Finite Group Databasebeta

← #14752778

Subgroups — #14752778

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622741C211yesmaximal, characteristic
2C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic
3#13071079C211yesmaximal, characteristic
4#13068482C211yesmaximal, characteristic, complemented
5C8×Dic11⋊C4C211yesmaximal, characteristic, complemented
6#13068470C211yesmaximal, characteristic, complemented
7#13068398C211yesmaximal, characteristic, complemented
8#13068394C211yesmaximal, characteristic, complemented
9#13068393C211yesmaximal, characteristic, complemented
10#13068384C211yesmaximal, characteristic, complemented
11#13068383C211yesmaximal, characteristic, complemented
12#13068360C211yesmaximal, characteristic, complemented
13#13068314C211yesmaximal, characteristic, complemented
14#13068311C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28#10622741C418yescomplemented
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622570C412yes—
38#10622557C412yes—
39C4×(C2×D11)⋊C4C2211yescharacteristic
40C4×Dic11⋊C4C2211yescharacteristic
41C42×Dic11C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44(C22⋊D11)⋊C8C418yescomplemented
45#10622283C412yes—
46#10622260C412yes—
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11C2×C411yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C2×C11×M16—41no—
61C2×C11×M16—41no—
62C2×C11×M16C2×C414yes—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C22⋊C4C2×C412yes—
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11C2×C412yes—
71C2×C22⋊Dic11C2×C411yescharacteristic
72C4×C22⋊D11C2×C414yes—
73C4×C22⋊D11C2×C414yes—
74C2×(C2×D11)⋊C4C2×C412yes—
75C2×(C2×D11)⋊C4C2×C412yes—
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77#66979—41no—
78#66979—41no—
79C2×C4⋊Dic11C2×C412yes—
80C2×Dic11⋊C4C2×C412yes—
81C2×Dic11⋊C4C2×C412yes—
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×C4×Dic11C2×C412yes—
84C2×C4×Dic11C2×C412yes—
85C2×C4×Dic11C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C22×C11⋊C8—41no—
89C22×C11⋊C8—41no—
90C22×C11⋊C8C2×C414yes—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C2×#4313—41no—
96C2×#4313—41no—
97C2×#4313C2×C414yes—
98C2×C8×D11—41no—
99C2×C8×D11—41no—
100C2×C8×D11C2×C414yes—
101#66925—41no—
102#66925—41no—
103C11×C22⋊C8C2×C414yes—
104C11×#97—41no—
105C4×C8×C11—41no—
106C11×#95C2×C412yes—
107C11⋊#95C2×C412yes—
108C11⋊#95C2×C412yes—
109C22⋊(C11⋊C8)C2×C414yes—
110(C2×D11)⋊C8C2×C414yes—
111(C2×D11)⋊C8C2×C414yes—
112#66879—41no—
113Dic11⋊C8C2×C414yes—
114Dic11⋊C8C2×C414yes—
115C8×Dic11—41no—
116C8×Dic11C2×C414yes—
117C8×Dic11C2×C414yes—
118#66867—41no—
119#66867—41no—
120#20565—111nomaximal, Sylow
121C24×C11C22×C411yescharacteristic
122C23×D11C22×C411yescharacteristic
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C2411yescharacteristic
133C2×C22⋊D11—24no—
134C2×C22⋊D11C4214yes—
135C22×Dic11C22×C412yes—
136C22×Dic11C22×C412yes—
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11C22×C412yes—
145C2×C4×D11C22×C412yes—
146C11×M16—44no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11C22×C412yes—
156C2×C8×C11C22×C412yes—
157C2×C8×C11C22×C412yes—
158C2×C8×C11C22×C412yes—
159C11×C22⋊C4—42no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C22⋊Dic11—42no—
165C22⋊Dic11C4214yes—
166(C2×D11)⋊C4—42no—
167(C2×D11)⋊C4—42no—
168(C2×D11)⋊C4C4214yes—
169C4⋊Dic11—42no—
170Dic11⋊C4—24no—
171Dic11⋊C4—42no—
172Dic11⋊C4C4214yes—
173C4×Dic11—24no—
174C4×Dic11—21no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—42no—
179C4×Dic11C22×C412yes—
180C4×Dic11C22×C412yes—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—44no—
190C2×C11⋊C8C22×C412yes—
