Finite Group Databasebeta

← C11×#18894 #14596087

Subgroups — C11×#18894 #14596087

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic, complemented
2C11×#3208C211yesmaximal, characteristic, complemented
3C11×#3208C211yesmaximal, characteristic, complemented
4C2×C11×#459C211yesmaximal, characteristic
5C11×#1627C214yesmaximal, complemented
6C11×#1622C214yesmaximal, complemented
7C11×#1542C211yesmaximal, characteristic, complemented
8C11×#1481C211yesmaximal, characteristic, complemented
9C11×#1478C211yesmaximal, characteristic, complemented
10C22×C11×D8—21no—
11C11×#554—21no—
12C11×#554—22no—
13C11×#554—22no—
14C11×#554C2212yescomplemented
15D4×Q8×C11—21no—
16D4×Q8×C11C2212yescomplemented
17C11×#544—21no—
18C11×#543—22no—
19C11×#533C2211yescharacteristic
20C11×#533C2211yescharacteristic
21C2×C11×#127C2211yescharacteristic
22C2×C11×C22⋊Q8—22no—
23C11×#518—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C11×#492—21no—
26C11×#492C2212yescomplemented
27C11×#486—21no—
28C11×#486C2212yescomplemented
29C11×#460—22no—
30C11×#460C2214yescomplemented
31C11×#459—22no—
32C11×#459C2214yes—
33C11×#450—22no—
34C11×#450—22no—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#102—21no—
39C11×#333C2212yescomplemented
40C11×#332C2212yescomplemented
41C11×Q8⋊C8C2214yescomplemented
42C11×D4⋊C8C2214yescomplemented
43C22×Q8×C11—22no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—21no—
49C2×C11×SD16—24no—
50C2×C11×SD16—24no—
51C2×C11×D8—24no—
52C2×C11×D8—44no—
53C22×C8×C11—21no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8C2311yescharacteristic
59C11×C4⋊Q8C2311yescharacteristic
60C11×#127—21no—
61C11×#127—21no—
62C11×#127—21no—
63C11×#127C2312yes—
64C11×#125—22no—
65C11×#125—22no—
66C11×#125—21no—
67C11×#125—21no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—24no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8D412yes—
79C11×C22⋊Q8D412yes—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11D412yes—
83C4×Q8×C11C2312yes—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11D412yes—
91C4×D4×C11C2312yes—
92C11×#117—21no—
93C11×#117—21no—
94C2×C11×C4⋊C4—24no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C22⋊C4—24no—
98C2×C11×C22⋊C4—21no—
99C2×C42×C11C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2312yes—
103C11×C4⋊C8C2312yes—
104C11×#102—24no—
105C11×#102—24no—
106C11×#102—24no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2312yes—
111#18894C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—21no—
113C24×C11—41no—
114C2×Q8×C11—24no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—84no—
118C2×Q8×C11C2×D412yes—
119C2×Q8×C11C2×D412yes—
120C2×D4×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—82no—
131C2×D4×C11—82no—
132C2×D4×C11SD1614yescomplemented
133C2×D4×C11C2×D412yes—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—82no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C11×SD16—84no—
144C11×SD16—84no—
145C11×D8—48no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—42no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4C2×D412yes—
165C11×C4⋊C4C2×D412yes—
166C11×C4⋊C4C2×D412yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11C2411yescharacteristic
179#3501C2×C1111yescharacteristic, complemented
180#3208C2×C1111yescharacteristic, complemented
181#3208C2×C1111yescharacteristic, complemented
182C2×#459C2×C1111yescharacteristic
183#1627C2×C1114yescomplemented
184#1622C2×C1114yescomplemented
185#1542C2×C1111yescharacteristic, complemented
