Finite Group Databasebeta

← #14752714

Subgroups — #14752714

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622319C211yesmaximal, characteristic
2C2×#10622447C211yesmaximal, characteristic
3#13071057C211yesmaximal, characteristic
4#13068485C211yesmaximal, characteristic, complemented
5#13068475C211yesmaximal, characteristic, complemented
6#13068398C211yesmaximal, characteristic, complemented
7#13068393C211yesmaximal, characteristic, complemented
8#13068391C211yesmaximal, characteristic, complemented
9C8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
10#13068383C211yesmaximal, characteristic, complemented
11#13068379C211yesmaximal, characteristic, complemented
12#13068369C211yesmaximal, characteristic, complemented
13#13068311C211yesmaximal, characteristic, complemented
14D11×#336C211yesmaximal, characteristic, complemented
15C11×#1771C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66925C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622603C412yes—
35#10622602C412yes—
36C4×(C2×D11)⋊C4C2211yescharacteristic
37C4×(C2×D11)⋊C4C2211yescharacteristic
38#10622545C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×#66867C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622447C418yescomplemented
44#10622319C418yescomplemented
45#10622278C412yes—
46#10622267C412yes—
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57C22×D44C2×C411yescharacteristic
58C22×C4×D11C2×C412yes—
59C22×C4×D11C2311yescharacteristic
60C22×C4×D11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2×C412yes—
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×(C2×D11)⋊C4C2×C412yes—
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×C4⋊Dic11C2×C411yescharacteristic
75C2×Dic11⋊C4C2×C412yes—
76C2×C4×Dic11C2×C412yes—
77C2×C4×Dic11C2311yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C2×#4313—41no—
84C2×#4313—41no—
85C2×#4313C2×C414yescomplemented
86C2×C8×D11—41no—
87C2×C8×D11—41no—
88C2×C8×D11—41no—
89C2×C8×D11—41no—
90C2×C8×D11—41no—
91C2×C8×D11—41no—
92C2×C8×D11C2×C414yes—
93C2×C8×D11C2×C414yes—
94C2×C8×D11C2×C414yescomplemented
95C4×D44C2×C414yes—
96C4×D44C2×C414yes—
97#66925—41no—
98#66925—41no—
99C42×D11—41no—
100C42×D11—41no—
101C11×C4⋊C8C2×C414yescomplemented
102C11×#97—41no—
103C11×#97C2×C414yescomplemented
104C4×C8×C11—41no—
105C11×#95C2×C412yes—
106C11⋊#95C2×C412yes—
107C11⋊#95C2×C412yes—
108C11⋊#95C2×C412yes—
109C11⋊#95C2×C412yes—
110(C2×D11)⋊C8C2×C414yes—
111(C2×D11)⋊C8C2×C414yes—
112(C2×D11)⋊C8C2×C414yescomplemented
113(C2×D11)⋊C8C2×C414yescomplemented
114#66879—41no—
115C8×Dic11—41no—
116C4⋊(C11⋊C8)C2×C414yescomplemented
117#66867—41no—
118#66867—41no—
119C4×C11⋊C8C2×C414yescomplemented
120#20560—111nomaximal, Sylow
121C23×D11C22×C411yescharacteristic
122C23×D11C22×C411yescharacteristic
123C22×C4×C11C22×C412yes—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11C22×C412yes—
129C22×Dic11C22×C412yes—
130C22×Dic11C22×C411yescharacteristic
131C22×Dic11C22×C411yescharacteristic
132C2×D44—24no—
133C2×D44C4214yes—
134C2×C4×D11—24no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11C22×C412yes—
146C2×C4×D11C22×C412yes—
147C2×C4×D11C22×C412yes—
148C2×C4×D11C22×C412yes—
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×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11C22×C412yes—
158C2×C8×C11C22×C412yes—
159C2×C8×C11C22×C412yes—
160C2×C8×C11C22×C412yes—
161C11×C4⋊C4—42no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11C22×C412yes—
167C42×C11C22×C412yes—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4C4214yes—
172(C2×D11)⋊C4C4214yes—
173C4⋊Dic11C4214yes—
174Dic11⋊C4—42no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—21no—
179C4×Dic11—42no—
180C2×C11⋊C8—21no—
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⋊C8C22×C412yes—
189C2×C11⋊C8C22×C412yes—
190C2×C11⋊C8C22×C412yes—
