Finite Group Databasebeta

← C11×#22097 #14599290

Subgroups — C11×#22097 #14599290

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3091C211yesmaximal, characteristic
2C11×#2930C211yesmaximal, characteristic
3C11×#2905C211yesmaximal, characteristic, complemented
4C11×#1946C211yesmaximal, characteristic, complemented
5C11×#1945C211yesmaximal, characteristic, complemented
6C11×#1938C211yesmaximal, characteristic, complemented
7C11×#1937C211yesmaximal, characteristic, complemented
8C11×#1922C211yesmaximal, characteristic, complemented
9C11×#1922C211yesmaximal, characteristic, complemented
10C11×#1871C211yesmaximal, characteristic
11C11×#1866C211yesmaximal, characteristic, complemented
12C11×#1866C211yesmaximal, characteristic, complemented
13C11×#1855C211yesmaximal, characteristic, complemented
14C11×#1826C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C11×#525C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C11×#485C411yescharacteristic, complemented
22C11×#485C411yescharacteristic, complemented
23C11×#484C411yescharacteristic, complemented
24C11×#483C411yescharacteristic, complemented
25C11×#482C411yescharacteristic, complemented
26C11×#482C411yescharacteristic, complemented
27C11×#481C411yescharacteristic, complemented
28C11×#480C411yescharacteristic, complemented
29C11×#436—21no—
30C11×#436—21no—
31C11×#435—21no—
32C11×#435—21no—
33C2×C11×#108C2211yescharacteristic
34C2×C11×#108C2211yescharacteristic
35C11×#427C2211yescharacteristic
36C11×#427C2211yescharacteristic
37C11×#424—21no—
38C11×#424—21no—
39C11×#424C2211yescharacteristic
40C11×#424C2211yescharacteristic
41C11×#424C2211yescharacteristic
42C11×#424C2211yescharacteristic
43C11×#424C2211yescharacteristic
44C11×#423—21no—
45C11×#423—21no—
46C2×C11×#104C2211yescharacteristic
47C2×C11×#104C2211yescharacteristic
48C11×#416C2211yescharacteristic
49C11×#416C2211yescharacteristic
50C11×#408C2211yescharacteristic
51C11×#407C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C11×#405C2211yescharacteristic
54C2×C11×#97C2211yescharacteristic
55C2×C4×C8×C11C2211yescharacteristic
56C4×C11×C22⋊C4C2211yescharacteristic
57C11×#341C2211yescharacteristic
58C11×#341C2211yescharacteristic
59C11×#339C2211yescharacteristic
60C11×#339C2211yescharacteristic
61C11×#339C2211yescharacteristic
62C11×#339C2211yescharacteristic
63C11×#339C2211yescharacteristic
64C11×#339C2211yescharacteristic
65C11×#336C2211yescharacteristic
66C11×#336C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C11×#131—41no—
70C11×#131—41no—
71C2×C11×M16—21no—
72C2×C11×M16—21no—
73C2×C11×M16—41no—
74C2×C11×M16—41no—
75C2×C11×M16—41no—
76C2×C11×M16—41no—
77C2×C11×M16D411yescharacteristic
78C2×C11×M16D411yescharacteristic
79C2×C11×M16D411yescharacteristic
80C2×C11×M16D411yescharacteristic
81C2×C11×M16C2311yescharacteristic
82C2×C11×M16C2311yescharacteristic
83C2×C11×M16C2311yescharacteristic
84C2×C11×M16C2311yescharacteristic
85C22×C8×C11—21no—
86C22×C8×C11—21no—
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C11×#123—21no—
92C11×C22⋊Q8C2×C411yescharacteristic
93C11×C22⋊Q8C2×C411yescharacteristic
94C11×#121C2×C411yescharacteristic
95C11×#121C2×C411yescharacteristic
96C11×#120—21no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C11×#117—21no—
100C11×#117—21no—
101C11×#117C2×C411yescharacteristic
102C11×#117C2×C411yescharacteristic
103C11×#117C2311yescharacteristic
