Finite Group Databasebeta

← #14738617

Subgroups — #14738617

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079834C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic, complemented
4#13068154C212yesmaximal, complemented
5#13068147C212yesmaximal, complemented
6#13068030C212yesmaximal, complemented
7#13068023C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067341C211yesmaximal, 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#10622678—21no—
29#10622668—21no—
30#10622656—21no—
31#10622646—21no—
32#10622637C2211yescharacteristic, complemented
33Q8×C11⋊C8C2211yescharacteristic, complemented
34#10622634C2212yescomplemented
35#10622625C2211yescharacteristic, complemented
36#10622624—21no—
37D4×C11⋊C8—21no—
38D4×C11⋊C8C2211yescharacteristic, complemented
39#10622621C2212yescomplemented
40#10622613—21no—
41#10622610—21no—
42#10622539C2211yescharacteristic
43#10622539C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622182C2212yes—
46#10622182C2212yes—
47#10622119C2212yescomplemented
48#10622119C2212yescomplemented
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×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×#4318—21no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8D411yescharacteristic
77C22×C11⋊C8D411yescharacteristic
78#66922—21no—
79#66922—21no—
80#66922—21no—
81#66922C2312yes—
82C11×C4⋊C8C2312yes—
83C11×#102—22no—
84C11×#102—22no—
85C11×C22⋊C8—21no—
86C11×#97—21no—
87#66899—22no—
88#66896—22no—
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#66872—22no—
98#66871—22no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)C2312yes—
102C4⋊(C11⋊C8)C2311yescharacteristic
103C4⋊(C11⋊C8)C2311yescharacteristic
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#19362—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
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—41no—
157C4⋊Dic11—41no—
158#4318—42no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—41no—
163C2×C11⋊C8—41no—
164C2×C11⋊C8—42no—
165C2×C11⋊C8C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169#3238—111no—
170#3217D1111yescharacteristic
171C2×#486—111no—
172#2966—111no—
173#1698—112no—
174#1697—112no—
175#1678—112no—
176#1677—112no—
177#1568—111no—
178#1558—111no—
179#1555—111no—
180C23×C11—21no—
181C23×C11—42no—
182C23×C11—82no—
183C23×C11—82no—
184C23×C11—82no—
185C23×C11#12111yescharacteristic
186Q8×C11—22no—
187D4×C11—22no—
188D4×C11—42no—
189D4×C11—42no—
190D4×C11—42no—
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—82no—
194D4×C11—82no—
195D4×C11—82no—
196D4×C11—82no—
197C2×C4×C11—22no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×Dic11—42no—
213C2×Dic11—82no—
214Dic22—82no—
215Dic22—82no—
216C8×C11—42no—
217C11⋊C8—21no—
218C11⋊C8—21no—
219C11⋊C8—21no—
220C11⋊C8—21no—
221C11⋊C8—41no—
222C11⋊C8—41no—
223C11⋊C8—42no—
224C2×C4⋊Q8—111no—
225C2×#127C2×D1111yescharacteristic
226#529C2×D1111yescharacteristic
227#501—221no—
228#496—21no—
229#490—21no—
230#489—221no—
231#486—112no—
232#486—112no—
233#486—221no—
234#486—221no—
235#483—221no—
236#480—221no—
237#477—112no—
238#476—112no—
239#460C2×D1112yes—
240#459C2×D1112yes—
241#450—21no—
242#447—21no—
243#446—111no—
244C8×Q8—111no—
245#436—111no—
246#435—221no—
247C8×D4—111no—
248C8×D4—221no—
249#433—221no—
250#432—111no—
251#432—111no—
252#432C2×D1111yescharacteristic
253C2×#102—221no—
254C2×#102—221no—
255#405—221no—
256C2×C4×C8—111no—
257#335—112no—
258#334—112no—
259#333—112no—
260#333—112no—
261#331—112no—
262#331—112no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—41no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—164no—
272C22×C11#47212yes—
273C22×C11C2×#12111yescharacteristic
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11—41no—
281C4×C11#57511yescharacteristic
282C4×C11#57511yescharacteristic
283C4×C11#57712yes—
284Dic11—82no—
285C22×Q8—221no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C2×SD16—22no—
290C2×D8—22no—
291C2×M16—221no—
292C22×C8—111no—
293C22×C8—111no—
294C22×C8—221no—
295C4⋊Q8—112no—
296C4⋊Q8—221no—
297C4⋊Q8—221no—
298C4⋊Q8—221no—