191C2×C11⋊C8C22×C412yes—
192C2×C11⋊C8C22×C412yes—
193C2×C11⋊C8C22×C412yes—
194#4313—44no—
195C8×D11—44no—
196C2×#436—111no—
197C2×C8×D4—111no—
198#2293—111no—
199#1770—111no—
200C8×C4⋊C4—111no—
201#1767—111no—
202#1753—111no—
203#1753D1111yescharacteristic, complemented
204#1752—111no—
205#1752—111no—
206#1750—111no—
207#1750—111no—
208#1744—111no—
209#1729—111no—
210#1729—111no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11C2×C4212yes—
216C23×C11C23×C411yescharacteristic
217C22×D11—21no—
218C22×D11—21no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11C2×C4212yes—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11C2×C4212yes—
235C2×C4×C11C23×C411yescharacteristic
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11H(5,𝔽2)11yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C22⋊D11—28no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11C2×C4212yes—
252C2×Dic11C2×C4212yes—
253C2×Dic11C2×C4212yes—
254C2×Dic11#13114yes—
255C4×D11—22no—
256C4×D11—22no—
257C4×D11—22no—
258C4×D11—22no—
259C8×C11—22no—
260C8×C11—22no—
261C8×C11—22no—
262C8×C11—22no—
263C11⋊C8—22no—
264C11⋊C8—22no—
265C11⋊C8—22no—
266C11⋊C8—22no—
267C22×M16—111no—
268C22×M16C2×D1111yescharacteristic
269C23×C8—111no—
270C23×C8—111no—
271C2×C4×D4—111no—
272C2×#117—111no—
273C2×#117—111no—
274#436—118no—
275C8×D4—118no—
276C2×C4⋊C8—111no—
277C2×C4⋊C8—111no—
278C2×C22⋊C8—111no—
279C2×C22⋊C8—111no—
280C2×C22⋊C8—111no—
281C2×C22⋊C8C2×D1111yescharacteristic
282C2×#97—111no—
283C2×#97—111no—
284C2×#97—111no—
285C2×#97C2×D1111yescharacteristic
286C2×C4×C8—111no—
287C2×C4×C8—111no—
288C2×C4×C8—111no—
289C2×C4×C8C2×D1111yescharacteristic
290#390—112no—
291#389—112no—
292#388—112no—
293#388—112no—
294C4×C4⋊C4—111no—
295C4×C22⋊C4—111no—
296C4×C22⋊C4C2×D1111yescharacteristic
297C43—111no—
298#336—111no—
299#336—111no—
300#336—111no—
301#336—111no—
302#336—111no—
303#336—111no—
304#336—111no—
305#336—111no—
306#336C2×D1111yescharacteristic
307#336C2×D1111yescharacteristic
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11C22×C4211yescharacteristic
314C22×C11#51811yescharacteristic
315C22×C11#52011yescharacteristic
316C22×C11C2×#13112yes—
317C22×C11#56812yes—
318C2×D11—22no—
319C2×D11—22no—
320C2×D11—22no—
321C2×D11—42no—
322C2×D11—42no—
323C4×C11—22no—
324C4×C11—42no—
325C4×C11—42no—
326C4×C11#51811yescharacteristic
327C4×C11#51811yescharacteristic
328C4×C11#52011yescharacteristic
329C4×C11#52011yescharacteristic
330Dic11—22no—
331Dic11—22no—
332Dic11—42no—
333Dic11—42no—
334Dic11#40514yes—
335C22×D4—111no—
336C23×C4—111no—
337C23×C4C22×D1111yescharacteristic
338C2×M16—41no—
339C2×M16—41no—
340C2×M16—114no—
341C2×M16—441no—
342C2×M16—441no—
343C2×M16C4×D1114yes—
344C22×C8—111no—
345C22×C8—111no—
346C22×C8—111no—
347C22×C8—111no—
348C22×C8—114no—
349C22×C8—114no—
350C22×C8—441no—
351C22×C8—441no—
352C22×C8—441no—
353C22×C8—441no—
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C22×C8C22×D1111yescharacteristic
358C4×D4—114no—
359C4×D4—114no—
360#117—441no—
361#117—441no—
362#117—441no—
363#117—441no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—112no—
368C2×C22⋊C4—111no—
369C2×C22⋊C4—111no—
370C2×C22⋊C4—112no—
371C2×C22⋊C4—112no—
372C2×C22⋊C4—112no—
373C2×C22⋊C4C4×D1112yes—
374C2×C42—111no—
375C2×C42—112no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—112no—
379C2×C42C22×D1111yescharacteristic
380C2×C42C22×D1111yescharacteristic
381C4⋊C8—114no—
382C4⋊C8—114no—
383C22⋊C8—114no—
384C22⋊C8—114no—
385C22⋊C8—114no—
386C22⋊C8C4×D1114yes—
387#97—41no—
388#97—441no—
389#97—441no—
390#97—441no—
391C4×C8—41no—
392C4×C8—114no—
393C4×C8—114no—
