Finite Group Databasebeta

← #14736313

Subgroups — #14736313

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079127C211yesmaximal, characteristic, complemented
2#13078623C212yesmaximal
3D11×#436C211yesmaximal, characteristic
4#13068140C211yesmaximal, characteristic, complemented
5#13068139C211yesmaximal, characteristic, complemented
6#13068126C211yesmaximal, characteristic, complemented
7#13068114C212yesmaximal, complemented
8#13068113C212yesmaximal, complemented
9#13067361C211yesmaximal, characteristic, complemented
10#13067272C212yesmaximal, complemented
11C11×#1693C211yesmaximal, characteristic, complemented
12C2×M16×D11—21no—
13#10623259C2212yes—
14C4×D4×D11C2211yescharacteristic
15C11×#500C2211yescharacteristic, complemented
16C11×#461C2212yes—
17C11×#436C2211yescharacteristic
18#10622782—22no—
19SD16×Dic11—22no—
20#10622741—21no—
21#10622696C2212yes—
22#10622692C2212yescomplemented
23#10622625C2211yescharacteristic
24#10622621C2212yes—
25#10622493—21no—
26#10622493—21no—
27#10622491—21no—
28#10622491—21no—
29#10622455C2212yes—
30#10622451C2211yescharacteristic
31#10622446C2212yes—
32D11×C4⋊C8C2211yescharacteristic
33#10622418—22no—
34#10622401—22no—
35#10622342—21no—
36D11×C22⋊C8—21no—
37#10622301C2211yescharacteristic
38C4×C8×D11C2211yescharacteristic
39#10622295C2211yescharacteristic, complemented
40C11×#334C2211yescharacteristic, complemented
41C11×#332C2212yescomplemented
42#10622185C2212yescomplemented
43#10622119C2212yescomplemented
44#10622119C2212yescomplemented
45#10622117C2212yescomplemented
46#10622095C2211yescharacteristic, complemented
47C2×D4×D11D411yescharacteristic
48C22×C4×D11—21no—
49C2×C11×SD16—22no—
50C2×C11×M16—21no—
51C11×C4⋊Q8C2312yes—
52C4×D4×C11C2311yescharacteristic
53#66999—22no—
54Q8×Dic11—22no—
55C2×#4325—22no—
56D4×Dic11D411yescharacteristic
57C4×C22⋊D11—21no—
58C2×#4318—21no—
59M16×D11—44no—
60C2×#4313—21no—
61C2×#4313—21no—
62C2×C8×D11—21no—
63C2×C8×D11D411yescharacteristic
64C2×C8×D11D411yescharacteristic
65#66950—22no—
66#66946D411yescharacteristic
67#66945—22no—
68C4⋊C4×D11D411yescharacteristic
69#66943—22no—
70#66940—22no—
71(C22⋊D11)⋊C4—21no—
72C22⋊C4×D11—21no—
73C4×D44C2311yescharacteristic
74C42×D11C2311yescharacteristic
75#66922C2312yes—
76C11×#107—21no—
77C11×#107—21no—
78C11×C4⋊C8C2311yescharacteristic
79C11×C4⋊C8C2312yes—
80C11×#103—22no—
81C11×C22⋊C8—21no—
82C4×C8×C11C2311yescharacteristic
83#66899—22no—
84#66896—22no—
85C22⋊(C11⋊C8)—21no—
86#66885—22no—
87(C2×D11)⋊C8—22no—
88(C2×D11)⋊C8—21no—
89(C2×D11)⋊C8—21no—
90#66882—21no—
91#66882—21no—
92#66881—22no—
93Dic11⋊C8—21no—
94C8×Dic11—22no—
95C8×Dic11D411yescharacteristic
96C8×Dic11D411yescharacteristic
97#66872—22no—
98#66872—22no—
99#66872—22no—
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4⋊(C11⋊C8)C2312yes—
102C4×C11⋊C8C2311yescharacteristic
103#19137—111nomaximal, Sylow
104C23×D11—21no—
105C2×Q8×C11—22no—
106C2×D4×C11C2×D411yescharacteristic
107C22×C4×C11—21no—
108C2×C22⋊D11—21no—
109C22×Dic11—21no—
110D4×D11—42no—
111C2×D44C2×D411yescharacteristic
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—21no—
115C2×C4×D11—42no—
116C2×C4×D11—42no—
117C2×C4×D11C2×D411yescharacteristic
118C2×C4×D11C2×D411yescharacteristic
119C2×C4×D11#4111yescharacteristic
120C2×Dic22—22no—
121C11×SD16—44no—
122C11×M16—42no—
123C2×C8×C11—22no—
124C2×C8×C11—21no—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4C2×D411yescharacteristic
130C11×C22⋊C4—21no—
131C42×C11C2411yescharacteristic
132C22⋊Dic11—21no—