299#127—21no—
300#127—21no—
301#127—21no—
302#127C22×D1112yes—
303#126—21no—
304#125C22⋊D1111yescharacteristic
305#124C22⋊D1111yescharacteristic
306#123—21no—
307C22⋊Q8C22⋊D1111yescharacteristic
308#121C22⋊D1111yescharacteristic
309C4×Q8C22×D1111yescharacteristic
310C4×D4—21no—
311C4×D4C22×D1111yescharacteristic
312#117—21no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—221no—
315C2×C42C22×D1111yescharacteristic
316#107—222no—
317#106—222no—
318C4⋊C8—111no—
319C4⋊C8—111no—
320C4⋊C8—112no—
321C4⋊C8—221no—
322C4⋊C8—221no—
323C4⋊C8C22×D1112yes—
324#103—222no—
325#102—22no—
326#102—22no—
327#102—222no—
328#102—222no—
329#102—222no—
330#102—222no—
331#102—222no—
332C22⋊C8—21no—
333C22⋊C8—221no—
334C22⋊C8—221no—
335C22⋊C8—221no—
336C22⋊C8—221no—
337#97—21no—
338#97—221no—
339#97—221no—
340#97—221no—
341C4×C8—111no—
342C4×C8—111no—
343C4×C8—111no—
344C4×C8—111no—
345C4×C8—221no—
346C2×C11—22no—
347C2×C11—81no—
348C2×C11—162no—
349C2×C11#304011yescharacteristic
350C2×C11#305711yescharacteristic
351C2×C11C2×#47211yescharacteristic
352C24—41no—
353C2×Q8—222no—
354C2×Q8—441no—
355C2×Q8—882no—
356C2×Q8C2×C22⋊D1111yescharacteristic
357C2×D4—21no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—82no—
367C2×D4—82no—
368C2×D4C2×C22⋊D1111yescharacteristic
369C22×C4—21no—
370C22×C4—441no—
371C22×C4D4×D1111yescharacteristic
372C22×C4#434111yescharacteristic
373C22×C4C2×C22⋊D1111yescharacteristic
374SD16—82no—
375D8—82no—
376M16—442no—
377C2×C8—22no—
378C2×C8—111no—
379C2×C8—111no—
380C2×C8—111no—
381C2×C8—111no—
382C2×C8—221no—
383C2×C8—221no—
384C2×C8—222no—
385C2×C8—441no—
386C2×C8—441no—
387C2×C8—442no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4C2×C22⋊D1111yescharacteristic
397C4⋊C4C2×C22⋊D1111yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—21no—
401C22⋊C4—21no—
402C22⋊C4—21no—
403C42—21no—
404C42D4×D1111yescharacteristic
405C42#434111yescharacteristic
406C42C2×C22⋊D1111yescharacteristic
407C42C23×D1111yescharacteristic
408C11#1936211yescharacteristic, complemented, Sylow
409C23—21no—
410C23—42no—
411C23—82no—
412C23—82no—
413C23—82no—
414C23#6699211yescharacteristic
415Q8—22no—
416Q8—882no—
417Q8—882no—
418D4—22no—
419D4—42no—
420D4—42no—
421D4—42no—
422D4—42no—
423D4—42no—
424D4—82no—
425D4—82no—
426D4—82no—
427D4—82no—
428C2×C4—22no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—442no—
438C2×C4—882no—
439C2×C4#6699211yescharacteristic
440C2×C4#6699211yescharacteristic
441C2×C4#6699211yescharacteristic
442C2×C4C2×D4×D1111yescharacteristic
443C2×C4C2×#434111yescharacteristic
444C2×C4C22×C22⋊D1111yescharacteristic
445C8—42no—
446C8—221no—
447C8—221no—
448C8—221no—
449C8—221no—
450C8—441no—
451C8—441no—
452C8—442no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—82no—
459C22—82no—
460C22—82no—
461C22—164no—
462C22#1062281212yes—
463C22C2×#6699211yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—882no—
472C4#1062330411yescharacteristic
473C4#1062330411yescharacteristic
474C4#1062336712yes—
475C2—22no—
476C2—81no—
477C2—162no—
478C2#1307810811yescharacteristic
479C2#1307825211yescharacteristic
480C2C2×#1062281211yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3217C2
socleC22×C11C2×#121
hypercenter#3217D11
hypocenterC11#19362
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. #13079834C2semidirect
2. C2×#10622683C2semidirect
3. #13077592C2semidirect
4. #13068154C2semidirect
5. #13068147C2semidirect
6. #13068030C2semidirect
7. #13068023C2semidirect
8. #13067377C2semidirect
9. #13067341C2semidirect
10. #13067330C2semidirect
32. #10622637C22semidirect
33. Q8×C11⋊C8C22semidirect
34. #10622634C22semidirect
35. #10622625C22semidirect
38. D4×C11⋊C8C22semidirect
39. #10622621C22semidirect
47. #10622119C22semidirect
48. #10622119C22semidirect
49. #10622118C22semidirect
50. #10622117C22semidirect
408. C11#19362semidirect

Maximal subgroups

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

subgroupindex
#130798342
C2×#106226832
#130775922
#130681542
#130681472
#130680302
#130680232
#130673772
#130673412
#130673302
C11×#32172
#1936211