Finite Group Databasebeta

← C11×#24308 #14601501

Subgroups — C11×#24308 #14601501

Order 2816.

1068 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic, complemented
2C2×C11×#478C211yesmaximal, characteristic, complemented
3C2×C11×#474C211yesmaximal, characteristic, complemented
4C11×#2324C211yesmaximal, characteristic
5C11×#2059C211yesmaximal, characteristic, complemented
6C11×#2057C211yesmaximal, characteristic, complemented
7C11×#2025C211yesmaximal, characteristic, complemented
8C11×#2023C211yesmaximal, characteristic, complemented
9C11×#1989C211yesmaximal, characteristic, complemented
10C11×#1987C211yesmaximal, characteristic, complemented
11C11×#1875C211yesmaximal, characteristic
12C11×#1874C211yesmaximal, characteristic
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1852C211yesmaximal, characteristic, complemented
15C11×#1798C211yesmaximal, characteristic, complemented
16C11×#544—24no—
17C11×#544—24no—
18C2×C11×C4⋊Q8—21no—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#125—21no—
22C2×C11×#125C2211yescharacteristic
23C2×C11×#125C2211yescharacteristic
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8—21no—
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C11×#478—24no—
32C11×#474—24no—
33C2×C11×#107C2211yescharacteristic
34C2×C11×#107C2211yescharacteristic
35C2×C11×#107C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2211yescharacteristic
45C11×#390—21no—
46C11×#390C2211yescharacteristic
47C11×#389C2211yescharacteristic
48C11×#388—21no—
49C11×#386—21no—
50C11×#385—21no—
51C11×#380C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C23×C4×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×C4⋊Q8—28no—
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8—22no—
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8D414yescomplemented
79C11×#125—28no—
80C11×#125—22no—
81C11×#125—22no—
82C11×#125—22no—
83C11×#125D414yescomplemented
84C11×C22⋊Q8—28no—
85C11×C22⋊Q8—28no—
86C11×#121—22no—
87C11×#121Q814yescomplemented
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C11×#117—22no—
91C11×#117—22no—
92C11×#117—22no—
93C11×#117—22no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4D411yescharacteristic
105C2×C11×C4⋊C4D411yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C11×C22⋊C4D411yescharacteristic
121C2×C42×C11—21no—
122C2×C42×C11—21no—
123C2×C42×C11C2311yescharacteristic
124C2×C42×C11C2311yescharacteristic
125C11×#107—22no—
126C11×#107—22no—
127C11×#107—22no—
128C11×#106—22no—
129C11×C4⋊C8—22no—
130C11×C4⋊C8—22no—
131C11×#102—22no—
132C11×#102—22no—
133C11×#102—22no—
134C11×#102—22no—
135C11×C22⋊C8—22no—
136C11×C22⋊C8—22no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140#24308C1111yesmaximal, characteristic, direct product factor, Sylow
141C24×C11—21no—
142C24×C11C2×D411yescharacteristic
143C2×Q8×C11—24no—
144C2×Q8×C11—24no—
145C2×Q8×C11—81no—
146C2×Q8×C11—81no—
147C2×Q8×C11—81no—
148C2×Q8×C11—81no—
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—81no—
156C2×D4×C11—81no—
157C2×D4×C11C2×Q812yes—
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—21no—
167C22×C4×C11—24no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—42no—
171C22×C4×C11—81no—
172C22×C4×C11—81no—
173C22×C4×C11—81no—
174C22×C4×C11—81no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×Q812yes—
