Finite Group Databasebeta

← C11×#22784 #14599977

Subgroups — C11×#22784 #14599977

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2943C211yesmaximal, characteristic
2C11×#2925C211yesmaximal, characteristic, complemented
3C11×#2906C211yesmaximal, characteristic, complemented
4C11×#1938C211yesmaximal, characteristic, complemented
5C11×#1937C211yesmaximal, characteristic, complemented
6C11×#1922C211yesmaximal, characteristic, complemented
7C11×#1922C211yesmaximal, characteristic, complemented
8C11×#1876C211yesmaximal, characteristic
9C11×#1876C211yesmaximal, characteristic
10C11×#1838C211yesmaximal, characteristic, complemented
11C11×#1806C211yesmaximal, characteristic, complemented
12C11×#1806C211yesmaximal, characteristic, complemented
13C11×#1771C211yesmaximal, characteristic, complemented
14C11×#1765C211yesmaximal, characteristic, complemented
15C11×#1764C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic
19C4×C11×#41C2211yescharacteristic
20C4×C11×#41C2211yescharacteristic
21C11×#442C411yescharacteristic, complemented
22C11×#442C411yescharacteristic, complemented
23C11×#441C411yescharacteristic, complemented
24C11×#441C411yescharacteristic, complemented
25C11×#440C411yescharacteristic, complemented
26C11×#440C411yescharacteristic, complemented
27C11×#440C411yescharacteristic, complemented
28C11×#440C411yescharacteristic, complemented
29C11×#433—21no—
30C11×#433—21no—
31C11×#432—21no—
32C11×#431—21no—
33C11×#427C2211yescharacteristic
34C11×#424—21no—
35C11×#424—21no—
36C11×#424C2211yescharacteristic
37C11×#424C2211yescharacteristic
38C11×#423—21no—
39C11×#423C2211yescharacteristic
40C11×#423C2211yescharacteristic
41C2×C11×C4⋊C8—21no—
42C2×C11×C4⋊C8C2211yescharacteristic
43C2×C11×#104C2211yescharacteristic
44C2×C11×#104C2211yescharacteristic
45C2×C11×#104C2211yescharacteristic
46C2×C11×#104C2211yescharacteristic
47C11×#416C2211yescharacteristic
48C11×#416C2211yescharacteristic
49C11×#408C2211yescharacteristic
50C11×#408C2211yescharacteristic
51C11×#405C2211yescharacteristic
52C11×#405C2211yescharacteristic
53C2×C11×#97C2211yescharacteristic
54C2×C11×#97C2211yescharacteristic
55C2×C4×C8×C11C2211yescharacteristic
56C4×C11×C4⋊C4C2211yescharacteristic
57C11×#341C2211yescharacteristic
58C11×#341C2211yescharacteristic
59C11×#341C2211yescharacteristic
60C11×#341C2211yescharacteristic
61C11×#339C2211yescharacteristic
62C11×#339C2211yescharacteristic
63C11×#339C2211yescharacteristic
64C11×#339C2211yescharacteristic
65C11×#336C2211yescharacteristic
66C11×#336C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C11×#135—22no—
70C11×#135—22no—
71C2×C11×Q16C2×C411yescharacteristic
72C2×C11×SD16C2×C411yescharacteristic
73C2×C11×SD16C2×C411yescharacteristic
74C2×C11×D8C2×C411yescharacteristic
75C11×#131—22no—
76C11×#131—22no—
77C11×#131—41no—
78C11×#131—41no—
79C2×C11×M16—21no—
80C2×C11×M16—21no—
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
91C4×Q8×C11C2×C411yescharacteristic
92C4×Q8×C11C2×C411yescharacteristic
93C4×Q8×C11C2×C411yescharacteristic
94C4×Q8×C11C2×C411yescharacteristic
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11C2×C411yescharacteristic
