Finite Group Databasebeta

← #14810393

Subgroups — #14810393

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×#10622694C211yesmaximal, characteristic, complemented
3#13076963C211yesmaximal, characteristic
4#13069765C214yesmaximal, complemented
5#13069578C211yesmaximal, characteristic, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13068925C214yesmaximal
8C4×(C2×D11)⋊C8C211yesmaximal, characteristic
9C2×C11×#487C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66999—21no—
13C2×#66999C2212yes—
14C2×Q8×Dic11—21no—
15#10623259—24no—
16#10623259—24no—
17C2×#66950—21no—
18C2×#66945C2212yes—
19C2×#66943C2212yes—
20C2×#66940—21no—
21C2×C42×D11C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C11×#487—24no—
24C2×C11×#103C2214yes—
25C2×C4×C8×C11C2211yescharacteristic
26#10622843C2212yes—
27C2×#66899C2214yes—
28C2×(C2×D11)⋊C8C2212yes—
29#10622694—24no—
30#10622600—21no—
31#10622600—21no—
32#10622586—21no—
33#10622586—21no—
34#10622548C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622189C2214yes—
37#10622188C2212yes—
38#10622167C2214yes—
39C22×Q8×C11—21no—
40C22×Q8×C11C2312yes—
41C22×C4×D11D411yescharacteristic
42C22×C4×D11D411yescharacteristic
43C22×C4×D11C2311yescharacteristic
44C22×Dic22—21no—
45C22×C8×C11C2312yes—
46C11×C4⋊Q8—22no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8D414yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C42×C11C2311yescharacteristic
55#66999—28no—
56#66999—28no—
57Q8×Dic11—28no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73#66950—28no—
74#66945—24no—
75#66945—24no—
76#66943—24no—
77#66943—24no—
78#66940—28no—
79C42×D11—22no—
80C42×D11—22no—
81#66922—22no—
82#66922D414yes—
83C11×#103—28no—
84C4×C8×C11—22no—
85#66899—28no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88(C2×D11)⋊C8—24no—
89C4×C11⋊C8—22no—
90#25904—111nomaximal, Sylow
91C23×D11C2×D411yescharacteristic
92C2×Q8×C11—24no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—24no—
96C2×Q8×C11—24no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11C2×D411yescharacteristic
107C22×Dic11C2×D411yescharacteristic
108C22×Dic11C2×D411yescharacteristic
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C4×D11—21no—
116C2×C4×D11—21no—
117C2×C4×D11—22no—
118C2×C4×D11#4114yes—
119C2×Dic22—24no—
120C2×Dic22—42no—
121C2×Dic22—42no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4C2×D414yes—
130C42×C11C2×D412yes—
131C42×C11C2×D412yes—
132(C2×D11)⋊C4—28no—
133(C2×D11)⋊C4—44no—
134C4⋊Dic11—28no—
135C4⋊Dic11—24no—
136C4⋊Dic11—22no—
137C4⋊Dic11—24no—
138C4⋊Dic11—42no—
139C4⋊Dic11—42no—
140C4⋊Dic11C2×D414yes—
141Dic11⋊C4—28no—
142Dic11⋊C4—44no—
143C4×Dic11—28no—
144C4×Dic11—22no—
145C4×Dic11—22no—
146C4×Dic11—21no—
147C4×Dic11—21no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×#533—111no—
152C2×#487—111no—
153C2×#487D1111yescharacteristic, complemented
154#2857—111no—
155#2026—114no—
156#1990—111no—
157#1990—111no—
158#1873—114no—
159C4×C22⋊C8—111no—
160C23×C11C22×D411yescharacteristic
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—21no—
167C22×D11#12412yes—
168Q8×C11—48no—
169Q8×C11—44no—
170Q8×C11—44no—
171C2×C4×C11—24no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11#12012yes—
178C2×C4×C11#12012yes—
179C2×C4×C11#13512yes—
180C2×C4×C11#13512yes—
181C2×C4×C11#13712yes—
182C2×C4×C11#13712yes—
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C2×#4112yes—
186C2×C4×C112−1+412yes—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—24no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11#12412yes—
202C4×D11—24no—
203C4×D11—24no—
204C4×D11—44no—
205C4×D11—44no—
206Dic22—48no—
207C8×C11—42no—
208C11⋊C8—42no—
209#533—224no—
210#533—224no—
211C2×C4⋊Q8—111no—
212C2×C4⋊Q8C2×D1111yescharacteristic
213C2×C4⋊Q8C2×D1111yescharacteristic
214C2×#125—112no—
215C2×C22⋊Q8—112no—
216C2×C22⋊Q8—221no—
217C2×C22⋊Q8—221no—
218C2×C4×Q8—221no—
219C2×C4×Q8—221no—
220C2×#117—112no—
221C22×C42—111no—
222#487—24no—
223#487—224no—
224C2×#103—114no—
225C2×#103C2×D1114yes—
226C2×C22⋊C8—112no—
227C2×C4×C8—111no—
228C2×C4×C8C2×D1111yescharacteristic
229#391—112no—
230#389—221no—
231#389—221no—
232#384—111no—
233#380—221no—
234#380—221no—
235#340—114no—
236#340—114no—
237#336—112no—
238C22×C11C2×#12011yescharacteristic
239C22×C11C2×#12411yescharacteristic
240C22×C11#53611yescharacteristic
241C22×C11C2×#13511yescharacteristic
242C22×C11C2×#13511yescharacteristic
243C22×C11C2×#13711yescharacteristic
