Finite Group Databasebeta

← #14755013

Subgroups — #14755013

Order 2816.

1934 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C22×#66979C211yesmaximal, characteristic
3C2×#10622733C212yesmaximal, complemented
4#13068926C214yesmaximal, complemented
5#13068921C214yesmaximal, complemented
6#13068336C212yesmaximal, complemented
7C2×C11×#407C211yesmaximal, characteristic
8C24×C4×C11C2211yescharacteristic
9C23×Dic22C2211yescharacteristic
10C22×C11×M16C2212yes—
11C22×C22⋊Dic11—21no—
12C22×C22⋊Dic11—21no—
13C2×#66979—21no—
14C2×#66979—21no—
15C2×#66979—28no—
16C2×#66979C2212yes—
17C2×#66979C2212yes—
18C22×C4⋊Dic11C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C2×#66977—21no—
21C2×#66977—21no—
22C2×#66977—24no—
23C2×#66977C418yescomplemented
24C2×#66977C2212yes—
25C2×#66977C2212yes—
26C22×Dic11⋊C4—21no—
27C22×C4×Dic11—21no—
28C11×#407—24no—
29C2×C11×C22⋊C8C2212yes—
30C2×C11×C22⋊C8C2212yes—
31#10622733—28no—
32C2×#66880C2218yescomplemented
33#10622189C2218yescomplemented
34C25×C11D411yescharacteristic
35C23×C4×C11—24no—
36C23×C4×C11—24no—
37C23×C4×C11C2×C414yes—
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D414yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—22no—
46C23×Dic11—21no—
47C23×Dic11—21no—
48C22×Dic22—24no—
49C22×Dic22—24no—
50C22×Dic22—21no—
51C22×Dic22—22no—
52C22×Dic22C2×C414yescomplemented
53C22×Dic22C2312yes—
54C2×C11×M16—24no—
55C2×C11×M16—24no—
56C2×C11×M16—24no—
57C22×C8×C11C2314yes—
58C2×C22⋊Dic11—28no—
59C2×C22⋊Dic11—28no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64#66979—28no—
65#66979—28no—
66#66979—24no—
67#66979—28no—
68#66979D418yes—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—28no—
73C2×C4⋊Dic11C2×C414yescomplemented
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2314yes—
76#66977—28no—
77#66977—28no—
78#66977—24no—
79#66977—24no—
80#66977C2×C418yes—
81#66977C2×C418yescomplemented
82C2×Dic11⋊C4—28no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—22no—
85C2×C4×Dic11—28no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C11×C22⋊C8—24no—
89C11×C22⋊C8—24no—
90#66880—216no—
91#20911—111nomaximal, Sylow
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—24no—
95C24×C11—42no—
96C24×C11C22⋊C414yes—
97C24×C11C2×D411yescharacteristic
98C24×C11C2×D411yescharacteristic
99C24×C11C2×D411yescharacteristic
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—216no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—216no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11C22⋊C414yes—
113C22×C4×C11C22⋊C414yes—
114C22×C4×C11C22⋊C414yes—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D414yes—
125C22×C4×C11#4114yes—
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—28no—
128C22×Dic11—24no—
129C22×Dic11—24no—
130C22×Dic11—24no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—44no—
134C22×Dic11—44no—
135C22×Dic11—42no—
136C22×Dic11—42no—
137C22×Dic11—44no—
138C2×Dic22—24no—
139C2×Dic22—216no—
140C2×Dic22—24no—
141C2×Dic22—22no—
142C2×Dic22—24no—
143C2×Dic22—42no—
144C2×Dic22—48no—
145C2×Dic22—42no—
146C2×Dic22C22×C414yes—
147C11×M16—48no—
148C2×C8×C11—24no—
149C2×C8×C11—24no—
150C2×C8×C11—24no—
151C22⋊Dic11—28no—
152C22⋊Dic11—28no—
153C22⋊Dic11—28no—
154C22⋊Dic11—28no—
155C4⋊Dic11—28no—
156C4⋊Dic11—24no—
157C4⋊Dic11—22no—
158C4⋊Dic11—24no—
159C4⋊Dic11C22×C414yes—
160C4⋊Dic11C2×D418yes—
161Dic11⋊C4—28no—
162Dic11⋊C4—28no—
163C4×Dic11—28no—
164C4×Dic11—28no—
165C22×C22⋊Q8—111no—
166C22×#117—111no—
167C2×#419—112no—
168C2×#407D1111yescharacteristic
169#1873—114no—
170#1872—114no—
171#1736—112no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—28no—
