Finite Group Databasebeta

← C11×#18083 #14595276

Subgroups — C11×#18083 #14595276

Order 2816.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3172C211yesmaximal, characteristic
2C11×#2994C211yesmaximal, characteristic
3C11×#2986C211yesmaximal, characteristic, complemented
4C11×#1593C211yesmaximal, characteristic, complemented
5C11×#1590C211yesmaximal, characteristic, complemented
6C11×#1588C211yesmaximal, characteristic, complemented
7C11×#1587C211yesmaximal, characteristic, complemented
8C11×#1584C211yesmaximal, characteristic, complemented
9C11×#1582C211yesmaximal, characteristic, complemented
10C11×SD16⋊C8C211yesmaximal, characteristic, complemented
11C8×C11×Q16C211yesmaximal, characteristic, complemented
12C11×#1565C211yesmaximal, characteristic, complemented
13C11×#1482C211yesmaximal, characteristic
14C11×#1481C211yesmaximal, characteristic, complemented
15C11×#1453C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#529C2211yescharacteristic
18C11×#501C411yescharacteristic
19C11×#497C411yescharacteristic
20C11×#491C411yescharacteristic
21C11×#489C411yescharacteristic
22C11×#470C411yescharacteristic
23C11×#470C411yescharacteristic
24C11×#468C411yescharacteristic
25C11×#468C411yescharacteristic
26C11×#446—21no—
27C11×#446C2211yescharacteristic
28C11×#446C2211yescharacteristic
29C11×#446C2211yescharacteristic
30C8×Q8×C11—21no—
31C8×Q8×C11C2211yescharacteristic
32C8×Q8×C11C2211yescharacteristic
33C8×Q8×C11C2211yescharacteristic
34C4×C11×Q16C2211yescharacteristic
35C4×C11×Q16C2211yescharacteristic
36C4×C11×SD16C2211yescharacteristic
37C4×C11×SD16C2211yescharacteristic
38C11×#436C2211yescharacteristic
39C11×#435—21no—
40C8×D4×C11—21no—
41C8×D4×C11C2211yescharacteristic
42C11×#433—21no—
43C11×#433—21no—
44C11×#433—21no—
45C11×#431C2211yescharacteristic
46C11×#431C2211yescharacteristic
47C11×#431C2211yescharacteristic
48C11×#424—21no—
49C2×C11×C4⋊C8C2211yescharacteristic
50C4×C11×M16C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#334C2211yescharacteristic
54C11×#334C2211yescharacteristic
55C11×Q8⋊C8C2211yescharacteristic
56C11×Q8⋊C8C2211yescharacteristic
57C11×Q8⋊C8C2211yescharacteristic
58C11×Q8⋊C8C2211yescharacteristic
59C11×Q8⋊C8C2211yescharacteristic
60C11×Q8⋊C8C2211yescharacteristic
61C11×D4⋊C8C2211yescharacteristic
62C11×D4⋊C8C2211yescharacteristic
63C11×#322C2211yescharacteristic
64C11×#322C2211yescharacteristic
65C11×#322C2211yescharacteristic
66C82×C11C2211yescharacteristic
67C2×C11×Q16C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×M16—21no—
72C2×C11×M16C2×C411yescharacteristic
73C2×C11×M16C2×C411yescharacteristic
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C11×C4⋊Q8C2×C411yescharacteristic
77C11×C4⋊Q8C2×C411yescharacteristic
78C11×#126—21no—
79C11×#125—21no—
80C11×#125C2×C411yescharacteristic
81C11×#124C2×C411yescharacteristic
82C11×#123—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8C2×C411yescharacteristic
85C11×C22⋊Q8C2×C411yescharacteristic
86C11×C22⋊Q8C2×C411yescharacteristic
87C11×#121C2×C411yescharacteristic
88C4×Q8×C11—21no—
89C4×Q8×C11C2311yescharacteristic
90C4×Q8×C11C2311yescharacteristic
91C4×Q8×C11C2311yescharacteristic
92C4×D4×C11—21no—
93C4×D4×C11C2311yescharacteristic
94C11×#117—21no—
95C11×#117—21no—
96C2×C42×C11C2311yescharacteristic
97C11×#107C2×C411yescharacteristic
98C11×#107C2×C411yescharacteristic
