Finite Group Databasebeta

← C11×#24768 #14601961

Subgroups — C11×#24768 #14601961

Order 2816.

1004 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#468C211yesmaximal, characteristic, complemented
2C2×C11×#465C211yesmaximal, characteristic, complemented
3C2×C11×#460C211yesmaximal, characteristic, complemented
4C2×C11×#424C211yesmaximal, characteristic, complemented
5C11×#2619C211yesmaximal, characteristic
6C11×#2323C211yesmaximal, characteristic, complemented
7C11×#2067C211yesmaximal, characteristic, complemented
8C11×#2065C211yesmaximal, characteristic, complemented
9C11×#2055C211yesmaximal, characteristic, complemented
10C11×#2055C211yesmaximal, characteristic, complemented
11C11×#1982C211yesmaximal, characteristic, complemented
12C11×#1949C211yesmaximal, characteristic, complemented
13C11×#1895C211yesmaximal, characteristic, complemented
14C11×#1893C211yesmaximal, characteristic, complemented
15C11×#1805C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×#127C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C11×#468—24no—
27C11×#465—24no—
28C11×#460—24no—
29C2×C11×#107C2211yescharacteristic
30C2×C11×#106C2211yescharacteristic
31C11×#424—24no—
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×C4⋊C8C2211yescharacteristic
34C2×C11×C4⋊C8C2211yescharacteristic
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×#103C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C11×#102C2211yescharacteristic
40C2×C11×#102C2211yescharacteristic
41C2×C11×#102C2211yescharacteristic
42C2×C11×#102C2211yescharacteristic
43C2×C11×#102C2211yescharacteristic
44C11×#394—21no—
45C11×#394—21no—
46C11×#392—21no—
47C11×#392—21no—
48C11×#391C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#390C2211yescharacteristic
51C11×#389—21no—
52C11×#389C2211yescharacteristic
53C11×#388—21no—
54C11×#388—21no—
55C11×#387—21no—
56C11×#382C2211yescharacteristic
57C11×#380C2211yescharacteristic
58C4×C11×C4⋊C4C2211yescharacteristic
59C11×#340C2211yescharacteristic
60C11×#340C2211yescharacteristic
61C11×#340C2211yescharacteristic
62C11×#340C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11—21no—
68C22×D4×C11C2311yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C2×C11×SD16—22no—
72C2×C11×SD16—22no—
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C2×C11×SD16—41no—
76C2×C11×SD16—41no—
77C2×C11×M16—22no—
78C2×C11×M16—22no—
79C2×C11×M16—41no—
80C22×C8×C11—22no—
81C22×C8×C11—22no—
82C22×C8×C11—41no—
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C11×#127—22no—
88C11×#127—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8D414yescomplemented
91C11×#121—22no—
92C11×#121—22no—
93C11×#121—22no—
94C11×#121—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C11×#117—22no—
98C11×#117—22no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4D411yescharacteristic
103C2×C11×C4⋊C4D411yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4D411yescharacteristic
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C42×C11—21no—
120C2×C42×C11—21no—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C11×#107—22no—
124C11×#106—22no—
125C11×C4⋊C8—22no—
126C11×C4⋊C8—22no—
127C11×C4⋊C8—22no—
128C11×C4⋊C8D414yescomplemented
129C11×#103—22no—
130C11×#103—22no—
131C11×#102—22no—
132C11×#102—22no—
133C11×#102—22no—
134C11×#102—22no—
135C11×#102—41no—
136C11×#102—41no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142C11×#95—21no—
143C11×#95—21no—
144#24768C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11—21no—
146C24×C11—21no—