182C23×C11—28no—
183C23×C11—44no—
184C23×C11—48no—
185C23×C11—48no—
186C23×C11C2×C22⋊C412yes—
187C23×C11C2×C22⋊C412yes—
188C23×C11C2×C22⋊C412yes—
189C23×C11#12012yes—
190C23×C11#12312yes—
191C23×C11#13714yes—
192C23×C11C22×D411yescharacteristic
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—28no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—28no—
203C2×C4×C11—28no—
204C2×C4×C11C2×C22⋊C412yes—
205C2×C4×C11C2×C22⋊C412yes—
206C2×C4×C11C2×C22⋊C412yes—
207C2×C4×C11C4×D418yes—
208C2×C4×C11#12012yes—
209C2×C4×C11#12118yes—
210C2×C4×C11#12312yes—
211C2×C4×C11C23×C411yescharacteristic
212C2×C4×C11C22×D412yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4112yes—
215C2×Dic11—24no—
216C2×Dic11—24no—
217C2×Dic11—28no—
218C2×Dic11—48no—
219C2×Dic11—416no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—44no—
223C2×Dic11—44no—
224C2×Dic11—44no—
225C2×Dic11—48no—
226Dic22—28no—
227Dic22—44no—
228Dic22—48no—
229C8×C11—44no—
230C23×Q8—111no—
231C24×C4C2×D1111yescharacteristic
232C22×M16C2×D1112yes—
233C2×C22⋊Q8—112no—
234C2×C22⋊Q8—112no—
235C2×C22⋊Q8—118no—
236C2×C22⋊Q8—221no—
237C2×C22⋊Q8—221no—
238C2×C22⋊Q8—224no—
239C2×#117—112no—
240C2×#117—112no—
241C2×#117—228no—
242C2×#117—221no—
243C2×#117—221no—
244C22×C4⋊C4—111no—
245C22×C4⋊C4—112no—
246C22×C4⋊C4—221no—
247C22×C22⋊C4—221no—
248C22×C22⋊C4—221no—
249C22×C42—221no—
250#419—228no—
251C2×#103—118no—
252#407—24no—
253C2×C22⋊C8C2×D1112yes—
254C2×C22⋊C8C2×D1112yes—
255#340—118no—
256C22×C11—24no—
257C22×C11—24no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—24no—
262C22×C11—24no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—416no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11#38614yes—
271C22×C11#41914yescomplemented
272C22×C11C22×C22⋊C411yescharacteristic
273C22×C11C2×#12011yescharacteristic
274C22×C11C2×#12311yescharacteristic
275C22×C11C2×#13712yes—
276C22×C11#57512yes—
277C4×C11—22no—
278C4×C11—22no—
279C4×C11#38614yes—
280C4×C11C2×C4×D412yes—
281C4×C11C2×#12112yes—
282Dic11—44no—
283Dic11—48no—
284Dic11—44no—
285C25D4411yescharacteristic
286C22×Q8—114no—
287C22×Q8—112no—
288C22×Q8—221no—
289C22×Q8—222no—
290C22×Q8—224no—
291C22×Q8—224no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—221no—
295C23×C4—222no—
296C23×C4—221no—
297C23×C4C4×D1114yes—
298C23×C4D4411yescharacteristic
299C23×C4D4411yescharacteristic
300C23×C4D4411yescharacteristic
301C23×C4C22⋊D1114yes—
302C23×C4C22×D1111yescharacteristic
303C23×C4C22×D1111yescharacteristic
304C23×C4C22×D1111yescharacteristic
305C2×M16—24no—
306C2×M16—24no—
307C2×M16—24no—
308C22×C8C22×D1114yes—
309C22⋊Q8—118no—
310C22⋊Q8—118no—
311C22⋊Q8—228no—
312C22⋊Q8—228no—
313C22⋊Q8—224no—
314C22⋊Q8—224no—
315#117—118no—
316#117—228no—
317#117—228no—
318#117—228no—
319#117—224no—
320C2×C4⋊C4—114no—
321C2×C4⋊C4—114no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—228no—
324C2×C4⋊C4—228no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—222no—
330C2×C22⋊C4—228no—
331C2×C22⋊C4—228no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—222no—
336C2×C42—228no—
337C2×C42—222no—
338C2×C42—222no—
339#103—2216no—
340C22⋊C8—24no—
341C22⋊C8—24no—
342C2×C11—24no—
343C2×C11—24no—
344C2×C11—42no—
345C2×C11C2×#38611yescharacteristic
346C2×C11C2×#41911yescharacteristic
347C2×C11#289611yescharacteristic
348C2×C11#300712yes—
349C2×C11#309512yes—
350C24—22no—
351C24—22no—
352C24—24no—
353C24—42no—
354C24(C2×D11)⋊C414yes—
355C24C2×D4411yescharacteristic
356C24C2×D4411yescharacteristic
357C24C2×D4411yescharacteristic
358C2×Q8—114no—
359C2×Q8—224no—
360C2×Q8—222no—
