Finite Group Databasebeta

← #14782611

Subgroups — #14782611

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622493C211yesmaximal, characteristic, complemented
2C2×D11×C22⋊C8C211yesmaximal, characteristic
3#13070998C212yesmaximal
4#13070054C212yesmaximal, complemented
5#13070052C212yesmaximal, complemented
6#13070046C211yesmaximal, characteristic, complemented
7#13070044C211yesmaximal, characteristic, complemented
8#13070040C211yesmaximal, characteristic, complemented
9#13068331C211yesmaximal, characteristic, complemented
10#13068331C212yesmaximal, complemented
11C11×#2075C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14C22×C8×D11C2211yescharacteristic
15C2×#66945C2212yes—
16C2×#66945C2212yes—
17C2×C11×#107C2211yescharacteristic, complemented
18C2×C11×C22⋊C8C2211yescharacteristic
19C11×#380C2212yes—
20#10622825C2212yes—
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×#66882C2211yescharacteristic, complemented
25#10622600C2212yes—
26#10622600C2212yes—
27C2×#66872C2212yescomplemented
28#10622568—22no—
29C22⋊C4×Dic11—22no—
30#10622493—24no—
31D11×C22⋊C8—24no—
32#10622279—22no—
33#10622277—22no—
34C11×#340C2211yescharacteristic, complemented
35C11×#340C2212yescomplemented
36#10622189C2211yescharacteristic, complemented
37#10622189C2212yescomplemented
38#10622167C2212yescomplemented
39#10622167C2212yescomplemented
40#10622167C2212yescomplemented
41C24×D11D411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11D411yescharacteristic
44C22×C4×D11—22no—
45C22×C4×D11—22no—
46C22×C4×D11—24no—
47C22×C4×D11—24no—
48C22×C4×D11D411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11C2311yescharacteristic
51C22×C4×D11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C22⋊C4—22no—
57C2×C22⋊Dic11—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2312yes—
64C2×C4×Dic11—22no—
65C2×C4×Dic11—22no—
66C22×C11⋊C8C2311yescharacteristic
67C22×C11⋊C8C2311yescharacteristic
68C2×C8×D11—24no—
69C2×C8×D11—22no—
70C2×C8×D11—24no—
71C2×C8×D11D414yes—
72#66945—24no—
73#66945—24no—
74#66945—24no—
75#66945—24no—
76C11×#107—22no—
77C11×C22⋊C8—22no—
78C11×#95—22no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C22⋊(C11⋊C8)—22no—
83(C2×D11)⋊C8—22no—
84(C2×D11)⋊C8—22no—
85#66882—22no—
86#66872—24no—
87#23638—111nomaximal, Sylow
88C24×C11C2×D411yescharacteristic
89C23×D11—22no—
90C23×D11—22no—
91C23×D11—22no—
92C23×D11—24no—
93C23×D11—42no—
94C23×D11C2×D411yescharacteristic
95C23×D11C2×D411yescharacteristic
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—24no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11C2×D411yescharacteristic
109C22×Dic11C2×D411yescharacteristic
110C2×C4×D11—22no—
111C2×C4×D11—24no—
112C2×C4×D11—22no—
113C2×C4×D11—24no—
114C2×C4×D11—21no—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—21no—
118C2×C4×D11—44no—
119C2×C4×D11—44no—
120C2×C4×D11—48no—
121C2×C4×D11C2×D412yes—
122C2×C4×D11#4112yes—
123C2×C4×D11#4114yes—
124C2×C4×D11#4114yes—
125C2×C8×C11—21no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11C2×D412yes—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C22⋊C4—44no—
134C22⋊Dic11—44no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4—44no—
137(C2×D11)⋊C4—44no—
138(C2×D11)⋊C4—44no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4×Dic11—44no—
144C4×Dic11—44no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8C2×D412yes—
149C8×D11—28no—
150C8×D11—44no—
151C2×#427—111no—
152C22×C22⋊C8—111no—
