Finite Group Databasebeta

← C11×#24025 #14601218

Subgroups — C11×#24025 #14601218

Order 2816.

1286 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3485C211yesmaximal, characteristic
2C11×#3092C212yesmaximal, complemented
3C11×#2311C211yesmaximal, characteristic, complemented
4C11×#2038C214yesmaximal, complemented
5C11×#1897C212yesmaximal, complemented
6C11×#1856C212yesmaximal, complemented
7C11×#1792C212yesmaximal, complemented
8C11×#1785C211yesmaximal, characteristic, complemented
9C2×C11×H(5,𝔽2)C2211yescharacteristic
10C22×C11×#41C2211yescharacteristic
11C11×#547—22no—
12C11×#547—22no—
13C11×#546—22no—
14C11×#546—22no—
15C11×#536C2212yes—
16C11×#534—22no—
17C11×#525C2212yes—
18C2×C11×#123—22no—
19C11×#518C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic, complemented
21C22×C11×C4⋊C4C2211yescharacteristic, complemented
22C11×#484—22no—
23C11×#483—22no—
24C11×#481—22no—
25C11×#480—22no—
26C11×#428C2214yescomplemented
27C2×C11×#104C2214yes—
28C11×#417C2214yes—
29C2×C11×#101C2212yescomplemented
30C2×C11×#100C2212yes—
31C11×#407C2212yescomplemented
32C11×#391C2212yescomplemented
33C11×#390C2212yes—
34C11×#386—22no—
35C11×#380—22no—
36C11×#339C2214yescomplemented
37C11×H(5,𝔽2)—24no—
38C11×H(5,𝔽2)—42no—
39C2×C11×#41—22no—
40C2×C11×#41—24no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—42no—
44C2×C11×#41C2312yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11D412yes—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11D412yes—
52C23×C4×C11C2311yescharacteristic
53C2×C11×M16C2314yes—
54C11×C4⋊Q8—22no—
55C11×#124—22no—
56C11×#123—24no—
57C11×#123—24no—
58C11×#123—24no—
59C11×#123—22no—
60C11×#123—24no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8D412yes—
64C11×C22⋊Q8D412yes—
65C11×#121—24no—
66C11×#121—24no—
67C11×#121D412yes—
68C11×#121D412yes—
69C11×#120—24no—
70C11×#120—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C11×#117—42no—
76C11×#117C2312yes—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—24no—
89C2×C42×C11C2312yes—
90C11×#107—24no—
91C11×#106—24no—
92C11×#104—44no—
93C11×#103—24no—
94C11×#102—24no—
95C11×#101—42no—
96C11×#100—24no—
97C11×C22⋊C8—22no—
98C11×C22⋊C8—22no—
99C11×#95—24no—
100#24025C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11—22no—
102C24×C11C2×D411yescharacteristic
103C24×C11C2×D412yes—
104C11×#41—24no—
105C11×#41—24no—
106C11×#41—48no—
107C11×#41—48no—
108C11×#41—48no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11C2×D412yes—
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—42no—
122C2×D4×C11—48no—
123C2×D4×C11—44no—
124C2×D4×C11—44no—
125C2×D4×C11C2×D412yes—
126C2×D4×C11#4114yes—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—82no—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2411yescharacteristic
146C11×M16—24no—
147C11×M16—24no—
148C2×C8×C11—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4C2×D412yes—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—42no—
168C11×C22⋊C4—84no—
169C42×C11—22no—
170C42×C11—24no—
171#3485C2×C1111yescharacteristic
172#3092C2×C1112yescomplemented
173#2311C2×C1111yescharacteristic, complemented
174#2038C2×C1114yescomplemented
175#1897C2×C1112yescomplemented
176#1856C2×C1112yescomplemented
177#1792C2×C1112yescomplemented
178#1785C2×C1111yescharacteristic, complemented
179C23×C11—22no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—44no—
189C23×C11—82no—
190C23×C11—82no—
191C23×C11#12012yes—
192C23×C11#12314yes—
193C23×C11C22×D411yescharacteristic
194Q8×C11—24no—
195Q8×C11—44no—
196D4×C11—28no—
197D4×C11—24no—
198D4×C11—48no—
199D4×C11—48no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—82no—
203D4×C11—82no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—44no—
215C2×C4×C11—44no—
216C2×C4×C11—44no—
217C2×C4×C11—44no—
218C2×C4×C11—42no—
219C2×C4×C11—44no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—82no—
224C2×C4×C11—82no—
225C2×C4×C11—84no—
226C2×C4×C11#12011yescharacteristic
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11C22×D412yes—
229C2×C4×C11C2×#4112yes—
230C2×C4×C11H(5,𝔽2)12yes—
231C8×C11—44no—
232C2×H(5,𝔽2)C22×C1111yescharacteristic
233C22×#41C22×C1111yescharacteristic
234#547—22no—
235#547—22no—
236#546—22no—
237#546—22no—
238#536C22×C1112yes—
239#534—22no—
240#525C22×C1112yes—
241C2×#123—22no—
242#518C22×C1111yescharacteristic
243C2×#117C22×C1111yescharacteristic, complemented
244C22×C4⋊C4C22×C1111yescharacteristic, complemented
245#484—22no—
246#483—22no—
247#481—22no—
248#480—22no—
249#428C22×C1114yescomplemented
250C2×#104C22×C1114yes—
251#417C22×C1114yes—
252C2×#101C22×C1112yescomplemented
253C2×#100C22×C1112yes—
254#407C22×C1112yescomplemented
255#391C22×C1112yescomplemented
256#390C22×C1112yes—
257#386—22no—
258#380—22no—
259#339C22×C1114yescomplemented
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—22no—
