Finite Group Databasebeta

← C11×#18077 #14595270

Subgroups — C11×#18077 #14595270

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3172C211yesmaximal, characteristic
2C11×#2969C211yesmaximal, characteristic
3C11×#2962C211yesmaximal, characteristic, complemented
4C11×#1592C211yesmaximal, characteristic, complemented
5C11×#1591C211yesmaximal, characteristic, complemented
6C11×#1588C211yesmaximal, characteristic, complemented
7C11×#1587C211yesmaximal, characteristic, complemented
8C11×#1584C211yesmaximal, characteristic, complemented
9C11×#1582C211yesmaximal, characteristic, complemented
10C11×#1579C211yesmaximal, characteristic, complemented
11C8×C11×SD16C211yesmaximal, characteristic, complemented
12C11×#1565C211yesmaximal, characteristic, complemented
13C11×#1485C211yesmaximal, characteristic, complemented
14C11×#1483C211yesmaximal, characteristic
15C11×#1455C211yesmaximal, 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×#446—21no—
28C11×#446C2211yescharacteristic
29C11×#446C2211yescharacteristic
30C11×#446C2211yescharacteristic
31C8×Q8×C11C2211yescharacteristic
32C8×Q8×C11C2211yescharacteristic
33C8×Q8×C11C2211yescharacteristic
34C4×C11×Q16C2211yescharacteristic
35C4×C11×Q16C2211yescharacteristic
36C4×C11×SD16C2211yescharacteristic
37C4×C11×SD16C2211yescharacteristic
38C11×#436—21no—
39C11×#436C2211yescharacteristic
40C11×#435—21no—
41C8×D4×C11C2211yescharacteristic
42C11×#433—21no—
43C11×#431C2211yescharacteristic
44C11×#424—21no—
45C2×C11×C4⋊C8C2211yescharacteristic
46C11×#405—21no—
47C11×#405—21no—
48C4×C11×M16C2211yescharacteristic
49C4×C11×M16C2211yescharacteristic
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×M16—21no—
73C2×C11×M16C2×C411yescharacteristic
74C2×C11×M16C2×C411yescharacteristic
75C2×C11×M16D411yescharacteristic
76C2×C11×M16D411yescharacteristic
77C22×C8×C11—21no—
78C22×C8×C11—21no—
79C11×C4⋊Q8C2×C411yescharacteristic
80C11×C4⋊Q8C2×C411yescharacteristic
81C11×#126—21no—
82C11×#125—21no—
83C11×#125C2×C411yescharacteristic
84C11×#124C2×C411yescharacteristic
85C11×#123—21no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8C2×C411yescharacteristic
88C11×C22⋊Q8C2×C411yescharacteristic
89C11×C22⋊Q8C2×C411yescharacteristic
90C11×#121C2×C411yescharacteristic
91C4×Q8×C11—21no—
92C4×Q8×C11C2311yescharacteristic
93C4×Q8×C11C2311yescharacteristic
94C4×Q8×C11C2311yescharacteristic
95C4×D4×C11—21no—
96C4×D4×C11C2311yescharacteristic
97C11×#117—21no—
98C11×#117—21no—
99C2×C42×C11C2311yescharacteristic
100C11×#107C2×C411yescharacteristic
101C11×#107C2×C411yescharacteristic
102C11×#106C2×C411yescharacteristic
103C11×#106C2×C411yescharacteristic
104C11×C4⋊C8—21no—
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8—21no—
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×#97—21no—
127C11×#97—21no—
128C11×#97—21no—
129C11×#97—21no—
130C11×#97C2×C411yescharacteristic
131C11×#97C2×C411yescharacteristic
132C11×#97D411yescharacteristic
133C11×#97D411yescharacteristic
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#18077C1111yesmaximal, 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—22no—
161C11×M16—41no—
162C11×M16—41no—
163C11×M16—42no—
164C11×M16—42no—
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×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C22×C411yescharacteristic
176C2×C8×C11C22×C411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
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⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C22×C411yescharacteristic
193C11×C4⋊C4C22×C411yescharacteristic
194C11×C4⋊C4C22×C411yescharacteristic
195C11×C4⋊C4C22×C411yescharacteristic
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11C22×C411yescharacteristic
207C42×C11C2×D411yescharacteristic
208C42×C11#4111yescharacteristic
209C42×C11C2411yescharacteristic
210#3172C2×C1111yescharacteristic
211#2969C2×C1111yescharacteristic
212#2962C2×C1111yescharacteristic, complemented
213#1592C2×C1111yescharacteristic, complemented
