Finite Group Databasebeta

← #14764008

Subgroups — #14764008

Order 2816.

1114 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622339C211yesmaximal, characteristic
2C22×(C2×D11)⋊C8C211yesmaximal, characteristic
3#13070997C211yesmaximal, characteristic
4#13068800C212yesmaximal, complemented
5#13068797C212yesmaximal, complemented
6#13068796C211yesmaximal, characteristic, complemented
7#13068794C211yesmaximal, characteristic, complemented
8#13068793C211yesmaximal, characteristic, complemented
9#13068599C212yesmaximal, complemented
10#13068597C212yesmaximal, complemented
11C11×#1850C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C22×#4313C2211yescharacteristic
16C22×#4313C2211yescharacteristic
17C2×#66925C2212yes—
18C2×C11×C4⋊C8C2212yescomplemented
19C2×C11×C22⋊C8C2211yescharacteristic
20C4×C11×C22⋊C4C2211yescharacteristic
21C4×C22⋊Dic11C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×(C2×D11)⋊C8—24no—
24C2×(C2×D11)⋊C8C2212yes—
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2212yes—
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2212yescomplemented
29C2×Dic11⋊C8C2212yescomplemented
30#10622568C411yescharacteristic
31#10622568C411yescharacteristic
32#10622555C411yescharacteristic
33#10622555C411yescharacteristic
34C4×(C2×D11)⋊C4C2212yes—
35C2×C4⋊(C11⋊C8)C2212yescomplemented
36#10622339—24no—
37#10622280C412yes—
38#10622277C412yes—
39C11×#336C2212yescomplemented
40#10622188C2212yescomplemented
41#10622188C2212yescomplemented
42#10622162C2212yescomplemented
43C24×D11C2×C411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2×C411yescharacteristic
46C22×C4×D11—42no—
47C22×C4×D11—42no—
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11D414yes—
51C22×C4×D11Q814yes—
52C22×C4×D11C2311yescharacteristic
53C22×C4×D11C2311yescharacteristic
54C22×C8×C11—22no—
55C22×C8×C11—42no—
56C22×C8×C11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C2×C11×C22⋊C4C2×C411yescharacteristic
60C2×C11×C22⋊C4C2×C411yescharacteristic
61C2×C42×C11C2312yes—
62C2×C22⋊Dic11C2×C411yescharacteristic
63C2×C22⋊Dic11C2×C411yescharacteristic
64C2×(C2×D11)⋊C4C2×C412yes—
65C2×(C2×D11)⋊C4C2×C412yes—
66C2×(C2×D11)⋊C4C2×C412yes—
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×Dic11⋊C4C2×C412yes—
69C2×Dic11⋊C4C2×C412yes—
70C2×C4×Dic11C2312yes—
71C22×C11⋊C8—22no—
72C22×C11⋊C8—42no—
73C22×C11⋊C8C2312yes—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C2×#4313—22no—
77C2×#4313—22no—
78C2×#4313—42no—
79C2×#4313—42no—
80#66925—42no—
81#66925—42no—
82C11×C4⋊C8—42no—
83C11×C22⋊C8—22no—
84C11×#95C2×C412yes—
85C11⋊#95C2×C412yes—
86C11⋊#95C2×C412yes—
87C11⋊#95C2×C412yes—
88C22⋊(C11⋊C8)—22no—
89(C2×D11)⋊C8—24no—
90(C2×D11)⋊C8—24no—
91(C2×D11)⋊C8—22no—
92(C2×D11)⋊C8—22no—
93Dic11⋊C8—42no—
94Dic11⋊C8—42no—
95C4⋊(C11⋊C8)—42no—
96#21933—111nomaximal, Sylow
97C24×C11C22×C411yescharacteristic
98C23×D11—22no—
99C23×D11—22no—
100C23×D11—42no—
101C23×D11—42no—
102C23×D11C4⋊C414yes—
103C23×D11C22×C411yescharacteristic
104C23×D11C22×C411yescharacteristic
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11C22×C412yes—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×Q812yes—
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—42no—
114C22×Dic11C4⋊C414yes—
115C22×Dic11C22×C412yes—
116C22×Dic11C22×C412yes—
117C22×Dic11C22×C411yescharacteristic
118C22×Dic11C22×C411yescharacteristic
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×C4×D11—44no—
126C2×C4×D11—44no—
127C2×C4×D11—48no—
128C2×C4×D11C4⋊C414yes—
129C2×C4×D11C4⋊C414yes—
130C2×C4×D11C2×D412yes—
131C2×C4×D11C2×D412yes—
132C2×C4×D11C2×Q812yes—
133C2×C4×D11C2×Q812yes—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—44no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C42×C11—22no—
145C42×C11—22no—
146C22⋊Dic11—22no—
147C22⋊Dic11—22no—
