Finite Group Databasebeta

← C11×#22487 #14599680

Subgroups — C11×#22487 #14599680

Order 2816.

1258 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
1C2×C11×#554C211yesmaximal, characteristic
2C2×C8×D4×C11C211yesmaximal, characteristic
3D4×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#1990C211yesmaximal, characteristic, complemented
5C11×#1987C211yesmaximal, characteristic, complemented
6C11×#1892C212yesmaximal, complemented
7C11×#1872C212yesmaximal, complemented
8C11×#1824C212yesmaximal, complemented
9C11×#1803C211yesmaximal, characteristic, complemented
10C4×C11×#103C211yesmaximal, characteristic, complemented
11C2×C11×#340C212yesmaximal, complemented
12C23×C8×C11C2212yes—
13C11×#554—24no—
14C11×#554C418yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4C2212yes—
24C22×C11×C4⋊C4C2212yes—
25C8×D4×C11—24no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×C22⋊C8C2212yes—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#389—21no—
33C11×#385—22no—
34C11×#384C2211yescharacteristic
35C11×#380C2212yes—
36C4×C11×C4⋊C4C2211yescharacteristic
37C11×#340C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2211yescharacteristic
42C11×#340C2212yes—
43C11×#340C2211yescharacteristic
44C22×Q8×C11—21no—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11C2312yes—
50C22×C8×C11—24no—
51C22×C8×C11—24no—
52C22×C8×C11—42no—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8C2×C414yescomplemented
58C11×#125—28no—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—216no—
61C11×C22⋊Q8C2×C418yescomplemented
62C4×Q8×C11—22no—
63C4×Q8×C11C2×C414yescomplemented
64C4×D4×C11—28no—
65C4×D4×C11—44no—
66C4×D4×C11C2×C414yes—
67C4×D4×C11D414yes—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—42no—
78C2×C11×C4⋊C4C2×C418yescomplemented
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4D412yes—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C11×C4⋊C8—22no—
92C11×#103—22no—
93C11×#103—22no—
94C11×#103—42no—
95C11×C22⋊C8—24no—
96C4×C8×C11—22no—
97C11×#95—21no—
98C11×#95—22no—
99#22487C1111yesmaximal, characteristic, direct product factor, Sylow
100C24×C11C2×D412yes—
101C2×Q8×C11—24no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—81no—
108C2×Q8×C11—81no—
109C2×Q8×C11C22×C412yes—
110C2×D4×C11C22⋊C414yes—
111C2×D4×C11SD1614yes—
112C2×D4×C11Q1614yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—28no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—44no—
125C22×C4×C11—44no—
126C22×C4×C11—82no—
127C22×C4×C11—82no—
128C22×C4×C11—82no—
129C22×C4×C11C22×C414yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D414yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—21no—
141C2×C8×C11—22no—
142C2×C8×C11—21no—
143C2×C8×C11—48no—
144C2×C8×C11#4112yes—
145C11×C4⋊C4—28no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—44no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—81no—
159C11×C4⋊C4C22⋊C414yes—
160C11×C4⋊C4C22×C412yes—
161C11×C4⋊C4C22×C414yes—
162C11×C4⋊C4#4112yes—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—44no—
165C11×C22⋊C4C22⋊C418yes—
166C42×C11—24no—
167C42×C11—42no—
168C42×C11C22×C412yes—
169C42×C11C2×D412yes—
170C2×#554C2×C1111yescharacteristic
171C2×C8×D4C2×C1111yescharacteristic
172D4×C4⋊C4C2×C1111yescharacteristic
173#1990C2×C1111yescharacteristic, complemented
174#1987C2×C1111yescharacteristic, complemented
175#1892C2×C1112yescomplemented
176#1872C2×C1112yescomplemented
177#1824C2×C1112yescomplemented
178#1803C2×C1111yescharacteristic, complemented
179C4×#103C2×C1111yescharacteristic, complemented
180C2×#340C2×C1112yescomplemented
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11C2×C22⋊C414yes—
