Finite Group Databasebeta

← C11×#18939 #14596132

Subgroups — C11×#18939 #14596132

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3550C211yesmaximal, characteristic
2C11×#3249C211yesmaximal, characteristic, complemented
3C11×#3237C211yesmaximal, characteristic, complemented
4C11×#3210C211yesmaximal, characteristic
5C11×#1645C212yesmaximal, complemented
6C11×#1640C212yesmaximal, complemented
7C11×#1633C212yesmaximal, complemented
8C11×#1630C212yesmaximal, complemented
9C11×#1551C211yesmaximal, characteristic
10C11×#1497C211yesmaximal, characteristic, complemented
11C11×#1481C211yesmaximal, characteristic, complemented
12C11×#563—22no—
13C11×#559C2212yes—
14Q82×C11C2212yes—
15C11×#556—21no—
16C11×#556—21no—
17D4×Q8×C11—21no—
18D4×Q8×C11—21no—
19C11×#542—22no—
20C11×#542—22no—
21C11×#536—22no—
22C11×#533C2211yescharacteristic
23C11×#533C2211yescharacteristic
24C11×#533C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#501—21no—
27C11×#494C2211yescharacteristic
28C11×#492C2211yescharacteristic
29C11×#491—21no—
30C11×#487C2211yescharacteristic
31C11×#486C2211yescharacteristic
32C11×#485—22no—
33C11×#477—21no—
34C11×#477C2212yes—
35C11×#477C2212yes—
36C11×#475C2212yes—
37C11×#467—22no—
38C11×#464—22no—
39C11×#462—21no—
40C11×#462C2212yes—
41C11×#452—22no—
42C11×#432C2211yescharacteristic
43C11×#431C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45C11×#333C2212yes—
46C11×#331C2212yes—
47C11×Q8⋊C8C2212yes—
48C11×Q8⋊C8C2212yes—
49C11×Q8⋊C8C2212yes—
50C11×Q8⋊C8C2212yes—
51C2×C11×#41D412yes—
52C22×Q8×C11—22no—
53C2×C11×Q16—22no—
54C2×C11×Q16—22no—
55C2×C11×SD16—22no—
56C22×C8×C11—21no—
57C11×C4⋊Q8—24no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8D411yescharacteristic
61C11×C4⋊Q8D411yescharacteristic
62C11×C4⋊Q8D411yescharacteristic
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8C2311yescharacteristic
65C11×C4⋊Q8C2311yescharacteristic
66C11×C4⋊Q8C2311yescharacteristic
67C11×#127C2311yescharacteristic
68C11×#126—24no—
69C11×#126—24no—
70C11×#125—21no—
71C11×#125—21no—
72C11×#125—21no—
73C11×#124—24no—
74C11×#124—22no—
75C11×#124—22no—
76C11×#124D412yes—
77C11×#123—24no—
78C11×#123—24no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—24no—
82C11×C22⋊Q8—24no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8D412yes—
88C11×C22⋊Q8D412yes—
89C11×#121—21no—
90C11×#121—21no—
91C4×Q8×C11—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11C2312yes—
98C4×Q8×C11C2312yes—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C11×#117—22no—
104C11×#117—21no—
105C11×#117—21no—
106C11×#117—21no—
107C2×C42×C11C2311yescharacteristic
108C11×#107—22no—
109C11×#107—22no—
110C11×#106—22no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8C2312yes—
114C11×C4⋊C8C2312yes—
115C11×#103—22no—
116C11×#103—22no—
117C11×#103—22no—
118C11×#103—22no—
119C11×#103—22no—
120C11×#102—22no—
121C11×C22⋊C8—21no—
122C11×C22⋊C8—21no—
123C11×#97—21no—
124C4×C8×C11C2311yescharacteristic
125C4×C8×C11C2311yescharacteristic
126#18939C1111yesmaximal, characteristic, direct product factor, Sylow
127C11×#41—82no—
128C2×Q8×C11—24no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—84no—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11C2×D412yes—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11C2×D412yes—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C11×Q16—82no—