99C11×#106C2×C411yescharacteristic
100C11×#106C2×C411yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8D411yescharacteristic
110C11×C4⋊C8D411yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×C4⋊C8C2311yescharacteristic
113C11×C4⋊C8C2311yescharacteristic
114C11×C4⋊C8C2311yescharacteristic
115C11×#103C2×C411yescharacteristic
116C11×#103C2×C411yescharacteristic
117C11×#103C2×C411yescharacteristic
118C11×#103C2×C411yescharacteristic
119C11×#103C2×C411yescharacteristic
120C11×#103C2×C411yescharacteristic
121C11×#102C2×C411yescharacteristic
122C11×#102C2×C411yescharacteristic
123C11×C22⋊C8—21no—
124C11×C22⋊C8—21no—
125C11×C22⋊C8—21no—
126C11×C22⋊C8—21no—
127C11×C22⋊C8D411yescharacteristic
128C11×C22⋊C8D411yescharacteristic
129C11×#97—21no—
130C11×#97—21no—
131C11×#97—21no—
132C11×#97C2×C411yescharacteristic
133C11×#97C2×C411yescharacteristic
134C4×C8×C11—21no—
135C4×C8×C11—21no—
136C4×C8×C11—21no—
137C4×C8×C11—21no—
138C4×C8×C11C2311yescharacteristic
139C4×C8×C11C2311yescharacteristic
140C4×C8×C11C2311yescharacteristic
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#18083C1111yesmaximal, characteristic, direct product factor, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C11×Q16—22no—
156C11×Q16—41no—
157C11×SD16—22no—
158C11×SD16—41no—
159C11×M16—22no—
160C11×M16—41no—
161C11×M16—81no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—81no—
169C2×C8×C11—81no—
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4C22×C411yescharacteristic
190C11×C4⋊C4C22×C411yescharacteristic
191C11×C4⋊C4C22×C411yescharacteristic
192C11×C4⋊C4C22×C411yescharacteristic
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11C22×C411yescharacteristic
204C42×C11C2×D411yescharacteristic
205C42×C11#4111yescharacteristic
206C42×C11C2411yescharacteristic
207#3172C2×C1111yescharacteristic
208#2994C2×C1111yescharacteristic
209#2986C2×C1111yescharacteristic, complemented
210#1593C2×C1111yescharacteristic, complemented
211#1590C2×C1111yescharacteristic, complemented
212#1588C2×C1111yescharacteristic, complemented
213#1587C2×C1111yescharacteristic, complemented
214#1584C2×C1111yescharacteristic, complemented
215#1582C2×C1111yescharacteristic, complemented
216SD16⋊C8C2×C1111yescharacteristic, complemented
217C8×Q16C2×C1111yescharacteristic, complemented
218#1565C2×C1111yescharacteristic, complemented
219#1482C2×C1111yescharacteristic
220#1481C2×C1111yescharacteristic, complemented
221#1453C2×C1111yescharacteristic, complemented
222C23×C11—21no—
223C23×C11C4×D411yescharacteristic
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—42no—
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—42no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C8×C11—21no—
255C8×C11—21no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—41no—
262C8×C11—41no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11#13112yes—
268#533C22×C1111yescharacteristic
269#529C22×C1111yescharacteristic
270#501C4×C1111yescharacteristic
271#497C4×C1111yescharacteristic
272#491C4×C1111yescharacteristic
273#489C4×C1111yescharacteristic
274#470C4×C1111yescharacteristic
275#470C4×C1111yescharacteristic
276#468C4×C1111yescharacteristic
277#468C4×C1111yescharacteristic
278#446—21no—
279#446C22×C1111yescharacteristic
280#446C22×C1111yescharacteristic
281#446C22×C1111yescharacteristic
282C8×Q8—21no—
283C8×Q8C22×C1111yescharacteristic