100C4×D4×C11C2×C411yescharacteristic
101C4×D4×C11C2×C411yescharacteristic
102C4×D4×C11C2×C411yescharacteristic
103C11×#117—21no—
104C11×#117—21no—
105C11×#117C2311yescharacteristic
106C11×#117C2311yescharacteristic
107C2×C11×C4⋊C4—21no—
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C11×#107C2×C411yescharacteristic
114C11×#107C2×C411yescharacteristic
115C11×#106C2×C411yescharacteristic
116C11×#106C2×C411yescharacteristic
117C11×C4⋊C8—21no—
118C11×C4⋊C8—21no—
119C11×C4⋊C8—21no—
120C11×C4⋊C8—21no—
121C11×C4⋊C8—21no—
122C11×C4⋊C8—21no—
123C11×C4⋊C8—21no—
124C11×C4⋊C8—21no—
125C11×C4⋊C8D411yescharacteristic
126C11×C4⋊C8D411yescharacteristic
127C11×C4⋊C8D411yescharacteristic
128C11×C4⋊C8D411yescharacteristic
129C11×#104—22no—
130C11×#104—22no—
131C11×#104—41no—
132C11×#104—41no—
133C11×#103C2×C411yescharacteristic
134C11×#103C2×C411yescharacteristic
135C11×#103C2×C411yescharacteristic
136C11×#103C2×C411yescharacteristic
137C11×#102C2×C411yescharacteristic
138C11×#102C2×C411yescharacteristic
139C11×#102C2×C411yescharacteristic
140C11×#102C2×C411yescharacteristic
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×C22⋊C8—21no—
144C11×C22⋊C8—21no—
145C11×#97—21no—
146C11×#97—21no—
147C11×#97—41no—
148C11×#97C2×C411yescharacteristic
149C11×#97C2×C411yescharacteristic
150C11×#97C2×C411yescharacteristic
151C11×#97C2×C411yescharacteristic
152C4×C8×C11—21no—
153C4×C8×C11—21no—
154C4×C8×C11—41no—
155C11×#95—21no—
156#22784C1111yesmaximal, 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#4112yes—
164C11×#41#4112yes—
165C2×Q8×C11C22×C411yescharacteristic
166C2×Q8×C11C22×C411yescharacteristic
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11C22×C411yescharacteristic
170C2×D4×C11C22×C411yescharacteristic
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
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×Q16—22no—
183C11×SD16—22no—
184C11×SD16—22no—
185C11×D8—22no—
186C11×M16—21no—
187C11×M16—21no—
188C11×M16—21no—
189C11×M16—21no—
190C11×M16—21no—
191C11×M16—21no—
192C11×M16—21no—
193C11×M16—21no—
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⋊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×C11—21no—
240C42×C11—21no—
241C42×C11—21no—
242C42×C11—21no—
243C42×C11C22×C411yescharacteristic
244C42×C11C22×C411yescharacteristic
245C42×C11C2×D411yescharacteristic
246C42×C11C2×D411yescharacteristic
247#2943C2×C1111yescharacteristic
248#2925C2×C1111yescharacteristic, complemented
249#2906C2×C1111yescharacteristic, complemented
250#1938C2×C1111yescharacteristic, complemented
251#1937C2×C1111yescharacteristic, complemented
252#1922C2×C1111yescharacteristic, complemented
253#1922C2×C1111yescharacteristic, complemented
254#1876C2×C1111yescharacteristic
255#1876C2×C1111yescharacteristic
256#1838C2×C1111yescharacteristic, complemented
257#1806C2×C1111yescharacteristic, complemented
258#1806C2×C1111yescharacteristic, complemented
259#1771C2×C1111yescharacteristic, complemented
260#1765C2×C1111yescharacteristic, complemented
261#1764C2×C1111yescharacteristic, complemented
262C23×C11—21no—
263C23×C11—21no—
264C23×C11C2×#4111yescharacteristic
265Q8×C11—21no—
