Finite Group Databasebeta

← #14738615

Subgroups — #14738615

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#13079837C211yesmaximal, characteristic, complemented
2#13079634C211yesmaximal, characteristic
3#13077591C211yesmaximal, characteristic, complemented
4#13068153C212yesmaximal, complemented
5#13068146C212yesmaximal, complemented
6#13068029C212yesmaximal, complemented
7#13068022C212yesmaximal, complemented
8#13067379C211yesmaximal, characteristic, complemented
9#13067342C211yesmaximal, characteristic, complemented
10#13067330C211yesmaximal, characteristic, complemented
11C2×C11×#486C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14#10623010C2211yescharacteristic
15C11×#486—21no—
16C11×#486—21no—
17C11×#486C2212yes—
18C11×#486C2212yes—
19C2×C11×#102—21no—
20C2×C11×#102—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622831—21no—
23#10622830—21no—
24#10622724—21no—
25C8×C22⋊D11—21no—
26#10622704C2212yescomplemented
27#10622702—21no—
28#10622697C2212yescomplemented
29#10622693—21no—
30#10622688C2212yes—
31#10622687—21no—
32#10622685C2212yes—
33#10622684—21no—
34#10622584—21no—
35#10622580—21no—
36#10622539C2211yescharacteristic
37#10622539C2211yescharacteristic
38#10622539C2211yescharacteristic
39#10622303—21no—
40#10622302—21no—
41#10622301C2211yescharacteristic, complemented
42C8×D44C2211yescharacteristic, complemented
43#10622292C2211yescharacteristic, complemented
44C8×Dic22C2211yescharacteristic, complemented
45#10622184C2212yescomplemented
46#10622184C2212yescomplemented
47#10622182C2212yes—
48#10622182C2212yes—
49#10622096C2212yescomplemented
50#10622095C2212yescomplemented
51C22×Q8×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×C8×C11D411yescharacteristic
56C22×C8×C11D411yescharacteristic
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8C2312yes—
61C11×#127—21no—
62C11×#127—21no—
63C11×#127—21no—
64C11×#127C2312yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4324—22no—
69C2×#4323—22no—
70#66983D411yescharacteristic
71#66982—21no—
72C4×C22⋊D11—21no—
73#66977D411yescharacteristic
74C2×#4313—21no—
75C2×C8×D11—21no—
76#66929—21no—
77#66928D411yescharacteristic
78C4×D44C2311yescharacteristic
79#66925—21no—
80#66923D411yescharacteristic
81C4×Dic22C2311yescharacteristic
82C11×#102—22no—
83C11×#102—22no—
84C11×#102—22no—
85C11×#102—22no—
86C4×C8×C11D411yescharacteristic
87C4×C8×C11D411yescharacteristic
88C4×C8×C11C2311yescharacteristic
89C4×C8×C11C2311yescharacteristic
90#66896—22no—
91#66896—22no—
92C22⋊(C11⋊C8)—21no—
93C22⋊(C11⋊C8)—21no—
94C22⋊(C11⋊C8)—21no—
95(C2×D11)⋊C8—21no—
96(C2×D11)⋊C8—21no—
97#66879—21no—
98Dic11⋊C8—21no—
99Dic11⋊C8—21no—
100C8×Dic11—21no—
101#66874—22no—
102#66873—22no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)C2311yescharacteristic
106C4⋊(C11⋊C8)C2311yescharacteristic
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109#66867—21no—
110#66867—21no—
111#66867—21no—
112#19362—111nomaximal, Sylow
113C24×C11—41no—
114C2×Q8×C11—22no—
115C2×Q8×C11—41no—
116C2×Q8×C11—82no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—82no—
126C2×D4×C11—82no—
127C22×C4×C11—41no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C2×C22⋊D11—21no—
132C2×D44C2×D411yescharacteristic
133C2×C4×D11—21no—
134C2×Dic22C2×D411yescharacteristic
135C2×C8×C11—41no—
136C2×C8×C11—41no—
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2×D411yescharacteristic
