Finite Group Databasebeta

← C11×#17937 #14595130

Subgroups — C11×#17937 #14595130

Order 2816.

596 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3102C211yesmaximal, characteristic
2C11×#2966C211yesmaximal, characteristic, complemented
3C11×#2965C211yesmaximal, characteristic, complemented
4C11×#1594C211yesmaximal, characteristic, complemented
5C11×#1593C211yesmaximal, characteristic, complemented
6C11×#1592C211yesmaximal, characteristic, complemented
7C11×#1592C211yesmaximal, characteristic, complemented
8C11×#1588C211yesmaximal, characteristic, complemented
9C11×#1587C211yesmaximal, characteristic, complemented
10C11×#1586C211yesmaximal, characteristic, complemented
11C11×#1585C211yesmaximal, characteristic, complemented
12C11×#1572C211yesmaximal, characteristic, complemented
13C11×#1488C211yesmaximal, characteristic, complemented
14C11×#1482C211yesmaximal, characteristic, complemented
15C11×#1452C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C11×#485C411yescharacteristic
19C11×#482C411yescharacteristic
20C11×#479C411yescharacteristic
21C11×#478C411yescharacteristic
22C11×#464C411yescharacteristic
23C11×#463C411yescharacteristic
24C11×#452C411yescharacteristic
25C11×#449C411yescharacteristic
26C11×#446C2211yescharacteristic
27C11×#446C2211yescharacteristic
28C11×#446C2211yescharacteristic
29C8×Q8×C11C2211yescharacteristic
30C4×C11×Q16C2211yescharacteristic
31C4×C11×SD16C2211yescharacteristic
32C4×C11×SD16C2211yescharacteristic
33C4×C11×D8C2211yescharacteristic
34C11×#436C2211yescharacteristic
35C11×#436C2211yescharacteristic
36C11×#436C2211yescharacteristic
37C11×#435—21no—
38C11×#435—21no—
39C11×#435—21no—
40C8×D4×C11—21no—
41C8×D4×C11C2211yescharacteristic
42C11×#433—21no—
43C11×#432C2211yescharacteristic
44C11×#431—21no—
45C11×#431C2211yescharacteristic
46C11×#431C2211yescharacteristic
47C11×#431C2211yescharacteristic
48C11×#405—21no—
49C4×C11×M16—21no—
50C2×C4×C8×C11C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#334C2211yescharacteristic
54C11×#334C2211yescharacteristic
55C11×Q8⋊C8C2211yescharacteristic
56C11×Q8⋊C8C2211yescharacteristic
57C11×Q8⋊C8C2211yescharacteristic
58C11×Q8⋊C8C2211yescharacteristic
59C11×D4⋊C8C2211yescharacteristic
60C11×D4⋊C8C2211yescharacteristic
61C11×D4⋊C8C2211yescharacteristic
62C11×D4⋊C8C2211yescharacteristic
63C11×#322C2211yescharacteristic
64C11×#322C2211yescharacteristic
65C11×#322C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×D8C2×C411yescharacteristic
72C2×C11×M16—21no—
73C2×C11×M16—21no—
74C2×C11×M16—21no—
75C22×C8×C11—21no—
76C22×C8×C11D411yescharacteristic
77C22×C8×C11D411yescharacteristic
78C11×#126—21no—
79C11×#125C2×C411yescharacteristic
80C11×#124C2×C411yescharacteristic
81C11×#123—21no—
82C11×C22⋊Q8C2×C411yescharacteristic
83C11×#121C2×C411yescharacteristic
84C4×Q8×C11C2×C411yescharacteristic
85C4×Q8×C11C2311yescharacteristic
86C4×Q8×C11C2311yescharacteristic
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11C2×C411yescharacteristic
91C4×D4×C11C2311yescharacteristic
92C4×D4×C11C2311yescharacteristic
93C11×#117—21no—
94C11×#117—21no—
95C11×#117C2×C411yescharacteristic
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C11×#107C2×C411yescharacteristic
99C11×#107C2×C411yescharacteristic
100C11×#106C2×C411yescharacteristic
101C11×#106C2×C411yescharacteristic
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⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×C4⋊C8C2311yescharacteristic
