Finite Group Databasebeta

← C11×#18922 #14596115

Subgroups — C11×#18922 #14596115

Order 2816.

1142 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3497C211yesmaximal, characteristic
2C11×#3226C211yesmaximal, characteristic, complemented
3C11×#3226C211yesmaximal, characteristic, complemented
4C2×C11×#462C211yesmaximal, characteristic, complemented
5C11×#1649C214yesmaximal, complemented
6C11×#1641C214yesmaximal, complemented
7C11×#1540C211yesmaximal, characteristic, complemented
8C11×#1480C211yesmaximal, characteristic, complemented
9C11×#1479C211yesmaximal, characteristic, complemented
10C2×C11×2−1+4—21no—
11C22×C11×Q16—21no—
12C11×#550—21no—
13C11×#550C2212yes—
14D4×Q8×C11—21no—
15D4×Q8×C11C2212yes—
16C11×#548—22no—
17C11×#548—22no—
18C11×#537—22no—
19C11×#537—21no—
20C11×#532—22no—
21C11×#532C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C2×C11×C4⋊Q8C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C11×#500—21no—
26C11×#500C2212yes—
27C11×#486—21no—
28C11×#486C2212yes—
29C11×#480—22no—
30C11×#480—22no—
31C11×#474—22no—
32C11×#474C2214yes—
33C11×#462—22no—
34C11×#462C2214yes—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103—21no—
39C11×#332C2212yes—
40C11×#331C2212yes—
41C11×Q8⋊C8C2214yes—
42C11×D4⋊C8C2214yes—
43C11×2−1+4—44no—
44C11×2−1+4—44no—
45C2×C11×#41—24no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—21no—
53C22×Q8×C11D411yescharacteristic
54C2×C11×Q16—24no—
55C2×C11×Q16—44no—
56C22×C8×C11—21no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8D411yescharacteristic
62C11×C4⋊Q8C2312yes—
63C11×C4⋊Q8C2311yescharacteristic
64C11×#127—22no—
65C11×#127D411yescharacteristic
66C11×#127C2311yescharacteristic
67C11×#124—24no—
68C11×#124—21no—
69C11×#124—21no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—24no—
74C11×#121—24no—
75C11×#121—22no—
76C11×#121—24no—
77C11×#121—24no—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121—22no—
81C11×#121D412yes—
82C11×#121D412yes—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11D412yes—
86C4×Q8×C11C2312yes—
87C4×D4×C11—24no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11D412yes—
93C4×D4×C11C2312yes—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100C11×#107—24no—
101C11×#107—24no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2312yes—
105C11×C4⋊C8C2312yes—
106C11×#103—24no—
107C11×#102—24no—
108C11×#102—24no—
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C4×C8×C11—21no—
112C4×C8×C11C2312yes—
113#18922C1111yesmaximal, characteristic, direct product factor, Sylow
114C11×#41—416no—
115C11×#41—44no—
116C11×#41—48no—
117C11×#41—44no—
118C11×#41—42no—
119C11×#41—42no—
120C11×#41—42no—
121C11×#41—42no—
122C2×Q8×C11—24no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—22no—
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—44no—
129C2×Q8×C11—48no—
130C2×Q8×C11—44no—
131C2×Q8×C11—41no—
132C2×Q8×C11—42no—
133C2×Q8×C11—42no—
134C2×Q8×C11D814yes—
135C2×Q8×C11C2×D412yes—
136C2×D4×C11—24no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—24no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11C2×D412yes—
145C2×D4×C11C2×D412yes—
146C22×C4×C11—21no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—41no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C11×Q16—48no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11—42no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4C2×D412yes—
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×D412yes—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11C2411yescharacteristic
