95—21no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95(C2×D11)⋊C8—24no—
96#66880—24no—
97Dic11⋊C8—24no—
98#66874—24no—
99#66871—24no—
100#24306—111nomaximal, Sylow
101C23×D11C2×D411yescharacteristic
102C2×Q8×C11—24no—
103C2×Q8×C11—42no—
104C2×Q8×C11—42no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11—21no—
114C22×Dic11C2×D411yescharacteristic
115C22×Dic11C2×D411yescharacteristic
116C22×Dic11C2×D411yescharacteristic
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—41no—
124C2×C4×D11—41no—
125C2×C4×D11C2×Q812yes—
126C2×C4×D11#4112yes—
127C2×Dic22—24no—
128C2×Dic22—22no—
129C2×Dic22—21no—
130C2×Dic22—22no—
131C2×Dic22—42no—
132C2×Dic22—42no—
133C2×Dic22C2×Q812yes—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4C2×D414yes—
143C11×C4⋊C4C2×Q812yes—
144C42×C11—22no—
145(C2×D11)⋊C4—28no—
146(C2×D11)⋊C4—24no—
147(C2×D11)⋊C4—42no—
148C4⋊Dic11—24no—
149C4⋊Dic11—28no—
150C4⋊Dic11—24no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11C2×D414yes—
154Dic11⋊C4—28no—
155Dic11⋊C4—42no—
156C4×Dic11—28no—
157C4×Dic11—22no—
158C4×Dic11—22no—
159C4×Dic11—42no—
160C4×Dic11—42no—
161C4×Dic11C2×D414yes—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×#533—111no—
166C2×#479—112no—
167C4×C22⋊Q8—111no—
168#2058D1111yescharacteristic, complemented
169#2057—111no—
170#2024—111no—
171#2024—111no—
172#1989—112no—
173#1873—112no—
174#1854—112no—
175#1797—111no—
176C23×C11C22×D411yescharacteristic
177C22×D11—21no—
178C22×D11—21no—
179C22×D11—21no—
180C22×D11—21no—
181C22×D11—21no—
182C22×D11—21no—
183C22×D11C22⋊Q812yes—
184Q8×C11—48no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—24no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11#13512yes—
199C2×C4×C11#13712yes—
200C2×C4×C11C22×D412yes—
201C2×C4×C11C22×Q811yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C112−1+412yes—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—24no—
211C2×Dic11—22no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11#12012yes—
220C2×Dic11#12012yes—
221C2×Dic11C22⋊Q812yes—
222C4×D11—24no—
223C4×D11—24no—
224C4×D11—44no—
225C4×D11—44no—
226Dic22—24no—
227Dic22—48no—
228Dic22—42no—
229C8×C11—42no—
230C11⋊C8—42no—
231#533—228no—
232C2×C4⋊Q8—111no—
233C2×C4⋊Q8C2×D1111yescharacteristic
234C2×#125—112no—
235C2×C22⋊Q8—111no—
236C2×C22⋊Q8—221no—
237C2×C22⋊Q8—221no—
238C2×C4×Q8—111no—
239C2×C4×Q8—221no—
240C2×C4×Q8—221no—
241C2×#117—112no—
242C22×C42—111no—
243#479—228no—
244C2×#107—112no—
245C2×#106C2×D1112yes—
246C2×C4⋊C8—112no—
247C2×#103—112no—
248C2×#103—112no—
249C2×C22⋊C8—112no—
250#391—111no—
251#389C2×D1111yescharacteristic
252#387—221no—
253#385—221no—
254#380—111no—
255C4×C4⋊C4—111no—
256C4×C4⋊C4—221no—
257C4×C22⋊C4—221no—
258#340—112no—
259#340—112no—
260#340—112no—
261#340C2×D1112yes—
262#336—111no—
263#336C2×D1111yescharacteristic
264C22×C11C2×#12011yescharacteristic
265C22×C11C2×C22⋊Q811yescharacteristic
266C22×C11#53611yescharacteristic
267C22×C11C2×#13511yescharacteristic
268C22×C11C2×#13711yescharacteristic
269C22×C11#57511yescharacteristic
270C22×C11#57511yescharacteristic
271C2×D11—22no—
272C2×D11—22no—
273C2×D11—22no—
274C2×D11—41no—
275C2×D11—41no—
276C2×D11—41no—
277C2×D11—41no—
278C4×C11—22no—
279C4×C11—22no—
280C4×C11—42no—
281C4×C11—44no—
282C4×C11—81no—
283C4×C11#54812yes—
284C4×C11D4×Q812yes—
285Dic11—22no—
286Dic11—22no—
287Dic11—22no—
288Dic11—42no—
289Dic11—44no—
290Dic11—81no—
291C22×Q8—21no—
292C22×Q8—111no—
293C22×Q8—221no—
294C23×C4—111no—
295C23×C4—111no—
296C23×C4—111no—
297C22×C8—112no—
298C22×C8C22×D1112yes—
299C4⋊Q8—24no—
300C4⋊Q8—224no—
301#125—118no—
302#125—224no—
303C22⋊Q8—114no—
304C22⋊Q8—222no—
305C22⋊Q8—228no—
306C22⋊Q8—228no—
307C4×Q8—224no—
308C4×Q8—228no—
309C4×Q8—228no—
310#117—224no—
311#117—224no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4C22×D1111yescharacteristic
322C2×C4⋊C4C22×D1112yes—
323C2×C4⋊C4C22×D1111yescharacteristic
