Finite Group Databasebeta

← #14764416

Subgroups — #14764416

Order 2816.

930 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C42×C22⋊D11C211yesmaximal, characteristic
2#13069222C212yesmaximal, complemented
3#13069173C212yesmaximal, complemented
4#13068906C212yesmaximal
5#13068793C212yesmaximal, complemented
6#13068758C211yesmaximal, characteristic, complemented
7#13068731C211yesmaximal, characteristic, complemented
8#13068683C211yesmaximal, characteristic, complemented
9#13068595C211yesmaximal, characteristic, complemented
10C2×#10622162C211yesmaximal, characteristic, complemented
11C4×C11×C22⋊C8C211yesmaximal, characteristic, complemented
12C22×C42×C11C2211yescharacteristic
13C2×C4×C22⋊D11C411yescharacteristic
14C2×C4×C22⋊D11C411yescharacteristic
15C2×C4×C22⋊D11C2211yescharacteristic
16C23×C11⋊C8C2212yes—
17C2×C42×D11C2211yescharacteristic
18C2×C11×C22⋊C8C2212yes—
19C2×C4×C8×C11C2212yes—
20C4×C22⋊Dic11C411yescharacteristic
21C4×C22⋊Dic11C411yescharacteristic
22C4×C22⋊Dic11C2211yescharacteristic
23C2×(C2×D11)⋊C8C2212yes—
24C2×(C2×D11)⋊C8C2212yes—
25C2×Dic11⋊C8C2212yes—
26C2×Dic11⋊C8C2212yes—
27C4×(C2×D11)⋊C4C411yescharacteristic
28C4×(C2×D11)⋊C4C411yescharacteristic
29C4×(C2×D11)⋊C4C2211yescharacteristic
30C4×Dic11⋊C4C411yescharacteristic
31C4×Dic11⋊C4C411yescharacteristic
32C4×Dic11⋊C4C2211yescharacteristic
33C42×Dic11C2211yescharacteristic
34C11×#336C2211yescharacteristic
35C11×#336C2211yescharacteristic
36#10622188C2212yes—
37#10622188C2212yes—
38#10622188C2212yes—
39#10622188C2212yes—
40#10622162C2211yescharacteristic
41#10622162C2212yes—
42#10622162C2211yescharacteristic
43C23×C4×C11C2×C411yescharacteristic
44C23×C4×C11C2×C411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11C2×C411yescharacteristic
47C22×C4×D11C2×C411yescharacteristic
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2312yes—
52C2×C42×C11—42no—
53C2×C42×C11C2×C411yescharacteristic
54C2×C42×C11C2×C411yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11C2×C411yescharacteristic
58C2×C22⋊Dic11C2×C411yescharacteristic
59C2×C22⋊Dic11C2×C411yescharacteristic
60C4×C22⋊D11—24no—
61C4×C22⋊D11—24no—
62C4×C22⋊D11C818yescomplemented
63C2×(C2×D11)⋊C4C2×C411yescharacteristic
64C2×(C2×D11)⋊C4C2×C411yescharacteristic
65C2×(C2×D11)⋊C4C2×C411yescharacteristic
66C2×Dic11⋊C4C2×C411yescharacteristic
67C2×Dic11⋊C4C2×C411yescharacteristic
68C2×Dic11⋊C4C2×C411yescharacteristic
69C2×C4×Dic11C2×C411yescharacteristic
70C2×C4×Dic11C2×C411yescharacteristic
71C2×C4×Dic11C2×C411yescharacteristic
72C2×C4×Dic11C2×C411yescharacteristic
73C2×C4×Dic11C2×C411yescharacteristic
74C2×C4×Dic11C2×C411yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C2×C4×Dic11C2311yescharacteristic
78C22×C11⋊C8—24no—
79C22×C11⋊C8—42no—
80C22×C11⋊C8—42no—
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2312yes—
83C42×D11—42no—
84C11×C22⋊C8—24no—
85C4×C8×C11—42no—
86C11⋊#95C2×C411yescharacteristic
87C11⋊#95C2×C411yescharacteristic
88C11⋊#95C2×C411yescharacteristic
89C11⋊#95C2×C411yescharacteristic