263C22×C11—24no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—44no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—82no—
275C22×C11—164no—
276C22×C11C2×#12011yescharacteristic
277C22×C11C2×#12311yescharacteristic
278C22×C11#53411yescharacteristic
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—82no—
286C4×C11—82no—
287C4×C11#54614yes—
288H(5,𝔽2)—24no—
289H(5,𝔽2)—42no—
290C2×#41—22no—
291C2×#41—24no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—42no—
295C2×#41C23×C1112yes—
296C22×Q8C23×C1111yescharacteristic
297C22×D4—22no—
298C22×D4—22no—
299C22×D4D4×C1112yes—
300C22×D4C23×C1111yescharacteristic
301C23×C4—21no—
302C23×C4D4×C1112yes—
303C23×C4C23×C1111yescharacteristic
304C2×M16C23×C1114yes—
305C4⋊Q8—22no—
306#124—22no—
307#123—24no—
308#123—24no—
309#123—24no—
310#123—22no—
311#123—24no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314C22⋊Q8D4×C1112yes—
315C22⋊Q8D4×C1112yes—
316#121—24no—
317#121—24no—
318#121D4×C1112yes—
319#121D4×C1112yes—
320#120—24no—
321#120—22no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—22no—
326#117—42no—
327#117C23×C1112yes—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4C23×C1112yes—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—24no—
340C2×C42C23×C1112yes—
341#107—24no—
342#106—24no—
343#104—44no—
344#103—24no—
345#102—24no—
346#101—42no—
347#100—24no—
348C22⋊C8—22no—
349C22⋊C8—22no—
350#95—24no—
351C2×C11—21no—
352C2×C11—21no—
353C2×C11—42no—
354C2×C11—44no—
355C2×C11—82no—
356C2×C11#240511yescharacteristic
357C2×C11#302111yescharacteristic
358C2×C11#302211yescharacteristic
359C24—22no—
360C24C2×D4×C1111yescharacteristic
361C24C2×D4×C1112yes—
362#41—24no—
363#41—24no—
364#41—48no—
365#41—48no—
366#41—48no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8C2×D4×C1112yes—
371C2×D4—24no—
372C2×D4—24no—
373C2×D4—24no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—42no—
380C2×D4—48no—
381C2×D4—44no—
382C2×D4—44no—
383C2×D4C2×D4×C1112yes—
384C2×D4C11×#4114yes—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—82no—
399C22×C4C2×D4×C1112yes—
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1112yes—
402C22×C4C2×D4×C1112yes—
403C22×C4C24×C1111yescharacteristic
404M16—24no—
405M16—24no—
406C2×C8—24no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—24no—
412C4⋊C4—42no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4C2×D4×C1112yes—
416C4⋊C4C2×D4×C1112yes—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—42no—
426C22⋊C4—84no—
427C42—22no—
428C42—24no—
429C11#2402511yescharacteristic, direct product factor, Sylow
430C23—22no—
431C23—21no—
432C23—21no—
433C23—22no—
434C23—22no—
435C23—41no—
436C23—41no—
437C23—42no—
438C23—42no—
439C23—44no—
440C23—82no—
441C23—82no—
442C23C11×#12012yes—
443C23C11×#12314yes—
444C23C22×D4×C1111yescharacteristic
445Q8—24no—
446Q8—44no—
447D4—28no—
448D4—24no—
449D4—48no—
450D4—48no—
451D4—42no—
452D4—42no—
453D4—82no—
454D4—82no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—44no—
469C2×C4—42no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4—84no—
477C2×C4C11×#12011yescharacteristic
478C2×C4C11×#12011yescharacteristic
479C2×C4C22×D4×C1112yes—
480C2×C4C2×C11×#4112yes—
481C2×C4C11×H(5,𝔽2)12yes—
482C8—44no—
483C22—21no—
484C22—21no—
485C22—22no—
486C22—24no—
487C22—22no—
488C22—22no—
489C22—44no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—82no—
498C22—164no—
499C22C2×C11×#12011yescharacteristic
500C22C2×C11×#12311yescharacteristic
501C22C11×#53411yescharacteristic
502C4—21no—
503C4—21no—
504C4—42no—
505C4—42no—
506C4—42no—
507C4—42no—
508C4—82no—
509C4—82no—
510C4C11×#54614yes—
511C2—21no—
512C2—21no—
513C2—42no—
514C2—44no—
515C2—82no—
516C2C11×#240511yescharacteristic
517C2C11×#302111yescharacteristic
518C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3485C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3092C2semidirect
3. C11×#2311C2semidirect
4. C11×#2038C2semidirect
5. C11×#1897C2semidirect
6. C11×#1856C2semidirect
7. C11×#1792C2semidirect
8. C11×#1785C2semidirect
20. C2×C11×#117C22semidirect
21. C22×C11×C4⋊C4C22semidirect
26. C11×#428C22semidirect
29. C2×C11×#101C22semidirect
31. C11×#407C22semidirect
32. C11×#391C22semidirect
36. C11×#339C22semidirect
100. #24025C11direct (N × H)
172. #3092C2×C11semidirect
173. #2311C2×C11semidirect
174. #2038C2×C11semidirect
175. #1897C2×C11semidirect
176. #1856C2×C11semidirect
177. #1792C2×C11semidirect
178. #1785C2×C11semidirect
243. C2×#117C22×C11semidirect
244. C22×C4⋊C4C22×C11semidirect
249. #428C22×C11semidirect
252. C2×#101C22×C11semidirect
254. #407C22×C11semidirect
255. #391C22×C11semidirect
259. #339C22×C11semidirect
429. C11#24025direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34852
C11×#30922
C11×#23112
C11×#20382
C11×#18972
C11×#18562
C11×#17922
C11×#17852
#2402511