Finite Group Databasebeta

← #14770243

Subgroups — #14770243

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic
2C2×#10622301C211yesmaximal, characteristic
3#13071516C211yesmaximal, characteristic
4#13069569C211yesmaximal, characteristic, complemented
5#13069048C212yesmaximal, complemented
6#13068922C212yesmaximal, complemented
7#13068710C212yesmaximal, complemented
8#13068618C211yesmaximal, characteristic, complemented
9C4×#66880C211yesmaximal, characteristic, complemented
10#13068334C212yesmaximal, complemented
11C11×#1990C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#67000—21no—
14C2×Q8×Dic11—21no—
15C22×#4313C2212yes—
16#10623263—24no—
17#10623263C418yescomplemented
18C2×#66951—22no—
19C2×#66950C2212yes—
20C2×#66946—21no—
21C2×#66945C2212yes—
22C2×C4⋊C4×D11C2212yes—
23C2×C4×D44C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C2×(C2×D11)⋊C8C2212yes—
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30#10622602—22no—
31#10622600C2212yes—
32#10622586—21no—
33C2×#66874C2212yes—
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622301—24no—
37C11×#340C2212yes—
38C11×#340C2212yes—
39#10622189C2211yescharacteristic
40#10622189C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×Q8×C11—21no—
45C22×D44D411yescharacteristic
46C22×C4×D11—22no—
47C22×C4×D11C2312yes—
48C22×Dic22C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8C2×C414yescomplemented
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C42×C11C2311yescharacteristic
59#67000—28no—
60Q8×Dic11—28no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4D412yes—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—21no—
75C22×C11⋊C8C2312yes—
76C2×#4313—24no—
77C2×#4313—24no—
78C2×#4313—42no—
79#66951—216no—
80#66950—24no—
81#66950C2×C418yescomplemented
82#66946—44no—
83#66945—24no—
84#66945C2×C418yescomplemented
85C4⋊C4×D11—24no—
86C4⋊C4×D11—42no—
87C4×D44C2×C414yes—
88C4×D44D414yes—
89C4×Dic22—22no—
90C4×Dic22C2×C414yescomplemented
91C4×C8×C11—22no—
92C11⋊#95—21no—
93C11⋊#95—22no—
94(C2×D11)⋊C8—24no—
95#66880—22no—
96#66880—22no—
97#66874—42no—
98C4⋊(C11⋊C8)—22no—
99#22504—111nomaximal, Sylow
100C23×D11C2×D412yes—
101C2×Q8×C11—24no—
102C2×Q8×C11—42no—
103C2×Q8×C11—42no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11C2×D412yes—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44C22⋊C414yes—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—44no—
122C2×C4×D11—44no—
123C2×C4×D11—82no—
124C2×C4×D11C22×C414yes—
125C2×C4×D11C2×D414yes—
126C2×Dic22—21no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22C22×C412yes—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11#4112yes—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—81no—
144C11×C4⋊C4C22×C414yes—
145C42×C11C22×C412yes—
146C42×C11C2×D412yes—
147(C2×D11)⋊C4—28no—
148(C2×D11)⋊C4—28no—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4C22⋊C418yes—
151C4⋊Dic11—28no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11C22⋊C414yes—
157C4⋊Dic11C22×C412yes—
158C4⋊Dic11#4112yes—
159Dic11⋊C4—24no—
160Dic11⋊C4—44no—
161C4×Dic11—28no—
162C4×Dic11—24no—
163C4×Dic11—42no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167#4313—48no—
168C2×#556—111no—
169C2×#436—111no—
170D4×C4⋊C4—111no—
171#1990D1111yescharacteristic, complemented
172#1988—111no—
173#1894—112no—
174#1872—112no—
175#1825—112no—
176#1803—111no—
177C4×#103—111no—
