Finite Group Databasebeta

← C11×#23126 #14600319

Subgroups — C11×#23126 #14600319

Order 2816.

994 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
2C11×#2361C211yesmaximal, characteristic
3C11×#2360C211yesmaximal, characteristic, complemented
4C11×#1934C211yesmaximal, characteristic, complemented
5C11×#1933C211yesmaximal, characteristic, complemented
6C11×#1920C211yesmaximal, characteristic, complemented
7C11×#1919C211yesmaximal, characteristic, complemented
8C11×#1880C211yesmaximal, characteristic, complemented
9C11×#1877C211yesmaximal, characteristic, complemented
10C11×#1874C211yesmaximal, characteristic
11C11×#1872C211yesmaximal, characteristic, complemented
12C4×C11×#103C211yesmaximal, characteristic, complemented
13C4×C11×#102C211yesmaximal, characteristic, complemented
14C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
15C2×C11×#340C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C11×#465C418yescomplemented
26C2×C11×#106C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic
35C2×C4×C8×C11C2211yescharacteristic
36C11×#391C2211yescharacteristic
37C11×#390C2211yescharacteristic
38C11×#389—21no—
39C11×#389C2211yescharacteristic
40C11×#389C2211yescharacteristic
41C11×#388—21no—
42C11×#387—21no—
43C11×#386—21no—
44C11×#385—21no—
45C11×#385—21no—
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C22⋊C4—21no—
49C4×C11×C22⋊C4C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C2×C11×SD16—41no—
68C2×C11×SD16—41no—
69C2×C11×SD16C2×C414yescomplemented
70C22×C8×C11—41no—
71C22×C8×C11—41no—
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—
85C4×D4×C11—44no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4—41no—
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⋊C4D411yescharacteristic
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11—21no—
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C11×#106C2×C414yescomplemented
115C11×#103—22no—
116C11×#103—41no—
117C11×#103C2×C414yescomplemented
118C11×#102—22no—
119C11×#102—41no—
120C11×#102C2×C414yescomplemented
121C11×C22⋊C8—22no—
122C4×C8×C11—41no—
123C4×C8×C11—41no—
124C11×#95—21no—
125C11×#95—21no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95D411yescharacteristic
131C11×#95D411yescharacteristic
132#23126C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11—21no—
134C24×C11C2×D411yescharacteristic
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11C22×C412yes—
141C2×D4×C11—24no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11C22×C412yes—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
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—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11—81no—
168C22×C4×C11—81no—
169C22×C4×C11—81no—
170C22×C4×C11C22×C412yes—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11#4112yes—
177C22×C4×C11C2411yescharacteristic
178C11×SD16—44no—
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×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—44no—
190C2×C8×C11C22×C412yes—
191C2×C8×C11C22×C412yes—
192C11×C4⋊C4—24no—
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—21no—
201C11×C4⋊C4—42no—
202C11×C4⋊C4—42no—
203C11×C4⋊C4—42no—
204C11×C4⋊C4—42no—
205C11×C4⋊C4—81no—
206C11×C4⋊C4C22×C412yes—
207C11×C4⋊C4C22×C412yes—
208C11×C4⋊C4#4112yes—
209C11×C4⋊C4#4112yes—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—81no—
216C11×C22⋊C4SD1614yescomplemented
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—42no—
222C42×C11—42no—
223C42×C11—81no—
224C2×#465C2×C1111yescharacteristic
225#2361C2×C1111yescharacteristic
226#2360C2×C1111yescharacteristic, complemented
227#1934C2×C1111yescharacteristic, complemented
228#1933C2×C1111yescharacteristic, complemented
229#1920C2×C1111yescharacteristic, complemented
230#1919C2×C1111yescharacteristic, complemented
231#1880C2×C1111yescharacteristic, complemented
232#1877C2×C1111yescharacteristic, complemented
233#1874C2×C1111yescharacteristic
234#1872C2×C1111yescharacteristic, complemented
235C4×#103C2×C1111yescharacteristic, complemented
236C4×#102C2×C1111yescharacteristic, complemented
237C8×C22⋊C4C2×C1111yescharacteristic, complemented
238C2×#340C2×C1111yescharacteristic, complemented
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—22no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11C4×D412yes—
