Finite Group Databasebeta

← #14770238

Subgroups — #14770238

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×#10623073C211yesmaximal, characteristic
2C2×#10622625C211yesmaximal, characteristic
3#13069576C211yesmaximal, characteristic, complemented
4#13069568C211yesmaximal, characteristic, complemented
5#13069047C212yesmaximal, complemented
6#13068923C212yesmaximal, complemented
7#13068708C212yesmaximal, complemented
8#13068618C211yesmaximal, characteristic, complemented
9C4×#66874C211yesmaximal, characteristic, complemented
10#13068335C212yesmaximal, complemented
11D4×C11×C4⋊C4C211yesmaximal, characteristic
12C2×C4×D4×C11—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C2×#66989—21no—
16C2×#66979C2212yes—
17C2×#66977C2212yes—
18C22×#4318C2212yes—
19#10623073—24no—
20#10623073C418yescomplemented
21C2×#66940—21no—
22C2×#66932—22no—
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C11×#389—21no—
26C11×#385—22no—
27C11×#384C2211yescharacteristic
28C11×#380C2212yes—
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622625—24no—
32C2×#66874C2211yescharacteristic
33C2×#66874C2211yescharacteristic
34C2×#66874C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2211yescharacteristic
44C22×D4×C11D411yescharacteristic
45C23×C4×C11—22no—
46C23×C4×C11C2312yes—
47C22×Dic22—21no—
48C22×Dic22C2311yescharacteristic
49C4×D4×C11—44no—
50C4×D4×C11C2×C414yes—
51C4×D4×C11D414yes—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—42no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4D412yes—
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67#66989—28no—
68#66979—24no—
69#66979C2×C418yescomplemented
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2312yes—
73#66977—24no—
74#66977C2×C418yescomplemented
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—22no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—22no—
79C2×#4318—24no—
80C2×#4318—24no—
81C2×#4318—42no—
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84C22×C11⋊C8C2311yescharacteristic
85#66940—28no—
86#66932—216no—
87#66922—22no—
88#66922C2×C414yescomplemented
89C4×Dic22—22no—
90C4×Dic22C2×C414yescomplemented
91C11×#95—21no—
92C11×#95—22no—
93C22⋊(C11⋊C8)—24no—
94#66874—22no—
95#66874—22no—
96#66874—42no—
97C4⋊(C11⋊C8)—22no—
98C4×C11⋊C8—22no—
99#22504—111nomaximal, Sylow
100C24×C11C2×D412yes—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11C22⋊C414yes—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—44no—
112C22×C4×C11—44no—
113C22×C4×C11—82no—
114C22×C4×C11C22×C414yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D414yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C2×Dic22—24no—
124C2×Dic22—21no—
125C2×Dic22—21no—
126C2×Dic22—21no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C2×Dic22—42no—
130C2×Dic22—42no—
131C2×Dic22C22×C412yes—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—44no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—81no—
140C11×C4⋊C4C22⋊C414yes—
141C11×C4⋊C4#4112yes—
142C11×C22⋊C4—44no—
143C11×C22⋊C4C22⋊C418yes—
144C42×C11—42no—
145C42×C11C22×C412yes—
146C42×C11C2×D412yes—
147C22⋊Dic11—28no—
148C22⋊Dic11—28no—
149C4⋊Dic11—24no—
150C4⋊Dic11—21no—
151C4⋊Dic11—22no—
152C4⋊Dic11C22×C412yes—
153C4⋊Dic11C22×C414yes—
154Dic11⋊C4—24no—
155Dic11⋊C4—28no—
156C4×Dic11—24no—
157C4×Dic11—28no—
158#4318—48no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8#4112yes—
168C2×#556—111no—
