Finite Group Databasebeta

← C11×#18904 #14596097

Subgroups — C11×#18904 #14596097

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic
2C11×#3229C211yesmaximal, characteristic, complemented
3C11×#3229C211yesmaximal, characteristic, complemented
4C2×C11×#461C211yesmaximal, characteristic
5C11×#1651C214yesmaximal, complemented
6C11×#1643C214yesmaximal, complemented
7C11×#1542C211yesmaximal, characteristic, complemented
8C11×#1481C211yesmaximal, characteristic, complemented
9C11×#1478C211yesmaximal, characteristic
10C22×C11×SD16—21no—
11C11×#554—21no—
12C11×#554—22no—
13C11×#554—22no—
14C11×#554C2212yes—
15D4×Q8×C11—21no—
16D4×Q8×C11C2212yes—
17C11×#544—21no—
18C11×#543—22no—
19C11×#533C2211yescharacteristic
20C11×#533C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8—22no—
23C11×#518—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C11×#498—21no—
26C11×#498C2212yescomplemented
27C11×#487—21no—
28C11×#487C2212yescomplemented
29C11×#483—22no—
30C11×#483—22no—
31C11×#475—22no—
32C11×#475C2214yescomplemented
33C11×#461—22no—
34C11×#461C2214yes—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×#103—21no—
39C11×#333C2212yescomplemented
40C11×#332C2212yescomplemented
41C11×Q8⋊C8C2214yescomplemented
42C11×D4⋊C8C2214yes—
43C22×Q8×C11—22no—
44C22×Q8×C11—21no—
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—21no—
47C2×C11×SD16—24no—
48C2×C11×SD16—44no—
49C22×C8×C11—21no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8D411yescharacteristic
56C11×C4⋊Q8D411yescharacteristic
57C11×C4⋊Q8C2312yes—
58C11×C4⋊Q8C2311yescharacteristic
59C11×C4⋊Q8C2311yescharacteristic
60C11×#125—22no—
61C11×#125—22no—
62C11×#125—21no—
63C11×#125—21no—
64C11×C22⋊Q8—24no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8D412yes—
75C11×C22⋊Q8D412yes—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11D412yes—
79C4×Q8×C11C2312yes—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11D412yes—
87C4×D4×C11C2312yes—
88C11×#117—21no—
89C11×#117—21no—
90C2×C11×C4⋊C4—24no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—21no—
97C2×C42×C11C2311yescharacteristic
98C11×#106—24no—
99C11×#106—24no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2312yes—
103C11×C4⋊C8C2312yes—
104C11×#103—24no—
105C11×#103—24no—
106C11×#103—24no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2312yes—
111#18904C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—21no—
113C2×Q8×C11—24no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—41no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C2×Q8×C11—84no—
121C2×Q8×C11C2×D412yes—
122C2×Q8×C11C2×D412yes—
123C2×D4×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11SD1614yes—
126C2×D4×C11C2×D412yes—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—41no—
133C22×C4×C11—82no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C11×SD16—48no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—42no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4C2×D412yes—
161C11×C4⋊C4C2×D412yes—
162C11×C4⋊C4C2×D412yes—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2411yescharacteristic
175#3501C2×C1111yescharacteristic
176#3229C2×C1111yescharacteristic, complemented
177#3229C2×C1111yescharacteristic, complemented
178C2×#461C2×C1111yescharacteristic
179#1651C2×C1114yescomplemented
180#1643C2×C1114yescomplemented
181#1542C2×C1111yescharacteristic, complemented
182#1481C2×C1111yescharacteristic, complemented
183#1478C2×C1111yescharacteristic
184C23×C11—22no—
185C23×C11—24no—
186C23×C11—81no—
187C23×C11—81no—
188C23×C11#12011yescharacteristic
189Q8×C11—24no—
190Q8×C11—42no—
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—42no—
194Q8×C11—81no—
195Q8×C11—84no—
196Q8×C11—82no—
197D4×C11—22no—
198D4×C11—24no—
199D4×C11C2×SD1614yes—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—44no—
208C2×C4×C11—42no—
209C2×C4×C11—82no—
210C2×C4×C11—81no—
211C2×C4×C11—84no—
212C2×C4×C11—84no—
213C2×C4×C11—82no—
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11C2×SD1612yes—
218C2×C4×C11#13712yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C8×C11—42no—
223C8×C11—42no—
224C8×C11—42no—
225C22×SD16—21no—
226#554—21no—
227#554—22no—
228#554—22no—
229#554C22×C1112yes—
230D4×Q8—21no—
231D4×Q8C22×C1112yes—
232#544—21no—
233#543—22no—
234#533C22×C1111yescharacteristic
235#533C22×C1111yescharacteristic
236C2×C4⋊Q8C22×C1111yescharacteristic
237C2×C22⋊Q8—22no—
238#518—21no—
239C2×C4×D4C22×C1111yescharacteristic
240#498—21no—
241#498C22×C1112yescomplemented
242#487—21no—
243#487C22×C1112yescomplemented
244#483—22no—
245#483—22no—
246#475—22no—
247#475C22×C1114yescomplemented
248#461—22no—
249#461C22×C1114yes—
250#431C22×C1111yescharacteristic
251#431C22×C1111yescharacteristic
252C2×C4⋊C8C22×C1111yescharacteristic
253C2×#103—21no—
254#333C22×C1112yescomplemented
255#332C22×C1112yescomplemented
256Q8⋊C8C22×C1114yescomplemented
