Finite Group Databasebeta

← C11×#21523 #14598716

Subgroups — C11×#21523 #14598716

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#465C211yesmaximal, characteristic
2C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
3C2×C11×#405C211yesmaximal, characteristic, complemented
4C11×#2324C211yesmaximal, characteristic
5C11×#2323C211yesmaximal, characteristic, complemented
6C11×#1968C211yesmaximal, characteristic, complemented
7C11×#1941C211yesmaximal, characteristic, complemented
8C11×#1936C211yesmaximal, characteristic, complemented
9C11×#1935C211yesmaximal, characteristic, complemented
10C11×#1895C211yesmaximal, characteristic
11C11×#1894C211yesmaximal, characteristic, complemented
12C11×#1807C211yesmaximal, characteristic, complemented
13C4×C11×#106C211yesmaximal, characteristic, complemented
14C11×#1763C211yesmaximal, characteristic, complemented
15C11×#1762C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#465C418yescomplemented
25C4×C11×SD16—24no—
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×#106C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C11×#405—24no—
36C2×C11×#97C2211yescharacteristic
37C2×C11×#97C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C2×C4×C8×C11C2211yescharacteristic
40C11×#391C2211yescharacteristic
41C11×#390—21no—
42C11×#390C2211yescharacteristic
43C11×#389—21no—
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#388—21no—
47C11×#388—21no—
48C11×#388—21no—
49C11×#387—21no—
50C11×#386—21no—
51C11×#385—21no—
52C11×#380C2211yescharacteristic
53C11×#380C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C4⋊C4C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16C2×C414yes—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C22×C8×C11—22no—
74C22×C8×C11—22no—
75C22×C8×C11C2×C414yescomplemented
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8C2×C414yescomplemented
82C11×#121—22no—
83C11×#121C2×C414yes—
84C4×Q8×C11—22no—
85C4×Q8×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C11×#117—22no—
89C11×#117—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
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×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C11×C22⋊C4D411yescharacteristic
111C2×C42×C11—21no—
112C2×C42×C11—21no—
113C2×C42×C11—21no—
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C11×#106—22no—
117C11×#106—22no—
118C11×#106C2×C414yescomplemented
119C11×#103—22no—
120C11×#103—22no—
121C11×#103C2×C414yescomplemented
122C11×#102—22no—
123C11×#102—22no—
124C11×#102C2×C414yes—
125C11×#97—22no—
126C11×#97—22no—
127C4×C8×C11—22no—
128C4×C8×C11D414yescomplemented
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137#21523C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
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—24no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—81no—
153C2×D4×C11—81no—
154C2×D4×C11C22×C412yes—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—81no—
168C22×C4×C11—81no—
169C22×C4×C11C22×C412yes—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11#4112yes—
176C22×C4×C11C2411yescharacteristic
177C11×SD16—28no—
178C11×M16—28no—
179C2×C8×C11—28no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11C22×C412yes—
187C2×C8×C11C22×C412yes—
188C2×C8×C11C2×D412yes—
189C2×C8×C11C2×D412yes—
190C2×C8×C11#4112yes—
191C2×C8×C11#4112yes—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
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—21no—
205C11×C4⋊C4—42no—
206C11×C4⋊C4—81no—
207C11×C4⋊C4—81no—
208C11×C4⋊C4C22×C412yes—
209C11×C4⋊C4C22×C412yes—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—81no—
216C11×C22⋊C4—81no—
217C11×C22⋊C4—81no—
218C11×C22⋊C4—81no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—42no—
222C42×C11—81no—
223C42×C11—81no—
224C42×C11C2×D412yes—
225C42×C11#4112yes—
226C2×#465C2×C1111yescharacteristic
227C2×C4×SD16C2×C1111yescharacteristic, complemented
228C2×#405C2×C1111yescharacteristic, complemented
229#2324C2×C1111yescharacteristic
230#2323C2×C1111yescharacteristic, complemented
231#1968C2×C1111yescharacteristic, complemented
232#1941C2×C1111yescharacteristic, complemented
233#1936C2×C1111yescharacteristic, complemented
234#1935C2×C1111yescharacteristic, complemented
235#1895C2×C1111yescharacteristic
236#1894C2×C1111yescharacteristic, complemented
237#1807C2×C1111yescharacteristic, complemented
