Finite Group Databasebeta

← C11×#23023 #14600216

Subgroups — C11×#23023 #14600216

Order 2816.

994 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
1C2×C11×#465C211yesmaximal, characteristic
2C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
3C2×C11×#427C211yesmaximal, characteristic, complemented
4C11×#2363C211yesmaximal, characteristic
5C11×#2362C211yesmaximal, characteristic, complemented
6C11×#1968C211yesmaximal, characteristic, complemented
7C11×#1941C211yesmaximal, characteristic, complemented
8C11×#1928C211yesmaximal, characteristic, complemented
9C11×#1925C211yesmaximal, characteristic, complemented
10C11×#1875C211yesmaximal, characteristic
11C11×#1873C211yesmaximal, characteristic, complemented
12C11×#1863C211yesmaximal, characteristic, complemented
13C11×#1862C211yesmaximal, characteristic, complemented
14C4×C11×#106C211yesmaximal, characteristic, complemented
15C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#465C418yescomplemented
25C4×C11×SD16—24no—
26C11×#427—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#107C2211yescharacteristic
29C2×C11×#106C2211yescharacteristic
30C2×C11×#106C2211yescharacteristic
31C2×C11×#106C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C4×C8×C11C2211yescharacteristic
40C2×C4×C8×C11C2211yescharacteristic
41C11×#391C2211yescharacteristic
42C11×#390—21no—
43C11×#390C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#388—21no—
47C11×#388—21no—
48C11×#388—21no—
49C11×#387—21no—
50C11×#386—21no—
51C4×C11×C4⋊C4—21no—
52C4×C11×C4⋊C4C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C22⋊C4—21no—
55C4×C11×C22⋊C4C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
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—
70C22×C8×C11—22no—
71C22×C8×C11—22no—
72C22×C8×C11C2×C414yescomplemented
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8C2×C414yescomplemented
79C11×#121—22no—
80C11×#121C2×C414yes—
81C4×Q8×C11—22no—
82C4×Q8×C11—41no—
83C4×D4×C11—22no—
84C4×D4×C11—41no—
85C11×#117—22no—
86C11×#117—22no—
87C11×#117—41no—
88C11×#117—41no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C42×C11—21no—
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11—21no—
112C2×C42×C11—21no—
113C2×C42×C11C2311yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C11×#107—22no—
116C11×#107—22no—
117C11×#106—22no—
118C11×#106C2×C414yescomplemented
119C11×#106D414yescomplemented
120C11×#103—22no—
121C11×#103—41no—
122C11×#103C2×C414yescomplemented
123C11×#102—22no—
124C11×#102—41no—
125C11×#102C2×C414yes—
126C11×C22⋊C8—22no—
127C4×C8×C11—22no—
128C4×C8×C11—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95D411yescharacteristic
136C11×#95D411yescharacteristic
137#23023C1111yesmaximal, 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—42no—
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—
178C2×C8×C11—28no—
179C2×C8×C11—21no—
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×C11—21no—
187C2×C8×C11C22×C412yes—
188C2×C8×C11C22×C412yes—
189C2×C8×C11C2×D412yes—
190C2×C8×C11#4112yes—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—42no—
201C11×C4⋊C4—42no—
202C11×C4⋊C4—81no—
203C11×C4⋊C4C22×C412yes—
204C11×C4⋊C4C22×C412yes—
205C11×C4⋊C4C2×D412yes—
206C11×C4⋊C4C2×D412yes—
207C11×C22⋊C4—24no—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—81no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—42no—
221C42×C11—42no—
222C42×C11—42no—
223C42×C11—42no—
224C42×C11—81no—
225C2×#465C2×C1111yescharacteristic
226C2×C4×SD16C2×C1111yescharacteristic, complemented
227C2×#427C2×C1111yescharacteristic, complemented
228#2363C2×C1111yescharacteristic
229#2362C2×C1111yescharacteristic, complemented
230#1968C2×C1111yescharacteristic, complemented
231#1941C2×C1111yescharacteristic, complemented
232#1928C2×C1111yescharacteristic, complemented
233#1925C2×C1111yescharacteristic, complemented
234#1875C2×C1111yescharacteristic
235#1873C2×C1111yescharacteristic, complemented
236#1863C2×C1111yescharacteristic, complemented
237#1862C2×C1111yescharacteristic, complemented
238C4×#106C2×C1111yescharacteristic, complemented
239C8×C22⋊C4C2×C1111yescharacteristic, complemented
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—22no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11C4×D412yes—
254C23×C11C22×D411yescharacteristic
