Finite Group Databasebeta

← C11×#17954 #14595147

Subgroups — C11×#17954 #14595147

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3102C211yesmaximal, characteristic
2C11×#2993C211yesmaximal, characteristic, complemented
3C11×#2989C211yesmaximal, characteristic, complemented
4C11×#1592C211yesmaximal, characteristic, complemented
5C11×#1592C211yesmaximal, characteristic, complemented
6C11×#1591C211yesmaximal, characteristic, complemented
7C11×#1589C211yesmaximal, characteristic, complemented
8C11×#1588C211yesmaximal, characteristic, complemented
9C11×#1585C211yesmaximal, characteristic, complemented
10C11×#1584C211yesmaximal, characteristic, complemented
11C11×#1581C211yesmaximal, characteristic, complemented
12C11×#1571C211yesmaximal, characteristic, complemented
13C11×#1489C211yesmaximal, characteristic, complemented
14C11×#1483C211yesmaximal, characteristic, complemented
15C11×#1453C211yesmaximal, 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×#436—21no—
35C11×#436C2211yescharacteristic
36C11×#436C2211yescharacteristic
37C11×#436C2211yescharacteristic
38C11×#435—21no—
39C11×#435—21no—
40C11×#435—21no—
41C8×D4×C11C2211yescharacteristic
42C11×#433—21no—
43C11×#432—21no—
44C11×#431C2211yescharacteristic
45C11×#431C2211yescharacteristic
46C11×#424—21no—
47C11×#423—21no—
48C11×#423C2211yescharacteristic
49C2×C11×C4⋊C8C2211yescharacteristic
50C4×C11×M16C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#335C2211yescharacteristic
54C11×#335C2211yescharacteristic
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
66C82×C11C2211yescharacteristic
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—
75C2×C11×M16—21no—
76C2×C11×M16—21no—
77C22×C8×C11—21no—
78C22×C8×C11—21no—
79C11×#126—21no—
80C11×#125C2×C411yescharacteristic
81C11×#124C2×C411yescharacteristic
82C11×#123—21no—
83C11×C22⋊Q8C2×C411yescharacteristic
84C11×#121C2×C411yescharacteristic
85C4×Q8×C11C2×C411yescharacteristic
86C4×Q8×C11C2311yescharacteristic
87C4×Q8×C11C2311yescharacteristic
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11C2×C411yescharacteristic
92C4×D4×C11C2311yescharacteristic
93C4×D4×C11C2311yescharacteristic
94C11×#117—21no—
95C11×#117—21no—
96C11×#117C2×C411yescharacteristic
97C2×C42×C11—21no—
98C2×C42×C11C2311yescharacteristic
99C11×#107C2×C411yescharacteristic
100C11×#107C2×C411yescharacteristic
101C11×#106C2×C411yescharacteristic
102C11×#106C2×C411yescharacteristic
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⋊C8D411yescharacteristic
112C11×C4⋊C8D411yescharacteristic
113C11×C4⋊C8C2311yescharacteristic
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×#103C2×C411yescharacteristic
118C11×#103C2×C411yescharacteristic
119C11×#103C2×C411yescharacteristic
120C11×#103C2×C411yescharacteristic
121C11×#102C2×C411yescharacteristic
122C11×#102C2×C411yescharacteristic
123C11×#102C2×C411yescharacteristic
124C11×#102C2×C411yescharacteristic
125C11×C22⋊C8—21no—
126C11×C22⋊C8—21no—
127C11×C22⋊C8—21no—
128C11×C22⋊C8—21no—
129C11×C22⋊C8C2×C411yescharacteristic
130C11×C22⋊C8C2×C411yescharacteristic
131C11×C22⋊C8D411yescharacteristic
132C11×C22⋊C8D411yescharacteristic
133C11×#97—21no—
134C11×#97—21no—
135C11×#97—21no—
136C11×#97—21no—
137C4×C8×C11—21no—
138C4×C8×C11C2311yescharacteristic
139C4×C8×C11C2311yescharacteristic
140C4×C8×C11C2311yescharacteristic
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#17954C1111yesmaximal, 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—81no—
166C11×M16—81no—
167C11×M16—81no—
168C11×M16—81no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—81no—
176C2×C8×C11—81no—
177C2×C8×C11C22×C411yescharacteristic
178C2×C8×C11C22×C411yescharacteristic
179C2×C8×C11C22×C411yescharacteristic
180C2×C8×C11C22×C411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
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—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11C22×C411yescharacteristic
208C42×C11C2×D411yescharacteristic
209C42×C11#4111yescharacteristic
210C42×C11C2411yescharacteristic
211#3102C2×C1111yescharacteristic
212#2993C2×C1111yescharacteristic, complemented
213#2989C2×C1111yescharacteristic, complemented
214#1592C2×C1111yescharacteristic, complemented
