Finite Group Databasebeta

← C11×#24194 #14601387

Subgroups — C11×#24194 #14601387

Order 2816.

1138 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#559C211yesmaximal, characteristic
2C2×C11×#464C211yesmaximal, characteristic, complemented
3C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
4C11×#2581C211yesmaximal, characteristic, complemented
5C11×#2042C211yesmaximal, characteristic, complemented
6C11×#2041C211yesmaximal, characteristic
7C11×#2015C211yesmaximal, characteristic, complemented
8C11×#2014C211yesmaximal, characteristic
9C11×#1984C211yesmaximal, characteristic, complemented
10C11×#1958C211yesmaximal, characteristic, complemented
11C11×#1878C211yesmaximal, characteristic, complemented
12C11×#1877C211yesmaximal, characteristic, complemented
13C11×#1865C211yesmaximal, characteristic, complemented
14C11×#1864C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C11×#559—24no—
20C11×#559—24no—
21C2×C11×#127C2211yescharacteristic
22C2×C11×#124—21no—
23C2×C11×#124C2211yescharacteristic
24C2×C11×#124C2211yescharacteristic
25C2×C11×#123—21no—
26C2×C11×#123—21no—
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11—21no—
31C2×C4×D4×C11C2211yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C11×#464—24no—
34C4×C11×SD16—24no—
35C2×C11×#106C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C11×#103C2211yescharacteristic
40C2×C11×#103C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C2×C11×#102C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C4×C8×C11C2211yescharacteristic
48C11×#400—21no—
49C11×#395—21no—
50C11×#391C2211yescharacteristic
51C11×#391C2211yescharacteristic
52C11×#389C2211yescharacteristic
53C11×#389C2211yescharacteristic
54C11×#387—21no—
55C11×#387—21no—
56C11×#382C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#340C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×Q8×C11D411yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11—21no—
67C22×D4×C11—21no—
68C22×D4×C11C2311yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C2×C11×Q16—22no—
73C2×C11×Q16—22no—
74C2×C11×Q16—41no—
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—22no—
78C2×C11×SD16—22no—
79C2×C11×SD16—22no—
80C2×C11×SD16—41no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C11×#127—22no—
86C11×#127—22no—
87C11×#124—28no—
88C11×#124—22no—
89C11×#124—22no—
90C11×#124—22no—
91C11×#124D414yes—
92C11×#123—28no—
93C11×#123—28no—
94C4×Q8×C11—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C4×Q8×C11—22no—
98C4×Q8×C11—22no—
99C4×Q8×C11—22no—
100C4×D4×C11—28no—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C4×D4×C11—22no—
104C4×D4×C11D414yes—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C42×C11—21no—
123C2×C42×C11—21no—
124C2×C42×C11C2311yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C11×#106—22no—
128C11×C4⋊C8—22no—
129C11×#103—22no—
130C11×#103—22no—
131C11×#103—22no—
132C11×#103—41no—
133C11×#102—22no—
134C11×#102—22no—
135C11×#102—22no—
136C11×#102—41no—
137C11×#102—41no—
138C11×#102—41no—
139C4×C8×C11—22no—
140C11×#95—21no—
141C11×#95—21no—
142C11×#95—21no—
143C11×#95—21no—
144C11×#95—21no—
145C11×#95—21no—
146C11×#95—21no—
147C11×#95—21no—
148#24194C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—21no—
150C24×C11—21no—
151C2×Q8×C11—22no—
152C2×Q8×C11—22no—
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×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—41no—
164C2×Q8×C11C2×D412yes—
165C2×Q8×C11#4112yes—
166C2×D4×C11—24no—
167C2×D4×C11—24no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—42no—
179C2×D4×C11—42no—
180C2×D4×C11—81no—
181C2×D4×C11—81no—
182C2×D4×C11C2×D412yes—
183C2×D4×C11C2×D412yes—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—24no—
188C22×C4×C11—24no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—81no—
193C22×C4×C11—81no—
194C22×C4×C11—81no—
195C22×C4×C11—81no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2411yescharacteristic
203C11×Q16—44no—
204C11×SD16—28no—
205C11×SD16—44no—
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—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11#4112yes—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—22no—
221C11×C4⋊C4—22no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—42no—
230C11×C4⋊C4—42no—
231C11×C4⋊C4—42no—
232C11×C4⋊C4C2×D412yes—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C42×C11—24no—
240C42×C11—21no—
241C42×C11—21no—
242C42×C11—21no—
243C42×C11—21no—
244C42×C11—42no—
245C42×C11C2×D412yes—
