Finite Group Databasebeta

← #14754813

Subgroups — #14754813

Order 2816.

1458 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623358C211yesmaximal, characteristic
2C22×#66872C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic
4#13071240C211yesmaximal, characteristic, complemented
5#13068882C214yesmaximal, complemented
6#13068875C214yesmaximal, complemented
7#13068336C211yesmaximal, characteristic, complemented
8#13068314C211yesmaximal, characteristic, complemented
9C2×C11×#417C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13#10623358—24no—
14#10623358—24no—
15C2×Q8×Dic11C2212yes—
16C2×D4×Dic11—22no—
17C2×D4×Dic11C2212yes—
18C2×#66979—21no—
19C2×#66979C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×C4⋊Dic11—21no—
22C22×C4⋊Dic11C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24C11×#417—24no—
25C2×C11×#103C2212yes—
26C2×C11×#102C2212yes—
27#10622846C418yescomplemented
28C2×#66899C2212yes—
29C2×#66896C2212yes—
30#10622823—22no—
31#10622590—21no—
32#10622589—21no—
33#10622586C2214yes—
34C2×#66872—24no—
35C2×#66872C2214yes—
36#10622189C2214yes—
37#10622188C2214yes—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41C2×C414yes—
42C2×C11×#41D414yes—
43C2×C11×#41Q814yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—21no—
51C23×Dic11—22no—
52C2×C11×M16—22no—
53C2×C11×M16—22no—
54C2×C11×M16—22no—
55C22×C8×C11C2312yes—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2312yes—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11D412yes—
63Q8×Dic11—24no—
64Q8×Dic11—24no—
65D4×Dic11—216no—
66D4×Dic11—24no—
67D4×Dic11—24no—
68#66979—28no—
69#66979—22no—
70#66979—22no—
71#66979—22no—
72#66979C2×C414yescomplemented
73C2×C4⋊Dic11—28no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11D414yes—
80C2×C4⋊Dic11C2312yes—
81C2×C4⋊Dic11C2312yes—
82C2×Dic11⋊C4—24no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11C2312yes—
86C22×C11⋊C8—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8C2×C414yescomplemented
89C22×C11⋊C8C2312yes—
90C11×#103—24no—
91C11×#102—24no—
92#66899C2×C418yescomplemented
93#66896C2×C418yescomplemented
94C11⋊#95—24no—
95#66872—28no—
96#20882—111nomaximal, Sylow
97C24×C11—21no—
98C24×C11C2×D411yescharacteristic
99C11×#41—28no—
100C11×#41—28no—
101C11×#41—28no—
102C11×#41C4⋊C4116yescomplemented
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11C22×C412yes—
107C2×Q8×C11C2×D412yes—
108C2×Q8×C11C2×Q812yes—
109C2×D4×C11—24no—
110C2×D4×C11—24no—
111C2×D4×C11—24no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11C22×C412yes—
116C2×D4×C11C2×D412yes—
117C2×D4×C11C2×Q812yes—
118C22×C4×C11—21no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—42no—
124C22×C4×C11—82no—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×Q812yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—28no—
134C22×Dic11—24no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—82no—
138C22×Dic11—84no—
139C22×Dic11C2×D412yes—
140C22×Dic11C2×D412yes—
141C11×M16—44no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—42no—
148C22⋊Dic11—28no—
149C22⋊Dic11—24no—
150C22⋊Dic11—24no—
151C4⋊Dic11—28no—
152C4⋊Dic11—22no—
153C4⋊Dic11—24no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11C22×C414yes—
158C4⋊Dic11C2×D414yes—
159Dic11⋊C4—84no—
160C4×Dic11—28no—
161C4×Dic11—24no—
162C4×Dic11—22no—
163C4×Dic11—22no—
164C2×C11⋊C8—28no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8C22×C414yes—
168C2×#520—111no—
169C22×#106—111no—
170C2×#417D1111yescharacteristic
171C2×#416—111no—
172#2317—111no—
173#1865—114no—
