Finite Group Databasebeta

← C11×#59928 #14637121

Subgroups — C11×#59928 #14637121

Order 2816.

1680 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2811C211yesmaximal, characteristic, complemented
2C11×#2809C211yesmaximal, characteristic, complemented
3C11×#2732C212yesmaximal
4C11×#2612C212yesmaximal, complemented
5C11×#2574C214yesmaximal, complemented
6C11×#2565C212yesmaximal, complemented
7C11×#2564C212yesmaximal
8C11×#2556C214yesmaximal, complemented
9C11×#2423C214yesmaximal, complemented
10C11×#2372C212yesmaximal
11C11×#2368C214yesmaximal, complemented
12C4×C11×#124C211yesmaximal, characteristic
13C11×#2295C212yesmaximal, complemented
14C2×C11×#125C2212yes—
15C2×C11×#124C2211yescharacteristic
16C2×C11×C22⋊Q8C2214yes—
17C2×C11×C22⋊Q8C2212yes—
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C11×#400C2212yes—
22C11×#399C2212yes—
23C11×#399C2214yes—
24C11×#398C2214yes—
25C11×#398C2214yes—
26C11×#398C2214yes—
27C11×#396C2214yes—
28C11×#395C2214yes—
29C11×#395C2212yes—
30C11×#393C2212yes—
31C11×#391C2214yes—
32C11×#391C2212yes—
33C11×#391C2212yes—
34C11×#391C2211yescharacteristic
35C11×#391C2212yes—
36C11×#391C2212yes—
37C11×#391C2214yes—
38C11×#390C2211yescharacteristic
39C11×#389C2214yes—
40C11×#389C2212yes—
41C11×#389C2212yes—
42C11×#388C2214yes—
43C11×#388C2214yes—
44C11×#388C2214yes—
45C11×#387C2214yes—
46C11×#387C2214yes—
47C11×#387C2214yes—
48C11×#387C2214yes—
49C11×#387C2214yes—
50C11×#387C2214yes—
51C11×#386C2214yes—
52C11×#385C2214yes—
53C11×#385C2214yes—
54C11×#384C2212yes—
55C11×#382C2211yescharacteristic
56C11×#382C2212yes—
57C11×#380C2214yes—
58C4×C11×C4⋊C4C2214yes—
59C4×C11×C4⋊C4C2212yes—
60C4×C11×C4⋊C4C2212yes—
61C4×C11×C22⋊C4C2214yes—
62C4×C11×C22⋊C4C2214yes—
63C4×C11×C22⋊C4C2214yes—
64C11×#376C2214yes—
65C2×C11×#95C2212yes—
66C43×C11C2211yescharacteristic
67C22×Q8×C11C2312yes—
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2312yes—
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11C2312yes—
72C23×C4×C11C2314yes—
73C11×#125—44no—
74C11×#124Q818yescomplemented
75C11×C22⋊Q8—216no—
76C11×C22⋊Q8—44no—
77C4×Q8×C11—28no—
78C4×Q8×C11—42no—
79C4×D4×C11—42no—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2314yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2314yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C22⋊C4C2314yes—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2312yes—
100C2×C11×C22⋊C4C2314yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2312yes—
104C2×C42×C11C2314yes—
105C2×C42×C11C2312yes—
106C2×C42×C11C2312yes—
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2314yes—
109C2×C42×C11C2312yes—
110C2×C42×C11C2312yes—
111C2×C42×C11C2311yescharacteristic
112C11×#95C2314yes—
113C11×#95C2312yes—
114C11×#95C2312yes—
115C11×#95C2314yes—
116C11×#95C2314yes—
117C11×#95C2314yes—
118C11×#95C2314yes—
119C11×#95C2314yes—
120C11×#95C2314yes—
121C11×#95C2314yes—