113C11×#103C2×C411yescharacteristic
114C11×#103C2×C411yescharacteristic
115C11×#103C2×C411yescharacteristic
116C11×#103C2×C411yescharacteristic
117C11×#102C2×C411yescharacteristic
118C11×#102C2×C411yescharacteristic
119C11×#102C2×C411yescharacteristic
120C11×#102C2×C411yescharacteristic
121C11×C22⋊C8—21no—
122C11×C22⋊C8—21no—
123C11×C22⋊C8—21no—
124C11×C22⋊C8—21no—
125C11×C22⋊C8—21no—
126C11×C22⋊C8—21no—
127C11×C22⋊C8—21no—
128C11×C22⋊C8C2×C411yescharacteristic
129C11×C22⋊C8C2×C411yescharacteristic
130C11×#97—21no—
131C11×#97—21no—
132C11×#97—21no—
133C11×#97—21no—
134C4×C8×C11—21no—
135C4×C8×C11—21no—
136C4×C8×C11D411yescharacteristic
137C4×C8×C11D411yescharacteristic
138C4×C8×C11C2311yescharacteristic
139C4×C8×C11C2311yescharacteristic
140C4×C8×C11C2311yescharacteristic
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#17937C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—41no—
146C11×#41—41no—
147C2×Q8×C11C22×C411yescharacteristic
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11C22×C411yescharacteristic
152C2×D4×C11C22×C411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C11×Q16—41no—
161C11×SD16—41no—
162C11×SD16—41no—
163C11×D8—41no—
164C11×M16—42no—
165C11×M16—42no—
166C11×M16—42no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—41no—
174C2×C8×C11—41no—
175C2×C8×C11—42no—
176C2×C8×C11C22×C411yescharacteristic
177C2×C8×C11C22×C411yescharacteristic
178C2×C8×C11C22×C411yescharacteristic
179C2×C8×C11C22×C411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
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⋊C4C22×C411yescharacteristic
191C11×C4⋊C4C22×C411yescharacteristic
192C11×C4⋊C4C22×C411yescharacteristic
193C11×C4⋊C4C22×C411yescharacteristic
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11C22×C411yescharacteristic
207C42×C11C2×D411yescharacteristic
208C42×C11#4111yescharacteristic
209C42×C11C2411yescharacteristic
210#3102C2×C1111yescharacteristic
211#2966C2×C1111yescharacteristic, complemented
212#2965C2×C1111yescharacteristic, complemented
213#1594C2×C1111yescharacteristic, complemented
214#1593C2×C1111yescharacteristic, complemented
215#1592C2×C1111yescharacteristic, complemented
216#1592C2×C1111yescharacteristic, complemented
217#1588C2×C1111yescharacteristic, complemented
218#1587C2×C1111yescharacteristic, complemented
219#1586C2×C1111yescharacteristic, complemented
220#1585C2×C1111yescharacteristic, complemented
221#1572C2×C1111yescharacteristic, complemented
222#1488C2×C1111yescharacteristic, complemented
223#1482C2×C1111yescharacteristic, complemented
224#1452C2×C1111yescharacteristic, complemented
225C23×C11—21no—
226C23×C11—21no—
227C23×C11C4×D411yescharacteristic
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232D4×C11—21no—
233D4×C11—21no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—42no—
237D4×C11—42no—
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—42no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11C4×D411yescharacteristic
256C2×C4×C11C4×D411yescharacteristic
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11—41no—
275#529C22×C1111yescharacteristic
276C4×#41C22×C1111yescharacteristic
277#485C4×C1111yescharacteristic
278#482C4×C1111yescharacteristic
279#479C4×C1111yescharacteristic
280#478C4×C1111yescharacteristic
281#464C4×C1111yescharacteristic
282#463C4×C1111yescharacteristic
283#452C4×C1111yescharacteristic
284#449C4×C1111yescharacteristic
285#446C22×C1111yescharacteristic