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—41no—
258Q8×C11—41no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—41no—
262D4×C11—41no—
263D4×C11—84no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—22no—
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—21no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
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—84no—
302C2×C4×C11C4×D412yes—
303C2×C4×C11#13512yes—
304C2×C4×C11#13512yes—
305C2×C4×C11C23×C411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C112−1+411yescharacteristic
311C8×C11—22no—
312C8×C11—41no—
313C8×C11—41no—
314C8×C11C4×D414yes—
315C22×SD16C22×C1111yescharacteristic
316C23×C8C22×C1111yescharacteristic
317C2×C22⋊Q8C22×C1111yescharacteristic
318C2×#121C22×C1111yescharacteristic
319C2×C4×Q8C22×C1111yescharacteristic
320C2×C4×D4C22×C1111yescharacteristic
321C2×#117C22×C1111yescharacteristic
322C2×#117C22×C1111yescharacteristic
323#465C4×C1118yescomplemented
324C4×SD16—24no—
325#427—24no—
326C2×#107C22×C1111yescharacteristic
327C2×#107C22×C1111yescharacteristic
328C2×#106C22×C1111yescharacteristic
329C2×#106C22×C1111yescharacteristic
330C2×#106C22×C1111yescharacteristic
331C2×#103C22×C1111yescharacteristic
332C2×#103C22×C1111yescharacteristic
333C2×#103C22×C1111yescharacteristic
334C2×#102C22×C1111yescharacteristic
335C2×#102C22×C1111yescharacteristic
336C2×#102C22×C1111yescharacteristic
337C2×C22⋊C8C22×C1111yescharacteristic
338C2×C4×C8C22×C1111yescharacteristic
339C2×C4×C8C22×C1111yescharacteristic
340#391C22×C1111yescharacteristic
341#390—21no—
342#390C22×C1111yescharacteristic
343#389C22×C1111yescharacteristic
344#389C22×C1111yescharacteristic
345#388—21no—
346#388—21no—
347#388—21no—
348#387—21no—
349#386—21no—
350C4×C4⋊C4—21no—
351C4×C4⋊C4C22×C1111yescharacteristic
352C4×C4⋊C4C22×C1111yescharacteristic
353C4×C22⋊C4—21no—
354C4×C22⋊C4C22×C1111yescharacteristic
355#340C22×C1111yescharacteristic
356#340C22×C1111yescharacteristic
357#340C22×C1111yescharacteristic
358#340C22×C1111yescharacteristic
359#336C22×C1111yescharacteristic
360#336C22×C1111yescharacteristic
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11C2×C4×D411yescharacteristic
376C22×C11D4211yescharacteristic
377C22×C11#54711yescharacteristic
378C22×C11C2×#13511yescharacteristic
379C22×C11C2×#13511yescharacteristic
380C22×C11#57711yescharacteristic
381C22×C11#57711yescharacteristic
382C4×C11—22no—
383C4×C11—22no—
384C4×C11—22no—
385C4×C11—41no—
386C4×C11—42no—
387C4×C11—42no—
388C4×C11—42no—
389C4×C11—42no—
390C4×C11—41no—
391C4×C11—42no—
392C4×C11—81no—
393C4×C11—81no—
394C4×C11C2×C4×D411yescharacteristic
395C4×C11#52011yescharacteristic
396C4×C11#54811yescharacteristic
397C4×C11#55311yescharacteristic
398C22×Q8C23×C1111yescharacteristic
399C22×D4—21no—
400C22×D4C23×C1111yescharacteristic
401C23×C4—21no—
402C23×C4C23×C1111yescharacteristic
403C2×SD16—22no—
404C2×SD16—22no—
405C2×SD16C2×C4×C1114yes—
406C22×C8—22no—
407C22×C8—22no—
408C22×C8C2×C4×C1114yescomplemented
409C22×C8C23×C1111yescharacteristic
410C22×C8C23×C1111yescharacteristic
411C22×C8C23×C1111yescharacteristic
412C22×C8C23×C1111yescharacteristic
413C22⋊Q8—22no—
414C22⋊Q8C2×C4×C1114yescomplemented
415#121—22no—
416#121C2×C4×C1114yes—
417C4×Q8—22no—
418C4×Q8—41no—
419C4×D4—22no—
420C4×D4—41no—
421#117—22no—
422#117—22no—
423#117—41no—
424#117—41no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4C23×C1111yescharacteristic
430C2×C4⋊C4C23×C1111yescharacteristic
431C2×C4⋊C4C23×C1111yescharacteristic
432C2×C4⋊C4C23×C1111yescharacteristic
433C2×C4⋊C4C23×C1111yescharacteristic
434C2×C4⋊C4C23×C1111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4D4×C1111yescharacteristic
443C2×C22⋊C4D4×C1111yescharacteristic
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42C23×C1111yescharacteristic
450C2×C42C23×C1111yescharacteristic
451#107—22no—
452#107—22no—
453#106—22no—
454#106C2×C4×C1114yescomplemented
455#106D4×C1114yescomplemented
456#103—22no—
457#103—41no—
458#103C2×C4×C1114yescomplemented
459#102—22no—
460#102—41no—
461#102C2×C4×C1114yes—
462C22⋊C8—22no—
463C4×C8—22no—
464C4×C8—22no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95D4×C1111yescharacteristic
472#95D4×C1111yescharacteristic
473C2×C11—42no—
474C2×C11—82no—
475C2×C11#236111yescharacteristic
476C2×C11C4×#13511yescharacteristic
477C2×C11#294911yescharacteristic
