Finite Group Databasebeta

← C11×#19079 #14596272

Subgroups — C11×#19079 #14596272

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3545C211yesmaximal, characteristic
2C11×#3181C212yesmaximal, complemented
3C11×#3140C211yesmaximal, characteristic, complemented
4C11×#1664C212yesmaximal, complemented
5C11×#1662C212yesmaximal, complemented
6C11×#1661C212yesmaximal, complemented
7C11×#1659C212yesmaximal, complemented
8C11×#1524C212yesmaximal, complemented
9C2×C11×#329C211yesmaximal, characteristic, complemented
10C11×#563C2211yescharacteristic
11C11×#562C2212yes—
12C11×H(3,𝔽4)C2211yescharacteristic
13C11×#555—21no—
14C11×#551—21no—
15C11×#551—22no—
16C11×#546—22no—
17C11×#542—22no—
18C11×#538—22no—
19C11×#536—21no—
20C11×#534—21no—
21C11×#533C2211yescharacteristic, complemented
22C11×#529C2212yes—
23C2×C11×#124C2211yescharacteristic
24C11×#501C2212yescomplemented
25C11×#497C2212yescomplemented
26C11×#491C2212yescomplemented
27C11×#489C2212yes—
28C11×#489C2212yescomplemented
29C11×#489C2212yescomplemented
30C11×#488—21no—
31C11×#488—21no—
32C11×#467—22no—
33C11×#465—22no—
34C11×#441—22no—
35C11×#440—22no—
36C11×#419—21no—
37C11×#418—21no—
38C4×C11×M16C2211yescharacteristic, complemented
39C2×C11×#97C2212yescomplemented
40C11×#330C2212yescomplemented
41C11×#330C2212yescomplemented
42C11×#329C2212yes—
43C11×#329C2212yescomplemented
44C11×#329C2212yescomplemented
45C11×#329C2211yescharacteristic, complemented
46C11×#329C2211yescharacteristic, complemented
47C2×C11×#41—21no—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11D411yescharacteristic
51C2×C11×Q16—22no—
52C2×C11×SD16—22no—
53C2×C11×M16—21no—
54C22×C8×C11—22no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8C2312yes—
58C11×#126—22no—
59C11×#126—22no—
60C11×#126—22no—
61C11×#125—21no—
62C11×#125C2312yes—
63C11×#124—21no—
64C11×#124—22no—
65C11×#124—21no—
66C11×#124—22no—
67C11×#124—22no—
68C11×#124D411yescharacteristic
69C11×#124D411yescharacteristic
70C11×#124C2311yescharacteristic
71C11×#124C2311yescharacteristic
72C11×#124C2312yes—
73C11×#123—21no—
74C11×#123—22no—
75C11×#123—22no—
76C11×#123—21no—
77C11×#123—22no—
78C11×#123—22no—
79C11×#123—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8D412yes—
86C11×#121—22no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121D412yes—
91C11×#120—21no—
92C11×#120—22no—
93C11×#120—21no—
94C11×#120—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11D412yes—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11D412yes—
101C11×#117—21no—
102C11×#117—22no—
103C11×#117—22no—
104C11×#117—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C42×C11C2311yescharacteristic
109C11×#107—22no—
110C11×#106—22no—
111C11×#103—22no—
112C11×#103—22no—
113C11×#103—22no—
114C11×#103—22no—
115C11×#103—22no—
116C11×#102—22no—
117C11×#102—22no—
118C11×#102—22no—
119C11×#97—22no—
120C11×#97C2312yes—
121C11×#97C2312yes—
122C11×#97C2312yes—
123C4×C8×C11—21no—
124#19079C1111yesmaximal, characteristic, direct product factor, Sylow
125C24×C11—21no—
126C24×C11—21no—
127C11×#41—82no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11—42no—
132C2×Q8×C11C2×D411yescharacteristic
133C2×Q8×C11C2×D411yescharacteristic
134C2×Q8×C11C2×D412yes—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—42no—
142C2×D4×C11—82no—
143C2×D4×C11C2×D411yescharacteristic
144C2×D4×C11C2×D411yescharacteristic
145C2×D4×C11C2×D412yes—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D412yes—
153C11×Q16—44no—
154C11×SD16—44no—
155C11×M16—42no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—44no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4C2×D412yes—
171C11×C4⋊C4C2×D412yes—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—41no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—22no—
