Finite Group Databasebeta

← C11×#23236 #14600429

Subgroups — C11×#23236 #14600429

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3135C211yesmaximal, characteristic
2C11×#2962C211yesmaximal, characteristic, complemented
3C11×#2935C211yesmaximal, characteristic
4C11×#1986C211yesmaximal, characteristic, complemented
5C11×#1980C211yesmaximal, characteristic
6C11×#1938C211yesmaximal, characteristic, complemented
7C11×#1937C211yesmaximal, characteristic, complemented
8C11×#1929C211yesmaximal, characteristic, complemented
9C11×#1929C211yesmaximal, characteristic, complemented
10C11×#1866C211yesmaximal, characteristic, complemented
11C11×#1866C211yesmaximal, characteristic, complemented
12C11×#1778C211yesmaximal, characteristic, complemented
13C11×#1771C211yesmaximal, characteristic, complemented
14C11×#1765C211yesmaximal, characteristic, complemented
15C11×#1764C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#491C411yescharacteristic, complemented
21C11×#491C411yescharacteristic, complemented
22C11×#490C411yescharacteristic, complemented
23C11×#490C411yescharacteristic, complemented
24C11×#489C411yescharacteristic, complemented
25C11×#489C411yescharacteristic, complemented
26C11×#489C411yescharacteristic, complemented
27C11×#489C411yescharacteristic, complemented
28C11×#446—21no—
29C11×#446—21no—
30C11×#446—21no—
31C8×Q8×C11—21no—
32C11×#436—21no—
33C11×#435—21no—
34C11×#435—21no—
35C8×D4×C11—21no—
36C2×C11×#108C2211yescharacteristic
37C2×C11×#108C2211yescharacteristic
38C11×#424C2211yescharacteristic
39C11×#424C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×#104C2211yescharacteristic
42C2×C11×#104C2211yescharacteristic
43C2×C11×#104C2211yescharacteristic
44C2×C11×#104C2211yescharacteristic
45C11×#416C2211yescharacteristic
46C11×#416C2211yescharacteristic
47C11×#416C2211yescharacteristic
48C11×#416C2211yescharacteristic
49C11×#408C2211yescharacteristic
50C11×#408C2211yescharacteristic
51C11×#405C2211yescharacteristic
52C11×#405C2211yescharacteristic
53C4×C11×M16C2211yescharacteristic
54C4×C11×M16C2211yescharacteristic
55C2×C11×#97C2211yescharacteristic
56C2×C11×#97C2211yescharacteristic
57C2×C4×C8×C11C2211yescharacteristic
58C4×C11×C4⋊C4C2211yescharacteristic
59C11×#341C2211yescharacteristic
60C11×#341C2211yescharacteristic
61C11×#339C2211yescharacteristic
62C11×#339C2211yescharacteristic
63C11×#339C2211yescharacteristic
64C11×#339C2211yescharacteristic
65C11×#336C2211yescharacteristic
66C11×#336C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C11×#131—22no—
70C11×#131—22no—
71C11×#131—41no—
72C11×#131—41no—
73C2×C11×M16—21no—
74C2×C11×M16—21no—
75C2×C11×M16C2311yescharacteristic
76C2×C11×M16C2311yescharacteristic
77C2×C11×M16C2311yescharacteristic
78C2×C11×M16C2311yescharacteristic
79C22×C8×C11—21no—
80C22×C8×C11—21no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C11×C4⋊Q8C2×C411yescharacteristic
86C11×C4⋊Q8C2×C411yescharacteristic
87C11×C4⋊Q8C2×C411yescharacteristic
88C11×#127C2×C411yescharacteristic
89C11×#125C2×C411yescharacteristic
90C11×#125C2×C411yescharacteristic
91C11×#124C2×C411yescharacteristic
92C11×#124C2×C411yescharacteristic
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8—21no—
95C11×#121—21no—
96C11×#121—21no—
97C4×Q8×C11—21no—
98C4×Q8×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C11×#117C2311yescharacteristic
102C11×#117C2311yescharacteristic
103C2×C11×C4⋊C4—21no—
