Finite Group Databasebeta

← #14722321

Subgroups — #14722321

Order 2816.

952 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2#13077246C211yesmaximal, characteristic
3D11×#432C211yesmaximal, characteristic
4#13067345C214yesmaximal, complemented
5#13067341C211yesmaximal, characteristic, complemented
6#13067341C211yesmaximal, characteristic, complemented
7#13067333C211yesmaximal, characteristic, complemented
8#13067272C214yesmaximal, complemented
9C11×#1556C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C2×Q8×Dic11—21no—
13#10623259—21no—
14#10623259—21no—
15#10623259—21no—
16#10623259—21no—
17#10623259C412yes—
18#10623259C412yes—
19#10623259C2212yes—
20#10623259C2212yes—
21C2×#66950C412yes—
22C2×#66945—21no—
23C2×#66943—21no—
24C2×#66940C412yes—
25C2×C42×D11C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#432C2211yescharacteristic
28C11×#432C2211yescharacteristic
29#10622539C2211yescharacteristic
30#10622539C2211yescharacteristic
31#10622450C2212yes—
32#10622448C2212yes—
33#10622446C2212yes—
34D11×C4⋊C8C2212yes—
35#10622339—21no—
36D11×C22⋊C8—21no—
37#10622332—21no—
38#10622331—21no—
39#10622320—21no—
40#10622318—21no—
41#10622318—21no—
42D11×#97—21no—
43C11×#332C2214yescomplemented
44#10622185C2214yescomplemented
45#10622119C2214yescomplemented
46#10622119C2214yescomplemented
47C22×Q8×C11—21no—
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11D411yescharacteristic
51C22×Dic22C2×C412yes—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8C2×C412yes—
55C11×C4⋊Q8C2312yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2×C412yes—
58C2×C42×C11C2311yescharacteristic
59#66999—22no—
60#66999—22no—
61#66999—22no—
62#66999—22no—
63Q8×Dic11—22no—
64Q8×Dic11—22no—
65Q8×Dic11—22no—
66Q8×Dic11—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—22no—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11C2×C411yescharacteristic
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×#4313—22no—
77C2×C8×D11—22no—
78#66950—22no—
79#66950—22no—
80#66950C2×C414yes—
81#66950C2×C414yes—
82#66945—22no—
83#66945—22no—
84#66945—22no—
85#66945—22no—
86#66943—22no—
87#66943—22no—
88#66943—22no—
89#66943—22no—
90#66940—22no—
91#66940—22no—
92#66940C2×C414yes—
93#66940C2×C414yes—
94C42×D11C2×C411yescharacteristic
95C42×D11C2×C411yescharacteristic
96C42×D11D411yescharacteristic
97C42×D11D411yescharacteristic
98C42×D11D411yescharacteristic
99C42×D11D411yescharacteristic
100C42×D11C2311yescharacteristic
101C42×D11C2311yescharacteristic
102#66922—21no—
103#66922—21no—
104#66922C2×C412yes—
105#66922C2312yes—
106C11×C4⋊C8C2312yes—
107C11×C4⋊C8C2312yes—
108C11×C22⋊C8—21no—
109C11×C22⋊C8—21no—
110C11×#97—21no—
111C11×#97—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)—21no—
114(C2×D11)⋊C8—22no—
115(C2×D11)⋊C8—22no—
116#66879—22no—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119C8×Dic11—22no—
120C4⋊(C11⋊C8)C2312yes—
121C4⋊(C11⋊C8)C2312yes—
122#66867—21no—
123#66867—21no—
124#17734—111nomaximal, Sylow
125C23×D11C22⋊C411yescharacteristic
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—44no—
129C22×C4×C11—22no—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×Dic11—22no—
134C22×Dic11C22⋊C411yescharacteristic
135C22×Dic11C22⋊C411yescharacteristic
136C22×Dic11C22⋊C411yescharacteristic
137C2×C4×D11—24no—
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×C4×D11C22⋊C411yescharacteristic
141C2×C4×D11C22⋊C411yescharacteristic
142C2×C4×D11C22⋊C411yescharacteristic
143C2×C4×D11C22⋊C411yescharacteristic
144C2×C4×D11C22⋊C411yescharacteristic
145C2×C4×D11C22⋊C411yescharacteristic
146C2×C4×D11C22×C411yescharacteristic
147C2×C4×D11C22×C411yescharacteristic
148C2×C4×D11C2×D411yescharacteristic
149C2×C4×D11C2×D411yescharacteristic
150C2×C4×D11C2×D411yescharacteristic
151C2×C4×D11C2×D411yescharacteristic
152C2×Dic22—22no—
153C2×Dic22—44no—
154C2×Dic22C22×C414yes—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C22×C414yes—
