Finite Group Databasebeta

← C11×#24161 #14601354

Subgroups — C11×#24161 #14601354

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#529C211yesmaximal, characteristic
2C2×C11×#479C211yesmaximal, characteristic, complemented
3C2×C11×#464C211yesmaximal, characteristic, complemented
4C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
5C11×#2036C211yesmaximal, characteristic, complemented
6C11×#2034C211yesmaximal, characteristic
7C11×#2001C211yesmaximal, characteristic, complemented
8C11×#2000C211yesmaximal, characteristic
9C11×#1989C211yesmaximal, characteristic, complemented
10C11×#1983C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1877C211yesmaximal, characteristic, complemented
13C11×#1865C211yesmaximal, characteristic, complemented
14C11×#1862C211yesmaximal, characteristic, complemented
15C11×#1797C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C11×#529—24no—
19C11×#529—24no—
20C2×C11×#126—21no—
21C2×C11×#125C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11—21no—
30C2×C4×D4×C11C2211yescharacteristic
31C2×C11×#117—21no—
32C22×C42×C11C2211yescharacteristic
33C11×#479—24no—
34C11×#464—24no—
35C2×C11×#107C2211yescharacteristic
36C2×C11×#106C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#103C2211yescharacteristic
42C2×C11×#103C2211yescharacteristic
43C2×C11×#103C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C11×#391C2211yescharacteristic
50C11×#389C2211yescharacteristic
51C11×#387—21no—
52C11×#385—21no—
53C11×#380C2211yescharacteristic
54C4×C11×C4⋊C4—21no—
55C4×C11×C4⋊C4C2211yescharacteristic
56C4×C11×C22⋊C4—21no—
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11D411yescharacteristic
69C23×C4×C11D411yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C2×C11×Q16—22no—
72C2×C11×Q16—22no—
73C2×C11×Q16—41no—
74C2×C11×SD16—22no—
75C2×C11×SD16—22no—
76C2×C11×SD16—41no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×#126—28no—
82C11×#125—22no—
83C11×#125D414yes—
84C11×#124—22no—
85C11×#124D414yes—
86C11×#123—28no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8—22no—
91C11×#121—22no—
92C11×#121—22no—
93C4×Q8×C11—22no—
94C4×Q8×C11—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C4×D4×C11—28no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C11×#117—28no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
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⋊C4—21no—
120C2×C42×C11—21no—
121C2×C42×C11—22no—
122C2×C42×C11—22no—
123C2×C42×C11—21no—
124C2×C42×C11—21no—
125C2×C42×C11D411yescharacteristic
126C2×C42×C11D411yescharacteristic
127C2×C42×C11C2311yescharacteristic
128C2×C42×C11C2311yescharacteristic
129C11×#107—22no—
130C11×#106—22no—
131C11×C4⋊C8—22no—
132C11×C4⋊C8—22no—
133C11×#103—22no—
134C11×#103—22no—
135C11×#103—22no—
136C11×#103—22no—
137C11×#103—41no—
138C11×#102—22no—
139C11×#102—22no—
140C11×#102—41no—
141C11×C22⋊C8—41no—
142C11×C22⋊C8—41no—
143C11×#95—21no—
144C11×#95—21no—
145C11×#95—21no—
146C11×#95—21no—
147C11×#95—21no—
148#24161C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—21no—
150C24×C11C2×D411yescharacteristic
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11C2×D412yes—
162C2×Q8×C11#4112yes—
163C2×D4×C11—24no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11C2×D412yes—
172C22×C4×C11—24no—
173C22×C4×C11—22no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—41no—
191C22×C4×C11—41no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C11×Q16—44no—
201C11×SD16—44no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4—24no—
216C11×C4⋊C4—24no—
217C11×C4⋊C4—24no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4—42no—
228C11×C4⋊C4C2×D412yes—
229C11×C4⋊C4C2×D412yes—
230C11×C4⋊C4#4112yes—
231C11×C22⋊C4—24no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—42no—
238C42×C11—24no—
239C42×C11—22no—
240C42×C11—22no—
241C42×C11—21no—
242C42×C11—21no—
243C42×C11—42no—
244C42×C11—42no—
245C42×C11C2×D412yes—
246C42×C11C2×D412yes—
247C2×#529C2×C1111yescharacteristic
248C2×#479C2×C1111yescharacteristic, complemented
249C2×#464C2×C1111yescharacteristic, complemented
250C4×C22⋊Q8C2×C1111yescharacteristic, complemented
251#2036C2×C1111yescharacteristic, complemented
252#2034C2×C1111yescharacteristic
253#2001C2×C1111yescharacteristic, complemented
