Finite Group Databasebeta

← C11×#22949 #14600142

Subgroups — C11×#22949 #14600142

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3091C211yesmaximal, characteristic
2C11×#2933C211yesmaximal, characteristic
3C11×#2924C211yesmaximal, characteristic, complemented
4C11×#1945C211yesmaximal, characteristic, complemented
5C11×#1938C211yesmaximal, characteristic, complemented
6C11×#1929C211yesmaximal, characteristic, complemented
7C11×#1922C211yesmaximal, characteristic, complemented
8C11×#1922C211yesmaximal, characteristic, complemented
9C11×#1897C211yesmaximal, characteristic
10C11×#1866C211yesmaximal, characteristic, complemented
11C11×#1855C211yesmaximal, characteristic, complemented
12C11×#1773C211yesmaximal, characteristic, complemented
13C11×#1764C211yesmaximal, characteristic, complemented
14C11×#1750C211yesmaximal, characteristic, complemented
15C11×#1733C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C11×#525C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
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×#435—21no—
31C11×#435—21no—
32C8×D4×C11—21no—
33C11×#433—21no—
34C11×#433—21no—
35C11×#432—21no—
36C11×#431—21no—
37C2×C11×#108C2211yescharacteristic
38C2×C11×#108C2211yescharacteristic
39C11×#427C2211yescharacteristic
40C11×#427C2211yescharacteristic
41C11×#424C2211yescharacteristic
42C11×#424C2211yescharacteristic
43C11×#424C2211yescharacteristic
44C2×C11×#104C2211yescharacteristic
45C2×C11×#104C2211yescharacteristic
46C11×#416C2211yescharacteristic
47C11×#416C2211yescharacteristic
48C11×#408C2211yescharacteristic
49C11×#407C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C11×#405C2211yescharacteristic
53C11×#405C2211yescharacteristic
54C11×#405C2211yescharacteristic
55C2×C11×#97C2211yescharacteristic
56C2×C4×C8×C11C2211yescharacteristic
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—22no—
70C11×#131—41no—
71C2×C11×M16—21no—
72C2×C11×M16—21no—
73C2×C11×M16—22no—
74C2×C11×M16—41no—
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×#123—21no—
86C11×C22⋊Q8C2×C411yescharacteristic
87C11×C22⋊Q8C2×C411yescharacteristic
88C11×#121C2×C411yescharacteristic
89C11×#121C2×C411yescharacteristic
90C11×#120—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C11×#117—21no—
94C11×#117—21no—
95C11×#117—22no—
96C11×#117—41no—
97C11×#117C2×C411yescharacteristic
98C11×#117C2×C411yescharacteristic
99C11×#117C2311yescharacteristic
100C11×#117C2311yescharacteristic
101C11×#117C2311yescharacteristic
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4C2×C411yescharacteristic
104C2×C11×C4⋊C4C2×C411yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C42×C11—21no—
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C11×#108—22no—
111C11×#108—41no—
112C11×#107C2×C411yescharacteristic
113C11×#107C2×C411yescharacteristic
114C11×#107C2×C411yescharacteristic
115C11×#107C2×C411yescharacteristic
116C11×#106C2×C411yescharacteristic
117C11×#106C2×C411yescharacteristic
118C11×#106C2×C411yescharacteristic
119C11×#106C2×C411yescharacteristic
120C11×C4⋊C8—21no—
121C11×C4⋊C8—21no—
122C11×C4⋊C8—21no—
123C11×C4⋊C8—21no—
124C11×C4⋊C8—21no—
125C11×C4⋊C8—21no—
126C11×#104—22no—
127C11×#104—41no—
128C11×#103C2×C411yescharacteristic
129C11×#103C2×C411yescharacteristic
130C11×#103C2×C411yescharacteristic
131C11×#103C2×C411yescharacteristic
132C11×#102C2×C411yescharacteristic
133C11×#102C2×C411yescharacteristic
134C11×#102C2×C411yescharacteristic
135C11×#102C2×C411yescharacteristic
136C11×C22⋊C8—21no—
137C11×C22⋊C8—21no—
138C11×C22⋊C8—21no—
139C11×C22⋊C8—21no—
140C11×C22⋊C8C2×C411yescharacteristic
141C11×C22⋊C8C2×C411yescharacteristic
142C11×C22⋊C8C2×C411yescharacteristic
143C11×C22⋊C8C2×C411yescharacteristic
144C11×C22⋊C8D411yescharacteristic
145C11×C22⋊C8D411yescharacteristic
146C11×C22⋊C8D411yescharacteristic