90C11⋊#95C2×C411yescharacteristic
91C11⋊#95C2×C411yescharacteristic
92(C2×D11)⋊C8—42no—
93(C2×D11)⋊C8—42no—
94Dic11⋊C8—42no—
95Dic11⋊C8—42no—
96#21996—111nomaximal, Sylow
97C24×C11C22×C411yescharacteristic
98C23×D11C22×C411yescharacteristic
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11C2×C814yes—
107C22×C4×C11M1614yes—
108C22×C4×C11C22×C411yescharacteristic
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11#4114yes—
114C22×C4×C11C2411yescharacteristic
115C2×C22⋊D11—22no—
116C2×C22⋊D11—22no—
117C2×C22⋊D11C2×C814yes—
118C22×Dic11C22×C411yescharacteristic
119C22×Dic11C22×C411yescharacteristic
120C22×Dic11C22×C411yescharacteristic
121C22×Dic11C22×C411yescharacteristic
122C22×Dic11C22×C411yescharacteristic
123C22×Dic11C22×C411yescharacteristic
124C22×Dic11C22×C411yescharacteristic
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—21no—
128C2×C4×D11—22no—
129C2×C4×D11—21no—
130C2×C4×D11—41no—
131C2×C4×D11—41no—
132C2×C4×D11—41no—
133C2×C4×D11—41no—
134C2×C4×D11C2×C814yescomplemented
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—41no—
144C42×C11—41no—
145C22⋊Dic11—22no—
146C22⋊Dic11—22no—
147C22⋊Dic11C2×C814yes—
148(C2×D11)⋊C4—22no—
149(C2×D11)⋊C4—22no—
150(C2×D11)⋊C4C2×C814yescomplemented
151Dic11⋊C4—22no—
152Dic11⋊C4—22no—
153Dic11⋊C4C2×C814yescomplemented
154C4×Dic11—22no—
155C4×Dic11—22no—
156C4×Dic11—21no—
157C4×Dic11—22no—
158C4×Dic11—21no—
159C4×Dic11—41no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163C4×Dic11C2×C814yescomplemented
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—48no—
171C42×D4—111no—
172#1923—112no—
173#1916—112no—
174#1869—112no—
175#1850—112no—
176#1839—111no—
177#1831—111no—
178#1817—111no—
179#1797—111no—
180C4×C22⋊C8D1111yescharacteristic, complemented
181C2×#336—111no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11#11712yes—
187C23×C11C22×C812yes—
188C23×C11C2×M1612yes—
189C23×C11C23×C411yescharacteristic
190C22×D11—21no—
191C22×D11—21no—
192C22×D11—21no—
193C22×D11—21no—
194C22×D11—21no—
195C22×D11—21no—
196C22×D11C22×C812yes—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11#11712yes—
212C2×C4×C11C22×C812yes—
213C2×C4×C11C22×C812yes—
214C2×C4×C11C2×M1612yes—
215C2×C4×C11C2×M1612yes—
216C2×C4×C11C2×#4112yes—
217C2×C4×C11H(5,𝔽2)12yes—
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C22⋊D11—28no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11C22×C812yes—
240C2×Dic11C22×C812yes—
241C2×Dic11C22×C812yes—
242C4×D11—44no—
243C4×D11—44no—
244C4×D11—42no—
245C4×D11—42no—
246C8×C11—42no—
247C8×C11—42no—
248C11⋊C8—42no—
249C11⋊C8—42no—
250C23×C8—112no—
251C2×C4×D4—111no—
252C2×C4×D4—111no—
253C2×C4×D4—111no—
254C22×C42—111no—
255C22×C42C2×D1111yescharacteristic
256C2×C4⋊C8—112no—
257C2×C4⋊C8—112no—
258C2×C22⋊C8—112no—
259C2×C22⋊C8—112no—
260C2×C22⋊C8C2×D1112yes—
261C2×C4×C8C2×D1112yes—
262C4×C4⋊C4—111no—
263C4×C4⋊C4—111no—
264C4×C4⋊C4—111no—
265C4×C22⋊C4—111no—
266C4×C22⋊C4—111no—
267C4×C22⋊C4—111no—
268C4×C22⋊C4—111no—
269C4×C22⋊C4—111no—
270C4×C22⋊C4—111no—
