Finite Group Databasebeta

← #14764294

Subgroups — #14764294

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622446C211yesmaximal, characteristic
2#13071020C211yesmaximal, characteristic
3D11×#384C211yesmaximal, characteristic
4#13069375C211yesmaximal, characteristic, complemented
5#13069374C211yesmaximal, characteristic, complemented
6#13069372C211yesmaximal, characteristic, complemented
7#13068805C212yesmaximal
8#13068802C212yesmaximal
9#13068774C212yesmaximal, complemented
10#13068742C212yesmaximal, complemented
11C11×#1947C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×D11—21no—
13C2×C4⋊C4×D11—21no—
14C2×C4⋊C4×D11C2212yes—
15C2×#66925—21no—
16C2×C42×D11C2211yescharacteristic
17C2×C11×#107C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C8C2212yes—
22C2×#66882C2212yes—
23C2×C8×Dic11C2212yes—
24#10622600C2211yescharacteristic
25#10622600C2211yescharacteristic
26#10622589—21no—
27#10622589—21no—
28#10622589C2212yes—
29#10622589C2211yescharacteristic
30#10622589C2211yescharacteristic
31C2×#66871C2212yes—
32C2×#66871C2212yes—
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C4×Dic11⋊C4—21no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622446C418yescomplemented
38#10622280—21no—
39#10622263—21no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×C4×D11—22no—
45C22×C4×D11D411yescharacteristic
46C22×C4×D11D411yescharacteristic
47C22×C4×D11C2311yescharacteristic
48C22×C8×C11C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—21no—
70C2×C4×Dic11—21no—
71C2×C4×Dic11D411yescharacteristic
72C2×C4×Dic11D411yescharacteristic
73C2×C4×Dic11C2311yescharacteristic
74C22×C11⋊C8C2312yes—
75C4⋊C4×D11—42no—
76C4⋊C4×D11—42no—
77C4⋊C4×D11—44no—
78C4⋊C4×D11—44no—
79#66925—44no—
80C42×D11C2×C414yes—
81C42×D11Q814yes—
82C11×#107—42no—
83C11×C4⋊C8C2×C414yescomplemented
84C11×#95—21no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88(C2×D11)⋊C8C2×C418yes—
89#66882—42no—
90C8×Dic11C2×C418yescomplemented
91#66871—42no—
92#66871—42no—
93C4⋊(C11⋊C8)C2×C414yescomplemented
94#21982—111nomaximal, Sylow
95C23×D11C2×D411yescharacteristic
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—22no—
105C22×Dic11C2×D411yescharacteristic
106C22×Dic11C2×D411yescharacteristic
107C22×Dic11C2×D411yescharacteristic
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—21no—
111C2×C4×D11—21no—
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—44no—
115C2×C4×D11—44no—
116C2×C4×D11—44no—
117C2×C4×D11C4⋊C414yes—
118C2×C4×D11C4⋊C414yes—
119C2×C4×D11D814yes—
120C2×C4×D11Q1614yes—
121C2×C4×D11C22×C412yes—
122C2×C4×D11C2×Q812yes—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11C22×C414yes—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—42no—
134C42×C11—42no—
135C42×C11C22×C412yes—
136C42×C11C2×Q812yes—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—42no—
139C4⋊Dic11—21no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—42no—
146C4⋊Dic11—42no—
147Dic11⋊C4—44no—
148Dic11⋊C4—42no—
149Dic11⋊C4—42no—
150Dic11⋊C4—44no—
151Dic11⋊C4—44no—
152Dic11⋊C4—42no—
153Dic11⋊C4—42no—
154C4×Dic11—42no—
155C4×Dic11C4⋊C414yes—
156C4×Dic11C4⋊C414yes—
157C4×Dic11C22×C412yes—
158C4×Dic11C2×Q812yes—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8C22×C414yes—
162C2×#431—111no—
163#2285—111no—
164C2×#384—111no—
165#1947—111no—
166#1947—111no—
167#1947—111no—
168#1947D1111yescharacteristic, complemented
169#1852—112no—
