Finite Group Databasebeta

← C11×#21510 #14598703

Subgroups — C11×#21510 #14598703

Order 2816.

1056 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#463C211yesmaximal, characteristic
2C2×C11×#442C211yesmaximal, characteristic
3C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
4C11×#2326C211yesmaximal, characteristic, complemented
5C11×#2275C211yesmaximal, characteristic, complemented
6C11×#1983C211yesmaximal, characteristic, complemented
7C11×#1948C211yesmaximal, characteristic, complemented
8C11×#1927C211yesmaximal, characteristic, complemented
9C11×#1926C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic
11C11×#1877C211yesmaximal, characteristic, complemented
12C11×#1802C211yesmaximal, characteristic, complemented
13C11×#1768C211yesmaximal, characteristic, complemented
14C11×#1763C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C11×#463C418yescomplemented
25C11×#442—24no—
26C4×C11×SD16—24no—
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#97C2211yescharacteristic
40C2×C4×C8×C11C2211yescharacteristic
41C11×#391C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#388—21no—
44C11×#388—21no—
45C11×#385—21no—
46C11×#385—21no—
47C11×#384C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2211yescharacteristic
51C4×C11×C22⋊C4—21no—
52C4×C11×C22⋊C4—21no—
53C4×C11×C22⋊C4—21no—
54C11×#376C2211yescharacteristic
55C2×C11×#95—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16C2×C414yescomplemented
72C2×C11×D8—22no—
73C2×C11×D8—22no—
74C2×C11×D8C2×C414yes—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C11×#124—22no—
80C11×#124C2×C414yescomplemented
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11C2×C414yescomplemented
90C4×D4×C11D414yes—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C42×C11—21no—
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11C2311yescharacteristic
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C11×#106—22no—
115C11×#106—22no—
116C11×C4⋊C8—22no—
117C11×C4⋊C8C2×C414yescomplemented
118C11×#103—22no—
119C11×#103—22no—
120C11×#103C2×C414yescomplemented
121C11×#102—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102—22no—
125C11×#102C2×C414yescomplemented
126C11×#97—22no—
127C4×C8×C11—22no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95D411yescharacteristic
134C11×#95D411yescharacteristic
135C11×#95D411yescharacteristic
136C11×#95D411yescharacteristic
137#21510C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C24×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11C22×C412yes—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11C22×C412yes—
155C2×D4×C11C22×C412yes—
156C2×D4×C11C2×D412yes—
157C2×D4×C11#4112yes—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—24no—
163C22×C4×C11—24no—
164C22×C4×C11—24no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—42no—
168C22×C4×C11—81no—
169C22×C4×C11—81no—
170C22×C4×C11—81no—
171C22×C4×C11—81no—
172C22×C4×C11—81no—
173C22×C4×C11—81no—
174C22×C4×C11—81no—
175C22×C4×C11—81no—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C11×SD16—28no—
184C11×D8—28no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11C22×C412yes—
196C2×C8×C11C22×C412yes—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—42no—
205C11×C4⋊C4—81no—
206C11×C4⋊C4—81no—
207C11×C4⋊C4C22×C412yes—
208C11×C4⋊C4C2×D412yes—
209C11×C4⋊C4#4112yes—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—24no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—81no—
217C11×C22⋊C4—81no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—42no—
221C42×C11—81no—
222C42×C11—81no—
223C42×C11—81no—
224C42×C11C22×C412yes—
225C42×C11C2×D412yes—
226C42×C11#4112yes—
227C42×C11#4112yes—
228C2×#463C2×C1111yescharacteristic
229C2×#442C2×C1111yescharacteristic
230C2×C4×SD16C2×C1111yescharacteristic, complemented
231#2326C2×C1111yescharacteristic, complemented
232#2275C2×C1111yescharacteristic, complemented
233#1983C2×C1111yescharacteristic, complemented
234#1948C2×C1111yescharacteristic, complemented
235#1927C2×C1111yescharacteristic, complemented
236#1926C2×C1111yescharacteristic, complemented
237#1879C2×C1111yescharacteristic
238#1877C2×C1111yescharacteristic, complemented
239#1802C2×C1111yescharacteristic, complemented
240#1768C2×C1111yescharacteristic, complemented
241#1763C2×C1111yescharacteristic, complemented
242C4×#102C2×C1111yescharacteristic, complemented
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11C22×D411yescharacteristic