271C43—111no—
272#336—112no—
273#336—112no—
274#336—112no—
275#336—112no—
276#336—111no—
277#336—111no—
278#336—112no—
279#336C2×D1111yescharacteristic
280#336C2×D1111yescharacteristic
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11#43114yes—
288C22×C11C2×#11711yescharacteristic
289C22×C11#51811yescharacteristic
290C22×C11#52011yescharacteristic
291C22×C11C23×C811yescharacteristic
292C22×C11C22×M1611yescharacteristic
293C22×C11#56811yescharacteristic
294C22×C11#56811yescharacteristic
295C2×D11—22no—
296C2×D11—22no—
297C2×D11—22no—
298C2×D11—41no—
299C2×D11—41no—
300C2×D11—41no—
301C2×D11—41no—
302C4×C11—22no—
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—22no—
306C4×C11—22no—
307C4×C11#53812yes—
308C4×C11#53912yes—
309Dic11—22no—
310Dic11—22no—
311Dic11—22no—
312Dic11—41no—
313Dic11—41no—
314Dic11—41no—
315Dic11—41no—
316C22×D4—111no—
317C23×C4—111no—
318C23×C4—111no—
319C23×C4—111no—
320C23×C4C4×D1111yescharacteristic
321C23×C4C4×D1111yescharacteristic
322C23×C4C22×D1111yescharacteristic
323C22×C8—112no—
324C22×C8—112no—
325C22×C8—224no—
326C22×C8—442no—
327C22×C8—442no—
328C22×C8C22×D1112yes—
329C22×C8C22×D1112yes—
330C4×D4—118no—
331C4×D4—224no—
332C4×D4—224no—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—111no—
336C2×C22⋊C4—111no—
337C2×C22⋊C4—111no—
338C2×C22⋊C4—111no—
339C2×C22⋊C4—111no—
340C2×C22⋊C4—111no—
341C2×C22⋊C4—111no—
342C2×C42—42no—
343C2×C42—111no—
344C2×C42—111no—
345C2×C42—111no—
346C2×C42—111no—
347C2×C42—111no—
348C2×C42—111no—
349C2×C42—111no—
350C2×C42—111no—
351C2×C42—111no—
352C2×C42—442no—
353C2×C42C4×D1111yescharacteristic
354C2×C42C4×D1111yescharacteristic
355C2×C42C22×D1111yescharacteristic
356C2×C42C22×D1111yescharacteristic
357C4⋊C8—442no—
358C4⋊C8—442no—
359C22⋊C8—24no—
360C22⋊C8—442no—
361C22⋊C8—442no—
362C4×C8—42no—
363#95—111no—
364#95—111no—
365#95—111no—
366#95—111no—
367#95—111no—
368#95—111no—
369C2×C11—24no—
370C2×C11#231811yescharacteristic
371C2×C11C2×#43111yescharacteristic
372C2×C11#292311yescharacteristic
373C2×C11#297211yescharacteristic
374C2×C11#297311yescharacteristic
375C2×C11#298811yescharacteristic
376C2×C11#298911yescharacteristic
377D11—42no—
378C24—111no—
379C24C2×C4×D1111yescharacteristic
380C2×D4—114no—
381C2×D4—222no—
382C2×D4—222no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—111no—
391C22×C4—111no—
392C22×C4—111no—
393C22×C4—114no—
394C22×C4—111no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—111no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—441no—
404C22×C4—441no—
405C22×C4—441no—
406C22×C4—441no—
407C22×C4C8×D1114yes—
408C22×C4#431314yes—
409C22×C4C2×C4×D1111yescharacteristic
410C22×C4C2×C4×D1111yescharacteristic
411C22×C4C2×C4×D1111yescharacteristic
412C22×C4C2×C4×D1111yescharacteristic
413C22×C4C2×C4×D1111yescharacteristic
414C22×C4#433914yes—
415C22×C4C23×D1111yescharacteristic
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8—222no—
425C2×C8—222no—
426C2×C8—222no—
427C2×C8—222no—
428C2×C8—448no—
429C4⋊C4—114no—
