Finite Group Databasebeta

← C11×#24561 #14601754

Subgroups — C11×#24561 #14601754

Order 2816.

1084 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#485C211yesmaximal, characteristic, complemented
2C2×C11×#407C211yesmaximal, characteristic
3C11×#2848C211yesmaximal, characteristic
4C11×#2280C211yesmaximal, characteristic
5C11×#2077C211yesmaximal, characteristic, complemented
6C11×#2076C211yesmaximal, characteristic, complemented
7C11×#2036C211yesmaximal, characteristic, complemented
8C11×#2035C211yesmaximal, characteristic, complemented
9C11×#1894C211yesmaximal, characteristic, complemented
10C11×#1894C211yesmaximal, characteristic, complemented
11C11×#1873C211yesmaximal, characteristic, complemented
12C11×#1854C211yesmaximal, characteristic, complemented
13C11×#1825C211yesmaximal, characteristic, complemented
14C11×#1809C211yesmaximal, characteristic, complemented
15C11×#1809C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#485—24no—
25C2×C11×#107C2211yescharacteristic, complemented
26C2×C11×#107C2211yescharacteristic, complemented
27C2×C11×#106C2211yescharacteristic, complemented
28C2×C11×#106C2211yescharacteristic, complemented
29C2×C11×#103C2211yescharacteristic, complemented
30C2×C11×#103C2211yescharacteristic, complemented
31C2×C11×#103C2211yescharacteristic, complemented
32C2×C11×#103C2211yescharacteristic, complemented
33C11×#407—24no—
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C11×#385—21no—
39C11×#385—21no—
40C11×#385—21no—
41C11×#381—21no—
42C11×#380C2211yescharacteristic
43C11×#380C2211yescharacteristic
44C11×#380C2211yescharacteristic
45C11×#380C2211yescharacteristic
46C11×#380C2211yescharacteristic
47C11×#380C2211yescharacteristic
48C11×#380C2211yescharacteristic
49C11×#379—21no—
50C11×#379—21no—
51C4×C11×C22⋊C4—21no—
52C4×C11×C22⋊C4—21no—
53C11×#340C2211yescharacteristic, complemented
54C11×#340C2211yescharacteristic, complemented
55C11×#340C2211yescharacteristic, complemented
56C11×#340C2211yescharacteristic, complemented
57C11×#340C2211yescharacteristic, complemented
58C11×#340C2211yescharacteristic, complemented
59C11×#340C2211yescharacteristic, complemented
60C11×#340C2211yescharacteristic, complemented
61C25×C11D411yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—41no—
68C23×C4×C11—41no—
69C23×C4×C11D411yescharacteristic
70C23×C4×C11D411yescharacteristic
71C23×C4×C11D411yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C2×C11×M16—22no—
76C2×C11×M16—22no—
77C2×C11×M16—22no—
78C2×C11×M16—22no—
79C2×C11×M16—41no—
80C2×C11×M16—41no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—41no—
90C11×C22⋊Q8—41no—
91C11×#117—22no—
92C11×#117—22no—
93C11×#117—41no—
94C11×#117—41no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
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×C42×C11—21no—
118C2×C42×C11—21no—
119C11×#107—22no—
120C11×#107—41no—
121C11×#106—22no—
122C11×#106—41no—
123C11×#103—22no—
124C11×#103—22no—
125C11×#103—41no—
126C11×#103—41no—
127C11×C22⋊C8—22no—
128C11×C22⋊C8—22no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8D414yes—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138#24561C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—22no—
140C24×C11—22no—
141C24×C11—22no—
142C24×C11—41no—
143C24×C11—41no—
144C24×C11—41no—
145C24×C11—41no—
146C24×C11C2×D411yescharacteristic
147C24×C11C2×D411yescharacteristic
148C24×C11C2×D411yescharacteristic
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×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—21no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—41no—
184C22×C4×C11—41no—
185C22×C4×C11—41no—