266Q8×C11—21no—
267Q8×C11—21no—
268Q8×C11#11712yes—
269D4×C11—22no—
270D4×C11—22no—
271D4×C11—21no—
272D4×C11—21no—
273D4×C11—21no—
274D4×C11—41no—
275D4×C11—41no—
276D4×C11#11712yes—
277C2×C4×C11—21no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—81no—
298C2×C4×C11—81no—
299C2×C4×C11C4×D411yescharacteristic
300C2×C4×C11C4×D411yescharacteristic
301C2×C4×C11C4×D411yescharacteristic
302C2×C4×C11C4×D411yescharacteristic
303C2×C4×C11C23×C411yescharacteristic
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11H(5,𝔽2)11yescharacteristic
308C2×C4×C112−1+411yescharacteristic
309C8×C11—21no—
310C8×C11—21no—
311C8×C11—21no—
312C8×C11—21no—
313C8×C11—21no—
314C8×C11—21no—
315C8×C11—21no—
316C8×C11—21no—
317C8×C11—41no—
318C8×C11—41no—
319C8×C11—41no—
320C8×C11—41no—
321C2×#135C22×C1111yescharacteristic
322C2×#131C22×C1111yescharacteristic
323C2×#131C22×C1111yescharacteristic
324C4×#41C22×C1111yescharacteristic
325C4×#41C22×C1111yescharacteristic
326#442C4×C1111yescharacteristic, complemented
327#442C4×C1111yescharacteristic, complemented
328#441C4×C1111yescharacteristic, complemented
329#441C4×C1111yescharacteristic, complemented
330#440C4×C1111yescharacteristic, complemented
331#440C4×C1111yescharacteristic, complemented
332#440C4×C1111yescharacteristic, complemented
333#440C4×C1111yescharacteristic, complemented
334#433—21no—
335#433—21no—
336#432—21no—
337#431—21no—
338#427C22×C1111yescharacteristic
339#424—21no—
340#424—21no—
341#424C22×C1111yescharacteristic
342#424C22×C1111yescharacteristic
343#423—21no—
344#423C22×C1111yescharacteristic
345#423C22×C1111yescharacteristic
346C2×C4⋊C8—21no—
347C2×C4⋊C8C22×C1111yescharacteristic
348C2×#104C22×C1111yescharacteristic
349C2×#104C22×C1111yescharacteristic
350C2×#104C22×C1111yescharacteristic
351C2×#104C22×C1111yescharacteristic
352#416C22×C1111yescharacteristic
353#416C22×C1111yescharacteristic
354#408C22×C1111yescharacteristic
355#408C22×C1111yescharacteristic
356#405C22×C1111yescharacteristic
357#405C22×C1111yescharacteristic
358C2×#97C22×C1111yescharacteristic
359C2×#97C22×C1111yescharacteristic
360C2×C4×C8C22×C1111yescharacteristic
361C4×C4⋊C4C22×C1111yescharacteristic
362#341C22×C1111yescharacteristic
363#341C22×C1111yescharacteristic
364#341C22×C1111yescharacteristic
365#341C22×C1111yescharacteristic
366#339C22×C1111yescharacteristic
367#339C22×C1111yescharacteristic
368#339C22×C1111yescharacteristic
369#339C22×C1111yescharacteristic
370#336C22×C1111yescharacteristic
371#336C22×C1111yescharacteristic
372C22×C11—21no—
373C22×C11—21no—
374C22×C11—22no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11C2×C4×D411yescharacteristic
381C22×C11#55211yescharacteristic
382C22×C11#55311yescharacteristic
383C4×C11—22no—
384C4×C11—21no—
385C4×C11—21no—
386C4×C11—21no—
387C4×C11—21no—
388C4×C11—42no—
389C4×C11—41no—
390C4×C11—41no—
391C4×C11—41no—
392C4×C11—41no—
393C4×C11—41no—
394C4×C11—81no—
395C4×C11C2×#11711yescharacteristic
396C4×C11#52011yescharacteristic
397C4×C11#54611yescharacteristic
398C4×C11#54811yescharacteristic
399C2×#41C23×C1111yescharacteristic
400C2×#41C23×C1111yescharacteristic
401#135—22no—
402#135—22no—