178#1736—112no—
179C23×C11C22×D411yescharacteristic
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—22no—
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—22no—
186C22×D11C2×C22⋊C414yes—
187Q8×C11—48no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—24no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11C2×C22⋊C412yes—
197C2×C4×C11C2×C22⋊C412yes—
198C2×C4×C11AGL(1,ℤ/8)12yes—
199C2×C4×C11#13712yes—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11H(5,𝔽2)11yescharacteristic
205C2×C4×C112−1+411yescharacteristic
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11C2×C22⋊C414yes—
221D44—28no—
222C4×D11—24no—
223C4×D11—24no—
224C4×D11—24no—
225C4×D11—24no—
226C4×D11—88no—
227Dic22—22no—
228Dic22—22no—
229Dic22—41no—
230Dic22—41no—
231C8×C11—22no—
232C8×C11—41no—
233C11⋊C8—42no—
234C22×M16—112no—
235#556—118no—
236#556—224no—
237C2×C4⋊Q8C2×D1111yescharacteristic
238C2×#126—222no—
239C2×#124—221no—
240C2×C22⋊Q8—112no—
241C2×C4×Q8—111no—
242C2×C4×Q8—221no—
243C2×C4×D4—111no—
244C2×C4×D4—221no—
245C2×#117—112no—
246C22×C4⋊C4—112no—
247#436—224no—
248C2×C4⋊C8—111no—
249C2×#103—111no—
250C2×#103—111no—
251C2×#103—112no—
252C2×C22⋊C8—112no—
253C2×C4×C8C2×D1111yescharacteristic
254#389—221no—
255#385—222no—
256#384C2×D1111yescharacteristic
257#380—112no—
258C4×C4⋊C4—111no—
259#340—111no—
260#340—111no—
261#340—112no—
262#340—112no—
263#340—112no—
264#340C2×D1112yes—
265#340C2×D1112yes—
266C22×C11C22×C22⋊C411yescharacteristic
267C22×C11#54611yescharacteristic
268C22×C11#54711yescharacteristic
269C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C11C2×#13711yescharacteristic
271C22×C11#57711yescharacteristic
272C22×C11#57811yescharacteristic
273C2×D11—24no—
274C2×D11—24no—
275C2×D11—24no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—42no—
280C4×C11—22no—
281C4×C11—44no—
282C4×C11—82no—
283C4×C11#41714yes—
284C4×C11C4×#4111yescharacteristic
285C4×C11#52011yescharacteristic
286C4×C11#54611yescharacteristic
287C4×C11#54711yescharacteristic
288Dic11—24no—
289Dic11—42no—
290Dic11—42no—
291Dic11—42no—
292Dic11—81no—
293C22×Q8—21no—
294C22×Q8—111no—
295C22×D4—111no—
296C23×C4—112no—
297C23×C4—222no—
298C2×M16—224no—
299C2×M16—224no—
300C2×M16—442no—
301C22×C8—112no—
302C22×C8C22×D1111yescharacteristic
303C22×C8C22×D1111yescharacteristic
304C4⋊Q8—22no—
305C4⋊Q8C4×D1114yescomplemented
306#126—2216no—
307#124—228no—
308C22⋊Q8—118no—
309C22⋊Q8—224no—
310C4×Q8—114no—
311C4×Q8—228no—
312C4×Q8—222no—
313C4×D4—114no—
314C4×D4—114no—
315C4×D4—444no—
316#117—118no—
317#117—224no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—224no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—442no—
330C2×C4⋊C4C22×D1112yes—
331C2×C4⋊C4C22×D1112yes—
332C2×C22⋊C4—112no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—222no—
336C2×C42—222no—
337C2×C42—221no—
338C2×C42—221no—
339C2×C42C22×D1111yescharacteristic
340C4⋊C8—222no—
341#103—222no—
342#103—222no—
343#103—442no—
344C22⋊C8—224no—
345C4×C8—22no—
346#95—222no—
347#95—221no—
348C2×C11#233911yescharacteristic
349C2×C11C2×#41711yescharacteristic
350C2×C11#289811yescharacteristic
351C2×C11#332411yescharacteristic
352C2×C11#332811yescharacteristic
353C2×C11#335311yescharacteristic
354C2×C11#335611yescharacteristic
355D11—44no—
356C24—112no—
357C2×Q8—24no—
358C2×Q8—42no—
359C2×Q8—42no—
360C2×Q8—112no—