238C4×#106C2×C1111yescharacteristic, complemented
239#1763C2×C1111yescharacteristic, complemented
240#1762C2×C1111yescharacteristic, complemented
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—22no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11C4×D412yes—
255C23×C11C22×D411yescharacteristic
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—41no—
259Q8×C11—41no—
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—41no—
263D4×C11—41no—
264D4×C11—84no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
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×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×C11C4×D412yes—
304C2×C4×C11#12112yes—
305C2×C4×C11#12112yes—
306C2×C4×C11C23×C411yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C8×C11—22no—
313C8×C11—22no—
314C8×C11—22no—
315C8×C11C4×D414yes—
316C22×SD16C22×C1111yescharacteristic
317C22×M16C22×C1111yescharacteristic
318C23×C8C22×C1111yescharacteristic
319C2×C22⋊Q8C22×C1111yescharacteristic
320C2×#121C22×C1111yescharacteristic
321C2×C4×Q8C22×C1111yescharacteristic
322C2×C4×D4C22×C1111yescharacteristic
323C2×#117C22×C1111yescharacteristic
324#465C4×C1118yescomplemented
325C4×SD16—24no—
326C2×#106C22×C1111yescharacteristic
327C2×#106C22×C1111yescharacteristic
328C2×#106C22×C1111yescharacteristic
329C2×#103C22×C1111yescharacteristic
330C2×#103C22×C1111yescharacteristic
331C2×#103C22×C1111yescharacteristic
332C2×#102C22×C1111yescharacteristic
333C2×#102C22×C1111yescharacteristic
334C2×#102C22×C1111yescharacteristic
335#405—24no—
336C2×#97C22×C1111yescharacteristic
337C2×#97C22×C1111yescharacteristic
338C2×C4×C8C22×C1111yescharacteristic
339C2×C4×C8C22×C1111yescharacteristic
340#391C22×C1111yescharacteristic
341#390—21no—
342#390C22×C1111yescharacteristic
343#389—21no—
344#389C22×C1111yescharacteristic
345#389C22×C1111yescharacteristic
346#388—21no—
347#388—21no—
348#388—21no—
349#387—21no—
350#386—21no—
351#385—21no—
352#380C22×C1111yescharacteristic
353#380C22×C1111yescharacteristic
354C4×C4⋊C4C22×C1111yescharacteristic
355C4×C4⋊C4C22×C1111yescharacteristic
356#340C22×C1111yescharacteristic
357#340C22×C1111yescharacteristic
358#340C22×C1111yescharacteristic
359#340C22×C1111yescharacteristic
360#340C22×C1111yescharacteristic
361#340C22×C1111yescharacteristic
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11—81no—
376C22×C11C2×C4×D411yescharacteristic
377C22×C11C2×#12111yescharacteristic
378C22×C11#53211yescharacteristic
379C22×C11#57711yescharacteristic
380C22×C11#57711yescharacteristic
381C22×C11#57711yescharacteristic
382C22×C11#57711yescharacteristic
383C4×C11—22no—
384C4×C11—22no—
385C4×C11—22no—
386C4×C11—42no—
387C4×C11—42no—
388C4×C11—41no—
389C4×C11—41no—
390C4×C11—42no—
391C4×C11—81no—
392C4×C11—81no—
393C4×C11—81no—
394C4×C11—81no—
395C4×C11C2×C4×D411yescharacteristic
396C4×C11C4×#4111yescharacteristic
397C4×C11#52511yescharacteristic
398C4×C11#52911yescharacteristic
399C22×Q8C23×C1111yescharacteristic
400C22×D4—21no—
401C22×D4C23×C1111yescharacteristic
402C23×C4—21no—
403C23×C4C23×C1111yescharacteristic
404C2×SD16—22no—
405C2×SD16—22no—
406C2×SD16C2×C4×C1114yes—
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—22no—
410C22×C8—22no—
411C22×C8—22no—
412C22×C8C2×C4×C1114yescomplemented
413C22×C8C23×C1111yescharacteristic
414C22×C8C23×C1111yescharacteristic
415C22×C8C23×C1111yescharacteristic
416C22×C8C23×C1111yescharacteristic
417C22⋊Q8—22no—
418C22⋊Q8C2×C4×C1114yescomplemented
419#121—22no—
420#121C2×C4×C1114yes—
421C4×Q8—22no—
422C4×Q8—22no—
423C4×D4—22no—
424C4×D4—22no—
425#117—22no—
426#117—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4D4×C1111yescharacteristic
432C2×C4⋊C4D4×C1111yescharacteristic
433C2×C4⋊C4C23×C1111yescharacteristic
434C2×C4⋊C4C23×C1111yescharacteristic
435C2×C4⋊C4C23×C1111yescharacteristic
436C2×C4⋊C4C23×C1111yescharacteristic
437C2×C4⋊C4C23×C1111yescharacteristic
438C2×C4⋊C4C23×C1111yescharacteristic
439C2×C22⋊C4—21no—
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⋊C4D4×C1111yescharacteristic
447C2×C22⋊C4D4×C1111yescharacteristic
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C1111yescharacteristic
452C2×C42C23×C1111yescharacteristic
453#106—22no—
454#106—22no—
455#106C2×C4×C1114yescomplemented
456#103—22no—
457#103—22no—
458#103C2×C4×C1114yescomplemented
459#102—22no—
460#102—22no—
461#102C2×C4×C1114yes—
