Finite Group Databasebeta

← C11×#19055 #14596248

Subgroups — C11×#19055 #14596248

Order 2816.

898 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3545C211yesmaximal, characteristic
2C11×#3239C211yesmaximal, characteristic, complemented
3C11×#3218C211yesmaximal, characteristic, complemented
4C2×C11×#489C211yesmaximal, characteristic, complemented
5C11×#1664C212yesmaximal, complemented
6C11×#1662C212yesmaximal, complemented
7C11×#1661C212yesmaximal, complemented
8C11×#1659C212yesmaximal, complemented
9C11×#1533C211yesmaximal, characteristic, complemented
10C11×#1532C211yesmaximal, characteristic, complemented
11C11×#1532C211yesmaximal, characteristic, complemented
12C11×#563C2211yescharacteristic
13C11×#562C2211yescharacteristic
14C11×#562C2211yescharacteristic
15C11×H(3,𝔽4)C2211yescharacteristic
16C11×#555—21no—
17C11×#551—21no—
18C11×#551—21no—
19C11×#551—21no—
20C11×#546—21no—
21C11×#546—21no—
22C11×#542—21no—
23C11×#542—21no—
24C11×#538—21no—
25C11×#538—21no—
26C11×#536—21no—
27C11×#534—21no—
28C2×C11×C4⋊Q8C2211yescharacteristic, complemented
29C11×#529C2211yescharacteristic
30C11×#529C2211yescharacteristic
31C2×C11×#124C2211yescharacteristic
32C11×#501C2212yescomplemented
33C11×#497C2212yescomplemented
34C11×#491C2212yescomplemented
35C11×#489—21no—
36C11×#489—21no—
37C11×#489C2212yes—
38C11×#489C2212yescomplemented
39C11×#489C2212yescomplemented
40C11×#484—21no—
41C11×#481—21no—
42C11×#475—21no—
43C11×#474—21no—
44C11×#462—21no—
45C11×#461—21no—
46C11×#451—21no—
47C11×#448—21no—
48C11×#432C2211yescharacteristic, complemented
49C11×#432C2211yescharacteristic, complemented
50C2×C11×#103—21no—
51C2×C11×#102—21no—
52C2×C11×#97C2211yescharacteristic, complemented
53C11×#330C2212yescomplemented
54C11×#330C2212yescomplemented
55C11×#329C2212yes—
56C11×#329C2212yescomplemented
57C11×#329C2212yescomplemented
58C11×#329C2212yescomplemented
59C2×C11×#41—21no—
60C22×Q8×C11—21no—
61C22×Q8×C11D411yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11D411yescharacteristic
64C2×C11×Q16—22no—
65C2×C11×SD16—22no—
66C22×C8×C11—21no—
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8—21no—
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8C2312yes—
73C11×#126—21no—
74C11×#126—21no—
75C11×#126—21no—
76C11×#126—21no—
77C11×#126—21no—
78C11×#126—21no—
79C11×#125C2311yescharacteristic
80C11×#125C2311yescharacteristic
81C11×#124—21no—
82C11×#124—21no—
83C11×#124—21no—
84C11×#124—21no—
85C11×#124—21no—
86C11×#124—21no—
87C11×#124—21no—
88C11×#124—21no—
89C11×#124D411yescharacteristic
90C11×#124D411yescharacteristic
91C11×#124C2311yescharacteristic
92C11×#124C2311yescharacteristic
93C11×#124C2311yescharacteristic
94C11×#124C2311yescharacteristic
95C11×#123—21no—
96C11×#123—21no—
97C11×#123—21no—
98C11×#123—21no—
99C11×#123—21no—
100C11×#123—21no—
101C11×#123—21no—
102C11×#123—21no—
103C11×#123—21no—
104C11×#123—21no—
105C11×#123—21no—
106C11×#123—21no—
107C11×C22⋊Q8—21no—
108C11×C22⋊Q8—21no—
109C11×C22⋊Q8—21no—
110C11×C22⋊Q8—21no—
111C11×C22⋊Q8—21no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8D411yescharacteristic