257D4⋊C8C22×C1114yes—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—24no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—84no—
264C22×C11#44812yes—
265C22×C11C2×#12011yescharacteristic
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—82no—
275C4×C11#44812yes—
276C4×C11C22×SD1611yescharacteristic
277C4×C11C2×#13711yescharacteristic
278C4×C11#57712yes—
279C22×Q8—22no—
280C22×Q8—21no—
281C22×D4D4×C1111yescharacteristic
282C23×C4—21no—
283C2×SD16—24no—
284C2×SD16—44no—
285C22×C8—21no—
286C4⋊Q8—22no—
287C4⋊Q8—22no—
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8D4×C1111yescharacteristic
292C4⋊Q8D4×C1111yescharacteristic
293C4⋊Q8C23×C1112yes—
294C4⋊Q8C23×C1111yescharacteristic
295C4⋊Q8C23×C1111yescharacteristic
296#125—22no—
297#125—22no—
298#125—21no—
299#125—21no—
300C22⋊Q8—24no—
301C22⋊Q8—24no—
302C22⋊Q8—24no—
303C22⋊Q8—24no—
304C22⋊Q8—22no—
305C22⋊Q8—24no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—22no—
309C22⋊Q8—24no—
310C22⋊Q8D4×C1112yes—
311C22⋊Q8D4×C1112yes—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8D4×C1112yes—
315C4×Q8C23×C1112yes—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—22no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4D4×C1112yes—
323C4×D4C23×C1112yes—
324#117—21no—
325#117—21no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4D4×C1111yescharacteristic
331C2×C22⋊C4—24no—
332C2×C22⋊C4—21no—
333C2×C42C23×C1111yescharacteristic
334#106—24no—
335#106—24no—
336C4⋊C8—21no—
337C4⋊C8—21no—
338C4⋊C8C23×C1112yes—
339C4⋊C8C23×C1112yes—
340#103—24no—
341#103—24no—
342#103—24no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C4×C8—21no—
346C4×C8C23×C1112yes—
347C2×C11—22no—
348C2×C11—44no—
349C2×C11C2×#44811yescharacteristic
350C2×C11#300911yescharacteristic
351C2×C11#302211yescharacteristic
352C24—21no—
353C2×Q8—24no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—41no—
358C2×Q8—42no—
359C2×Q8—42no—
360C2×Q8—84no—
361C2×Q8C2×D4×C1112yes—
362C2×Q8C2×D4×C1112yes—
363C2×D4—21no—
364C2×D4—22no—
365C2×D4C11×SD1614yes—
366C2×D4C2×D4×C1112yes—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—41no—
373C22×C4—82no—
374C22×C4C2×D4×C1111yescharacteristic
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C2×D4×C1111yescharacteristic
377SD16—48no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—42no—
382C4⋊C4—24no—
383C4⋊C4—24no—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4C2×D4×C1112yes—
401C4⋊C4C2×D4×C1112yes—
402C4⋊C4C2×D4×C1112yes—
403C22⋊C4—24no—
404C22⋊C4—24no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C42—22no—
410C42—22no—
411C42C2×D4×C1111yescharacteristic
412C42C2×D4×C1111yescharacteristic
413C42C2×D4×C1111yescharacteristic
414C42C24×C1111yescharacteristic
415C11#1890411yescharacteristic, direct product factor, Sylow
416C23—22no—
417C23—24no—
418C23—81no—
419C23—81no—
420C23C11×#12011yescharacteristic
421Q8—24no—
422Q8—42no—
423Q8—42no—
424Q8—42no—
425Q8—42no—
426Q8—81no—
427Q8—84no—
428Q8—82no—
429D4—22no—
430D4—24no—
431D4C2×C11×SD1614yes—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—82no—
442C2×C4—81no—
443C2×C4—84no—
444C2×C4—84no—
445C2×C4—82no—
446C2×C4C11×#12011yescharacteristic
447C2×C4C11×#12011yescharacteristic
448C2×C4C11×#12011yescharacteristic
449C2×C4C2×C11×SD1612yes—
450C2×C4C11×#13712yes—
451C2×C4C22×D4×C1111yescharacteristic
452C2×C4C22×D4×C1111yescharacteristic
453C2×C4C22×D4×C1111yescharacteristic
454C8—42no—
455C8—42no—
456C8—42no—
457C22—21no—
458C22—21no—
459C22—24no—
460C22—42no—
461C22—42no—
462C22—84no—
463C22C11×#44812yes—
464C22C2×C11×#12011yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—42no—
469C4—42no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—82no—
474C4C11×#44812yes—
475C4C22×C11×SD1611yescharacteristic
476C4C2×C11×#13711yescharacteristic
477C4C11×#57712yes—
478C2—22no—
479C2—44no—
480C2C2×C11×#44811yescharacteristic
481C2C11×#300911yescharacteristic
482C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC22×D4×C11D4
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×#3229C2semidirect
3. C11×#3229C2semidirect
5. C11×#1651C2semidirect
6. C11×#1643C2semidirect
7. C11×#1542C2semidirect
8. C11×#1481C2semidirect
26. C11×#498C22semidirect
28. C11×#487C22semidirect
32. C11×#475C22semidirect
39. C11×#333C22semidirect
40. C11×#332C22semidirect
41. C11×Q8⋊C8C22semidirect
111. #18904C11direct (N × H)
176. #3229C2×C11semidirect
177. #3229C2×C11semidirect
179. #1651C2×C11semidirect
180. #1643C2×C11semidirect
181. #1542C2×C11semidirect
182. #1481C2×C11semidirect
241. #498C22×C11semidirect
243. #487C22×C11semidirect
247. #475C22×C11semidirect
254. #333C22×C11semidirect
255. #332C22×C11semidirect
256. Q8⋊C8C22×C11semidirect
415. C11#18904direct (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×#32292
C2×C11×#4612
C11×#16512
C11×#16432
C11×#15422
C11×#14812
C11×#14782
#1890411