147C11×C22⋊C8D411yescharacteristic
148C11×#97—21no—
149C11×#97—21no—
150C11×#97—21no—
151C11×#97—22no—
152C4×C8×C11—21no—
153C4×C8×C11—21no—
154C4×C8×C11—21no—
155C4×C8×C11—41no—
156#22949C1111yesmaximal, 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—42no—
190C11×M16—42no—
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—42no—
219C11×C4⋊C4C22×C411yescharacteristic
220C11×C4⋊C4C22×C411yescharacteristic
221C11×C4⋊C4C22×C411yescharacteristic
222C11×C4⋊C4C22×C411yescharacteristic
223C11×C4⋊C4C22×C411yescharacteristic
224C11×C4⋊C4C22×C411yescharacteristic
225C11×C22⋊C4—21no—
226C11×C22⋊C4—21no—
227C11×C22⋊C4—21no—
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—42no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—21no—
240C42×C11—21no—
241C42×C11—21no—
242C42×C11—21no—
243C42×C11#4112yes—
244#3091C2×C1111yescharacteristic
245#2933C2×C1111yescharacteristic
246#2924C2×C1111yescharacteristic, complemented
247#1945C2×C1111yescharacteristic, complemented
248#1938C2×C1111yescharacteristic, complemented
249#1929C2×C1111yescharacteristic, complemented
250#1922C2×C1111yescharacteristic, complemented
251#1922C2×C1111yescharacteristic, complemented
252#1897C2×C1111yescharacteristic
253#1866C2×C1111yescharacteristic, complemented
254#1855C2×C1111yescharacteristic, complemented
255#1773C2×C1111yescharacteristic, complemented
256#1764C2×C1111yescharacteristic, complemented
257#1750C2×C1111yescharacteristic, complemented
258#1733C2×C1111yescharacteristic, complemented
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11C4×D411yescharacteristic
265C23×C11C4×D411yescharacteristic
266C23×C11C2×#4111yescharacteristic
267Q8×C11—21no—
268Q8×C11—21no—
269D4×C11—21no—
270D4×C11—21no—
271D4×C11—42no—
272D4×C11—41no—
273D4×C11—41no—
274D4×C11—81no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
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—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—42no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—81no—
302C2×C4×C11C4×D411yescharacteristic
303C2×C4×C11C4×D411yescharacteristic
304C2×C4×C11C23×C411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C2×C4×C112−1+411yescharacteristic
310C8×C11—21no—
311C8×C11—21no—
312C8×C11—21no—
313C8×C11—21no—
314C8×C11—21no—
315C8×C11—21no—
316C8×C11—22no—
317C8×C11—21no—
318C8×C11—21no—
319C8×C11—41no—
320C8×C11—41no—
321C8×C11—41no—
322C2×#131C22×C1111yescharacteristic
323C22×M16C22×C1111yescharacteristic
324#525C22×C1111yescharacteristic
325C2×#117C22×C1111yescharacteristic
326C2×#117C22×C1111yescharacteristic
327#485C4×C1111yescharacteristic, complemented
328#485C4×C1111yescharacteristic, complemented
329#484C4×C1111yescharacteristic, complemented
330#483C4×C1111yescharacteristic, complemented
331#482C4×C1111yescharacteristic, complemented
332#482C4×C1111yescharacteristic, complemented
333#481C4×C1111yescharacteristic, complemented
334#480C4×C1111yescharacteristic, complemented
335#436—21no—
336#435—21no—
337#435—21no—
338C8×D4—21no—
339#433—21no—
340#433—21no—
341#432—21no—
342#431—21no—
343C2×#108C22×C1111yescharacteristic
344C2×#108C22×C1111yescharacteristic
345#427C22×C1111yescharacteristic
346#427C22×C1111yescharacteristic
347#424C22×C1111yescharacteristic
348#424C22×C1111yescharacteristic
349#424C22×C1111yescharacteristic
350C2×#104C22×C1111yescharacteristic
351C2×#104C22×C1111yescharacteristic
352#416C22×C1111yescharacteristic
353#416C22×C1111yescharacteristic
354#408C22×C1111yescharacteristic
355#407C22×C1111yescharacteristic
356C2×C22⋊C8C22×C1111yescharacteristic
357C2×C22⋊C8C22×C1111yescharacteristic
358#405C22×C1111yescharacteristic
359#405C22×C1111yescharacteristic
360#405C22×C1111yescharacteristic
361C2×#97C22×C1111yescharacteristic
362C2×C4×C8C22×C1111yescharacteristic
363#341C22×C1111yescharacteristic