116C11×C22⋊Q8D411yescharacteristic
117C11×#121—21no—
118C11×#121—21no—
119C11×#121—21no—
120C11×#121—21no—
121C11×#121—21no—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121—21no—
125C11×#121D411yescharacteristic
126C11×#121D411yescharacteristic
127C11×#120—21no—
128C11×#120—21no—
129C11×#120—21no—
130C11×#120—21no—
131C11×#120—21no—
132C11×#120—21no—
133C4×Q8×C11D411yescharacteristic
134C4×Q8×C11D411yescharacteristic
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11—21no—
138C4×D4×C11—21no—
139C4×D4×C11—21no—
140C4×D4×C11—21no—
141C4×D4×C11D411yescharacteristic
142C4×D4×C11D411yescharacteristic
143C11×#117—21no—
144C11×#117—21no—
145C11×#117—21no—
146C11×#117—21no—
147C11×#117—21no—
148C2×C11×C4⋊C4—21no—
149C2×C11×C4⋊C4—21no—
150C2×C11×C22⋊C4—21no—
151C2×C11×C22⋊C4—21no—
152C2×C11×C22⋊C4—21no—
153C2×C11×C22⋊C4—21no—
154C2×C11×C22⋊C4—21no—
155C2×C42×C11C2311yescharacteristic
156C11×#107—22no—
157C11×#106—22no—
158C11×C4⋊C8—21no—
159C11×C4⋊C8—21no—
160C11×#103—22no—
161C11×#103—22no—
162C11×#103—22no—
163C11×#103—22no—
164C11×#103—22no—
165C11×#102—22no—
166C11×#102—22no—
167C11×#102—22no—
168C11×C22⋊C8—21no—
169C11×C22⋊C8—21no—
170C11×#97—21no—
171C11×#97C2312yes—
172C11×#97C2312yes—
173C11×#97C2312yes—
174#19055C1111yesmaximal, characteristic, direct product factor, Sylow
175C24×C11—21no—
176C24×C11—21no—
177C11×#41—82no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—22no—
181C2×Q8×C11—42no—
182C2×Q8×C11—41no—
183C2×Q8×C11—82no—
184C2×Q8×C11C2×D411yescharacteristic
185C2×Q8×C11C2×D411yescharacteristic
186C2×Q8×C11C2×D411yescharacteristic
187C2×Q8×C11C2×D411yescharacteristic
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—21no—
191C2×D4×C11—21no—
192C2×D4×C11—21no—
193C2×D4×C11—21no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11—21no—
197C2×D4×C11—21no—
198C2×D4×C11—42no—
199C2×D4×C11—82no—
200C2×D4×C11C2×D411yescharacteristic
201C2×D4×C11C2×D411yescharacteristic
202C2×D4×C11C2×D411yescharacteristic
203C2×D4×C11C2×D411yescharacteristic
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—41no—
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C11×Q16—82no—
217C11×SD16—82no—
218C2×C8×C11—22no—
219C2×C8×C11—22no—
220C2×C8×C11—22no—
221C2×C8×C11—42no—
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—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—22no—
237C11×C4⋊C4—22no—
238C11×C4⋊C4—41no—
239C11×C4⋊C4—41no—
240C11×C4⋊C4C2×D411yescharacteristic
241C11×C4⋊C4C2×D411yescharacteristic
242C11×C4⋊C4C2×D411yescharacteristic
243C11×C4⋊C4C2×D411yescharacteristic
244C11×C22⋊C4—21no—
245C11×C22⋊C4—21no—
246C11×C22⋊C4—21no—
247C11×C22⋊C4—21no—
248C11×C22⋊C4—21no—
249C11×C22⋊C4—21no—
250C11×C22⋊C4—21no—
251C11×C22⋊C4—21no—
252C11×C22⋊C4—21no—
253C11×C22⋊C4—21no—
254C11×C22⋊C4—21no—
255C11×C22⋊C4—21no—
256C11×C22⋊C4—21no—
257C11×C22⋊C4—21no—
258C11×C22⋊C4—21no—
259C11×C22⋊C4—21no—
260C11×C22⋊C4—21no—
261C11×C22⋊C4—21no—
262C11×C22⋊C4—21no—
263C11×C22⋊C4—21no—
264C11×C22⋊C4—21no—
265C11×C22⋊C4—21no—
266C11×C22⋊C4—21no—