324C2×C22⋊C4—222no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—221no—
327C2×C42—111no—
328C2×C42—111no—
329C2×C42—111no—
330C2×C42—224no—
331C2×C42—222no—
332C2×C42—221no—
333C2×C42—221no—
334C2×C42C22×D1111yescharacteristic
335#107—224no—
336#106—24no—
337C4⋊C8—224no—
338#103—224no—
339#103—224no—
340C22⋊C8—224no—
341#95—21no—
342#95—221no—
343#95—221no—
344#95—221no—
345#95—221no—
346C2×C11#240911yescharacteristic
347C2×C11#300211yescharacteristic
348C2×C11#300711yescharacteristic
349C2×C11#307611yescharacteristic
350C2×C11#307811yescharacteristic
351C2×C11#323111yescharacteristic
352C2×C11#324011yescharacteristic
353D11—42no—
354C24—111no—
355C2×Q8—24no—
356C2×Q8—42no—
357C2×Q8—42no—
358C2×Q8—112no—
359C2×Q8—224no—
360C2×Q8—221no—
361C2×Q8—222no—
362C2×Q8—222no—
363C2×Q8—442no—
364C2×Q8—442no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—111no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—112no—
372C22×C4—112no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—221no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—221no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4D4×D1111yescharacteristic
385C22×C4D4×D1111yescharacteristic
386C22×C4C23×D1111yescharacteristic
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—222no—
391C2×C8—222no—
392C2×C8—222no—
393C4⋊C4—24no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—42no—
398C4⋊C4—114no—
399C4⋊C4—228no—
400C4⋊C4—228no—
401C4⋊C4—224no—
402C4⋊C4—224no—
403C4⋊C4—222no—
404C4⋊C4—222no—
405C4⋊C4—442no—
406C4⋊C4D4×D1114yes—
407C4⋊C4Q8×D1112yes—
408C22⋊C4—224no—
409C22⋊C4—228no—
410C22⋊C4—442no—
411C42—22no—
412C42—114no—
413C42—222no—
414C42—222no—
415C42—228no—
416C42—442no—
417C42—442no—
418C11#2430611yescharacteristic, complemented, Sylow
419C23—112no—
420C23—221no—
421C23—221no—
422C23—221no—
423C23—221no—
424C23—221no—
425C23—221no—
426C23C2×D4×D1111yescharacteristic
427Q8—48no—
428Q8—224no—
429Q8—448no—
430Q8—442no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—112no—
445C2×C4—112no—
446C2×C4—112no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—224no—
454C2×C4—224no—
455C2×C4—224no—
456C2×C4—222no—
457C2×C4—444no—
458C2×C4—444no—
459C2×C4—441no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4#6696812yes—
467C2×C4#6696912yes—
468C2×C4C2×D4×D1112yes—
469C2×C4C2×Q8×D1111yescharacteristic
470C2×C4#6704012yes—
471C2×C4#41×D1111yescharacteristic
472C8—42no—
473C8—442no—
474C22—222no—
475C22—222no—
476C22—222no—
477C22—441no—
478C22—441no—
479C22—441no—
480C22—441no—
481C22D11×#12011yescharacteristic
482C22D11×C22⋊Q811yescharacteristic
483C22#1062325511yescharacteristic
484C22C2×#6696811yescharacteristic
485C22C2×#6696911yescharacteristic
486C22#1062330411yescharacteristic
487C22#1062330811yescharacteristic
488C4—22no—
489C4—22no—
490C4—44no—
491C4—42no—
492C4—81no—
493C4—222no—
494C4—222no—
495C4—222no—
496C4—444no—
497C4—442no—
498C4—881no—
499C4#1062316412yes—
500C4#1062325812yes—
501C2—442no—
502C2#1307197611yescharacteristic
503C2#1307783311yescharacteristic
504C2#1307787111yescharacteristic
505C2#1307840511yescharacteristic
506C2#1307841611yescharacteristic
507C2#1307977811yescharacteristic
508C2#1307985711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2058C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2058D11
hypocenterC11#24306
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2058

Complements

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

NH ≅ G/Ntype
2. C2×#10622470C2semidirect
4. #13069944C2semidirect
5. #13069758C2semidirect
6. #13069754C2semidirect
7. #13069570C2semidirect
11. C11×#2058C2semidirect
80. #66950Q8semidirect
168. #2058D11semidirect
418. C11#24306semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106224702
#130711462
#130699442
#130697582
#130697542
#130695702
#130689272
#130688142
#130685952
C11×#20582
#2430611