Finite Group Databasebeta

← C11×#24674 #14601867

Subgroups — C11×#24674 #14601867

Order 2816.

796 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3040C211yesmaximal, characteristic, complemented
2C2×C11×#463C211yesmaximal, characteristic, complemented
3C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4C11×#2925C211yesmaximal, characteristic, complemented
5C11×#2052C211yesmaximal, characteristic, complemented
6C11×#2051C211yesmaximal, characteristic, complemented
7C11×#2019C211yesmaximal, characteristic, complemented
8C11×#2018C211yesmaximal, characteristic
9C11×#1978C211yesmaximal, characteristic, complemented
10C11×#1977C211yesmaximal, characteristic, complemented
11C11×#1967C211yesmaximal, characteristic, complemented
12C11×#1950C211yesmaximal, characteristic, complemented
13C11×#1931C211yesmaximal, characteristic, complemented
14C11×#1930C211yesmaximal, characteristic, complemented
15C11×#1800C211yesmaximal, characteristic, complemented
16C2×C11×#137C2211yescharacteristic
17C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
18C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×D8C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C4×C11×#41C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C11×#464—21no—
25C11×#464—21no—
26C11×#463—21no—
27C11×#463—21no—
28C11×#463—21no—
29C11×#463—21no—
30C11×#463—21no—
31C11×#463—21no—
32C11×#442—21no—
33C11×#440—21no—
34C4×C11×SD16—21no—
35C4×C11×D8—21no—
36C11×#433—21no—
37C11×#433—21no—
38C11×#432—21no—
39C11×#431—21no—
40C2×C11×#108C2211yescharacteristic
41C2×C11×#108C2211yescharacteristic
42C11×#428C2211yescharacteristic
43C11×#423C2211yescharacteristic
44C11×#423C2211yescharacteristic
45C2×C11×C4⋊C8C2211yescharacteristic
46C11×#419C2211yescharacteristic
47C11×#418C2211yescharacteristic
48C11×#418C2211yescharacteristic
49C11×#417C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×#101C2211yescharacteristic
53C2×C11×#101C2211yescharacteristic
54C2×C11×#100C2211yescharacteristic
55C2×C11×#100C2211yescharacteristic
56C2×C11×#100C2211yescharacteristic
57C2×C11×#100C2211yescharacteristic
58C11×#408C2211yescharacteristic
59C11×#408C2211yescharacteristic
60C11×#405C2211yescharacteristic
61C11×#405C2211yescharacteristic
62C4×C11×M16C2211yescharacteristic
63C11×#343C2211yescharacteristic
64C11×#343C2211yescharacteristic
65C11×#341C2211yescharacteristic
66C11×#341C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11—21no—
72C11×#137—41no—
73C11×#137—41no—
74C11×AGL(1,ℤ/8)—22no—
75C11×AGL(1,ℤ/8)—22no—
76C11×AGL(1,ℤ/8)—41no—
77C11×AGL(1,ℤ/8)—41no—
78C2×C11×Q16—21no—
79C2×C11×SD16—21no—
80C2×C11×SD16—21no—
81C2×C11×SD16—21no—
82C2×C11×SD16—22no—
83C2×C11×SD16—21no—
84C2×C11×SD16—21no—
85C2×C11×SD16—41no—
86C2×C11×D8—21no—
87C2×C11×D8—21no—
88C2×C11×D8—22no—
89C2×C11×D8—21no—
90C2×C11×D8—21no—
91C2×C11×D8—41no—
92C2×C11×M16C2311yescharacteristic
93C2×C11×M16C2311yescharacteristic
94C2×C11×M16C2311yescharacteristic
95C2×C11×M16C2311yescharacteristic
96C2×C11×M16C2311yescharacteristic
97C2×C11×M16C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C11×#124—21no—
101C11×#124—21no—
102C11×#124—21no—
103C11×#124—21no—
104C4×Q8×C11D411yescharacteristic
105C4×Q8×C11D411yescharacteristic
106C4×D4×C11—21no—
107C4×D4×C11—21no—
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C4×D4×C11—21no—
111C4×D4×C11—21no—
112C4×D4×C11D411yescharacteristic
113C4×D4×C11D411yescharacteristic
114C11×#117—21no—
115C11×#117C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C42×C11—21no—
121C2×C42×C11C2311yescharacteristic
122C11×#108—41no—
123C11×#108—41no—
124C11×#107—21no—
125C11×#106—21no—
126C11×C4⋊C8—21no—
127C11×C4⋊C8—21no—
128C11×C4⋊C8—21no—
129C11×C4⋊C8—21no—
130C11×C4⋊C8D411yescharacteristic
131C11×C4⋊C8D411yescharacteristic
132C11×C4⋊C8D411yescharacteristic
133C11×C4⋊C8D411yescharacteristic
134C11×#103—21no—
135C11×#103—21no—
136C11×#103—21no—
137C11×#103—21no—
138C11×#103—21no—
139C11×#102—21no—
140C11×#102—21no—
141C11×#102—21no—
142C11×#102—21no—
143C11×#102—21no—
144C11×#102—21no—
145C11×#102—21no—
146C11×#101—22no—
147C11×#101—41no—
148C11×#100—22no—
149C11×#100—41no—
150C11×#100—41no—
151C11×#100—41no—
152C11×C22⋊C8—21no—
153C11×C22⋊C8—21no—
154C11×C22⋊C8—21no—
155C11×C22⋊C8—21no—
156C11×#97—21no—
157C11×#97—21no—
158C11×#97—21no—
159C4×C8×C11—21no—
160C4×C8×C11—21no—
161C4×C8×C11—21no—
162#24674C1111yesmaximal, characteristic, direct product factor, Sylow
163C24×C11—21no—