148(C2×D11)⋊C4—42no—
149(C2×D11)⋊C4—42no—
150(C2×D11)⋊C4—42no—
151(C2×D11)⋊C4—42no—
152Dic11⋊C4—42no—
153Dic11⋊C4—42no—
154C4×Dic11—22no—
155C4×Dic11—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—44no—
164#4313—44no—
165#4313—44no—
166C2×#407—111no—
167C22×C22⋊C8—111no—
168#2280—111no—
169#1851—112no—
170#1851—112no—
171#1850—111no—
172#1850—111no—
173#1850—111no—
174#1850D1111yescharacteristic, complemented
175#1798—112no—
176#1798—112no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11C2×C4⋊C412yes—
180C23×C11#13112yes—
181C23×C11#13112yes—
182C23×C11C23×C411yescharacteristic
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—21no—
186C22×D11—21no—
187C22×D11—21no—
188C22×D11—21no—
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—28no—
192C22×D11—44no—
193C22×D11—44no—
194C22×D11—48no—
195C22×D11—48no—
196C22×D11C2×C4⋊C412yes—
197C22×D11C2×C4⋊C412yes—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11C2×C4⋊C412yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×Q811yescharacteristic
211C2×C4×C11H(5,𝔽2)12yes—
212C2×C4×C11H(5,𝔽2)12yes—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—44no—
222C2×Dic11C2×C4⋊C412yes—
223C2×Dic11C2×C4⋊C412yes—
224C4×D11—22no—
225C4×D11—22no—
226C4×D11—22no—
227C4×D11—22no—
228C4×D11—24no—
229C4×D11—24no—
230C4×D11—44no—
231C4×D11—44no—
232C8×C11—41no—
233C8×C11—41no—
234C8×C11—42no—
235C11⋊C8—41no—
236C11⋊C8—41no—
237C11⋊C8—42no—
238C24×C4—111no—
239C22×M16—111no—
240C22×M16—111no—
241C23×C8—111no—
242C23×C8C2×D1111yescharacteristic
243C2×#117—112no—
244C2×C4⋊C8—112no—
245C2×C4⋊C8—112no—
246C2×C4⋊C8—112no—
247C2×C4⋊C8C2×D1112yescomplemented
248#407—224no—
249C2×C22⋊C8—111no—
250C2×C22⋊C8—112no—
251C2×C22⋊C8—111no—
252C2×C22⋊C8—111no—
253C2×C22⋊C8—112no—
254C2×C22⋊C8—224no—
255C2×C22⋊C8C2×D1111yescharacteristic
256#381—112no—
257#380—111no—
258#380—111no—
259#380—112no—
260#379—111no—
261#379—111no—
262C4×C22⋊C4—111no—
263C4×C22⋊C4—112no—
264C4×C22⋊C4C2×D1111yescharacteristic
265#336—112no—
266#336—112no—
267#336—112no—
268#336C2×D1112yescomplemented
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—24no—
272C22×C11—24no—
273C22×C11#42414yes—
274C22×C11C22×C4⋊C411yescharacteristic
275C22×C11#51812yes—
276C22×C11C2×#13111yescharacteristic
277C22×C11C2×#13111yescharacteristic
278C22×C11#56812yes—
279C2×D11—22no—
280C2×D11—22no—
281C2×D11—22no—
282C2×D11—22no—
283C2×D11—22no—
284C2×D11—22no—
285C2×D11—416no—
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—42no—
289C2×D11—42no—
290C4×C11—22no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11#53411yescharacteristic
294C4×C11#53411yescharacteristic
295C4×C11#54312yes—
296Dic11—22no—
297Dic11—22no—
298Dic11—42no—
299Dic11—42no—
300C25—111no—
301C23×C4—111no—
302C23×C4—111no—
303C23×C4—111no—
304C23×C4—111no—
305C23×C4—111no—
306C23×C4—114no—
307C23×C4—114no—
308C23×C4—442no—
309C23×C4—442no—
310C23×C4C22×D1111yescharacteristic
311C2×M16—222no—
312C2×M16—222no—
313C2×M16—442no—
314C2×M16—442no—
315C22×C8—22no—
316C22×C8—42no—
317C22×C8—112no—
318C22×C8—111no—
319C22×C8—111no—
320C22×C8—222no—
321C22×C8—442no—
322C22×C8C22×D1112yes—
323C22×C8C22×D1111yescharacteristic
324C22×C8C22×D1111yescharacteristic
325#117—442no—
326#117—442no—
327C2×C4⋊C4—112no—
328C2×C4⋊C4—112no—
329C2×C22⋊C4—111no—
330C2×C22⋊C4—111no—
331C2×C22⋊C4—112no—
332C2×C22⋊C4—112no—
333C2×C22⋊C4—112no—
334C2×C22⋊C4—112no—
335C2×C22⋊C4C4×D1111yescharacteristic
336C2×C22⋊C4C4×D1111yescharacteristic
337C2×C42—112no—
338C2×C42C22×D1112yes—
339C4⋊C8—42no—
340C4⋊C8—442no—
341C4⋊C8—442no—
342C4⋊C8—442no—
343C22⋊C8—22no—
344C22⋊C8—224no—
345C22⋊C8—224no—
346C22⋊C8—222no—
347C22⋊C8—222no—
348C22⋊C8—222no—
349#95—112no—
350#95—112no—
351#95—112no—
352#95C4×D1112yes—
353C2×C11—24no—
354C2×C11#231511yescharacteristic