258Q8×C11—22no—
259Q8×C11—22no—
260Q8×C11—41no—
261Q8×C11—41no—
262D4×C11—22no—
263D4×C11—22no—
264D4×C11—22no—
265D4×C11—22no—
266D4×C11—22no—
267D4×C11—41no—
268D4×C11—41no—
269D4×C11C4×D414yes—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
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—22no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
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×C11—41no—
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—84no—
303C2×C4×C11—84no—
304C2×C4×C11—84no—
305C2×C4×C11—84no—
306C2×C4×C11C4×D412yes—
307C2×C4×C11C4×D412yes—
308C2×C4×C11#12112yes—
309C2×C4×C11#12112yes—
310C2×C4×C11C23×C411yescharacteristic
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C8×C11—22no—
317C8×C11—22no—
318C8×C11—41no—
319C8×C11—41no—
320C22×SD16C22×C1111yescharacteristic
321C22×D8C22×C1111yescharacteristic
322C2×#124C22×C1111yescharacteristic
323C2×C4×Q8C22×C1111yescharacteristic
324C2×C4×D4C22×C1111yescharacteristic
325C2×C4×D4C22×C1111yescharacteristic
326C2×C4×D4C22×C1111yescharacteristic
327C2×C4×D4C22×C1111yescharacteristic
328#463C4×C1118yescomplemented
329#442—24no—
330C4×SD16—24no—
331C2×#106C22×C1111yescharacteristic
332C2×#106C22×C1111yescharacteristic
333C2×C4⋊C8C22×C1111yescharacteristic
334C2×C4⋊C8C22×C1111yescharacteristic
335C2×#103C22×C1111yescharacteristic
336C2×#103C22×C1111yescharacteristic
337C2×#103C22×C1111yescharacteristic
338C2×#102C22×C1111yescharacteristic
339C2×#102C22×C1111yescharacteristic
340C2×#102C22×C1111yescharacteristic
341C2×#102C22×C1111yescharacteristic
342C2×#102C22×C1111yescharacteristic
343C2×#97C22×C1111yescharacteristic
344C2×C4×C8C22×C1111yescharacteristic
345#391C22×C1111yescharacteristic
346#390C22×C1111yescharacteristic
347#388—21no—
348#388—21no—
349#385—21no—
350#385—21no—
351#384C22×C1111yescharacteristic
352C4×C4⋊C4C22×C1111yescharacteristic
353C4×C4⋊C4C22×C1111yescharacteristic
354C4×C4⋊C4C22×C1111yescharacteristic
355C4×C22⋊C4—21no—
356C4×C22⋊C4—21no—
357C4×C22⋊C4—21no—
358#376C22×C1111yescharacteristic
359C2×#95—21no—
360#340C22×C1111yescharacteristic
361#340C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364#336C22×C1111yescharacteristic
365#336C22×C1111yescharacteristic
366C22×C11—24no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11C2×C4×D411yescharacteristic
381C22×C11C2×#12111yescharacteristic
382C22×C11#52511yescharacteristic
383C22×C11#57611yescharacteristic
384C22×C11#57711yescharacteristic
385C22×C11#57711yescharacteristic
386C22×C11#57711yescharacteristic
387C4×C11—22no—
388C4×C11—22no—
389C4×C11—22no—
390C4×C11—22no—
391C4×C11—41no—
392C4×C11—42no—
393C4×C11—41no—
394C4×C11—42no—
395C4×C11—42no—
396C4×C11—42no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11C2×C4×D411yescharacteristic
400C4×C11C4×#4111yescharacteristic
401C4×C11#52911yescharacteristic
402C4×C11#53211yescharacteristic
403C22×Q8C23×C1111yescharacteristic
404C22×D4C23×C1111yescharacteristic
405C22×D4C23×C1111yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—21no—
409C23×C4—21no—
410C2×SD16—22no—
411C2×SD16—22no—
412C2×SD16C2×C4×C1114yescomplemented
413C2×D8—22no—
414C2×D8—22no—
415C2×D8C2×C4×C1114yes—
416C22×C8C23×C1111yescharacteristic
417C22×C8C23×C1111yescharacteristic
418C22×C8C23×C1111yescharacteristic
419C22×C8C23×C1111yescharacteristic
420#124—22no—
421#124C2×C4×C1114yescomplemented
422C4×Q8—22no—
423C4×Q8—22no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4C2×C4×C1114yescomplemented
431C4×D4D4×C1114yes—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4C23×C1111yescharacteristic
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C4⋊C4C23×C1111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42C23×C1111yescharacteristic
453C2×C42C23×C1111yescharacteristic
454C2×C42C23×C1111yescharacteristic
455#106—22no—
456#106—22no—
457C4⋊C8—22no—
458C4⋊C8C2×C4×C1114yescomplemented
459#103—22no—
460#103—22no—
461#103C2×C4×C1114yescomplemented
462#102—22no—
463#102—22no—
464#102—22no—
465#102—22no—
466#102C2×C4×C1114yescomplemented
467#97—22no—
468C4×C8—22no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95D4×C1111yescharacteristic
475#95D4×C1111yescharacteristic
476#95D4×C1111yescharacteristic
477#95D4×C1111yescharacteristic
478C2×C11—44no—
479C2×C11—82no—
480C2×C11C4×#12111yescharacteristic
481C2×C11#294611yescharacteristic
482C2×C11#295211yescharacteristic