181C22×C4×C11#4112yes—
182C22×C4×C11C2411yescharacteristic
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—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—24no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—81no—
214C11×C4⋊C4C2×D412yes—
215C11×C4⋊C4C2×D412yes—
216C11×C4⋊C4C2×D412yes—
217C11×C4⋊C4C2×D412yes—
218C11×C4⋊C4C2×Q812yes—
219C11×C22⋊C4—24no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—24no—
223C11×C22⋊C4—42no—
224C11×C22⋊C4—81no—
225C11×C22⋊C4—81no—
226C11×C22⋊C4—81no—
227C42×C11—24no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—81no—
231C42×C11C2×D412yes—
232C42×C11C2×D412yes—
233C2×#544C2×C1111yescharacteristic, complemented
234C2×#478C2×C1111yescharacteristic, complemented
235C2×#474C2×C1111yescharacteristic, complemented
236#2324C2×C1111yescharacteristic
237#2059C2×C1111yescharacteristic, complemented
238#2057C2×C1111yescharacteristic, complemented
239#2025C2×C1111yescharacteristic, complemented
240#2023C2×C1111yescharacteristic, complemented
241#1989C2×C1111yescharacteristic, complemented
242#1987C2×C1111yescharacteristic, complemented
243#1875C2×C1111yescharacteristic
244#1874C2×C1111yescharacteristic
245#1854C2×C1111yescharacteristic, complemented
246#1852C2×C1111yescharacteristic, complemented
247#1798C2×C1111yescharacteristic, complemented
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—22no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11C22⋊Q812yes—
262C23×C11C22×D411yescharacteristic
263Q8×C11—84no—
264Q8×C11—84no—
265D4×C11—22no—
266D4×C11—22no—
267D4×C11—41no—
268D4×C11—41no—
269D4×C11—84no—
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—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
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—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—84no—
308C2×C4×C11—84no—
309C2×C4×C11#12012yes—
310C2×C4×C11#12012yes—
311C2×C4×C11C22⋊Q812yes—
312C2×C4×C11C22×D411yescharacteristic
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C22×Q811yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C112−1+411yescharacteristic
317C2×C4×C112−1+411yescharacteristic
318C8×C11—41no—
319C8×C11—41no—
320C8×C11—41no—
321C8×C11—41no—
322#544—24no—
323#544—24no—
324C2×C4⋊Q8—21no—
325C2×C4⋊Q8C22×C1111yescharacteristic
326C2×C4⋊Q8C22×C1111yescharacteristic
327C2×#125—21no—
328C2×#125C22×C1111yescharacteristic
329C2×#125C22×C1111yescharacteristic
330C2×C22⋊Q8—21no—
331C2×C22⋊Q8—21no—
332C2×#121C22×C1111yescharacteristic
333C2×C4×D4C22×C1111yescharacteristic
334C2×#117C22×C1111yescharacteristic
335C2×#117C22×C1111yescharacteristic
336C22×C4⋊C4C22×C1111yescharacteristic
337#478—24no—
338#474—24no—
339C2×#107C22×C1111yescharacteristic
340C2×#107C22×C1111yescharacteristic
341C2×#107C22×C1111yescharacteristic
342C2×#106C22×C1111yescharacteristic
343C2×C4⋊C8C22×C1111yescharacteristic
344C2×C4⋊C8C22×C1111yescharacteristic
345C2×#102C22×C1111yescharacteristic
346C2×#102C22×C1111yescharacteristic
347C2×#102C22×C1111yescharacteristic
348C2×#102C22×C1111yescharacteristic
349C2×C22⋊C8C22×C1111yescharacteristic
350C2×C22⋊C8C22×C1111yescharacteristic
351#390—21no—
352#390C22×C1111yescharacteristic
353#389C22×C1111yescharacteristic
354#388—21no—
355#386—21no—
356#385—21no—
357#380C22×C1111yescharacteristic
358C4×C4⋊C4C22×C1111yescharacteristic