186C23×C11C2×SD1614yes—
187C23×C11C2×Q1614yes—
188C23×C11C22×D411yescharacteristic
189Q8×C11—22no—
190Q8×C11—22no—
191Q8×C11—41no—
192Q8×C11—41no—
193Q8×C11—84no—
194D4×C11#103116yescomplemented
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—22no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—88no—
222C2×C4×C11—88no—
223C2×C4×C11C2×C22⋊C412yes—
224C2×C4×C11C2×C22⋊C414yes—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C2×SD1612yes—
227C2×C4×C11C2×Q1612yes—
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C8×C11—22no—
235C8×C11—42no—
236C8×C11—41no—
237C23×C8C22×C1112yes—
238#554—24no—
239#554C4×C1118yescomplemented
240C2×C4⋊Q8C22×C1111yescharacteristic
241C2×#125—21no—
242C2×C22⋊Q8—22no—
243C2×C22⋊Q8C22×C1112yes—
244C2×C4×Q8C22×C1111yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4C22×C1111yescharacteristic
248C22×C4⋊C4C22×C1112yes—
249C22×C4⋊C4C22×C1112yes—
250C8×D4—24no—
251C2×C4⋊C8C22×C1111yescharacteristic
252C2×#103C22×C1111yescharacteristic
253C2×#103C22×C1111yescharacteristic
254C2×#103C22×C1112yes—
255C2×C22⋊C8C22×C1112yes—
256C2×C4×C8C22×C1111yescharacteristic
257#389—21no—
258#385—22no—
259#384C22×C1111yescharacteristic
260#380C22×C1112yes—
261C4×C4⋊C4C22×C1111yescharacteristic
262#340C22×C1112yes—
263#340C22×C1111yescharacteristic
264#340C22×C1112yes—
265#340C22×C1112yes—
266#340C22×C1112yes—
267#340C22×C1112yes—
268#340C22×C1111yescharacteristic
269C22×C11—24no—
270C22×C11—24no—
271C22×C11—24no—
272C22×C11—24no—
273C22×C11—24no—
274C22×C11—24no—
275C22×C11C2×#10318yes—
276C22×C11C22×C22⋊C411yescharacteristic
277C22×C11#54611yescharacteristic
278C22×C11#54711yescharacteristic
279C22×C11C22×SD1611yescharacteristic
280C22×C11C22×Q1611yescharacteristic
281C22×C11#57611yescharacteristic
282C22×C11#57711yescharacteristic
283C4×C11—24no—
284C4×C11—22no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—44no—
288C4×C11—42no—
289C4×C11—81no—
290C4×C11—82no—
291C4×C11C2×#10314yes—
292C4×C11C4×#4111yescharacteristic
293C4×C11#52011yescharacteristic
294C4×C11#54611yescharacteristic
295C4×C11#54711yescharacteristic
296C22×Q8—21no—
297C22×Q8C23×C1111yescharacteristic
298C22×D4D4×C1111yescharacteristic
299C23×C4—22no—
300C23×C4—22no—
301C23×C4C23×C1112yes—
302C22×C8—24no—
303C22×C8—24no—
304C22×C8—42no—
305C22×C8C23×C1112yes—
306C22×C8C23×C1111yescharacteristic
307C22×C8C23×C1111yescharacteristic
308C4⋊Q8—22no—
309C4⋊Q8C2×C4×C1114yescomplemented
310#125—28no—
311C22⋊Q8—24no—
312C22⋊Q8—216no—
313C22⋊Q8C2×C4×C1118yescomplemented
314C4×Q8—22no—
315C4×Q8C2×C4×C1114yescomplemented
316C4×D4—28no—
317C4×D4—44no—
318C4×D4C2×C4×C1114yes—
319C4×D4D4×C1114yes—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4C2×C4×C1118yescomplemented
331C2×C4⋊C4D4×C1111yescharacteristic
332C2×C4⋊C4C23×C1112yes—
333C2×C4⋊C4C23×C1111yescharacteristic
334C2×C4⋊C4C23×C1111yescharacteristic
335C2×C4⋊C4C23×C1112yes—
336C2×C4⋊C4C23×C1111yescharacteristic
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4D4×C1112yes—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42C23×C1111yescharacteristic
343C4⋊C8—22no—
344#103—22no—
345#103—22no—
346#103—42no—
347C22⋊C8—24no—
348C4×C8—22no—
349#95—21no—
350#95—22no—
351C2×C11—28no—
352C2×C11#233911yescharacteristic
353C2×C11C22×#10311yescharacteristic
354C2×C11#289711yescharacteristic
355C2×C11#329511yescharacteristic
356C2×C11#329911yescharacteristic
357C2×C11#333511yescharacteristic
358C2×C11#333811yescharacteristic
359C24C2×D4×C1112yes—
360C2×Q8—24no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—81no—
367C2×Q8—81no—
368C2×Q8C22×C4×C1112yes—
369C2×D4C11×C22⋊C414yes—
370C2×D4C11×SD1614yes—