174#1864—114no—
175#1736—111no—
176#1729—111no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11C4×D412yes—
185C23×C11#12012yes—
186C23×C11C22⋊Q812yes—
187C23×C11C22×D411yescharacteristic
188Q8×C11—22no—
189Q8×C11—22no—
190Q8×C11—22no—
191Q8×C11C2×C4⋊C414yes—
192D4×C11—216no—
193D4×C11—22no—
194D4×C11—22no—
195D4×C11—22no—
196D4×C11C2×C4⋊C414yes—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—216no—
201C2×C4×C11—42no—
202C2×C4×C11—44no—
203C2×C4×C11—84no—
204C2×C4×C11C2×C4⋊C414yes—
205C2×C4×C11C4×D414yes—
206C2×C4×C11C4×D412yes—
207C2×C4×C11#12012yes—
208C2×C4×C11C22⋊Q814yes—
209C2×C4×C11C22⋊Q812yes—
210C2×C4×C11#12314yes—
211C2×C4×C11C23×C411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×Q811yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×Dic11—24no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—44no—
226C2×Dic11—84no—
227C2×Dic11—88no—
228C8×C11—42no—
229C11⋊C8—24no—
230C22×#41C2×D1111yescharacteristic
231C22×M16C2×D1111yescharacteristic
232C23×C8—111no—
233#520—224no—
234#520—224no—
235C2×C4×Q8—112no—
236C2×C4×D4—112no—
237C2×C4×D4—222no—
238C2×#117—111no—
239C2×#117—111no—
240C2×#117—221no—
241C22×C4⋊C4—111no—
242C22×C4⋊C4—221no—
243C22×C4⋊C4C2×D1111yescharacteristic
244C2×#106—114no—
245C2×#106—224no—
246#417—24no—
247#416—118no—
248C2×#103—112no—
249C2×#103C2×D1112yes—
250C2×#102—112no—
251C2×#102C2×D1112yes—
252#389—114no—
253#385—222no—
254#384—221no—
255#382—221no—
256#340—114no—
257#336—114no—
258C22×C11—24no—
259C22×C11—24no—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—24no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11#38514yes—
268C22×C11C2×C4×D411yescharacteristic
269C22×C11C2×#12011yescharacteristic
270C22×C11C2×C22⋊Q811yescharacteristic
271C22×C11#57712yes—
272C22×C11#57712yes—
273C4×C11—24no—
274C4×C11—82no—
275C4×C11#38514yes—
276C4×C11C22×C4⋊C411yescharacteristic
277C4×C11C2×C4×D411yescharacteristic
278C4×C11C2×C22⋊Q811yescharacteristic
279C4×C11C2×#12311yescharacteristic
280Dic11—44no—
281Dic11—42no—
282Dic11—44no—
283Dic11—42no—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—22no—
287C2×#41Dic2214yes—
288C2×#41C4×D1114yes—
289C2×#41C22⋊D1114yes—
290C22×Q8C22×D1111yescharacteristic
291C22×D4—21no—
292C22×D4C22×D1111yescharacteristic
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—222no—
296C23×C4—221no—
297C23×C4C22×D1111yescharacteristic
298C2×M16—22no—
299C2×M16—22no—
300C2×M16—22no—
301C22×C8—114no—
302C22×C8—112no—
303C22×C8—222no—
304C22×C8—222no—
305C22×C8C22×D1112yes—
306C4×Q8—224no—
307C4×Q8—224no—
308C4×D4—224no—
309C4×D4—2216no—
310C4×D4—224no—
311#117—114no—
312#117—228no—
313#117—222no—
314#117—222no—
315#117—222no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—114no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—112no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—228no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—224no—
329C2×C4⋊C4C22×D1112yes—
330C2×C22⋊C4—112no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—221no—
333C2×C42—112no—
334C2×C42—222no—
335C2×C42—221no—
336#106—228no—
337#103—24no—
338#103—118no—
339#102—24no—
340#102—118no—
341#95—224no—
342C2×C11—24no—
343C2×C11—44no—
344C2×C11C2×#38511yescharacteristic
345C2×C11#295212yes—
346C2×C11#300911yescharacteristic
347C2×C11#301011yescharacteristic
348C2×C11#308412yes—
349C24—21no—
350C24D4×D1111yescharacteristic
351#41—28no—
352#41—28no—
353#41—28no—
354#41Dic11⋊C4116yescomplemented
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8C2×Dic2212yes—
359C2×Q8C2×C4×D1112yes—