104C11×#117C2311yescharacteristic
105C11×#117C2311yescharacteristic
106C2×C11×C4⋊C4C2×C411yescharacteristic
107C2×C11×C4⋊C4C2×C411yescharacteristic
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C11×#108—41no—
114C11×#108—41no—
115C11×#107C2×C411yescharacteristic
116C11×#107C2×C411yescharacteristic
117C11×#107C2×C411yescharacteristic
118C11×#107C2×C411yescharacteristic
119C11×#106C2×C411yescharacteristic
120C11×#106C2×C411yescharacteristic
121C11×#106C2×C411yescharacteristic
122C11×#106C2×C411yescharacteristic
123C11×C4⋊C8—21no—
124C11×C4⋊C8—21no—
125C11×C4⋊C8—21no—
126C11×C4⋊C8—21no—
127C11×C4⋊C8—21no—
128C11×C4⋊C8—21no—
129C11×C4⋊C8—21no—
130C11×C4⋊C8—21no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×#104—41no—
134C11×#104—41no—
135C11×#103C2×C411yescharacteristic
136C11×#103C2×C411yescharacteristic
137C11×#103C2×C411yescharacteristic
138C11×#103C2×C411yescharacteristic
139C11×#102C2×C411yescharacteristic
140C11×#102C2×C411yescharacteristic
141C11×#102C2×C411yescharacteristic
142C11×#102C2×C411yescharacteristic
143C11×C22⋊C8—21no—
144C11×C22⋊C8—21no—
145C11×C22⋊C8—21no—
146C11×C22⋊C8—21no—
147C11×C22⋊C8C2×C411yescharacteristic
148C11×C22⋊C8C2×C411yescharacteristic
149C11×C22⋊C8C2×C411yescharacteristic
150C11×C22⋊C8C2×C411yescharacteristic
151C11×#97—21no—
152C11×#97—41no—
153C4×C8×C11—21no—
154C4×C8×C11—41no—
155C11×#95—21no—
156#22097C1111yesmaximal, characteristic, direct product factor, Sylow
157C24×C11#4111yescharacteristic
158C11×#41—21no—
159C11×#41—21no—
160C11×#41—21no—
161C11×#41—21no—
162C2×Q8×C11C22×C411yescharacteristic
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11C22×C411yescharacteristic
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11#4111yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16—21no—
186C11×M16—21no—
187C11×M16—21no—
188C11×M16—21no—
189C11×M16—21no—
190C11×M16—41no—
191C11×M16—41no—
192C11×M16—41no—
193C11×M16—41no—
194C11×M16—42no—
195C11×M16—42no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—42no—
209C2×C8×C11—42no—
210C2×C8×C11C22×C411yescharacteristic
211C2×C8×C11C22×C411yescharacteristic
212C2×C8×C11C22×C411yescharacteristic
213C2×C8×C11C22×C411yescharacteristic
214C2×C8×C11C2×D411yescharacteristic
215C2×C8×C11C2×D411yescharacteristic
216C2×C8×C11C2×D411yescharacteristic
217C2×C8×C11C2×D411yescharacteristic
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4C22×C411yescharacteristic
223C11×C4⋊C4C22×C411yescharacteristic
224C11×C4⋊C4C22×C411yescharacteristic
225C11×C4⋊C4C22×C411yescharacteristic
226C11×C4⋊C4C22×C411yescharacteristic
227C11×C4⋊C4C22×C411yescharacteristic
228C11×C22⋊C4—21no—
229C11×C22⋊C4—21no—
230C11×C22⋊C4—21no—
231C11×C22⋊C4—21no—
232C11×C22⋊C4—21no—
233C11×C22⋊C4—21no—
234C11×C22⋊C4—21no—
235C11×C22⋊C4—21no—
236C11×C22⋊C4—21no—
237C11×C22⋊C4—42no—
238C42×C11—21no—
239C42×C11—21no—
240C42×C11—21no—
241C42×C11—21no—
242C42×C11—21no—
243C42×C11—21no—
244C42×C11—21no—
245C42×C11—21no—
246C42×C11—21no—
247#3091C2×C1111yescharacteristic
248#2930C2×C1111yescharacteristic
249#2905C2×C1111yescharacteristic, complemented
250#1946C2×C1111yescharacteristic, complemented
251#1945C2×C1111yescharacteristic, complemented
252#1938C2×C1111yescharacteristic, complemented
253#1937C2×C1111yescharacteristic, complemented
254#1922C2×C1111yescharacteristic, complemented
255#1922C2×C1111yescharacteristic, complemented