122C11×#95C2314yes—
123C11×#95C2314yes—
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11×#95C2314yes—
127#59928C1111yesmaximal, characteristic, direct product factor, Sylow
128C24×C11C2412yes—
129C2×Q8×C11—41no—
130C2×Q8×C11—41no—
131C2×Q8×C11—42no—
132C2×Q8×C11—42no—
133C2×Q8×C11—42no—
134C2×Q8×C11—44no—
135C2×Q8×C11C2×Q814yes—
136C2×Q8×C11#4118yes—
137C2×D4×C11—41no—
138C2×D4×C11—41no—
139C2×D4×C11C2×Q814yes—
140C22×C4×C11—28no—
141C22×C4×C11—24no—
142C22×C4×C11—44no—
143C22×C4×C11—44no—
144C22×C4×C11—44no—
145C22×C4×C11C2414yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2411yescharacteristic
149C22×C4×C11C2414yes—
150C22×C4×C11C2412yes—
151C22×C4×C11C2411yescharacteristic
152C22×C4×C11C2412yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2414yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2411yescharacteristic
157C11×C4⋊C4—24no—
158C11×C4⋊C4—28no—
159C11×C4⋊C4—28no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—44no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—41no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—44no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—44no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—44no—
178C11×C22⋊C4C2×Q8116yes—
179C42×C11—24no—
180C42×C11—28no—
181C42×C11—22no—
182C42×C11—24no—
183C42×C11—42no—
184C42×C11—44no—
185C42×C11—42no—
186C42×C11—42no—
187C42×C11—41no—
188C42×C11C2×Q814yes—
189#2811C2×C1111yescharacteristic, complemented
190#2809C2×C1111yescharacteristic, complemented
191#2732C2×C1112yes—
192#2612C2×C1112yescomplemented
193#2574C2×C1114yescomplemented
194#2565C2×C1112yescomplemented
195#2564C2×C1112yes—
196#2556C2×C1114yescomplemented
197#2423C2×C1114yescomplemented
198#2372C2×C1112yes—
199#2368C2×C1114yescomplemented
200C4×#124C2×C1111yescharacteristic
201#2295C2×C1112yescomplemented
202C23×C11—24no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—22no—
206C23×C11C22×Q814yes—
207C23×C11C2511yescharacteristic
208Q8×C11—44no—
209Q8×C11—48no—
210Q8×C11—84no—
211D4×C11—44no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—21no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—88no—
239C2×C4×C11—84no—
240C2×C4×C11C22×Q814yes—
241C2×C4×C11C22×Q812yes—
242C2×C4×C11C22×Q814yes—
243C2×C4×C11C2×#4114yes—
244C2×C4×C11C2×#4118yes—
245C2×C4×C11H(5,𝔽2)12yes—
246C2×#125C22×C1112yes—
247C2×#124C22×C1111yescharacteristic
248C2×C22⋊Q8C22×C1114yes—
249C2×C22⋊Q8C22×C1112yes—
250C2×C4×Q8C22×C1112yes—
251C2×C4×Q8C22×C1111yescharacteristic
252C2×C4×D4C22×C1111yescharacteristic
253#400C22×C1112yes—
254#399C22×C1112yes—
255#399C22×C1114yes—
256#398C22×C1114yes—
257#398C22×C1114yes—
258#398C22×C1114yes—
259#396C22×C1114yes—
260#395C22×C1112yes—
261#395C22×C1114yes—
262#393C22×C1112yes—
263#391C22×C1112yes—
264#391C22×C1112yes—
265#391C22×C1114yes—
266#391C22×C1112yes—
267#391C22×C1114yes—
268#391C22×C1112yes—