191C42×C11—41no—
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D412yes—
194C42×C11C2411yescharacteristic
195#3545C2×C1111yescharacteristic
196#3181C2×C1112yescomplemented
197#3140C2×C1111yescharacteristic, complemented
198#1664C2×C1112yescomplemented
199#1662C2×C1112yescomplemented
200#1661C2×C1112yescomplemented
201#1659C2×C1112yescomplemented
202#1524C2×C1112yescomplemented
203C2×#329C2×C1111yescharacteristic, complemented
204C23×C11—21no—
205C23×C11—22no—
206C23×C11—21no—
207C23×C11—42no—
208C23×C11—82no—
209C23×C11—81no—
210C23×C11—82no—
211C23×C11#12011yescharacteristic
212Q8×C11—42no—
213Q8×C11—41no—
214Q8×C11—41no—
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—81no—
218Q8×C11—81no—
219D4×C11—42no—
220D4×C11—41no—
221D4×C11—41no—
222D4×C11—44no—
223D4×C11—81no—
224D4×C11—82no—
225D4×C11—82no—
226D4×C11—82no—
227D4×C11—81no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—82no—
238C2×C4×C11—82no—
239C2×C4×C11—81no—
240C2×C4×C11—82no—
241C2×C4×C11#12012yes—
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D411yescharacteristic
245C8×C11—24no—
246C8×C11—42no—
247C8×C11—42no—
248#563C22×C1111yescharacteristic
249#562C22×C1112yes—
250H(3,𝔽4)C22×C1111yescharacteristic
251#555—21no—
252#551—21no—
253#551—22no—
254#546—22no—
255#542—22no—
256#538—22no—
257#536—21no—
258#534—21no—
259#533C22×C1111yescharacteristic, complemented
260#529C22×C1112yes—
261C2×#124C22×C1111yescharacteristic
262#501C22×C1112yescomplemented
263#497C22×C1112yescomplemented
264#491C22×C1112yescomplemented
265#489C22×C1112yes—
266#489C22×C1112yescomplemented
267#489C22×C1112yescomplemented
268#488—21no—
269#488—21no—
270#467—22no—
271#465—22no—
272#441—22no—
273#440—22no—
274#419—21no—
275#418—21no—
276C4×M16C22×C1111yescharacteristic, complemented
277C2×#97C22×C1112yescomplemented
278#330C22×C1112yescomplemented
279#330C22×C1112yescomplemented
280#329C22×C1112yes—
281#329C22×C1112yescomplemented
282#329C22×C1112yescomplemented
283#329C22×C1111yescharacteristic, complemented
284#329C22×C1111yescharacteristic, complemented
285C22×C11—22no—
286C22×C11—42no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—162no—
294C22×C11—162no—
295C22×C11#45512yes—
296C22×C11C2×#12011yescharacteristic
297C4×C11—21no—
298C4×C11—21no—
299C4×C11—22no—
300C4×C11—22no—
301C4×C11—41no—
302C4×C11—41no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—82no—
307C2×#41—21no—
308C22×Q8D4×C1111yescharacteristic
309C22×D4—21no—
310C22×D4D4×C1111yescharacteristic
311C2×Q16—22no—
312C2×SD16—22no—
313C2×M16—21no—
314C22×C8—22no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8C23×C1112yes—
318#126—22no—
319#126—22no—
320#126—22no—
321#125—21no—
322#125C23×C1112yes—
323#124—21no—
324#124—22no—
325#124—21no—
326#124—22no—
327#124—22no—
328#124D4×C1111yescharacteristic
329#124D4×C1111yescharacteristic
330#124C23×C1111yescharacteristic
331#124C23×C1111yescharacteristic
332#124C23×C1112yes—
333#123—21no—
334#123—22no—
335#123—22no—
336#123—21no—
337#123—22no—
338#123—22no—
339#123—22no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8D4×C1112yes—
346#121—22no—
347#121—22no—
348#121—22no—
349#121—22no—
350#121D4×C1112yes—
351#120—21no—
352#120—22no—
353#120—21no—
354#120—22no—
355C4×Q8—22no—
356C4×Q8D4×C1112yes—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4D4×C1112yes—
361#117—21no—
362#117—22no—
363#117—22no—
364#117—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C42C23×C1111yescharacteristic
369#107—22no—
370#106—22no—
371#103—22no—
372#103—22no—
373#103—22no—
374#103—22no—
375#103—22no—
376#102—22no—
377#102—22no—
378#102—22no—
379#97—22no—
380#97C23×C1112yes—
381#97C23×C1112yes—