267C11×C22⋊C4—21no—
268C11×C22⋊C4—21no—
269C11×C22⋊C4—21no—
270C11×C22⋊C4—21no—
271C11×C22⋊C4—21no—
272C42×C11—21no—
273C42×C11—21no—
274C42×C11—21no—
275C42×C11—21no—
276C42×C11C2×D411yescharacteristic
277C42×C11C2×D411yescharacteristic
278C42×C11C2×D411yescharacteristic
279C42×C11C2411yescharacteristic
280#3545C2×C1111yescharacteristic
281#3239C2×C1111yescharacteristic, complemented
282#3218C2×C1111yescharacteristic, complemented
283C2×#489C2×C1111yescharacteristic, complemented
284#1664C2×C1112yescomplemented
285#1662C2×C1112yescomplemented
286#1661C2×C1112yescomplemented
287#1659C2×C1112yescomplemented
288#1533C2×C1111yescharacteristic, complemented
289#1532C2×C1111yescharacteristic, complemented
290#1532C2×C1111yescharacteristic, complemented
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—42no—
296C23×C11—81no—
297C23×C11—81no—
298C23×C11—81no—
299C23×C11—81no—
300C23×C11—81no—
301C23×C11#12011yescharacteristic
302Q8×C11—41no—
303Q8×C11—41no—
304Q8×C11—41no—
305Q8×C11—41no—
306Q8×C11—42no—
307Q8×C11—42no—
308Q8×C11—81no—
309Q8×C11—82no—
310Q8×C11—81no—
311D4×C11—41no—
312D4×C11—41no—
313D4×C11—41no—
314D4×C11—41no—
315D4×C11—42no—
316D4×C11—42no—
317D4×C11—81no—
318D4×C11—81no—
319D4×C11—81no—
320D4×C11—81no—
321D4×C11—81no—
322D4×C11—81no—
323D4×C11—81no—
324D4×C11—81no—
325C2×C4×C11—22no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11—81no—
339C2×C4×C11—81no—
340C2×C4×C11—81no—
341C2×C4×C11—81no—
342C2×C4×C11—81no—
343C2×C4×C11—81no—
344C2×C4×C11—81no—
345C2×C4×C11—82no—
346C2×C4×C11#12011yescharacteristic
347C2×C4×C11#12011yescharacteristic
348C2×C4×C11#12011yescharacteristic
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C8×C11—42no—
353C8×C11—42no—
354C8×C11—42no—
355#563C22×C1111yescharacteristic
356#562C22×C1111yescharacteristic
357#562C22×C1111yescharacteristic
358H(3,𝔽4)C22×C1111yescharacteristic
359#555—21no—
360#551—21no—
361#551—21no—
362#551—21no—
363#546—21no—
364#546—21no—
365#542—21no—
366#542—21no—
367#538—21no—
368#538—21no—
369#536—21no—
370#534—21no—
371C2×C4⋊Q8C22×C1111yescharacteristic, complemented
372#529C22×C1111yescharacteristic
373#529C22×C1111yescharacteristic
374C2×#124C22×C1111yescharacteristic
375#501C22×C1112yescomplemented
376#497C22×C1112yescomplemented
377#491C22×C1112yescomplemented
378#489—21no—
379#489—21no—
380#489C22×C1112yes—
381#489C22×C1112yescomplemented
382#489C22×C1112yescomplemented
383#484—21no—
384#481—21no—
385#475—21no—
386#474—21no—
387#462—21no—
388#461—21no—
389#451—21no—
390#448—21no—
391#432C22×C1111yescharacteristic, complemented
392#432C22×C1111yescharacteristic, complemented
393C2×#103—21no—
394C2×#102—21no—
395C2×#97C22×C1111yescharacteristic, complemented
396#330C22×C1112yescomplemented
397#330C22×C1112yescomplemented
398#329C22×C1112yes—
399#329C22×C1112yescomplemented
400#329C22×C1112yescomplemented
401#329C22×C1112yescomplemented
402C22×C11—21no—
403C22×C11—21no—
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×C11—162no—
417C22×C11—162no—
418C22×C11#45512yes—
419C22×C11C2×#12011yescharacteristic