403C2×Q16C2×C4×C1111yescharacteristic
404C2×SD16C2×C4×C1111yescharacteristic
405C2×SD16C2×C4×C1111yescharacteristic
406C2×D8C2×C4×C1111yescharacteristic
407#131—22no—
408#131—22no—
409#131—41no—
410#131—41no—
411C2×M16—21no—
412C2×M16—21no—
413C2×M16C23×C1111yescharacteristic
414C2×M16C23×C1111yescharacteristic
415C2×M16C23×C1111yescharacteristic
416C2×M16C23×C1111yescharacteristic
417C22×C8—21no—
418C22×C8—21no—
419C22×C8C23×C1111yescharacteristic
420C22×C8C23×C1111yescharacteristic
421C22×C8C23×C1111yescharacteristic
422C22×C8C23×C1111yescharacteristic
423C4×Q8C2×C4×C1111yescharacteristic
424C4×Q8C2×C4×C1111yescharacteristic
425C4×Q8C2×C4×C1111yescharacteristic
426C4×Q8C2×C4×C1111yescharacteristic
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4C2×C4×C1111yescharacteristic
432C4×D4C2×C4×C1111yescharacteristic
433C4×D4C2×C4×C1111yescharacteristic
434C4×D4C2×C4×C1111yescharacteristic
435#117—21no—
436#117—21no—
437#117C23×C1111yescharacteristic
438#117C23×C1111yescharacteristic
439C2×C4⋊C4—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42C23×C1111yescharacteristic
443C2×C42C23×C1111yescharacteristic
444C2×C42C23×C1111yescharacteristic
445#107C2×C4×C1111yescharacteristic
446#107C2×C4×C1111yescharacteristic
447#106C2×C4×C1111yescharacteristic
448#106C2×C4×C1111yescharacteristic
449C4⋊C8—21no—
450C4⋊C8—21no—
451C4⋊C8—21no—
452C4⋊C8—21no—
453C4⋊C8—21no—
454C4⋊C8—21no—
455C4⋊C8—21no—
456C4⋊C8—21no—
457C4⋊C8D4×C1111yescharacteristic
458C4⋊C8D4×C1111yescharacteristic
459C4⋊C8D4×C1111yescharacteristic
460C4⋊C8D4×C1111yescharacteristic
461#104—22no—
462#104—22no—
463#104—41no—
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—
477#97—21no—
478#97—21no—
479#97—41no—
480#97C2×C4×C1111yescharacteristic
481#97C2×C4×C1111yescharacteristic
482#97C2×C4×C1111yescharacteristic
483#97C2×C4×C1111yescharacteristic
484C4×C8—21no—
485C4×C8—21no—
486C4×C8—41no—
487#95—21no—
488C2×C11—21no—
489C2×C11—21no—
490C2×C11—42no—
491C2×C11—81no—
492C2×C11#235211yescharacteristic
493C2×C11#295511yescharacteristic
494C2×C11#295611yescharacteristic
495#41—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500#41—21no—
501#41C11×#4112yes—
502#41C11×#4112yes—
503C2×Q8C22×C4×C1111yescharacteristic
504C2×Q8C22×C4×C1111yescharacteristic
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×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4C11×#4111yescharacteristic
518C22×C4C11×#4111yescharacteristic
519C22×C4C24×C1111yescharacteristic
520Q16—22no—
521SD16—22no—
522SD16—22no—
523D8—22no—
524M16—21no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—42no—
533M16—42no—
534C2×C8—21no—
535C2×C8—21no—
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—42no—
547C2×C8—42no—
548C2×C8C22×C4×C1111yescharacteristic
549C2×C8C22×C4×C1111yescharacteristic
550C2×C8C22×C4×C1111yescharacteristic
551C2×C8C22×C4×C1111yescharacteristic
552C2×C8C2×D4×C1111yescharacteristic
553C2×C8C2×D4×C1111yescharacteristic
554C2×C8C2×D4×C1111yescharacteristic
555C2×C8C2×D4×C1111yescharacteristic
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4C22×C4×C1111yescharacteristic
562C4⋊C4C22×C4×C1111yescharacteristic