361C2×Q8—221no—
362C2×Q8—221no—
363C2×Q8—221no—
364C2×Q8—221no—
365C2×Q8—221no—
366C2×D4—114no—
367C2×D4—222no—
368C2×D4—222no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—112no—
372C22×C4—114no—
373C22×C4—114no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—444no—
383C22×C4—444no—
384C22×C4—882no—
385C22×C4D4×D1111yescharacteristic
386C22×C4D4×D1111yescharacteristic
387C22×C4C23×D1111yescharacteristic
388M16—448no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8#434312yes—
398C4⋊C4—24no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4—81no—
404C4⋊C4—114no—
405C4⋊C4—112no—
406C4⋊C4—112no—
407C4⋊C4—228no—
408C4⋊C4—224no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—444no—
414C4⋊C4C2×C4×D1114yes—
415C22⋊C4—118no—
416C22⋊C4—228no—
417C22⋊C4—228no—
418C22⋊C4—444no—
419C42—228no—
420C42—224no—
421C42—442no—
422C42C2×C4×D1112yes—
423C42D4×D1112yes—
424C11#2250411yescharacteristic, complemented, Sylow
425C23—114no—
426C23—222no—
427C23—222no—
428C23—222no—
429C23—222no—
430C23—222no—
431C23—222no—
432C23C2×D4×D1111yescharacteristic
433Q8—48no—
434Q8—222no—
435Q8—222no—
436Q8—441no—
437Q8—441no—
438D4—228no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—24no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—114no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—224no—
451C2×C4—224no—
452C2×C4—224no—
453C2×C4—224no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—888no—
467C2×C4C22⋊C4×D1112yes—
468C2×C4C22⋊C4×D1112yes—
469C2×C4#6696412yes—
470C2×C4#6696812yes—
471C2×C4C22×C4×D1111yescharacteristic
472C2×C4C2×D4×D1111yescharacteristic
473C2×C4C2×#434311yescharacteristic
474C2×C4#6704011yescharacteristic
475C2×C4#41×D1111yescharacteristic
476C2×C4#6704211yescharacteristic
477C8—22no—
478C8—41no—
479C8—442no—
480C22—224no—
481C22—224no—
482C22—224no—
483C22—442no—
484C22—442no—
485C22—442no—
486C22—442no—
487C22C2×C22⋊C4×D1111yescharacteristic
488C22#1062320711yescharacteristic
489C22#1062325711yescharacteristic
490C22C2×#6696411yescharacteristic
491C22C2×#6696811yescharacteristic
492C22#1062329311yescharacteristic
493C22#1062329711yescharacteristic
494C4—22no—
495C4—44no—
496C4—82no—
497C4—224no—
498C4—442no—
499C4—442no—
500C4—442no—
501C4—881no—
502C4#1062238414yes—
503C4C4×#434311yescharacteristic
504C4#1062310511yescharacteristic
505C4#1062316111yescharacteristic
506C4#1062316211yescharacteristic
507C2—444no—
508C2#1307144511yescharacteristic
509C2C2×#1062238411yescharacteristic
510C2#1307714411yescharacteristic
511C2#1308084611yescharacteristic
512C2#1308089811yescharacteristic
513C2#1308119911yescharacteristic
514C2#1308123011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenter#1990D11
hypocenterC11#22504
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. #13069569C2semidirect
5. #13069048C2semidirect
6. #13068922C2semidirect
7. #13068710C2semidirect
8. #13068618C2semidirect
9. C4×#66880C2semidirect
10. #13068334C2semidirect
11. C11×#1990C2semidirect
17. #10623263C4semidirect
52. C11×C4⋊Q8C2×C4semidirect
81. #66950C2×C4semidirect
84. #66945C2×C4semidirect
90. C4×Dic22C2×C4semidirect
171. #1990D11semidirect
305. C4⋊Q8C4×D11semidirect
424. C11#22504semidirect

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106223012
#130715162
#130695692
#130690482
#130689222
#130687102
#130686182
C4×#668802
#130683342
C11×#19902
#2250411