244C22×C11C2×#13711yescharacteristic
245C2×D11—22no—
246C2×D11—22no—
247C2×D11—22no—
248C2×D11—41no—
249C2×D11—41no—
250C2×D11—41no—
251C2×D11—41no—
252C4×C11—44no—
253C4×C11—82no—
254C4×C11#45214yes—
255C4×C11#45214yes—
256C4×C11#54812yes—
257C4×C11#54812yes—
258Dic11—22no—
259Dic11—44no—
260Dic11—41no—
261Dic11—41no—
262Dic11—82no—
263C22×Q8—21no—
264C22×Q8—221no—
265C22×Q8C22×D1112yes—
266C23×C4—111no—
267C23×C4—111no—
268C23×C4—111no—
269C22×C8—112no—
270C22×C8C22×D1112yes—
271C4⋊Q8—22no—
272C4⋊Q8—22no—
273C4⋊Q8—22no—
274C4⋊Q8—114no—
275C4⋊Q8—222no—
276C4⋊Q8C22⋊D1114yes—
277#125—224no—
278#125—224no—
279C22⋊Q8—228no—
280C22⋊Q8—228no—
281C22⋊Q8—228no—
282C4×Q8—228no—
283C4×Q8—228no—
284#117—224no—
285#117—224no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4C22×D1112yes—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—222no—
300C2×C42—111no—
301C2×C42—111no—
302C2×C42—111no—
303C2×C42—222no—
304C2×C42—222no—
305C2×C42—222no—
306C2×C42C22×D1111yescharacteristic
307#103—28no—
308#103—228no—
309C22⋊C8—224no—
310C4×C8—22no—
311C4×C8—222no—
312#95—222no—
313#95—222no—
314C2×C11#243611yescharacteristic
315C2×C11C2×#45211yescharacteristic
316C2×C11C2×#45211yescharacteristic
317C2×C11#313111yescharacteristic
318C2×C11#313911yescharacteristic
319C2×C11#323111yescharacteristic
320C2×C11#323111yescharacteristic
321D11—42no—
322C24—111no—
323C2×Q8—24no—
324C2×Q8—22no—
325C2×Q8—24no—
326C2×Q8—24no—
327C2×Q8—22no—
328C2×Q8—42no—
329C2×Q8—42no—
330C2×Q8—224no—
331C2×Q8—442no—
332C2×Q8—442no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—111no—
336C22×C4—114no—
337C22×C4—111no—
338C22×C4—111no—
339C22×C4—221no—
340C22×C4—222no—
341C22×C4—221no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4D4×D1111yescharacteristic
351C22×C4D4×D1111yescharacteristic
352C22×C4C23×D1111yescharacteristic
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—222no—
359C4⋊C4—24no—
360C4⋊C4—22no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—114no—
364C4⋊C4—228no—
365C4⋊C4—228no—
366C4⋊C4—224no—
367C4⋊C4—222no—
368C4⋊C4—224no—
369C4⋊C4—444no—
370C4⋊C4—442no—
371C4⋊C4—442no—
372C4⋊C4C2×C22⋊D1114yes—
373C22⋊C4—228no—
374C22⋊C4—444no—
375C42—228no—
376C42—222no—
377C42—222no—
378C42—221no—
379C42—221no—
380C42D4×D1112yes—
381C42C2×C22⋊D1112yes—
382C11#2590411yescharacteristic, complemented, Sylow
383C23—112no—
384C23—221no—
385C23—221no—
386C23—221no—
387C23—221no—
388C23—221no—
389C23—221no—
390C23C2×D4×D1111yescharacteristic
391Q8—48no—
392Q8—44no—
393Q8—44no—
394Q8—448no—
395C2×C4—24no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—112no—
402C2×C4—221no—
403C2×C4—221no—
404C2×C4—224no—
405C2×C4—224no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—224no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—444no—
416C2×C4—444no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4#6696812yes—
421C2×C4#6696912yes—
422C2×C4#6697112yes—
423C2×C4#6697212yes—
424C2×C4#6699012yes—
425C2×C4#6699012yes—
426C2×C4C2×D4×D1111yescharacteristic
427C2×C4#41×D1112yes—
428C2×C4#6704312yes—
429C2×C4C22×C22⋊D1111yescharacteristic
430C8—42no—
431C8—442no—
432C22—222no—
433C22—222no—
434C22—222no—
435C22—441no—
436C22—441no—
437C22—441no—
438C22—441no—
439C22D11×#12411yescharacteristic
440C22#1062320611yescharacteristic
441C22C2×#6696811yescharacteristic
442C22C2×#6696911yescharacteristic
443C22C2×#6697111yescharacteristic
444C22C2×#6697211yescharacteristic
445C22C2×#6699011yescharacteristic
446C4—44no—
447C4—82no—
448C4—222no—
449C4—441no—
450C4—441no—
451C4—444no—
452C4—882no—
453C4#1062278614yes—
454C4#1062280014yes—
455C4#1062320812yes—
456C4#1062336212yes—
457C2—442no—
458C2#1307227111yescharacteristic
459C2C2×#1062278611yescharacteristic
460C2C2×#1062280011yescharacteristic
461C2#1307894011yescharacteristic
462C2#1307899311yescharacteristic
463C2#1307977011yescharacteristic
464C2#1307977211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#487C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#487D11
hypocenterC11#25904
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
2. C2×#10622694C2semidirect
4. #13069765C2semidirect
5. #13069578C2semidirect
6. #13069577C2semidirect
9. C2×C11×#487C2semidirect
153. C2×#487D11semidirect
382. C11#25904semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106226942
#130769632
#130697652
#130695782
#130695772
#130689252
C4×(C2×D11)⋊C82
C2×C11×#4872
#2590411