215#1592C2×C1111yescharacteristic, complemented
216#1591C2×C1111yescharacteristic, complemented
217#1589C2×C1111yescharacteristic, complemented
218#1588C2×C1111yescharacteristic, complemented
219#1585C2×C1111yescharacteristic, complemented
220#1584C2×C1111yescharacteristic, complemented
221#1581C2×C1111yescharacteristic, complemented
222#1571C2×C1111yescharacteristic, complemented
223#1489C2×C1111yescharacteristic, complemented
224#1483C2×C1111yescharacteristic, complemented
225#1453C2×C1111yescharacteristic, complemented
226C23×C11—21no—
227C23×C11—21no—
228C23×C11C4×D411yescharacteristic
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—21no—
233D4×C11—21no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—42no—
238D4×C11—81no—
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—21no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—81no—
256C2×C4×C11C4×D411yescharacteristic
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11C4×D411yescharacteristic
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C8×C11—22no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276#529C22×C1111yescharacteristic
277C4×#41C22×C1111yescharacteristic
278#485C4×C1111yescharacteristic
279#482C4×C1111yescharacteristic
280#479C4×C1111yescharacteristic
281#478C4×C1111yescharacteristic
282#464C4×C1111yescharacteristic
283#463C4×C1111yescharacteristic
284#452C4×C1111yescharacteristic
285#449C4×C1111yescharacteristic
286#446C22×C1111yescharacteristic
287#446C22×C1111yescharacteristic
288#446C22×C1111yescharacteristic
289C8×Q8C22×C1111yescharacteristic
290C4×Q16C22×C1111yescharacteristic
291C4×SD16C22×C1111yescharacteristic
292C4×SD16C22×C1111yescharacteristic
293C4×D8C22×C1111yescharacteristic
294#436—21no—
295#436C22×C1111yescharacteristic
296#436C22×C1111yescharacteristic
297#436C22×C1111yescharacteristic
298#435—21no—
299#435—21no—
300#435—21no—
301C8×D4C22×C1111yescharacteristic
302#433—21no—
303#432—21no—
304#431C22×C1111yescharacteristic
305#431C22×C1111yescharacteristic
306#424—21no—
307#423—21no—
308#423C22×C1111yescharacteristic
309C2×C4⋊C8C22×C1111yescharacteristic
310C4×M16C22×C1111yescharacteristic
311#335C22×C1111yescharacteristic
312#335C22×C1111yescharacteristic
313#335C22×C1111yescharacteristic
314#335C22×C1111yescharacteristic
315Q8⋊C8C22×C1111yescharacteristic
316Q8⋊C8C22×C1111yescharacteristic
317Q8⋊C8C22×C1111yescharacteristic
318Q8⋊C8C22×C1111yescharacteristic
319D4⋊C8C22×C1111yescharacteristic
320D4⋊C8C22×C1111yescharacteristic
321D4⋊C8C22×C1111yescharacteristic
322D4⋊C8C22×C1111yescharacteristic
323#322C22×C1111yescharacteristic
324#322C22×C1111yescharacteristic
325#322C22×C1111yescharacteristic
326C82C22×C1111yescharacteristic
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C2×C4×D411yescharacteristic
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11#56811yescharacteristic
348C4×C11#56811yescharacteristic
349C4×C11#57611yescharacteristic
350C4×C11#57811yescharacteristic
351C2×#41C2×C4×C1111yescharacteristic
352C2×Q16C2×C4×C1111yescharacteristic
353C2×SD16C2×C4×C1111yescharacteristic
354C2×SD16C2×C4×C1111yescharacteristic
355C2×D8C2×C4×C1111yescharacteristic
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C22×C8—21no—
362C22×C8—21no—
363#126—21no—
364#125C2×C4×C1111yescharacteristic
365#124C2×C4×C1111yescharacteristic
366#123—21no—
367C22⋊Q8C2×C4×C1111yescharacteristic
368#121C2×C4×C1111yescharacteristic
369C4×Q8C2×C4×C1111yescharacteristic
370C4×Q8C23×C1111yescharacteristic
371C4×Q8C23×C1111yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4C2×C4×C1111yescharacteristic
376C4×D4C23×C1111yescharacteristic
377C4×D4C23×C1111yescharacteristic
378#117—21no—
379#117—21no—
380#117C2×C4×C1111yescharacteristic
381C2×C42—21no—
382C2×C42C23×C1111yescharacteristic
383#107C2×C4×C1111yescharacteristic
384#107C2×C4×C1111yescharacteristic
385#106C2×C4×C1111yescharacteristic
386#106C2×C4×C1111yescharacteristic
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8C2×C4×C1111yescharacteristic
394C4⋊C8C2×C4×C1111yescharacteristic
395C4⋊C8D4×C1111yescharacteristic
396C4⋊C8D4×C1111yescharacteristic
397C4⋊C8C23×C1111yescharacteristic
