Finite Group Databasebeta

← #14738639

Subgroups — #14738639

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079640C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic, complemented
4#13068182C212yesmaximal, complemented
5#13068175C212yesmaximal, complemented
6#13068058C212yesmaximal, complemented
7#13068051C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067334C211yesmaximal, characteristic, complemented
10#13067330C211yesmaximal, characteristic, complemented
11C11×#3217C211yesmaximal, characteristic
12C2×C11×#127C2211yescharacteristic
13C11×#529C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#496—21no—
16C11×#490—21no—
17C11×#460C2212yes—
18C11×#459C2212yes—
19C11×#450—21no—
20C11×#447—21no—
21C11×#432C2211yescharacteristic
22C2×#66896—21no—
23C2×#66896—21no—
24#10622683—21no—
25#10622683—21no—
26#10622683C2212yes—
27#10622683C2212yes—
28#10622682—21no—
29#10622673—21no—
30#10622663—21no—
31#10622653—21no—
32#10622644C2212yescomplemented
33#10622637C2211yescharacteristic, complemented
34Q8×C11⋊C8C2211yescharacteristic, complemented
35#10622632C2212yescomplemented
36#10622625C2211yescharacteristic, complemented
37#10622624—21no—
38D4×C11⋊C8—21no—
39D4×C11⋊C8C2211yescharacteristic, complemented
40#10622613—21no—
41#10622610—21no—
42#10622539C2211yescharacteristic
43#10622539C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622182C2212yes—
46#10622182C2212yes—
47#10622120C2212yescomplemented
48#10622120C2212yescomplemented
49#10622118C2212yescomplemented
50#10622117C2212yescomplemented
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×Dic22—21no—
55C2×C11×SD16—22no—
56C2×C11×D8—22no—
57C11×#127—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127C2312yes—
61C11×#126—21no—
62C11×#125D411yescharacteristic
63C11×#124D411yescharacteristic
64C11×#123—21no—
65C11×C22⋊Q8D411yescharacteristic
66C11×#121D411yescharacteristic
67C4×Q8×C11C2311yescharacteristic
68C4×D4×C11—21no—
69C4×D4×C11C2311yescharacteristic
70C11×#117—21no—
71C2×C42×C11C2311yescharacteristic
72C2×#4326—22no—
73C2×#4324—22no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×#4318—21no—
77C22×C11⋊C8—21no—
78C22×C11⋊C8D411yescharacteristic
79C22×C11⋊C8D411yescharacteristic
80#66922—21no—
81#66922—21no—
82#66922—21no—
83#66922C2312yes—
84C11×C4⋊C8C2312yes—
85C11×#102—22no—
86C11×#102—22no—
87C11×C22⋊C8—21no—
88C11×#97—21no—
89#66896—22no—
90#66896—22no—
91#66896—22no—
92#66896—22no—
93C22⋊(C11⋊C8)—21no—
94C22⋊(C11⋊C8)—21no—
95C22⋊(C11⋊C8)—21no—
96C22⋊(C11⋊C8)—21no—
97#66874—22no—
98#66874—22no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4⋊(C11⋊C8)C2311yescharacteristic
103C4⋊(C11⋊C8)C2312yes—
104#66867—21no—
105#66867—21no—
106#66867—21no—
107C4×C11⋊C8—21no—
108C4×C11⋊C8D411yescharacteristic
109C4×C11⋊C8D411yescharacteristic
110C4×C11⋊C8C2311yescharacteristic
111C4×C11⋊C8C2311yescharacteristic
112#19364—111nomaximal, Sylow
113C24×C11—41no—
114C2×Q8×C11C2×D411yescharacteristic
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—82no—
125C2×D4×C11—82no—
126C2×D4×C11C2×D411yescharacteristic
127C22×C4×C11—21no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C22×Dic11—41no—
132C2×Dic22—22no—
133C2×Dic22—41no—
134C2×Dic22—82no—
135C11×SD16—82no—
136C11×D8—82no—
137C2×C8×C11—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4C2×D411yescharacteristic
143C11×C4⋊C4C2×D411yescharacteristic