420C4×C11—21no—
421C4×C11—21no—
422C4×C11—21no—
423C4×C11—21no—
424C4×C11—21no—
425C4×C11—21no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—41no—
433C4×C11—41no—
434C4×C11—82no—
435C2×#41—21no—
436C22×Q8—21no—
437C22×Q8D4×C1111yescharacteristic
438C22×D4—21no—
439C22×D4D4×C1111yescharacteristic
440C2×Q16—22no—
441C2×SD16—22no—
442C22×C8—21no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—21no—
446C4⋊Q8—21no—
447C4⋊Q8—21no—
448C4⋊Q8C23×C1112yes—
449#126—21no—
450#126—21no—
451#126—21no—
452#126—21no—
453#126—21no—
454#126—21no—
455#125C23×C1111yescharacteristic
456#125C23×C1111yescharacteristic
457#124—21no—
458#124—21no—
459#124—21no—
460#124—21no—
461#124—21no—
462#124—21no—
463#124—21no—
464#124—21no—
465#124D4×C1111yescharacteristic
466#124D4×C1111yescharacteristic
467#124C23×C1111yescharacteristic
468#124C23×C1111yescharacteristic
469#124C23×C1111yescharacteristic
470#124C23×C1111yescharacteristic
471#123—21no—
472#123—21no—
473#123—21no—
474#123—21no—
475#123—21no—
476#123—21no—
477#123—21no—
478#123—21no—
479#123—21no—
480#123—21no—
481#123—21no—
482#123—21no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8D4×C1111yescharacteristic
492C22⋊Q8D4×C1111yescharacteristic
493#121—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121D4×C1111yescharacteristic
502#121D4×C1111yescharacteristic
503#120—21no—
504#120—21no—
505#120—21no—
506#120—21no—
507#120—21no—
508#120—21no—
509C4×Q8D4×C1111yescharacteristic
510C4×Q8D4×C1111yescharacteristic
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4D4×C1111yescharacteristic
518C4×D4D4×C1111yescharacteristic
519#117—21no—
520#117—21no—
521#117—21no—
522#117—21no—
523#117—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C42C23×C1111yescharacteristic
532#107—22no—
533#106—22no—
534C4⋊C8—21no—
535C4⋊C8—21no—
536#103—22no—
537#103—22no—
538#103—22no—
539#103—22no—
540#103—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544C22⋊C8—21no—
545C22⋊C8—21no—
546#97—21no—
547#97C23×C1112yes—
548#97C23×C1112yes—
549#97C23×C1112yes—
550C2×C11—22no—
551C2×C11—81no—
552C2×C11—81no—
553C2×C11—81no—
554C2×C11—81no—
555C2×C11C2×#45511yescharacteristic
556C2×C11#302111yescharacteristic
557C2×C11#302211yescharacteristic
558C24—21no—
559C24—21no—
560#41—82no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—42no—
565C2×Q8—41no—
566C2×Q8—82no—
567C2×Q8C2×D4×C1111yescharacteristic
568C2×Q8C2×D4×C1111yescharacteristic
569C2×Q8C2×D4×C1111yescharacteristic
570C2×Q8C2×D4×C1111yescharacteristic
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—42no—
582C2×D4—82no—
583C2×D4C2×D4×C1111yescharacteristic
584C2×D4C2×D4×C1111yescharacteristic
585C2×D4C2×D4×C1111yescharacteristic
586C2×D4C2×D4×C1111yescharacteristic
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—41no—
596C22×C4C2×D4×C1111yescharacteristic
597C22×C4C2×D4×C1111yescharacteristic
598C22×C4C2×D4×C1111yescharacteristic
599Q16—82no—
600SD16—82no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—42no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4C2×D4×C1111yescharacteristic