364#341C22×C1111yescharacteristic
365#339C22×C1111yescharacteristic
366#339C22×C1111yescharacteristic
367#339C22×C1111yescharacteristic
368#339C22×C1111yescharacteristic
369#339C22×C1111yescharacteristic
370#339C22×C1111yescharacteristic
371#336C22×C1111yescharacteristic
372#336C22×C1111yescharacteristic
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—21no—
376C22×C11—21no—
377C22×C11—21no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—21no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11C2×C4×D411yescharacteristic
387C22×C11#55111yescharacteristic
388C22×C11#55211yescharacteristic
389C4×C11—21no—
390C4×C11—21no—
391C4×C11—42no—
392C4×C11—41no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11—41no—
396C4×C11—41no—
397C4×C11—41no—
398C4×C11—41no—
399C4×C11—81no—
400C4×C11C4×#4111yescharacteristic
401C4×C11#52011yescharacteristic
402C4×C11#54611yescharacteristic
403C4×C11#54711yescharacteristic
404C2×#41C23×C1111yescharacteristic
405C23×C4C23×C1111yescharacteristic
406#131—22no—
407#131—41no—
408C2×M16—21no—
409C2×M16—21no—
410C2×M16—22no—
411C2×M16—41no—
412C2×M16C23×C1111yescharacteristic
413C2×M16C23×C1111yescharacteristic
414C2×M16C23×C1111yescharacteristic
415C2×M16C23×C1111yescharacteristic
416C22×C8—21no—
417C22×C8—21no—
418C22×C8C23×C1111yescharacteristic
419C22×C8C23×C1111yescharacteristic
420C22×C8C23×C1111yescharacteristic
421C22×C8C23×C1111yescharacteristic
422#123—21no—
423C22⋊Q8C2×C4×C1111yescharacteristic
424C22⋊Q8C2×C4×C1111yescharacteristic
425#121C2×C4×C1111yescharacteristic
426#121C2×C4×C1111yescharacteristic
427#120—21no—
428C4×D4—21no—
429C4×D4—21no—
430#117—21no—
431#117—21no—
432#117—22no—
433#117—41no—
434#117C2×C4×C1111yescharacteristic
435#117C2×C4×C1111yescharacteristic
436#117C23×C1111yescharacteristic
437#117C23×C1111yescharacteristic
438#117C23×C1111yescharacteristic
439C2×C4⋊C4—21no—
440C2×C4⋊C4C2×C4×C1111yescharacteristic
441C2×C4⋊C4C2×C4×C1111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C42—21no—
445C2×C42C23×C1111yescharacteristic
446C2×C42C23×C1111yescharacteristic
447#108—22no—
448#108—41no—
449#107C2×C4×C1111yescharacteristic
450#107C2×C4×C1111yescharacteristic
451#107C2×C4×C1111yescharacteristic
452#107C2×C4×C1111yescharacteristic
453#106C2×C4×C1111yescharacteristic
454#106C2×C4×C1111yescharacteristic
455#106C2×C4×C1111yescharacteristic
456#106C2×C4×C1111yescharacteristic
457C4⋊C8—21no—
458C4⋊C8—21no—
459C4⋊C8—21no—
460C4⋊C8—21no—
461C4⋊C8—21no—
462C4⋊C8—21no—
463#104—22no—
464#104—41no—
465#103C2×C4×C1111yescharacteristic
466#103C2×C4×C1111yescharacteristic
467#103C2×C4×C1111yescharacteristic
468#103C2×C4×C1111yescharacteristic
469#102C2×C4×C1111yescharacteristic
470#102C2×C4×C1111yescharacteristic
471#102C2×C4×C1111yescharacteristic
472#102C2×C4×C1111yescharacteristic
473C22⋊C8—21no—
474C22⋊C8—21no—
475C22⋊C8—21no—
476C22⋊C8—21no—
477C22⋊C8C2×C4×C1111yescharacteristic
478C22⋊C8C2×C4×C1111yescharacteristic
479C22⋊C8C2×C4×C1111yescharacteristic
480C22⋊C8C2×C4×C1111yescharacteristic
481C22⋊C8D4×C1111yescharacteristic
482C22⋊C8D4×C1111yescharacteristic
483C22⋊C8D4×C1111yescharacteristic
484C22⋊C8D4×C1111yescharacteristic
485#97—21no—
486#97—21no—
487#97—21no—
488#97—22no—
489C4×C8—21no—
490C4×C8—21no—
491C4×C8—21no—
492C4×C8—41no—
493C2×C11—21no—
494C2×C11—21no—
495C2×C11—41no—
496C2×C11—41no—
497C2×C11—81no—
498C2×C11#235911yescharacteristic
499C2×C11#295511yescharacteristic
500C2×C11#295711yescharacteristic
501C24C11×#4111yescharacteristic
502#41—21no—
503#41—21no—
504#41—21no—
505#41—21no—
506C2×Q8C22×C4×C1111yescharacteristic
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4C22×C4×C1111yescharacteristic
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4C22×C4×C1111yescharacteristic
521C22×C4C22×C4×C1111yescharacteristic