398C4⋊C8C23×C1111yescharacteristic
399C4⋊C8C23×C1111yescharacteristic
400C4⋊C8C23×C1111yescharacteristic
401#103C2×C4×C1111yescharacteristic
402#103C2×C4×C1111yescharacteristic
403#103C2×C4×C1111yescharacteristic
404#103C2×C4×C1111yescharacteristic
405#102C2×C4×C1111yescharacteristic
406#102C2×C4×C1111yescharacteristic
407#102C2×C4×C1111yescharacteristic
408#102C2×C4×C1111yescharacteristic
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8C2×C4×C1111yescharacteristic
414C22⋊C8C2×C4×C1111yescharacteristic
415C22⋊C8D4×C1111yescharacteristic
416C22⋊C8D4×C1111yescharacteristic
417#97—21no—
418#97—21no—
419#97—21no—
420#97—21no—
421C4×C8—21no—
422C4×C8C23×C1111yescharacteristic
423C4×C8C23×C1111yescharacteristic
424C4×C8C23×C1111yescharacteristic
425C4×C8C23×C1111yescharacteristic
426C4×C8C23×C1111yescharacteristic
427C4×C8C23×C1111yescharacteristic
428C2×C11—41no—
429C2×C11—81no—
430C2×C11—81no—
431C2×C11#293011yescharacteristic
432C2×C11#295111yescharacteristic
433C2×C11#295611yescharacteristic
434#41—41no—
435#41—41no—
436C2×Q8C22×C4×C1111yescharacteristic
437C2×Q8C22×C4×C1111yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C22×C4×C1111yescharacteristic
441C2×D4C22×C4×C1111yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4C22×C4×C1111yescharacteristic
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C11×#4111yescharacteristic
449Q16—41no—
450SD16—41no—
451SD16—41no—
452D8—41no—
453M16—42no—
454M16—81no—
455M16—81no—
456M16—81no—
457M16—81no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—81no—
465C2×C8—81no—
466C2×C8C22×C4×C1111yescharacteristic
467C2×C8C22×C4×C1111yescharacteristic
468C2×C8C22×C4×C1111yescharacteristic
469C2×C8C22×C4×C1111yescharacteristic
470C2×C8C2×D4×C1111yescharacteristic
471C2×C8C2×D4×C1111yescharacteristic
472C2×C8C2×D4×C1111yescharacteristic
473C2×C8C2×D4×C1111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4C22×C4×C1111yescharacteristic
481C4⋊C4C22×C4×C1111yescharacteristic
482C4⋊C4C22×C4×C1111yescharacteristic
483C4⋊C4C22×C4×C1111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42C22×C4×C1111yescharacteristic
497C42C2×D4×C1111yescharacteristic
498C42C11×#4111yescharacteristic
499C42C24×C1111yescharacteristic
500C11#1795411yescharacteristic, direct product factor, Sylow
501C23—21no—
502C23—21no—
503C23C4×D4×C1111yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—42no—
513D4—81no—
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—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4C4×D4×C1111yescharacteristic
532C2×C4C4×D4×C1111yescharacteristic
533C2×C4C4×D4×C1111yescharacteristic
534C2×C4C23×C4×C1111yescharacteristic
535C2×C4C22×D4×C1111yescharacteristic
536C2×C4C2×C11×#4111yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22C2×C4×D4×C1111yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4C11×#56811yescharacteristic
572C4C11×#56811yescharacteristic
573C4C11×#57611yescharacteristic
574C4C11×#57811yescharacteristic
575C2—41no—
576C2—81no—
577C2—81no—
578C2C11×#293011yescharacteristic
579C2C11×#295111yescharacteristic
580C2C11×#295611yescharacteristic
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 ◁ C11×#431 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2993C2semidirect
3. C11×#2989C2semidirect
4. C11×#1592C2semidirect
5. C11×#1592C2semidirect
6. C11×#1591C2semidirect
7. C11×#1589C2semidirect
8. C11×#1588C2semidirect
9. C11×#1585C2semidirect
10. C11×#1584C2semidirect
11. C11×#1581C2semidirect
12. C11×#1571C2semidirect
13. C11×#1489C2semidirect
14. C11×#1483C2semidirect
15. C11×#1453C2semidirect
144. #17954C11direct (N × H)
212. #2993C2×C11semidirect
213. #2989C2×C11semidirect
214. #1592C2×C11semidirect
215. #1592C2×C11semidirect
216. #1591C2×C11semidirect
217. #1589C2×C11semidirect
218. #1588C2×C11semidirect
219. #1585C2×C11semidirect
220. #1584C2×C11semidirect
221. #1581C2×C11semidirect
222. #1571C2×C11semidirect
223. #1489C2×C11semidirect
224. #1483C2×C11semidirect
225. #1453C2×C11semidirect
500. C11#17954direct (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×#29932
C11×#29892
C11×#15922
C11×#15912
C11×#15892
C11×#15882
C11×#15852
C11×#15842
C11×#15812
C11×#15712
C11×#14892
C11×#14832
C11×#14532
#1795411