254#2000C2×C1111yescharacteristic
255#1989C2×C1111yescharacteristic, complemented
256#1983C2×C1111yescharacteristic, complemented
257#1878C2×C1111yescharacteristic, complemented
258#1877C2×C1111yescharacteristic, complemented
259#1865C2×C1111yescharacteristic, complemented
260#1862C2×C1111yescharacteristic, complemented
261#1797C2×C1111yescharacteristic, complemented
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—22no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11#13712yes—
276C23×C11C22×D411yescharacteristic
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—22no—
280Q8×C11—22no—
281Q8×C11—41no—
282Q8×C11—41no—
283Q8×C11—41no—
284Q8×C11—41no—
285D4×C11—22no—
286D4×C11—22no—
287D4×C11—48no—
288D4×C11—41no—
289D4×C11—41no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—44no—
308C2×C4×C11—44no—
309C2×C4×C11—48no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11#12012yes—
331C2×C4×C11#12012yes—
332C2×C4×C11#13512yes—
333C2×C4×C11C22×D411yescharacteristic
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C2×#4111yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C2×C4×C112−1+411yescharacteristic
339C8×C11—41no—
340C8×C11—41no—
341C8×C11—41no—
342C8×C11—41no—
343C22×Q16C22×C1111yescharacteristic
344C22×SD16C22×C1111yescharacteristic
345#529—24no—
346#529—24no—
347C2×#126—21no—
348C2×#125C22×C1111yescharacteristic
349C2×#124C22×C1111yescharacteristic
350C2×#123—21no—
351C2×C22⋊Q8C22×C1111yescharacteristic
352C2×C22⋊Q8C22×C1111yescharacteristic
353C2×#121C22×C1111yescharacteristic
354C2×C4×Q8C22×C1111yescharacteristic
355C2×C4×Q8C22×C1111yescharacteristic
356C2×C4×D4—21no—
357C2×C4×D4C22×C1111yescharacteristic
358C2×#117—21no—
359C22×C42C22×C1111yescharacteristic
360#479—24no—
361#464—24no—
362C2×#107C22×C1111yescharacteristic
363C2×#106C22×C1111yescharacteristic
364C2×C4⋊C8C22×C1111yescharacteristic
365C2×C4⋊C8C22×C1111yescharacteristic
366C2×#103C22×C1111yescharacteristic
367C2×#103C22×C1111yescharacteristic
368C2×#103C22×C1111yescharacteristic
369C2×#103C22×C1111yescharacteristic
370C2×#103C22×C1111yescharacteristic
371C2×#102C22×C1111yescharacteristic
372C2×#102C22×C1111yescharacteristic
373C2×#102C22×C1111yescharacteristic
374C2×C22⋊C8C22×C1111yescharacteristic
375C2×C22⋊C8C22×C1111yescharacteristic
376#391C22×C1111yescharacteristic
377#389C22×C1111yescharacteristic
378#387—21no—
379#385—21no—
380#380C22×C1111yescharacteristic
381C4×C4⋊C4—21no—
382C4×C4⋊C4C22×C1111yescharacteristic
383C4×C22⋊C4—21no—
384#340C22×C1111yescharacteristic
385#340C22×C1111yescharacteristic
386#340C22×C1111yescharacteristic
387#340C22×C1111yescharacteristic
388#336C22×C1111yescharacteristic
389#336C22×C1111yescharacteristic
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11C2×#12011yescharacteristic
405C22×C11#52511yescharacteristic
406C22×C11#53711yescharacteristic
407C22×C11C2×#13511yescharacteristic
408C22×C11C2×#13711yescharacteristic
409C22×C11#57511yescharacteristic
410C22×C11#57511yescharacteristic
411C4×C11—22no—
412C4×C11—22no—
413C4×C11—22no—
414C4×C11—42no—
415C4×C11—41no—
416C4×C11—42no—
417C4×C11—42no—
418C4×C11—42no—
419C4×C11—41no—
420C4×C11—42no—
421C4×C11—81no—
422C4×C11—81no—
423C4×C11#54611yescharacteristic
424C4×C11#54711yescharacteristic
425C4×C11#54811yescharacteristic
426C4×C11#55011yescharacteristic
427C22×Q8C23×C1111yescharacteristic
428C22×Q8C23×C1111yescharacteristic
429C22×D4—21no—
430C22×D4C23×C1111yescharacteristic
431C23×C4—21no—
432C23×C4D4×C1111yescharacteristic
433C23×C4D4×C1111yescharacteristic
434C23×C4C23×C1111yescharacteristic
435C2×Q16—22no—
436C2×Q16—22no—
437C2×Q16—41no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×SD16—41no—
441C22×C8C23×C1111yescharacteristic
442C22×C8C23×C1111yescharacteristic
443C22×C8C23×C1111yescharacteristic
444C22×C8C23×C1111yescharacteristic
445#126—28no—
446#125—22no—
447#125D4×C1114yes—
448#124—22no—
449#124D4×C1114yes—
450#123—28no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455#121—22no—
456#121—22no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×D4—28no—
462C4×D4—22no—
463C4×D4—22no—
464#117—28no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4C23×C1111yescharacteristic
473C2×C4⋊C4C23×C1111yescharacteristic
