Finite Group Databasebeta

← #14767593

Subgroups — #14767593

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
1C4⋊Q8×Dic11C211yesmaximal, characteristic, complemented
2#124×Dic11C211yesmaximal, characteristic
3#13069437C211yesmaximal, characteristic, complemented
4#13069433C211yesmaximal, characteristic
5#13068973C212yesmaximal
6#13068959C212yesmaximal, complemented
7#13068959C212yesmaximal, complemented
8#13068952C212yesmaximal
9#13068750C211yesmaximal, characteristic, complemented
10#13068364C211yesmaximal, characteristic, complemented
11C2×C11×#497C211yesmaximal, characteristic
12C22×C11×Q16C2212yes—
13C22×C11×SD16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×Q8×Dic11C2211yescharacteristic
17C2×Q8×Dic11C2212yes—
18C2×D4×Dic11C2211yescharacteristic
19C11×#497C418yescomplemented
20C2×C11×#97C2211yescharacteristic
21#10622843C2211yescharacteristic
22#10622843C2212yes—
23C2×#66899C2212yes—
24C2×#66899C2212yes—
25C2×#66899C2212yes—
26#10622834C2211yescharacteristic
27C2×#66896C2212yes—
28#10622598—21no—
29#10622598—21no—
30C4⋊C4×Dic11—21no—
31C4⋊C4×Dic11—21no—
32#10622564—21no—
33#10622564—21no—
34C22⋊C4×Dic11—21no—
35C22⋊C4×Dic11—21no—
36#10622549C2211yescharacteristic
37#10622548C2211yescharacteristic
38C42×Dic11C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40#10622189C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622188C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C22×Q8×C11C2312yes—
46C22×D4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C2×C11×Q16—42no—
49C2×C11×Q16—42no—
50C2×C11×Q16C2×C418yescomplemented
51C2×C11×SD16—42no—
52C2×C11×SD16—42no—
53C2×C11×SD16C2×C418yes—
54C22×C8×C11C2312yes—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8C2×C414yescomplemented
57C11×#124—22no—
58C11×#124C2×C414yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—21no—
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—21no—
67Q8×Dic11—42no—
68Q8×Dic11—42no—
69Q8×Dic11—42no—
70D4×Dic11—42no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11C2312yes—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4×Dic11—21no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C22×C11⋊C8C2312yes—
87C11×#97C2×C414yescomplemented
88#66899—42no—
89#66899—42no—
90#66899—42no—
91#66896—42no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98#66867—22no—
99#22273—111nomaximal, Sylow
100C24×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11C22×C412yes—
110C2×Q8×C11C22×C414yes—
111C2×D4×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11C22×C412yes—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—21no—
121C22×Dic11—22no—
122C22×Dic11—21no—
123C22×Dic11—42no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129C22×Dic11C2×D411yescharacteristic
130C11×Q16—48no—
131C11×SD16—48no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11C22×C414yes—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C42×C11C22×C412yes—
140C42×C11#4112yes—
141C22⋊Dic11—42no—
142C22⋊Dic11—42no—
143C22⋊Dic11—42no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—42no—
149C4⋊Dic11—42no—
150C4⋊Dic11—44no—
151C4⋊Dic11—42no—
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⋊C8—22no—
163C2×#497D1111yescharacteristic
164C4×C4⋊Q8—111no—
165C4×#124—111no—
166#1960—111no—
167#1959—111no—
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—24no—
184Q8×C11—24no—
185Q8×C11—42no—
186Q8×C11—42no—
187Q8×C11—42no—
188D4×C11—24no—
189D4×C11—42no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11C4×D412yes—
201C2×C4×C11C4×D412yes—
202C2×C4×C11C23×C411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11H(5,𝔽2)12yes—
205C2×C4×C11H(5,𝔽2)12yes—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—84no—
226C2×Dic11#13712yes—
227C2×Dic11#13712yes—
228C8×C11—24no—
229C11⋊C8—42no—
230C22×Q16C2×D1112yes—
231C22×SD16C2×D1112yes—
232C2×C4⋊Q8C2×D1111yescharacteristic
233C2×#124C2×D1111yescharacteristic
234C2×C4×Q8—112no—
235C2×C4×Q8—111no—
236C2×C4×D4—111no—
237#497Dic1118yescomplemented
238C2×#103—112no—
239C2×#103—112no—
240C2×#103—112no—