161C42×C11C22×C411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C42×C11C2411yescharacteristic
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—24no—
167C4⋊Dic11—24no—
168C4⋊Dic11—24no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173Dic11⋊C4—24no—
174Dic11⋊C4—24no—
175C4×Dic11—24no—
176C4×Dic11—24no—
177C4×Dic11C22⋊C411yescharacteristic
178C4×Dic11C22⋊C411yescharacteristic
179C4×Dic11C22⋊C411yescharacteristic
180C4×Dic11C22⋊C411yescharacteristic
181C4×Dic11C22⋊C411yescharacteristic
182C4×Dic11C22⋊C411yescharacteristic
183C4×Dic11C22×C411yescharacteristic
184C4×Dic11C22×C411yescharacteristic
185C4×Dic11C2×D411yescharacteristic
186C4×Dic11C2×D411yescharacteristic
187C4×Dic11C2×D411yescharacteristic
188C4×Dic11C2×D411yescharacteristic
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191#4313—44no—
192C8×D11—44no—
193C2×#533—111no—
194#2920—111no—
195C2×#432—111no—
196#1559—114no—
197#1558—111no—
198#1558—111no—
199#1556—111no—
200#1556D1111yescharacteristic, complemented
201#1542—114no—
202C23×C11C2×C22⋊C411yescharacteristic
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—41no—
206C22×D11C2×C22⋊C411yescharacteristic
207C22×D11C2×C22⋊C411yescharacteristic
208Q8×C11—44no—
209Q8×C11—44no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—44no—
215C2×C4×C11C2×C22⋊C411yescharacteristic
216C2×C4×C11C2×C22⋊C411yescharacteristic
217C2×C4×C11C2×C22⋊C411yescharacteristic
218C2×C4×C11C23×C411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—24no—
224C2×Dic11—41no—
225C2×Dic11—44no—
226C2×Dic11C2×C22⋊C411yescharacteristic
227C2×Dic11C2×C22⋊C411yescharacteristic
228C2×Dic11C2×C22⋊C411yescharacteristic
229C2×Dic11C2×C22⋊C411yescharacteristic
230C2×Dic11C2×C22⋊C411yescharacteristic
231C2×Dic11C2×C22⋊C411yescharacteristic
232C4×D11—22no—
233C4×D11—22no—
234C4×D11—22no—
235C4×D11—22no—
236C4×D11—22no—
237C4×D11—41no—
238C4×D11—41no—
239C4×D11—41no—
240C4×D11—41no—
241C4×D11—41no—
242C4×D11—41no—
243C4×D11#13714yes—
244Dic22—44no—
245Dic22—44no—
246C8×C11—42no—
247C8×C11—42no—
248C11⋊C8—42no—
249C11⋊C8—42no—
250#533—112no—
251#533—112no—
252#533—112no—
253#533—112no—
254#533—221no—
255#533—221no—
256#533—221no—
257#533—221no—
258C2×C4⋊Q8—111no—
259C2×C4⋊Q8C2×D1111yescharacteristic
260C2×#125—221no—
261C2×C22⋊Q8—112no—
262C2×C22⋊Q8—221no—
263C2×C4×Q8—112no—
264C2×C4×Q8—221no—
265C2×#117—221no—
266C22×C42—111no—
267#432—111no—
268#432—111no—
269#432—112no—
270#432—221no—
271#432—221no—
272#432—221no—
273#432C2×D1111yescharacteristic
274#432C2×D1111yescharacteristic
275#431—112no—
276#431—221no—
277#423—112no—
278C2×C4⋊C8—112no—
279#407—221no—
280C2×C22⋊C8—221no—
281C4×M16—221no—
282C2×#97—221no—
283#333—114no—
284#333—114no—
285#332—114no—
286#332C2×D1114yescomplemented
287C22×C11—21no—
288C22×C11—21no—
289C22×C11#41312yes—
290C22×C11C22×C22⋊C411yescharacteristic
291C2×D11—21no—
292C2×D11—21no—
293C2×D11—21no—
294C2×D11—21no—
295C2×D11—21no—
296C2×D11—44no—
297C2×D11#41912yes—
298C4×C11—21no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—44no—
303C4×C11C2×#13712yes—
304C4×C11#57512yes—
305Dic11—21no—
306Dic11—21no—
307Dic11—21no—
308Dic11—21no—
309Dic11—21no—
310Dic11—44no—
311Dic11#41912yes—
312C22×Q8—21no—
313C22×Q8—112no—
314C23×C4—111no—
315C23×C4—111no—
316C23×C4—111no—
317C2×M16—222no—
318C22×C8—222no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—112no—
322C4⋊Q8—112no—
323C4⋊Q8—221no—
324C4⋊Q8—221no—
325C4⋊Q8C4×D1112yes—
326C4⋊Q8C22×D1112yes—
327#125—222no—
328#125—222no—
329#125—222no—
330#125—222no—
331C22⋊Q8—114no—
332C22⋊Q8—114no—
333C22⋊Q8—222no—
334C22⋊Q8—222no—
335C22⋊Q8—222no—
336C22⋊Q8—222no—
337C22⋊Q8—222no—
338C22⋊Q8—222no—
339C4×Q8—114no—
340C4×Q8—114no—
341C4×Q8—222no—
342C4×Q8—222no—
343C4×Q8—222no—
344C4×Q8—222no—
345C4×Q8—222no—
346C4×Q8—222no—
347#117—222no—
348#117—222no—
349#117—222no—
350#117—222no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4C4×D1112yes—