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C42×C11C2×D411yescharacteristic
146C42×C11C2×D411yescharacteristic
147C42×C11#4111yescharacteristic
148C42×C11C2411yescharacteristic
149C22⋊Dic11—21no—
150#4324—82no—
151#4323—82no—
152(C2×D11)⋊C4—21no—
153(C2×D11)⋊C4—21no—
154(C2×D11)⋊C4—21no—
155(C2×D11)⋊C4—21no—
156C4⋊Dic11C2×D411yescharacteristic
157C4⋊Dic11C2×D411yescharacteristic
158Dic11⋊C4—21no—
159Dic11⋊C4—21no—
160Dic11⋊C4—21no—
161Dic11⋊C4—21no—
162C4×Dic11—21no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—22no—
167#4313—42no—
168C8×D11—42no—
169#3238—111no—
170#3217—111no—
171C2×#486D1111yescharacteristic, complemented
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—42no—
181C23×C11—82no—
182C23×C11—82no—
183C23×C11—82no—
184C23×C11#12111yescharacteristic
185C22×D11—21no—
186Q8×C11—82no—
187Q8×C11—82no—
188D4×C11—42no—
189D4×C11—42no—
190D4×C11—42no—
191D4×C11—42no—
192D4×C11—82no—
193D4×C11—82no—
194D4×C11—82no—
195D4×C11—82no—
196C2×C4×C11—22no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—42no—
201C2×C4×C11—82no—
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C22⋊D11—42no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212D44—22no—
213C4×D11—41no—
214C4×D11—41no—
215Dic22—22no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11—21no—
220C11⋊C8—41no—
221C11⋊C8—41no—
222C11⋊C8—42no—
223C11⋊C8—42no—
224C2×C4⋊Q8C2×D1111yescharacteristic
225C2×#127C2×D1111yescharacteristic
226#529—111no—
227#501—221no—
228#496—221no—
229#490—221no—
230#489—221no—
231#486—21no—
232#486—21no—
233#486C2×D1112yes—
234#486C2×D1112yes—
235#483—221no—
236#480—221no—
237#477—112no—
238#476—112no—
239#460—112no—
240#459—112no—
241#450—221no—
242#447—221no—
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#432—111no—
253C2×#102—21no—
254C2×#102—21no—
255#405—221no—
256C2×C4×C8C2×D1111yescharacteristic
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—82no—
266C22×C11—82no—
267C22×C11—82no—
268C22×C11—164no—
269C22×C11#47212yes—
270C22×C11C2×#12111yescharacteristic
271C2×D11—41no—
272C2×D11—41no—
273C2×D11—41no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—82no—
279C4×C11#57511yescharacteristic
280C4×C11#57511yescharacteristic
281C4×C11#57712yes—
282Dic11—41no—
283Dic11—41no—
284Dic11—41no—
285C22×Q8—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C2×SD16—222no—
290C2×D8—222no—
291C2×M16—221no—
292C22×C8—221no—
293C22×C8C22⋊D1111yescharacteristic
294C22×C8C22⋊D1111yescharacteristic
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8C22×D1112yes—
299#127—21no—
300#127—21no—
301#127—21no—
302#127C22×D1112yes—
303#126—221no—
304#125—111no—
305#124—111no—
306#123—221no—
307C22⋊Q8—111no—
308#121—111no—
309C4×Q8—111no—
310C4×D4—111no—
311C4×D4—221no—
312#117—221no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C42C22×D1111yescharacteristic
316#107—222no—
317#106—222no—
318C4⋊C8—111no—
319C4⋊C8—111no—
320C4⋊C8—112no—
321C4⋊C8—112no—
322C4⋊C8—221no—
323C4⋊C8—221no—
324#103—222no—
325#102—22no—
326#102—22no—
327#102—22no—
328#102—22no—
329#102—222no—
330#102—222no—
331#102—222no—
332C22⋊C8—221no—
333C22⋊C8—221no—
334C22⋊C8—221no—
335C22⋊C8—221no—
336C22⋊C8—221no—
337#97—221no—
338#97—221no—
339#97—221no—
340#97—221no—
341C4×C8—221no—
342C4×C8C22⋊D1111yescharacteristic
343C4×C8C22⋊D1111yescharacteristic
344C4×C8C22×D1111yescharacteristic
345C4×C8C22×D1111yescharacteristic
