Finite Group Databasebeta

← C11×#17947 #14595140

Subgroups — C11×#17947 #14595140

Order 2816.

568 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3108C211yesmaximal, characteristic
2C11×#2993C211yesmaximal, characteristic
3C11×#2983C211yesmaximal, characteristic, complemented
4C11×#1593C211yesmaximal, characteristic, complemented
5C11×#1592C211yesmaximal, characteristic, complemented
6C11×#1591C211yesmaximal, characteristic, complemented
7C11×#1590C211yesmaximal, characteristic, complemented
8C11×#1587C211yesmaximal, characteristic, complemented
9C11×#1585C211yesmaximal, characteristic, complemented
10C11×#1584C211yesmaximal, characteristic, complemented
11C11×#1582C211yesmaximal, characteristic, complemented
12C11×#1574C211yesmaximal, characteristic, complemented
13C11×#1487C211yesmaximal, characteristic, complemented
14C11×#1482C211yesmaximal, characteristic
15C11×#1454C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#483C411yescharacteristic
19C11×#480C411yescharacteristic
20C11×#479C411yescharacteristic
21C11×#479C411yescharacteristic
22C11×#464C411yescharacteristic
23C11×#464C411yescharacteristic
24C11×#451C411yescharacteristic
25C11×#448C411yescharacteristic
26C11×#446—21no—
27C11×#446—21no—
28C11×#446C2211yescharacteristic
29C11×#446C2211yescharacteristic
30C11×#446C2211yescharacteristic
31C11×#446C2211yescharacteristic
32C11×#446C2211yescharacteristic
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×#432—21no—
44C11×#432—21no—
45C11×#431C2211yescharacteristic
46C11×#431C2211yescharacteristic
47C11×#431C2211yescharacteristic
48C11×#431C2211yescharacteristic
49C11×#424—21no—
50C11×#423C2211yescharacteristic
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
67C22×Q8×C11C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C2×C11×Q16C2×C411yescharacteristic
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×SD16C2×C411yescharacteristic
72C2×C11×M16—21no—
73C2×C11×M16—21no—
74C22×C8×C11—21no—
75C11×#126—21no—
76C11×#125C2×C411yescharacteristic
77C11×#124C2×C411yescharacteristic
78C11×#123—21no—
79C11×C22⋊Q8C2×C411yescharacteristic
80C11×#121C2×C411yescharacteristic
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11C2×C411yescharacteristic
84C4×Q8×C11C2×C411yescharacteristic
85C4×Q8×C11C2311yescharacteristic
86C4×Q8×C11C2311yescharacteristic
87C4×Q8×C11C2311yescharacteristic
88C4×D4×C11—21no—
89C4×D4×C11C2311yescharacteristic
90C11×#117—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4C2×C411yescharacteristic
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C11×#107C2×C411yescharacteristic
96C11×#107C2×C411yescharacteristic
97C11×#106C2×C411yescharacteristic
98C11×#106C2×C411yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
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⋊C8C2×C411yescharacteristic
108C11×C4⋊C8C2×C411yescharacteristic
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⋊C8C2×C411yescharacteristic
128C11×C22⋊C8C2×C411yescharacteristic
129C11×C22⋊C8D411yescharacteristic
130C11×C22⋊C8D411yescharacteristic
131C11×#97—21no—
132C11×#97—21no—
133C11×#97—21no—
134C11×#97—21no—
135C11×#97—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#17947C1111yesmaximal, characteristic, direct product factor, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—41no—
147C2×Q8×C11—41no—
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—41no—
162C11×SD16—41no—
163C11×M16—81no—
164C11×M16—81no—
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—81no—
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C22×C411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
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—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11C22×C411yescharacteristic
204C42×C11C2×D411yescharacteristic
205C42×C11#4111yescharacteristic
206C42×C11C2411yescharacteristic
207#3108C2×C1111yescharacteristic
208#2993C2×C1111yescharacteristic
