Finite Group Databasebeta

← C11×#18009 #14595202

Subgroups — C11×#18009 #14595202

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3107C211yesmaximal, characteristic
2C11×#2970C211yesmaximal, characteristic
3C11×#2962C211yesmaximal, characteristic, complemented
4C11×#1593C211yesmaximal, characteristic, complemented
5C11×#1591C211yesmaximal, characteristic, complemented
6C11×#1587C211yesmaximal, characteristic, complemented
7C11×#1585C211yesmaximal, characteristic, complemented
8C11×#1584C211yesmaximal, characteristic, complemented
9C11×#1582C211yesmaximal, characteristic, complemented
10C11×SD16⋊C8C211yesmaximal, characteristic, complemented
11C8×C11×SD16C211yesmaximal, characteristic, complemented
12C11×#1573C211yesmaximal, characteristic, complemented
13C11×#1497C211yesmaximal, characteristic, complemented
14C11×#1477C211yesmaximal, characteristic
15C11×#1453C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C11×#485C411yescharacteristic
19C11×#485C411yescharacteristic
20C11×#475C411yescharacteristic
21C11×#474C411yescharacteristic
22C11×#462C411yescharacteristic
23C11×#461C411yescharacteristic
24C11×#452C411yescharacteristic
25C11×#452C411yescharacteristic
26C11×#446—21no—
27C11×#446—21no—
28C11×#446C2211yescharacteristic
29C11×#446C2211yescharacteristic
30C11×#446C2211yescharacteristic
31C11×#446C2211yescharacteristic
32C8×Q8×C11C2211yescharacteristic
33C8×Q8×C11C2211yescharacteristic
34C4×C11×Q16C2211yescharacteristic
35C4×C11×Q16C2211yescharacteristic
36C4×C11×SD16C2211yescharacteristic
37C4×C11×SD16C2211yescharacteristic
38C11×#435—21no—
39C11×#435—21no—
40C8×D4×C11C2211yescharacteristic
41C8×D4×C11C2211yescharacteristic
42C11×#432—21no—
43C11×#432C2211yescharacteristic
44C11×#431C2211yescharacteristic
45C11×#431C2211yescharacteristic
46C11×#424—21no—
47C2×C11×C4⋊C8C2211yescharacteristic
48C11×#405—21no—
49C4×C11×M16C2211yescharacteristic
50C2×C11×#97—21no—
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×#41C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C2×C11×Q16C2×C411yescharacteristic
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×SD16C2×C411yescharacteristic
72C2×C11×M16D411yescharacteristic
73C2×C11×M16D411yescharacteristic
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C22×C8×C11—21no—
77C11×C4⋊Q8C2×C411yescharacteristic
78C11×C4⋊Q8C2×C411yescharacteristic
79C11×#125—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8C2×C411yescharacteristic
82C11×C22⋊Q8C2×C411yescharacteristic
83C4×Q8×C11—21no—
84C4×Q8×C11C2×C411yescharacteristic
85C4×Q8×C11C2311yescharacteristic
86C4×Q8×C11C2311yescharacteristic
87C4×Q8×C11C2311yescharacteristic
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11C2×C411yescharacteristic
91C4×D4×C11C2311yescharacteristic
92C11×#117—21no—
93C11×#117—21no—
94C11×#117C2×C411yescharacteristic
95C2×C42×C11—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⋊C8C2×C411yescharacteristic
110C11×C4⋊C8C2×C411yescharacteristic
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⋊C8C2×C411yescharacteristic
128C11×C22⋊C8C2×C411yescharacteristic
129C11×#97—21no—
130C11×#97—21no—
131C11×#97—21no—
132C11×#97—21no—
133C11×#97—21no—
134C11×#97D411yescharacteristic
135C11×#97D411yescharacteristic
