Finite Group Databasebeta

← C11×#22474 #14599667

Subgroups — C11×#22474 #14599667

Order 2816.

1196 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C211yesmaximal, characteristic
2C2×C11×#436C211yesmaximal, characteristic, complemented
3C2×C8×D4×C11C211yesmaximal, characteristic, complemented
4C11×#1984C211yesmaximal, characteristic, complemented
5C11×#1984C211yesmaximal, characteristic, complemented
6C11×#1870C212yesmaximal, complemented
7C11×#1869C212yesmaximal, complemented
8C11×#1818C212yesmaximal, complemented
9C11×#1797C211yesmaximal, characteristic, complemented
10C4×C11×C22⋊C8C211yesmaximal, characteristic, complemented
11C11×#1729C212yesmaximal, complemented
12C22×C11×M16C2212yes—
13C23×C8×C11C2212yes—
14C11×#529—24no—
15C11×#529—24no—
16C2×C11×#126C412yes—
17C2×C11×#125C411yescharacteristic
18C2×C11×#124C411yescharacteristic
19C2×C11×#123C412yes—
20C2×C11×C22⋊Q8C411yescharacteristic
21C2×C11×#121C411yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2212yes—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117C2212yes—
26C22×C42×C11C2211yescharacteristic
27C11×#436—24no—
28C8×D4×C11—24no—
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2212yes—
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C4×C8×C11C2211yescharacteristic
37C2×C4×C8×C11C2211yescharacteristic
38C11×#336C2212yes—
39C11×#336C2212yes—
40C11×#336C2212yes—
41C11×#336C2212yes—
42C11×#336C2211yescharacteristic
43C11×#336C2212yes—
44C11×#336C2211yescharacteristic
45C22×Q8×C11C2×C411yescharacteristic
46C22×D4×C11C2×C412yes—
47C22×D4×C11C2×C411yescharacteristic
48C23×C4×C11C2×C411yescharacteristic
49C23×C4×C11C2×C411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C2×C11×M16—24no—
53C2×C11×M16—24no—
54C2×C11×M16—42no—
55C22×C8×C11—24no—
56C22×C8×C11—24no—
57C22×C8×C11—42no—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2312yes—
61C22×C8×C11C2312yes—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×#126—28no—
65C11×#125—24no—
66C11×#124—24no—
67C11×#123—28no—
68C11×C22⋊Q8—24no—
69C11×#121—24no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×D4×C11—24no—
73C4×D4×C11—24no—
74C4×D4×C11D414yes—
75C4×D4×C11D414yes—
76C11×#117—24no—
77C11×#117—24no—
78C2×C11×C4⋊C4C2×C412yes—
79C2×C11×C4⋊C4C2×C412yes—
80C2×C11×C4⋊C4C2×C412yes—
81C2×C11×C4⋊C4C2×C411yescharacteristic
82C2×C11×C4⋊C4C2×C412yes—
83C2×C11×C4⋊C4C2×C411yescharacteristic
84C2×C11×C22⋊C4C2×C412yes—
85C2×C11×C22⋊C4C2×C412yes—
86C2×C11×C22⋊C4C2×C412yes—
87C2×C11×C22⋊C4C2×C412yes—
88C2×C11×C22⋊C4C2×C412yes—
89C2×C42×C11—22no—
90C2×C42×C11—22no—
91C2×C42×C11C2×C411yescharacteristic
92C2×C42×C11C2×C411yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2312yes—
95C2×C42×C11C2311yescharacteristic
96C11×C4⋊C8—22no—
97C11×C4⋊C8—22no—
98C11×C22⋊C8—24no—
99C11×C22⋊C8—24no—
100C11×C22⋊C8—22no—
101C11×C22⋊C8—22no—
102C11×C22⋊C8—42no—
103C4×C8×C11—22no—
104C4×C8×C11—22no—
105#22474C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11C22×C412yes—
107C24×C11C22×C411yescharacteristic
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×D4×C11—24no—
112C2×D4×C11—24no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—42no—
116C2×D4×C11C22⋊C414yes—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—41no—
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C412yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C412yes—
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C2×D414yes—
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2411yescharacteristic
144C11×M16—48no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—48no—
162C2×C8×C11#4112yes—
163C2×C8×C11#4112yes—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4C22⋊C414yes—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4C22⋊C418yes—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11C2×D412yes—
182C42×C11C2×D412yes—
183C2×#529C2×C1111yescharacteristic
184C2×#436C2×C1111yescharacteristic, complemented
185C2×C8×D4C2×C1111yescharacteristic, complemented