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C11×#108—22no—
108C11×#108—22no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8D411yescharacteristic
114C11×C4⋊C8D411yescharacteristic
115C11×C4⋊C8D411yescharacteristic
116C11×C4⋊C8D411yescharacteristic
117C11×#104—22no—
118C11×#104—22no—
119C11×#104—41no—
120C11×#104—41no—
121C11×#103C2×C411yescharacteristic
122C11×#103C2×C411yescharacteristic
123C11×#103C2×C411yescharacteristic
124C11×#103C2×C411yescharacteristic
125C11×#103C2×C411yescharacteristic
126C11×#103C2×C411yescharacteristic
127C11×#103C2×C411yescharacteristic
128C11×#103C2×C411yescharacteristic
129C11×#102C2×C411yescharacteristic
130C11×#102C2×C411yescharacteristic
131C11×#102C2×C411yescharacteristic
132C11×#102C2×C411yescharacteristic
133C11×#102C2×C411yescharacteristic
134C11×#102C2×C411yescharacteristic
135C11×#102C2×C411yescharacteristic
136C11×#102C2×C411yescharacteristic
137C11×C22⋊C8—21no—
138C11×C22⋊C8—21no—
139C11×C22⋊C8—21no—
140C11×C22⋊C8—21no—
141C11×#97—21no—
142C11×#97—21no—
143C11×#97—21no—
144C11×#97—21no—
145C11×#97—41no—
146C11×#97C2×C411yescharacteristic
147C11×#97C2×C411yescharacteristic
148C11×#97C2×C411yescharacteristic
149C11×#97C2×C411yescharacteristic
150C4×C8×C11—21no—
151C4×C8×C11—21no—
152C4×C8×C11—21no—
153C4×C8×C11—21no—
154C4×C8×C11—41no—
155C11×#95—21no—
156#23236C1111yesmaximal, characteristic, direct product factor, Sylow
157C11×#41—21no—
158C11×#41—21no—
159C11×#41—21no—
160C11×#41—21no—
161C11×#41—21no—
162C11×#41—21no—
163C11×#41—21no—
164C11×#41—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11C22×C411yescharacteristic
168C2×Q8×C11C22×C411yescharacteristic
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11C22×C411yescharacteristic
174C2×D4×C11C22×C411yescharacteristic
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11#4111yescharacteristic
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—42no—
189C11×M16—42no—
190C11×M16#4112yes—
191C11×M16#4112yes—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
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—42no—
205C2×C8×C11—42no—
206C2×C8×C11C22×C411yescharacteristic
207C2×C8×C11C22×C411yescharacteristic
208C2×C8×C11C22×C411yescharacteristic
209C2×C8×C11C22×C411yescharacteristic
210C2×C8×C11C2×D411yescharacteristic
211C2×C8×C11C2×D411yescharacteristic
212C2×C8×C11C2×D411yescharacteristic
213C2×C8×C11C2×D411yescharacteristic
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—42no—
223C11×C4⋊C4C22×C411yescharacteristic
224C11×C4⋊C4C22×C411yescharacteristic
225C11×C4⋊C4C22×C411yescharacteristic
226C11×C4⋊C4C22×C411yescharacteristic
227C11×C22⋊C4—21no—
228C11×C22⋊C4—21no—
229C11×C22⋊C4—21no—
230C11×C22⋊C4—21no—
231C11×C22⋊C4—21no—
232C11×C22⋊C4—21no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11C22×C411yescharacteristic
240C42×C11C22×C411yescharacteristic
241C42×C11C2×D411yescharacteristic
242C42×C11C2×D411yescharacteristic
243#3135C2×C1111yescharacteristic
244#2962C2×C1111yescharacteristic, complemented
245#2935C2×C1111yescharacteristic
246#1986C2×C1111yescharacteristic, complemented
247#1980C2×C1111yescharacteristic
248#1938C2×C1111yescharacteristic, complemented
249#1937C2×C1111yescharacteristic, complemented
250#1929C2×C1111yescharacteristic, complemented
251#1929C2×C1111yescharacteristic, complemented
252#1866C2×C1111yescharacteristic, complemented