359#340C22×C1111yescharacteristic
360#340C22×C1111yescharacteristic
361#340C22×C1111yescharacteristic
362#340C22×C1111yescharacteristic
363#340C22×C1111yescharacteristic
364#340C22×C1111yescharacteristic
365#340C22×C1111yescharacteristic
366#340C22×C1111yescharacteristic
367#336C22×C1111yescharacteristic
368#336C22×C1111yescharacteristic
369C22×C11—22no—
370C22×C11—22no—
371C22×C11—22no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11C2×#12011yescharacteristic
384C22×C11C2×C22⋊Q811yescharacteristic
385C22×C11#53611yescharacteristic
386C22×C11#57611yescharacteristic
387C22×C11#57611yescharacteristic
388C22×C11#57711yescharacteristic
389C22×C11#57811yescharacteristic
390C4×C11—22no—
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—42no—
394C4×C11—41no—
395C4×C11—42no—
396C4×C11—42no—
397C4×C11—42no—
398C4×C11—41no—
399C4×C11—42no—
400C4×C11—81no—
401C4×C11—81no—
402C4×C11#54811yescharacteristic
403C4×C11#54811yescharacteristic
404C4×C11D4×Q811yescharacteristic
405C4×C11D4×Q811yescharacteristic
406C22×Q8—21no—
407C22×Q8—21no—
408C22×D4—21no—
409C22×D4C23×C1111yescharacteristic
410C23×C4—21no—
411C23×C4—21no—
412C23×C4C23×C1111yescharacteristic
413C22×C8C23×C1111yescharacteristic
414C22×C8C23×C1111yescharacteristic
415C22×C8C23×C1111yescharacteristic
416C22×C8C23×C1111yescharacteristic
417C4⋊Q8—28no—
418C4⋊Q8—22no—
419C4⋊Q8—22no—
420C4⋊Q8—22no—
421C4⋊Q8D4×C1114yescomplemented
422#125—28no—
423#125—22no—
424#125—22no—
425#125—22no—
426#125D4×C1114yescomplemented
427C22⋊Q8—28no—
428C22⋊Q8—28no—
429#121—22no—
430#121Q8×C1114yescomplemented
431C4×D4—22no—
432C4×D4—22no—
433#117—22no—
434#117—22no—
435#117—22no—
436#117—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4D4×C1111yescharacteristic
448C2×C4⋊C4D4×C1111yescharacteristic
449C2×C4⋊C4C23×C1111yescharacteristic
450C2×C4⋊C4C23×C1111yescharacteristic
451C2×C4⋊C4C23×C1111yescharacteristic
452C2×C4⋊C4C23×C1111yescharacteristic
453C2×C4⋊C4C23×C1111yescharacteristic
454C2×C4⋊C4C23×C1111yescharacteristic
455C2×C4⋊C4C23×C1111yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4D4×C1111yescharacteristic
463C2×C22⋊C4D4×C1111yescharacteristic
464C2×C42—21no—
465C2×C42—21no—
466C2×C42C23×C1111yescharacteristic
467C2×C42C23×C1111yescharacteristic
468#107—22no—
469#107—22no—
470#107—22no—
471#106—22no—
472C4⋊C8—22no—
473C4⋊C8—22no—
474#102—22no—
475#102—22no—
476#102—22no—
477#102—22no—
478C22⋊C8—22no—
479C22⋊C8—22no—
480#95—21no—
481#95—21no—
482#95—21no—
483C2×C11—42no—
484C2×C11—82no—
485C2×C11#240911yescharacteristic
486C2×C11#300811yescharacteristic
487C2×C11#301311yescharacteristic
488C2×C11#308111yescharacteristic
489C2×C11#308311yescharacteristic
490C2×C11#324111yescharacteristic
491C2×C11#324311yescharacteristic
492C24—21no—
493C24C2×D4×C1111yescharacteristic
494C2×Q8—24no—
495C2×Q8—24no—
496C2×Q8—81no—
497C2×Q8—81no—
498C2×Q8—81no—
499C2×Q8—81no—
500C2×D4—24no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4C2×Q8×C1112yes—
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×C4—21no—
518C22×C4—24no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4C2×D4×C1111yescharacteristic
527C22×C4C2×D4×C1111yescharacteristic
528C22×C4C2×D4×C1111yescharacteristic
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×Q8×C1112yes—
532C22×C4C11×#4112yes—
533C22×C4C24×C1111yescharacteristic