284C8×Q8C22×C1111yescharacteristic
285C8×Q8C22×C1111yescharacteristic
286C4×Q16C22×C1111yescharacteristic
287C4×Q16C22×C1111yescharacteristic
288C4×SD16C22×C1111yescharacteristic
289C4×SD16C22×C1111yescharacteristic
290#436C22×C1111yescharacteristic
291#435—21no—
292C8×D4—21no—
293C8×D4C22×C1111yescharacteristic
294#433—21no—
295#433—21no—
296#433—21no—
297#431C22×C1111yescharacteristic
298#431C22×C1111yescharacteristic
299#431C22×C1111yescharacteristic
300#424—21no—
301C2×C4⋊C8C22×C1111yescharacteristic
302C4×M16C22×C1111yescharacteristic
303#335C22×C1111yescharacteristic
304#335C22×C1111yescharacteristic
305#334C22×C1111yescharacteristic
306#334C22×C1111yescharacteristic
307Q8⋊C8C22×C1111yescharacteristic
308Q8⋊C8C22×C1111yescharacteristic
309Q8⋊C8C22×C1111yescharacteristic
310Q8⋊C8C22×C1111yescharacteristic
311Q8⋊C8C22×C1111yescharacteristic
312Q8⋊C8C22×C1111yescharacteristic
313D4⋊C8C22×C1111yescharacteristic
314D4⋊C8C22×C1111yescharacteristic
315#322C22×C1111yescharacteristic
316#322C22×C1111yescharacteristic
317#322C22×C1111yescharacteristic
318C82C22×C1111yescharacteristic
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11C2×C4×D411yescharacteristic
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11C2×#13111yescharacteristic
338C4×C11#56811yescharacteristic
339C4×C11#57711yescharacteristic
340C4×C11#57811yescharacteristic
341C2×Q16C2×C4×C1111yescharacteristic
342C2×Q16C2×C4×C1111yescharacteristic
343C2×SD16C2×C4×C1111yescharacteristic
344C2×SD16C2×C4×C1111yescharacteristic
345C2×M16—21no—
346C2×M16C2×C4×C1111yescharacteristic
347C2×M16C2×C4×C1111yescharacteristic
348C22×C8—21no—
349C22×C8—21no—
350C4⋊Q8C2×C4×C1111yescharacteristic
351C4⋊Q8C2×C4×C1111yescharacteristic
352#126—21no—
353#125—21no—
354#125C2×C4×C1111yescharacteristic
355#124C2×C4×C1111yescharacteristic
356#123—21no—
357C22⋊Q8—21no—
358C22⋊Q8C2×C4×C1111yescharacteristic
359C22⋊Q8C2×C4×C1111yescharacteristic
360C22⋊Q8C2×C4×C1111yescharacteristic
361#121C2×C4×C1111yescharacteristic
362C4×Q8—21no—
363C4×Q8C23×C1111yescharacteristic
364C4×Q8C23×C1111yescharacteristic
365C4×Q8C23×C1111yescharacteristic
366C4×D4—21no—
367C4×D4C23×C1111yescharacteristic
368#117—21no—
369#117—21no—
370C2×C42C23×C1111yescharacteristic
371#107C2×C4×C1111yescharacteristic
372#107C2×C4×C1111yescharacteristic
373#106C2×C4×C1111yescharacteristic
374#106C2×C4×C1111yescharacteristic
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8D4×C1111yescharacteristic
384C4⋊C8D4×C1111yescharacteristic
385C4⋊C8C23×C1111yescharacteristic
386C4⋊C8C23×C1111yescharacteristic
387C4⋊C8C23×C1111yescharacteristic
388C4⋊C8C23×C1111yescharacteristic
389#103C2×C4×C1111yescharacteristic
390#103C2×C4×C1111yescharacteristic
391#103C2×C4×C1111yescharacteristic
392#103C2×C4×C1111yescharacteristic
393#103C2×C4×C1111yescharacteristic
394#103C2×C4×C1111yescharacteristic
395#102C2×C4×C1111yescharacteristic
396#102C2×C4×C1111yescharacteristic
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8—21no—
401C22⋊C8D4×C1111yescharacteristic
402C22⋊C8D4×C1111yescharacteristic
403#97—21no—
404#97—21no—
405#97—21no—
406#97C2×C4×C1111yescharacteristic
407#97C2×C4×C1111yescharacteristic
408C4×C8—21no—
409C4×C8—21no—
410C4×C8—21no—
411C4×C8—21no—
412C4×C8C23×C1111yescharacteristic
413C4×C8C23×C1111yescharacteristic
414C4×C8C23×C1111yescharacteristic
