Finite Group Databasebeta

← C11×#22045 #14599238

Subgroups — C11×#22045 #14599238

Order 2816.

1096 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#449C211yesmaximal, characteristic
2C4×C11×#121C211yesmaximal, characteristic, complemented
3C11×#2297C211yesmaximal, characteristic, complemented
4C11×#1970C211yesmaximal, characteristic, complemented
5C11×#1968C211yesmaximal, characteristic, complemented
6C11×#1934C211yesmaximal, characteristic, complemented
7C11×#1933C211yesmaximal, characteristic, complemented
8C11×#1928C211yesmaximal, characteristic, complemented
9C11×#1926C211yesmaximal, characteristic, complemented
10C11×#1879C211yesmaximal, characteristic, complemented
11C11×#1877C211yesmaximal, characteristic, complemented
12C11×#1875C211yesmaximal, characteristic, complemented
13C11×#1854C211yesmaximal, characteristic, complemented
14C11×#1788C211yesmaximal, characteristic, complemented
15C4×C11×C22⋊C8C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C11×#449C418yescomplemented
25C2×C11×#107C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C4×C8×C11C2211yescharacteristic
38C2×C4×C8×C11C2211yescharacteristic
39C11×#391C2211yescharacteristic
40C11×#391C2211yescharacteristic
41C11×#390C2211yescharacteristic
42C11×#390C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#388—21no—
46C11×#386—21no—
47C11×#386—21no—
48C11×#386—21no—
49C11×#380C2211yescharacteristic
50C4×C11×C4⋊C4C2211yescharacteristic
51C4×C11×C22⋊C4—21no—
52C4×C11×C22⋊C4—21no—
53C4×C11×C22⋊C4—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C2×C11×#41—22no—
61C2×C11×#41—41no—
62C2×C11×#41—41no—
63C2×C11×#41—41no—
64C2×C11×#41—41no—
65C2×C11×#41C2×C414yescomplemented
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11—21no—
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C23×C4×C11—21no—
73C23×C4×C11D411yescharacteristic
74C23×C4×C11D411yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C2×C11×SD16—41no—
77C2×C11×SD16—41no—
78C2×C11×SD16C2×C414yescomplemented
79C2×C11×D8—41no—
80C2×C11×D8—41no—
81C2×C11×D8C2×C414yescomplemented
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C11×#121—22no—
87C11×#121C2×C414yes—
88C4×D4×C11—41no—
89C4×D4×C11—41no—
90C4×D4×C11—44no—
91C11×#117—41no—
92C11×#117—41no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C42×C11—21no—
110C2×C42×C11—21no—
111C2×C42×C11—41no—
112C2×C42×C11—41no—
113C2×C42×C11D411yescharacteristic
114C2×C42×C11D411yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C11×#107—41no—
118C11×#106—41no—
119C11×#103—41no—
120C11×#103—41no—
121C11×#103C2×C414yescomplemented
122C11×#102—41no—
123C11×#102—41no—
124C11×#102—41no—
125C11×#102—41no—
126C11×#102C2×C414yescomplemented
127C11×C22⋊C8—22no—
128C11×C22⋊C8C2×C414yescomplemented
129C4×C8×C11—41no—
130C4×C8×C11—41no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136C11×#95—21no—
137C11×#95—21no—
138#22045C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—21no—
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C22×C412yes—
152C2×D4×C11—24no—
153C2×D4×C11—24no—
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—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11C22×C412yes—
169C2×D4×C11C22×C412yes—
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—24no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—41no—
185C22×C4×C11—41no—
186C22×C4×C11—41no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11C22×C412yes—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11#4112yes—