286#446C22×C1111yescharacteristic
287#446C22×C1111yescharacteristic
288C8×Q8C22×C1111yescharacteristic
289C4×Q16C22×C1111yescharacteristic
290C4×SD16C22×C1111yescharacteristic
291C4×SD16C22×C1111yescharacteristic
292C4×D8C22×C1111yescharacteristic
293#436C22×C1111yescharacteristic
294#436C22×C1111yescharacteristic
295#436C22×C1111yescharacteristic
296#435—21no—
297#435—21no—
298#435—21no—
299C8×D4—21no—
300C8×D4C22×C1111yescharacteristic
301#433—21no—
302#432C22×C1111yescharacteristic
303#431—21no—
304#431C22×C1111yescharacteristic
305#431C22×C1111yescharacteristic
306#431C22×C1111yescharacteristic
307#405—21no—
308C4×M16—21no—
309C2×C4×C8C22×C1111yescharacteristic
310#335C22×C1111yescharacteristic
311#335C22×C1111yescharacteristic
312#334C22×C1111yescharacteristic
313#334C22×C1111yescharacteristic
314Q8⋊C8C22×C1111yescharacteristic
315Q8⋊C8C22×C1111yescharacteristic
316Q8⋊C8C22×C1111yescharacteristic
317Q8⋊C8C22×C1111yescharacteristic
318D4⋊C8C22×C1111yescharacteristic
319D4⋊C8C22×C1111yescharacteristic
320D4⋊C8C22×C1111yescharacteristic
321D4⋊C8C22×C1111yescharacteristic
322#322C22×C1111yescharacteristic
323#322C22×C1111yescharacteristic
324#322C22×C1111yescharacteristic
325#322C22×C1111yescharacteristic
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11C2×C4×D411yescharacteristic
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11#56811yescharacteristic
347C4×C11#56811yescharacteristic
348C4×C11#57511yescharacteristic
349C4×C11#57511yescharacteristic
350C2×#41C2×C4×C1111yescharacteristic
351C2×Q16C2×C4×C1111yescharacteristic
352C2×SD16C2×C4×C1111yescharacteristic
353C2×SD16C2×C4×C1111yescharacteristic
354C2×D8C2×C4×C1111yescharacteristic
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C22×C8—21no—
359C22×C8D4×C1111yescharacteristic
360C22×C8D4×C1111yescharacteristic
361#126—21no—
362#125C2×C4×C1111yescharacteristic
363#124C2×C4×C1111yescharacteristic
364#123—21no—
365C22⋊Q8C2×C4×C1111yescharacteristic
366#121C2×C4×C1111yescharacteristic
367C4×Q8C2×C4×C1111yescharacteristic
368C4×Q8C23×C1111yescharacteristic
369C4×Q8C23×C1111yescharacteristic
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4C2×C4×C1111yescharacteristic
374C4×D4C23×C1111yescharacteristic
375C4×D4C23×C1111yescharacteristic
376#117—21no—
377#117—21no—
378#117C2×C4×C1111yescharacteristic
379C2×C42—21no—
380C2×C42C23×C1111yescharacteristic
381#107C2×C4×C1111yescharacteristic
382#107C2×C4×C1111yescharacteristic
383#106C2×C4×C1111yescharacteristic
384#106C2×C4×C1111yescharacteristic
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8C2×C4×C1111yescharacteristic
391C4⋊C8C2×C4×C1111yescharacteristic
392C4⋊C8C23×C1111yescharacteristic
393C4⋊C8C23×C1111yescharacteristic
394C4⋊C8C23×C1111yescharacteristic
395C4⋊C8C23×C1111yescharacteristic
396#103C2×C4×C1111yescharacteristic
397#103C2×C4×C1111yescharacteristic
398#103C2×C4×C1111yescharacteristic
399#103C2×C4×C1111yescharacteristic
400#102C2×C4×C1111yescharacteristic
401#102C2×C4×C1111yescharacteristic
402#102C2×C4×C1111yescharacteristic
403#102C2×C4×C1111yescharacteristic
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8C2×C4×C1111yescharacteristic
412C22⋊C8C2×C4×C1111yescharacteristic
413#97—21no—
414#97—21no—
415#97—21no—
416#97—21no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8D4×C1111yescharacteristic
420C4×C8D4×C1111yescharacteristic
421C4×C8C23×C1111yescharacteristic
422C4×C8C23×C1111yescharacteristic
423C4×C8C23×C1111yescharacteristic