147C11×Q16—82no—
148C11×SD16—82no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—81no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—41no—
174C11×C4⋊C4C2×D412yes—
175C11×C4⋊C4C2×D412yes—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—41no—
184C42×C11—24no—
185C42×C11—22no—
186C42×C11—22no—
187C42×C11—41no—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C42×C11C2411yescharacteristic
192#3550C2×C1111yescharacteristic
193#3249C2×C1111yescharacteristic, complemented
194#3237C2×C1111yescharacteristic, complemented
195#3210C2×C1111yescharacteristic
196#1645C2×C1112yescomplemented
197#1640C2×C1112yescomplemented
198#1633C2×C1112yescomplemented
199#1630C2×C1112yescomplemented
200#1551C2×C1111yescharacteristic
201#1497C2×C1111yescharacteristic, complemented
202#1481C2×C1111yescharacteristic, complemented
203C23×C11—22no—
204C23×C11#12011yescharacteristic
205Q8×C11—22no—
206Q8×C11—24no—
207Q8×C11—22no—
208Q8×C11—42no—
209Q8×C11—42no—
210Q8×C11—42no—
211Q8×C11—42no—
212Q8×C11—41no—
213Q8×C11—41no—
214Q8×C11—84no—
215D4×C11—42no—
216D4×C11—41no—
217D4×C11—42no—
218D4×C11—41no—
219D4×C11—82no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—41no—
229C2×C4×C11—44no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—84no—
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C8×C11—41no—
240C8×C11—41no—
241C8×C11—42no—
242C8×C11—42no—
243#563—22no—
244#559C22×C1112yes—
245Q82C22×C1112yes—
246#556—21no—
247#556—21no—
248D4×Q8—21no—
249D4×Q8—21no—
250#542—22no—
251#542—22no—
252#536—22no—
253#533C22×C1111yescharacteristic
254#533C22×C1111yescharacteristic
255#533C22×C1111yescharacteristic
256#532C22×C1111yescharacteristic
257#501—21no—
258#494C22×C1111yescharacteristic
259#492C22×C1111yescharacteristic
260#491—21no—
261#487C22×C1111yescharacteristic
262#486C22×C1111yescharacteristic
263#485—22no—
264#477—21no—
265#477C22×C1112yes—
266#477C22×C1112yes—
267#475C22×C1112yes—
268#467—22no—
269#464—22no—
270#462—21no—
271#462C22×C1112yes—
272#452—22no—
273#432C22×C1111yescharacteristic
274#431C22×C1111yescharacteristic
275C2×C4⋊C8C22×C1111yescharacteristic
276#333C22×C1112yes—
277#331C22×C1112yes—
278Q8⋊C8C22×C1112yes—
279Q8⋊C8C22×C1112yes—
280Q8⋊C8C22×C1112yes—
281Q8⋊C8C22×C1112yes—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11C2×#12011yescharacteristic
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11—81no—
299C4×C11—81no—
300C4×C11#57711yescharacteristic
301C4×C11#57812yes—
302C4×C11#57811yescharacteristic
303C2×#41D4×C1112yes—
304C22×Q8—22no—
305C2×Q16—22no—
306C2×Q16—22no—
307C2×SD16—22no—
308C22×C8—21no—
309C4⋊Q8—24no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8D4×C1111yescharacteristic
313C4⋊Q8D4×C1111yescharacteristic
314C4⋊Q8D4×C1111yescharacteristic
315C4⋊Q8D4×C1111yescharacteristic
316C4⋊Q8C23×C1111yescharacteristic
317C4⋊Q8C23×C1111yescharacteristic
318C4⋊Q8C23×C1111yescharacteristic
319#127C23×C1111yescharacteristic
320#126—24no—
321#126—24no—
322#125—21no—
323#125—21no—
324#125—21no—
325#124—24no—
326#124—22no—
327#124—22no—
328#124D4×C1112yes—
329#123—24no—
330#123—24no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339C22⋊Q8D4×C1112yes—