357C2×C22⋊C4—222no—
358C2×C42—111no—
359C2×C42—111no—
360C2×C42—111no—
361C2×C42—111no—
362C2×C42—111no—
363C2×C42—111no—
364C2×C42—111no—
365C2×C42—111no—
366C2×C42—111no—
367C2×C42—111no—
368C2×C42—111no—
369C2×C42—222no—
370C2×C42C22×D1111yescharacteristic
371C4⋊C8—112no—
372C4⋊C8—112no—
373C4⋊C8—222no—
374C4⋊C8—222no—
375C4⋊C8C22×D1112yes—
376C4⋊C8C22×D1112yes—
377C22⋊C8—21no—
378C22⋊C8—21no—
379C22⋊C8—222no—
380C22⋊C8—222no—
381C22⋊C8—221no—
382C22⋊C8—221no—
383#97—21no—
384#97—21no—
385#97—222no—
386#97—221no—
387#97—221no—
388C4×C8—222no—
389C2×C11—22no—
390C2×C11C2×#41311yescharacteristic
391C2×C11C2×#41911yescharacteristic
392C2×C11#289611yescharacteristic
393D11—22no—
394D11—41no—
395C24—111no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—44no—
399C2×Q8—114no—
400C2×Q8—222no—
401C2×Q8—444no—
402C22×C4—22no—
403C22×C4—111no—
404C22×C4—111no—
405C22×C4—111no—
406C22×C4—111no—
407C22×C4—111no—
408C22×C4—111no—
409C22×C4—111no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—111no—
417C22×C4—111no—
418C22×C4—224no—
419C22×C4—222no—
420C22×C4—442no—
421C22×C4—442no—
422C22×C4C2×C4×D1111yescharacteristic
423C22×C4D4×D1111yescharacteristic
424C22×C4D4×D1111yescharacteristic
425M16—444no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—222no—
429C2×C8—222no—
430C2×C8—444no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—224no—
435C4⋊C4—224no—
436C4⋊C4—224no—
437C4⋊C4—224no—
438C4⋊C4—222no—
439C4⋊C4—222no—
440C4⋊C4—222no—
441C4⋊C4—222no—
442C4⋊C4C2×C4×D1114yes—
443C22⋊C4—224no—
444C22⋊C4—224no—
445C42—111no—
446C42—111no—
447C42—111no—
448C42—111no—
449C42—111no—
450C42—111no—
451C42—111no—
452C42—111no—
453C42—111no—
454C42—111no—
455C42—111no—
456C42—111no—
457C42—224no—
458C42—224no—
459C42C2×C4×D1111yescharacteristic
460C42D4×D1111yescharacteristic
461C42D4×D1111yescharacteristic
462C42C23×D1111yescharacteristic
463C11#1773411yescharacteristic, complemented, Sylow
464C23—111no—
465C23—111no—
466C23—222no—
467C23—222no—
468C23—441no—
469C23C22⋊C4×D1111yescharacteristic
470Q8—44no—
471Q8—44no—
472Q8—444no—
473Q8—444no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—44no—
479C2×C4—111no—
480C2×C4—114no—
481C2×C4—111no—
482C2×C4—111no—
483C2×C4—111no—
484C2×C4—111no—
485C2×C4—111no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—224no—
494C2×C4—441no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—444no—
502C2×C4C22⋊C4×D1111yescharacteristic
503C2×C4C22⋊C4×D1111yescharacteristic
504C2×C4C22⋊C4×D1111yescharacteristic
505C2×C4C22×C4×D1111yescharacteristic
506C2×C4C2×D4×D1111yescharacteristic
507C2×C4C2×D4×D1111yescharacteristic
508C8—42no—
509C8—42no—
510C8—442no—
511C8—442no—
512C22—21no—
513C22—21no—
514C22—112no—
515C22—221no—
516C22—221no—
517C22—221no—
518C22—221no—
519C22—221no—
520C22—444no—
521C22#1062236412yes—
522C22C2×C22⋊C4×D1111yescharacteristic
523C4—21no—
524C4—21no—
525C4—21no—
526C4—21no—
527C4—44no—
528C4—112no—
529C4—221no—
530C4—221no—
531C4—221no—
532C4—221no—
533C4—221no—
534C4—444no—
535C4#1062330412yes—
536C4D11×#13712yes—
537C2—22no—
538C2—222no—
539C2—441no—
540C2C2×#1062236411yescharacteristic
541C2D11×#41911yescharacteristic
542C2#1307713011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1556C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1556D11
hypocenterC11#17734
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

Complements

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

NH ≅ G/Ntype
4. #13067345C2semidirect
5. #13067341C2semidirect
6. #13067341C2semidirect
7. #13067333C2semidirect
8. #13067272C2semidirect
9. C11×#1556C2semidirect
43. C11×#332C22semidirect
44. #10622185C22semidirect
45. #10622119C22semidirect
46. #10622119C22semidirect
200. #1556D11semidirect
286. #332C2×D11semidirect
463. C11#17734semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130772462
D11×#4322
#130673452
#130673412
#130673332
#130672722
C11×#15562
#1773411