186#1984C2×C1111yescharacteristic, complemented
187#1984C2×C1111yescharacteristic, complemented
188#1870C2×C1112yescomplemented
189#1869C2×C1112yescomplemented
190#1818C2×C1112yescomplemented
191#1797C2×C1111yescharacteristic, complemented
192C4×C22⋊C8C2×C1111yescharacteristic, complemented
193#1729C2×C1112yescomplemented
194C23×C11—21no—
195C23×C11—22no—
196C23×C11—21no—
197C23×C11—22no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—21no—
205C23×C11—22no—
206C23×C11C2×C22⋊C414yes—
207C23×C11#13112yes—
208C23×C11C23×C411yescharacteristic
209Q8×C11—44no—
210D4×C11—28no—
211D4×C11—48no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—44no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—44no—
241C2×C4×C11C2×C22⋊C412yes—
242C2×C4×C11C2×C22⋊C414yes—
243C2×C4×C11C2×C22⋊C412yes—
244C2×C4×C11#13112yes—
245C2×C4×C11#13112yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C8×C11—22no—
253C8×C11—22no—
254C8×C11—42no—
255C8×C11—42no—
256C8×C11—41no—
257C8×C11—41no—
258C22×M16C22×C1112yes—
259C23×C8C22×C1112yes—
260#529—24no—
261#529—24no—
262C2×#126C4×C1112yes—
263C2×#125C4×C1111yescharacteristic
264C2×#124C4×C1111yescharacteristic
265C2×#123C4×C1112yes—
266C2×C22⋊Q8C4×C1111yescharacteristic
267C2×#121C4×C1111yescharacteristic
268C2×C4×Q8C22×C1111yescharacteristic
269C2×C4×D4C22×C1112yes—
270C2×C4×D4C22×C1111yescharacteristic
271C2×#117C22×C1112yes—
272C22×C42C22×C1111yescharacteristic
273#436—24no—
274C8×D4—24no—
275C2×C4⋊C8C22×C1111yescharacteristic
276C2×C4⋊C8C22×C1111yescharacteristic
277C2×C22⋊C8C22×C1112yes—
278C2×C22⋊C8C22×C1112yes—
279C2×C22⋊C8C22×C1111yescharacteristic
280C2×C22⋊C8C22×C1111yescharacteristic
281C2×C22⋊C8C22×C1112yes—
282C2×C4×C8C22×C1111yescharacteristic
283C2×C4×C8C22×C1111yescharacteristic
284#336C22×C1112yes—
285#336C22×C1111yescharacteristic
286#336C22×C1112yes—
287#336C22×C1112yes—
288#336C22×C1112yes—
289#336C22×C1112yes—
290#336C22×C1111yescharacteristic
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—42no—
300C22×C11—41no—
301C22×C11—42no—
302C22×C11—41no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11C22×C22⋊C411yescharacteristic
306C22×C11C4×#4111yescharacteristic
307C22×C11#52011yescharacteristic
308C22×C11C2×#13111yescharacteristic
309C22×C11C2×#13111yescharacteristic
310C22×C11C2×#13111yescharacteristic
311C22×C11#56811yescharacteristic
312C4×C11—24no—
313C4×C11—22no—
314C4×C11—41no—
315C4×C11—41no—
316C4×C11—42no—
317C4×C11—41no—
318C4×C11—42no—
319C4×C11#40814yes—
320C4×C11#54611yescharacteristic
321C4×C11#54611yescharacteristic
322C4×C11#54711yescharacteristic
323C4×C11#54711yescharacteristic
324C22×Q8C2×C4×C1111yescharacteristic
325C22×D4C2×C4×C1112yes—
326C22×D4C2×C4×C1111yescharacteristic
327C23×C4C2×C4×C1111yescharacteristic
328C23×C4C2×C4×C1111yescharacteristic
329C23×C4C23×C1111yescharacteristic
330C23×C4C23×C1112yes—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16—42no—
334C22×C8—24no—
335C22×C8—24no—
336C22×C8—42no—
337C22×C8C23×C1112yes—
338C22×C8C23×C1112yes—
339C22×C8C23×C1111yescharacteristic
340C22×C8C23×C1111yescharacteristic
341C22×C8C23×C1111yescharacteristic
342C22×C8C23×C1111yescharacteristic
343#126—28no—
344#125—24no—
345#124—24no—
346#123—28no—
347C22⋊Q8—24no—
348#121—24no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×D4—24no—
352C4×D4—24no—
353C4×D4D4×C1114yes—
354C4×D4D4×C1114yes—
355#117—24no—
356#117—24no—
357C2×C4⋊C4C2×C4×C1112yes—
358C2×C4⋊C4C2×C4×C1112yes—
359C2×C4⋊C4C2×C4×C1112yes—
360C2×C4⋊C4C2×C4×C1111yescharacteristic
361C2×C4⋊C4C2×C4×C1112yes—
362C2×C4⋊C4C2×C4×C1111yescharacteristic
363C2×C22⋊C4C2×C4×C1112yes—
364C2×C22⋊C4C2×C4×C1112yes—
365C2×C22⋊C4C2×C4×C1112yes—
366C2×C22⋊C4C2×C4×C1112yes—
367C2×C22⋊C4C2×C4×C1112yes—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42C2×C4×C1111yescharacteristic
371C2×C42C2×C4×C1111yescharacteristic
372C2×C42C23×C1111yescharacteristic
373C2×C42C23×C1112yes—
374C2×C42C23×C1111yescharacteristic
375C4⋊C8—22no—
376C4⋊C8—22no—