170#1852—112no—
171#1845—112no—
172#1834—112no—
173C23×C11C22×D411yescharacteristic
174C22×D11—21no—
175C22×D11—21no—
176C22×D11—21no—
177C22×D11—21no—
178C22×D11C2×C4⋊C412yes—
179C22×D11C2×D812yes—
180C22×D11C2×Q1612yes—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11C2×C4⋊C412yes—
193C2×C4×C11C2×C4⋊C412yes—
194C2×C4×C11C2×D812yes—
195C2×C4×C11C2×Q1612yes—
196C2×C4×C11C23×C411yescharacteristic
197C2×C4×C11C22×Q811yescharacteristic
198C2×C4×C11H(5,𝔽2)11yescharacteristic
199C2×C4×C11H(5,𝔽2)11yescharacteristic
200C2×C4×C112−1+411yescharacteristic
201C2×C4×C112−1+411yescharacteristic
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11C2×C4⋊C412yes—
214C2×Dic11C2×C4⋊C412yes—
215C2×Dic11C2×C4⋊C412yes—
216C2×Dic11C2×D812yes—
217C2×Dic11C2×Q1612yes—
218C2×Dic11AGL(1,ℤ/8)12yes—
219C2×Dic11#13712yes—
220C4×D11—22no—
221C4×D11—22no—
222C4×D11—22no—
223C4×D11—22no—
224C4×D11—28no—
225C4×D11—88no—
226C4×D11#107116yescomplemented
227C8×C11—24no—
228C11⋊C8—24no—
229C2×#117—221no—
230C22×C4⋊C4—112no—
231C22×C4⋊C4—221no—
232C22×C4⋊C4—221no—
233C22×C42—111no—
234#431—118no—
235C2×#107—112no—
236C2×#107—112no—
237C2×#107—112no—
238C2×#107C2×D1112yes—
239C2×C4⋊C8—111no—
240C2×C4⋊C8C2×D1111yescharacteristic
241C2×C22⋊C8—112no—
242C2×C4×C8—112no—
243#384—111no—
244#384—112no—
245#384—111no—
246#384—111no—
247#384—221no—
248#384—221no—
249#384C2×D1111yescharacteristic
250#382—221no—
251#380—111no—
252#380—111no—
253#380—221no—
254C4×C4⋊C4—111no—
255C4×C4⋊C4—221no—
256C4×C4⋊C4C2×D1111yescharacteristic
257#340—112no—
258#340—112no—
259#340—112no—
260#340C2×D1112yes—
261C22×C11C22×C4⋊C411yescharacteristic
262C22×C11#53511yescharacteristic
263C22×C11#53611yescharacteristic
264C22×C11C22×D811yescharacteristic
265C22×C11C22×Q1611yescharacteristic
266C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C11C2×#13711yescharacteristic
268C2×D11—22no—
269C2×D11—22no—
270C2×D11—22no—
271C2×D11—22no—
272C2×D11—22no—
273C2×D11—22no—
274C2×D11C2×#10714yes—
275C4×C11—22no—
276C4×C11—81no—
277C4×C11—82no—
278C4×C11—81no—
279C4×C11C2×#10714yes—
280C4×C11#52011yescharacteristic
281C4×C11#52011yescharacteristic
282C4×C11#54411yescharacteristic
283C4×C11#54411yescharacteristic
284Dic11—22no—
285Dic11—82no—
286Dic11—81no—
287Dic11—81no—
288Dic11C2×#10714yes—
289Dic11#42814yes—
290C23×C4—111no—
291C23×C4—111no—
292C23×C4—111no—
293C23×C4—222no—
294C22×C8—112no—
295C22×C8C22×D1112yes—
296#117—444no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—442no—
312C2×C4⋊C4—442no—
313C2×C4⋊C4—444no—
314C2×C4⋊C4—444no—
315C2×C4⋊C4C22×D1112yes—
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C4⋊C4C22×D1111yescharacteristic
318C2×C22⋊C4—221no—
319C2×C22⋊C4—221no—
320C2×C42—21no—
321C2×C42—111no—
322C2×C42—111no—
323C2×C42—111no—
324C2×C42—114no—
325C2×C42—114no—
326C2×C42—221no—
327C2×C42C22×D1111yescharacteristic
328#107—42no—
329#107—442no—
330#107—442no—
331#107—442no—
332C4⋊C8—114no—
333C4⋊C8C4×D1114yescomplemented
334C22⋊C8—118no—
335C4×C8—118no—
336#95—21no—
337#95—221no—
338#95—221no—
339#95—221no—
340C2×C11#231711yescharacteristic
341C2×C11C22×#10711yescharacteristic
342C2×C11C2×#42811yescharacteristic
343C2×C11#320511yescharacteristic
344C2×C11#320911yescharacteristic
345C2×C11#322611yescharacteristic
346C2×C11#323011yescharacteristic
347D11—24no—
348C24—111no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—111no—
353C22×C4—111no—
354C22×C4—114no—