133#4325—44no—
134(C2×D11)⋊C4—21no—
135(C2×D11)⋊C4—21no—
136(C2×D11)⋊C4—42no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—42no—
140C4⋊Dic11C2×D411yescharacteristic
141Dic11⋊C4—21no—
142Dic11⋊C4—42no—
143C4×Dic11—42no—
144C4×Dic11C2×D411yescharacteristic
145C4×Dic11C2×D411yescharacteristic
146C4×Dic11#4111yescharacteristic
147#4318—42no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8C2×D411yescharacteristic
151C2×C11⋊C8C2×D411yescharacteristic
152#4313—42no—
153#4313—42no—
154C8×D11—22no—
155C8×D11—42no—
156C8×D11SD1614yescomplemented
157#3160—111no—
158#3101—112no—
159C2×#436—111no—
160#1695—111no—
161#1695—111no—
162#1693—111no—
163#1693D1111yescharacteristic, complemented
164#1691—112no—
165#1691—112no—
166#1564—111no—
167#1542—112no—
168C23×C11—21no—
169C22×D11—21no—
170C22×D11—42no—
171C22×D11—42no—
172C22×D11—42no—
173C22×D11#12111yescharacteristic
174Q8×C11—42no—
175Q8×C11—42no—
176D4×C11—22no—
177C2×C4×C11—21no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C22⋊D11—42no—
185C2×Dic11—21no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11#12111yescharacteristic
189C2×Dic11#12111yescharacteristic
190C2×Dic11#12111yescharacteristic
191D44—22no—
192C4×D11—22no—
193C4×D11—41no—
194C4×D11—42no—
195C4×D11—41no—
196C4×D11—41no—
197C4×D11—42no—
198C4×D11C2×SD1612yes—
199C4×D11#13712yes—
200Dic22—82no—
201C8×C11—21no—
202C8×C11—41no—
203C8×C11—42no—
204C8×C11C2×SD1612yes—
205C11⋊C8—21no—
206C11⋊C8—41no—
207C11⋊C8—42no—
208C11⋊C8C2×SD1612yes—
209C22×M16—221no—
210#533—112no—
211C2×C4×D4—111no—
212#500—111no—
213#500C2×D1111yescharacteristic, complemented
214#499—221no—
215#499—221no—
216#498—112no—
217#483—222no—
218#476—112no—
219#476—112no—
220#461—112no—
221#461C2×D1112yes—
222#450—222no—
223C4×SD16—222no—
224C4×SD16—222no—
225#436—111no—
226#436—111no—
227#436—111no—
228#436—221no—
229#436—221no—
230#436C2×D1111yescharacteristic
231#431—112no—
232#427—221no—
233#427—221no—
234C2×C4⋊C8—111no—
235C2×C22⋊C8—221no—
236C2×C4×C8—111no—
237#335—112no—
238#334—111no—
239#334C2×D1111yescharacteristic, complemented
240#333—112no—
241#333—112no—
242#332—112no—
243#332C2×D1112yescomplemented
244C22×C11—41no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11C2×#12111yescharacteristic
248C2×D11—21no—
249C2×D11—21no—
250C2×D11—41no—
251C2×D11—41no—
252C2×D11—41no—
253C2×D11—84no—
254C2×D11#46112yes—
255C4×C11—21no—
256C4×C11—41no—
257C4×C11—82no—
258C4×C11C22×SD1611yescharacteristic
259C4×C11C2×#13711yescharacteristic
260C4×C11#57512yes—
261Dic11—21no—
262Dic11—21no—
263Dic11—41no—
264Dic11—82no—
265Dic11#46112yes—
266C22×D4—111no—
267C23×C4—221no—
268C2×SD16—22no—
269C2×SD16—222no—
270C2×M16—21no—
271C2×M16—221no—
272C2×M16—221no—
273C2×M16—221no—
274C2×M16—444no—
275C22×C8—111no—
276C22×C8—111no—
277C22×C8—221no—
278C4⋊Q8—112no—
279C4⋊Q8C22×D1112yes—
280#125—222no—
281C22⋊Q8—222no—
282C22⋊Q8—222no—
283C4×Q8—222no—
284C4×Q8—222no—
285C4×D4—111no—
286C4×D4—111no—
287C4×D4—111no—
288C4×D4—221no—
289C4×D4—221no—
290C4×D4C22×D1111yescharacteristic
291#117—222no—
292C2×C4⋊C4—111no—
293C2×C22⋊C4—221no—
294C2×C42—111no—
295#107—21no—
296#107—21no—
297#107—221no—
298#107—221no—
299#106—222no—
300#106—222no—
301#106—222no—
302#106—222no—
303C4⋊C8—111no—
304C4⋊C8—112no—
305C4⋊C8—221no—
306C4⋊C8C22×D1111yescharacteristic
307C4⋊C8C22×D1112yes—
308#103—22no—
309#103—222no—
310#102—222no—
311#102—222no—
312C22⋊C8—21no—
313C22⋊C8—221no—
314C22⋊C8—222no—
315C22⋊C8—221no—
316C22⋊C8—221no—
317C4×C8—111no—
318C4×C8—111no—
