Finite Group Databasebeta

← C11×#18953 #14596146

Subgroups — C11×#18953 #14596146

Order 2816.

846 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3550C211yesmaximal, characteristic
2C11×#3249C211yesmaximal, characteristic, complemented
3C11×#3235C211yesmaximal, characteristic
4C11×#3231C211yesmaximal, characteristic, complemented
5C11×#1652C212yesmaximal, complemented
6C11×#1649C212yesmaximal, complemented
7C11×#1638C212yesmaximal, complemented
8C11×#1637C212yesmaximal, complemented
9C11×#1552C211yesmaximal, characteristic, complemented
10C11×#1497C211yesmaximal, characteristic, complemented
11C11×#1480C211yesmaximal, characteristic
12C11×#563—22no—
13C11×#559—21no—
14Q82×C11—21no—
15C11×#556—21no—
16C11×#556C2212yes—
17D4×Q8×C11—21no—
18D4×Q8×C11C2212yes—
19C11×#542—22no—
20C11×#542—22no—
21C11×#536—22no—
22C11×#533C2211yescharacteristic
23C11×#533C2211yescharacteristic
24C11×#533C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#501—21no—
27C11×#500C2211yescharacteristic
28C11×#498C2211yescharacteristic
29C11×#490—21no—
30C11×#487C2211yescharacteristic
31C11×#487C2211yescharacteristic
32C11×#485—22no—
33C11×#482—22no—
34C11×#479—22no—
35C11×#477—21no—
36C11×#477C2212yes—
37C11×#476C2212yes—
38C11×#474C2212yes—
39C11×#467—22no—
40C11×#462—21no—
41C11×#462C2212yes—
42C11×#432C2211yescharacteristic
43C11×#431C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45C11×#332C2212yes—
46C11×#332C2212yes—
47C11×Q8⋊C8C2212yes—
48C11×Q8⋊C8C2212yes—
49C11×D4⋊C8C2212yes—
50C11×D4⋊C8C2212yes—
51C2×C11×#41—21no—
52C22×Q8×C11—22no—
53C2×C11×Q16—22no—
54C22×C8×C11—21no—
55C11×C4⋊Q8—24no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8D411yescharacteristic
60C11×C4⋊Q8D411yescharacteristic
61C11×C4⋊Q8C2311yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×C4⋊Q8C2311yescharacteristic
65C11×#127D411yescharacteristic
66C11×#126—24no—
67C11×#126—24no—
68C11×#125—21no—
69C11×#125—21no—
70C11×#125D412yes—
71C11×#124—24no—
72C11×#124—22no—
73C11×#124—22no—
74C11×#124—21no—
75C11×#123—24no—
76C11×#123—24no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—24no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8D412yes—
87C11×#121—21no—
88C11×#121D412yes—
89C4×Q8×C11—22no—
90C4×Q8×C11—22no—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11C2312yes—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—21no—
100C4×D4×C11C2312yes—
101C11×#117—21no—
102C11×#117—22no—
103C11×#117—21no—
104C11×#117D412yes—
105C2×C42×C11C2311yescharacteristic
106C11×#107—22no—
107C11×#107—22no—
108C11×#107—22no—
109C11×#106—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×#102—22no—
120C11×#102—22no—
121C11×C22⋊C8—21no—
122C11×C22⋊C8—21no—
123C11×#97—21no—
124C4×C8×C11C2311yescharacteristic
125C4×C8×C11C2311yescharacteristic
126#18953C1111yesmaximal, characteristic, direct product factor, Sylow
127C11×#41—81no—
128C11×#41—81no—
129C2×Q8×C11—24no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—82no—
137C2×Q8×C11—82no—
138C2×Q8×C11C2×D412yes—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11C2×D412yes—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C11×Q16—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—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×D412yes—
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#3235C2×C1111yescharacteristic
195#3231C2×C1111yescharacteristic, complemented
196#1652C2×C1112yescomplemented
197#1649C2×C1112yescomplemented
198#1638C2×C1112yescomplemented
199#1637C2×C1112yescomplemented
200#1552C2×C1111yescharacteristic, complemented
201#1497C2×C1111yescharacteristic, complemented
202#1480C2×C1111yescharacteristic
203C23×C11—22no—
204C23×C11#12011yescharacteristic
205Q8×C11—22no—
206Q8×C11—22no—
207Q8×C11—42no—
208Q8×C11—42no—
209Q8×C11—41no—
210Q8×C11—41no—
211Q8×C11—42no—
212Q8×C11—41no—
213Q8×C11—41no—
214Q8×C11—81no—
215Q8×C11—84no—
216D4×C11—24no—
217D4×C11—42no—
218D4×C11—81no—
219D4×C11—82no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
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—42no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—84no—
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C8×C11—41no—
241C8×C11—41no—
242C8×C11—42no—
243C8×C11—42no—
244#563—22no—
245#559—21no—
246Q82—21no—
247#556—21no—
248#556C22×C1112yes—
249D4×Q8—21no—
250D4×Q8C22×C1112yes—
251#542—22no—
252#542—22no—
253#536—22no—
254#533C22×C1111yescharacteristic
255#533C22×C1111yescharacteristic
256#533C22×C1111yescharacteristic
257#532C22×C1111yescharacteristic
258#501—21no—
259#500C22×C1111yescharacteristic
260#498C22×C1111yescharacteristic
261#490—21no—
262#487C22×C1111yescharacteristic
263#487C22×C1111yescharacteristic
264#485—22no—
265#482—22no—
266#479—22no—
267#477—21no—