462#97—22no—
463#97—22no—
464C4×C8—22no—
465C4×C8D4×C1114yescomplemented
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474C2×C11—42no—
475C2×C11—82no—
476C2×C11C4×#12111yescharacteristic
477C2×C11#294911yescharacteristic
478C2×C11#295211yescharacteristic
479C2×C11#305711yescharacteristic
480C2×C11#306011yescharacteristic
481C2×C11#317311yescharacteristic
482C2×C11#317411yescharacteristic
483C24—21no—
484C24C2×D4×C1111yescharacteristic
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8C22×C4×C1112yes—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4C22×C4×C1112yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4C22×C4×C1112yes—
515C22×C4C2×D4×C1111yescharacteristic
516C22×C4C2×D4×C1111yescharacteristic
517C22×C4C2×D4×C1111yescharacteristic
518C22×C4C2×D4×C1111yescharacteristic
519C22×C4C2×D4×C1111yescharacteristic
520C22×C4C11×#4112yes—
521C22×C4C24×C1111yescharacteristic
522SD16—28no—
523M16—28no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—28no—
531C2×C8C22×C4×C1112yes—
532C2×C8C22×C4×C1112yes—
533C2×C8C2×D4×C1112yes—
534C2×C8C2×D4×C1112yes—
535C2×C8C11×#4112yes—
536C2×C8C11×#4112yes—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—81no—
552C4⋊C4—81no—
553C4⋊C4C22×C4×C1112yes—
554C4⋊C4C22×C4×C1112yes—
555C22⋊C4—24no—
556C22⋊C4—24no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C42—21no—
565C42—21no—
566C42—42no—
567C42—81no—
568C42—81no—
569C42C2×D4×C1112yes—
570C42C11×#4112yes—
571C11#2152311yescharacteristic, direct product factor, Sylow
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23C4×D4×C1112yes—
586C23C22×D4×C1111yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—41no—
590Q8—41no—
591D4—22no—
592D4—22no—
593D4—41no—
594D4—41no—
595D4—84no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
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—84no—
634C2×C4C4×D4×C1112yes—
635C2×C4C11×#12112yes—
636C2×C4C11×#12112yes—
637C2×C4C23×C4×C1111yescharacteristic
638C2×C4C22×D4×C1111yescharacteristic
639C2×C4C2×C11×#4111yescharacteristic
640C2×C4C2×C11×#4111yescharacteristic
641C2×C4C2×C11×#4111yescharacteristic
642C2×C4C2×C11×#4111yescharacteristic
643C8—22no—
644C8—22no—
645C8—22no—
646C8C4×D4×C1114yes—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22C2×C4×D4×C1111yescharacteristic
662C22C2×C11×#12111yescharacteristic
663C22C11×#53211yescharacteristic
664C22C11×#57711yescharacteristic
665C22C11×#57711yescharacteristic
666C22C11×#57711yescharacteristic
667C22C11×#57711yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—42no—
672C4—42no—
673C4—41no—
674C4—41no—
675C4—42no—
676C4—81no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4C2×C4×D4×C1111yescharacteristic
681C4C4×C11×#4111yescharacteristic
682C4C11×#52511yescharacteristic
683C4C11×#52911yescharacteristic
684C2—42no—
685C2—82no—
686C2C4×C11×#12111yescharacteristic
687C2C11×#294911yescharacteristic
688C2C11×#295211yescharacteristic
689C2C11×#305711yescharacteristic
690C2C11×#306011yescharacteristic
691C2C11×#317311yescharacteristic
692C2C11×#317411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×SD16C2semidirect
3. C2×C11×#405C2semidirect
5. C11×#2323C2semidirect
6. C11×#1968C2semidirect
7. C11×#1941C2semidirect
8. C11×#1936C2semidirect
9. C11×#1935C2semidirect
11. C11×#1894C2semidirect
12. C11×#1807C2semidirect
13. C4×C11×#106C2semidirect
14. C11×#1763C2semidirect
15. C11×#1762C2semidirect
24. C11×#465C4semidirect
75. C22×C8×C11C2×C4semidirect
81. C11×C22⋊Q8C2×C4semidirect
118. C11×#106C2×C4semidirect
121. C11×#103C2×C4semidirect
128. C4×C8×C11D4semidirect
137. #21523C11direct (N × H)
227. C2×C4×SD16C2×C11semidirect
228. C2×#405C2×C11semidirect
230. #2323C2×C11semidirect
231. #1968C2×C11semidirect
232. #1941C2×C11semidirect
233. #1936C2×C11semidirect
234. #1935C2×C11semidirect
236. #1894C2×C11semidirect
237. #1807C2×C11semidirect
238. C4×#106C2×C11semidirect
239. #1763C2×C11semidirect
240. #1762C2×C11semidirect
324. #465C4×C11semidirect
412. C22×C8C2×C4×C11semidirect
418. C22⋊Q8C2×C4×C11semidirect
455. #106C2×C4×C11semidirect
458. #103C2×C4×C11semidirect
465. C4×C8D4×C11semidirect
571. C11#21523direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4652
C2×C4×C11×SD162
C2×C11×#4052
C11×#23242
C11×#23232
C11×#19682
C11×#19412
C11×#19362
C11×#19352
C11×#18952
C11×#18942
C11×#18072
C4×C11×#1062
C11×#17632
C11×#17622
#2152311