253#1866C2×C1111yescharacteristic, complemented
254#1778C2×C1111yescharacteristic, complemented
255#1771C2×C1111yescharacteristic, complemented
256#1765C2×C1111yescharacteristic, complemented
257#1764C2×C1111yescharacteristic, complemented
258C23×C11—21no—
259C23×C11—21no—
260C23×C11C2×#4111yescharacteristic
261Q8×C11—21no—
262Q8×C11—21no—
263Q8×C11—21no—
264Q8×C11—21no—
265Q8×C11—42no—
266Q8×C11—81no—
267D4×C11—21no—
268D4×C11—21no—
269D4×C11—21no—
270D4×C11—21no—
271D4×C11—42no—
272D4×C11—41no—
273D4×C11—41no—
274D4×C11—41no—
275D4×C11—41no—
276D4×C11—81no—
277C2×C4×C11—22no—
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—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11C4×D411yescharacteristic
296C2×C4×C11C4×D411yescharacteristic
297C2×C4×C11C4×D411yescharacteristic
298C2×C4×C11C4×D411yescharacteristic
299C2×C4×C11C23×C411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11H(5,𝔽2)11yescharacteristic
304C2×C4×C112−1+411yescharacteristic
305C8×C11—21no—
306C8×C11—21no—
307C8×C11—21no—
308C8×C11—21no—
309C8×C11—21no—
310C8×C11—21no—
311C8×C11—21no—
312C8×C11—21no—
313C8×C11—22no—
314C8×C11—22no—
315C8×C11—41no—
316C8×C11—41no—
317C2×#131C22×C1111yescharacteristic
318C2×#131C22×C1111yescharacteristic
319#533C22×C1111yescharacteristic
320#532C22×C1111yescharacteristic
321#491C4×C1111yescharacteristic, complemented
322#491C4×C1111yescharacteristic, complemented
323#490C4×C1111yescharacteristic, complemented
324#490C4×C1111yescharacteristic, complemented
325#489C4×C1111yescharacteristic, complemented
326#489C4×C1111yescharacteristic, complemented
327#489C4×C1111yescharacteristic, complemented
328#489C4×C1111yescharacteristic, complemented
329#446—21no—
330#446—21no—
331#446—21no—
332C8×Q8—21no—
333#436—21no—
334#435—21no—
335#435—21no—
336C8×D4—21no—
337C2×#108C22×C1111yescharacteristic
338C2×#108C22×C1111yescharacteristic
339#424C22×C1111yescharacteristic
340#424C22×C1111yescharacteristic
341C2×C4⋊C8C22×C1111yescharacteristic
342C2×#104C22×C1111yescharacteristic
343C2×#104C22×C1111yescharacteristic
344C2×#104C22×C1111yescharacteristic
345C2×#104C22×C1111yescharacteristic
346#416C22×C1111yescharacteristic
347#416C22×C1111yescharacteristic
348#416C22×C1111yescharacteristic
349#416C22×C1111yescharacteristic
350#408C22×C1111yescharacteristic
351#408C22×C1111yescharacteristic
352#405C22×C1111yescharacteristic
353#405C22×C1111yescharacteristic
354C4×M16C22×C1111yescharacteristic
355C4×M16C22×C1111yescharacteristic
356C2×#97C22×C1111yescharacteristic
357C2×#97C22×C1111yescharacteristic
358C2×C4×C8C22×C1111yescharacteristic
359C4×C4⋊C4C22×C1111yescharacteristic
360#341C22×C1111yescharacteristic
361#341C22×C1111yescharacteristic
362#339C22×C1111yescharacteristic
363#339C22×C1111yescharacteristic
364#339C22×C1111yescharacteristic
365#339C22×C1111yescharacteristic
366#336C22×C1111yescharacteristic
367#336C22×C1111yescharacteristic
368C22×C11—21no—
369C22×C11—21no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11C2×C4×D411yescharacteristic
377C22×C11#55611yescharacteristic
378C22×C11#55911yescharacteristic
379C4×C11—21no—
380C4×C11—21no—
381C4×C11—21no—
382C4×C11—21no—
383C4×C11—42no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—41no—
389C4×C11—41no—
390C4×C11—81no—
391C4×C11C4×#4111yescharacteristic
392C4×C11#52011yescharacteristic
393C4×C11#54611yescharacteristic
394C4×C11#54811yescharacteristic
395C2×#41C23×C1111yescharacteristic
