Finite Group Databasebeta

← #14738637

Subgroups — #14738637

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#13079643C211yesmaximal, characteristic, complemented
2#13079634C211yesmaximal, characteristic
3#13077591C211yesmaximal, characteristic, complemented
4#13068181C212yesmaximal, complemented
5#13068174C212yesmaximal, complemented
6#13068057C212yesmaximal, complemented
7#13068050C212yesmaximal, complemented
8#13067379C211yesmaximal, characteristic, complemented
9#13067333C211yesmaximal, 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#10622841—21no—
23#10622840—21no—
24#10622831—21no—
25#10622830—21no—
26#10622724—21no—
27C8×C22⋊D11—21no—
28#10622703C2212yescomplemented
29#10622699—21no—
30#10622696C2212yescomplemented
31#10622695—21no—
32#10622688C2212yes—
33#10622687—21no—
34#10622685C2212yes—
35#10622684—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#10622185C2212yescomplemented
46#10622185C2212yescomplemented
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×#4326—22no—
69C2×#4325—22no—
70C2×#4324—22no—
71C2×#4323—22no—
72#66983D411yescharacteristic
73#66982—21no—
74C4×C22⋊D11—21no—
75#66977D411yescharacteristic
76C2×#4313—21no—
77C2×C8×D11—21no—
78#66929—21no—
79#66928D411yescharacteristic
80C4×D44C2311yescharacteristic
81#66925—21no—
82#66923D411yescharacteristic
83C4×Dic22C2311yescharacteristic
84C11×#102—22no—
85C11×#102—22no—
86C11×#102—22no—
87C11×#102—22no—
88C4×C8×C11D411yescharacteristic
89C4×C8×C11D411yescharacteristic
90C4×C8×C11C2311yescharacteristic
91C4×C8×C11C2311yescharacteristic
92#66899—22no—
93#66899—22no—
94#66896—22no—
95#66896—22no—
96C22⋊(C11⋊C8)—21no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—21no—
99(C2×D11)⋊C8—21no—
100(C2×D11)⋊C8—21no—
101#66879—21no—
102Dic11⋊C8—21no—
103Dic11⋊C8—21no—
104C8×Dic11—21no—
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#19364—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#4326—82no—
151#4325—82no—
152#4324—82no—
153#4323—82no—
154(C2×D11)⋊C4—21no—
155(C2×D11)⋊C4—21no—
156(C2×D11)⋊C4—21no—
157(C2×D11)⋊C4—21no—
158C4⋊Dic11C2×D411yescharacteristic
159C4⋊Dic11C2×D411yescharacteristic
160Dic11⋊C4—21no—
161Dic11⋊C4—21no—
162Dic11⋊C4—21no—
163Dic11⋊C4—21no—
164C4×Dic11—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169#4313—42no—
170C8×D11—42no—
171#3218—111no—
172#3217—111no—
173C2×#486D1111yescharacteristic, complemented
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—42no—
183C23×C11—82no—
184C23×C11—82no—
185C23×C11—82no—
186C23×C11#12111yescharacteristic
187C22×D11—21no—
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—82no—
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—42no—
204C2×C4×C11—82no—
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C22⋊D11—42no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215D44—22no—
216C4×D11—41no—
217C4×D11—41no—
218Dic22—22no—
219C8×C11—21no—
220C8×C11—21no—
221C8×C11—21no—
222C8×C11—21no—
223C11⋊C8—41no—
224C11⋊C8—41no—
225C11⋊C8—42no—
226C11⋊C8—42no—
227C2×C4⋊Q8C2×D1111yescharacteristic
228C2×#127C2×D1111yescharacteristic
229#529—111no—
230#497—221no—
231#496—221no—
232#491—221no—
233#490—221no—
234#486—21no—
235#486—21no—
236#486C2×D1112yes—
237#486C2×D1112yes—
238#462—112no—
239#461—112no—
240#460—112no—
241#459—112no—
242#451—221no—
243#450—221no—
244#448—221no—
245#447—221no—
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#432—111no—
256C2×#102—21no—
257C2×#102—21no—
258#405—221no—
259C2×C4×C8C2×D1111yescharacteristic
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—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—164no—
272C22×C11#47112yes—
273C22×C11C2×#12111yescharacteristic
274C2×D11—41no—
275C2×D11—41no—
276C2×D11—41no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—82no—
282C4×C11#57511yescharacteristic
283C4×C11#57511yescharacteristic
284C4×C11#57612yes—
285Dic11—41no—
286Dic11—41no—
287Dic11—41no—
288C22×Q8—21no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C2×Q16—222no—
293C2×SD16—222no—
294C2×SD16—222no—
295C2×D8—222no—
296C2×M16—221no—
297C22×C8—221no—
298C22×C8C22⋊D1111yescharacteristic
299C22×C8C22⋊D1111yescharacteristic
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8C22×D1112yes—