147C24×C11C2×D411yescharacteristic
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11C2×D412yes—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C2×D4×C11—81no—
171C2×D4×C11—81no—
172C2×D4×C11—81no—
173C2×D4×C11—81no—
174C2×D4×C11—81no—
175C2×D4×C11—81no—
176C2×D4×C11—81no—
177C2×D4×C11—81no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
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×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D412yes—
194C22×C4×C11#4112yes—
195C22×C4×C11C2411yescharacteristic
196C11×SD16—44no—
197C11×SD16—44no—
198C11×M16—44no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
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—44no—
210C2×C8×C11C2×D412yes—
211C2×C8×C11C2×D412yes—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—42no—
225C11×C4⋊C4—81no—
226C11×C4⋊C4C2×D412yes—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—81no—
233C11×C22⋊C4—81no—
234C11×C22⋊C4—81no—
235C11×C22⋊C4—81no—
236C11×C22⋊C4—81no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—42no—
240C42×C11—81no—
241C42×C11C2×D412yes—
242C42×C11#4112yes—
243C2×#468C2×C1111yescharacteristic, complemented
244C2×#465C2×C1111yescharacteristic, complemented
245C2×#460C2×C1111yescharacteristic, complemented
246C2×#424C2×C1111yescharacteristic, complemented
247#2619C2×C1111yescharacteristic
248#2323C2×C1111yescharacteristic, complemented
249#2067C2×C1111yescharacteristic, complemented
250#2065C2×C1111yescharacteristic, complemented
251#2055C2×C1111yescharacteristic, complemented
252#2055C2×C1111yescharacteristic, complemented
253#1982C2×C1111yescharacteristic, complemented
254#1949C2×C1111yescharacteristic, complemented
255#1895C2×C1111yescharacteristic, complemented
256#1893C2×C1111yescharacteristic, complemented
257#1805C2×C1111yescharacteristic, complemented
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
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×C11—41no—
277C23×C11—41no—
278C23×C11#12112yes—
279C23×C11C22×D411yescharacteristic
280Q8×C11—22no—
281Q8×C11—22no—
282Q8×C11—41no—
283Q8×C11—41no—
284D4×C11—41no—
285D4×C11—41no—
286D4×C11—41no—
287D4×C11—41no—
288D4×C11—41no—
289D4×C11—41no—
290D4×C11—41no—
291D4×C11—41no—
292D4×C11—84no—
293D4×C11—84no—
294D4×C11—84no—
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—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
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—41no—
330C2×C4×C11#12112yes—
331C2×C4×C11#12112yes—
332C2×C4×C11#12112yes—
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—22no—
340C8×C11—22no—
341C8×C11—41no—
342C8×C11—41no—
343C22×SD16C22×C1111yescharacteristic
344C22×SD16C22×C1111yescharacteristic
345C22×M16C22×C1111yescharacteristic
346C23×C8C22×C1111yescharacteristic
347C2×#127C22×C1111yescharacteristic
348C2×C22⋊Q8C22×C1111yescharacteristic
349C2×#121C22×C1111yescharacteristic
350C2×#121C22×C1111yescharacteristic
351C2×C4×Q8C22×C1111yescharacteristic
352C2×#117C22×C1111yescharacteristic
353#468—24no—
354#465—24no—
355#460—24no—
356C2×#107C22×C1111yescharacteristic
357C2×#106C22×C1111yescharacteristic
358#424—24no—
359C2×C4⋊C8C22×C1111yescharacteristic
360C2×C4⋊C8C22×C1111yescharacteristic
361C2×C4⋊C8C22×C1111yescharacteristic
362C2×C4⋊C8C22×C1111yescharacteristic
363C2×#103C22×C1111yescharacteristic
364C2×#103C22×C1111yescharacteristic
365C2×#102C22×C1111yescharacteristic
366C2×#102C22×C1111yescharacteristic
367C2×#102C22×C1111yescharacteristic
368C2×#102C22×C1111yescharacteristic