153#2280—112no—
154#2077—112no—
155#2077—112no—
156#2076—111no—
157#2076—111no—
158#2075—111no—
159#2075D1111yescharacteristic, complemented
160#1735—112no—
161#1735—111no—
162C23×C11—21no—
163C23×C11—22no—
164C23×C11—21no—
165C23×C11—22no—
166C23×C11#13512yes—
167C23×C11C22×D411yescharacteristic
168C22×D11—21no—
169C22×D11—21no—
170C22×D11—22no—
171C22×D11—28no—
172C22×D11—21no—
173C22×D11—22no—
174C22×D11—21no—
175C22×D11—22no—
176C22×D11—48no—
177C22×D11—48no—
178C22×D11—44no—
179C22×D11—44no—
180C22×D11#12112yes—
181C22×D11#12314yes—
182C22×D11#13512yes—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4112yes—
196C2×C4×C11C2×#4112yes—
197C2×C4×C11C2×#4111yescharacteristic
198C2×Dic11—21no—
199C2×Dic11—22no—
200C2×Dic11—44no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11#12112yes—
208C2×Dic11#12314yes—
209C4×D11—44no—
210C4×D11—41no—
211C4×D11—41no—
212C4×D11—42no—
213C4×D11—44no—
214C4×D11#12314yes—
215C4×D11#12414yes—
216C4×D11#12618yes—
217C8×C11—22no—
218C8×C11—41no—
219C11⋊C8—22no—
220C11⋊C8—41no—
221C24×C4—111no—
222C23×C8—111no—
223C23×C8—111no—
224C2×#117—112no—
225C2×#117—112no—
226#427—224no—
227C2×#107—111no—
228C2×#107C2×D1111yescharacteristic, complemented
229C2×#106—112no—
230C2×C22⋊C8—111no—
231C2×C22⋊C8—111no—
232C2×C22⋊C8—111no—
233C2×C22⋊C8—224no—
234C2×C22⋊C8C2×D1111yescharacteristic
235#381—222no—
236#380—112no—
237#380—112no—
238#380—112no—
239#380C2×D1112yes—
240#379—222no—
241C4×C22⋊C4—222no—
242C4×C22⋊C4—222no—
243#340—111no—
244#340—112no—
245#340—112no—
246#340—112no—
247#340—112no—
248#340C2×D1111yescharacteristic, complemented
249#340C2×D1112yescomplemented
250C22×C11—24no—
251C22×C11—22no—
252C22×C11—42no—
253C22×C11—41no—
254C22×C11—41no—
255C22×C11C2×#12111yescharacteristic
256C22×C11C2×#12312yes—
257C22×C11C2×#13511yescharacteristic
258C22×C11C2×#13511yescharacteristic
259C22×C11#57512yes—
260C2×D11—24no—
261C2×D11—24no—
262C2×D11—22no—
263C2×D11—22no—
264C2×D11—24no—
265C2×D11—22no—
266C2×D11—416no—
267C2×D11—42no—
268C2×D11—41no—
269C2×D11—41no—
270C2×D11#39714yes—
271C4×C11—41no—
272C4×C11—82no—
273C4×C11—82no—
274C4×C11C2×#12311yescharacteristic
275C4×C11C2×#12411yescharacteristic
276C4×C11C2×#12612yes—
277Dic11—41no—
278Dic11—82no—
279Dic11—82no—
280Dic11#39714yes—
281C25—111no—
282C23×C4—111no—
283C23×C4—111no—
284C23×C4—111no—
285C23×C4—111no—
286C23×C4—111no—
287C23×C4—222no—
288C23×C4—222no—
289C23×C4—224no—
290C23×C4—224no—
291C23×C4C22×D1111yescharacteristic
292C22×C8—111no—
293C22×C8—114no—
294C22×C8—111no—
295C22×C8—224no—
296C22×C8—224no—
297C22×C8—222no—
298C22×C8C22×D1111yescharacteristic
299C22×C8C22×D1111yescharacteristic
300#117—224no—
301#117—224no—
302#117—224no—
303#117—224no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4C22×D1112yes—
307C2×C4⋊C4C22×D1112yes—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—222no—
310C2×C22⋊C4—222no—
311C2×C22⋊C4—222no—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C42—222no—
315C2×C42—222no—
316#107—22no—
317#107—222no—
318#106—224no—
319C22⋊C8—22no—
320C22⋊C8—222no—
321C22⋊C8—222no—
322C22⋊C8—222no—
323#95—22no—
324#95—222no—
325#95—222no—
326#95—222no—
327C2×C11—42no—
328C2×C11C2×#39711yescharacteristic
329C2×C11#305011yescharacteristic
330C2×C11#305411yescharacteristic
331C2×C11#309112yes—
332C2×C11#309112yes—
333D11—24no—
334D11—42no—
335C24—111no—
336C24—111no—
337C24—222no—
338C24—222no—
339C24—224no—
340C24—222no—
341C24—442no—