319C4×C8—111no—
320C4×C8—222no—
321C4×C8C22×D1111yescharacteristic
322C2×C11—81no—
323C2×C11C2×#46111yescharacteristic
324C2×C11#305411yescharacteristic
325C2×C11#306711yescharacteristic
326D11—22no—
327D11—81no—
328C24—221no—
329C2×Q8—22no—
330C2×Q8—222no—
331C2×D4—111no—
332C2×D4—221no—
333C2×D4—442no—
334C2×D4D4×D1111yescharacteristic
335C22×C4—21no—
336C22×C4—111no—
337C22×C4—111no—
338C22×C4—111no—
339C22×C4—221no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—442no—
344C22×C4—442no—
345SD16—44no—
346SD16—444no—
347M16—42no—
348M16—442no—
349M16—442no—
350M16—442no—
351C2×C8—22no—
352C2×C8—21no—
353C2×C8—111no—
354C2×C8—114no—
355C2×C8—111no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—221no—
359C2×C8—442no—
360C2×C8D4×D1111yescharacteristic
361C2×C8D4×D1111yescharacteristic
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—111no—
365C4⋊C4—221no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—442no—
369C4⋊C4—442no—
370C4⋊C4D4×D1111yescharacteristic
371C22⋊C4—21no—
372C22⋊C4—221no—
373C22⋊C4—221no—
374C22⋊C4—221no—
375C22⋊C4—442no—
376C42—111no—
377C42—111no—
378C42—111no—
379C42—442no—
380C42C23×D1111yescharacteristic
381C11#1913711yescharacteristic, complemented, Sylow
382C23—21no—
383C23—111no—
384C23—221no—
385C23—442no—
386C23—442no—
387C23—442no—
388Q8—42no—
389Q8—42no—
390Q8—882no—
391D4—22no—
392D4—222no—
393D4—442no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—111no—
399C2×C4—112no—
400C2×C4—112no—
401C2×C4—111no—
402C2×C4—111no—
403C2×C4—222no—
404C2×C4—221no—
405C2×C4—441no—
406C2×C4—442no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—442no—
412C2×C4C2×D4×D1111yescharacteristic
413C2×C4C2×D4×D1111yescharacteristic
414C2×C4#41×D1111yescharacteristic
415C8—21no—
416C8—41no—
417C8—42no—
418C8—112no—
419C8—221no—
420C8—441no—
421C8—442no—
422C8SD16×D1112yes—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—112no—
427C22—221no—
428C22—221no—
429C22—441no—
430C22—441no—
431C22—441no—
432C22—884no—
433C22D11×#12111yescharacteristic
434C4—21no—
435C4—41no—
436C4—82no—
437C4—112no—
438C4—221no—
439C4—221no—
440C4—441no—
441C4—882no—
442C4C2×SD16×D1111yescharacteristic
443C4#1062330412yes—
444C4D11×#13711yescharacteristic
445C2—81no—
446C2—222no—
447C2—881no—
448C2D11×#46111yescharacteristic
449C2#1307822311yescharacteristic
450C2#1307833811yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1693C2
socleC22×C11C2×#121
prime radicalC2×D4×D11D4
hypercenter#1693D11
hypocenterC11#19137
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1693

Complements

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

NH ≅ G/Ntype
1. #13079127C2semidirect
4. #13068140C2semidirect
5. #13068139C2semidirect
6. #13068126C2semidirect
7. #13068114C2semidirect
8. #13068113C2semidirect
9. #13067361C2semidirect
10. #13067272C2semidirect
11. C11×#1693C2semidirect
15. C11×#500C22semidirect
22. #10622692C22semidirect
39. #10622295C22semidirect
40. C11×#334C22semidirect
41. C11×#332C22semidirect
42. #10622185C22semidirect
43. #10622119C22semidirect
44. #10622119C22semidirect
45. #10622117C22semidirect
46. #10622095C22semidirect
156. C8×D11SD16semidirect
163. #1693D11semidirect
213. #500C2×D11semidirect
239. #334C2×D11semidirect
243. #332C2×D11semidirect
381. C11#19137semidirect

Maximal subgroups

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

subgroupindex
#130791272
#130786232
D11×#4362
#130681402
#130681392
#130681262
#130681142
#130681132
#130673612
#130672722
C11×#16932
#1913711