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#18009C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—22no—
146C11×#41—41no—
147C2×Q8×C11—21no—
148C2×Q8×C11C22×C411yescharacteristic
149C2×Q8×C11C22×C411yescharacteristic
150C2×Q8×C11C22×C411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11C22×C411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C11×Q16—41no—
160C11×Q16—41no—
161C11×SD16—22no—
162C11×SD16—22no—
163C11×M16—22no—
164C11×M16—41no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—42no—
172C2×C8×C11—42no—
173C2×C8×C11—42no—
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C22×C411yescharacteristic
176C2×C8×C11C22×C411yescharacteristic
177C2×C8×C11C22×C411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
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⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4C22×C411yescharacteristic
192C11×C4⋊C4C22×C411yescharacteristic
193C11×C4⋊C4C22×C411yescharacteristic
194C11×C4⋊C4C22×C411yescharacteristic
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×C11—21no—
204C42×C11—21no—
205C42×C11C22×C411yescharacteristic
206C42×C11C2×D411yescharacteristic
207C42×C11#4111yescharacteristic
208C42×C11C2411yescharacteristic
209#3107C2×C1111yescharacteristic
210#2970C2×C1111yescharacteristic
211#2962C2×C1111yescharacteristic, complemented
212#1593C2×C1111yescharacteristic, complemented
213#1591C2×C1111yescharacteristic, complemented
214#1587C2×C1111yescharacteristic, complemented
215#1585C2×C1111yescharacteristic, complemented
216#1584C2×C1111yescharacteristic, complemented
217#1582C2×C1111yescharacteristic, complemented
218SD16⋊C8C2×C1111yescharacteristic, complemented
219C8×SD16C2×C1111yescharacteristic, complemented
220#1573C2×C1111yescharacteristic, complemented
221#1497C2×C1111yescharacteristic, complemented
222#1477C2×C1111yescharacteristic
223#1453C2×C1111yescharacteristic, complemented
224C23×C11—21no—
225C23×C11C4×D411yescharacteristic
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—81no—
233D4×C11—21no—
234D4×C11—42no—
235D4×C11#13112yes—
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—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—81no—
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11C4×D411yescharacteristic
255C2×C4×C11C23×C411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11#13712yes—
272#533C22×C1111yescharacteristic
273C4×#41C22×C1111yescharacteristic
274#485C4×C1111yescharacteristic
275#485C4×C1111yescharacteristic
276#475C4×C1111yescharacteristic
277#474C4×C1111yescharacteristic
278#462C4×C1111yescharacteristic
279#461C4×C1111yescharacteristic
280#452C4×C1111yescharacteristic
281#452C4×C1111yescharacteristic
282#446—21no—
283#446—21no—
284#446C22×C1111yescharacteristic
285#446C22×C1111yescharacteristic
286#446C22×C1111yescharacteristic
287#446C22×C1111yescharacteristic
288C8×Q8C22×C1111yescharacteristic
289C8×Q8C22×C1111yescharacteristic
290C4×Q16C22×C1111yescharacteristic
291C4×Q16C22×C1111yescharacteristic
292C4×SD16C22×C1111yescharacteristic
293C4×SD16C22×C1111yescharacteristic
294#435—21no—
295#435—21no—
296C8×D4C22×C1111yescharacteristic
297C8×D4C22×C1111yescharacteristic
298#432—21no—
299#432C22×C1111yescharacteristic