522C22×C4C2×D4×C1111yescharacteristic
523C22×C4C2×D4×C1111yescharacteristic
524C22×C4C11×#4111yescharacteristic
525C22×C4C24×C1111yescharacteristic
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—42no—
534M16—42no—
535M16C11×#4112yes—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—42no—
549C2×C8—42no—
550C2×C8C22×C4×C1111yescharacteristic
551C2×C8C22×C4×C1111yescharacteristic
552C2×C8C22×C4×C1111yescharacteristic
553C2×C8C22×C4×C1111yescharacteristic
554C2×C8C2×D4×C1111yescharacteristic
555C2×C8C2×D4×C1111yescharacteristic
556C2×C8C2×D4×C1111yescharacteristic
557C2×C8C2×D4×C1111yescharacteristic
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—42no—
563C4⋊C4C22×C4×C1111yescharacteristic
564C4⋊C4C22×C4×C1111yescharacteristic
565C4⋊C4C22×C4×C1111yescharacteristic
566C4⋊C4C22×C4×C1111yescharacteristic
567C4⋊C4C22×C4×C1111yescharacteristic
568C4⋊C4C22×C4×C1111yescharacteristic
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—42no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42C11×#4112yes—
588C11#2294911yescharacteristic, direct product factor, Sylow
589C23—21no—
590C23—21no—
591C23—21no—
592C23—41no—
593C23—41no—
594C23C4×D4×C1111yescharacteristic
595C23C4×D4×C1111yescharacteristic
596C23C2×C11×#4111yescharacteristic
597Q8—21no—
598Q8—21no—
599D4—21no—
600D4—21no—
601D4—42no—
602D4—41no—
603D4—41no—
604D4—81no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
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—21no—
622C2×C4—22no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—81no—
632C2×C4C4×D4×C1111yescharacteristic
633C2×C4C4×D4×C1111yescharacteristic
634C2×C4C23×C4×C1111yescharacteristic
635C2×C4C22×D4×C1111yescharacteristic
636C2×C4C2×C11×#4111yescharacteristic
637C2×C4C2×C11×#4111yescharacteristic
638C2×C4C11×H(5,𝔽2)11yescharacteristic
639C2×C4C11×2−1+411yescharacteristic
640C8—21no—
641C8—21no—
642C8—21no—
643C8—21no—
644C8—21no—
645C8—21no—
646C8—22no—
647C8—21no—
648C8—21no—
649C8—41no—
650C8—41no—
651C8—41no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—81no—
664C22—81no—
665C22C2×C4×D4×C1111yescharacteristic
666C22C11×#55111yescharacteristic
667C22C11×#55211yescharacteristic
668C4—21no—
669C4—21no—
670C4—42no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—81no—
679C4C4×C11×#4111yescharacteristic
680C4C11×#52011yescharacteristic
681C4C11×#54611yescharacteristic
682C4C11×#54711yescharacteristic
683C2—21no—
684C2—21no—
685C2—41no—
686C2—41no—
687C2—81no—
688C2C11×#235911yescharacteristic
689C2C11×#295511yescharacteristic
690C2C11×#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 ◁ C2×C11×C22⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2924C2semidirect
4. C11×#1945C2semidirect
5. C11×#1938C2semidirect
6. C11×#1929C2semidirect
7. C11×#1922C2semidirect
8. C11×#1922C2semidirect
10. C11×#1866C2semidirect
11. C11×#1855C2semidirect
12. C11×#1773C2semidirect
13. C11×#1764C2semidirect
14. C11×#1750C2semidirect
15. C11×#1733C2semidirect
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. #22949C11direct (N × H)
246. #2924C2×C11semidirect
247. #1945C2×C11semidirect
248. #1938C2×C11semidirect
249. #1929C2×C11semidirect
250. #1922C2×C11semidirect
251. #1922C2×C11semidirect
253. #1866C2×C11semidirect
254. #1855C2×C11semidirect
255. #1773C2×C11semidirect
256. #1764C2×C11semidirect
257. #1750C2×C11semidirect
258. #1733C2×C11semidirect
327. #485C4×C11semidirect
328. #485C4×C11semidirect
329. #484C4×C11semidirect
330. #483C4×C11semidirect
331. #482C4×C11semidirect
332. #482C4×C11semidirect
333. #481C4×C11semidirect
334. #480C4×C11semidirect
588. C11#22949direct (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×#29332
C11×#29242
C11×#19452
C11×#19382
C11×#19292
C11×#19222
C11×#18972
C11×#18662
C11×#18552
C11×#17732
C11×#17642
C11×#17502
C11×#17332
#2294911