191C2×C11⋊C8C22×C412yes—
192#4313—44no—
193C8×D11—44no—
194C8×D11—44no—
195C8×D11—44no—
196C2×#435—111no—
197C2×C8×D4—111no—
198#2290—111no—
199#1771D1111yescharacteristic, complemented
200#1770—111no—
201#1768—111no—
202#1753—111no—
203#1752—111no—
204#1752—111no—
205C8×C22⋊C4—111no—
206#1750—111no—
207#1749—111no—
208#1746—111no—
209#1729—111no—
210C2×#336—111no—
211C23×C11C23×C411yescharacteristic
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—22no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11C2×C4212yes—
220C22×D11C2×C4212yes—
221C22×D11#13114yes—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
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×C11C2×C4212yes—
231C2×C4×C11C2×C4212yes—
232C2×C4×C11C23×C411yescharacteristic
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11C2×C4212yes—
249C2×Dic11C2×C4212yes—
250D44—28no—
251C4×D11—22no—
252C4×D11—22no—
253C4×D11—22no—
254C4×D11—22no—
255C4×D11—22no—
256C4×D11—22no—
257C4×D11—22no—
258C4×D11—22no—
259C4×D11—48no—
260C8×C11—22no—
261C8×C11—22no—
262C8×C11—22no—
263C8×C11—22no—
264C11⋊C8—22no—
265C11⋊C8—22no—
266C11⋊C8—22no—
267C11⋊C8—22no—
268C22×M16—111no—
269C23×C8—111no—
270C23×C8—111no—
271C23×C8—111no—
272C2×C4×D4—111no—
273C2×#117—111no—
274C22×C42—111no—
275#435—118no—
276C8×D4—118no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×C22⋊C8—111no—
280C2×C22⋊C8—111no—
281C2×C22⋊C8—111no—
282C2×C22⋊C8—111no—
283C2×#97—111no—
284C2×#97—111no—
285C2×#97—111no—
286C2×#97C2×D1111yescharacteristic
287C2×#97C2×D1111yescharacteristic
288C2×C4×C8—111no—
289C2×C4×C8—111no—
290C2×C4×C8C2×D1111yescharacteristic
291#388—112no—
292#387—112no—
293#386—112no—
294#385—112no—
295C4×C4⋊C4C2×D1111yescharacteristic
296C4×C22⋊C4—111no—
297C4×C22⋊C4—111no—
298#376—111no—
299#336—111no—
300#336—111no—
301#336—111no—
302#336—111no—
303#336—111no—
304#336—111no—
305#336—111no—
306#336—111no—
307#336C2×D1111yescharacteristic
308#336C2×D1111yescharacteristic
309C22×C11C22×C4211yescharacteristic
310C22×C11#51811yescharacteristic
311C22×C11#52011yescharacteristic
312C22×C11C2×#13112yes—
313C22×C11#56812yes—
314C2×D11—22no—
315C2×D11—24no—
316C2×D11—24no—
317C2×D11—22no—
318C2×D11—22no—
319C2×D11—22no—
320C2×D11—22no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11#40514yes—
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11#51811yescharacteristic
329C4×C11#51811yescharacteristic
330C4×C11#52011yescharacteristic
331C4×C11#52011yescharacteristic
332Dic11—22no—
333Dic11—22no—
334Dic11—42no—
335Dic11—42no—
336C22×D4—111no—
337C23×C4—111no—
338C23×C4—111no—
339C23×C4—112no—
340C2×M16—114no—
341C2×M16—441no—
342C2×M16—441no—
343C22×C8—111no—
344C22×C8—111no—
345C22×C8—111no—
346C22×C8—111no—
347C22×C8—114no—
348C22×C8—114no—
349C22×C8—114no—
350C22×C8—441no—
351C22×C8—441no—
352C22×C8—441no—
353C22×C8—441no—
354C22×C8—441no—
355C22×C8—441no—
356C22×C8C22×D1111yescharacteristic
357C22×C8C22×D1111yescharacteristic
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360C4×D4—114no—
361C4×D4—114no—
362#117—441no—
363#117—441no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4C4×D1112yes—
367C2×C22⋊C4—111no—
368C2×C22⋊C4—111no—
369C2×C22⋊C4—112no—
370C2×C22⋊C4—112no—
371C2×C22⋊C4—112no—
372C2×C42—111no—
373C2×C42—111no—
374C2×C42—112no—
375C2×C42—441no—
376C2×C42—441no—
377C2×C42C22×D1111yescharacteristic
378C2×C42C22×D1111yescharacteristic
379C2×C42C22×D1111yescharacteristic
380C4⋊C8—114no—
381C4⋊C8C4×D1114yescomplemented
382C22⋊C8—114no—
383C22⋊C8—114no—
384C22⋊C8—114no—
385C22⋊C8—114no—
386#97—41no—
387#97—441no—
388#97—441no—
389#97—441no—
390#97C4×D1114yescomplemented
391C4×C8—41no—
392C4×C8—114no—
393C4×C8—441no—
394#95—112no—
395#95—112no—
396#95—112no—
397#95—112no—
398#95C4×D1112yes—
399C2×C11#227511yescharacteristic