342C24D4×D1111yescharacteristic
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—111no—
350C22×C4—112no—
351C22×C4—112no—
352C22×C4—114no—
353C22×C4—114no—
354C22×C4—111no—
355C22×C4—222no—
356C22×C4—224no—
357C22×C4—222no—
358C22×C4—224no—
359C22×C4—222no—
360C22×C4—224no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—448no—
368C22×C4—444no—
369C22×C4—444no—
370C22×C4D4×D1111yescharacteristic
371C22×C4C23×D1111yescharacteristic
372C2×C8—22no—
373C2×C8—21no—
374C2×C8—22no—
375C2×C8—112no—
376C2×C8—228no—
377C2×C8—222no—
378C2×C8—221no—
379C2×C8—222no—
380C2×C8—444no—
381C2×C8D4×D1112yes—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—222no—
390C22⋊C4—44no—
391C22⋊C4—444no—
392C22⋊C4—444no—
393C22⋊C4—444no—
394C22⋊C4—444no—
395C22⋊C4—444no—
396C42—444no—
397C42—444no—
398C11#2363811yescharacteristic, complemented, Sylow
399C23—21no—
400C23—22no—
401C23—21no—
402C23—22no—
403C23—112no—
404C23—114no—
405C23—112no—
406C23—228no—
407C23—221no—
408C23—221no—
409C23—222no—
410C23—221no—
411C23—222no—
412C23—221no—
413C23—222no—
414C23—448no—
415C23—444no—
416C23—448no—
417C23—444no—
418C23#6696512yes—
419C23C2×D4×D1111yescharacteristic
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—112no—
432C2×C4—114no—
433C2×C4—118no—
434C2×C4—114no—
435C2×C4—114no—
436C2×C4—221no—
437C2×C4—222no—
438C2×C4—444no—
439C2×C4—444no—
440C2×C4—444no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4C2×D4×D1111yescharacteristic
451C2×C4#41×D1111yescharacteristic
452C2×C4#41×D1112yes—
453C2×C4#41×D1112yes—
454C8—22no—
455C8—41no—
456C8—222no—
457C8—441no—
458C22—22no—
459C22—24no—
460C22—42no—
461C22—41no—
462C22—41no—
463C22—114no—
464C22—224no—
465C22—222no—
466C22—222no—
467C22—224no—
468C22—224no—
469C22—222no—
470C22—4416no—
471C22—441no—
472C22—441no—
473C22—442no—
474C22D11×#12111yescharacteristic
475C22D11×#12312yes—
476C22C2×#6696511yescharacteristic
477C22D11×#13511yescharacteristic
478C22#1062330812yes—
479C4—41no—
480C4—82no—
481C4—82no—
482C4—114no—
483C4—441no—
484C4—882no—
485C4—882no—
486C4D11×#12311yescharacteristic
487C4D11×#12411yescharacteristic
488C4D11×#12612yes—
489C2—42no—
490C2—224no—
491C2—442no—
492C2D11×#39711yescharacteristic
493C2#1307819511yescharacteristic
494C2#1307822711yescharacteristic
495C2#1307852412yes—
496C2#1307853412yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2075C2
socleC23×C11C22×D4
prime radicalC24×D11D4
hypercenter#2075D11
hypocenterC11#23638
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2075

Complements

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

NH ≅ G/Ntype
1. C2×#10622493C2semidirect
4. #13070054C2semidirect
5. #13070052C2semidirect
6. #13070046C2semidirect
7. #13070044C2semidirect
8. #13070040C2semidirect
9. #13068331C2semidirect
10. #13068331C2semidirect
11. C11×#2075C2semidirect
17. C2×C11×#107C22semidirect
24. C2×#66882C22semidirect
27. C2×#66872C22semidirect
34. C11×#340C22semidirect
35. C11×#340C22semidirect
36. #10622189C22semidirect
37. #10622189C22semidirect
38. #10622167C22semidirect
39. #10622167C22semidirect
40. #10622167C22semidirect
159. #2075D11semidirect
228. C2×#107C2×D11semidirect
248. #340C2×D11semidirect
249. #340C2×D11semidirect
398. C11#23638semidirect

Maximal subgroups

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

subgroupindex
C2×#106224932
C2×D11×C22⋊C82
#130709982
#130700542
#130700522
#130700462
#130700442
#130700402
#130683312
C11×#20752
#2363811