371C2×D4C11×Q1614yes—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—28no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—44no—
384C22×C4—44no—
385C22×C4—82no—
386C22×C4—82no—
387C22×C4—82no—
388C22×C4C22×C4×C1114yes—
389C22×C4C2×D4×C1111yescharacteristic
390C22×C4C2×D4×C1112yes—
391C22×C4C2×D4×C1114yes—
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C24×C1111yescharacteristic
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—22no—
398C2×C8—21no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—21no—
402C2×C8—48no—
403C2×C8C11×#4112yes—
404C4⋊C4—28no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—28no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—44no—
416C4⋊C4—42no—
417C4⋊C4—81no—
418C4⋊C4C11×C22⋊C414yes—
419C4⋊C4C22×C4×C1112yes—
420C4⋊C4C22×C4×C1114yes—
421C4⋊C4C11×#4112yes—
422C22⋊C4—28no—
423C22⋊C4—44no—
424C22⋊C4C11×C22⋊C418yes—
425C42—24no—
426C42—42no—
427C42C22×C4×C1112yes—
428C42C2×D4×C1112yes—
429C11#2248711yescharacteristic, direct product factor, Sylow
430C23—22no—
431C23—22no—
432C23—22no—
433C23—22no—
434C23C2×C11×C22⋊C414yes—
435C23C2×C11×SD1614yes—
436C23C2×C11×Q1614yes—
437C23C22×D4×C1111yescharacteristic
438Q8—22no—
439Q8—22no—
440Q8—41no—
441Q8—41no—
442Q8—84no—
443D4C11×#103116yescomplemented
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—88no—
471C2×C4—88no—
472C2×C4C2×C11×C22⋊C412yes—
473C2×C4C2×C11×C22⋊C414yes—
474C2×C4C2×C11×C22⋊C412yes—
475C2×C4C2×C11×SD1612yes—
476C2×C4C2×C11×Q1612yes—
477C2×C4C23×C4×C1111yescharacteristic
478C2×C4C22×D4×C1111yescharacteristic
479C2×C4C2×C11×#4111yescharacteristic
480C2×C4C2×C11×#4111yescharacteristic
481C2×C4C11×H(5,𝔽2)11yescharacteristic
482C2×C4C11×2−1+411yescharacteristic
483C8—22no—
484C8—42no—
485C8—41no—
486C22—24no—
487C22—24no—
488C22—24no—
489C22—24no—
490C22—24no—
491C22—24no—
492C22C2×C11×#10318yes—
493C22C22×C11×C22⋊C411yescharacteristic
494C22C11×#54611yescharacteristic
495C22C11×#54711yescharacteristic
496C22C22×C11×SD1611yescharacteristic
497C22C22×C11×Q1611yescharacteristic
498C22C11×#57611yescharacteristic
499C22C11×#57711yescharacteristic
500C4—22no—
501C4—24no—
502C4—42no—
503C4—44no—
504C4—42no—
505C4—42no—
506C4—82no—
507C4—81no—
508C4C2×C11×#10314yes—
509C4C4×C11×#4111yescharacteristic
510C4C11×#52011yescharacteristic
511C4C11×#54611yescharacteristic
512C4C11×#54711yescharacteristic
513C2—28no—
514C2C11×#233911yescharacteristic
515C2C22×C11×#10311yescharacteristic
516C2C11×#289711yescharacteristic
517C2C11×#329511yescharacteristic
518C2C11×#329911yescharacteristic
519C2C11×#333511yescharacteristic
520C2C11×#333811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1990C2semidirect
5. C11×#1987C2semidirect
6. C11×#1892C2semidirect
7. C11×#1872C2semidirect
8. C11×#1824C2semidirect
9. C11×#1803C2semidirect
10. C4×C11×#103C2semidirect
11. C2×C11×#340C2semidirect
14. C11×#554C4semidirect
57. C11×C4⋊Q8C2×C4semidirect
61. C11×C22⋊Q8C2×C4semidirect
63. C4×Q8×C11C2×C4semidirect
78. C2×C11×C4⋊C4C2×C4semidirect
99. #22487C11direct (N × H)
173. #1990C2×C11semidirect
174. #1987C2×C11semidirect
175. #1892C2×C11semidirect
176. #1872C2×C11semidirect
177. #1824C2×C11semidirect
178. #1803C2×C11semidirect
179. C4×#103C2×C11semidirect
180. C2×#340C2×C11semidirect
194. D4×C11#103semidirect
239. #554C4×C11semidirect
309. C4⋊Q8C2×C4×C11semidirect
313. C22⋊Q8C2×C4×C11semidirect
315. C4×Q8C2×C4×C11semidirect
330. C2×C4⋊C4C2×C4×C11semidirect
429. C11#22487direct (N × H)
443. D4C11×#103semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5542
C2×C8×D4×C112
D4×C11×C4⋊C42
C11×#19902
C11×#19872
C11×#18922
C11×#18722
C11×#18242
C11×#18032
C4×C11×#1032
C2×C11×#3402
#2248711