199C22×C4×C11C2411yescharacteristic
200C11×SD16—44no—
201C11×D8—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×C11C22×C412yes—
213C2×C8×C11C22×C412yes—
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—42no—
224C11×C4⋊C4C22×C412yes—
225C11×C22⋊C4—24no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊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—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—41no—
240C42×C11—41no—
241C42×C11—42no—
242C42×C11—42no—
243C2×#449C2×C1111yescharacteristic
244C4×#121C2×C1111yescharacteristic, complemented
245#2297C2×C1111yescharacteristic, complemented
246#1970C2×C1111yescharacteristic, complemented
247#1968C2×C1111yescharacteristic, complemented
248#1934C2×C1111yescharacteristic, complemented
249#1933C2×C1111yescharacteristic, complemented
250#1928C2×C1111yescharacteristic, complemented
251#1926C2×C1111yescharacteristic, complemented
252#1879C2×C1111yescharacteristic, complemented
253#1877C2×C1111yescharacteristic, complemented
254#1875C2×C1111yescharacteristic, complemented
255#1854C2×C1111yescharacteristic, complemented
256#1788C2×C1111yescharacteristic, complemented
257C4×C22⋊C8C2×C1111yescharacteristic, complemented
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—22no—
265C23×C11—22no—
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×C11C4×D412yes—
279C23×C11C22×D411yescharacteristic
280Q8×C11—22no—
281Q8×C11—22no—
282Q8×C11—41no—
283Q8×C11—41no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—22no—
287D4×C11—22no—
288D4×C11—48no—
289D4×C11—48no—
290D4×C11—41no—
291D4×C11—41no—
292D4×C11—41no—
293D4×C11—41no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
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—22no—
307C2×C4×C11—22no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—44no—
312C2×C4×C11—44no—
313C2×C4×C11—48no—
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—84no—
331C2×C4×C11C4×D412yes—
332C2×C4×C11#13512yes—
333C2×C4×C11#13512yes—
334C2×C4×C11AGL(1,ℤ/8)12yes—
335C2×C4×C11C23×C411yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C2×C4×C11H(5,𝔽2)11yescharacteristic
340C2×C4×C11H(5,𝔽2)11yescharacteristic
341C8×C11—22no—
342C8×C11—22no—
343C8×C11—41no—
344C8×C11—41no—
345C22×#41C22×C1111yescharacteristic
346C22×SD16C22×C1111yescharacteristic
347C22×D8C22×C1111yescharacteristic
348C2×#121C22×C1111yescharacteristic
349C2×C4×D4—21no—
350C2×C4×D4C22×C1111yescharacteristic
351C2×#117C22×C1111yescharacteristic
352C22×C42C22×C1111yescharacteristic
353#449C4×C1118yescomplemented
354C2×#107C22×C1111yescharacteristic
355C2×#106C22×C1111yescharacteristic
356C2×#103C22×C1111yescharacteristic
357C2×#103C22×C1111yescharacteristic
358C2×#103C22×C1111yescharacteristic
359C2×#102C22×C1111yescharacteristic
360C2×#102C22×C1111yescharacteristic
361C2×#102C22×C1111yescharacteristic
362C2×#102C22×C1111yescharacteristic
363C2×#102C22×C1111yescharacteristic
364C2×C22⋊C8C22×C1111yescharacteristic
365C2×C22⋊C8C22×C1111yescharacteristic
366C2×C4×C8C22×C1111yescharacteristic
367C2×C4×C8C22×C1111yescharacteristic
368#391C22×C1111yescharacteristic
369#391C22×C1111yescharacteristic
370#390C22×C1111yescharacteristic
371#390C22×C1111yescharacteristic
372#390C22×C1111yescharacteristic
373#389C22×C1111yescharacteristic
374#388—21no—
375#386—21no—
376#386—21no—
377#386—21no—
378#380C22×C1111yescharacteristic
379C4×C4⋊C4C22×C1111yescharacteristic
380C4×C22⋊C4—21no—
381C4×C22⋊C4—21no—
