Finite Group Databasebeta

← C11×#18903 #14596096

Subgroups — C11×#18903 #14596096

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic
2C11×#3227C211yesmaximal, characteristic, complemented
3C11×#3206C211yesmaximal, characteristic, complemented
4C2×C11×#474C211yesmaximal, characteristic, complemented
5C11×#1654C214yesmaximal, complemented
6C11×#1639C214yesmaximal, complemented
7C11×#1540C211yesmaximal, characteristic, complemented
8C11×#1480C211yesmaximal, characteristic, complemented
9C11×#1478C211yesmaximal, characteristic, complemented
10C2×C11×H(5,𝔽2)—21no—
11C11×#547—21no—
12C11×#547C2212yes—
13C11×#546—22no—
14C11×#546—22no—
15D42×C11—21no—
16D42×C11C2212yes—
17C11×#537—21no—
18C11×#534—22no—
19C11×#532C2211yescharacteristic
20C11×#532C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic, complemented
22C2×C11×#121—22no—
23C2×C4×D4×C11C2211yescharacteristic
24C11×#498C2212yescomplemented
25C11×#492—21no—
26C11×#487—21no—
27C11×#486C2212yescomplemented
28C11×#481—22no—
29C11×#476—22no—
30C11×#474—22no—
31C11×#474C2214yescomplemented
32C11×#461C2214yescomplemented
33C11×#448—22no—
34C11×#431C2211yescharacteristic, complemented
35C11×#431C2211yescharacteristic, complemented
36C2×C11×#107—21no—
37C2×C11×C4⋊C8C2211yescharacteristic, complemented
38C2×C11×#102—21no—
39C11×#332C2212yescomplemented
40C11×#331C2212yescomplemented
41C11×D4⋊C8C2214yescomplemented
42C11×D4⋊C8C2214yescomplemented
43C11×H(5,𝔽2)—44no—
44C11×H(5,𝔽2)—44no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C22×Q8×C11—21no—
50C22×D4×C11—24no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11D411yescharacteristic
55C23×C4×C11—21no—
56C2×C11×SD16—24no—
57C22×C8×C11—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8D411yescharacteristic
62C11×C4⋊Q8C2312yes—
63C11×C4⋊Q8C2311yescharacteristic
64C11×#127D411yescharacteristic
65C11×#127C2311yescharacteristic
66C11×#124—21no—
67C11×#124—21no—
68C11×#123—24no—
69C11×#123—24no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×#121—24no—
73C11×#121—24no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#121—21no—
77C11×#121—21no—
78C11×#121—22no—
79C11×#121—22no—
80C11×#121D412yes—
81C11×#121D412yes—
82C11×#120—24no—
83C11×#120—24no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11D412yes—
89C4×D4×C11D412yes—
90C4×D4×C11C2312yes—
91C4×D4×C11C2312yes—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4—21no—
98C2×C42×C11C2311yescharacteristic
99C11×#107—24no—
100C11×#106—24no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2312yes—
104C11×C4⋊C8C2312yes—
105C11×#103—24no—
106C11×#102—24no—
107C11×#102—24no—
108C11×C22⋊C8—21no—
109C11×C22⋊C8—21no—
110C4×C8×C11—21no—
111C4×C8×C11C2312yes—
112#18903C1111yesmaximal, characteristic, direct product factor, Sylow
113C24×C11—21no—
114C24×C11—24no—
115C11×#41—44no—
116C11×#41—48no—
117C11×#41—44no—
118C11×#41—42no—
119C11×#41—42no—
120C11×#41—42no—
121C11×#41—42no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—22no—
125C2×Q8×C11—41no—
126C2×Q8×C11—82no—
127C2×D4×C11—24no—
128C2×D4×C11—24no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—22no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—44no—
139C2×D4×C11—48no—
140C2×D4×C11—416no—
141C2×D4×C11—44no—
142C2×D4×C11—84no—
143C2×D4×C11SD1614yescomplemented
144C2×D4×C11C2×D412yes—
145C2×D4×C11C2×D412yes—
146C2×D4×C11C2×D412yes—
147C22×C4×C11—24no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—41no—
154C22×C4×C11—82no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C11×SD16—84no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—42no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
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—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11C2411yescharacteristic
186#3496C2×C1111yescharacteristic
187#3227C2×C1111yescharacteristic, complemented
188#3206C2×C1111yescharacteristic, complemented
189C2×#474C2×C1111yescharacteristic, complemented
190#1654C2×C1114yescomplemented