144C11×C22⋊C4—21no—
145C11×C22⋊C4—21no—
146C11×C22⋊C4—21no—
147C11×C22⋊C4—21no—
148C11×C22⋊C4—21no—
149C42×C11—21no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11#4111yescharacteristic
153C42×C11C2411yescharacteristic
154#4326—82no—
155#4324—82no—
156C4⋊Dic11—22no—
157C4⋊Dic11—22no—
158C4⋊Dic11—41no—
159C4⋊Dic11—41no—
160#4318—42no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—41no—
165C2×C11⋊C8—41no—
166C2×C11⋊C8—42no—
167C2×C11⋊C8C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169C2×C11⋊C8C2×D411yescharacteristic
170C2×C11⋊C8C2×D411yescharacteristic
171#3218—111no—
172#3217D1111yescharacteristic
173C2×#486—111no—
174#2966—111no—
175#1702—112no—
176#1701—112no—
177#1682—112no—
178#1681—112no—
179#1568—111no—
180#1556—111no—
181#1555—111no—
182C23×C11—21no—
183C23×C11—42no—
184C23×C11—82no—
185C23×C11—82no—
186C23×C11—82no—
187C23×C11#12111yescharacteristic
188Q8×C11—22no—
189D4×C11—22no—
190D4×C11—42no—
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—82no—
196D4×C11—82no—
197D4×C11—82no—
198D4×C11—82no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×Dic11—42no—
215C2×Dic11—82no—
216Dic22—42no—
217Dic22—42no—
218Dic22—82no—
219C8×C11—42no—
220C11⋊C8—21no—
221C11⋊C8—21no—
222C11⋊C8—21no—
223C11⋊C8—21no—
224C11⋊C8—41no—
225C11⋊C8—41no—
226C11⋊C8—42no—
227C2×C4⋊Q8—111no—
228C2×#127C2×D1111yescharacteristic
229#529C2×D1111yescharacteristic
230#497—221no—
231#496—21no—
232#491—221no—
233#490—21no—
234#486—112no—
235#486—112no—
236#486—221no—
237#486—221no—
238#462—112no—
239#461—112no—
240#460C2×D1112yes—
241#459C2×D1112yes—
242#451—221no—
243#450—21no—
244#448—221no—
245#447—21no—
246#446—111no—
247C8×Q8—111no—
248#436—111no—
249#435—221no—
250C8×D4—111no—
251C8×D4—221no—
252#433—221no—
253#432—111no—
254#432—111no—
255#432C2×D1111yescharacteristic
256C2×#102—221no—
257C2×#102—221no—
258#405—221no—
259C2×C4×C8—111no—
260#335—112no—
261#334—112no—
262#332—112no—
263#332—112no—
264#331—112no—
265#331—112no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—41no—
269C22×C11—41no—
270C22×C11—41no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11—164no—
275C22×C11#47112yes—
276C22×C11C2×#12111yescharacteristic
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—41no—
282C4×C11—41no—
283C4×C11—41no—
284C4×C11#57511yescharacteristic
285C4×C11#57511yescharacteristic
286C4×C11#57612yes—
287Dic11—82no—
288C22×Q8—221no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C2×Q16—222no—
293C2×SD16—22no—
294C2×SD16—222no—
295C2×D8—22no—
296C2×M16—221no—
297C22×C8—111no—
298C22×C8—111no—
299C22×C8—221no—
300C4⋊Q8—112no—
301C4⋊Q8—221no—
302C4⋊Q8—221no—
303C4⋊Q8—221no—
304#127—21no—
305#127—21no—
306#127—21no—
307#127C22×D1112yes—
308#126—21no—
309#125C22⋊D1111yescharacteristic
310#124C22⋊D1111yescharacteristic
311#123—21no—
312C22⋊Q8C22⋊D1111yescharacteristic
313#121C22⋊D1111yescharacteristic
314C4×Q8C22×D1111yescharacteristic
315C4×D4—21no—
316C4×D4C22×D1111yescharacteristic
317#117—21no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C42C22×D1111yescharacteristic
321C4⋊C8—111no—
322C4⋊C8—111no—
323C4⋊C8—112no—
324C4⋊C8—221no—
325C4⋊C8—221no—
326C4⋊C8C22×D1112yes—
327#103—222no—
328#103—222no—
329#102—22no—
330#102—22no—
331#102—222no—
332#102—222no—
333#102—222no—
334#102—222no—
335C22⋊C8—21no—
336C22⋊C8—221no—
337C22⋊C8—221no—
338C22⋊C8—221no—
339C22⋊C8—221no—
340#97—21no—