340C22⋊Q8D4×C1112yes—
341#121—21no—
342#121—21no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8C23×C1112yes—
350C4×Q8C23×C1112yes—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—21no—
354C4×D4—21no—
355#117—22no—
356#117—21no—
357#117—21no—
358#117—21no—
359C2×C42C23×C1111yescharacteristic
360#107—22no—
361#107—22no—
362#106—22no—
363C4⋊C8—21no—
364C4⋊C8—21no—
365C4⋊C8C23×C1112yes—
366C4⋊C8C23×C1112yes—
367#103—22no—
368#103—22no—
369#103—22no—
370#103—22no—
371#103—22no—
372#102—22no—
373C22⋊C8—21no—
374C22⋊C8—21no—
375#97—21no—
376C4×C8C23×C1111yescharacteristic
377C4×C8C23×C1111yescharacteristic
378C2×C11—41no—
379C2×C11—82no—
380C2×C11#301111yescharacteristic
381C2×C11#301311yescharacteristic
382C2×C11#301911yescharacteristic
383#41—82no—
384C2×Q8—24no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—84no—
390C2×Q8C2×D4×C1112yes—
391C2×Q8C2×D4×C1112yes—
392C2×Q8C2×D4×C1112yes—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4C2×D4×C1112yes—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1111yescharacteristic
402Q16—82no—
403Q16—82no—
404SD16—82no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—81no—
410C4⋊C4—24no—
411C4⋊C4—24no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4C2×D4×C1112yes—
431C4⋊C4C2×D4×C1112yes—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—41no—
440C42—24no—
441C42—22no—
442C42—22no—
443C42—41no—
444C42C2×D4×C1111yescharacteristic
445C42C2×D4×C1111yescharacteristic
446C42C2×D4×C1111yescharacteristic
447C42C24×C1111yescharacteristic
448C11#1893911yescharacteristic, direct product factor, Sylow
449C23—22no—
450C23C11×#12011yescharacteristic
451Q8—22no—
452Q8—24no—
453Q8—22no—
454Q8—42no—
455Q8—42no—
456Q8—42no—
457Q8—42no—
458Q8—41no—
459Q8—41no—
460Q8—84no—
461D4—42no—
462D4—41no—
463D4—42no—
464D4—41no—
465D4—82no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—44no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—84no—
479C2×C4C11×#12011yescharacteristic
480C2×C4C11×#12011yescharacteristic
481C2×C4C11×#12011yescharacteristic
482C2×C4C22×D4×C1111yescharacteristic
483C2×C4C22×D4×C1111yescharacteristic
484C2×C4C22×D4×C1111yescharacteristic
485C8—41no—
486C8—41no—
487C8—42no—
488C8—42no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22C2×C11×#12011yescharacteristic
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—81no—
506C4—81no—
507C4C11×#57711yescharacteristic
508C4C11×#57812yes—
509C4C11×#57811yescharacteristic
510C2—41no—
511C2—82no—
512C2C11×#301111yescharacteristic
513C2C11×#301311yescharacteristic
514C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3249C2semidirect
3. C11×#3237C2semidirect
5. C11×#1645C2semidirect
6. C11×#1640C2semidirect
7. C11×#1633C2semidirect
8. C11×#1630C2semidirect
10. C11×#1497C2semidirect
11. C11×#1481C2semidirect
126. #18939C11direct (N × H)
193. #3249C2×C11semidirect
194. #3237C2×C11semidirect
196. #1645C2×C11semidirect
197. #1640C2×C11semidirect
198. #1633C2×C11semidirect
199. #1630C2×C11semidirect
201. #1497C2×C11semidirect
202. #1481C2×C11semidirect
448. C11#18939direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35502
C11×#32492
C11×#32372
C11×#32102
C11×#16452
C11×#16402
C11×#16332
C11×#16302
C11×#15512
C11×#14972
C11×#14812
#1893911