300#431C22×C1111yescharacteristic
301#431C22×C1111yescharacteristic
302#424—21no—
303C2×C4⋊C8C22×C1111yescharacteristic
304#405—21no—
305C4×M16C22×C1111yescharacteristic
306C2×#97—21no—
307#335C22×C1111yescharacteristic
308#335C22×C1111yescharacteristic
309#334C22×C1111yescharacteristic
310#334C22×C1111yescharacteristic
311Q8⋊C8C22×C1111yescharacteristic
312Q8⋊C8C22×C1111yescharacteristic
313Q8⋊C8C22×C1111yescharacteristic
314Q8⋊C8C22×C1111yescharacteristic
315Q8⋊C8C22×C1111yescharacteristic
316Q8⋊C8C22×C1111yescharacteristic
317D4⋊C8C22×C1111yescharacteristic
318D4⋊C8C22×C1111yescharacteristic
319#322C22×C1111yescharacteristic
320#322C22×C1111yescharacteristic
321#322C22×C1111yescharacteristic
322C82C22×C1111yescharacteristic
323C22×C11—21no—
324C22×C11—22no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11C2×C4×D411yescharacteristic
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11C2×#13111yescharacteristic
342C4×C11#56811yescharacteristic
343C4×C11C2×#13711yescharacteristic
344C4×C11#57511yescharacteristic
345C2×#41C2×C4×C1111yescharacteristic
346C2×Q16C2×C4×C1111yescharacteristic
347C2×Q16C2×C4×C1111yescharacteristic
348C2×SD16C2×C4×C1111yescharacteristic
349C2×SD16C2×C4×C1111yescharacteristic
350C2×M16D4×C1111yescharacteristic
351C2×M16D4×C1111yescharacteristic
352C22×C8—21no—
353C22×C8—21no—
354C22×C8—21no—
355C4⋊Q8C2×C4×C1111yescharacteristic
356C4⋊Q8C2×C4×C1111yescharacteristic
357#125—21no—
358C22⋊Q8—21no—
359C22⋊Q8C2×C4×C1111yescharacteristic
360C22⋊Q8C2×C4×C1111yescharacteristic
361C4×Q8—21no—
362C4×Q8C2×C4×C1111yescharacteristic
363C4×Q8C23×C1111yescharacteristic
364C4×Q8C23×C1111yescharacteristic
365C4×Q8C23×C1111yescharacteristic
366C4×D4—21no—
367C4×D4—21no—
368C4×D4C2×C4×C1111yescharacteristic
369C4×D4C23×C1111yescharacteristic
370#117—21no—
371#117—21no—
372#117C2×C4×C1111yescharacteristic
373C2×C42—21no—
374C2×C42C23×C1111yescharacteristic
375#107C2×C4×C1111yescharacteristic
376#107C2×C4×C1111yescharacteristic
377#106C2×C4×C1111yescharacteristic
378#106C2×C4×C1111yescharacteristic
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8C2×C4×C1111yescharacteristic
388C4⋊C8C2×C4×C1111yescharacteristic
389C4⋊C8C23×C1111yescharacteristic
390C4⋊C8C23×C1111yescharacteristic
391C4⋊C8C23×C1111yescharacteristic
392C4⋊C8C23×C1111yescharacteristic
393#103C2×C4×C1111yescharacteristic
394#103C2×C4×C1111yescharacteristic
395#103C2×C4×C1111yescharacteristic
396#103C2×C4×C1111yescharacteristic
397#103C2×C4×C1111yescharacteristic
398#103C2×C4×C1111yescharacteristic
399#102C2×C4×C1111yescharacteristic
400#102C2×C4×C1111yescharacteristic
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404C22⋊C8—21no—
405C22⋊C8C2×C4×C1111yescharacteristic
406C22⋊C8C2×C4×C1111yescharacteristic
407#97—21no—
408#97—21no—
409#97—21no—
410#97—21no—
411#97—21no—
412#97D4×C1111yescharacteristic
413#97D4×C1111yescharacteristic
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C23×C1111yescharacteristic
417C4×C8C23×C1111yescharacteristic
418C4×C8C23×C1111yescharacteristic
419C4×C8C23×C1111yescharacteristic
420C4×C8C23×C1111yescharacteristic
421C4×C8C23×C1111yescharacteristic
422C2×C11—41no—
423C2×C11—42no—
424C2×C11#293311yescharacteristic
425C2×C11C4×#13711yescharacteristic