256#1871C2×C1111yescharacteristic
257#1866C2×C1111yescharacteristic, complemented
258#1866C2×C1111yescharacteristic, complemented
259#1855C2×C1111yescharacteristic, complemented
260#1826C2×C1111yescharacteristic, complemented
261#1753C2×C1111yescharacteristic, complemented
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11C4×D411yescharacteristic
268C23×C11C4×D411yescharacteristic
269C23×C11C2×#4111yescharacteristic
270Q8×C11—21no—
271Q8×C11—21no—
272D4×C11—21no—
273D4×C11—21no—
274D4×C11—41no—
275D4×C11—41no—
276D4×C11—81no—
277D4×C11—81no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—81no—
304C2×C4×C11—81no—
305C2×C4×C11C4×D411yescharacteristic
306C2×C4×C11C4×D411yescharacteristic
307C2×C4×C11C23×C411yescharacteristic
308C2×C4×C11C22×D411yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C2×C4×C112−1+411yescharacteristic
312C2×C4×C112−1+411yescharacteristic
313C8×C11—21no—
314C8×C11—21no—
315C8×C11—21no—
316C8×C11—21no—
317C8×C11—21no—
318C8×C11—21no—
319C8×C11—21no—
320C8×C11—21no—
321C8×C11—41no—
322C8×C11—41no—
323C8×C11—41no—
324C8×C11—41no—
325C2×#131C22×C1111yescharacteristic
326C22×M16C22×C1111yescharacteristic
327C22×M16C22×C1111yescharacteristic
328#525C22×C1111yescharacteristic
329C2×#117C22×C1111yescharacteristic
330#485C4×C1111yescharacteristic, complemented
331#485C4×C1111yescharacteristic, complemented
332#484C4×C1111yescharacteristic, complemented
333#483C4×C1111yescharacteristic, complemented
334#482C4×C1111yescharacteristic, complemented
335#482C4×C1111yescharacteristic, complemented
336#481C4×C1111yescharacteristic, complemented
337#480C4×C1111yescharacteristic, complemented
338#436—21no—
339#436—21no—
340#435—21no—
341#435—21no—
342C2×#108C22×C1111yescharacteristic
343C2×#108C22×C1111yescharacteristic
344#427C22×C1111yescharacteristic
345#427C22×C1111yescharacteristic
346#424—21no—
347#424—21no—
348#424C22×C1111yescharacteristic
349#424C22×C1111yescharacteristic
350#424C22×C1111yescharacteristic
351#424C22×C1111yescharacteristic
352#424C22×C1111yescharacteristic
353#423—21no—
354#423—21no—
355C2×#104C22×C1111yescharacteristic
356C2×#104C22×C1111yescharacteristic
357#416C22×C1111yescharacteristic
358#416C22×C1111yescharacteristic
359#408C22×C1111yescharacteristic
360#407C22×C1111yescharacteristic
361C2×C22⋊C8C22×C1111yescharacteristic
362#405C22×C1111yescharacteristic
363C2×#97C22×C1111yescharacteristic
364C2×C4×C8C22×C1111yescharacteristic
365C4×C22⋊C4C22×C1111yescharacteristic
366#341C22×C1111yescharacteristic
367#341C22×C1111yescharacteristic
368#339C22×C1111yescharacteristic
369#339C22×C1111yescharacteristic
370#339C22×C1111yescharacteristic
371#339C22×C1111yescharacteristic
372#339C22×C1111yescharacteristic
373#339C22×C1111yescharacteristic
374#336C22×C1111yescharacteristic
375#336C22×C1111yescharacteristic
376C22×C11—21no—
377C22×C11—21no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—21no—
381C22×C11—21no—
382C22×C11—21no—
383C22×C11—21no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11C2×C4×D411yescharacteristic
390C22×C11#53911yescharacteristic
391C22×C11#53911yescharacteristic
392C4×C11—21no—
393C4×C11—21no—
394C4×C11—42no—
395C4×C11—41no—
396C4×C11—41no—
397C4×C11—41no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11—41no—
401C4×C11—41no—
402C4×C11—81no—
403C4×C11#52011yescharacteristic
404C4×C11#52011yescharacteristic
405C4×C11#53411yescharacteristic