191#1639C2×C1114yescomplemented
192#1540C2×C1111yescharacteristic, complemented
193#1480C2×C1111yescharacteristic, complemented
194#1478C2×C1111yescharacteristic, complemented
195C23×C11—22no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—48no—
200C23×C11—81no—
201C23×C11—81no—
202C23×C11—84no—
203C23×C11—84no—
204C23×C11#12011yescharacteristic
205Q8×C11—41no—
206Q8×C11—41no—
207Q8×C11—42no—
208Q8×C11—44no—
209Q8×C11—82no—
210D4×C11—22no—
211D4×C11—24no—
212D4×C11—24no—
213D4×C11—42no—
214D4×C11—48no—
215D4×C11—48no—
216D4×C11—44no—
217D4×C11—44no—
218D4×C11—41no—
219D4×C11—41no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—81no—
223D4×C11—84no—
224D4×C11C2×SD1614yes—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—48no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—44no—
234C2×C4×C11—44no—
235C2×C4×C11—42no—
236C2×C4×C11—82no—
237C2×C4×C11—81no—
238C2×C4×C11—82no—
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11C2×SD1612yes—
243C2×C4×C11AGL(1,ℤ/8)12yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C8×C11—42no—
248C8×C11—42no—
249C8×C11—42no—
250C2×H(5,𝔽2)—21no—
251#547—21no—
252#547C22×C1112yes—
253#546—22no—
254#546—22no—
255D42—21no—
256D42C22×C1112yes—
257#537—21no—
258#534—22no—
259#532C22×C1111yescharacteristic
260#532C22×C1111yescharacteristic
261C2×C4⋊Q8C22×C1111yescharacteristic, complemented
262C2×#121—22no—
263C2×C4×D4C22×C1111yescharacteristic
264#498C22×C1112yescomplemented
265#492—21no—
266#487—21no—
267#486C22×C1112yescomplemented
268#481—22no—
269#476—22no—
270#474—22no—
271#474C22×C1114yescomplemented
272#461C22×C1114yescomplemented
273#448—22no—
274#431C22×C1111yescharacteristic, complemented
275#431C22×C1111yescharacteristic, complemented
276C2×#107—21no—
277C2×C4⋊C8C22×C1111yescharacteristic, complemented
278C2×#102—21no—
279#332C22×C1112yescomplemented
280#331C22×C1112yescomplemented
281D4⋊C8C22×C1114yescomplemented
282D4⋊C8C22×C1114yescomplemented
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—24no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—84no—
295C22×C11—168no—
296C22×C11#45012yes—
297C22×C11C2×#12011yescharacteristic
298C4×C11—21no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11—82no—
305C4×C11#45012yes—
306C4×C11C22×SD1611yescharacteristic
307C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
308C4×C11#57612yes—
309H(5,𝔽2)—44no—
310H(5,𝔽2)—44no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41—21no—
314C2×#41—21no—
315C22×Q8—21no—
316C22×D4—24no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4D4×C1111yescharacteristic
321C23×C4—21no—
322C2×SD16—24no—
323C22×C8—21no—
324C4⋊Q8—21no—
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327C4⋊Q8D4×C1111yescharacteristic
328C4⋊Q8C23×C1112yes—
329C4⋊Q8C23×C1111yescharacteristic
330#127D4×C1111yescharacteristic
331#127C23×C1111yescharacteristic
332#124—21no—
333#124—21no—
334#123—24no—
335#123—24no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338#121—24no—
339#121—24no—
340#121—22no—
341#121—22no—
342#121—21no—
343#121—21no—
344#121—22no—
345#121—22no—
346#121D4×C1112yes—
347#121D4×C1112yes—
348#120—24no—
349#120—24no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4D4×C1112yes—
355C4×D4D4×C1112yes—
356C4×D4C23×C1112yes—
357C4×D4C23×C1112yes—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4D4×C1111yescharacteristic
362C2×C22⋊C4—24no—
363C2×C22⋊C4—21no—
364C2×C42C23×C1111yescharacteristic
365#107—24no—
366#106—24no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8C23×C1112yes—
370C4⋊C8C23×C1112yes—
371#103—24no—
372#102—24no—
373#102—24no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C4×C8—21no—
377C4×C8C23×C1112yes—
378C2×C11—22no—
379C2×C11—44no—
380C2×C11—82no—
381C2×C11—82no—
382C2×C11C2×#45011yescharacteristic
383C2×C11#300811yescharacteristic
384C2×C11#302211yescharacteristic
385C24—21no—
386C24—24no—
387#41—44no—
388#41—48no—
389#41—44no—
390#41—42no—
391#41—42no—
392#41—42no—