382#97C23×C1112yes—
383C4×C8—21no—
384C2×C11—22no—
385C2×C11—82no—
386C2×C11—81no—
387C2×C11—81no—
388C2×C11C2×#45511yescharacteristic
389C2×C11#301812yes—
390C24—21no—
391C24—21no—
392#41—82no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—22no—
396C2×Q8—42no—
397C2×Q8C2×D4×C1111yescharacteristic
398C2×Q8C2×D4×C1111yescharacteristic
399C2×Q8C2×D4×C1112yes—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—42no—
407C2×D4—82no—
408C2×D4C2×D4×C1111yescharacteristic
409C2×D4C2×D4×C1111yescharacteristic
410C2×D4C2×D4×C1112yes—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4C2×D4×C1111yescharacteristic
417C22×C4C2×D4×C1112yes—
418Q16—44no—
419SD16—44no—
420M16—42no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—44no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—42no—
435C4⋊C4C2×D4×C1112yes—
436C4⋊C4C2×D4×C1112yes—
437C22⋊C4—22no—
438C22⋊C4—21no—
439C22⋊C4—21no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—41no—
453C42—21no—
454C42—21no—
455C42—22no—
456C42—41no—
457C42C2×D4×C1111yescharacteristic
458C42C2×D4×C1112yes—
459C42C24×C1111yescharacteristic
460C11#1907911yescharacteristic, direct product factor, Sylow
461C23—21no—
462C23—22no—
463C23—21no—
464C23—42no—
465C23—82no—
466C23—81no—
467C23—82no—
468C23C11×#12011yescharacteristic
469Q8—42no—
470Q8—41no—
471Q8—41no—
472Q8—42no—
473Q8—42no—
474Q8—81no—
475Q8—81no—
476D4—42no—
477D4—41no—
478D4—41no—
479D4—44no—
480D4—81no—
481D4—82no—
482D4—82no—
483D4—82no—
484D4—81no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—21no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—82no—
495C2×C4—82no—
496C2×C4—81no—
497C2×C4—82no—
498C2×C4C11×#12012yes—
499C2×C4C11×#12011yescharacteristic
500C2×C4C22×D4×C1112yes—
501C2×C4C22×D4×C1111yescharacteristic
502C8—24no—
503C8—42no—
504C8—42no—
505C22—22no—
506C22—42no—
507C22—41no—
508C22—41no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—162no—
514C22—162no—
515C22C11×#45512yes—
516C22C2×C11×#12011yescharacteristic
517C4—21no—
518C4—21no—
519C4—22no—
520C4—22no—
521C4—41no—
522C4—41no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—82no—
527C2—22no—
528C2—81no—
529C2—82no—
530C2—81no—
531C2C2×C11×#45511yescharacteristic
532C2C11×#301812yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3545C2
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×#3181C2semidirect
3. C11×#3140C2semidirect
4. C11×#1664C2semidirect
5. C11×#1662C2semidirect
6. C11×#1661C2semidirect
7. C11×#1659C2semidirect
8. C11×#1524C2semidirect
9. C2×C11×#329C2semidirect
21. C11×#533C22semidirect
24. C11×#501C22semidirect
25. C11×#497C22semidirect
26. C11×#491C22semidirect
28. C11×#489C22semidirect
29. C11×#489C22semidirect
38. C4×C11×M16C22semidirect
39. C2×C11×#97C22semidirect
40. C11×#330C22semidirect
41. C11×#330C22semidirect
43. C11×#329C22semidirect
44. C11×#329C22semidirect
45. C11×#329C22semidirect
46. C11×#329C22semidirect
124. #19079C11direct (N × H)
196. #3181C2×C11semidirect
197. #3140C2×C11semidirect
198. #1664C2×C11semidirect
199. #1662C2×C11semidirect
200. #1661C2×C11semidirect
201. #1659C2×C11semidirect
202. #1524C2×C11semidirect
203. C2×#329C2×C11semidirect
259. #533C22×C11semidirect
262. #501C22×C11semidirect
263. #497C22×C11semidirect
264. #491C22×C11semidirect
266. #489C22×C11semidirect
267. #489C22×C11semidirect
276. C4×M16C22×C11semidirect
277. C2×#97C22×C11semidirect
278. #330C22×C11semidirect
279. #330C22×C11semidirect
281. #329C22×C11semidirect
282. #329C22×C11semidirect
283. #329C22×C11semidirect
284. #329C22×C11semidirect
460. C11#19079direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35452
C11×#31812
C11×#31402
C11×#16642
C11×#16622
C11×#16612
C11×#16592
C11×#15242
C2×C11×#3292
#1907911