304#127—21no—
305#127—21no—
306#127—21no—
307#127C22×D1112yes—
308#126—221no—
309#125—111no—
310#124—111no—
311#123—221no—
312C22⋊Q8—111no—
313#121—111no—
314C4×Q8—111no—
315C4×D4—111no—
316C4×D4—221no—
317#117—221no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C42C22×D1111yescharacteristic
321C4⋊C8—111no—
322C4⋊C8—111no—
323C4⋊C8—112no—
324C4⋊C8—112no—
325C4⋊C8—221no—
326C4⋊C8—221no—
327#103—222no—
328#103—222no—
329#102—22no—
330#102—22no—
331#102—22no—
332#102—22no—
333#102—222no—
334#102—222no—
335C22⋊C8—221no—
336C22⋊C8—221no—
337C22⋊C8—221no—
338C22⋊C8—221no—
339C22⋊C8—221no—
340#97—221no—
341#97—221no—
342#97—221no—
343#97—221no—
344C4×C8—221no—
345C4×C8C22⋊D1111yescharacteristic
346C4×C8C22⋊D1111yescharacteristic
347C4×C8C22×D1111yescharacteristic
348C4×C8C22×D1111yescharacteristic
349C2×C11—22no—
350C2×C11—162no—
351C2×C11#304011yescharacteristic
352C2×C11#305811yescharacteristic
353C2×C11C2×#47111yescharacteristic
354D11—81no—
355C24—41no—
356C2×Q8—22no—
357C2×Q8—41no—
358C2×Q8—82no—
359C2×Q8—111no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—82no—
369C2×D4—82no—
370C2×D4—111no—
371C2×D4—221no—
372C22×C4—41no—
373C22×C4—221no—
374C22×C4D4×D1111yescharacteristic
375C22×C4#434111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377Q16—882no—
378SD16—882no—
379SD16—882no—
380D8—882no—
381M16—442no—
382C2×C8—41no—
383C2×C8—41no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—221no—
387C2×C8—221no—
388C2×C8—442no—
389C2×C8C2×C22⋊D1111yescharacteristic
390C2×C8C2×C22⋊D1111yescharacteristic
391C2×C8C2×C22⋊D1111yescharacteristic
392C2×C8C2×C22⋊D1111yescharacteristic
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—111no—
398C4⋊C4—111no—
399C4⋊C4—221no—
400C4⋊C4—221no—
401C4⋊C4—221no—
402C4⋊C4—221no—
403C22⋊C4—221no—
404C22⋊C4—221no—
405C22⋊C4—221no—
406C22⋊C4—221no—
407C22⋊C4—221no—
408C42—221no—
409C42D4×D1111yescharacteristic
410C42#434111yescharacteristic
411C42C2×C22⋊D1111yescharacteristic
412C42C23×D1111yescharacteristic
413C11#1936411yescharacteristic, complemented, Sylow
414C23—42no—
415C23—82no—
416C23—82no—
417C23—82no—
418C23—221no—
419C23#6699111yescharacteristic
420Q8—42no—
421Q8—42no—
422Q8—82no—
423Q8—222no—
424D4—42no—
425D4—42no—
426D4—42no—
427D4—42no—
428D4—82no—
429D4—82no—
430D4—82no—
431D4—82no—
432D4—222no—
433D4—442no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—42no—
439C2×C4—82no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4#6699111yescharacteristic
446C2×C4#6699111yescharacteristic
447C2×C4#6699111yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C2×C4C2×#434111yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C8—21no—
452C8—21no—
453C8—21no—
454C8—21no—
455C8—442no—
456C8—442no—
457C8—441no—
458C8—441no—
459C22—21no—
460C22—21no—
461C22—82no—
462C22—82no—
463C22—82no—
464C22—164no—
465C22—441no—
466C22—441no—
467C22—441no—
468C22#1062279012yes—
469C22C2×#6699111yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—82no—
475C4—441no—
476C4—441no—
477C4—441no—
478C4#1062328812yes—
479C4#1062335311yescharacteristic
480C4#1062335311yescharacteristic
481C2—22no—
482C2—162no—
483C2—881no—
484C2#1307810611yescharacteristic
485C2#1307826011yescharacteristic
486C2C2×#1062279011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#486C2
socleC22×C11C2×#121
prime radical#13079634C2
hypercenterC2×#486D11
hypocenterC11#19364
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. #13079643C2semidirect
3. #13077591C2semidirect
4. #13068181C2semidirect
5. #13068174C2semidirect
6. #13068057C2semidirect
7. #13068050C2semidirect
8. #13067379C2semidirect
9. #13067333C2semidirect
10. #13067330C2semidirect
11. C2×C11×#486C2semidirect
28. #10622703C22semidirect
30. #10622696C22semidirect
41. #10622301C22semidirect
42. C8×D44C22semidirect
43. #10622292C22semidirect
44. C8×Dic22C22semidirect
45. #10622185C22semidirect
46. #10622185C22semidirect
49. #10622096C22semidirect
50. #10622095C22semidirect
173. C2×#486D11semidirect
413. C11#19364semidirect

Maximal subgroups

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

subgroupindex
#130796432
#130796342
#130775912
#130681812
#130681742
#130680572
#130680502
#130673792
#130673332
#130673302
C2×C11×#4862
#1936411