624C4⋊C4C2×D4×C1111yescharacteristic
625C4⋊C4C2×D4×C1111yescharacteristic
626C4⋊C4C2×D4×C1111yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42C2×D4×C1111yescharacteristic
660C42C2×D4×C1111yescharacteristic
661C42C2×D4×C1111yescharacteristic
662C42C24×C1111yescharacteristic
663C11#1905511yescharacteristic, direct product factor, Sylow
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—42no—
669C23—81no—
670C23—81no—
671C23—81no—
672C23—81no—
673C23—81no—
674C23C11×#12011yescharacteristic
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—42no—
680Q8—42no—
681Q8—81no—
682Q8—82no—
683Q8—81no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—42no—
689D4—42no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—81no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—82no—
719C2×C4C11×#12011yescharacteristic
720C2×C4C11×#12011yescharacteristic
721C2×C4C11×#12011yescharacteristic
722C2×C4C22×D4×C1111yescharacteristic
723C2×C4C22×D4×C1111yescharacteristic
724C2×C4C22×D4×C1111yescharacteristic
725C8—42no—
726C8—42no—
727C8—42no—
728C22—21no—
729C22—21no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—162no—
743C22—162no—
744C22C11×#45512yes—
745C22C2×C11×#12011yescharacteristic
746C4—21no—
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—82no—
761C2—22no—
762C2—81no—
763C2—81no—
764C2—81no—
765C2—81no—
766C2C2×C11×#45511yescharacteristic
767C2C11×#302111yescharacteristic
768C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3545C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3239C2semidirect
3. C11×#3218C2semidirect
4. C2×C11×#489C2semidirect
5. C11×#1664C2semidirect
6. C11×#1662C2semidirect
7. C11×#1661C2semidirect
8. C11×#1659C2semidirect
9. C11×#1533C2semidirect
10. C11×#1532C2semidirect
11. C11×#1532C2semidirect
28. C2×C11×C4⋊Q8C22semidirect
32. C11×#501C22semidirect
33. C11×#497C22semidirect
34. C11×#491C22semidirect
38. C11×#489C22semidirect
39. C11×#489C22semidirect
48. C11×#432C22semidirect
49. C11×#432C22semidirect
52. C2×C11×#97C22semidirect
53. C11×#330C22semidirect
54. C11×#330C22semidirect
56. C11×#329C22semidirect
57. C11×#329C22semidirect
58. C11×#329C22semidirect
174. #19055C11direct (N × H)
281. #3239C2×C11semidirect
282. #3218C2×C11semidirect
283. C2×#489C2×C11semidirect
284. #1664C2×C11semidirect
285. #1662C2×C11semidirect
286. #1661C2×C11semidirect
287. #1659C2×C11semidirect
288. #1533C2×C11semidirect
289. #1532C2×C11semidirect
290. #1532C2×C11semidirect
371. C2×C4⋊Q8C22×C11semidirect
375. #501C22×C11semidirect
376. #497C22×C11semidirect
377. #491C22×C11semidirect
381. #489C22×C11semidirect
382. #489C22×C11semidirect
391. #432C22×C11semidirect
392. #432C22×C11semidirect
395. C2×#97C22×C11semidirect
396. #330C22×C11semidirect
397. #330C22×C11semidirect
399. #329C22×C11semidirect
400. #329C22×C11semidirect
401. #329C22×C11semidirect
663. C11#19055direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35452
C11×#32392
C11×#32182
C2×C11×#4892
C11×#16642
C11×#16622
C11×#16612
C11×#16592
C11×#15332
C11×#15322
#1905511