Finite Group Databasebeta

← #14728694

Subgroups — #14728694

Order 2816.

1030 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
1#13079764C211yesmaximal, characteristic, complemented
2#13079741C211yesmaximal, characteristic, complemented
3#13073569C211yesmaximal, characteristic, complemented
4#13067664C218yesmaximal, complemented
5#13067115C211yesmaximal, characteristic, complemented
6#13067111C211yesmaximal, characteristic, complemented
7#13066937C211yesmaximal, characteristic, complemented
8C11×#3506C211yesmaximal, characteristic
9C11×#559—22no—
10C11×#556—21no—
11C11×#555—21no—
12C11×#553—22no—
13C11×#550—21no—
14C11×#547—21no—
15C11×#538C2214yes—
16C11×#535—21no—
17C11×#533C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C11×#525—22no—
20C11×#520—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66977—22no—
23C2×#66922C2211yescharacteristic
24#10622834—21no—
25#10622694—21no—
26#10622692—21no—
27#10622691—21no—
28#10622683—21no—
29#10622657C2214yes—
30#10622647C2214yes—
31#10622634—22no—
32#10622621—22no—
33#10622589—21no—
34#10622562C2214yes—
35C4×C4⋊Dic11C2211yescharacteristic
36#10622538C2211yescharacteristic
37#10622538C2211yescharacteristic
38#10622176C2214yes—
39#10622175C2214yes—
40#10622163C2214yes—
41C2×C11×#41—22no—
42C2×C11×#41—21no—
43C22×D4×C11D411yescharacteristic
44C23×C4×C11D412yes—
45C22×Dic22—21no—
46C11×C4⋊Q8D411yescharacteristic
47C11×C4⋊Q8D411yescharacteristic
48C11×C4⋊Q8D411yescharacteristic
49C11×#127—22no—
50C11×#127D411yescharacteristic
51C11×#126—24no—
52C11×#125—21no—
53C11×#124—22no—
54C11×#124—24no—
55C11×#124—21no—
56C11×#123—24no—
57C11×#123—24no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8C2312yes—
61C11×#121—22no—
62C11×#121—22no—
63C11×#121—22no—
64C11×#121—24no—
65C11×#121—21no—
66C11×#121C2312yes—
67C11×#120—24no—
68C4×Q8×C11—22no—
69C4×Q8×C11—21no—
70C4×Q8×C11D412yes—
71C4×D4×C11—22no—
72C4×D4×C11—24no—
73C4×D4×C11—24no—
74C4×D4×C11—21no—
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11D412yes—
80C11×#117—22no—
81C11×#117—22no—
82C11×#117—21no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C22⋊C4C2312yes—
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—24no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2312yes—
91#66977—48no—
92C2×Dic11⋊C4—24no—
93C2×C4×Dic11—21no—
94#66922—21no—
95#66922—21no—
96#66922—21no—
97#66922—21no—
98#66899—24no—
99#66896—24no—
100C11⋊#95C2312yes—
101C22⋊(C11⋊C8)C2312yes—
102C22⋊(C11⋊C8)C2312yes—
103#66872—24no—
104#66871—24no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4×C11⋊C8—21no—
108C4×C11⋊C8—21no—
109#18413—111nomaximal, Sylow
110C24×C11C2×D412yes—
111C11×#41—42no—
112C11×#41—42no—
113C11×#41—84no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11C2×D412yes—
117C2×D4×C11—22no—
118C2×D4×C11—24no—
119C2×D4×C11—24no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11C2×D412yes—
127C22×C4×C11—24no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—44no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—22no—
137C22×Dic11—22no—
138C2×Dic22—44no—
139C2×Dic22—41no—
140C2×Dic22—41no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4C2×D412yes—
151C11×C4⋊C4C2×D412yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C42×C11—24no—
161C42×C11—22no—
162C42×C11C2×D411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C22⋊Dic11—48no—
167C4⋊Dic11—24no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—41no—
171C4⋊Dic11—41no—
172Dic11⋊C4—48no—
173C4×Dic11—42no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176#3506D1111yescharacteristic
177#3230—111no—
178#3227—111no—
179#2542—111no—
180#1618—118no—
181#1503—111no—
182#1502—111no—
183#1460—111no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11C22×D411yescharacteristic
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—42no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—42no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—84no—
202D4×C11—84no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—41no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11—42no—
212C2×C4×C11—82no—
213C2×C4×C11—84no—
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11#13512yes—
219C2×C4×C11#13712yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×Dic11—24no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—44no—
226C2×Dic11—42no—
227Dic22—82no—
228Dic22—82no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231#559—22no—
232#556—21no—
233#555—21no—
234#553—22no—
235#550—21no—
236#547—21no—
237#538C2×D1114yes—
238#535—21no—
239#533C2×D1111yescharacteristic
240#532C2×D1111yescharacteristic
241C2×C4⋊Q8—111no—
242#525—22no—
243C2×C22⋊Q8—222no—
244#520—21no—
245C2×C4×D4C2×D1111yescharacteristic
246#500—221no—
247#498—221no—
248#487—221no—
249#486—221no—
250#484—114no—
251#481—114no—
252#477—222no—
253#476—222no—