246C42×C11C2×D412yes—
247C2×#559C2×C1111yescharacteristic
248C2×#464C2×C1111yescharacteristic, complemented
249C2×C4×SD16C2×C1111yescharacteristic, complemented
250#2581C2×C1111yescharacteristic, complemented
251#2042C2×C1111yescharacteristic, complemented
252#2041C2×C1111yescharacteristic
253#2015C2×C1111yescharacteristic, complemented
254#2014C2×C1111yescharacteristic
255#1984C2×C1111yescharacteristic, complemented
256#1958C2×C1111yescharacteristic, complemented
257#1878C2×C1111yescharacteristic, complemented
258#1877C2×C1111yescharacteristic, complemented
259#1865C2×C1111yescharacteristic, complemented
260#1864C2×C1111yescharacteristic, complemented
261#1804C2×C1111yescharacteristic, complemented
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11C22×D411yescharacteristic
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—22no—
280Q8×C11—22no—
281Q8×C11—44no—
282Q8×C11—41no—
283Q8×C11—41no—
284Q8×C11—41no—
285Q8×C11—41no—
286D4×C11—22no—
287D4×C11—22no—
288D4×C11—22no—
289D4×C11—22no—
290D4×C11—48no—
291D4×C11—41no—
292D4×C11—41no—
293D4×C11—41no—
294D4×C11—41no—
295D4×C11—84no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—22no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—22no—
306C2×C4×C11—21no—
307C2×C4×C11—22no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
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—84no—
330C2×C4×C11—84no—
331C2×C4×C11#12012yes—
332C2×C4×C11#12012yes—
333C2×C4×C11#13512yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C2×C4×C112−1+411yescharacteristic
340C8×C11—22no—
341C8×C11—41no—
342C8×C11—41no—
343C8×C11—41no—
344C22×Q16C22×C1111yescharacteristic
345C22×SD16C22×C1111yescharacteristic
346C22×SD16C22×C1111yescharacteristic
347#559—24no—
348#559—24no—
349C2×#127C22×C1111yescharacteristic
350C2×#124—21no—
351C2×#124C22×C1111yescharacteristic
352C2×#124C22×C1111yescharacteristic
353C2×#123—21no—
354C2×#123—21no—
355C2×C4×Q8C22×C1111yescharacteristic
356C2×C4×Q8C22×C1111yescharacteristic
357C2×C4×Q8C22×C1111yescharacteristic
358C2×C4×D4—21no—
359C2×C4×D4C22×C1111yescharacteristic
360C2×C4×D4C22×C1111yescharacteristic
361#464—24no—
362C4×SD16—24no—
363C2×#106C22×C1111yescharacteristic
364C2×C4⋊C8C22×C1111yescharacteristic
365C2×#103C22×C1111yescharacteristic
366C2×#103C22×C1111yescharacteristic
367C2×#103C22×C1111yescharacteristic
368C2×#103C22×C1111yescharacteristic
369C2×#102C22×C1111yescharacteristic
370C2×#102C22×C1111yescharacteristic
371C2×#102C22×C1111yescharacteristic
372C2×#102C22×C1111yescharacteristic
373C2×#102C22×C1111yescharacteristic
374C2×#102C22×C1111yescharacteristic
375C2×C4×C8C22×C1111yescharacteristic
376#400—21no—
377#395—21no—
378#391C22×C1111yescharacteristic
379#391C22×C1111yescharacteristic
380#389C22×C1111yescharacteristic
381#389C22×C1111yescharacteristic
382#387—21no—
383#387—21no—
384#382C22×C1111yescharacteristic
385#340C22×C1111yescharacteristic
386#340C22×C1111yescharacteristic
387#336C22×C1111yescharacteristic
388#336C22×C1111yescharacteristic
389#336C22×C1111yescharacteristic
390#336C22×C1111yescharacteristic
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11C2×#12011yescharacteristic
406C22×C11#54811yescharacteristic
407C22×C11#55011yescharacteristic
408C22×C11C2×#13511yescharacteristic
409C22×C11#57511yescharacteristic
410C22×C11#57711yescharacteristic
411C22×C11#57711yescharacteristic
412C4×C11—22no—
413C4×C11—22no—
414C4×C11—22no—
415C4×C11—42no—
416C4×C11—42no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—42no—
421C4×C11—81no—
422C4×C11—81no—
423C4×C11—81no—
424C4×C11#52511yescharacteristic
425C4×C11#53711yescharacteristic
426C4×C11#54611yescharacteristic
427C4×C11#54711yescharacteristic
428C22×Q8D4×C1111yescharacteristic
429C22×Q8C23×C1111yescharacteristic
430C22×Q8C23×C1111yescharacteristic
431C22×D4—21no—
432C22×D4—21no—
433C22×D4C23×C1111yescharacteristic
434C22×D4C23×C1111yescharacteristic
435C23×C4—21no—
436C23×C4—21no—
437C2×Q16—22no—
438C2×Q16—22no—
439C2×Q16—41no—
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—22no—
445C2×SD16—41no—
446C22×C8C23×C1111yescharacteristic
447C22×C8C23×C1111yescharacteristic
448C22×C8C23×C1111yescharacteristic
449C22×C8C23×C1111yescharacteristic
450#127—22no—
451#127—22no—
452#124—28no—
453#124—22no—
454#124—22no—
455#124—22no—
456#124D4×C1114yes—
457#123—28no—
458#123—28no—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×Q8—22no—
462C4×Q8—22no—
463C4×Q8—22no—
464C4×Q8—22no—
465C4×D4—28no—