369C2×#102C22×C1111yescharacteristic
370C2×#102C22×C1111yescharacteristic
371#394—21no—
372#394—21no—
373#392—21no—
374#392—21no—
375#391C22×C1111yescharacteristic
376#390C22×C1111yescharacteristic
377#390C22×C1111yescharacteristic
378#389—21no—
379#389C22×C1111yescharacteristic
380#388—21no—
381#388—21no—
382#387—21no—
383#382C22×C1111yescharacteristic
384#380C22×C1111yescharacteristic
385C4×C4⋊C4C22×C1111yescharacteristic
386#340C22×C1111yescharacteristic
387#340C22×C1111yescharacteristic
388#340C22×C1111yescharacteristic
389#340C22×C1111yescharacteristic
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
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×C11—81no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11C2×#12111yescharacteristic
412C22×C11C2×#12111yescharacteristic
413C22×C11#53711yescharacteristic
414C22×C11#57611yescharacteristic
415C22×C11#57711yescharacteristic
416C22×C11#57711yescharacteristic
417C22×C11#57711yescharacteristic
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—42no—
422C4×C11—42no—
423C4×C11—41no—
424C4×C11—41no—
425C4×C11—81no—
426C4×C11—81no—
427C4×C11—81no—
428C4×C11—81no—
429C4×C11D4211yescharacteristic
430C4×C11#54711yescharacteristic
431C4×C11#54811yescharacteristic
432C4×C11#55311yescharacteristic
433C22×Q8C23×C1111yescharacteristic
434C22×D4—21no—
435C22×D4—21no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4C23×C1111yescharacteristic
439C22×D4C23×C1111yescharacteristic
440C23×C4C23×C1111yescharacteristic
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—22no—
445C2×SD16—41no—
446C2×SD16—41no—
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—41no—
450C22×C8—22no—
451C22×C8—22no—
452C22×C8—41no—
453C22×C8C23×C1111yescharacteristic
454C22×C8C23×C1111yescharacteristic
455C22×C8C23×C1111yescharacteristic
456C22×C8C23×C1111yescharacteristic
457#127—22no—
458#127—22no—
459C22⋊Q8—22no—
460C22⋊Q8D4×C1114yescomplemented
461#121—22no—
462#121—22no—
463#121—22no—
464#121—22no—
465C4×Q8—22no—
466C4×Q8—22no—
467#117—22no—
468#117—22no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4D4×C1111yescharacteristic
473C2×C4⋊C4D4×C1111yescharacteristic
474C2×C4⋊C4C23×C1111yescharacteristic
475C2×C4⋊C4C23×C1111yescharacteristic
476C2×C4⋊C4C23×C1111yescharacteristic
477C2×C4⋊C4C23×C1111yescharacteristic
478C2×C4⋊C4C23×C1111yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
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×C22⋊C4D4×C1111yescharacteristic
488C2×C22⋊C4D4×C1111yescharacteristic
489C2×C42—21no—
490C2×C42—21no—
491C2×C42C23×C1111yescharacteristic
492C2×C42C23×C1111yescharacteristic
493#107—22no—
494#106—22no—
495C4⋊C8—22no—
496C4⋊C8—22no—
497C4⋊C8—22no—
498C4⋊C8D4×C1114yescomplemented
499#103—22no—
500#103—22no—
501#102—22no—
502#102—22no—
503#102—22no—
504#102—22no—
505#102—41no—
506#102—41no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514C2×C11—42no—
515C2×C11—161no—
516C2×C11—161no—
517C2×C11#241611yescharacteristic
518C2×C11#304311yescharacteristic
519C2×C11#304511yescharacteristic
520C2×C11#305711yescharacteristic
521C2×C11#306211yescharacteristic
522C2×C11#325711yescharacteristic
523C2×C11#326011yescharacteristic
524C24—21no—
525C24—21no—
526C24C2×D4×C1111yescharacteristic
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8C2×D4×C1112yes—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4—81no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4—81no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4C2×D4×C1111yescharacteristic