186#1481C2×C1111yescharacteristic, complemented
187#1478C2×C1111yescharacteristic, complemented
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—42no—
191C23×C11—81no—
192C23×C11—81no—
193C23×C11—82no—
194C23×C11—82no—
195C23×C11—82no—
196C23×C11#12011yescharacteristic
197Q8×C11—24no—
198Q8×C11—42no—
199Q8×C11—42no—
200Q8×C11—81no—
201Q8×C11—84no—
202D4×C11—22no—
203D4×C11—24no—
204D4×C11—44no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—44no—
208D4×C11—82no—
209D4×C11—82no—
210D4×C11—82no—
211D4×C11C2×SD1614yes—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—44no—
220C2×C4×C11—82no—
221C2×C4×C11—81no—
222C2×C4×C11—84no—
223C2×C4×C11—84no—
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12011yescharacteristic
227C2×C4×C11C2×SD1612yes—
228C2×C4×C11#13712yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C8×C11—42no—
233C8×C11—42no—
234C8×C11—42no—
235C22×D8—21no—
236#554—21no—
237#554—22no—
238#554—22no—
239#554C22×C1112yescomplemented
240D4×Q8—21no—
241D4×Q8C22×C1112yescomplemented
242#544—21no—
243#543—22no—
244#533C22×C1111yescharacteristic
245#533C22×C1111yescharacteristic
246C2×#127C22×C1111yescharacteristic
247C2×C22⋊Q8—22no—
248#518—21no—
249C2×C4×D4C22×C1111yescharacteristic
250#492—21no—
251#492C22×C1112yescomplemented
252#486—21no—
253#486C22×C1112yescomplemented
254#460—22no—
255#460C22×C1114yescomplemented
256#459—22no—
257#459C22×C1114yes—
258#450—22no—
259#450—22no—
260#431C22×C1111yescharacteristic
261#431C22×C1111yescharacteristic
262C2×C4⋊C8C22×C1111yescharacteristic
263C2×#102—21no—
264#333C22×C1112yescomplemented
265#332C22×C1112yescomplemented
266Q8⋊C8C22×C1114yescomplemented
267D4⋊C8C22×C1114yescomplemented
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—24no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—84no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—164no—
278C22×C11#44812yes—
279C22×C11C2×#12011yescharacteristic
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11#44812yes—
289C4×C11C22×SD1611yescharacteristic
290C4×C11C2×#13711yescharacteristic
291C4×C11#57612yes—
292C22×Q8—22no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4D4×C1111yescharacteristic
297C23×C4—21no—
298C2×SD16—24no—
299C2×SD16—24no—
300C2×D8—24no—
301C2×D8—44no—
302C22×C8—21no—
303C4⋊Q8—22no—
304C4⋊Q8—22no—
305C4⋊Q8D4×C1111yescharacteristic
306C4⋊Q8D4×C1111yescharacteristic
307C4⋊Q8C23×C1111yescharacteristic
308C4⋊Q8C23×C1111yescharacteristic
309#127—21no—
310#127—21no—
311#127—21no—
312#127C23×C1112yes—
313#125—22no—
314#125—22no—
315#125—21no—
316#125—21no—
317C22⋊Q8—24no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—24no—
321C22⋊Q8—22no—
322C22⋊Q8—24no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—22no—
326C22⋊Q8—24no—
327C22⋊Q8D4×C1112yes—
328C22⋊Q8D4×C1112yes—
329C4×Q8—21no—
330C4×Q8—21no—
331C4×Q8D4×C1112yes—
332C4×Q8C23×C1112yes—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4D4×C1112yes—
340C4×D4C23×C1112yes—
341#117—21no—
342#117—21no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4D4×C1111yescharacteristic
346C2×C22⋊C4—24no—
347C2×C22⋊C4—21no—
348C2×C42C23×C1111yescharacteristic
349C4⋊C8—21no—
350C4⋊C8—21no—
351C4⋊C8C23×C1112yes—
352C4⋊C8C23×C1112yes—
353#102—24no—
354#102—24no—
355#102—24no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C4×C8—21no—
359C4×C8C23×C1112yes—
360C2×C11—22no—
361C2×C11—44no—
362C2×C11—162no—
363C2×C11C2×#44811yescharacteristic
364C2×C11#300811yescharacteristic
365C2×C11#302111yescharacteristic
366C24—21no—