466C4×D4—22no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4D4×C1114yes—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4D4×C1111yescharacteristic
475C2×C4⋊C4D4×C1111yescharacteristic
476C2×C4⋊C4D4×C1111yescharacteristic
477C2×C4⋊C4C23×C1111yescharacteristic
478C2×C4⋊C4C23×C1111yescharacteristic
479C2×C4⋊C4C23×C1111yescharacteristic
480C2×C4⋊C4C23×C1111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42C23×C1111yescharacteristic
490C2×C42C23×C1111yescharacteristic
491C2×C42C23×C1111yescharacteristic
492#106—22no—
493C4⋊C8—22no—
494#103—22no—
495#103—22no—
496#103—22no—
497#103—41no—
498#102—22no—
499#102—22no—
500#102—22no—
501#102—41no—
502#102—41no—
503#102—41no—
504C4×C8—22no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513C2×C11—82no—
514C2×C11—82no—
515C2×C11#240711yescharacteristic
516C2×C11#300211yescharacteristic
517C2×C11#300911yescharacteristic
518C2×C11#336511yescharacteristic
519C2×C11#337111yescharacteristic
520C2×C11#339411yescharacteristic
521C2×C11#340111yescharacteristic
522C24—21no—
523C24—21no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—41no—
537C2×Q8C2×D4×C1112yes—
538C2×Q8C11×#4112yes—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—81no—
554C2×D4—81no—
555C2×D4C2×D4×C1112yes—
556C2×D4C2×D4×C1112yes—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—81no—
566C22×C4—81no—
567C22×C4—81no—
568C22×C4—81no—
569C22×C4C2×D4×C1111yescharacteristic
570C22×C4C2×D4×C1111yescharacteristic
571C22×C4C2×D4×C1111yescharacteristic
572C22×C4C2×D4×C1111yescharacteristic
573C22×C4C2×D4×C1111yescharacteristic
574C22×C4C2×D4×C1111yescharacteristic
575C22×C4C24×C1111yescharacteristic
576Q16—44no—
577SD16—28no—
578SD16—44no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8C11×#4112yes—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4C2×D4×C1112yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C42—24no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—42no—
618C42C2×D4×C1112yes—
619C42C2×D4×C1112yes—
620C11#2419411yescharacteristic, direct product factor, Sylow
621C23—22no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23C22×D4×C1111yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—44no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—22no—
649D4—48no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—84no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
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×C4—84no—
689C2×C4—84no—
690C2×C4C11×#12012yes—
691C2×C4C11×#12012yes—
692C2×C4C11×#13512yes—
693C2×C4C22×D4×C1111yescharacteristic
694C2×C4C22×D4×C1111yescharacteristic
695C2×C4C2×C11×#4111yescharacteristic
696C2×C4C2×C11×#4111yescharacteristic
697C2×C4C11×H(5,𝔽2)11yescharacteristic
698C2×C4C11×2−1+411yescharacteristic
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22C2×C11×#12011yescharacteristic
718C22C11×#54811yescharacteristic
719C22C11×#55011yescharacteristic
720C22C2×C11×#13511yescharacteristic
721C22C11×#57511yescharacteristic
722C22C11×#57711yescharacteristic
723C22C11×#57711yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—42no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4C11×#52511yescharacteristic
737C4C11×#53711yescharacteristic
738C4C11×#54611yescharacteristic
739C4C11×#54711yescharacteristic
740C2—82no—
741C2—82no—
742C2C11×#240711yescharacteristic
743C2C11×#300211yescharacteristic
744C2C11×#300911yescharacteristic
745C2C11×#336511yescharacteristic
746C2C11×#337111yescharacteristic
747C2C11×#339411yescharacteristic
748C2C11×#340111yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#464C2semidirect
3. C2×C4×C11×SD16C2semidirect
4. C11×#2581C2semidirect
5. C11×#2042C2semidirect
7. C11×#2015C2semidirect
9. C11×#1984C2semidirect
10. C11×#1958C2semidirect
11. C11×#1878C2semidirect
12. C11×#1877C2semidirect
13. C11×#1865C2semidirect
14. C11×#1864C2semidirect
15. C11×#1804C2semidirect
148. #24194C11direct (N × H)
248. C2×#464C2×C11semidirect
249. C2×C4×SD16C2×C11semidirect
250. #2581C2×C11semidirect
251. #2042C2×C11semidirect
253. #2015C2×C11semidirect
255. #1984C2×C11semidirect
256. #1958C2×C11semidirect
257. #1878C2×C11semidirect
258. #1877C2×C11semidirect
259. #1865C2×C11semidirect
260. #1864C2×C11semidirect
261. #1804C2×C11semidirect
620. C11#24194direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5592
C2×C11×#4642
C2×C4×C11×SD162
C11×#25812
C11×#20422
C11×#20412
C11×#20152
C11×#20142
C11×#19842
C11×#19582
C11×#18782
C11×#18772
C11×#18652
C11×#18642
C11×#18042
#2419411