Finite Group Databasebeta

← #14753281

Subgroups — #14753281

Order 2816.

1602 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623052C211yesmaximal, characteristic
2C2×#10622732C211yesmaximal, characteristic, complemented
3C2×#10622744C211yesmaximal, characteristic
4C22×#66873C211yesmaximal, characteristic
5#13071240C211yesmaximal, characteristic, complemented
6#13068625C214yesmaximal, complemented
7#13068615C214yesmaximal, complemented
8#13068332C211yesmaximal, characteristic, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17#10623052—24no—
18#10623052C418yescomplemented
19C2×#66946C2214yes—
20C2×C22⋊C4×D11—22no—
21C2×C4×D44—22no—
22#10622823—22no—
23#10622744—24no—
24#10622732—24no—
25C2×#66885C2212yes—
26C2×#66885C2212yes—
27C2×Dic11⋊C8C2214yescomplemented
28#10622590C2212yescomplemented
29#10622589C2212yescomplemented
30#10622586—22no—
31C2×#66873—24no—
32C2×#66873C2214yes—
33C11×#340C2214yescomplemented
34#10622167C2212yescomplemented
35#10622167C2212yescomplemented
36C24×D11—21no—
37C23×C4×C11—21no—
38C23×C4×C11C2311yescharacteristic
39C22×D44—21no—
40C22×D44—22no—
41C22×D44—22no—
42C22×D44—22no—
43C22×D44C2×C414yes—
44C22×D44D414yes—
45C22×D44Q814yes—
46C22×D44C2312yes—
47C22×C4×D11—24no—
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C22×C8×C11C2312yes—
52C11×#117—22no—
53C11×#117C2×C414yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C22⋊C4—21no—
60C2×C42×C11—21no—
61C2×C22⋊Dic11—21no—
62C2×C22⋊Dic11D412yes—
63C2×(C2×D11)⋊C4—24no—
64#66979—22no—
65#66979—22no—
66#66979C2×C414yes—
67#66979D414yes—
68C2×C4⋊Dic11D412yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×Dic11⋊C4—24no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11C2312yes—
74C22×C11⋊C8—22no—
75C22×C11⋊C8—22no—
76C22×C11⋊C8—22no—
77C22×C11⋊C8C2312yes—
78#66946—28no—
79#66946C2×C4116yescomplemented
80C22⋊C4×D11—216no—
81C4×D44—216no—
82C11⋊#95—24no—
83#66885—24no—
84#66885—24no—
85Dic11⋊C8—28no—
86#66873—28no—
87#20650—111nomaximal, Sylow
88C24×C11C2×D411yescharacteristic
89C23×D11—22no—
90C23×D11—24no—
91C23×D11—24no—
92C23×D11—24no—
93C23×D11—82no—
94C23×D11—82no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—42no—
98C22×C4×C11—82no—
99C22×C4×C11C22×C412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×Q812yes—
104C22×C4×C11#4112yes—
105C22×C4×C11#4112yes—
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11C2×D414yes—
110C2×D44—24no—
111C2×D44—28no—
112C2×D44—28no—
113C2×D44—24no—
114C2×D44—28no—
115C2×D44—24no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44C4⋊C4116yescomplemented
120C2×D44C22×C414yes—
121C2×D44C2×D414yes—
122C2×D44C2×Q814yes—
123C2×C4×D11—216no—
124C2×C4×D11—84no—
125C2×C4×D11—84no—
126C11×M16—44no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4C22×C414yes—
135C11×C22⋊C4—24no—
136C42×C11—24no—
137C22⋊Dic11—42no—
138C22⋊Dic11C22⋊C418yes—
139(C2×D11)⋊C4—216no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11C22⋊C418yes—
145Dic11⋊C4—84no—
146C4×Dic11—42no—
147C4×Dic11C22×C414yes—
148C4×Dic11C2×D414yes—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—44no—
153C2×#518—111no—
154C2×#424—111no—
155C2×#418—111no—
156C22×#102—111no—
157#2317—111no—
158#1804—114no—
159#1802—114no—
160#1736D1111yescharacteristic, complemented