360C2×Q8C2×C22⋊D1112yes—
361C2×D4—24no—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4C2×Dic2212yes—
368C2×D4C2×C4×D1112yes—
369C2×D4C2×C22⋊D1112yes—
370C22×C4—21no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—42no—
376C22×C4—82no—
377C22×C4—112no—
378C22×C4—112no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—228no—
382C22×C4—224no—
383C22×C4—884no—
384C22×C4—882no—
385C22×C4C2×Dic2212yes—
386C22×C4C2×C4×D1112yes—
387C22×C4D4×D1111yescharacteristic
388C22×C4D4×D1112yes—
389C22×C4#434112yes—
390C22×C4#434112yes—
391C22×C4C2×C22⋊D1112yes—
392C22×C4C23×D1111yescharacteristic
393M16—44no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—114no—
398C2×C8—228no—
399C2×C8—222no—
400C2×C8—222no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—42no—
404C4⋊C4—114no—
405C4⋊C4—114no—
406C4⋊C4—228no—
407C4⋊C4—224no—
408C4⋊C4—222no—
409C4⋊C4—222no—
410C4⋊C4—222no—
411C4⋊C4—222no—
412C4⋊C4—884no—
413C22⋊C4—228no—
414C22⋊C4—224no—
415C22⋊C4—224no—
416C42—228no—
417C42—224no—
418C42—222no—
419C42—222no—
420C11#2088211yescharacteristic, complemented, Sylow
421C23—22no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—42no—
427C23—42no—
428C23#6693112yes—
429C23(C22⋊D11)⋊C412yes—
430C23#6699012yes—
431C23C2×D4×D1111yescharacteristic
432Q8—22no—
433Q8—22no—
434Q8—22no—
435Q8C2×Dic11⋊C414yes—
436D4—216no—
437D4—22no—
438D4—22no—
439D4—22no—
440D4C2×Dic11⋊C414yes—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—216no—
445C2×C4—44no—
446C2×C4—42no—
447C2×C4—84no—
448C2×C4—224no—
449C2×C4—224no—
450C2×C4—224no—
451C2×C4—222no—
452C2×C4—224no—
453C2×C4—222no—
454C2×C4—442no—
455C2×C4—444no—
456C2×C4—442no—
457C2×C4—884no—
458C2×C4—888no—
459C2×C4#6693114yes—
460C2×C4#6693112yes—
461C2×C4(C22⋊D11)⋊C414yes—
462C2×C4(C22⋊D11)⋊C412yes—
463C2×C4C2×Dic11⋊C414yes—
464C2×C4#6698814yes—
465C2×C4#6699012yes—
466C2×C4C22×Dic2211yescharacteristic
467C2×C4C22×C4×D1111yescharacteristic
468C2×C4C2×D4×D1111yescharacteristic
469C2×C4C2×#434111yescharacteristic
470C2×C4C2×#434111yescharacteristic
471C2×C4C22×C22⋊D1111yescharacteristic
472C8—42no—
473C8—224no—
474C22—22no—
475C22—22no—
476C22—24no—
477C22—24no—
478C22—24no—
479C22—42no—
480C22—42no—
481C22—44no—
482C22—44no—
483C22#1062255914yes—
484C22C2×#6693111yescharacteristic
485C22C2×(C22⋊D11)⋊C411yescharacteristic
486C22#1062330612yes—
487C22#1062330912yes—
488C22C2×#6699011yescharacteristic
489C4—24no—
490C4—82no—
491C4—442no—
492C4—444no—
493C4—442no—
494C4—444no—
495C4#1062255914yes—
496C4C2×#6693111yescharacteristic
497C4C2×(C22⋊D11)⋊C411yescharacteristic
498C4C22×Dic11⋊C411yescharacteristic
499C4C2×#6698811yescharacteristic
500C2—24no—
501C2—44no—
502C2C2×#1062255911yescharacteristic
503C2#1307749512yes—
504C2#1307789211yescharacteristic
505C2#1307790111yescharacteristic
506C2#1307848212yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#417D11
hypocenterC11#20882
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C22×#66872C2semidirect
4. #13071240C2semidirect
5. #13068882C2semidirect
6. #13068875C2semidirect
7. #13068336C2semidirect
8. #13068314C2semidirect
27. #10622846C4semidirect
72. #66979C2×C4semidirect
88. C22×C11⋊C8C2×C4semidirect
92. #66899C2×C4semidirect
93. #66896C2×C4semidirect
102. C11×#41C4⋊C4semidirect
354. #41Dic11⋊C4semidirect
420. C11#20882semidirect

Maximal subgroups

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

subgroupindex
C2×#106233582
C22×#668722
C2×#106228462
#130712402
#130688822
#130688752
#130683362
#130683142
C2×C11×#4172
#2088211