424C4×C8C23×C1111yescharacteristic
425C4×C8C23×C1111yescharacteristic
426C4×C8C23×C1111yescharacteristic
427C2×C11—41no—
428C2×C11—81no—
429C2×C11—81no—
430C2×C11#293011yescharacteristic
431C2×C11#294311yescharacteristic
432C2×C11#295511yescharacteristic
433#41—41no—
434#41—41no—
435C2×Q8C22×C4×C1111yescharacteristic
436C2×Q8C22×C4×C1111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4C22×C4×C1111yescharacteristic
440C2×D4C22×C4×C1111yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4C22×C4×C1111yescharacteristic
446C22×C4C2×D4×C1111yescharacteristic
447C22×C4C11×#4111yescharacteristic
448Q16—41no—
449SD16—41no—
450SD16—41no—
451D8—41no—
452M16—42no—
453M16—42no—
454M16—42no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—42no—
464C2×C8C22×C4×C1111yescharacteristic
465C2×C8C22×C4×C1111yescharacteristic
466C2×C8C22×C4×C1111yescharacteristic
467C2×C8C22×C4×C1111yescharacteristic
468C2×C8C2×D4×C1111yescharacteristic
469C2×C8C2×D4×C1111yescharacteristic
470C2×C8C2×D4×C1111yescharacteristic
471C2×C8C2×D4×C1111yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4C22×C4×C1111yescharacteristic
479C4⋊C4C22×C4×C1111yescharacteristic
480C4⋊C4C22×C4×C1111yescharacteristic
481C4⋊C4C22×C4×C1111yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42C22×C4×C1111yescharacteristic
495C42C2×D4×C1111yescharacteristic
496C42C11×#4111yescharacteristic
497C42C24×C1111yescharacteristic
498C11#1793711yescharacteristic, direct product factor, Sylow
499C23—21no—
500C23—21no—
501C23C4×D4×C1111yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—21no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—42no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4C4×D4×C1111yescharacteristic
530C2×C4C4×D4×C1111yescharacteristic
531C2×C4C4×D4×C1111yescharacteristic
532C2×C4C23×C4×C1111yescharacteristic
533C2×C4C22×D4×C1111yescharacteristic
534C2×C4C2×C11×#4111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—41no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22C2×C4×D4×C1111yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4C11×#56811yescharacteristic
570C4C11×#56811yescharacteristic
571C4C11×#57511yescharacteristic
572C4C11×#57511yescharacteristic
573C2—41no—
574C2—81no—
575C2—81no—
576C2C11×#293011yescharacteristic
577C2C11×#294311yescharacteristic
578C2C11×#295511yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC42C24×C11
socleC22×C11C2×C4×D4
prime radicalC11×#449C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2966C2semidirect
3. C11×#2965C2semidirect
4. C11×#1594C2semidirect
5. C11×#1593C2semidirect
6. C11×#1592C2semidirect
7. C11×#1592C2semidirect
8. C11×#1588C2semidirect
9. C11×#1587C2semidirect
10. C11×#1586C2semidirect
11. C11×#1585C2semidirect
12. C11×#1572C2semidirect
13. C11×#1488C2semidirect
14. C11×#1482C2semidirect
15. C11×#1452C2semidirect
144. #17937C11direct (N × H)
211. #2966C2×C11semidirect
212. #2965C2×C11semidirect
213. #1594C2×C11semidirect
214. #1593C2×C11semidirect
215. #1592C2×C11semidirect
216. #1592C2×C11semidirect
217. #1588C2×C11semidirect
218. #1587C2×C11semidirect
219. #1586C2×C11semidirect
220. #1585C2×C11semidirect
221. #1572C2×C11semidirect
222. #1488C2×C11semidirect
223. #1482C2×C11semidirect
224. #1452C2×C11semidirect
498. C11#17937direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31022
C11×#29662
C11×#29652
C11×#15942
C11×#15932
C11×#15922
C11×#15882
C11×#15872
C11×#15862
C11×#15852
C11×#15722
C11×#14882
C11×#14822
C11×#14522
#1793711