483C2×C11#304211yescharacteristic
484C2×C11#304511yescharacteristic
485C2×C11#311811yescharacteristic
486C2×C11#312511yescharacteristic
487C24—21no—
488C24—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C22×C4×C1112yes—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4C22×C4×C1112yes—
504C2×D4C22×C4×C1112yes—
505C2×D4C2×D4×C1112yes—
506C2×D4C11×#4112yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—42no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4C2×D4×C1111yescharacteristic
526C22×C4C2×D4×C1111yescharacteristic
527C22×C4C2×D4×C1111yescharacteristic
528C22×C4C2×D4×C1111yescharacteristic
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C24×C1111yescharacteristic
532SD16—28no—
533D8—28no—
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×C8C22×C4×C1112yes—
545C2×C8C22×C4×C1112yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—42no—
554C4⋊C4—81no—
555C4⋊C4—81no—
556C4⋊C4C22×C4×C1112yes—
557C4⋊C4C2×D4×C1112yes—
558C4⋊C4C11×#4112yes—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C22⋊C4—81no—
567C42—21no—
568C42—21no—
569C42—42no—
570C42—81no—
571C42—81no—
572C42—81no—
573C42C22×C4×C1112yes—
574C42C2×D4×C1112yes—
575C42C11×#4112yes—
576C42C11×#4112yes—
577C11#2151011yescharacteristic, direct product factor, Sylow
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23C22×D4×C1111yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—41no—
596Q8—41no—
597D4—22no—
598D4—22no—
599D4—22no—
600D4—22no—
601D4—22no—
602D4—41no—
603D4—41no—
604D4C4×D4×C1114yes—
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—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—84no—
638C2×C4—84no—
639C2×C4—84no—
640C2×C4—84no—
641C2×C4C4×D4×C1112yes—
642C2×C4C4×D4×C1112yes—
643C2×C4C11×#12112yes—
644C2×C4C11×#12112yes—
645C2×C4C23×C4×C1111yescharacteristic
646C2×C4C22×D4×C1111yescharacteristic
647C2×C4C2×C11×#4111yescharacteristic
648C2×C4C2×C11×#4111yescharacteristic
649C2×C4C2×C11×#4111yescharacteristic
650C2×C4C2×C11×#4111yescharacteristic
651C8—22no—
652C8—22no—
653C8—41no—
654C8—41no—
655C22—24no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22C2×C4×D4×C1111yescharacteristic
670C22C2×C11×#12111yescharacteristic
671C22C11×#52511yescharacteristic
672C22C11×#57611yescharacteristic
673C22C11×#57711yescharacteristic
674C22C11×#57711yescharacteristic
675C22C11×#57711yescharacteristic
676C4—22no—
677C4—22no—
678C4—22no—
679C4—22no—
680C4—42no—
681C4—42no—
682C4—42no—
683C4—41no—
684C4—42no—
685C4—41no—
686C4—81no—
687C4—81no—
688C4C2×C4×D4×C1111yescharacteristic
689C4C4×C11×#4111yescharacteristic
690C4C11×#52911yescharacteristic
691C4C11×#53211yescharacteristic
692C2—44no—
693C2—82no—
694C2C4×C11×#12111yescharacteristic
695C2C11×#294611yescharacteristic
696C2C11×#295211yescharacteristic
697C2C11×#304211yescharacteristic
698C2C11×#304511yescharacteristic
699C2C11×#311811yescharacteristic
700C2C11×#312511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×D8C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C11×#376 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C11×SD16C2semidirect
4. C11×#2326C2semidirect
5. C11×#2275C2semidirect
6. C11×#1983C2semidirect
7. C11×#1948C2semidirect
8. C11×#1927C2semidirect
9. C11×#1926C2semidirect
11. C11×#1877C2semidirect
12. C11×#1802C2semidirect
13. C11×#1768C2semidirect
14. C11×#1763C2semidirect
15. C4×C11×#102C2semidirect
24. C11×#463C4semidirect
71. C2×C11×SD16C2×C4semidirect
80. C11×#124C2×C4semidirect
89. C4×D4×C11C2×C4semidirect
117. C11×C4⋊C8C2×C4semidirect
120. C11×#103C2×C4semidirect
125. C11×#102C2×C4semidirect
137. #21510C11direct (N × H)
230. C2×C4×SD16C2×C11semidirect
231. #2326C2×C11semidirect
232. #2275C2×C11semidirect
233. #1983C2×C11semidirect
234. #1948C2×C11semidirect
235. #1927C2×C11semidirect
236. #1926C2×C11semidirect
238. #1877C2×C11semidirect
239. #1802C2×C11semidirect
240. #1768C2×C11semidirect
241. #1763C2×C11semidirect
242. C4×#102C2×C11semidirect
328. #463C4×C11semidirect
412. C2×SD16C2×C4×C11semidirect
421. #124C2×C4×C11semidirect
430. C4×D4C2×C4×C11semidirect
458. C4⋊C8C2×C4×C11semidirect
461. #103C2×C4×C11semidirect
466. #102C2×C4×C11semidirect
577. C11#21510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4632
C2×C11×#4422
C2×C4×C11×SD162
C11×#23262
C11×#22752
C11×#19832
C11×#19482
C11×#19272
C11×#19262
C11×#18792
C11×#18772
C11×#18022
C11×#17682
C11×#17632
C4×C11×#1022
#2151011