346C2×C11—22no—
347C2×C11—162no—
348C2×C11#304011yescharacteristic
349C2×C11#305711yescharacteristic
350C2×C11C2×#47211yescharacteristic
351D11—81no—
352C24—41no—
353C2×Q8—22no—
354C2×Q8—41no—
355C2×Q8—82no—
356C2×Q8—111no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—82no—
366C2×D4—82no—
367C2×D4—111no—
368C2×D4—221no—
369C22×C4—41no—
370C22×C4—221no—
371C22×C4D4×D1111yescharacteristic
372C22×C4#434111yescharacteristic
373C22×C4C2×C22⋊D1111yescharacteristic
374SD16—882no—
375D8—882no—
376M16—442no—
377C2×C8—41no—
378C2×C8—41no—
379C2×C8—222no—
380C2×C8—222no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—442no—
384C2×C8C2×C22⋊D1111yescharacteristic
385C2×C8C2×C22⋊D1111yescharacteristic
386C2×C8C2×C22⋊D1111yescharacteristic
387C2×C8C2×C22⋊D1111yescharacteristic
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—111no—
393C4⋊C4—111no—
394C4⋊C4—221no—
395C4⋊C4—221no—
396C4⋊C4—221no—
397C4⋊C4—221no—
398C22⋊C4—221no—
399C22⋊C4—221no—
400C22⋊C4—221no—
401C22⋊C4—221no—
402C22⋊C4—221no—
403C42—221no—
404C42D4×D1111yescharacteristic
405C42#434111yescharacteristic
406C42C2×C22⋊D1111yescharacteristic
407C42C23×D1111yescharacteristic
408C11#1936211yescharacteristic, complemented, Sylow
409C23—42no—
410C23—82no—
411C23—82no—
412C23—82no—
413C23—221no—
414C23#6699111yescharacteristic
415Q8—82no—
416Q8—82no—
417Q8—222no—
418D4—42no—
419D4—42no—
420D4—42no—
421D4—42no—
422D4—82no—
423D4—82no—
424D4—82no—
425D4—82no—
426D4—222no—
427D4—442no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—42no—
433C2×C4—82no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4#6699111yescharacteristic
440C2×C4#6699111yescharacteristic
441C2×C4#6699111yescharacteristic
442C2×C4C2×D4×D1111yescharacteristic
443C2×C4C2×#434111yescharacteristic
444C2×C4C22×C22⋊D1111yescharacteristic
445C8—21no—
446C8—21no—
447C8—21no—
448C8—21no—
449C8—442no—
450C8—442no—
451C8—441no—
452C8—441no—
453C22—21no—
454C22—21no—
455C22—82no—
456C22—82no—
457C22—82no—
458C22—164no—
459C22—441no—
460C22—441no—
461C22—441no—
462C22#1062277312yes—
463C22C2×#6699111yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—82no—
469C4—441no—
470C4—441no—
471C4—441no—
472C4#1062329312yes—
473C4#1062335311yescharacteristic
474C4#1062335311yescharacteristic
475C2—22no—
476C2—162no—
477C2—881no—
478C2#1307810611yescharacteristic
479C2#1307825111yescharacteristic
480C2C2×#1062277311yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#486C2
socleC22×C11C2×#121
prime radical#13079634C2
hypercenterC2×#486D11
hypocenterC11#19362
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. #13079837C2semidirect
3. #13077591C2semidirect
4. #13068153C2semidirect
5. #13068146C2semidirect
6. #13068029C2semidirect
7. #13068022C2semidirect
8. #13067379C2semidirect
9. #13067342C2semidirect
10. #13067330C2semidirect
11. C2×C11×#486C2semidirect
26. #10622704C22semidirect
28. #10622697C22semidirect
41. #10622301C22semidirect
42. C8×D44C22semidirect
43. #10622292C22semidirect
44. C8×Dic22C22semidirect
45. #10622184C22semidirect
46. #10622184C22semidirect
49. #10622096C22semidirect
50. #10622095C22semidirect
171. C2×#486D11semidirect
408. C11#19362semidirect

Maximal subgroups

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

subgroupindex
#130798372
#130796342
#130775912
#130681532
#130681462
#130680292
#130680222
#130673792
#130673422
#130673302
C2×C11×#4862
#1936211