186#3497C2×C1111yescharacteristic
187#3226C2×C1111yescharacteristic, complemented
188#3226C2×C1111yescharacteristic, complemented
189C2×#462C2×C1111yescharacteristic, complemented
190#1649C2×C1114yescomplemented
191#1641C2×C1114yescomplemented
192#1540C2×C1111yescharacteristic, complemented
193#1480C2×C1111yescharacteristic, complemented
194#1479C2×C1111yescharacteristic, complemented
195C23×C11—22no—
196C23×C11—22no—
197C23×C11#12011yescharacteristic
198Q8×C11—22no—
199Q8×C11—24no—
200Q8×C11—48no—
201Q8×C11—41no—
202Q8×C11—41no—
203Q8×C11—42no—
204Q8×C11—42no—
205Q8×C11—42no—
206Q8×C11—82no—
207Q8×C11C2×D814yes—
208D4×C11—24no—
209D4×C11—42no—
210D4×C11—48no—
211D4×C11—44no—
212D4×C11—44no—
213D4×C11—41no—
214D4×C11—41no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—81no—
218D4×C11—84no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—41no—
226C2×C4×C11—48no—
227C2×C4×C11—48no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—44no—
231C2×C4×C11—42no—
232C2×C4×C11—81no—
233C2×C4×C11—82no—
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11#12011yescharacteristic
237C2×C4×C11C2×D812yes—
238C2×C4×C11AGL(1,ℤ/8)12yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C8×C11—42no—
243C8×C11—42no—
244C8×C11—42no—
245C2×2−1+4—21no—
246C22×Q16—21no—
247#550—21no—
248#550C22×C1112yes—
249D4×Q8—21no—
250D4×Q8C22×C1112yes—
251#548—22no—
252#548—22no—
253#537—22no—
254#537—21no—
255#532—22no—
256#532C22×C1111yescharacteristic
257#532C22×C1111yescharacteristic
258C2×C4⋊Q8C22×C1111yescharacteristic
259C2×C4×Q8C22×C1111yescharacteristic
260#500—21no—
261#500C22×C1112yes—
262#486—21no—
263#486C22×C1112yes—
264#480—22no—
265#480—22no—
266#474—22no—
267#474C22×C1114yes—
268#462—22no—
269#462C22×C1114yes—
270#431C22×C1111yescharacteristic
271#431C22×C1111yescharacteristic
272C2×C4⋊C8C22×C1111yescharacteristic
273C2×#103—21no—
274#332C22×C1112yes—
275#331C22×C1112yes—
276Q8⋊C8C22×C1114yes—
277D4⋊C8C22×C1114yes—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11#44712yes—
287C22×C11C2×#12011yescharacteristic
288C4×C11—24no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—42no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—82no—
296C4×C11#44712yes—
297C4×C11C22×D811yescharacteristic
298C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C11#57812yes—
3002−1+4—44no—
3012−1+4—44no—
302C2×#41—24no—
303C2×#41—22no—
304C2×#41—22no—
305C2×#41—21no—
306C2×#41—21no—
307C22×Q8—22no—
308C22×Q8—22no—
309C22×Q8—21no—
310C22×Q8D4×C1111yescharacteristic
311C2×Q16—24no—
312C2×Q16—44no—
313C22×C8—21no—
314C4⋊Q8—22no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8D4×C1111yescharacteristic
319C4⋊Q8C23×C1112yes—
320C4⋊Q8C23×C1111yescharacteristic
321#127—22no—
322#127D4×C1111yescharacteristic
323#127C23×C1111yescharacteristic
324#124—24no—
325#124—21no—
326#124—21no—
327C22⋊Q8—22no—
328C22⋊Q8—24no—
329C22⋊Q8—22no—
330C22⋊Q8—24no—
331#121—24no—
332#121—22no—
333#121—24no—
334#121—24no—
335#121—21no—
336#121—21no—
337#121—22no—
338#121D4×C1112yes—
339#121D4×C1112yes—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8D4×C1112yes—
343C4×Q8C23×C1112yes—
344C4×D4—24no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4D4×C1112yes—
350C4×D4C23×C1112yes—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4D4×C1111yescharacteristic
355C2×C42—21no—
356C2×C42C23×C1111yescharacteristic
357#107—24no—