382C4×C22⋊C4—21no—
383#340C22×C1111yescharacteristic
384#340C22×C1111yescharacteristic
385#340C22×C1111yescharacteristic
386#340C22×C1111yescharacteristic
387#336C22×C1111yescharacteristic
388#336C22×C1111yescharacteristic
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
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×C11C2×C4×D411yescharacteristic
411C22×C11#53411yescharacteristic
412C22×C11#53511yescharacteristic
413C22×C11C2×#13511yescharacteristic
414C22×C11C2×#13511yescharacteristic
415C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
416C22×C11#57511yescharacteristic
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—42no—
422C4×C11—41no—
423C4×C11—42no—
424C4×C11—81no—
425C4×C11—81no—
426C4×C11—81no—
427C4×C11—81no—
428C4×C11#51811yescharacteristic
429C4×C11#51811yescharacteristic
430C4×C11#53811yescharacteristic
431C4×C11#53811yescharacteristic
432C2×#41—22no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41—41no—
436C2×#41—41no—
437C2×#41C2×C4×C1114yescomplemented
438C22×Q8C23×C1111yescharacteristic
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C23×C1111yescharacteristic
442C22×D4C23×C1111yescharacteristic
443C23×C4—21no—
444C23×C4—21no—
445C23×C4D4×C1111yescharacteristic
446C23×C4D4×C1111yescharacteristic
447C23×C4C23×C1111yescharacteristic
448C2×SD16—41no—
449C2×SD16—41no—
450C2×SD16C2×C4×C1114yescomplemented
451C2×D8—41no—
452C2×D8—41no—
453C2×D8C2×C4×C1114yescomplemented
454C22×C8C23×C1111yescharacteristic
455C22×C8C23×C1111yescharacteristic
456C22×C8C23×C1111yescharacteristic
457C22×C8C23×C1111yescharacteristic
458#121—22no—
459#121C2×C4×C1114yes—
460C4×D4—41no—
461C4×D4—41no—
462C4×D4—44no—
463#117—41no—
464#117—41no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4C23×C1111yescharacteristic
467C2×C4⋊C4C23×C1111yescharacteristic
468C2×C4⋊C4C23×C1111yescharacteristic
469C2×C4⋊C4C23×C1111yescharacteristic
470C2×C4⋊C4C23×C1111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—41no—
484C2×C42—41no—
485C2×C42D4×C1111yescharacteristic
486C2×C42D4×C1111yescharacteristic
487C2×C42C23×C1111yescharacteristic
488C2×C42C23×C1111yescharacteristic
489#107—41no—
490#106—41no—
491#103—41no—
492#103—41no—
493#103C2×C4×C1114yescomplemented
494#102—41no—
495#102—41no—
496#102—41no—
497#102—41no—
498#102C2×C4×C1114yescomplemented
499C22⋊C8—22no—
500C22⋊C8C2×C4×C1114yescomplemented
501C4×C8—41no—
502C4×C8—41no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510C2×C11—42no—
511C2×C11—82no—
512C2×C11—82no—
513C2×C11#232111yescharacteristic
514C2×C11C4×#13511yescharacteristic
515C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
516C2×C11#318811yescharacteristic
517C2×C11#319111yescharacteristic
518C2×C11#320711yescharacteristic
519C2×C11#321211yescharacteristic
520C24—21no—
521C24—21no—
522C24C2×D4×C1111yescharacteristic
523#41—44no—
524#41—44no—
525#41—44no—
526#41—44no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8C22×C4×C1112yes—
533C2×D4—24no—
534C2×D4—24no—
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×D4C22×C4×C1112yes—
550C2×D4C22×C4×C1112yes—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4C22×C4×C1112yes—
574C22×C4C2×D4×C1111yescharacteristic
575C22×C4C2×D4×C1111yescharacteristic
576C22×C4C2×D4×C1111yescharacteristic
577C22×C4C2×D4×C1111yescharacteristic
578C22×C4C2×D4×C1111yescharacteristic
579C22×C4C11×#4112yes—
580C22×C4C24×C1111yescharacteristic
581SD16—44no—
582D8—44no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8C22×C4×C1112yes—