355C2×C11C2×#42411yescharacteristic
356C2×C11#290511yescharacteristic
357C2×C11#297612yes—
358C2×C11#297612yes—
359D11—42no—
360D11—42no—
361C24—111no—
362C24—111no—
363C24—114no—
364C24—222no—
365C24—222no—
366C24—442no—
367C24—442no—
368C24C2×C4×D1111yescharacteristic
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—114no—
374C22×C4—112no—
375C22×C4—112no—
376C22×C4—112no—
377C22×C4—112no—
378C22×C4—114no—
379C22×C4—114no—
380C22×C4—112no—
381C22×C4—112no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—444no—
387C22×C4—448no—
388C22×C4—444no—
389C22×C4—442no—
390C22×C4—442no—
391C22×C4—442no—
392C22×C4C2×C4×D1112yes—
393C22×C4C2×C4×D1112yes—
394C22×C4C2×C4×D1111yescharacteristic
395C22×C4D4×D1112yes—
396C22×C4Q8×D1112yes—
397C22×C4C23×D1111yescharacteristic
398M16—444no—
399M16—444no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—44no—
408C2×C8—222no—
409C2×C8—221no—
410C2×C8—221no—
411C2×C8—222no—
412C2×C8—222no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8—444no—
416C4⋊C4—442no—
417C4⋊C4—442no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—222no—
421C22⋊C4—222no—
422C22⋊C4—442no—
423C22⋊C4—442no—
424C22⋊C4—442no—
425C22⋊C4—442no—
426C42—22no—
427C42—22no—
428C42—222no—
429C42—222no—
430C11#2193311yescharacteristic, complemented, Sylow
431C23—22no—
432C23—22no—
433C23—112no—
434C23—112no—
435C23—221no—
436C23—221no—
437C23—221no—
438C23—221no—
439C23—222no—
440C23—222no—
441C23—222no—
442C23—222no—
443C23—228no—
444C23—444no—
445C23—444no—
446C23—448no—
447C23—448no—
448C23C4⋊C4×D1112yes—
449C23#6695412yes—
450C23#6696012yes—
451C23C22×C4×D1111yescharacteristic
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—112no—
463C2×C4—112no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—224no—
469C2×C4—224no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—444no—
479C2×C4—444no—
480C2×C4—444no—
481C2×C4C4⋊C4×D1112yes—
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4#6703712yes—
484C2×C4C2×Q8×D1111yescharacteristic
485C2×C4#6704212yes—
486C8—42no—
487C8—41no—
488C8—41no—
489C8—441no—
490C8—442no—
491C8—441no—
492C22—22no—
493C22—24no—
494C22—24no—
495C22—22no—
496C22—222no—
497C22—222no—
498C22—222no—
499C22—222no—
500C22—222no—
501C22—222no—
502C22—4416no—
503C22—442no—
504C22—442no—
505C22—442no—
506C22—442no—
507C22#1062245214yes—
508C22C2×C4⋊C4×D1111yescharacteristic
509C22#1062307612yes—
510C22C2×#6695411yescharacteristic
511C22C2×#6696011yescharacteristic
512C22#1062328112yes—
513C4—22no—
514C4—42no—
515C4—42no—
516C4—222no—
517C4—222no—
518C4—442no—
519C4—442no—
520C4#1062312011yescharacteristic
521C4#1062316512yes—
522C4#1062318411yescharacteristic
523C2—24no—
524C2—442no—
525C2—442no—
526C2#1307122711yescharacteristic
527C2C2×#1062245211yescharacteristic
528C2#1307717711yescharacteristic
529C2#1307765812yes—
530C2#1307766512yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1850C2
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1850D11
hypocenterC11#21933
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
4. #13068800C2semidirect
5. #13068797C2semidirect
6. #13068796C2semidirect
7. #13068794C2semidirect
8. #13068793C2semidirect
9. #13068599C2semidirect
10. #13068597C2semidirect
11. C11×#1850C2semidirect
18. C2×C11×C4⋊C8C22semidirect
28. C2×Dic11⋊C8C22semidirect
29. C2×Dic11⋊C8C22semidirect
35. C2×C4⋊(C11⋊C8)C22semidirect
39. C11×#336C22semidirect
40. #10622188C22semidirect
41. #10622188C22semidirect
42. #10622162C22semidirect
174. #1850D11semidirect
247. C2×C4⋊C8C2×D11semidirect
268. #336C2×D11semidirect
430. C11#21933semidirect

Maximal subgroups

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

subgroupindex
C2×#106223392
C22×(C2×D11)⋊C82
#130709972
#130688002
#130687972
#130687962
#130687942
#130687932
#130685992
#130685972
C11×#18502
#2193311