251C23×C11C2×SD1612yes—
252C23×C11#13512yes—
253C23×C11C22×D411yescharacteristic
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—41no—
257Q8×C11—41no—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—48no—
261D4×C11—41no—
262D4×C11—41no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
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—21no—
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—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—84no—
301C2×C4×C11—84no—
302C2×C4×C11—84no—
303C2×C4×C11C4×D412yes—
304C2×C4×C11C2×SD1612yes—
305C2×C4×C11C2×SD1612yes—
306C2×C4×C11C23×C411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C8×C11—22no—
313C8×C11—22no—
314C8×C11—41no—
315C8×C11—41no—
316C22×SD16C22×C1111yescharacteristic
317C23×C8C22×C1111yescharacteristic
318C2×C22⋊Q8C22×C1111yescharacteristic
319C2×#121C22×C1111yescharacteristic
320C2×C4×Q8C22×C1111yescharacteristic
321C2×C4×D4—21no—
322C2×C4×D4C22×C1111yescharacteristic
323C22×C4⋊C4C22×C1111yescharacteristic
324C22×C4⋊C4C22×C1111yescharacteristic
325#465C4×C1118yescomplemented
326C2×#106C22×C1111yescharacteristic
327C2×#103C22×C1111yescharacteristic
328C2×#103C22×C1111yescharacteristic
329C2×#103C22×C1111yescharacteristic
330C2×#102C22×C1111yescharacteristic
331C2×#102C22×C1111yescharacteristic
332C2×#102C22×C1111yescharacteristic
333C2×C22⋊C8C22×C1111yescharacteristic
334C2×C4×C8C22×C1111yescharacteristic
335C2×C4×C8C22×C1111yescharacteristic
336#391C22×C1111yescharacteristic
337#390C22×C1111yescharacteristic
338#389—21no—
339#389C22×C1111yescharacteristic
340#389C22×C1111yescharacteristic
341#388—21no—
342#387—21no—
343#386—21no—
344#385—21no—
345#385—21no—
346C4×C4⋊C4C22×C1111yescharacteristic
347C4×C4⋊C4C22×C1111yescharacteristic
348C4×C22⋊C4—21no—
349C4×C22⋊C4C22×C1111yescharacteristic
350#340C22×C1111yescharacteristic
351#340C22×C1111yescharacteristic
352#340C22×C1111yescharacteristic
353#340C22×C1111yescharacteristic
354#340C22×C1111yescharacteristic
355#340C22×C1111yescharacteristic
356#340C22×C1111yescharacteristic
357#340C22×C1111yescharacteristic
358#336C22×C1111yescharacteristic
359#336C22×C1111yescharacteristic
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11C4×SD1614yes—
374C22×C11C2×C4×D411yescharacteristic
375C22×C11#54611yescharacteristic
376C22×C11#54611yescharacteristic
377C22×C11C22×SD1611yescharacteristic
378C22×C11C2×#13511yescharacteristic
379C22×C11#57611yescharacteristic
380C22×C11#57811yescharacteristic
381C4×C11—22no—
382C4×C11—22no—
383C4×C11—22no—
384C4×C11—42no—
385C4×C11—42no—
386C4×C11—42no—
387C4×C11—42no—
388C4×C11—41no—
389C4×C11—42no—
390C4×C11—41no—
391C4×C11—81no—
392C4×C11—81no—
393C4×C11C4×#4111yescharacteristic
394C4×C11#51811yescharacteristic
395C4×C11#55311yescharacteristic
396C4×C11#55311yescharacteristic
397C22×Q8C23×C1111yescharacteristic
398C22×D4—21no—
399C22×D4C23×C1111yescharacteristic
400C23×C4—21no—
401C23×C4—21no—
402C23×C4—21no—
403C23×C4C23×C1111yescharacteristic
404C2×SD16—41no—
405C2×SD16—41no—
406C2×SD16C2×C4×C1114yescomplemented
407C22×C8—41no—
408C22×C8—41no—
409C22×C8C2×C4×C1114yescomplemented
410C22×C8C23×C1111yescharacteristic
411C22×C8C23×C1111yescharacteristic
412C22×C8C23×C1111yescharacteristic
413C22×C8C23×C1111yescharacteristic
414C22⋊Q8—22no—
415C22⋊Q8C2×C4×C1114yescomplemented
416#121—22no—
417#121C2×C4×C1114yes—
418C4×Q8—22no—
419C4×Q8—41no—
420C4×D4—22no—
421C4×D4—41no—
422C4×D4—44no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4—41no—
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⋊C4D4×C1111yescharacteristic
445C2×C22⋊C4D4×C1111yescharacteristic
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42C23×C1111yescharacteristic
450C2×C42C23×C1111yescharacteristic
451#106C2×C4×C1114yescomplemented
452#103—22no—
453#103—41no—
454#103C2×C4×C1114yescomplemented
455#102—22no—
456#102—41no—
457#102C2×C4×C1114yescomplemented
458C22⋊C8—22no—
459C4×C8—41no—
460C4×C8—41no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95D4×C1111yescharacteristic
468#95D4×C1111yescharacteristic
469C2×C11—24no—
470C2×C11—82no—
471C2×C11#236411yescharacteristic
472C2×C11C2×C4×SD1611yescharacteristic
473C2×C11#295111yescharacteristic
474C2×C11#329511yescharacteristic
475C2×C11#329711yescharacteristic
476C2×C11#329811yescharacteristic