361C2×Q8—2216no—
362C2×Q8—224no—
363C2×Q8—224no—
364C2×Q8—442no—
365C2×Q8—442no—
366C2×Q8—448no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—216no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—216no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—228no—
380C22×C4—224no—
381C22×C4—224no—
382C22×C4—224no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—444no—
386C22×C4—444no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4—444no—
390C22×C4(C2×D11)⋊C414yes—
391C22×C4(C2×D11)⋊C414yes—
392C22×C4(C2×D11)⋊C414yes—
393C22×C4C2×C4×D1112yes—
394C22×C4C2×C4×D1112yes—
395C22×C4C2×C4×D1112yes—
396C22×C4C2×D4411yescharacteristic
397C22×C4C2×D4411yescharacteristic
398C22×C4C2×D4411yescharacteristic
399C22×C4D4×D1114yes—
400C22×C4#434114yes—
401C22×C4C2×C22⋊D1112yes—
402C22×C4C2×C22⋊D1112yes—
403C22×C4C2×C22⋊D1112yes—
404C22×C4C23×D1111yescharacteristic
405M16—48no—
406C2×C8—24no—
407C2×C8—24no—
408C2×C8—24no—
409C4⋊C4—114no—
410C4⋊C4—118no—
411C4⋊C4—228no—
412C4⋊C4—224no—
413C4⋊C4—228no—
414C4⋊C4—228no—
415C4⋊C4—224no—
416C4⋊C4—222no—
417C22⋊C4—228no—
418C22⋊C4—228no—
419C22⋊C4—228no—
420C22⋊C4—228no—
421C42—228no—
422C42—228no—
423C11#2091111yescharacteristic, complemented, Sylow
424C23—21no—
425C23—22no—
426C23—21no—
427C23—22no—
428C23—22no—
429C23—28no—
430C23—21no—
431C23—22no—
432C23—21no—
433C23—22no—
434C23—28no—
435C23—44no—
436C23—48no—
437C23—48no—
438C23#6693512yes—
439C23#6693912yes—
440C23#6696214yes—
441C23C2×(C2×D11)⋊C412yes—
442C23C2×(C2×D11)⋊C412yes—
443C23C2×(C2×D11)⋊C412yes—
444C23C22×D4411yescharacteristic
445Q8—228no—
446Q8—444no—
447Q8—448no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—28no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—28no—
458C2×C4—28no—
459C2×C4—228no—
460C2×C4—224no—
461C2×C4—224no—
462C2×C4—4416no—
463C2×C4—448no—
464C2×C4—442no—
465C2×C4—444no—
466C2×C4—442no—
467C2×C4—444no—
468C2×C4—444no—
469C2×C4—448no—
470C2×C4(C22⋊D11)⋊C418yes—
471C2×C4#6693512yes—
472C2×C4#6693912yes—
473C2×C4C2×(C2×D11)⋊C412yes—
474C2×C4C2×(C2×D11)⋊C412yes—
475C2×C4C2×(C2×D11)⋊C412yes—
476C2×C4#6699218yes—
477C2×C4C22×C4×D1111yescharacteristic
478C2×C4C2×D4×D1112yes—
479C2×C4C2×#434112yes—
480C2×C4C22×C22⋊D1111yescharacteristic
481C8—44no—
482C22—24no—
483C22—24no—
484C22—24no—
485C22—24no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—416no—
494C22—42no—
495C22—42no—
496C22#1062257114yes—
497C22#1062273314yescomplemented
498C22C2×#6693511yescharacteristic
499C22C2×#6693911yescharacteristic
500C22C2×#6696212yes—
501C22#1062327912yes—
502C22C22×(C2×D11)⋊C411yescharacteristic
503C4—22no—
504C4—22no—
505C4—448no—
506C4—444no—
507C4—444no—
508C4#1062257114yes—
509C4C2×(C22⋊D11)⋊C412yes—
510C4C2×#6699212yes—
511C2—24no—
512C2—24no—
513C2—42no—
514C2C2×#1062257111yescharacteristic
515C2C2×#1062273311yescharacteristic
516C2#1307713611yescharacteristic
517C2#1307787812yes—
518C2#1307856512yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#407C2
socleC23×C11C22×D4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11#20911
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
3. C2×#10622733C2semidirect
4. #13068926C2semidirect
5. #13068921C2semidirect
6. #13068336C2semidirect
23. C2×#66977C4semidirect
32. C2×#66880C22semidirect
33. #10622189C22semidirect
52. C22×Dic22C2×C4semidirect
73. C2×C4⋊Dic11C2×C4semidirect
81. #66977C2×C4semidirect
271. C22×C11#419semidirect
423. C11#20911semidirect
497. C22#10622733semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
C22×#669792
C2×#106227332
#130689262
#130689212
#130683362
C2×C11×#4072
#2091111