430C4⋊C4—222no—
431C4⋊C4—222no—
432C22⋊C4—114no—
433C22⋊C4—114no—
434C22⋊C4—222no—
435C22⋊C4—222no—
436C22⋊C4—222no—
437C22⋊C4—222no—
438C42—22no—
439C42—22no—
440C42—41no—
441C42—41no—
442C42—114no—
443C42—222no—
444C42—222no—
445C42—222no—
446C42—221no—
447C42—221no—
448C42—441no—
449C42—441no—
450C42—441no—
451C42—441no—
452C11#2199611yescharacteristic, complemented, Sylow
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—112no—
458C23—221no—
459C23—221no—
460C23—221no—
461C23—221no—
462C23—221no—
463C23—221no—
464C23#6692512yes—
465C23C2×C8×D1112yes—
466C23C2×#431312yes—
467C23C22×C4×D1111yescharacteristic
468D4—228no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—112no—
484C2×C4—112no—
485C2×C4—112no—
486C2×C4—221no—
487C2×C4—221no—
488C2×C4—221no—
489C2×C4—221no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—221no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—444no—
505C2×C4—444no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4#6692512yes—
509C2×C4C2×C8×D1112yes—
510C2×C4C2×C8×D1112yes—
511C2×C4C2×#431312yes—
512C2×C4C2×#431312yes—
513C2×C4C2×#433912yes—
514C2×C4#6703712yes—
515C2×C4#6704211yescharacteristic
516C2×C4#6704311yescharacteristic
517C8—42no—
518C8—42no—
519C8—442no—
520C8—442no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—222no—
528C22—222no—
529C22—222no—
530C22—441no—
531C22—441no—
532C22—441no—
533C22—441no—
534C22#1062229814yes—
535C22C2×#6692511yescharacteristic
536C22#1062301711yescharacteristic
537C22#1062305411yescharacteristic
538C22C22×C8×D1111yescharacteristic
539C22C22×#431311yescharacteristic
540C22#1062327611yescharacteristic
541C22#1062327611yescharacteristic
542C4—22no—
543C4—22no—
544C4—22no—
545C4—22no—
546C4—22no—
547C4—222no—
548C4—222no—
549C4—222no—
550C4—441no—
551C4—441no—
552C4—441no—
553C4—441no—
554C4#1062309112yes—
555C4#1062309512yes—
556C2—24no—
557C2—442no—
558C2#1307124311yescharacteristic
559C2C2×#1062229811yescharacteristic
560C2#1307726811yescharacteristic
561C2#1307763811yescharacteristic
562C2#1307764211yescharacteristic
563C2#1307772411yescharacteristic
564C2#1307772911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC4×C11×C22⋊C8C2
socleC23×C11C23×C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenterC4×C22⋊C8D11
hypocenterC11#21996
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #13069222C2semidirect
3. #13069173C2semidirect
5. #13068793C2semidirect
6. #13068758C2semidirect
7. #13068731C2semidirect
8. #13068683C2semidirect
9. #13068595C2semidirect
10. C2×#10622162C2semidirect
11. C4×C11×C22⋊C8C2semidirect
62. C4×C22⋊D11C8semidirect
134. C2×C4×D11C2×C8semidirect
150. (C2×D11)⋊C4C2×C8semidirect
153. Dic11⋊C4C2×C8semidirect
163. C4×Dic11C2×C8semidirect
180. C4×C22⋊C8D11semidirect
452. C11#21996semidirect

Maximal subgroups

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

subgroupindex
C42×C22⋊D112
#130692222
#130691732
#130689062
#130687932
#130687582
#130687312
#130686832
#130685952
C2×#106221622
C4×C11×C22⋊C82
#2199611