393#41—42no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—22no—
397C2×Q8—41no—
398C2×Q8—82no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—24no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—22no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—44no—
411C2×D4—48no—
412C2×D4—416no—
413C2×D4—44no—
414C2×D4—84no—
415C2×D4C11×SD1614yescomplemented
416C2×D4C2×D4×C1112yes—
417C2×D4C2×D4×C1112yes—
418C2×D4C2×D4×C1112yes—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—41no—
426C22×C4—82no—
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1111yescharacteristic
430SD16—84no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—42no—
435C4⋊C4—24no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—41no—
442C4⋊C4—41no—
443C4⋊C4C2×D4×C1112yes—
444C4⋊C4C2×D4×C1112yes—
445C4⋊C4C2×D4×C1112yes—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C42C2×D4×C1111yescharacteristic
455C42C2×D4×C1111yescharacteristic
456C42C2×D4×C1111yescharacteristic
457C42C24×C1111yescharacteristic
458C11#1890311yescharacteristic, direct product factor, Sylow
459C23—22no—
460C23—24no—
461C23—22no—
462C23—22no—
463C23—48no—
464C23—81no—
465C23—81no—
466C23—84no—
467C23—84no—
468C23C11×#12011yescharacteristic
469Q8—41no—
470Q8—41no—
471Q8—42no—
472Q8—44no—
473Q8—82no—
474D4—22no—
475D4—24no—
476D4—24no—
477D4—42no—
478D4—48no—
479D4—48no—
480D4—44no—
481D4—44no—
482D4—41no—
483D4—41no—
484D4—42no—
485D4—42no—
486D4—81no—
487D4—84no—
488D4C2×C11×SD1614yes—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—41no—
494C2×C4—48no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—44no—
498C2×C4—44no—
499C2×C4—42no—
500C2×C4—82no—
501C2×C4—81no—
502C2×C4—82no—
503C2×C4C11×#12011yescharacteristic
504C2×C4C11×#12011yescharacteristic
505C2×C4C11×#12011yescharacteristic
506C2×C4C2×C11×SD1612yes—
507C2×C4C11×AGL(1,ℤ/8)12yes—
508C2×C4C22×D4×C1111yescharacteristic
509C2×C4C22×D4×C1111yescharacteristic
510C2×C4C22×D4×C1111yescharacteristic
511C8—42no—
512C8—42no—
513C8—42no—
514C22—21no—
515C22—21no—
516C22—24no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—84no—
526C22—168no—
527C22C11×#45012yes—
528C22C2×C11×#12011yescharacteristic
529C4—21no—
530C4—21no—
531C4—21no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—82no—
536C4C11×#45012yes—
537C4C22×C11×SD1611yescharacteristic
538C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
539C4C11×#57612yes—
540C2—22no—
541C2—44no—
542C2—82no—
543C2—82no—
544C2C2×C11×#45011yescharacteristic
545C2C11×#300811yescharacteristic
546C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3496C2
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×#3227C2semidirect
3. C11×#3206C2semidirect
4. C2×C11×#474C2semidirect
5. C11×#1654C2semidirect
6. C11×#1639C2semidirect
7. C11×#1540C2semidirect
8. C11×#1480C2semidirect
9. C11×#1478C2semidirect
21. C2×C11×C4⋊Q8C22semidirect
24. C11×#498C22semidirect
27. C11×#486C22semidirect
31. C11×#474C22semidirect
32. C11×#461C22semidirect
34. C11×#431C22semidirect
35. C11×#431C22semidirect
37. C2×C11×C4⋊C8C22semidirect
39. C11×#332C22semidirect
40. C11×#331C22semidirect
41. C11×D4⋊C8C22semidirect
42. C11×D4⋊C8C22semidirect
112. #18903C11direct (N × H)
143. C2×D4×C11SD16semidirect
187. #3227C2×C11semidirect
188. #3206C2×C11semidirect
189. C2×#474C2×C11semidirect
190. #1654C2×C11semidirect
191. #1639C2×C11semidirect
192. #1540C2×C11semidirect
193. #1480C2×C11semidirect
194. #1478C2×C11semidirect
261. C2×C4⋊Q8C22×C11semidirect
264. #498C22×C11semidirect
267. #486C22×C11semidirect
271. #474C22×C11semidirect
272. #461C22×C11semidirect
274. #431C22×C11semidirect
275. #431C22×C11semidirect
277. C2×C4⋊C8C22×C11semidirect
279. #332C22×C11semidirect
280. #331C22×C11semidirect
281. D4⋊C8C22×C11semidirect
282. D4⋊C8C22×C11semidirect
415. C2×D4C11×SD16semidirect
458. C11#18903direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34962
C11×#32272
C11×#32062
C2×C11×#4742
C11×#16542
C11×#16392
C11×#15402
C11×#14802
C11×#14782
#1890311