Finite Group Databasebeta

← #14767589

Subgroups — #14767589

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622673C211yesmaximal, characteristic
2#13071183C211yesmaximal, characteristic, complemented
3#124×Dic11C211yesmaximal, characteristic
4#13069436C211yesmaximal, characteristic, complemented
5#13068968C212yesmaximal
6#13068955C212yesmaximal, complemented
7#13068954C212yesmaximal, complemented
8#13068948C212yesmaximal
9#13068751C211yesmaximal, characteristic, complemented
10#13068364C211yesmaximal, characteristic, complemented
11C11×#1959C211yesmaximal, characteristic
12C2×C11×#124C2211yescharacteristic
13C2×Q8×Dic11C2211yescharacteristic
14C22×#4326C2212yes—
15C2×D4×Dic11C2211yescharacteristic
16C22×#4324C2212yes—
17C2×#66940C2212yes—
18C2×#66922C2211yescharacteristic
19C2×C11×#103C2212yes—
20C2×C11×#102C2212yes—
21C2×C11×#97C2211yescharacteristic
22C11×#384C2211yescharacteristic
23#10622843C2211yescharacteristic
24#10622834C2211yescharacteristic
25C2×#66880C2212yes—
26C2×#66880C2212yes—
27#10622673C418yescomplemented
28C4⋊C4×Dic11—21no—
29C4⋊C4×Dic11—21no—
30#10622587C2212yes—
31#10622586—21no—
32#10622586—21no—
33#10622564—21no—
34#10622564—21no—
35C22⋊C4×Dic11—21no—
36C22⋊C4×Dic11—21no—
37#10622549C2211yescharacteristic
38C42×Dic11C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40#10622188C2212yes—
41#10622188C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C23×Dic11—21no—
47C22×Dic22C2312yes—
48C22×C8×C11C2312yes—
49C11×#124—22no—
50C11×#124C2×C414yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—21no—
55C2×C11×C22⋊C4—21no—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11—21no—
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—21no—
60Q8×Dic11—42no—
61C2×#4326—42no—
62C2×#4326—42no—
63C2×#4326C2×C418yescomplemented
64D4×Dic11—42no—
65C2×#4324—42no—
66C2×#4324—42no—
67C2×#4324C2×C418yes—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8C2312yes—
83#66940—42no—
84#66940—42no—
85#66922—22no—
86#66922C2×C414yescomplemented
87C11×#103—42no—
88C11×#102—42no—
89C11×#97—22no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96#66880—42no—
97#66880—42no—
98#66867C2×C414yescomplemented
99#22273—111nomaximal, Sylow
100C24×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11C22×C412yes—
105C2×D4×C11—21no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11C22×C412yes—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—22no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—42no—
118C22×Dic11—42no—
119C22×Dic11—42no—
120C22×Dic11C2×D411yescharacteristic
121C22×Dic11C2×D411yescharacteristic
122C22×Dic11C2×D411yescharacteristic
123C22×Dic11C2×D411yescharacteristic
124C2×Dic22—22no—
125C2×Dic22—22no—
126C2×Dic22—22no—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C2×Dic22C22×C414yes—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—42no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C42×C11C22×C412yes—
140C42×C11#4112yes—
141C22⋊Dic11—42no—
142C22⋊Dic11—42no—
143C22⋊Dic11—42no—
144#4326—48no—
145#4324—48no—
146C4⋊Dic11—24no—
147C4⋊Dic11—24no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—42no—
151Dic11⋊C4—44no—
152C4×Dic11—22no—
153C4×Dic11—22no—
154C4×Dic11—22no—
155C4×Dic11—22no—
156C4×Dic11—41no—
157C4×Dic11—41no—
158C4×Dic11—44no—
159C4×Dic11—42no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8C22×C414yes—
163C2×#497—111no—
164C4×C4⋊Q8—111no—
165C4×#124—111no—
166#1960—111no—
167#1959D1111yescharacteristic
168#1880—112no—
169#1878—112no—
170#1878—112no—
171#1877—112no—
172#1836—111no—
173#1745—111no—
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11C22×D411yescharacteristic
182Q8×C11—24no—
183Q8×C11—42no—
184D4×C11—24no—
185D4×C11—42no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11C4×D412yes—
197C2×C4×C11C4×D412yes—
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11H(5,𝔽2)12yes—
201C2×C4×C11H(5,𝔽2)12yes—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—24no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—84no—
222C2×Dic11#13712yes—
223C2×Dic11#13712yes—
224Dic22—24no—
225Dic22—24no—
226Dic22—42no—
227Dic22—42no—
228C8×C11—42no—
229C11⋊C8—24no—
230C22×Q16—112no—
231C22×SD16—112no—
232C2×C4⋊Q8—111no—
233C2×#124C2×D1111yescharacteristic
234C2×C4×Q8—111no—
235C2×C4×Q8—112no—
236C2×C4×D4—111no—
237#497—118no—
238C2×#103—112no—
239C2×#103—112no—
240C2×#103C2×D1112yes—
241C2×#102C2×D1112yes—
242C2×#97—111no—
243C2×#97C2×D1111yescharacteristic
244#391—111no—
245#391—112no—
246#390—111no—
247#389—221no—
248#389—221no—
249#388—221no—
250#388—221no—
251#384C2×D1111yescharacteristic
252#382—111no—
253C4×C4⋊C4—221no—
254C4×C4⋊C4—221no—
255C4×C22⋊C4—221no—
256C4×C22⋊C4—221no—
257C43—111no—
258#340—112no—
259#340—112no—
260#336—112no—
261#336—112no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11C2×C4×D411yescharacteristic