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—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—81no—
565C4⋊C4C2×D4×C1112yes—
566C4⋊C4C2×D4×C1112yes—
567C4⋊C4C2×D4×C1112yes—
568C4⋊C4C2×D4×C1112yes—
569C4⋊C4C2×Q8×C1112yes—
570C22⋊C4—24no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—24no—
574C22⋊C4—42no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C42—24no—
579C42—21no—
580C42—21no—
581C42—81no—
582C42C2×D4×C1112yes—
583C42C2×D4×C1112yes—
584C11#2430811yescharacteristic, direct product factor, Sylow
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—22no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C11×C22⋊Q812yes—
599C23C22×D4×C1111yescharacteristic
600Q8—84no—
601Q8—84no—
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—84no—
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—22no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
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—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—84no—
645C2×C4—84no—
646C2×C4C11×#12012yes—
647C2×C4C11×#12012yes—
648C2×C4C11×C22⋊Q812yes—
649C2×C4C22×D4×C1111yescharacteristic
650C2×C4C22×D4×C1111yescharacteristic
651C2×C4C22×Q8×C1111yescharacteristic
652C2×C4C2×C11×#4111yescharacteristic
653C2×C4C11×2−1+411yescharacteristic
654C2×C4C11×2−1+411yescharacteristic
655C8—41no—
656C8—41no—
657C8—41no—
658C8—41no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22C2×C11×#12011yescharacteristic
674C22C2×C11×C22⋊Q811yescharacteristic
675C22C11×#53611yescharacteristic
676C22C11×#57611yescharacteristic
677C22C11×#57611yescharacteristic
678C22C11×#57711yescharacteristic
679C22C11×#57811yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—41no—
684C4—42no—
685C4—42no—
686C4—42no—
687C4—41no—
688C4—42no—
689C4—42no—
690C4—81no—
691C4—81no—
692C4C11×#54811yescharacteristic
693C4C11×#54811yescharacteristic
694C4D4×Q8×C1111yescharacteristic
695C4D4×Q8×C1111yescharacteristic
696C2—42no—
697C2—82no—
698C2C11×#240911yescharacteristic
699C2C11×#300811yescharacteristic
700C2C11×#301311yescharacteristic
701C2C11×#308111yescharacteristic
702C2C11×#308311yescharacteristic
703C2C11×#324111yescharacteristic
704C2C11×#324311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#544C2semidirect
2. C2×C11×#478C2semidirect
3. C2×C11×#474C2semidirect
5. C11×#2059C2semidirect
6. C11×#2057C2semidirect
7. C11×#2025C2semidirect
8. C11×#2023C2semidirect
9. C11×#1989C2semidirect
10. C11×#1987C2semidirect
13. C11×#1854C2semidirect
14. C11×#1852C2semidirect
15. C11×#1798C2semidirect
78. C11×C4⋊Q8D4semidirect
83. C11×#125D4semidirect
87. C11×#121Q8semidirect
140. #24308C11direct (N × H)
233. C2×#544C2×C11semidirect
234. C2×#478C2×C11semidirect
235. C2×#474C2×C11semidirect
237. #2059C2×C11semidirect
238. #2057C2×C11semidirect
239. #2025C2×C11semidirect
240. #2023C2×C11semidirect
241. #1989C2×C11semidirect
242. #1987C2×C11semidirect
245. #1854C2×C11semidirect
246. #1852C2×C11semidirect
247. #1798C2×C11semidirect
421. C4⋊Q8D4×C11semidirect
426. #125D4×C11semidirect
430. #121Q8×C11semidirect
584. C11#24308direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5442
C2×C11×#4782
C2×C11×#4742
C11×#23242
C11×#20592
C11×#20572
C11×#20252
C11×#20232
C11×#19892
C11×#19872
C11×#18752
C11×#18742
C11×#18542
C11×#18522
C11×#17982
#2430811