358#107—24no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8C23×C1112yes—
362C4⋊C8C23×C1112yes—
363#103—24no—
364#102—24no—
365#102—24no—
366C22⋊C8—21no—
367C22⋊C8—21no—
368C4×C8—21no—
369C4×C8C23×C1112yes—
370C2×C11—22no—
371C2×C11—82no—
372C2×C11—82no—
373C2×C11C2×#44711yescharacteristic
374C2×C11#301111yescharacteristic
375C2×C11#302211yescharacteristic
376#41—416no—
377#41—44no—
378#41—48no—
379#41—44no—
380#41—42no—
381#41—42no—
382#41—42no—
383#41—42no—
384C2×Q8—24no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—22no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—44no—
391C2×Q8—48no—
392C2×Q8—44no—
393C2×Q8—41no—
394C2×Q8—42no—
395C2×Q8—42no—
396C2×Q8C11×D814yes—
397C2×Q8C2×D4×C1112yes—
398C2×D4—24no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4C2×D4×C1112yes—
407C2×D4C2×D4×C1112yes—
408C22×C4—21no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—41no—
415C22×C4C2×D4×C1111yescharacteristic
416C22×C4C2×D4×C1111yescharacteristic
417C22×C4C2×D4×C1111yescharacteristic
418Q16—48no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—42no—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4C2×D4×C1112yes—
434C4⋊C4C2×D4×C1112yes—
435C4⋊C4C2×D4×C1112yes—
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C42—22no—
443C42—22no—
444C42C2×D4×C1111yescharacteristic
445C42C2×D4×C1111yescharacteristic
446C42C2×D4×C1111yescharacteristic
447C42C24×C1111yescharacteristic
448C11#1892211yescharacteristic, direct product factor, Sylow
449C23—22no—
450C23—22no—
451C23C11×#12011yescharacteristic
452Q8—22no—
453Q8—24no—
454Q8—48no—
455Q8—41no—
456Q8—41no—
457Q8—42no—
458Q8—42no—
459Q8—42no—
460Q8—82no—
461Q8C2×C11×D814yes—
462D4—24no—
463D4—42no—
464D4—48no—
465D4—44no—
466D4—44no—
467D4—41no—
468D4—41no—
469D4—42no—
470D4—42no—
471D4—81no—
472D4—84no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—48no—
481C2×C4—48no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—44no—
485C2×C4—42no—
486C2×C4—81no—
487C2×C4—82no—
488C2×C4C11×#12011yescharacteristic
489C2×C4C11×#12011yescharacteristic
490C2×C4C11×#12011yescharacteristic
491C2×C4C2×C11×D812yes—
492C2×C4C11×AGL(1,ℤ/8)12yes—
493C2×C4C22×D4×C1111yescharacteristic
494C2×C4C22×D4×C1111yescharacteristic
495C2×C4C22×D4×C1111yescharacteristic
496C8—42no—
497C8—42no—
498C8—42no—
499C22—21no—
500C22—21no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22C11×#44712yes—
508C22C2×C11×#12011yescharacteristic
509C4—24no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—42no—
514C4—42no—
515C4—42no—
516C4—82no—
517C4C11×#44712yes—
518C4C22×C11×D811yescharacteristic
519C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
520C4C11×#57812yes—
521C2—22no—
522C2—82no—
523C2—82no—
524C2C2×C11×#44711yescharacteristic
525C2C11×#301111yescharacteristic
526C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3497C2
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×#3226C2semidirect
3. C11×#3226C2semidirect
4. C2×C11×#462C2semidirect
5. C11×#1649C2semidirect
6. C11×#1641C2semidirect
7. C11×#1540C2semidirect
8. C11×#1480C2semidirect
9. C11×#1479C2semidirect
113. #18922C11direct (N × H)
187. #3226C2×C11semidirect
188. #3226C2×C11semidirect
189. C2×#462C2×C11semidirect
190. #1649C2×C11semidirect
191. #1641C2×C11semidirect
192. #1540C2×C11semidirect
193. #1480C2×C11semidirect
194. #1479C2×C11semidirect
448. C11#18922direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34972
C11×#32262
C2×C11×#4622
C11×#16492
C11×#16412
C11×#15402
C11×#14802
C11×#14792
#1892211