394C4×C8—441no—
395#95—112no—
396#95—112no—
397#95C4×D1112yes—
398C2×C11—42no—
399C2×C11#227511yescharacteristic
400C2×C11C2×#40511yescharacteristic
401C2×C11#287511yescharacteristic
402C2×C11#298112yes—
403C2×C11#299312yes—
404D11—42no—
405C24—111no—
406C24C2×C4×D1111yescharacteristic
407C2×D4—114no—
408C2×D4—224no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—111no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—112no—
417C22×C4—112no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4C2×C4×D1112yes—
425C22×C4C2×C4×D1112yes—
426C22×C4C2×C4×D1111yescharacteristic
427C22×C4C2×C4×D1112yes—
428C22×C4C2×C4×D1112yes—
429C22×C4C23×D1111yescharacteristic
430M16—44no—
431M16—444no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—112no—
441C2×C8—112no—
442C2×C8—112no—
443C2×C8—112no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—444no—
453C2×C8—444no—
454C2×C8C2×C4×D1112yes—
455C2×C8C2×C4×D1112yes—
456C2×C8C2×C4×D1112yes—
457C2×C8C2×C4×D1112yes—
458C4⋊C4—114no—
459C4⋊C4—224no—
460C4⋊C4—442no—
461C4⋊C4—442no—
462C22⋊C4—42no—
463C22⋊C4—114no—
464C22⋊C4—114no—
465C22⋊C4—442no—
466C22⋊C4—442no—
467C22⋊C4—442no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—112no—
473C42—112no—
474C42—224no—
475C42—221no—
476C42—221no—
477C42—221no—
478C42—221no—
479C42—442no—
480C11#2056511yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—21no—
484C23—21no—
485C23—112no—
486C23—222no—
487C23—222no—
488C23—221no—
489C23—221no—
490C23C42×D1112yes—
491C23C22×C4×D1111yescharacteristic
492D4—228no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—112no—
506C2×C4—114no—
507C2×C4—112no—
508C2×C4—112no—
509C2×C4—222no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4C42×D1112yes—
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4C22×C4×D1111yescharacteristic
525C2×C4#6703711yescharacteristic
526C2×C4#6703711yescharacteristic
527C2×C4#6704211yescharacteristic
528C2×C4#6704311yescharacteristic
529C8—22no—
530C8—22no—
531C8—22no—
532C8—22no—
533C8—222no—
534C8—222no—
535C8—222no—
536C8—222no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—42no—
541C22—42no—
542C22—222no—
543C22—222no—
544C22—222no—
545C22—442no—
546C22—442no—
547C22C2×C42×D1111yescharacteristic
548C22#1062307611yescharacteristic
549C22#1062307711yescharacteristic
550C22#1062327612yes—
551C22D11×#13112yes—
552C4—22no—
553C4—42no—
554C4—42no—
555C4—114no—
556C4—222no—
557C4—222no—
558C4—442no—
559C4—442no—
560C4#1062301711yescharacteristic
561C4#1062305411yescharacteristic
562C4#1062307611yescharacteristic
563C4#1062307711yescharacteristic
564C2—42no—
565C2—442no—
566C2#1307097511yescharacteristic
567C2D11×#40511yescharacteristic
568C2#1307704511yescharacteristic
569C2#1307768812yes—
570C2#1307776212yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC11×#1753C2
socleC23×C11C23×C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#20565
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
4. #13068482C2semidirect
5. C8×Dic11⋊C4C2semidirect
6. #13068470C2semidirect
7. #13068398C2semidirect
8. #13068394C2semidirect
9. #13068393C2semidirect
10. #13068384C2semidirect
11. #13068383C2semidirect
12. #13068360C2semidirect
13. #13068314C2semidirect
14. #13068311C2semidirect
15. C11×#1753C2semidirect
28. #10622741C4semidirect
44. (C22⋊D11)⋊C8C4semidirect
203. #1753D11semidirect
480. C11#20565semidirect

Maximal subgroups

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

subgroupindex
C2×#106227412
C2×(C22⋊D11)⋊C82
#130710792
#130684822
C8×Dic11⋊C42
#130684702
#130683982
#130683942
#130683932
#130683842
#130683832
#130683602
#130683142
#130683112
C11×#17532
#2056511