367C24—41no—
368C2×Q8—24no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—84no—
372C2×Q8C2×D4×C1112yes—
373C2×Q8C2×D4×C1112yes—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—82no—
385C2×D4—82no—
386C2×D4C11×SD1614yescomplemented
387C2×D4C2×D4×C1112yes—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—82no—
394C22×C4C2×D4×C1111yescharacteristic
395C22×C4C2×D4×C1111yescharacteristic
396C22×C4C2×D4×C1111yescharacteristic
397SD16—84no—
398SD16—84no—
399D8—48no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—42no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4C2×D4×C1112yes—
419C4⋊C4C2×D4×C1112yes—
420C4⋊C4C2×D4×C1112yes—
421C22⋊C4—24no—
422C22⋊C4—24no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C42—22no—
428C42—22no—
429C42C2×D4×C1111yescharacteristic
430C42C2×D4×C1111yescharacteristic
431C42C2×D4×C1111yescharacteristic
432C42C24×C1111yescharacteristic
433C11#1889411yescharacteristic, direct product factor, Sylow
434C23—22no—
435C23—24no—
436C23—42no—
437C23—81no—
438C23—81no—
439C23—82no—
440C23—82no—
441C23—82no—
442C23C11×#12011yescharacteristic
443Q8—24no—
444Q8—42no—
445Q8—42no—
446Q8—81no—
447Q8—84no—
448D4—22no—
449D4—24no—
450D4—44no—
451D4—42no—
452D4—42no—
453D4—44no—
454D4—82no—
455D4—82no—
456D4—82no—
457D4C2×C11×SD1614yes—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—44no—
466C2×C4—82no—
467C2×C4—81no—
468C2×C4—84no—
469C2×C4—84no—
470C2×C4C11×#12011yescharacteristic
471C2×C4C11×#12011yescharacteristic
472C2×C4C11×#12011yescharacteristic
473C2×C4C2×C11×SD1612yes—
474C2×C4C11×#13712yes—
475C2×C4C22×D4×C1111yescharacteristic
476C2×C4C22×D4×C1111yescharacteristic
477C2×C4C22×D4×C1111yescharacteristic
478C8—42no—
479C8—42no—
480C8—42no—
481C22—21no—
482C22—21no—
483C22—24no—
484C22—42no—
485C22—42no—
486C22—84no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—164no—
491C22C11×#44812yes—
492C22C2×C11×#12011yescharacteristic
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—42no—
500C4—42no—
501C4C11×#44812yes—
502C4C22×C11×SD1611yescharacteristic
503C4C2×C11×#13711yescharacteristic
504C4C11×#57612yes—
505C2—22no—
506C2—44no—
507C2—162no—
508C2C2×C11×#44811yescharacteristic
509C2C11×#300811yescharacteristic
510C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC2×C11×#459C2
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
1. C11×#3501C2semidirect
2. C11×#3208C2semidirect
3. C11×#3208C2semidirect
5. C11×#1627C2semidirect
6. C11×#1622C2semidirect
7. C11×#1542C2semidirect
8. C11×#1481C2semidirect
9. C11×#1478C2semidirect
14. C11×#554C22semidirect
16. D4×Q8×C11C22semidirect
26. C11×#492C22semidirect
28. C11×#486C22semidirect
30. C11×#460C22semidirect
39. C11×#333C22semidirect
40. C11×#332C22semidirect
41. C11×Q8⋊C8C22semidirect
42. C11×D4⋊C8C22semidirect
111. #18894C11direct (N × H)
132. C2×D4×C11SD16semidirect
179. #3501C2×C11semidirect
180. #3208C2×C11semidirect
181. #3208C2×C11semidirect
183. #1627C2×C11semidirect
184. #1622C2×C11semidirect
185. #1542C2×C11semidirect
186. #1481C2×C11semidirect
187. #1478C2×C11semidirect
239. #554C22×C11semidirect
241. D4×Q8C22×C11semidirect
251. #492C22×C11semidirect
253. #486C22×C11semidirect
255. #460C22×C11semidirect
264. #333C22×C11semidirect
265. #332C22×C11semidirect
266. Q8⋊C8C22×C11semidirect
267. D4⋊C8C22×C11semidirect
386. C2×D4C11×SD16semidirect
433. C11#18894direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C11×#32082
C2×C11×#4592
C11×#16272
C11×#16222
C11×#15422
C11×#14812
C11×#14782
#1889411