400C2×C11C2×#40511yescharacteristic
401C2×C11#287511yescharacteristic
402C2×C11#297612yes—
403C2×C11#299212yes—
404D11—24no—
405D11—42no—
406C24—111no—
407C24—111no—
408C2×D4—114no—
409C2×D4—224no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—112no—
417C22×C4—112no—
418C22×C4—224no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4C2×C4×D1112yes—
430C22×C4C2×C4×D1112yes—
431C22×C4C2×C4×D1111yescharacteristic
432C22×C4C2×C4×D1111yescharacteristic
433C22×C4C23×D1111yescharacteristic
434M16—444no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—112no—
444C2×C8—112no—
445C2×C8—112no—
446C2×C8—112no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—444no—
456C2×C8—444no—
457C2×C8—444no—
458C2×C8C2×C4×D1112yes—
459C2×C8C2×C4×D1112yes—
460C2×C8C2×C4×D1112yes—
461C2×C8C2×C4×D1112yes—
462C4⋊C4—42no—
463C4⋊C4—114no—
464C4⋊C4—442no—
465C22⋊C4—114no—
466C22⋊C4—114no—
467C22⋊C4—224no—
468C22⋊C4—442no—
469C22⋊C4—442no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—221no—
475C42—221no—
476C42—221no—
477C42—221no—
478C42—442no—
479C42C2×C4×D1112yes—
480C42C2×C4×D1112yes—
481C11#2056011yescharacteristic, complemented, Sylow
482C23—112no—
483C23—114no—
484C23—112no—
485C23—222no—
486C23—221no—
487C23—221no—
488C23—222no—
489C23—222no—
490C23—221no—
491C23—221no—
492C23C22×C4×D1111yescharacteristic
493D4—228no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—112no—
503C2×C4—112no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—222no—
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×C4—448no—
523C2×C4C42×D1112yes—
524C2×C4C42×D1112yes—
525C2×C4C22×C4×D1111yescharacteristic
526C2×C4C22×C4×D1111yescharacteristic
527C2×C4#6703711yescharacteristic
528C2×C4#6704011yescharacteristic
529C2×C4#6704211yescharacteristic
530C2×C4#6704211yescharacteristic
531C8—22no—
532C8—22no—
533C8—22no—
534C8—22no—
535C8—222no—
536C8—222no—
537C8—222no—
538C8—222no—
539C22—114no—
540C22—222no—
541C22—222no—
542C22—224no—
543C22—224no—
544C22—222no—
545C22—222no—
546C22—222no—
547C22—442no—
548C22—442no—
549C22C2×C42×D1111yescharacteristic
550C22#1062307611yescharacteristic
551C22#1062310511yescharacteristic
552C22#1062327612yes—
553C22D11×#13112yes—
554C4—22no—
555C4—22no—
556C4—42no—
557C4—42no—
558C4—222no—
559C4—222no—
560C4—442no—
561C4—442no—
562C4#1062303511yescharacteristic
563C4#1062305211yescharacteristic
564C4#1062307611yescharacteristic
565C4#1062310511yescharacteristic
566C2—224no—
567C2—442no—
568C2#1307097611yescharacteristic
569C2D11×#40511yescharacteristic
570C2#1307704511yescharacteristic
571C2#1307766312yes—
572C2#1307775412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC11×#1771C2
socleC23×C11C23×C4
prime radicalC22×D44C2×C4
cosocleC22×C4×C11C24
hypercenter#1771D11
hypocenterC11#20560
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
4. #13068485C2semidirect
5. #13068475C2semidirect
6. #13068398C2semidirect
7. #13068393C2semidirect
8. #13068391C2semidirect
9. C8×(C2×D11)⋊C4C2semidirect
10. #13068383C2semidirect
11. #13068379C2semidirect
12. #13068369C2semidirect
13. #13068311C2semidirect
14. D11×#336C2semidirect
15. C11×#1771C2semidirect
43. #10622447C4semidirect
44. #10622319C4semidirect
85. C2×#4313C2×C4semidirect
94. C2×C8×D11C2×C4semidirect
101. C11×C4⋊C8C2×C4semidirect
103. C11×#97C2×C4semidirect
112. (C2×D11)⋊C8C2×C4semidirect
113. (C2×D11)⋊C8C2×C4semidirect
116. C4⋊(C11⋊C8)C2×C4semidirect
119. C4×C11⋊C8C2×C4semidirect
199. #1771D11semidirect
381. C4⋊C8C4×D11semidirect
390. #97C4×D11semidirect
481. C11#20560semidirect

Maximal subgroups

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

subgroupindex
C2×#106223192
C2×#106224472
#130710572
#130684852
#130684752
#130683982
#130683932
#130683912
C8×(C2×D11)⋊C42
#130683832
#130683792
#130683692
#130683112
D11×#3362
C11×#17712
#2056011