254#431—111no—
255#431—111no—
256#399—114no—
257#390—221no—
258#384—221no—
259C4×C4⋊C4—111no—
260#328—114no—
261#327—114no—
262#323—114no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—44no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—82no—
273C22×C11C2×#12011yescharacteristic
274C22×C11C2×#13511yescharacteristic
275C22×C11C2×#13711yescharacteristic
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11#45212yes—
284C4×C11#45212yes—
285C4×C11#45312yes—
286Dic11—44no—
287Dic11—82no—
288C2×#41—22no—
289C2×#41—21no—
290C22×Q8—221no—
291C22×D4C22⋊D1111yescharacteristic
292C23×C4C22⋊D1112yes—
293C4⋊Q8—221no—
294C4⋊Q8—221no—
295C4⋊Q8—221no—
296C4⋊Q8—221no—
297C4⋊Q8C22⋊D1111yescharacteristic
298C4⋊Q8C22⋊D1111yescharacteristic
299C4⋊Q8C22⋊D1111yescharacteristic
300#127—22no—
301#127C22⋊D1111yescharacteristic
302#126—24no—
303#125—21no—
304#124—22no—
305#124—24no—
306#124—21no—
307#123—24no—
308#123—24no—
309C22⋊Q8—22no—
310C22⋊Q8—21no—
311C22⋊Q8—448no—
312C22⋊Q8C22×D1112yes—
313#121—22no—
314#121—22no—
315#121—22no—
316#121—24no—
317#121—21no—
318#121C22×D1112yes—
319#120—24no—
320C4×Q8—22no—
321C4×Q8—21no—
322C4×Q8C22⋊D1112yes—
323C4×D4—22no—
324C4×D4—24no—
325C4×D4—24no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4C22⋊D1112yes—
332#117—22no—
333#117—22no—
334#117—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—112no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—224no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4C22⋊D1111yescharacteristic
341C2×C22⋊C4—224no—
342C2×C22⋊C4C22×D1112yes—
343C2×C42—221no—
344C2×C42C22×D1111yescharacteristic
345#107—224no—
346#106—224no—
347C4⋊C8—221no—
348C4⋊C8—221no—
349#103—224no—
350#102—224no—
351C22⋊C8—112no—
352C22⋊C8—112no—
353C4×C8—221no—
354C4×C8—221no—
355#95—112no—
356C2×C11—21no—
357C2×C11—21no—
358C2×C11—82no—
359C2×C11—82no—
360C2×C11C2×#45211yescharacteristic
361C2×C11C2×#45311yescharacteristic
362C2×C11#302811yescharacteristic
363C24C2×C22⋊D1112yes—
364#41—42no—
365#41—42no—
366#41—84no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—444no—
370C2×Q8—441no—
371C2×Q8—441no—
372C2×Q8C2×C22⋊D1112yes—
373C2×D4—22no—
374C2×D4—24no—
375C2×D4—24no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4C2×C22⋊D1112yes—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—44no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1112yes—
392C22×C4C2×C22⋊D1111yescharacteristic
393C22×C4C23×D1111yescharacteristic
394C2×C8—222no—
395C2×C8—222no—
396C4⋊C4—24no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—224no—
406C4⋊C4—222no—
407C4⋊C4—222no—
408C4⋊C4—448no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4C2×C22⋊D1112yes—
412C4⋊C4C2×C22⋊D1112yes—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—448no—
422C42—24no—
423C42—22no—
424C42—442no—
425C42C2×C22⋊D1111yescharacteristic
426C42C2×C22⋊D1111yescharacteristic
427C42C2×C22⋊D1111yescharacteristic
428C42C2×C22⋊D1111yescharacteristic
429C11#1841311yescharacteristic, complemented, Sylow
430C23—22no—
431C23—22no—
432C23—22no—
433C23—22no—
434C23—42no—
435C23—42no—
436C23C22×C22⋊D1111yescharacteristic
437Q8—42no—
438Q8—42no—
439Q8—42no—
440Q8—882no—
441Q8—882no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—84no—
450D4—84no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—44no—
458C2×C4—44no—
459C2×C4—42no—
460C2×C4—82no—
461C2×C4—84no—
462C2×C4—224no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—444no—
466C2×C4—442no—
467C2×C4#6700312yes—
468C2×C4#6700412yes—
469C2×C4#6700611yescharacteristic
470C2×C4#6700611yescharacteristic
471C2×C4#6700611yescharacteristic
472C2×C4#6700611yescharacteristic
473C2×C4C22×C22⋊D1111yescharacteristic
474C2×C4C22×C22⋊D1111yescharacteristic
475C8—442no—
476C8—442no—
477C22—21no—
478C22—21no—
479C22—44no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—82no—
487C22C2×#6700311yescharacteristic
488C22C2×#6700411yescharacteristic
489C22C2×#6700611yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—42no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—444no—
498C4—882no—
499C4#1062285212yes—
500C4#1062285212yes—
501C4#1062285412yes—
502C2—21no—
503C2—21no—
504C2—82no—
505C2—82no—
506C2C2×#1062285211yescharacteristic
507C2C2×#1062285411yescharacteristic
508C2#1307802211yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3506C2
socleC22×C11C2×#120
hypercenter#3506D11
hypocenterC11#18413
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #13079764C2semidirect
2. #13079741C2semidirect
3. #13073569C2semidirect
4. #13067664C2semidirect
5. #13067115C2semidirect
6. #13067111C2semidirect
7. #13066937C2semidirect
429. C11#18413semidirect

Maximal subgroups

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

subgroupindex
#130797642
#130797412
#130735692
#130676642
#130671152
#130671112
#130669372
C11×#35062
#1841311