269#391C22×C1111yescharacteristic
270#390C22×C1111yescharacteristic
271#389C22×C1114yes—
272#389C22×C1112yes—
273#389C22×C1112yes—
274#388C22×C1114yes—
275#388C22×C1114yes—
276#388C22×C1114yes—
277#387C22×C1114yes—
278#387C22×C1114yes—
279#387C22×C1114yes—
280#387C22×C1114yes—
281#387C22×C1114yes—
282#387C22×C1114yes—
283#386C22×C1114yes—
284#385C22×C1114yes—
285#385C22×C1114yes—
286#384C22×C1112yes—
287#382C22×C1112yes—
288#382C22×C1111yescharacteristic
289#380C22×C1114yes—
290C4×C4⋊C4C22×C1112yes—
291C4×C4⋊C4C22×C1112yes—
292C4×C4⋊C4C22×C1114yes—
293C4×C22⋊C4C22×C1114yes—
294C4×C22⋊C4C22×C1114yes—
295C4×C22⋊C4C22×C1114yes—
296#376C22×C1114yes—
297C2×#95C22×C1112yes—
298C43C22×C1111yescharacteristic
299C22×C11—28no—
300C22×C11—24no—
301C22×C11—42no—
302C22×C11—44no—
303C22×C11—42no—
304C22×C11C23×Q811yescharacteristic
305C22×C11C22×#4112yes—
306C22×C11C2×H(5,𝔽2)11yescharacteristic
307C22×C11#58512yes—
308C22×C11#58511yescharacteristic
309C4×C11—24no—
310C4×C11—28no—
311C4×C11—24no—
312C4×C11—22no—
313C4×C11—24no—
314C4×C11—22no—
315C4×C11—41no—
316C4×C11—44no—
317C4×C11—42no—
318C4×C11—44no—
319C4×C11—42no—
320C4×C11—44no—
321C22×Q8C23×C1112yes—
322C22×Q8C23×C1111yescharacteristic
323C22×Q8C23×C1112yes—
324C22×D4C23×C1111yescharacteristic
325C23×C4C23×C1112yes—
326C23×C4C23×C1114yes—
327#125—44no—
328#124Q8×C1118yescomplemented
329C22⋊Q8—216no—
330C22⋊Q8—44no—
331C4×Q8—28no—
332C4×Q8—42no—
333C4×D4—42no—
334C2×C4⋊C4C23×C1114yes—
335C2×C4⋊C4C23×C1112yes—
336C2×C4⋊C4C23×C1114yes—
337C2×C4⋊C4C23×C1114yes—
338C2×C4⋊C4C23×C1114yes—
339C2×C4⋊C4C23×C1114yes—
340C2×C4⋊C4C23×C1111yescharacteristic
341C2×C4⋊C4C23×C1112yes—
342C2×C4⋊C4C23×C1111yescharacteristic
343C2×C4⋊C4C23×C1112yes—
344C2×C4⋊C4C23×C1112yes—
345C2×C4⋊C4C23×C1112yes—
346C2×C4⋊C4C23×C1114yes—
347C2×C4⋊C4C23×C1112yes—
348C2×C4⋊C4C23×C1112yes—
349C2×C4⋊C4C23×C1114yes—
350C2×C22⋊C4C23×C1114yes—
351C2×C22⋊C4C23×C1114yes—
352C2×C22⋊C4C23×C1112yes—
353C2×C22⋊C4C23×C1114yes—
354C2×C22⋊C4C23×C1114yes—
355C2×C22⋊C4C23×C1114yes—
356C2×C42C23×C1111yescharacteristic
357C2×C42C23×C1112yes—
358C2×C42C23×C1112yes—
359C2×C42C23×C1114yes—
360C2×C42C23×C1112yes—
361C2×C42C23×C1111yescharacteristic
362C2×C42C23×C1114yes—
363C2×C42C23×C1112yes—
364C2×C42C23×C1112yes—
365C2×C42C23×C1111yescharacteristic
366#95C23×C1114yes—
367#95C23×C1112yes—
368#95C23×C1112yes—
369#95C23×C1114yes—
370#95C23×C1114yes—
371#95C23×C1114yes—
372#95C23×C1114yes—
373#95C23×C1114yes—
374#95C23×C1114yes—
375#95C23×C1114yes—
376#95C23×C1114yes—
377#95C23×C1114yes—
378#95C23×C1114yes—
379#95C23×C1114yes—
380#95C23×C1114yes—
381C2×C11—44no—
382C2×C11Q8×#4112yes—
383C2×C11#348311yescharacteristic
384C2×C11#349112yes—
385C2×C11#350111yescharacteristic
386C2×C11#354511yescharacteristic
387C24C24×C1112yes—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×Q8—42no—
391C2×Q8—42no—
392C2×Q8—42no—
393C2×Q8—44no—