268#477C22×C1112yes—
269#476C22×C1112yes—
270#474C22×C1112yes—
271#467—22no—
272#462—21no—
273#462C22×C1112yes—
274#432C22×C1111yescharacteristic
275#431C22×C1111yescharacteristic
276C2×C4⋊C8C22×C1111yescharacteristic
277#332C22×C1112yes—
278#332C22×C1112yes—
279Q8⋊C8C22×C1112yes—
280Q8⋊C8C22×C1112yes—
281D4⋊C8C22×C1112yes—
282D4⋊C8C22×C1112yes—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11C2×#12011yescharacteristic
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—81no—
300C4×C11—81no—
301C4×C11#57611yescharacteristic
302C4×C11#57711yescharacteristic
303C4×C11#57812yes—
304C2×#41—21no—
305C22×Q8—22no—
306C2×Q16—22no—
307C22×C8—21no—
308C4⋊Q8—24no—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8D4×C1111yescharacteristic
312C4⋊Q8D4×C1111yescharacteristic
313C4⋊Q8D4×C1111yescharacteristic
314C4⋊Q8C23×C1111yescharacteristic
315C4⋊Q8C23×C1111yescharacteristic
316C4⋊Q8C23×C1111yescharacteristic
317C4⋊Q8C23×C1111yescharacteristic
318#127D4×C1111yescharacteristic
319#126—24no—
320#126—24no—
321#125—21no—
322#125—21no—
323#125D4×C1112yes—
324#124—24no—
325#124—22no—
326#124—22no—
327#124—21no—
328#123—24no—
329#123—24no—
330C22⋊Q8—24no—
331C22⋊Q8—22no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—22no—
336C22⋊Q8—24no—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339C22⋊Q8D4×C1112yes—
340#121—21no—
341#121D4×C1112yes—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8—21no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8C23×C1112yes—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—21no—
353C4×D4C23×C1112yes—
354#117—21no—
355#117—22no—
356#117—21no—
357#117D4×C1112yes—
358C2×C42C23×C1111yescharacteristic
359#107—22no—
360#107—22no—
361#107—22no—
362#106—22no—
363#106—22no—
364C4⋊C8—21no—
365C4⋊C8—21no—
366C4⋊C8C23×C1112yes—
367C4⋊C8C23×C1112yes—
368#103—22no—
369#103—22no—
370#103—22no—
371#103—22no—
372#102—22no—
373#102—22no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376#97—21no—
377C4×C8C23×C1111yescharacteristic
378C4×C8C23×C1111yescharacteristic
379C2×C11—41no—
380C2×C11—82no—
381C2×C11#301111yescharacteristic
382C2×C11#301211yescharacteristic
383C2×C11#302011yescharacteristic
384#41—81no—
385#41—81no—
386C2×Q8—24no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—82no—
394C2×Q8—82no—
395C2×Q8C2×D4×C1112yes—
396C2×D4—22no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4C2×D4×C1112yes—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4C2×D4×C1111yescharacteristic
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C2×D4×C1111yescharacteristic
405Q16—82no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—81no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C2×D4×C1112yes—
430C4⋊C4C2×D4×C1112yes—
431C4⋊C4C2×D4×C1112yes—
432C4⋊C4C2×D4×C1112yes—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—41no—
441C42—24no—
442C42—22no—
443C42—22no—
444C42—41no—
445C42C2×D4×C1111yescharacteristic
446C42C2×D4×C1111yescharacteristic
447C42C2×D4×C1111yescharacteristic
448C42C24×C1111yescharacteristic
449C11#1895311yescharacteristic, direct product factor, Sylow
450C23—22no—
451C23C11×#12011yescharacteristic
452Q8—22no—
453Q8—22no—
454Q8—42no—
455Q8—42no—
456Q8—41no—
457Q8—41no—
458Q8—42no—
459Q8—41no—
460Q8—41no—
461Q8—81no—
462Q8—84no—
463D4—24no—
464D4—42no—
465D4—81no—
466D4—82no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—84no—
481C2×C4C11×#12011yescharacteristic
482C2×C4C11×#12011yescharacteristic
483C2×C4C11×#12011yescharacteristic
484C2×C4C22×D4×C1111yescharacteristic
485C2×C4C22×D4×C1111yescharacteristic
486C2×C4C22×D4×C1111yescharacteristic
487C8—41no—
488C8—41no—
489C8—42no—
490C8—42no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22C2×C11×#12011yescharacteristic
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—42no—
503C4—42no—
504C4—42no—
505C4—42no—
506C4—42no—
507C4—81no—
508C4—81no—
509C4C11×#57611yescharacteristic
510C4C11×#57711yescharacteristic
511C4C11×#57812yes—
512C2—41no—
513C2—82no—
514C2C11×#301111yescharacteristic
515C2C11×#301211yescharacteristic
516C2C11×#302011yescharacteristic
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
4. C11×#3231C2semidirect
5. C11×#1652C2semidirect
6. C11×#1649C2semidirect
7. C11×#1638C2semidirect
8. C11×#1637C2semidirect
9. C11×#1552C2semidirect
10. C11×#1497C2semidirect
126. #18953C11direct (N × H)
193. #3249C2×C11semidirect
195. #3231C2×C11semidirect
196. #1652C2×C11semidirect
197. #1649C2×C11semidirect
198. #1638C2×C11semidirect
199. #1637C2×C11semidirect
200. #1552C2×C11semidirect
201. #1497C2×C11semidirect
449. C11#18953direct (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×#32352
C11×#32312
C11×#16522
C11×#16492
C11×#16382
C11×#16372
C11×#15522
C11×#14972
C11×#14802
#1895311