474C2×C4⋊C4C23×C1111yescharacteristic
475C2×C4⋊C4C23×C1111yescharacteristic
476C2×C4⋊C4C23×C1111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C42—21no—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42D4×C1111yescharacteristic
490C2×C42D4×C1111yescharacteristic
491C2×C42C23×C1111yescharacteristic
492C2×C42C23×C1111yescharacteristic
493#107—22no—
494#106—22no—
495C4⋊C8—22no—
496C4⋊C8—22no—
497#103—22no—
498#103—22no—
499#103—22no—
500#103—22no—
501#103—41no—
502#102—22no—
503#102—22no—
504#102—41no—
505C22⋊C8—41no—
506C22⋊C8—41no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512C2×C11—42no—
513C2×C11—82no—
514C2×C11#240711yescharacteristic
515C2×C11#300211yescharacteristic
516C2×C11#300711yescharacteristic
517C2×C11#310211yescharacteristic
518C2×C11#311711yescharacteristic
519C2×C11#324811yescharacteristic
520C2×C11#325611yescharacteristic
521C24—21no—
522C24C2×D4×C1111yescharacteristic
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C2×D4×C1112yes—
534C2×Q8C11×#4112yes—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4C2×D4×C1112yes—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4C2×D4×C1111yescharacteristic
567C22×C4C2×D4×C1111yescharacteristic
568C22×C4C2×D4×C1111yescharacteristic
569C22×C4C2×D4×C1111yescharacteristic
570C22×C4C2×D4×C1111yescharacteristic
571C22×C4C24×C1111yescharacteristic
572Q16—44no—
573SD16—44no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4C2×D4×C1112yes—
601C4⋊C4C2×D4×C1112yes—
602C4⋊C4C11×#4112yes—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—42no—
610C42—24no—
611C42—22no—
612C42—22no—
613C42—21no—
614C42—21no—
615C42—42no—
616C42—42no—
617C42C2×D4×C1112yes—
618C42C2×D4×C1112yes—
619C11#2416111yescharacteristic, direct product factor, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23C11×#13712yes—
634C23C22×D4×C1111yescharacteristic
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643D4—22no—
644D4—22no—
645D4—48no—
646D4—41no—
647D4—41no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—48no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4C11×#12012yes—
689C2×C4C11×#12012yes—
690C2×C4C11×#13512yes—
691C2×C4C22×D4×C1111yescharacteristic
692C2×C4C22×D4×C1111yescharacteristic
693C2×C4C2×C11×#4111yescharacteristic
694C2×C4C2×C11×#4111yescharacteristic
695C2×C4C11×H(5,𝔽2)11yescharacteristic
696C2×C4C11×2−1+411yescharacteristic
697C8—41no—
698C8—41no—
699C8—41no—
700C8—41no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22C2×C11×#12011yescharacteristic
716C22C11×#52511yescharacteristic
717C22C11×#53711yescharacteristic
718C22C2×C11×#13511yescharacteristic
719C22C2×C11×#13711yescharacteristic
720C22C11×#57511yescharacteristic
721C22C11×#57511yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—41no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—41no—
730C4—42no—
731C4—42no—
732C4—81no—
733C4—81no—
734C4C11×#54611yescharacteristic
735C4C11×#54711yescharacteristic
736C4C11×#54811yescharacteristic
737C4C11×#55011yescharacteristic
738C2—42no—
739C2—82no—
740C2C11×#240711yescharacteristic
741C2C11×#300211yescharacteristic
742C2C11×#300711yescharacteristic
743C2C11×#310211yescharacteristic
744C2C11×#311711yescharacteristic
745C2C11×#324811yescharacteristic
746C2C11×#325611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#479C2semidirect
3. C2×C11×#464C2semidirect
4. C4×C11×C22⋊Q8C2semidirect
5. C11×#2036C2semidirect
7. C11×#2001C2semidirect
9. C11×#1989C2semidirect
10. C11×#1983C2semidirect
11. C11×#1878C2semidirect
12. C11×#1877C2semidirect
13. C11×#1865C2semidirect
14. C11×#1862C2semidirect
15. C11×#1797C2semidirect
148. #24161C11direct (N × H)
248. C2×#479C2×C11semidirect
249. C2×#464C2×C11semidirect
250. C4×C22⋊Q8C2×C11semidirect
251. #2036C2×C11semidirect
253. #2001C2×C11semidirect
255. #1989C2×C11semidirect
256. #1983C2×C11semidirect
257. #1878C2×C11semidirect
258. #1877C2×C11semidirect
259. #1865C2×C11semidirect
260. #1862C2×C11semidirect
261. #1797C2×C11semidirect
619. C11#24161direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5292
C2×C11×#4792
C2×C11×#4642
C4×C11×C22⋊Q82
C11×#20362
C11×#20342
C11×#20012
C11×#20002
C11×#19892
C11×#19832
C11×#18782
C11×#18772
C11×#18652
C11×#18622
C11×#17972
#2416111