161#1735—111no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11C2×C22⋊C412yes—
165C23×C11#12112yes—
166C23×C11C22⋊Q812yes—
167C23×C11C22×D411yescharacteristic
168C22×D11—24no—
169C22×D11—24no—
170C22×D11—24no—
171C22×D11—216no—
172C22×D11—44no—
173C22×D11—44no—
174C22×D11—88no—
175C22×D11—88no—
176C22×D11—84no—
177C22×D11—84no—
178C2×C4×C11—24no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—44no—
183C2×C4×C11—84no—
184C2×C4×C11C2×C22⋊C412yes—
185C2×C4×C11C2×C4⋊C414yes—
186C2×C4×C11#11714yes—
187C2×C4×C11#12114yes—
188C2×C4×C11#12112yes—
189C2×C4×C11C22⋊Q814yes—
190C2×C4×C11C22⋊Q812yes—
191C2×C4×C11C23×C411yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×Q811yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11C2×C22⋊C418yes—
204D44—24no—
205D44—24no—
206D44—24no—
207D44—216no—
208D44C2×C4⋊C418yes—
209C4×D11—816no—
210C8×C11—42no—
211C11⋊C8—42no—
212C23×D4—111no—
213C22×M16C2×D1111yescharacteristic
214C23×C8—111no—
215#518—118no—
216#518—224no—
217C2×C4×D4—114no—
218C2×C4×D4—222no—
219C2×#117—111no—
220C2×#117—111no—
221C2×#117C2×D1111yescharacteristic
222C22×C4⋊C4C2×D1111yescharacteristic
223C22×C22⋊C4—222no—
224#424—224no—
225C2×C4⋊C8—114no—
226#418—224no—
227C2×#102—112no—
228C2×#102—112no—
229C2×#102—114no—
230C2×#102—224no—
231#389—222no—
232#385—222no—
233#384—112no—
234#382—112no—
235#340—112no—
236#340—112no—
237#340C2×D1114yescomplemented
238C22×C11—24no—
239C22×C11—24no—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11#38014yes—
243C22×C11C22×C22⋊C411yescharacteristic
244C22×C11C2×#12111yescharacteristic
245C22×C11C2×C22⋊Q811yescharacteristic
246C22×C11#57612yes—
247C22×C11#57712yes—
248C2×D11—28no—
249C2×D11—48no—
250C2×D11—48no—
251C2×D11—44no—
252C2×D11—44no—
253C2×D11—816no—
254C4×C11—44no—
255C4×C11—82no—
256C4×C11#38014yes—
257C4×C11C22×C4⋊C411yescharacteristic
258C4×C11C2×#11711yescharacteristic
259C4×C11C2×#12111yescharacteristic
260C4×C11C2×C22⋊Q811yescharacteristic
261Dic11—28no—
262Dic11—81no—
263Dic11—81no—
264C25—221no—
265C22×D4—114no—
266C22×D4—114no—
267C22×D4—114no—
268C22×D4—112no—
269C22×D4—222no—
270C22×D4—222no—
271C22×D4—221no—
272C22×D4—222no—
273C23×C4—21no—
274C23×C4—224no—
275C23×C4C22×D1111yescharacteristic
276C2×M16—22no—
277C2×M16—22no—
278C2×M16—22no—
279C22×C8—112no—
280C22×C8—222no—
281C22×C8—222no—
282C22×C8—222no—
283C22×C8C22×D1112yes—
284C4×D4—1116no—
285C4×D4—2216no—
286C4×D4—228no—
287#117—22no—
288#117—114no—
289#117—114no—
290#117—222no—
291#117—222no—
292#117C4×D1114yes—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—224no—
300C2×C4⋊C4C22×D1112yes—
301C2×C4⋊C4C22×D1112yes—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—112no—
304C2×C22⋊C4—2216no—
305C2×C22⋊C4—224no—
306C2×C22⋊C4—221no—
307C2×C42—21no—
308C2×C42—112no—
309C2×C42—221no—
310C4⋊C8—228no—
311#102—228no—
312#102—224no—
313#102—224no—
314#95—224no—
315C2×C11—24no—
316C2×C11C2×#38011yescharacteristic
317C2×C11#289712yes—
318C2×C11#304111yescharacteristic
319C2×C11#304211yescharacteristic
320C2×C11#308112yes—
321D11—48no—
322C24—222no—
323C24—224no—
324C24—224no—
325C24—224no—
326C24—882no—
327C24—882no—
328C24D4×D1111yescharacteristic
329C2×D4—1116no—
330C2×D4—114no—
331C2×D4—114no—
332C2×D4—114no—
333C2×D4—228no—
334C2×D4—224no—
335C2×D4—228no—
336C2×D4—224no—
337C2×D4—228no—
338C2×D4—224no—
339C2×D4—222no—