169C2×#436—111no—
170D4×C4⋊C4D1111yescharacteristic
171#1990—111no—
172#1988—111no—
173#1894—112no—
174#1872—112no—
175#1825—112no—
176#1803—111no—
177C4×#103—111no—
178#1736—112no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11C2×C22⋊C414yes—
186C23×C11C22×D411yescharacteristic
187D4×C11—28no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—88no—
206C2×C4×C11C2×C22⋊C414yes—
207C2×C4×C11C2×C22⋊C412yes—
208C2×C4×C11C2×C22⋊C412yes—
209C2×C4×C11AGL(1,ℤ/8)12yes—
210C2×C4×C11#13712yes—
211C2×C4×C11C23×C411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11H(5,𝔽2)11yescharacteristic
216C2×C4×C112−1+411yescharacteristic
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226Dic22—22no—
227Dic22—22no—
228Dic22—41no—
229Dic22—41no—
230Dic22—48no—
231C11⋊C8—22no—
232C11⋊C8—42no—
233C11⋊C8—41no—
234C22×M16—112no—
235#556—118no—
236#556—224no—
237C2×C4⋊Q8—111no—
238C2×#126—222no—
239C2×#124—221no—
240C2×C22⋊Q8—112no—
241C2×C4×Q8—111no—
242C2×C4×Q8—221no—
243C2×C4×D4—21no—
244C2×C4×D4C2×D1111yescharacteristic
245C2×#117—112no—
246C22×C4⋊C4C2×D1112yes—
247#436—224no—
248C2×C4⋊C8—111no—
249C2×#103—111no—
250C2×#103—111no—
251C2×#103—112no—
252C2×C22⋊C8—112no—
253C2×C4×C8—111no—
254#389—21no—
255#385—22no—
256#384C2×D1111yescharacteristic
257#380C2×D1112yes—
258C4×C4⋊C4C2×D1111yescharacteristic
259#340—112no—
260#340—111no—
261#340—112no—
262#340—112no—
263#340—112no—
264#340—112no—
265#340—111no—
266C22×C11—24no—
267C22×C11—24no—
268C22×C11—24no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11C22×C22⋊C411yescharacteristic
274C22×C11#54611yescharacteristic
275C22×C11#54711yescharacteristic
276C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C11C2×#13711yescharacteristic
278C22×C11#57711yescharacteristic
279C22×C11#57811yescharacteristic
280C4×C11—24no—
281C4×C11—22no—
282C4×C11—42no—
283C4×C11—81no—
284C4×C11—82no—
285C4×C11#41714yes—
286C4×C11C4×#4111yescharacteristic
287C4×C11#52011yescharacteristic
288C4×C11#54611yescharacteristic
289C4×C11#54711yescharacteristic
290Dic11—42no—
291Dic11—44no—
292Dic11—42no—
293C22×Q8—111no—
294C22×Q8—221no—
295C22×D4C22⋊D1111yescharacteristic
296C23×C4—22no—
297C23×C4C22×D1112yes—
298C2×M16—224no—
299C2×M16—224no—
300C2×M16—442no—
301C22×C8—111no—
302C22×C8—112no—
303C22×C8—111no—
304C4⋊Q8—114no—
305C4⋊Q8—222no—
306#126—2216no—
307#124—228no—
308C22⋊Q8—118no—
309C22⋊Q8—224no—
310C4×Q8—114no—
311C4×Q8—228no—
312C4×Q8—222no—
313C4×D4—44no—
314C4×D4C4×D1114yes—
315C4×D4D4414yes—
316#117—118no—
317#117—224no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4C22⋊D1111yescharacteristic
329C2×C4⋊C4C22×D1112yes—
330C2×C4⋊C4C22×D1111yescharacteristic
331C2×C4⋊C4C22×D1111yescharacteristic
332C2×C22⋊C4—22no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4C22⋊D1112yes—
336C2×C42—21no—
337C2×C42—222no—
338C2×C42—221no—
339C2×C42C22×D1111yescharacteristic
340C4⋊C8—222no—
341#103—222no—
342#103—222no—
343#103—442no—
344C22⋊C8—224no—
345C4×C8—222no—
346#95—21no—
347#95—22no—
348C2×C11—44no—
349C2×C11#233911yescharacteristic
350C2×C11C2×#41711yescharacteristic
351C2×C11#289811yescharacteristic
352C2×C11#332411yescharacteristic
353C2×C11#332811yescharacteristic
354C2×C11#335311yescharacteristic
355C2×C11#335611yescharacteristic
356C24C2×C22⋊D1112yes—
357C2×Q8—112no—
358C2×Q8—224no—
359C2×Q8—221no—
360C2×Q8—221no—
361C2×Q8—221no—
362C2×Q8—221no—
363C2×Q8—221no—