377C22⋊C8—24no—
378C22⋊C8—24no—
379C22⋊C8—22no—
380C22⋊C8—22no—
381C22⋊C8—42no—
382C4×C8—22no—
383C4×C8—22no—
384C2×C11—44no—
385C2×C11—42no—
386C2×C11#233911yescharacteristic
387C2×C11C2×#40811yescharacteristic
388C2×C11#288011yescharacteristic
389C2×C11#296611yescharacteristic
390C2×C11#296911yescharacteristic
391C2×C11#299311yescharacteristic
392C2×C11#299411yescharacteristic
393C24C22×C4×C1112yes—
394C24C22×C4×C1111yescharacteristic
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—42no—
403C2×D4C11×C22⋊C414yes—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—41no—
420C22×C4C22×C4×C1111yescharacteristic
421C22×C4C22×C4×C1111yescharacteristic
422C22×C4C22×C4×C1111yescharacteristic
423C22×C4C22×C4×C1112yes—
424C22×C4C22×C4×C1112yes—
425C22×C4C22×C4×C1111yescharacteristic
426C22×C4C22×C4×C1112yes—
427C22×C4C22×C4×C1111yescharacteristic
428C22×C4C2×D4×C1114yes—
429C22×C4C2×D4×C1114yes—
430C22×C4C24×C1111yescharacteristic
431M16—48no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—48no—
449C2×C8C11×#4112yes—
450C2×C8C11×#4112yes—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—24no—
456C4⋊C4C11×C22⋊C414yes—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4C11×C22⋊C418yes—
462C42—22no—
463C42—22no—
464C42—21no—
465C42—21no—
466C42—22no—
467C42—22no—
468C42C2×D4×C1112yes—
469C42C2×D4×C1112yes—
470C11#2247411yescharacteristic, direct product factor, Sylow
471C23—21no—
472C23—21no—
473C23—22no—
474C23—21no—
475C23—22no—
476C23—21no—
477C23—21no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—21no—
482C23—22no—
483C23C2×C11×C22⋊C414yes—
484C23C11×#13112yes—
485C23C23×C4×C1111yescharacteristic
486Q8—44no—
487D4—28no—
488D4—48no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4C2×C11×C22⋊C412yes—
519C2×C4C2×C11×C22⋊C414yes—
520C2×C4C2×C11×C22⋊C412yes—
521C2×C4C11×#13112yes—
522C2×C4C11×#13112yes—
523C2×C4C22×D4×C1111yescharacteristic
524C2×C4C22×D4×C1111yescharacteristic
525C2×C4C2×C11×#4111yescharacteristic
526C2×C4C2×C11×#4111yescharacteristic
527C2×C4C11×H(5,𝔽2)11yescharacteristic
528C2×C4C11×2−1+411yescharacteristic
529C8—22no—
530C8—22no—
531C8—42no—
532C8—42no—
533C8—41no—
534C8—41no—
535C22—22no—
536C22—22no—
537C22—24no—
538C22—24no—
539C22—22no—
540C22—24no—
541C22—42no—
542C22—41no—
543C22—42no—
544C22—41no—
545C22—42no—
546C22—42no—
547C22—41no—
548C22—41no—
549C22C22×C11×C22⋊C411yescharacteristic
550C22C4×C11×#4111yescharacteristic
551C22C11×#52011yescharacteristic
552C22C2×C11×#13111yescharacteristic
553C22C2×C11×#13111yescharacteristic
554C22C2×C11×#13111yescharacteristic
555C22C11×#56811yescharacteristic
556C4—24no—
557C4—22no—
558C4—41no—
559C4—41no—
560C4—42no—
561C4—41no—
562C4—42no—
563C4C11×#40814yes—
564C4C11×#54611yescharacteristic
565C4C11×#54611yescharacteristic
566C4C11×#54711yescharacteristic
567C4C11×#54711yescharacteristic
568C2—42no—
569C2—44no—
570C2C11×#233911yescharacteristic
571C2C2×C11×#40811yescharacteristic
572C2C11×#288011yescharacteristic
573C2C11×#296611yescharacteristic
574C2C11×#296911yescharacteristic
575C2C11×#299311yescharacteristic
576C2C11×#299411yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC2×C11×#121C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#436C2semidirect
3. C2×C8×D4×C11C2semidirect
4. C11×#1984C2semidirect
5. C11×#1984C2semidirect
6. C11×#1870C2semidirect
7. C11×#1869C2semidirect
8. C11×#1818C2semidirect
9. C11×#1797C2semidirect
10. C4×C11×C22⋊C8C2semidirect
11. C11×#1729C2semidirect
105. #22474C11direct (N × H)
184. C2×#436C2×C11semidirect
185. C2×C8×D4C2×C11semidirect
186. #1984C2×C11semidirect
187. #1984C2×C11semidirect
188. #1870C2×C11semidirect
189. #1869C2×C11semidirect
190. #1818C2×C11semidirect
191. #1797C2×C11semidirect
192. C4×C22⋊C8C2×C11semidirect
193. #1729C2×C11semidirect
470. C11#22474direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C2×C11×#4362
C2×C8×D4×C112
C11×#19842
C11×#18702
C11×#18692
C11×#18182
C11×#17972
C4×C11×C22⋊C82
C11×#17292
#2247411