415C4×C8C23×C1111yescharacteristic
416C4×C8C23×C1111yescharacteristic
417C4×C8C23×C1111yescharacteristic
418C2×C11—41no—
419C2×C11—81no—
420C2×C11#293511yescharacteristic
421C2×C11#294711yescharacteristic
422C2×C11#295511yescharacteristic
423C2×Q8—21no—
424C2×Q8C22×C4×C1111yescharacteristic
425C2×Q8C22×C4×C1111yescharacteristic
426C2×Q8C22×C4×C1111yescharacteristic
427C2×D4—21no—
428C2×D4C22×C4×C1111yescharacteristic
429C22×C4—21no—
430C22×C4C22×C4×C1111yescharacteristic
431C22×C4C2×D4×C1111yescharacteristic
432C22×C4C11×#4111yescharacteristic
433Q16—22no—
434Q16—41no—
435SD16—22no—
436SD16—41no—
437M16—22no—
438M16—41no—
439M16—81no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—81no—
447C2×C8—81no—
448C2×C8C22×C4×C1111yescharacteristic
449C2×C8C22×C4×C1111yescharacteristic
450C2×C8C22×C4×C1111yescharacteristic
451C2×C8C22×C4×C1111yescharacteristic
452C2×C8C2×D4×C1111yescharacteristic
453C2×C8C2×D4×C1111yescharacteristic
454C2×C8C2×D4×C1111yescharacteristic
455C2×C8C2×D4×C1111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4C22×C4×C1111yescharacteristic
468C4⋊C4C22×C4×C1111yescharacteristic
469C4⋊C4C22×C4×C1111yescharacteristic
470C4⋊C4C22×C4×C1111yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42C22×C4×C1111yescharacteristic
482C42C2×D4×C1111yescharacteristic
483C42C11×#4111yescharacteristic
484C42C24×C1111yescharacteristic
485C11#1808311yescharacteristic, direct product factor, Sylow
486C23—21no—
487C23C4×D4×C1111yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—42no—
495D4—21no—
496D4—21no—
497D4—42no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4C4×D4×C1111yescharacteristic
513C2×C4C4×D4×C1111yescharacteristic
514C2×C4C4×D4×C1111yescharacteristic
515C2×C4C23×C4×C1111yescharacteristic
516C2×C4C22×D4×C1111yescharacteristic
517C2×C4C2×C11×#4111yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8C11×#13112yes—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×C4×D4×C1111yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4C2×C11×#13111yescharacteristic
551C4C11×#56811yescharacteristic
552C4C11×#57711yescharacteristic
553C4C11×#57811yescharacteristic
554C2—41no—
555C2—81no—
556C2C11×#293511yescharacteristic
557C2C11×#294711yescharacteristic
558C2C11×#295511yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC42C24×C11
socleC22×C11C2×C4×D4
prime radicalC11×#121C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C11×#431 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2986C2semidirect
4. C11×#1593C2semidirect
5. C11×#1590C2semidirect
6. C11×#1588C2semidirect
7. C11×#1587C2semidirect
8. C11×#1584C2semidirect
9. C11×#1582C2semidirect
10. C11×SD16⋊C8C2semidirect
11. C8×C11×Q16C2semidirect
12. C11×#1565C2semidirect
14. C11×#1481C2semidirect
15. C11×#1453C2semidirect
144. #18083C11direct (N × H)
209. #2986C2×C11semidirect
210. #1593C2×C11semidirect
211. #1590C2×C11semidirect
212. #1588C2×C11semidirect
213. #1587C2×C11semidirect
214. #1584C2×C11semidirect
215. #1582C2×C11semidirect
216. SD16⋊C8C2×C11semidirect
217. C8×Q16C2×C11semidirect
218. #1565C2×C11semidirect
220. #1481C2×C11semidirect
221. #1453C2×C11semidirect
485. C11#18083direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31722
C11×#29942
C11×#29862
C11×#15932
C11×#15902
C11×#15882
C11×#15872
C11×#15842
C11×#15822
C11×SD16⋊C82
C8×C11×Q162
C11×#15652
C11×#14822
C11×#14812
C11×#14532
#1808311