241C2×#102—112no—
242C2×#97—111no—
243C2×#97C2×D1111yescharacteristic
244#391—112no—
245#391—111no—
246#390—111no—
247#389—221no—
248#389—221no—
249#388—221no—
250#388—221no—
251#384—111no—
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—44no—
280C4×C11#51812yes—
281C4×C11#54012yes—
282Dic11—22no—
283Dic11—22no—
284Dic11—41no—
285Dic11—41no—
286Dic11—81no—
287Dic11—81no—
288Dic11—82no—
289C22×Q8C22×D1111yescharacteristic
290C22×Q8C22×D1112yes—
291C22×D4C22×D1111yescharacteristic
292C23×C4—221no—
293C2×Q16—42no—
294C2×Q16—42no—
295C2×Q16C2×Dic1118yescomplemented
296C2×SD16—42no—
297C2×SD16—42no—
298C2×SD16C2×Dic1118yes—
299C22×C8—112no—
300C22×C8C22×D1112yes—
301C4⋊Q8—22no—
302C4⋊Q8C2×Dic1114yescomplemented
303#124—22no—
304#124C2×Dic1114yes—
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—112no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
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—442no—
333#103—442no—
334#103—442no—
335#102—442no—
336#97—222no—
337#97C2×Dic1114yescomplemented
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—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8C22×Dic1112yes—
362C2×Q8C22×Dic1114yes—
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4C22×Dic1112yes—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—221no—
374C22×C4—221no—
375C22×C4—222no—
376C22×C4—442no—
377C22×C4—442no—
378C22×C4—442no—
379C22×C4D4×D1111yescharacteristic
380C22×C4D4×D1111yescharacteristic
381C22×C4C23×D1111yescharacteristic
382Q16—48no—
383SD16—48no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—222no—
387C2×C8—222no—
388C2×C8—222no—
389C2×C8C22×Dic1114yes—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4—222no—
395C4⋊C4—222no—
396C4⋊C4—442no—
397C4⋊C4—442no—
398C4⋊C4—442no—
399C4⋊C4—444no—
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—444no—
412C42—442no—
413C42#434112yes—
414C42C22×Dic1112yes—
415C11#2227311yescharacteristic, complemented, Sylow
416C23—22no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23C2×D4×D1111yescharacteristic
424Q8—24no—
425Q8—24no—
426Q8—24no—
427Q8—42no—
428Q8—42no—
429Q8—42no—
430D4—24no—
431D4—42no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—112no—
443C2×C4—112no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—221no—
454C2×C4—441no—
455C2×C4—442no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—441no—
463C2×C4—884no—
464C2×C4D4×Dic1112yes—
465C2×C4D4×Dic1112yes—
466C2×C4C2×#434111yescharacteristic
467C2×C4#6703712yes—
468C2×C4#6703712yes—
469C2×C4C23×Dic1111yescharacteristic
470C8—24no—
471C8—442no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22#1062324611yescharacteristic
480C22#1062324611yescharacteristic
481C22D11×#13711yescharacteristic
482C22D11×#13711yescharacteristic
483C22#1062330811yescharacteristic
484C22#1062330811yescharacteristic
485C22C2×D4×Dic1111yescharacteristic
486C4—22no—
487C4—22no—
488C4—42no—
489C4—44no—
490C4—222no—
491C4—222no—
492C4—441no—
493C4—441no—
494C4—881no—
495C4—881no—
496C4—882no—
497C4#1062325012yes—
498C4#1062332912yes—
499C2—82no—
500C2#1307134211yescharacteristic
501C2#137×Dic1111yescharacteristic
502C2#137×Dic1111yescharacteristic
503C2#1307961411yescharacteristic
504C2#1307962211yescharacteristic
505C2#1307963911yescharacteristic
506C2#1307965011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#497C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×#497D11
hypocenterC11#22273
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×Dic11C2semidirect
3. #13069437C2semidirect
6. #13068959C2semidirect
7. #13068959C2semidirect
9. #13068750C2semidirect
10. #13068364C2semidirect
19. C11×#497C4semidirect
50. C2×C11×Q16C2×C4semidirect
56. C11×C4⋊Q8C2×C4semidirect
87. C11×#97C2×C4semidirect
237. #497Dic11semidirect
295. C2×Q16C2×Dic11semidirect
302. C4⋊Q8C2×Dic11semidirect
337. #97C2×Dic11semidirect
415. C11#22273semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×Dic112
#124×Dic112
#130694372
#130694332
#130689732
#130689592
#130689522
#130687502
#130683642
C2×C11×#4972
#2227311