394C2×Q8C2×Q8×C1114yes—
395C2×Q8C11×#4118yes—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4C2×Q8×C1114yes—
399C22×C4—28no—
400C22×C4—24no—
401C22×C4—44no—
402C22×C4—44no—
403C22×C4—44no—
404C22×C4C24×C1114yes—
405C22×C4C24×C1112yes—
406C22×C4C24×C1114yes—
407C22×C4C24×C1111yescharacteristic
408C22×C4C24×C1114yes—
409C22×C4C24×C1112yes—
410C22×C4C24×C1111yescharacteristic
411C22×C4C24×C1112yes—
412C22×C4C24×C1112yes—
413C22×C4C24×C1114yes—
414C22×C4C24×C1112yes—
415C22×C4C24×C1111yescharacteristic
416C4⋊C4—24no—
417C4⋊C4—28no—
418C4⋊C4—28no—
419C4⋊C4—28no—
420C4⋊C4—28no—
421C4⋊C4—28no—
422C4⋊C4—41no—
423C4⋊C4—42no—
424C4⋊C4—41no—
425C4⋊C4—42no—
426C4⋊C4—42no—
427C4⋊C4—42no—
428C4⋊C4—44no—
429C4⋊C4—42no—
430C4⋊C4—42no—
431C4⋊C4—44no—
432C22⋊C4—28no—
433C22⋊C4—28no—
434C22⋊C4—42no—
435C22⋊C4—44no—
436C22⋊C4—44no—
437C22⋊C4C2×Q8×C11116yes—
438C42—24no—
439C42—28no—
440C42—22no—
441C42—24no—
442C42—42no—
443C42—44no—
444C42—42no—
445C42—42no—
446C42—41no—
447C42C2×Q8×C1114yes—
448C11#5992811yescharacteristic, direct product factor, Sylow
449C23—24no—
450C23—22no—
451C23—24no—
452C23—22no—
453C23C22×Q8×C1114yes—
454C23C25×C1111yescharacteristic
455Q8—44no—
456Q8—48no—
457Q8—84no—
458D4—44no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—21no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—88no—
486C2×C4—84no—
487C2×C4C22×Q8×C1114yes—
488C2×C4C22×Q8×C1112yes—
489C2×C4C22×Q8×C1114yes—
490C2×C4C2×C11×#4114yes—
491C2×C4C2×C11×#4118yes—
492C2×C4C11×H(5,𝔽2)12yes—
493C22—28no—
494C22—24no—
495C22—42no—
496C22—44no—
497C22—42no—
498C22C23×Q8×C1111yescharacteristic
499C22C22×C11×#4112yes—
500C22C2×C11×H(5,𝔽2)11yescharacteristic
501C22C11×#58512yes—
502C22C11×#58511yescharacteristic
503C4—24no—
504C4—28no—
505C4—24no—
506C4—22no—
507C4—24no—
508C4—22no—
509C4—41no—
510C4—44no—
511C4—42no—
512C4—44no—
513C4—42no—
514C4—44no—
515C2—44no—
516C2Q8×C11×#4112yes—
517C2C11×#348311yescharacteristic
518C2C11×#349112yes—
519C2C11×#350111yescharacteristic
520C2C11×#354511yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC22×D4×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2811C2semidirect
2. C11×#2809C2semidirect
4. C11×#2612C2semidirect
5. C11×#2574C2semidirect
6. C11×#2565C2semidirect
8. C11×#2556C2semidirect
9. C11×#2423C2semidirect
11. C11×#2368C2semidirect
13. C11×#2295C2semidirect
74. C11×#124Q8semidirect
127. #59928C11direct (N × H)
189. #2811C2×C11semidirect
190. #2809C2×C11semidirect
192. #2612C2×C11semidirect
193. #2574C2×C11semidirect
194. #2565C2×C11semidirect
196. #2556C2×C11semidirect
197. #2423C2×C11semidirect
199. #2368C2×C11semidirect
201. #2295C2×C11semidirect
328. #124Q8×C11semidirect
448. C11#59928direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28112
C11×#28092
C11×#27322
C11×#26122
C11×#25742
C11×#25652
C11×#25642
C11×#25562
C11×#24232
C11×#23722
C11×#23682
C4×C11×#1242
C11×#22952
#5992811