364C2×Q8—442no—
365C2×Q8—442no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4(C2×D11)⋊C414yes—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—44no—
377C22×C4—44no—
378C22×C4—82no—
379C22×C4—221no—
380C22×C4—222no—
381C22×C4—221no—
382C22×C4C2×C4×D1114yes—
383C22×C4C2×D4414yes—
384C22×C4C2×C22⋊D1112yes—
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C23×D1111yescharacteristic
388M16—448no—
389C2×C8—112no—
390C2×C8—221no—
391C2×C8—221no—
392C2×C8—221no—
393C2×C8—222no—
394C2×C8—221no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—221no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—44no—
404C4⋊C4—42no—
405C4⋊C4—81no—
406C4⋊C4—112no—
407C4⋊C4—114no—
408C4⋊C4—224no—
409C4⋊C4—228no—
410C4⋊C4—224no—
411C4⋊C4—221no—
412C4⋊C4—222no—
413C4⋊C4(C2×D11)⋊C414yes—
414C4⋊C4#434112yes—
415C22⋊C4—44no—
416C22⋊C4—228no—
417C22⋊C4—228no—
418C22⋊C4(C2×D11)⋊C418yes—
419C42—42no—
420C42—228no—
421C42—224no—
422C42C2×C4×D1112yes—
423C42C2×D4412yes—
424C11#2250411yescharacteristic, complemented, Sylow
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23C2×(C2×D11)⋊C414yes—
432C23C22×C22⋊D1111yescharacteristic
433Q8—222no—
434Q8—222no—
435Q8—441no—
436Q8—441no—
437Q8—448no—
438D4—28no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—88no—
457C2×C4—222no—
458C2×C4—224no—
459C2×C4—222no—
460C2×C4—442no—
461C2×C4—441no—
462C2×C4—442no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4C2×(C2×D11)⋊C414yes—
467C2×C4C2×(C2×D11)⋊C412yes—
468C2×C4C2×(C2×D11)⋊C412yes—
469C2×C4#6698512yes—
470C2×C4#6699512yes—
471C2×C4C22×C4×D1111yescharacteristic
472C2×C4C22×D4411yescharacteristic
473C2×C4C2×#434111yescharacteristic
474C2×C4#6703711yescharacteristic
475C2×C4#41×D1111yescharacteristic
476C2×C4#6704311yescharacteristic
477C8—222no—
478C8—442no—
479C8—441no—
480C22—24no—
481C22—24no—
482C22—24no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22C22×(C2×D11)⋊C411yescharacteristic
488C22C2×#6698511yescharacteristic
489C22#1062333711yescharacteristic
490C22C2×#6699511yescharacteristic
491C22#1062335511yescharacteristic
492C22#1062336711yescharacteristic
493C22#1062336911yescharacteristic
494C4—24no—
495C4—22no—
496C4—42no—
497C4—82no—
498C4—81no—
499C4—442no—
500C4—444no—
501C4—442no—
502C4#1062257914yes—
503C4C4×#434111yescharacteristic
504C4#1062307711yescharacteristic
505C4#1062308511yescharacteristic
506C4#1062308611yescharacteristic
507C2—44no—
508C2#1307144111yescharacteristic
509C2C2×#1062257911yescharacteristic
510C2#1307714611yescharacteristic
511C2#1308084711yescharacteristic
512C2#1308089911yescharacteristic
513C2#1308120011yescharacteristic
514C2#1308123111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
cosocleC22×C4×C11C24
hypercenterD4×C4⋊C4D11
hypocenterC11#22504
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13069576C2semidirect
4. #13069568C2semidirect
5. #13069047C2semidirect
6. #13068923C2semidirect
7. #13068708C2semidirect
8. #13068618C2semidirect
9. C4×#66874C2semidirect
10. #13068335C2semidirect
20. #10623073C4semidirect
69. #66979C2×C4semidirect
74. #66977C2×C4semidirect
88. #66922C2×C4semidirect
90. C4×Dic22C2×C4semidirect
424. C11#22504semidirect

Maximal subgroups

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

subgroupindex
C2×#106230732
C2×#106226252
#130695762
#130695682
#130690472
#130689232
#130687082
#130686182
C4×#668742
#130683352
D4×C11×C4⋊C42
#2250411