186C22×C4×C11—44no—
187C22×C4×C11—44no—
188C22×C4×C11—44no—
189C22×C4×C11—44no—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11#4112yes—
195C22×C4×C11#4112yes—
196C22×C4×C11#4112yes—
197C22×C4×C11C2411yescharacteristic
198C11×M16—44no—
199C11×M16—44no—
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—21no—
210C2×C8×C11C2×D412yes—
211C2×C8×C11C2×D412yes—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
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—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4—42no—
228C11×C4⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—42no—
233C11×C22⋊C4—42no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—42no—
236C11×C22⋊C4—42no—
237C11×C22⋊C4—42no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4—42no—
240C11×C22⋊C4—42no—
241C42×C11—42no—
242C42×C11—42no—
243C2×#485C2×C1111yescharacteristic, complemented
244C2×#407C2×C1111yescharacteristic
245#2848C2×C1111yescharacteristic
246#2280C2×C1111yescharacteristic
247#2077C2×C1111yescharacteristic, complemented
248#2076C2×C1111yescharacteristic, complemented
249#2036C2×C1111yescharacteristic, complemented
250#2035C2×C1111yescharacteristic, complemented
251#1894C2×C1111yescharacteristic, complemented
252#1894C2×C1111yescharacteristic, complemented
253#1873C2×C1111yescharacteristic, complemented
254#1854C2×C1111yescharacteristic, complemented
255#1825C2×C1111yescharacteristic, complemented
256#1809C2×C1111yescharacteristic, complemented
257#1809C2×C1111yescharacteristic, complemented
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—44no—
277C23×C11—44no—
278C23×C11—44no—
279C23×C11—44no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11—44no—
283C23×C11#12112yes—
284C23×C11#12312yes—
285C23×C11#13712yes—
286C23×C11C22×D411yescharacteristic
287Q8×C11—41no—
288Q8×C11—41no—
289Q8×C11—41no—
290Q8×C11—41no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
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—44no—
307C2×C4×C11—44no—
308C2×C4×C11—44no—
309C2×C4×C11—41no—
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—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11#12112yes—
338C2×C4×C11#12312yes—
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C2×#4111yescharacteristic
341C2×C4×C11C2×#4111yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11H(5,𝔽2)11yescharacteristic
344C2×C4×C11H(5,𝔽2)11yescharacteristic
345C8×C11—22no—
346C8×C11—22no—
347C8×C11—41no—
348C8×C11—41no—
349C24×C4C22×C1111yescharacteristic
350C22×M16C22×C1111yescharacteristic
351C22×M16C22×C1111yescharacteristic
352C2×C22⋊Q8C22×C1111yescharacteristic
353C2×C22⋊Q8C22×C1111yescharacteristic
354C2×C22⋊Q8C22×C1111yescharacteristic
355C2×#117C22×C1111yescharacteristic
356C2×#117C22×C1111yescharacteristic
357#485—24no—
358C2×#107C22×C1111yescharacteristic, complemented
359C2×#107C22×C1111yescharacteristic, complemented
360C2×#106C22×C1111yescharacteristic, complemented
361C2×#106C22×C1111yescharacteristic, complemented
362C2×#103C22×C1111yescharacteristic, complemented
363C2×#103C22×C1111yescharacteristic, complemented
364C2×#103C22×C1111yescharacteristic, complemented
365C2×#103C22×C1111yescharacteristic, complemented
366#407—24no—
367C2×C22⋊C8C22×C1111yescharacteristic
368C2×C22⋊C8C22×C1111yescharacteristic
369C2×C22⋊C8C22×C1111yescharacteristic
370C2×C22⋊C8C22×C1111yescharacteristic
371#385—21no—
372#385—21no—
373#385—21no—
374#381—21no—
375#380C22×C1111yescharacteristic
376#380C22×C1111yescharacteristic
377#380C22×C1111yescharacteristic
378#380C22×C1111yescharacteristic
379#380C22×C1111yescharacteristic
380#380C22×C1111yescharacteristic