341#97—221no—
342#97—221no—
343#97—221no—
344C4×C8—111no—
345C4×C8—111no—
346C4×C8—111no—
347C4×C8—111no—
348C4×C8—221no—
349C2×C11—22no—
350C2×C11—81no—
351C2×C11—162no—
352C2×C11#304011yescharacteristic
353C2×C11#305811yescharacteristic
354C2×C11C2×#47111yescharacteristic
355C24—41no—
356C2×Q8—222no—
357C2×Q8—441no—
358C2×Q8—882no—
359C2×Q8C2×C22⋊D1111yescharacteristic
360C2×D4—21no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—82no—
370C2×D4—82no—
371C2×D4C2×C22⋊D1111yescharacteristic
372C22×C4—21no—
373C22×C4—441no—
374C22×C4D4×D1111yescharacteristic
375C22×C4#434111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377Q16—882no—
378SD16—82no—
379SD16—882no—
380D8—82no—
381M16—442no—
382C2×C8—22no—
383C2×C8—111no—
384C2×C8—111no—
385C2×C8—111no—
386C2×C8—111no—
387C2×C8—221no—
388C2×C8—221no—
389C2×C8—222no—
390C2×C8—441no—
391C2×C8—441no—
392C2×C8—442no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C4⋊C4C2×C22⋊D1111yescharacteristic
402C4⋊C4C2×C22⋊D1111yescharacteristic
403C22⋊C4—21no—
404C22⋊C4—21no—
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—21no—
408C42—21no—
409C42D4×D1111yescharacteristic
410C42#434111yescharacteristic
411C42C2×C22⋊D1111yescharacteristic
412C42C23×D1111yescharacteristic
413C11#1936411yescharacteristic, complemented, Sylow
414C23—21no—
415C23—42no—
416C23—82no—
417C23—82no—
418C23—82no—
419C23#6699211yescharacteristic
420Q8—22no—
421Q8—442no—
422Q8—442no—
423Q8—882no—
424D4—22no—
425D4—42no—
426D4—42no—
427D4—42no—
428D4—42no—
429D4—42no—
430D4—82no—
431D4—82no—
432D4—82no—
433D4—82no—
434C2×C4—22no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—442no—
444C2×C4—882no—
445C2×C4#6699211yescharacteristic
446C2×C4#6699211yescharacteristic
447C2×C4#6699211yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C2×C4C2×#434111yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C8—42no—
452C8—221no—
453C8—221no—
454C8—221no—
455C8—221no—
456C8—441no—
457C8—441no—
458C8—442no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—164no—
468C22#1062281312yes—
469C22C2×#6699211yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—882no—
478C4#1062330411yescharacteristic
479C4#1062330411yescharacteristic
480C4#1062336612yes—
481C2—22no—
482C2—81no—
483C2—162no—
484C2#1307810811yescharacteristic
485C2#1307826111yescharacteristic
486C2C2×#1062281311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3217C2
socleC22×C11C2×#121
hypercenter#3217D11
hypocenterC11#19364
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3217

Complements

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

NH ≅ G/Ntype
1. #13079640C2semidirect
2. C2×#10622683C2semidirect
3. #13077592C2semidirect
4. #13068182C2semidirect
5. #13068175C2semidirect
6. #13068058C2semidirect
7. #13068051C2semidirect
8. #13067377C2semidirect
9. #13067334C2semidirect
10. #13067330C2semidirect
32. #10622644C22semidirect
33. #10622637C22semidirect
34. Q8×C11⋊C8C22semidirect
35. #10622632C22semidirect
36. #10622625C22semidirect
39. D4×C11⋊C8C22semidirect
47. #10622120C22semidirect
48. #10622120C22semidirect
49. #10622118C22semidirect
50. #10622117C22semidirect
413. C11#19364semidirect

Maximal subgroups

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

subgroupindex
#130796402
C2×#106226832
#130775922
#130681822
#130681752
#130680582
#130680512
#130673772
#130673342
#130673302
C11×#32172
#1936411