426C2×C11#295711yescharacteristic
427#41—22no—
428#41—41no—
429C2×Q8—21no—
430C2×Q8C22×C4×C1111yescharacteristic
431C2×Q8C22×C4×C1111yescharacteristic
432C2×Q8C22×C4×C1111yescharacteristic
433C2×D4—21no—
434C2×D4C22×C4×C1111yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4C22×C4×C1111yescharacteristic
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C11×#4111yescharacteristic
441Q16—41no—
442Q16—41no—
443SD16—22no—
444SD16—22no—
445M16—22no—
446M16—41no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—42no—
455C2×C8—42no—
456C2×C8C22×C4×C1111yescharacteristic
457C2×C8C22×C4×C1111yescharacteristic
458C2×C8C22×C4×C1111yescharacteristic
459C2×C8C22×C4×C1111yescharacteristic
460C2×C8C2×D4×C1111yescharacteristic
461C2×C8C2×D4×C1111yescharacteristic
462C2×C8C2×D4×C1111yescharacteristic
463C2×C8C2×D4×C1111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4C22×C4×C1111yescharacteristic
474C4⋊C4C22×C4×C1111yescharacteristic
475C4⋊C4C22×C4×C1111yescharacteristic
476C4⋊C4C22×C4×C1111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42C22×C4×C1111yescharacteristic
488C42C2×D4×C1111yescharacteristic
489C42C11×#4111yescharacteristic
490C42C24×C1111yescharacteristic
491C11#1800911yescharacteristic, direct product factor, Sylow
492C23—21no—
493C23C4×D4×C1111yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—81no—
501D4—21no—
502D4—42no—
503D4C11×#13112yes—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—81no—
520C2×C4C4×D4×C1111yescharacteristic
521C2×C4C4×D4×C1111yescharacteristic
522C2×C4C4×D4×C1111yescharacteristic
523C2×C4C23×C4×C1111yescharacteristic
524C2×C4C22×D4×C1111yescharacteristic
525C2×C4C2×C11×#4111yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8C11×#13712yes—
540C22—21no—
541C22—22no—
542C22—21no—
543C22—21no—
544C22—41no—
545C22—41no—
546C22C2×C4×D4×C1111yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4C2×C11×#13111yescharacteristic
559C4C11×#56811yescharacteristic
560C4C2×C11×#13711yescharacteristic
561C4C11×#57511yescharacteristic
562C2—41no—
563C2—42no—
564C2C11×#293311yescharacteristic
565C2C4×C11×#13711yescharacteristic
566C2C11×#295711yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC42C24×C11
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C4×C11×M16 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2962C2semidirect
4. C11×#1593C2semidirect
5. C11×#1591C2semidirect
6. C11×#1587C2semidirect
7. C11×#1585C2semidirect
8. C11×#1584C2semidirect
9. C11×#1582C2semidirect
10. C11×SD16⋊C8C2semidirect
11. C8×C11×SD16C2semidirect
12. C11×#1573C2semidirect
13. C11×#1497C2semidirect
15. C11×#1453C2semidirect
144. #18009C11direct (N × H)
211. #2962C2×C11semidirect
212. #1593C2×C11semidirect
213. #1591C2×C11semidirect
214. #1587C2×C11semidirect
215. #1585C2×C11semidirect
216. #1584C2×C11semidirect
217. #1582C2×C11semidirect
218. SD16⋊C8C2×C11semidirect
219. C8×SD16C2×C11semidirect
220. #1573C2×C11semidirect
221. #1497C2×C11semidirect
223. #1453C2×C11semidirect
491. C11#18009direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31072
C11×#29702
C11×#29622
C11×#15932
C11×#15912
C11×#15872
C11×#15852
C11×#15842
C11×#15822
C11×SD16⋊C82
C8×C11×SD162
C11×#15732
C11×#14972
C11×#14772
C11×#14532
#1800911