568C22×C4C2×D4×C1111yescharacteristic
569C22×C4C2×D4×C1111yescharacteristic
570C22×C4C2×D4×C1111yescharacteristic
571C22×C4C2×D4×C1111yescharacteristic
572C22×C4C2×D4×C1112yes—
573C22×C4C11×#4112yes—
574C22×C4C24×C1111yescharacteristic
575SD16—44no—
576SD16—44no—
577M16—44no—
578C2×C8—21no—
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—44no—
589C2×C8C2×D4×C1112yes—
590C2×C8C2×D4×C1112yes—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—81no—
605C4⋊C4C2×D4×C1112yes—
606C22⋊C4—24no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C42—21no—
617C42—21no—
618C42—42no—
619C42—81no—
620C42C2×D4×C1112yes—
621C42C11×#4112yes—
622C11#2476811yescharacteristic, direct product factor, Sylow
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23C11×#12112yes—
644C23C22×D4×C1111yescharacteristic
645Q8—22no—
646Q8—22no—
647Q8—41no—
648Q8—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—84no—
658D4—84no—
659D4—84no—
660D4—84no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
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—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4C11×#12112yes—
696C2×C4C11×#12112yes—
697C2×C4C11×#12112yes—
698C2×C4C22×D4×C1111yescharacteristic
699C2×C4C22×D4×C1111yescharacteristic
700C2×C4C2×C11×#4111yescharacteristic
701C2×C4C2×C11×#4111yescharacteristic
702C2×C4C11×H(5,𝔽2)11yescharacteristic
703C2×C4C11×2−1+411yescharacteristic
704C8—22no—
705C8—22no—
706C8—41no—
707C8—41no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22C2×C11×#12111yescharacteristic
730C22C2×C11×#12111yescharacteristic
731C22C11×#53711yescharacteristic
732C22C11×#57611yescharacteristic
733C22C11×#57711yescharacteristic
734C22C11×#57711yescharacteristic
735C22C11×#57711yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—42no—
740C4—42no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4—81no—
745C4—81no—
746C4—81no—
747C4D42×C1111yescharacteristic
748C4C11×#54711yescharacteristic
749C4C11×#54811yescharacteristic
750C4C11×#55311yescharacteristic
751C2—42no—
752C2—161no—
753C2—161no—
754C2C11×#241611yescharacteristic
755C2C11×#304311yescharacteristic
756C2C11×#304511yescharacteristic
757C2C11×#305711yescharacteristic
758C2C11×#306211yescharacteristic
759C2C11×#325711yescharacteristic
760C2C11×#326011yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2619C2
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×#468C2semidirect
2. C2×C11×#465C2semidirect
3. C2×C11×#460C2semidirect
4. C2×C11×#424C2semidirect
6. C11×#2323C2semidirect
7. C11×#2067C2semidirect
8. C11×#2065C2semidirect
9. C11×#2055C2semidirect
10. C11×#2055C2semidirect
11. C11×#1982C2semidirect
12. C11×#1949C2semidirect
13. C11×#1895C2semidirect
14. C11×#1893C2semidirect
15. C11×#1805C2semidirect
90. C11×C22⋊Q8D4semidirect
128. C11×C4⋊C8D4semidirect
144. #24768C11direct (N × H)
243. C2×#468C2×C11semidirect
244. C2×#465C2×C11semidirect
245. C2×#460C2×C11semidirect
246. C2×#424C2×C11semidirect
248. #2323C2×C11semidirect
249. #2067C2×C11semidirect
250. #2065C2×C11semidirect
251. #2055C2×C11semidirect
252. #2055C2×C11semidirect
253. #1982C2×C11semidirect
254. #1949C2×C11semidirect
255. #1895C2×C11semidirect
256. #1893C2×C11semidirect
257. #1805C2×C11semidirect
460. C22⋊Q8D4×C11semidirect
498. C4⋊C8D4×C11semidirect
622. C11#24768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4682
C2×C11×#4652
C2×C11×#4602
C2×C11×#4242
C11×#26192
C11×#23232
C11×#20672
C11×#20652
C11×#20552
C11×#19822
C11×#19492
C11×#18952
C11×#18932
C11×#18052
#2476811