381#380C22×C1111yescharacteristic
382#379—21no—
383#379—21no—
384C4×C22⋊C4—21no—
385C4×C22⋊C4—21no—
386#340C22×C1111yescharacteristic, complemented
387#340C22×C1111yescharacteristic, complemented
388#340C22×C1111yescharacteristic, complemented
389#340C22×C1111yescharacteristic, complemented
390#340C22×C1111yescharacteristic, complemented
391#340C22×C1111yescharacteristic, complemented
392#340C22×C1111yescharacteristic, complemented
393#340C22×C1111yescharacteristic, complemented
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—416no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11C2×#12111yescharacteristic
417C22×C11C2×#12311yescharacteristic
418C22×C11#53411yescharacteristic
419C22×C11C2×#13711yescharacteristic
420C22×C11#57511yescharacteristic
421C22×C11#57511yescharacteristic
422C22×C11#57511yescharacteristic
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—41no—
426C4×C11—81no—
427C4×C11—81no—
428C4×C11—81no—
429C4×C11—81no—
430C4×C11—81no—
431C4×C11—81no—
432C4×C11—81no—
433C4×C11—81no—
434C4×C11#54611yescharacteristic
435C4×C11#54611yescharacteristic
436C4×C11#55111yescharacteristic
437C4×C11#55111yescharacteristic
438C25D4×C1111yescharacteristic
439C22×Q8C23×C1111yescharacteristic
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—22no—
444C23×C4—41no—
445C23×C4—41no—
446C23×C4D4×C1111yescharacteristic
447C23×C4D4×C1111yescharacteristic
448C23×C4D4×C1111yescharacteristic
449C23×C4C23×C1111yescharacteristic
450C23×C4C23×C1111yescharacteristic
451C23×C4C23×C1111yescharacteristic
452C2×M16—22no—
453C2×M16—22no—
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C2×M16—41no—
458C22×C8C23×C1111yescharacteristic
459C22×C8C23×C1111yescharacteristic
460C22×C8C23×C1111yescharacteristic
461C22×C8C23×C1111yescharacteristic
462C22⋊Q8—22no—
463C22⋊Q8—22no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—41no—
467C22⋊Q8—41no—
468#117—22no—
469#117—22no—
470#117—41no—
471#117—41no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4C23×C1111yescharacteristic
476C2×C4⋊C4C23×C1111yescharacteristic
477C2×C4⋊C4C23×C1111yescharacteristic
478C2×C4⋊C4C23×C1111yescharacteristic
479C2×C4⋊C4C23×C1111yescharacteristic
480C2×C4⋊C4C23×C1111yescharacteristic
481C2×C4⋊C4C23×C1111yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C42—21no—
495C2×C42—21no—
496#107—22no—
497#107—41no—
498#106—22no—
499#106—41no—
500#103—22no—
501#103—22no—
502#103—41no—
503#103—41no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8D4×C1114yes—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515C2×C11—42no—
516C2×C11—42no—
517C2×C11—42no—
518C2×C11#241211yescharacteristic
519C2×C11#305411yescharacteristic
520C2×C11#305611yescharacteristic
521C2×C11#309311yescharacteristic
522C2×C11#309511yescharacteristic
523C2×C11#319611yescharacteristic
524C2×C11#319711yescharacteristic
525C24—22no—
526C24—22no—
527C24—22no—
528C24—41no—
529C24—41no—
530C24—41no—
531C24—41no—
532C24C2×D4×C1111yescharacteristic
533C24C2×D4×C1111yescharacteristic
534C24C2×D4×C1111yescharacteristic
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
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×C4—21no—
568C22×C4—21no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4C2×D4×C1111yescharacteristic
577C22×C4C2×D4×C1111yescharacteristic
578C22×C4C2×D4×C1112yes—
579C22×C4C2×D4×C1111yescharacteristic
580C22×C4C11×#4112yes—
581C22×C4C11×#4112yes—
582C22×C4C11×#4112yes—
583C22×C4C24×C1111yescharacteristic
584M16—44no—
585M16—44no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8C2×D4×C1112yes—
597C2×C8C2×D4×C1112yes—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C42—42no—