340C2×D4—222no—
341C2×D4—222no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—42no—
345C22×C4—82no—
346C22×C4—114no—
347C22×C4—2216no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—884no—
351C22×C4—884no—
352C22×C4C2×C4×D1112yes—
353C22×C4#433912yes—
354C22×C4#433912yes—
355C22×C4D4×D1111yescharacteristic
356C22×C4D4×D1112yes—
357C22×C4D4×D1112yes—
358C22×C4Q8×D1112yes—
359C22×C4C23×D1111yescharacteristic
360M16—44no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—222no—
365C2×C8—222no—
366C2×C8—222no—
367C2×C8—444no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—42no—
372C4⋊C4—118no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—884no—
378C4⋊C4C2×C4×D1114yes—
379C22⋊C4—24no—
380C22⋊C4—118no—
381C22⋊C4—2216no—
382C22⋊C4—442no—
383C42—24no—
384C42—114no—
385C42—114no—
386C42—442no—
387C11#2065011yescharacteristic, complemented, Sylow
388C23—22no—
389C23—22no—
390C23—224no—
391C23—224no—
392C23—224no—
393C23—2216no—
394C23—444no—
395C23—444no—
396C23—884no—
397C23—884no—
398C23—888no—
399C23—888no—
400C23C22⋊C4×D1112yes—
401C23#6693712yes—
402C23#6694912yes—
403C23C2×D4×D1111yescharacteristic
404D4—118no—
405D4—224no—
406D4—224no—
407D4—224no—
408D4—2216no—
409C2×C4—24no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—84no—
415C2×C4—118no—
416C2×C4—224no—
417C2×C4—224no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—8816no—
423C2×C4#6692514yes—
424C2×C4C22⋊C4×D1112yes—
425C2×C4#6693714yes—
426C2×C4#6693712yes—
427C2×C4C4⋊C4×D1114yes—
428C2×C4#6694914yes—
429C2×C4#6694912yes—
430C2×C4C22×C4×D1111yescharacteristic
431C2×C4C2×#433911yescharacteristic
432C2×C4C2×#433911yescharacteristic
433C2×C4C2×D4×D1111yescharacteristic
434C2×C4C2×D4×D1111yescharacteristic
435C2×C4C2×Q8×D1111yescharacteristic
436C8—42no—
437C8—442no—
438C22—22no—
439C22—22no—
440C22—24no—
441C22—24no—
442C22—228no—
443C22—444no—
444C22—444no—
445C22—448no—
446C22—448no—
447C22—8816no—
448C22#1062228014yes—
449C22C2×C22⋊C4×D1111yescharacteristic
450C22C2×#6693711yescharacteristic
451C22C2×#6694911yescharacteristic
452C22#1062330512yes—
453C22#1062330912yes—
454C4—44no—
455C4—82no—
456C4—228no—
457C4—881no—
458C4—881no—
459C4#1062228014yes—
460C4C2×#6692511yescharacteristic
461C4C2×#6693711yescharacteristic
462C4C2×C4⋊C4×D1111yescharacteristic
463C4C2×#6694911yescharacteristic
464C2—24no—
465C2—448no—
466C2C2×#1062228011yescharacteristic
467C2#1307714012yes—
468C2#1307811811yescharacteristic
469C2#1307812711yescharacteristic
470C2#1307844512yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#20650
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#10622732C2semidirect
5. #13071240C2semidirect
6. #13068625C2semidirect
7. #13068615C2semidirect
8. #13068332C2semidirect
9. C11×#1736C2semidirect
18. #10623052C4semidirect
27. C2×Dic11⋊C8C22semidirect
28. #10622590C22semidirect
29. #10622589C22semidirect
33. C11×#340C22semidirect
34. #10622167C22semidirect
35. #10622167C22semidirect
79. #66946C2×C4semidirect
119. C2×D44C4⋊C4semidirect
160. #1736D11semidirect
237. #340C2×D11semidirect
387. C11#20650semidirect

Maximal subgroups

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

subgroupindex
C2×#106230522
C2×#106227322
C2×#106227442
C22×#668732
#130712402
#130686252
#130686152
#130683322
C11×#17362
#2065011