209#2983C2×C1111yescharacteristic, complemented
210#1593C2×C1111yescharacteristic, complemented
211#1592C2×C1111yescharacteristic, complemented
212#1591C2×C1111yescharacteristic, complemented
213#1590C2×C1111yescharacteristic, complemented
214#1587C2×C1111yescharacteristic, complemented
215#1585C2×C1111yescharacteristic, complemented
216#1584C2×C1111yescharacteristic, complemented
217#1582C2×C1111yescharacteristic, complemented
218#1574C2×C1111yescharacteristic, complemented
219#1487C2×C1111yescharacteristic, complemented
220#1482C2×C1111yescharacteristic
221#1454C2×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—81no—
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—42no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—81no—
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C23×C411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C8×C11—21no—
257C8×C11—21no—
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—41no—
270#529C22×C1111yescharacteristic
271C2×C4×Q8C22×C1111yescharacteristic
272#483C4×C1111yescharacteristic
273#480C4×C1111yescharacteristic
274#479C4×C1111yescharacteristic
275#479C4×C1111yescharacteristic
276#464C4×C1111yescharacteristic
277#464C4×C1111yescharacteristic
278#451C4×C1111yescharacteristic
279#448C4×C1111yescharacteristic
280#446—21no—
281#446—21no—
282#446C22×C1111yescharacteristic
283#446C22×C1111yescharacteristic
284#446C22×C1111yescharacteristic
285#446C22×C1111yescharacteristic
286#446C22×C1111yescharacteristic
287C8×Q8C22×C1111yescharacteristic
288C4×Q16C22×C1111yescharacteristic
289C4×Q16C22×C1111yescharacteristic
290C4×SD16C22×C1111yescharacteristic
291C4×SD16C22×C1111yescharacteristic
292#436—21no—
293#436C22×C1111yescharacteristic
294#435—21no—
295C8×D4C22×C1111yescharacteristic
296#433—21no—
297#432—21no—
298#432—21no—
299#431C22×C1111yescharacteristic
300#431C22×C1111yescharacteristic
301#431C22×C1111yescharacteristic
302#431C22×C1111yescharacteristic
303#424—21no—
304#423C22×C1111yescharacteristic
305#335C22×C1111yescharacteristic
306#335C22×C1111yescharacteristic
307#334C22×C1111yescharacteristic
308#334C22×C1111yescharacteristic
309Q8⋊C8C22×C1111yescharacteristic
310Q8⋊C8C22×C1111yescharacteristic
311Q8⋊C8C22×C1111yescharacteristic
312Q8⋊C8C22×C1111yescharacteristic
313Q8⋊C8C22×C1111yescharacteristic
314Q8⋊C8C22×C1111yescharacteristic
315D4⋊C8C22×C1111yescharacteristic
316D4⋊C8C22×C1111yescharacteristic
317#322C22×C1111yescharacteristic
318#322C22×C1111yescharacteristic
319#322C22×C1111yescharacteristic
320C82C22×C1111yescharacteristic
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11C2×C4×D411yescharacteristic
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11#56811yescharacteristic
340C4×C11#56811yescharacteristic
341C4×C11#57711yescharacteristic
342C4×C11#57811yescharacteristic
343C22×Q8C2×C4×C1111yescharacteristic
344C2×Q16C2×C4×C1111yescharacteristic
345C2×Q16C2×C4×C1111yescharacteristic
346C2×SD16C2×C4×C1111yescharacteristic
347C2×SD16C2×C4×C1111yescharacteristic
348C2×M16—21no—
349C2×M16—21no—
350C22×C8—21no—
351#126—21no—
352#125C2×C4×C1111yescharacteristic
353#124C2×C4×C1111yescharacteristic
354#123—21no—
355C22⋊Q8C2×C4×C1111yescharacteristic
356#121C2×C4×C1111yescharacteristic
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8C2×C4×C1111yescharacteristic
360C4×Q8C2×C4×C1111yescharacteristic
361C4×Q8C23×C1111yescharacteristic
362C4×Q8C23×C1111yescharacteristic
363C4×Q8C23×C1111yescharacteristic
364C4×D4—21no—
365C4×D4C23×C1111yescharacteristic
366#117—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4C2×C4×C1111yescharacteristic
369C2×C42—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⋊C8C2×C4×C1111yescharacteristic
384C4⋊C8C2×C4×C1111yescharacteristic
385C4⋊C8D4×C1111yescharacteristic
386C4⋊C8D4×C1111yescharacteristic
387C4⋊C8C23×C1111yescharacteristic
388C4⋊C8C23×C1111yescharacteristic
389C4⋊C8C23×C1111yescharacteristic
390C4⋊C8C23×C1111yescharacteristic