214#1591C2×C1111yescharacteristic, complemented
215#1588C2×C1111yescharacteristic, complemented
216#1587C2×C1111yescharacteristic, complemented
217#1584C2×C1111yescharacteristic, complemented
218#1582C2×C1111yescharacteristic, complemented
219#1579C2×C1111yescharacteristic, complemented
220C8×SD16C2×C1111yescharacteristic, complemented
221#1565C2×C1111yescharacteristic, complemented
222#1485C2×C1111yescharacteristic, complemented
223#1483C2×C1111yescharacteristic
224#1455C2×C1111yescharacteristic, complemented
225C23×C11—21no—
226C23×C11C4×D411yescharacteristic
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—81no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—81no—
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—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C8×C11—22no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11#13112yes—
270C8×C11#13712yes—
271#533C22×C1111yescharacteristic
272#529C22×C1111yescharacteristic
273#501C4×C1111yescharacteristic
274#497C4×C1111yescharacteristic
275#491C4×C1111yescharacteristic
276#489C4×C1111yescharacteristic
277#470C4×C1111yescharacteristic
278#470C4×C1111yescharacteristic
279#468C4×C1111yescharacteristic
280#468C4×C1111yescharacteristic
281#446—21no—
282#446—21no—
283#446C22×C1111yescharacteristic
284#446C22×C1111yescharacteristic
285#446C22×C1111yescharacteristic
286C8×Q8C22×C1111yescharacteristic
287C8×Q8C22×C1111yescharacteristic
288C8×Q8C22×C1111yescharacteristic
289C4×Q16C22×C1111yescharacteristic
290C4×Q16C22×C1111yescharacteristic
291C4×SD16C22×C1111yescharacteristic
292C4×SD16C22×C1111yescharacteristic
293#436—21no—
294#436C22×C1111yescharacteristic
295#435—21no—
296C8×D4C22×C1111yescharacteristic
297#433—21no—
298#431C22×C1111yescharacteristic
299#424—21no—
300C2×C4⋊C8C22×C1111yescharacteristic
301#405—21no—
302#405—21no—
303C4×M16C22×C1111yescharacteristic
304C4×M16C22×C1111yescharacteristic
305C4×M16C22×C1111yescharacteristic
306#335C22×C1111yescharacteristic
307#335C22×C1111yescharacteristic
308#334C22×C1111yescharacteristic
309#334C22×C1111yescharacteristic
310Q8⋊C8C22×C1111yescharacteristic
311Q8⋊C8C22×C1111yescharacteristic
312Q8⋊C8C22×C1111yescharacteristic
313Q8⋊C8C22×C1111yescharacteristic
314Q8⋊C8C22×C1111yescharacteristic
315Q8⋊C8C22×C1111yescharacteristic
316D4⋊C8C22×C1111yescharacteristic
317D4⋊C8C22×C1111yescharacteristic
318#322C22×C1111yescharacteristic
319#322C22×C1111yescharacteristic
320#322C22×C1111yescharacteristic
321C82C22×C1111yescharacteristic
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11C2×C4×D411yescharacteristic
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11C2×#13111yescharacteristic
341C4×C11#56811yescharacteristic
342C4×C11C2×#13711yescharacteristic
343C4×C11#57511yescharacteristic
344C2×Q16C2×C4×C1111yescharacteristic
345C2×Q16C2×C4×C1111yescharacteristic
346C2×SD16C2×C4×C1111yescharacteristic
347C2×SD16C2×C4×C1111yescharacteristic
348C2×M16—21no—
349C2×M16—21no—
350C2×M16C2×C4×C1111yescharacteristic
351C2×M16C2×C4×C1111yescharacteristic
352C2×M16D4×C1111yescharacteristic
353C2×M16D4×C1111yescharacteristic
354C22×C8—21no—
355C22×C8—21no—
356C4⋊Q8C2×C4×C1111yescharacteristic
357C4⋊Q8C2×C4×C1111yescharacteristic
358#126—21no—
359#125—21no—
360#125C2×C4×C1111yescharacteristic
361#124C2×C4×C1111yescharacteristic
362#123—21no—
363C22⋊Q8—21no—
364C22⋊Q8C2×C4×C1111yescharacteristic
365C22⋊Q8C2×C4×C1111yescharacteristic
366C22⋊Q8C2×C4×C1111yescharacteristic
367#121C2×C4×C1111yescharacteristic
368C4×Q8—21no—
369C4×Q8C23×C1111yescharacteristic
370C4×Q8C23×C1111yescharacteristic
371C4×Q8C23×C1111yescharacteristic
372C4×D4—21no—
373C4×D4C23×C1111yescharacteristic
374#117—21no—
375#117—21no—
376C2×C42C23×C1111yescharacteristic
377#107C2×C4×C1111yescharacteristic
378#107C2×C4×C1111yescharacteristic
379#106C2×C4×C1111yescharacteristic
380#106C2×C4×C1111yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8C23×C1111yescharacteristic
389C4⋊C8C23×C1111yescharacteristic