594C2×C8C22×C4×C1112yes—
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—21no—
604C4⋊C4—42no—
605C4⋊C4C22×C4×C1112yes—
606C22⋊C4—24no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—41no—
621C42—41no—
622C42—42no—
623C42—42no—
624C11#2204511yescharacteristic, direct product factor, Sylow
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23C4×D4×C1112yes—
646C23C22×D4×C1111yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—48no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
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—48no—
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—84no—
698C2×C4C4×D4×C1112yes—
699C2×C4C11×#13512yes—
700C2×C4C11×#13512yes—
701C2×C4C11×AGL(1,ℤ/8)12yes—
702C2×C4C23×C4×C1111yescharacteristic
703C2×C4C2×C11×#4111yescharacteristic
704C2×C4C11×H(5,𝔽2)11yescharacteristic
705C2×C4C11×H(5,𝔽2)11yescharacteristic
706C2×C4C11×H(5,𝔽2)11yescharacteristic
707C2×C4C11×H(5,𝔽2)11yescharacteristic
708C8—22no—
709C8—22no—
710C8—41no—
711C8—41no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C2×C4×D4×C1111yescharacteristic
734C22C11×#53411yescharacteristic
735C22C11×#53511yescharacteristic
736C22C2×C11×#13511yescharacteristic
737C22C2×C11×#13511yescharacteristic
738C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
739C22C11×#57511yescharacteristic
740C4—22no—
741C4—22no—
742C4—22no—
743C4—22no—
744C4—41no—
745C4—42no—
746C4—42no—
747C4—81no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4C11×#51811yescharacteristic
752C4C11×#51811yescharacteristic
753C4C11×#53811yescharacteristic
754C4C11×#53811yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2C11×#232111yescharacteristic
759C2C4×C11×#13511yescharacteristic
760C2C4×C11×AGL(1,ℤ/8)11yescharacteristic
761C2C11×#318811yescharacteristic
762C2C11×#319111yescharacteristic
763C2C11×#320711yescharacteristic
764C2C11×#321211yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#449C2
LCSG ▷ C2×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. C4×C11×#121C2semidirect
3. C11×#2297C2semidirect
4. C11×#1970C2semidirect
5. C11×#1968C2semidirect
6. C11×#1934C2semidirect
7. C11×#1933C2semidirect
8. C11×#1928C2semidirect
9. C11×#1926C2semidirect
10. C11×#1879C2semidirect
11. C11×#1877C2semidirect
12. C11×#1875C2semidirect
13. C11×#1854C2semidirect
14. C11×#1788C2semidirect
15. C4×C11×C22⋊C8C2semidirect
24. C11×#449C4semidirect
65. C2×C11×#41C2×C4semidirect
78. C2×C11×SD16C2×C4semidirect
81. C2×C11×D8C2×C4semidirect
121. C11×#103C2×C4semidirect
126. C11×#102C2×C4semidirect
128. C11×C22⋊C8C2×C4semidirect
138. #22045C11direct (N × H)
244. C4×#121C2×C11semidirect
245. #2297C2×C11semidirect
246. #1970C2×C11semidirect
247. #1968C2×C11semidirect
248. #1934C2×C11semidirect
249. #1933C2×C11semidirect
250. #1928C2×C11semidirect
251. #1926C2×C11semidirect
252. #1879C2×C11semidirect
253. #1877C2×C11semidirect
254. #1875C2×C11semidirect
255. #1854C2×C11semidirect
256. #1788C2×C11semidirect
257. C4×C22⋊C8C2×C11semidirect
353. #449C4×C11semidirect
437. C2×#41C2×C4×C11semidirect
450. C2×SD16C2×C4×C11semidirect
453. C2×D8C2×C4×C11semidirect
493. #103C2×C4×C11semidirect
498. #102C2×C4×C11semidirect
500. C22⋊C8C2×C4×C11semidirect
624. C11#22045direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4492
C4×C11×#1212
C11×#22972
C11×#19702
C11×#19682
C11×#19342
C11×#19332
C11×#19282
C11×#19262
C11×#18792
C11×#18772
C11×#18752
C11×#18542
C11×#17882
C4×C11×C22⋊C82
#2204511