391#103C2×C4×C1111yescharacteristic
392#103C2×C4×C1111yescharacteristic
393#103C2×C4×C1111yescharacteristic
394#103C2×C4×C1111yescharacteristic
395#103C2×C4×C1111yescharacteristic
396#103C2×C4×C1111yescharacteristic
397#102C2×C4×C1111yescharacteristic
398#102C2×C4×C1111yescharacteristic
399C22⋊C8—21no—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8C2×C4×C1111yescharacteristic
404C22⋊C8C2×C4×C1111yescharacteristic
405C22⋊C8D4×C1111yescharacteristic
406C22⋊C8D4×C1111yescharacteristic
407#97—21no—
408#97—21no—
409#97—21no—
410#97—21no—
411#97—21no—
412C4×C8—21no—
413C4×C8—21no—
414C4×C8C23×C1111yescharacteristic
415C4×C8C23×C1111yescharacteristic
416C4×C8C23×C1111yescharacteristic
417C4×C8C23×C1111yescharacteristic
418C4×C8C23×C1111yescharacteristic
419C4×C8C23×C1111yescharacteristic
420C2×C11—41no—
421C2×C11—81no—
422C2×C11#293011yescharacteristic
423C2×C11#294711yescharacteristic
424C2×C11#295711yescharacteristic
425C2×Q8—21no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8C22×C4×C1111yescharacteristic
429C2×Q8C22×C4×C1111yescharacteristic
430C2×Q8C22×C4×C1111yescharacteristic
431C2×D4—21no—
432C2×D4C22×C4×C1111yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4C22×C4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C11×#4111yescharacteristic
439Q16—41no—
440Q16—41no—
441SD16—41no—
442SD16—41no—
443M16—81no—
444M16—81no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—81no—
452C2×C8C22×C4×C1111yescharacteristic
453C2×C8C22×C4×C1111yescharacteristic
454C2×C8C22×C4×C1111yescharacteristic
455C2×C8C22×C4×C1111yescharacteristic
456C2×C8C2×D4×C1111yescharacteristic
457C2×C8C2×D4×C1111yescharacteristic
458C2×C8C2×D4×C1111yescharacteristic
459C2×C8C2×D4×C1111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4C22×C4×C1111yescharacteristic
470C4⋊C4C22×C4×C1111yescharacteristic
471C4⋊C4C22×C4×C1111yescharacteristic
472C4⋊C4C22×C4×C1111yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42C22×C4×C1111yescharacteristic
484C42C2×D4×C1111yescharacteristic
485C42C11×#4111yescharacteristic
486C42C24×C1111yescharacteristic
487C11#1794711yescharacteristic, direct product factor, Sylow
488C23—21no—
489C23C4×D4×C1111yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—42no—
497D4—21no—
498D4—21no—
499D4—81no—
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—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4C4×D4×C1111yescharacteristic
517C2×C4C4×D4×C1111yescharacteristic
518C2×C4C4×D4×C1111yescharacteristic
519C2×C4C23×C4×C1111yescharacteristic
520C2×C4C22×D4×C1111yescharacteristic
521C2×C4C2×C11×#4111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22C2×C4×D4×C1111yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4C11×#56811yescharacteristic
555C4C11×#56811yescharacteristic
556C4C11×#57711yescharacteristic
557C4C11×#57811yescharacteristic
558C2—41no—
559C2—81no—
560C2C11×#293011yescharacteristic
561C2C11×#294711yescharacteristic
562C2C11×#295711yescharacteristic
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×#2983C2semidirect
4. C11×#1593C2semidirect
5. C11×#1592C2semidirect
6. C11×#1591C2semidirect
7. C11×#1590C2semidirect
8. C11×#1587C2semidirect
9. C11×#1585C2semidirect
10. C11×#1584C2semidirect
11. C11×#1582C2semidirect
12. C11×#1574C2semidirect
13. C11×#1487C2semidirect
15. C11×#1454C2semidirect
144. #17947C11direct (N × H)
209. #2983C2×C11semidirect
210. #1593C2×C11semidirect
211. #1592C2×C11semidirect
212. #1591C2×C11semidirect
213. #1590C2×C11semidirect
214. #1587C2×C11semidirect
215. #1585C2×C11semidirect
216. #1584C2×C11semidirect
217. #1582C2×C11semidirect
218. #1574C2×C11semidirect
219. #1487C2×C11semidirect
221. #1454C2×C11semidirect
487. C11#17947direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31082
C11×#29932
C11×#29832
C11×#15932
C11×#15922
C11×#15912
C11×#15902
C11×#15872
C11×#15852
C11×#15842
C11×#15822
C11×#15742
C11×#14872
C11×#14822
C11×#14542
#1794711