396C2×#41C23×C1111yescharacteristic
397#131—22no—
398#131—22no—
399#131—41no—
400#131—41no—
401C2×M16—21no—
402C2×M16—21no—
403C2×M16C23×C1111yescharacteristic
404C2×M16C23×C1111yescharacteristic
405C2×M16C23×C1111yescharacteristic
406C2×M16C23×C1111yescharacteristic
407C22×C8—21no—
408C22×C8—21no—
409C22×C8C23×C1111yescharacteristic
410C22×C8C23×C1111yescharacteristic
411C22×C8C23×C1111yescharacteristic
412C22×C8C23×C1111yescharacteristic
413C4⋊Q8C2×C4×C1111yescharacteristic
414C4⋊Q8C2×C4×C1111yescharacteristic
415C4⋊Q8C2×C4×C1111yescharacteristic
416#127C2×C4×C1111yescharacteristic
417#125C2×C4×C1111yescharacteristic
418#125C2×C4×C1111yescharacteristic
419#124C2×C4×C1111yescharacteristic
420#124C2×C4×C1111yescharacteristic
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423#121—21no—
424#121—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×D4—21no—
428C4×D4—21no—
429#117C23×C1111yescharacteristic
430#117C23×C1111yescharacteristic
431C2×C4⋊C4—21no—
432C2×C42C23×C1111yescharacteristic
433C2×C42C23×C1111yescharacteristic
434C2×C42C23×C1111yescharacteristic
435#108—22no—
436#108—22no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—21no—
441C4⋊C8D4×C1111yescharacteristic
442C4⋊C8D4×C1111yescharacteristic
443C4⋊C8D4×C1111yescharacteristic
444C4⋊C8D4×C1111yescharacteristic
445#104—22no—
446#104—22no—
447#104—41no—
448#104—41no—
449#103C2×C4×C1111yescharacteristic
450#103C2×C4×C1111yescharacteristic
451#103C2×C4×C1111yescharacteristic
452#103C2×C4×C1111yescharacteristic
453#103C2×C4×C1111yescharacteristic
454#103C2×C4×C1111yescharacteristic
455#103C2×C4×C1111yescharacteristic
456#103C2×C4×C1111yescharacteristic
457#102C2×C4×C1111yescharacteristic
458#102C2×C4×C1111yescharacteristic
459#102C2×C4×C1111yescharacteristic
460#102C2×C4×C1111yescharacteristic
461#102C2×C4×C1111yescharacteristic
462#102C2×C4×C1111yescharacteristic
463#102C2×C4×C1111yescharacteristic
464#102C2×C4×C1111yescharacteristic
465C22⋊C8—21no—
466C22⋊C8—21no—
467C22⋊C8—21no—
468C22⋊C8—21no—
469#97—21no—
470#97—21no—
471#97—21no—
472#97—21no—
473#97—41no—
474#97C2×C4×C1111yescharacteristic
475#97C2×C4×C1111yescharacteristic
476#97C2×C4×C1111yescharacteristic
477#97C2×C4×C1111yescharacteristic
478C4×C8—21no—
479C4×C8—21no—
480C4×C8—21no—
481C4×C8—21no—
482C4×C8—41no—
483#95—21no—
484C2×C11—21no—
485C2×C11—21no—
486C2×C11—81no—
487C2×C11—81no—
488C2×C11#236711yescharacteristic
489C2×C11#295511yescharacteristic
490C2×C11#295611yescharacteristic
491#41—21no—
492#41—21no—
493#41—21no—
494#41—21no—
495#41—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8C22×C4×C1111yescharacteristic
502C2×Q8C22×C4×C1111yescharacteristic
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4C22×C4×C1111yescharacteristic
508C2×D4C22×C4×C1111yescharacteristic
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4C11×#4111yescharacteristic
514C22×C4C11×#4111yescharacteristic
515C22×C4C24×C1111yescharacteristic
516M16—21no—
517M16—21no—
518M16—21no—
519M16—21no—
520M16—21no—
521M16—21no—
522M16—42no—
523M16—42no—
524M16C11×#4112yes—
525M16C11×#4112yes—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—42no—
539C2×C8—42no—
540C2×C8C22×C4×C1111yescharacteristic
541C2×C8C22×C4×C1111yescharacteristic
542C2×C8C22×C4×C1111yescharacteristic
543C2×C8C22×C4×C1111yescharacteristic
544C2×C8C2×D4×C1111yescharacteristic
545C2×C8C2×D4×C1111yescharacteristic