477C2×C11#330011yescharacteristic
478C24—21no—
479C24C2×D4×C1111yescharacteristic
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8C22×C4×C1112yes—
486C2×D4—24no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4C22×C4×C1112yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4C22×C4×C1112yes—
516C22×C4C2×D4×C1111yescharacteristic
517C22×C4C2×D4×C1111yescharacteristic
518C22×C4C2×D4×C1111yescharacteristic
519C22×C4C2×D4×C1111yescharacteristic
520C22×C4C2×D4×C1111yescharacteristic
521C22×C4C11×#4112yes—
522C22×C4C24×C1111yescharacteristic
523SD16—44no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—44no—
535C2×C8C22×C4×C1112yes—
536C2×C8C22×C4×C1112yes—
537C4⋊C4—24no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—81no—
551C4⋊C4C22×C4×C1112yes—
552C4⋊C4C22×C4×C1112yes—
553C4⋊C4C11×#4112yes—
554C4⋊C4C11×#4112yes—
555C22⋊C4—24no—
556C22⋊C4—22no—
557C22⋊C4—24no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C22⋊C4C11×SD1614yescomplemented
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—42no—
567C42—42no—
568C42—81no—
569C11#2312611yescharacteristic, direct product factor, Sylow
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—22no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23C4×D4×C1112yes—
582C23C2×C11×SD1612yes—
583C23C11×#13512yes—
584C23C22×D4×C1111yescharacteristic
585Q8—22no—
586Q8—22no—
587Q8—41no—
588Q8—41no—
589D4—22no—
590D4—22no—
591D4—48no—
592D4—41no—
593D4—41no—
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—21no—
609C2×C4—22no—
610C2×C4—22no—
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×C4—84no—
633C2×C4—84no—
634C2×C4C4×D4×C1112yes—
635C2×C4C2×C11×SD1612yes—
636C2×C4C2×C11×SD1612yes—
637C2×C4C23×C4×C1111yescharacteristic
638C2×C4C2×C11×#4111yescharacteristic
639C2×C4C2×C11×#4111yescharacteristic
640C2×C4C2×C11×#4111yescharacteristic
641C2×C4C11×H(5,𝔽2)11yescharacteristic
642C2×C4C11×H(5,𝔽2)11yescharacteristic
643C8—22no—
644C8—22no—
645C8—41no—
646C8—41no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22C4×C11×SD1614yes—
661C22C2×C4×D4×C1111yescharacteristic
662C22C11×#54611yescharacteristic
663C22C11×#54611yescharacteristic
664C22C22×C11×SD1611yescharacteristic
665C22C2×C11×#13511yescharacteristic
666C22C11×#57611yescharacteristic
667C22C11×#57811yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—42no—
672C4—42no—
673C4—42no—
674C4—41no—
675C4—42no—
676C4—41no—
677C4—42no—
678C4—81no—
679C4—81no—
680C4C4×C11×#4111yescharacteristic
681C4C11×#51811yescharacteristic
682C4C11×#55311yescharacteristic
683C4C11×#55311yescharacteristic
684C2—24no—
685C2—82no—
686C2C11×#236411yescharacteristic
687C2C2×C4×C11×SD1611yescharacteristic
688C2C11×#295111yescharacteristic
689C2C11×#329511yescharacteristic
690C2C11×#329711yescharacteristic
691C2C11×#329811yescharacteristic
692C2C11×#330011yescharacteristic
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
3. C11×#2360C2semidirect
4. C11×#1934C2semidirect
5. C11×#1933C2semidirect
6. C11×#1920C2semidirect
7. C11×#1919C2semidirect
8. C11×#1880C2semidirect
9. C11×#1877C2semidirect
11. C11×#1872C2semidirect
12. C4×C11×#103C2semidirect
13. C4×C11×#102C2semidirect
14. C8×C11×C22⋊C4C2semidirect
15. C2×C11×#340C2semidirect
25. C11×#465C4semidirect
69. C2×C11×SD16C2×C4semidirect
72. C22×C8×C11C2×C4semidirect
78. C11×C22⋊Q8C2×C4semidirect
114. C11×#106C2×C4semidirect
117. C11×#103C2×C4semidirect
120. C11×#102C2×C4semidirect
132. #23126C11direct (N × H)
216. C11×C22⋊C4SD16semidirect
226. #2360C2×C11semidirect
227. #1934C2×C11semidirect
228. #1933C2×C11semidirect
229. #1920C2×C11semidirect
230. #1919C2×C11semidirect
231. #1880C2×C11semidirect
232. #1877C2×C11semidirect
234. #1872C2×C11semidirect
235. C4×#103C2×C11semidirect
236. C4×#102C2×C11semidirect
237. C8×C22⋊C4C2×C11semidirect
238. C2×#340C2×C11semidirect
325. #465C4×C11semidirect
406. C2×SD16C2×C4×C11semidirect
409. C22×C8C2×C4×C11semidirect
415. C22⋊Q8C2×C4×C11semidirect
451. #106C2×C4×C11semidirect
454. #103C2×C4×C11semidirect
457. #102C2×C4×C11semidirect
561. C22⋊C4C11×SD16semidirect
569. C11#23126direct (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
C11×#23612
C11×#23602
C11×#19342
C11×#19332
C11×#19202
C11×#19192
C11×#18802
C11×#18772
C11×#18742
C11×#18722
C4×C11×#1032
C4×C11×#1022
C8×C11×C22⋊C42
C2×C11×#3402
#2312611