563C4⋊C4C22×C4×C1111yescharacteristic
564C4⋊C4C22×C4×C1111yescharacteristic
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42C22×C4×C1111yescharacteristic
582C42C22×C4×C1111yescharacteristic
583C42C2×D4×C1111yescharacteristic
584C42C2×D4×C1111yescharacteristic
585C11#2278411yescharacteristic, direct product factor, Sylow
586C23—21no—
587C23—21no—
588C23C2×C11×#4111yescharacteristic
589Q8—21no—
590Q8—21no—
591Q8—21no—
592Q8C11×#11712yes—
593D4—22no—
594D4—22no—
595D4—21no—
596D4—21no—
597D4—21no—
598D4—41no—
599D4—41no—
600D4C11×#11712yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—81no—
622C2×C4—81no—
623C2×C4C4×D4×C1111yescharacteristic
624C2×C4C4×D4×C1111yescharacteristic
625C2×C4C4×D4×C1111yescharacteristic
626C2×C4C4×D4×C1111yescharacteristic
627C2×C4C23×C4×C1111yescharacteristic
628C2×C4C22×D4×C1111yescharacteristic
629C2×C4C2×C11×#4111yescharacteristic
630C2×C4C2×C11×#4111yescharacteristic
631C2×C4C11×H(5,𝔽2)11yescharacteristic
632C2×C4C11×2−1+411yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—21no—
638C8—21no—
639C8—21no—
640C8—21no—
641C8—41no—
642C8—41no—
643C8—41no—
644C8—41no—
645C22—21no—
646C22—21no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22C2×C4×D4×C1111yescharacteristic
654C22C11×#55211yescharacteristic
655C22C11×#55311yescharacteristic
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—22no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—81no—
668C4C2×C11×#11711yescharacteristic
669C4C11×#52011yescharacteristic
670C4C11×#54611yescharacteristic
671C4C11×#54811yescharacteristic
672C2—21no—
673C2—21no—
674C2—42no—
675C2—81no—
676C2C11×#235211yescharacteristic
677C2C11×#295511yescharacteristic
678C2C11×#295611yescharacteristic
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×C4×D4
prime radicalC2×C11×#135C22
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×#2925C2semidirect
3. C11×#2906C2semidirect
4. C11×#1938C2semidirect
5. C11×#1937C2semidirect
6. C11×#1922C2semidirect
7. C11×#1922C2semidirect
10. C11×#1838C2semidirect
11. C11×#1806C2semidirect
12. C11×#1806C2semidirect
13. C11×#1771C2semidirect
14. C11×#1765C2semidirect
15. C11×#1764C2semidirect
21. C11×#442C4semidirect
22. C11×#442C4semidirect
23. C11×#441C4semidirect
24. C11×#441C4semidirect
25. C11×#440C4semidirect
26. C11×#440C4semidirect
27. C11×#440C4semidirect
28. C11×#440C4semidirect
156. #22784C11direct (N × H)
248. #2925C2×C11semidirect
249. #2906C2×C11semidirect
250. #1938C2×C11semidirect
251. #1937C2×C11semidirect
252. #1922C2×C11semidirect
253. #1922C2×C11semidirect
256. #1838C2×C11semidirect
257. #1806C2×C11semidirect
258. #1806C2×C11semidirect
259. #1771C2×C11semidirect
260. #1765C2×C11semidirect
261. #1764C2×C11semidirect
326. #442C4×C11semidirect
327. #442C4×C11semidirect
328. #441C4×C11semidirect
329. #441C4×C11semidirect
330. #440C4×C11semidirect
331. #440C4×C11semidirect
332. #440C4×C11semidirect
333. #440C4×C11semidirect
585. C11#22784direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29432
C11×#29252
C11×#29062
C11×#19382
C11×#19372
C11×#19222
C11×#18762
C11×#18382
C11×#18062
C11×#17712
C11×#17652
C11×#17642
#2278411