406C4×C11#53611yescharacteristic
407C2×#41C23×C1111yescharacteristic
408C23×C4C23×C1111yescharacteristic
409#131—41no—
410#131—41no—
411C2×M16—21no—
412C2×M16—21no—
413C2×M16—41no—
414C2×M16—41no—
415C2×M16—41no—
416C2×M16—41no—
417C2×M16D4×C1111yescharacteristic
418C2×M16D4×C1111yescharacteristic
419C2×M16D4×C1111yescharacteristic
420C2×M16D4×C1111yescharacteristic
421C2×M16C23×C1111yescharacteristic
422C2×M16C23×C1111yescharacteristic
423C2×M16C23×C1111yescharacteristic
424C2×M16C23×C1111yescharacteristic
425C22×C8—21no—
426C22×C8—21no—
427C22×C8C23×C1111yescharacteristic
428C22×C8C23×C1111yescharacteristic
429C22×C8C23×C1111yescharacteristic
430C22×C8C23×C1111yescharacteristic
431#123—21no—
432C22⋊Q8C2×C4×C1111yescharacteristic
433C22⋊Q8C2×C4×C1111yescharacteristic
434#121C2×C4×C1111yescharacteristic
435#121C2×C4×C1111yescharacteristic
436#120—21no—
437C4×D4—21no—
438C4×D4—21no—
439#117—21no—
440#117—21no—
441#117C2×C4×C1111yescharacteristic
442#117C2×C4×C1111yescharacteristic
443#117C23×C1111yescharacteristic
444#117C23×C1111yescharacteristic
445#117C23×C1111yescharacteristic
446C2×C4⋊C4C2×C4×C1111yescharacteristic
447C2×C4⋊C4C2×C4×C1111yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C42—21no—
451C2×C42C23×C1111yescharacteristic
452C2×C42C23×C1111yescharacteristic
453#108—41no—
454#108—41no—
455#107C2×C4×C1111yescharacteristic
456#107C2×C4×C1111yescharacteristic
457#107C2×C4×C1111yescharacteristic
458#107C2×C4×C1111yescharacteristic
459#106C2×C4×C1111yescharacteristic
460#106C2×C4×C1111yescharacteristic
461#106C2×C4×C1111yescharacteristic
462#106C2×C4×C1111yescharacteristic
463C4⋊C8—21no—
464C4⋊C8—21no—
465C4⋊C8—21no—
466C4⋊C8—21no—
467C4⋊C8—21no—
468C4⋊C8—21no—
469C4⋊C8—21no—
470C4⋊C8—21no—
471C4⋊C8—21no—
472C4⋊C8—21no—
473#104—41no—
474#104—41no—
475#103C2×C4×C1111yescharacteristic
476#103C2×C4×C1111yescharacteristic
477#103C2×C4×C1111yescharacteristic
478#103C2×C4×C1111yescharacteristic
479#102C2×C4×C1111yescharacteristic
480#102C2×C4×C1111yescharacteristic
481#102C2×C4×C1111yescharacteristic
482#102C2×C4×C1111yescharacteristic
483C22⋊C8—21no—
484C22⋊C8—21no—
485C22⋊C8—21no—
486C22⋊C8—21no—
487C22⋊C8C2×C4×C1111yescharacteristic
488C22⋊C8C2×C4×C1111yescharacteristic
489C22⋊C8C2×C4×C1111yescharacteristic
490C22⋊C8C2×C4×C1111yescharacteristic
491#97—21no—
492#97—41no—
493C4×C8—21no—
494C4×C8—41no—
495#95—21no—
496C2×C11—21no—
497C2×C11—21no—
498C2×C11—41no—
499C2×C11—41no—
500C2×C11—81no—
501C2×C11#232211yescharacteristic
502C2×C11#295611yescharacteristic
503C2×C11#295711yescharacteristic
504C24C11×#4111yescharacteristic
505#41—21no—
506#41—21no—
507#41—21no—
508#41—21no—
509C2×Q8C22×C4×C1111yescharacteristic
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4C22×C4×C1111yescharacteristic
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4C22×C4×C1111yescharacteristic
524C22×C4C22×C4×C1111yescharacteristic
525C22×C4C2×D4×C1111yescharacteristic
526C22×C4C2×D4×C1111yescharacteristic
527C22×C4C11×#4111yescharacteristic
528C22×C4C24×C1111yescharacteristic
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—41no—
538M16—41no—
539M16—41no—
540M16—41no—
541M16—42no—
542M16—42no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—42no—
556C2×C8—42no—
557C2×C8C22×C4×C1111yescharacteristic
558C2×C8C22×C4×C1111yescharacteristic
559C2×C8C22×C4×C1111yescharacteristic