546C2×C8C2×D4×C1111yescharacteristic
547C2×C8C2×D4×C1111yescharacteristic
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4C22×C4×C1111yescharacteristic
558C4⋊C4C22×C4×C1111yescharacteristic
559C4⋊C4C22×C4×C1111yescharacteristic
560C4⋊C4C22×C4×C1111yescharacteristic
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42C22×C4×C1111yescharacteristic
574C42C22×C4×C1111yescharacteristic
575C42C2×D4×C1111yescharacteristic
576C42C2×D4×C1111yescharacteristic
577C11#2323611yescharacteristic, direct product factor, Sylow
578C23—21no—
579C23—21no—
580C23C2×C11×#4111yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—21no—
584Q8—21no—
585Q8—42no—
586Q8—81no—
587D4—21no—
588D4—21no—
589D4—21no—
590D4—21no—
591D4—42no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—81no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4C4×D4×C1111yescharacteristic
616C2×C4C4×D4×C1111yescharacteristic
617C2×C4C4×D4×C1111yescharacteristic
618C2×C4C4×D4×C1111yescharacteristic
619C2×C4C23×C4×C1111yescharacteristic
620C2×C4C22×D4×C1111yescharacteristic
621C2×C4C2×C11×#4111yescharacteristic
622C2×C4C2×C11×#4111yescharacteristic
623C2×C4C11×H(5,𝔽2)11yescharacteristic
624C2×C4C11×2−1+411yescharacteristic
625C8—21no—
626C8—21no—
627C8—21no—
628C8—21no—
629C8—21no—
630C8—21no—
631C8—21no—
632C8—21no—
633C8—22no—
634C8—22no—
635C8—41no—
636C8—41no—
637C22—21no—
638C22—21no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22C2×C4×D4×C1111yescharacteristic
646C22C11×#55611yescharacteristic
647C22C11×#55911yescharacteristic
648C4—21no—
649C4—21no—
650C4—21no—
651C4—21no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—81no—
660C4C4×C11×#4111yescharacteristic
661C4C11×#52011yescharacteristic
662C4C11×#54611yescharacteristic
663C4C11×#54811yescharacteristic
664C2—21no—
665C2—21no—
666C2—81no—
667C2—81no—
668C2C11×#236711yescharacteristic
669C2C11×#295511yescharacteristic
670C2C11×#295611yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×C4×D4
prime radicalC11×#532C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C11×C4⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2962C2semidirect
4. C11×#1986C2semidirect
6. C11×#1938C2semidirect
7. C11×#1937C2semidirect
8. C11×#1929C2semidirect
9. C11×#1929C2semidirect
10. C11×#1866C2semidirect
11. C11×#1866C2semidirect
12. C11×#1778C2semidirect
13. C11×#1771C2semidirect
14. C11×#1765C2semidirect
15. C11×#1764C2semidirect
20. C11×#491C4semidirect
21. C11×#491C4semidirect
22. C11×#490C4semidirect
23. C11×#490C4semidirect
24. C11×#489C4semidirect
25. C11×#489C4semidirect
26. C11×#489C4semidirect
27. C11×#489C4semidirect
156. #23236C11direct (N × H)
244. #2962C2×C11semidirect
246. #1986C2×C11semidirect
248. #1938C2×C11semidirect
249. #1937C2×C11semidirect
250. #1929C2×C11semidirect
251. #1929C2×C11semidirect
252. #1866C2×C11semidirect
253. #1866C2×C11semidirect
254. #1778C2×C11semidirect
255. #1771C2×C11semidirect
256. #1765C2×C11semidirect
257. #1764C2×C11semidirect
321. #491C4×C11semidirect
322. #491C4×C11semidirect
323. #490C4×C11semidirect
324. #490C4×C11semidirect
325. #489C4×C11semidirect
326. #489C4×C11semidirect
327. #489C4×C11semidirect
328. #489C4×C11semidirect
577. C11#23236direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31352
C11×#29622
C11×#29352
C11×#19862
C11×#19802
C11×#19382
C11×#19372
C11×#19292
C11×#18662
C11×#17782
C11×#17712
C11×#17652
C11×#17642
#2323611