270C22×C11#53511yescharacteristic
271C22×C11#53511yescharacteristic
272C22×C11C2×#13711yescharacteristic
273C22×C11C2×#13711yescharacteristic
274C22×C11#57511yescharacteristic
275C22×C11#57511yescharacteristic
276C4×C11—22no—
277C4×C11—22no—
278C4×C11—42no—
279C4×C11—82no—
280C4×C11#51812yes—
281C4×C11#54012yes—
282Dic11—22no—
283Dic11—22no—
284Dic11—44no—
285Dic11—41no—
286Dic11—41no—
287Dic11—81no—
288Dic11—81no—
289C22×Q8—112no—
290C22×Q8C22×D1111yescharacteristic
291C22×D4C22×D1111yescharacteristic
292C23×C4—221no—
293C2×Q16—118no—
294C2×Q16—442no—
295C2×Q16—442no—
296C2×SD16—118no—
297C2×SD16—442no—
298C2×SD16—442no—
299C22×C8—112no—
300C22×C8C22×D1112yes—
301C4⋊Q8—114no—
302C4⋊Q8—222no—
303#124—22no—
304#124C4×D1114yes—
305C4×Q8—442no—
306C4×Q8—442no—
307C4×Q8—442no—
308C4×D4—442no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4C22×D1112yes—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—221no—
321C2×C22⋊C4—221no—
322C2×C22⋊C4—221no—
323C2×C42—111no—
324C2×C42—111no—
325C2×C42—111no—
326C2×C42—111no—
327C2×C42—111no—
328C2×C42—111no—
329C2×C42—221no—
330C2×C42—222no—
331C2×C42C22×D1111yescharacteristic
332#103—42no—
333#103—442no—
334#103—442no—
335#102—42no—
336#97—22no—
337#97—114no—
338#95—221no—
339#95—221no—
340#95—222no—
341#95—222no—
342#95—221no—
343#95—221no—
344C2×C11—82no—
345C2×C11#232811yescharacteristic
346C2×C11C4×#13711yescharacteristic
347C2×C11C4×#13711yescharacteristic
348C2×C11#321511yescharacteristic
349C2×C11#321611yescharacteristic
350C2×C11#321811yescharacteristic
351C2×C11#321911yescharacteristic
352C24—21no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—114no—
357C2×Q8—222no—
358C2×Q8—222no—
359C2×Q8—222no—
360C2×Q8—222no—
361C2×Q8—222no—
362C2×Q8C2×C4×D1112yes—
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4C2×C4×D1112yes—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—222no—
374C22×C4—221no—
375C22×C4—221no—
376C22×C4—442no—
377C22×C4—442no—
378C22×C4—442no—
379C22×C4D4×D1111yescharacteristic
380C22×C4D4×D1111yescharacteristic
381C22×C4C23×D1111yescharacteristic
382Q16—448no—
383SD16—448no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—114no—
388C2×C8—222no—
389C2×C8—222no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—42no—
393C4⋊C4—42no—
394C4⋊C4—224no—
395C4⋊C4—224no—
396C4⋊C4—222no—
397C4⋊C4—222no—
398C4⋊C4—444no—
399C4⋊C4—442no—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—442no—
403C22⋊C4—442no—
404C22⋊C4—442no—
405C42—222no—
406C42—222no—
407C42—222no—
408C42—222no—
409C42—441no—
410C42—441no—
411C42—442no—
412C42—444no—
413C42C2×C4×D1112yes—
414C42#434112yes—
415C11#2227311yescharacteristic, complemented, Sylow
416C23—22no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23C2×D4×D1111yescharacteristic
424Q8—24no—
425Q8—42no—
426Q8—224no—
427Q8—224no—
428Q8—442no—
429Q8—442no—
430D4—24no—
431D4—42no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—112no—
443C2×C4—112no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—224no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—884no—
464C2×C4(C22⋊D11)⋊C412yes—
465C2×C4(C22⋊D11)⋊C412yes—
466C2×C4C22×C4×D1111yescharacteristic
467C2×C4C2×#434111yescharacteristic
468C2×C4#6703712yes—
469C2×C4#6704212yes—
470C8—42no—
471C8—224no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22C2×(C22⋊D11)⋊C411yescharacteristic
480C22#1062320511yescharacteristic
481C22#1062324611yescharacteristic
482C22#1062330411yescharacteristic
483C22#1062330411yescharacteristic
484C22D11×#13711yescharacteristic
485C22D11×#13711yescharacteristic
486C4—22no—
487C4—22no—
488C4—42no—
489C4—82no—
490C4—222no—
491C4—222no—
492C4—441no—
493C4—441no—
494C4—444no—
495C4—881no—
496C4—881no—
497C4#1062307612yes—
498C4#1062315012yes—
499C2—82no—
500C2#1307134011yescharacteristic
501C2#1307744011yescharacteristic
502C2#1307744011yescharacteristic
503C2#1307962011yescharacteristic
504C2#1307962811yescharacteristic
505C2#1307963911yescharacteristic
506C2#1307964811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1959C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1959D11
hypocenterC11#22273
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1959

Complements

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

NH ≅ G/Ntype
2. #13071183C2semidirect
4. #13069436C2semidirect
6. #13068955C2semidirect
7. #13068954C2semidirect
9. #13068751C2semidirect
10. #13068364C2semidirect
27. #10622673C4semidirect
63. C2×#4326C2×C4semidirect
86. #66922C2×C4semidirect
98. #66867C2×C4semidirect
415. C11#22273semidirect

Maximal subgroups

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

subgroupindex
C2×#106226732
#130711832
#124×Dic112
#130694362
#130689682
#130689552
#130689542
#130689482
#130687512
#130683642
C11×#19592
#2227311