560C2×C8C22×C4×C1111yescharacteristic
561C2×C8C2×D4×C1111yescharacteristic
562C2×C8C2×D4×C1111yescharacteristic
563C2×C8C2×D4×C1111yescharacteristic
564C2×C8C2×D4×C1111yescharacteristic
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4C22×C4×C1111yescharacteristic
570C4⋊C4C22×C4×C1111yescharacteristic
571C4⋊C4C22×C4×C1111yescharacteristic
572C4⋊C4C22×C4×C1111yescharacteristic
573C4⋊C4C22×C4×C1111yescharacteristic
574C4⋊C4C22×C4×C1111yescharacteristic
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C22⋊C4—42no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C11#2209711yescharacteristic, direct product factor, Sylow
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23C4×D4×C1111yescharacteristic
601C23C4×D4×C1111yescharacteristic
602C23C2×C11×#4111yescharacteristic
603Q8—21no—
604Q8—21no—
605D4—21no—
606D4—21no—
607D4—41no—
608D4—41no—
609D4—81no—
610D4—81no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4C4×D4×C1111yescharacteristic
639C2×C4C4×D4×C1111yescharacteristic
640C2×C4C23×C4×C1111yescharacteristic
641C2×C4C22×D4×C1111yescharacteristic
642C2×C4C11×H(5,𝔽2)11yescharacteristic
643C2×C4C11×H(5,𝔽2)11yescharacteristic
644C2×C4C11×2−1+411yescharacteristic
645C2×C4C11×2−1+411yescharacteristic
646C8—21no—
647C8—21no—
648C8—21no—
649C8—21no—
650C8—21no—
651C8—21no—
652C8—21no—
653C8—21no—
654C8—41no—
655C8—41no—
656C8—41no—
657C8—41no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—81no—
670C22—81no—
671C22C2×C4×D4×C1111yescharacteristic
672C22C11×#53911yescharacteristic
673C22C11×#53911yescharacteristic
674C4—21no—
675C4—21no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—81no—
685C4C11×#52011yescharacteristic
686C4C11×#52011yescharacteristic
687C4C11×#53411yescharacteristic
688C4C11×#53611yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—81no—
694C2C11×#232211yescharacteristic
695C2C11×#295611yescharacteristic
696C2C11×#295711yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×C4×D4
prime radicalC11×#525C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C22×C11×M16 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2905C2semidirect
4. C11×#1946C2semidirect
5. C11×#1945C2semidirect
6. C11×#1938C2semidirect
7. C11×#1937C2semidirect
8. C11×#1922C2semidirect
9. C11×#1922C2semidirect
11. C11×#1866C2semidirect
12. C11×#1866C2semidirect
13. C11×#1855C2semidirect
14. C11×#1826C2semidirect
15. C11×#1753C2semidirect
21. C11×#485C4semidirect
22. C11×#485C4semidirect
23. C11×#484C4semidirect
24. C11×#483C4semidirect
25. C11×#482C4semidirect
26. C11×#482C4semidirect
27. C11×#481C4semidirect
28. C11×#480C4semidirect
156. #22097C11direct (N × H)
249. #2905C2×C11semidirect
250. #1946C2×C11semidirect
251. #1945C2×C11semidirect
252. #1938C2×C11semidirect
253. #1937C2×C11semidirect
254. #1922C2×C11semidirect
255. #1922C2×C11semidirect
257. #1866C2×C11semidirect
258. #1866C2×C11semidirect
259. #1855C2×C11semidirect
260. #1826C2×C11semidirect
261. #1753C2×C11semidirect
330. #485C4×C11semidirect
331. #485C4×C11semidirect
332. #484C4×C11semidirect
333. #483C4×C11semidirect
334. #482C4×C11semidirect
335. #482C4×C11semidirect
336. #481C4×C11semidirect
337. #480C4×C11semidirect
594. C11#22097direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30912
C11×#29302
C11×#29052
C11×#19462
C11×#19452
C11×#19382
C11×#19372
C11×#19222
C11×#18712
C11×#18662
C11×#18552
C11×#18262
C11×#17532
#2209711