355C22×C4—114no—
356C22×C4—114no—
357C22×C4—111no—
358C22×C4—114no—
359C22×C4—112no—
360C22×C4—112no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—221no—
369C22×C4—222no—
370C22×C4—444no—
371C22×C4—444no—
372C22×C4—444no—
373C22×C4D4×D1111yescharacteristic
374C22×C4D4×D1111yescharacteristic
375C22×C4C23×D1111yescharacteristic
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—114no—
379C2×C8—222no—
380C2×C8—222no—
381C2×C8C2×C4×D1114yes—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4—221no—
391C4⋊C4—222no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C4⋊C4—222no—
395C4⋊C4—221no—
396C4⋊C4—442no—
397C4⋊C4—444no—
398C4⋊C4—444no—
399C4⋊C4—442no—
400C4⋊C4—442no—
401C4⋊C4—442no—
402C4⋊C4—442no—
403C4⋊C4—444no—
404C4⋊C4—442no—
405C22⋊C4—442no—
406C22⋊C4—442no—
407C42—42no—
408C42—114no—
409C42—114no—
410C42—112no—
411C42—112no—
412C42—442no—
413C42C2×C4×D1112yes—
414C42Q8×D1112yes—
415C11#2198211yescharacteristic, complemented, Sylow
416C23—112no—
417C23—112no—
418C23—112no—
419C23—221no—
420C23—221no—
421C23—221no—
422C23—221no—
423C23C2×D4×D1111yescharacteristic
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—112no—
436C2×C4—112no—
437C2×C4—112no—
438C2×C4—112no—
439C2×C4—112no—
440C2×C4—112no—
441C2×C4—1116no—
442C2×C4—112no—
443C2×C4—228no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—442no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—888no—
460C2×C4C4⋊C4×D1112yes—
461C2×C4C4⋊C4×D1112yes—
462C2×C4D8×D1112yes—
463C2×C4Q16×D1112yes—
464C2×C4C22×C4×D1111yescharacteristic
465C2×C4#6703711yescharacteristic
466C2×C4C2×Q8×D1111yescharacteristic
467C2×C4#6704011yescharacteristic
468C2×C4#6704211yescharacteristic
469C2×C4#6704311yescharacteristic
470C8—24no—
471C8—224no—
472C22—114no—
473C22—222no—
474C22—222no—
475C22—222no—
476C22—222no—
477C22—222no—
478C22—222no—
479C22C2×C4⋊C4×D1111yescharacteristic
480C22#1062313811yescharacteristic
481C22#1062315911yescharacteristic
482C22C2×D8×D1111yescharacteristic
483C22C2×Q16×D1111yescharacteristic
484C22D11×AGL(1,ℤ/8)11yescharacteristic
485C22D11×#13711yescharacteristic
486C4—22no—
487C4—81no—
488C4—82no—
489C4—81no—
490C4—114no—
491C4—114no—
492C4—222no—
493C4—881no—
494C4—882no—
495C4—881no—
496C4D11×#10714yes—
497C4#1062307711yescharacteristic
498C4#1062310511yescharacteristic
499C4#1062322011yescharacteristic
500C4#1062326011yescharacteristic
501C2—224no—
502C2#1307123811yescharacteristic
503C2C2×D11×#10711yescharacteristic
504C2D11×#42811yescharacteristic
505C2#1307953311yescharacteristic
506C2#1307956311yescharacteristic
507C2#1307973611yescharacteristic
508C2#1307976611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1947C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1947D11
hypocenterC11#21982
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
4. #13069375C2semidirect
5. #13069374C2semidirect
6. #13069372C2semidirect
9. #13068774C2semidirect
10. #13068742C2semidirect
11. C11×#1947C2semidirect
37. #10622446C4semidirect
83. C11×C4⋊C8C2×C4semidirect
90. C8×Dic11C2×C4semidirect
93. C4⋊(C11⋊C8)C2×C4semidirect
168. #1947D11semidirect
226. C4×D11#107semidirect
333. C4⋊C8C4×D11semidirect
415. C11#21982semidirect

Maximal subgroups

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

subgroupindex
C2×#106224462
#130710202
D11×#3842
#130693752
#130693742
#130693722
#130688052
#130688022
#130687742
#130687422
C11×#19472
#2198211