390C4⋊C8C23×C1111yescharacteristic
391C4⋊C8C23×C1111yescharacteristic
392#103C2×C4×C1111yescharacteristic
393#103C2×C4×C1111yescharacteristic
394#103C2×C4×C1111yescharacteristic
395#103C2×C4×C1111yescharacteristic
396#103C2×C4×C1111yescharacteristic
397#103C2×C4×C1111yescharacteristic
398#102C2×C4×C1111yescharacteristic
399#102C2×C4×C1111yescharacteristic
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403#97—21no—
404#97—21no—
405#97—21no—
406#97—21no—
407#97C2×C4×C1111yescharacteristic
408#97C2×C4×C1111yescharacteristic
409#97D4×C1111yescharacteristic
410#97D4×C1111yescharacteristic
411C4×C8—21no—
412C4×C8—21no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8C23×C1111yescharacteristic
416C4×C8C23×C1111yescharacteristic
417C4×C8C23×C1111yescharacteristic
418C4×C8C23×C1111yescharacteristic
419C4×C8C23×C1111yescharacteristic
420C4×C8C23×C1111yescharacteristic
421C2×C11—41no—
422C2×C11—81no—
423C2×C11#293511yescharacteristic
424C2×C11C4×#13711yescharacteristic
425C2×C11#295611yescharacteristic
426C2×Q8—21no—
427C2×Q8C22×C4×C1111yescharacteristic
428C2×Q8C22×C4×C1111yescharacteristic
429C2×Q8C22×C4×C1111yescharacteristic
430C2×D4—21no—
431C2×D4C22×C4×C1111yescharacteristic
432C22×C4—21no—
433C22×C4C22×C4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C11×#4111yescharacteristic
436Q16—22no—
437Q16—41no—
438SD16—22no—
439SD16—41no—
440M16—22no—
441M16—22no—
442M16—41no—
443M16—41no—
444M16—42no—
445M16—42no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8—42no—
454C2×C8C22×C4×C1111yescharacteristic
455C2×C8C22×C4×C1111yescharacteristic
456C2×C8C22×C4×C1111yescharacteristic
457C2×C8C22×C4×C1111yescharacteristic
458C2×C8C2×D4×C1111yescharacteristic
459C2×C8C2×D4×C1111yescharacteristic
460C2×C8C2×D4×C1111yescharacteristic
461C2×C8C2×D4×C1111yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
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—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42C22×C4×C1111yescharacteristic
488C42C2×D4×C1111yescharacteristic
489C42C11×#4111yescharacteristic
490C42C24×C1111yescharacteristic
491C11#1807711yescharacteristic, 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—21no—
503D4—81no—
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—41no—
517C2×C4—41no—
518C2×C4C4×D4×C1111yescharacteristic
519C2×C4C4×D4×C1111yescharacteristic
520C2×C4C4×D4×C1111yescharacteristic
521C2×C4C23×C4×C1111yescharacteristic
522C2×C4C22×D4×C1111yescharacteristic
523C2×C4C2×C11×#4111yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8C11×#13112yes—
537C8C11×#13712yes—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22C2×C4×D4×C1111yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4C2×C11×#13111yescharacteristic
557C4C11×#56811yescharacteristic
558C4C2×C11×#13711yescharacteristic
559C4C11×#57511yescharacteristic
560C2—41no—
561C2—81no—
562C2C11×#293511yescharacteristic
563C2C4×C11×#13711yescharacteristic
564C2C11×#295611yescharacteristic
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 ◁ C4×C11×M16 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2962C2semidirect
4. C11×#1592C2semidirect
5. C11×#1591C2semidirect
6. C11×#1588C2semidirect
7. C11×#1587C2semidirect
8. C11×#1584C2semidirect
9. C11×#1582C2semidirect
10. C11×#1579C2semidirect
11. C8×C11×SD16C2semidirect
12. C11×#1565C2semidirect
13. C11×#1485C2semidirect
15. C11×#1455C2semidirect
144. #18077C11direct (N × H)
212. #2962C2×C11semidirect
213. #1592C2×C11semidirect
214. #1591C2×C11semidirect
215. #1588C2×C11semidirect
216. #1587C2×C11semidirect
217. #1584C2×C11semidirect
218. #1582C2×C11semidirect
219. #1579C2×C11semidirect
220. C8×SD16C2×C11semidirect
221. #1565C2×C11semidirect
222. #1485C2×C11semidirect
224. #1455C2×C11semidirect
491. C11#18077direct (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×#29692
C11×#29622
C11×#15922
C11×#15912
C11×#15882
C11×#15872
C11×#15842
C11×#15822
C11×#15792
C8×C11×SD162
C11×#15652
C11×#14852
C11×#14832
C11×#14552
#1807711