628C42—42no—
629C11#2456111yescharacteristic, direct product factor, Sylow
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23C11×#12112yes—
656C23C11×#12312yes—
657C23C11×#13712yes—
658C23C22×D4×C1111yescharacteristic
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
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—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
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×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4C11×#12112yes—
710C2×C4C11×#12312yes—
711C2×C4C22×D4×C1111yescharacteristic
712C2×C4C2×C11×#4111yescharacteristic
713C2×C4C2×C11×#4111yescharacteristic
714C2×C4C2×C11×#4111yescharacteristic
715C2×C4C11×H(5,𝔽2)11yescharacteristic
716C2×C4C11×H(5,𝔽2)11yescharacteristic
717C8—22no—
718C8—22no—
719C8—41no—
720C8—41no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—416no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22C2×C11×#12111yescharacteristic
744C22C2×C11×#12311yescharacteristic
745C22C11×#53411yescharacteristic
746C22C2×C11×#13711yescharacteristic
747C22C11×#57511yescharacteristic
748C22C11×#57511yescharacteristic
749C22C11×#57511yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—81no—
754C4—81no—
755C4—81no—
756C4—81no—
757C4—81no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4C11×#54611yescharacteristic
762C4C11×#54611yescharacteristic
763C4C11×#55111yescharacteristic
764C4C11×#55111yescharacteristic
765C2—42no—
766C2—42no—
767C2—42no—
768C2C11×#241211yescharacteristic
769C2C11×#305411yescharacteristic
770C2C11×#305611yescharacteristic
771C2C11×#309311yescharacteristic
772C2C11×#309511yescharacteristic
773C2C11×#319611yescharacteristic
774C2C11×#319711yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC25×C11D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#485C2semidirect
5. C11×#2077C2semidirect
6. C11×#2076C2semidirect
7. C11×#2036C2semidirect
8. C11×#2035C2semidirect
9. C11×#1894C2semidirect
10. C11×#1894C2semidirect
11. C11×#1873C2semidirect
12. C11×#1854C2semidirect
13. C11×#1825C2semidirect
14. C11×#1809C2semidirect
15. C11×#1809C2semidirect
25. C2×C11×#107C22semidirect
26. C2×C11×#107C22semidirect
27. C2×C11×#106C22semidirect
28. C2×C11×#106C22semidirect
29. C2×C11×#103C22semidirect
30. C2×C11×#103C22semidirect
31. C2×C11×#103C22semidirect
32. C2×C11×#103C22semidirect
53. C11×#340C22semidirect
54. C11×#340C22semidirect
55. C11×#340C22semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. C11×#340C22semidirect
59. C11×#340C22semidirect
60. C11×#340C22semidirect
138. #24561C11direct (N × H)
243. C2×#485C2×C11semidirect
247. #2077C2×C11semidirect
248. #2076C2×C11semidirect
249. #2036C2×C11semidirect
250. #2035C2×C11semidirect
251. #1894C2×C11semidirect
252. #1894C2×C11semidirect
253. #1873C2×C11semidirect
254. #1854C2×C11semidirect
255. #1825C2×C11semidirect
256. #1809C2×C11semidirect
257. #1809C2×C11semidirect
358. C2×#107C22×C11semidirect
359. C2×#107C22×C11semidirect
360. C2×#106C22×C11semidirect
361. C2×#106C22×C11semidirect
362. C2×#103C22×C11semidirect
363. C2×#103C22×C11semidirect
364. C2×#103C22×C11semidirect
365. C2×#103C22×C11semidirect
386. #340C22×C11semidirect
387. #340C22×C11semidirect
388. #340C22×C11semidirect
389. #340C22×C11semidirect
390. #340C22×C11semidirect
391. #340C22×C11semidirect
392. #340C22×C11semidirect
393. #340C22×C11semidirect
629. C11#24561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4852
C2×C11×#4072
C11×#28482
C11×#22802
C11×#20772
C11×#20762
C11×#20362
C11×#20352
C11×#18942
C11×#18732
C11×#18542
C11×#18252
C11×#18092
#2456111