478C2×C11#328211yescharacteristic
479C2×C11#328411yescharacteristic
480C2×C11#333711yescharacteristic
481C2×C11#334011yescharacteristic
482C24—21no—
483C24C2×D4×C1111yescharacteristic
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8C22×C4×C1112yes—
490C2×D4—24no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—81no—
497C2×D4—81no—
498C2×D4C22×C4×C1112yes—
499C22×C4—21no—
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—42no—
511C22×C4—42no—
512C22×C4—81no—
513C22×C4C22×C4×C1112yes—
514C22×C4C2×D4×C1111yescharacteristic
515C22×C4C2×D4×C1111yescharacteristic
516C22×C4C2×D4×C1111yescharacteristic
517C22×C4C2×D4×C1111yescharacteristic
518C22×C4C2×D4×C1111yescharacteristic
519C22×C4C11×#4112yes—
520C22×C4C24×C1111yescharacteristic
521SD16—28no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—28no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8C22×C4×C1112yes—
532C2×C8C22×C4×C1112yes—
533C2×C8C2×D4×C1112yes—
534C2×C8C11×#4112yes—
535C4⋊C4—24no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—81no—
547C4⋊C4C22×C4×C1112yes—
548C4⋊C4C22×C4×C1112yes—
549C4⋊C4C2×D4×C1112yes—
550C4⋊C4C2×D4×C1112yes—
551C22⋊C4—24no—
552C22⋊C4—24no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—81no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—42no—
565C42—42no—
566C42—42no—
567C42—42no—
568C42—81no—
569C11#2302311yescharacteristic, direct product factor, Sylow
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23C4×D4×C1112yes—
584C23C22×D4×C1111yescharacteristic
585Q8—22no—
586Q8—22no—
587Q8—41no—
588Q8—41no—
589D4—22no—
590D4—22no—
591D4—41no—
592D4—41no—
593D4—84no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
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—84no—
632C2×C4C4×D4×C1112yes—
633C2×C4C11×#13512yes—
634C2×C4C11×#13512yes—
635C2×C4C23×C4×C1111yescharacteristic
636C2×C4C22×D4×C1111yescharacteristic
637C2×C4C2×C11×#4111yescharacteristic
638C2×C4C2×C11×#4111yescharacteristic
639C2×C4C11×H(5,𝔽2)11yescharacteristic
640C2×C4C11×2−1+411yescharacteristic
641C8—22no—
642C8—41no—
643C8—41no—
644C8C4×D4×C1114yes—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22C2×C4×D4×C1111yescharacteristic
660C22D42×C1111yescharacteristic
661C22C11×#54711yescharacteristic
662C22C2×C11×#13511yescharacteristic
663C22C2×C11×#13511yescharacteristic
664C22C11×#57711yescharacteristic
665C22C11×#57711yescharacteristic
666C4—22no—
667C4—22no—
668C4—22no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—41no—
673C4—42no—
674C4—41no—
675C4—42no—
676C4—81no—
677C4—81no—
678C4C2×C4×D4×C1111yescharacteristic
679C4C11×#52011yescharacteristic
680C4C11×#54811yescharacteristic
681C4C11×#55311yescharacteristic
682C2—42no—
683C2—82no—
684C2C11×#236111yescharacteristic
685C2C4×C11×#13511yescharacteristic
686C2C11×#294911yescharacteristic
687C2C11×#328211yescharacteristic
688C2C11×#328411yescharacteristic
689C2C11×#333711yescharacteristic
690C2C11×#334011yescharacteristic
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 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×SD16C2semidirect
3. C2×C11×#427C2semidirect
5. C11×#2362C2semidirect
6. C11×#1968C2semidirect
7. C11×#1941C2semidirect
8. C11×#1928C2semidirect
9. C11×#1925C2semidirect
11. C11×#1873C2semidirect
12. C11×#1863C2semidirect
13. C11×#1862C2semidirect
14. C4×C11×#106C2semidirect
15. C8×C11×C22⋊C4C2semidirect
24. C11×#465C4semidirect
72. C22×C8×C11C2×C4semidirect
78. C11×C22⋊Q8C2×C4semidirect
118. C11×#106C2×C4semidirect
119. C11×#106D4semidirect
122. C11×#103C2×C4semidirect
137. #23023C11direct (N × H)
226. C2×C4×SD16C2×C11semidirect
227. C2×#427C2×C11semidirect
229. #2362C2×C11semidirect
230. #1968C2×C11semidirect
231. #1941C2×C11semidirect
232. #1928C2×C11semidirect
233. #1925C2×C11semidirect
235. #1873C2×C11semidirect
236. #1863C2×C11semidirect
237. #1862C2×C11semidirect
238. C4×#106C2×C11semidirect
239. C8×C22⋊C4C2×C11semidirect
323. #465C4×C11semidirect
408. C22×C8C2×C4×C11semidirect
414. C22⋊Q8C2×C4×C11semidirect
454. #106C2×C4×C11semidirect
455. #106D4×C11semidirect
458. #103C2×C4×C11semidirect
569. C11#23023direct (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×#4272
C11×#23632
C11×#23622
C11×#19682
C11×#19412
C11×#19282
C11×#19252
C11×#18752
C11×#18732
C11×#18632
C11×#18622
C4×C11×#1062
C8×C11×C22⋊C42
#2302311