164C24×C11—21no—
165C11×#41—21no—
166C11×#41—21no—
167C11×#41—21no—
168C11×#41—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11C2×D411yescharacteristic
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11C2×D411yescharacteristic
189C2×D4×C11#4112yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—41no—
196C22×C4×C11—41no—
197C22×C4×C11—82no—
198C22×C4×C11#4111yescharacteristic
199C22×C4×C11#4111yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C11×Q16—42no—
202C11×SD16—24no—
203C11×SD16—42no—
204C11×SD16—42no—
205C11×SD16—42no—
206C11×SD16—42no—
207C11×D8—24no—
208C11×D8—42no—
209C11×D8—42no—
210C11×D8—42no—
211C11×M16—21no—
212C11×M16—21no—
213C11×M16—21no—
214C11×M16—21no—
215C11×M16—21no—
216C11×M16—21no—
217C11×M16—21no—
218C11×M16—21no—
219C11×M16—21no—
220C11×M16—21no—
221C11×M16—21no—
222C11×M16#4112yes—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11C2×D411yescharacteristic
234C2×C8×C11C2×D411yescharacteristic
235C2×C8×C11C2×D411yescharacteristic
236C2×C8×C11C2×D411yescharacteristic
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4C2×D411yescharacteristic
242C11×C4⋊C4C2×D411yescharacteristic
243C11×C22⋊C4—21no—
244C11×C22⋊C4—21no—
245C11×C22⋊C4—21no—
246C11×C22⋊C4—41no—
247C11×C22⋊C4—41no—
248C11×C22⋊C4—41no—
249C11×C22⋊C4—41no—
250C11×C22⋊C4—41no—
251C11×C22⋊C4—41no—
252C42×C11—21no—
253C42×C11—21no—
254C42×C11—21no—
255C42×C11C2×D411yescharacteristic
256C42×C11C2×D411yescharacteristic
257C42×C11C2×D411yescharacteristic
258C42×C11C2×D411yescharacteristic
259#3040C2×C1111yescharacteristic, complemented
260C2×#463C2×C1111yescharacteristic, complemented
261C4×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
262#2925C2×C1111yescharacteristic, complemented
263#2052C2×C1111yescharacteristic, complemented
264#2051C2×C1111yescharacteristic, complemented
265#2019C2×C1111yescharacteristic, complemented
266#2018C2×C1111yescharacteristic
267#1978C2×C1111yescharacteristic, complemented
268#1977C2×C1111yescharacteristic, complemented
269#1967C2×C1111yescharacteristic, complemented
270#1950C2×C1111yescharacteristic, complemented
271#1931C2×C1111yescharacteristic, complemented
272#1930C2×C1111yescharacteristic, complemented
273#1800C2×C1111yescharacteristic, complemented
274C23×C11—21no—
275C23×C11—22no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—81no—
282C23×C11—81no—
283C23×C11—81no—
284C23×C11—81no—
285C23×C11C2×#4111yescharacteristic
286Q8×C11—21no—
287Q8×C11—21no—
288Q8×C11—41no—
289Q8×C11—41no—
290Q8×C11—41no—
291Q8×C11—41no—
292D4×C11—21no—
293D4×C11—22no—
294D4×C11—21no—
295D4×C11—22no—
296D4×C11—41no—
297D4×C11—41no—
298D4×C11—41no—
299D4×C11—41no—
300D4×C11—41no—
301D4×C11—41no—
302D4×C11—41no—
303D4×C11—41no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—42no—
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—81no—
317C2×C4×C11—82no—
318C2×C4×C11—82no—
319C2×C4×C11—81no—
320C2×C4×C11#12111yescharacteristic
321C2×C4×C11#12111yescharacteristic
322C2×C4×C11#12111yescharacteristic
323C2×C4×C11#12111yescharacteristic
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11C2×#4111yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C2×C4×C11H(5,𝔽2)11yescharacteristic
330C8×C11—22no—
331C8×C11—21no—
332C8×C11—21no—
333C8×C11—21no—
334C8×C11—21no—
335C8×C11—41no—
336C8×C11—41no—
337C8×C11—41no—
338C8×C11—41no—
339C8×C11—41no—
340C2×#137C22×C1111yescharacteristic
341C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
342C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
343C22×SD16C22×C1111yescharacteristic
344C22×D8C22×C1111yescharacteristic
345C2×#124C22×C1111yescharacteristic
346C4×#41C22×C1111yescharacteristic
347C2×C4×D4C22×C1111yescharacteristic
348#464—21no—
349#464—21no—
350#463—21no—
351#463—21no—
352#463—21no—
353#463—21no—
354#463—21no—
355#463—21no—
356#442—21no—
357#440—21no—
358C4×SD16—21no—
359C4×D8—21no—
360#433—21no—
361#433—21no—
362#432—21no—
363#431—21no—
364C2×#108C22×C1111yescharacteristic
365C2×#108C22×C1111yescharacteristic
366#428C22×C1111yescharacteristic
367#423C22×C1111yescharacteristic
368#423C22×C1111yescharacteristic
369C2×C4⋊C8C22×C1111yescharacteristic
370#419C22×C1111yescharacteristic
371#418C22×C1111yescharacteristic
372#418C22×C1111yescharacteristic
373#417C22×C1111yescharacteristic
374C2×#103C22×C1111yescharacteristic
375C2×#102C22×C1111yescharacteristic
376C2×#101C22×C1111yescharacteristic
377C2×#101C22×C1111yescharacteristic
378C2×#100C22×C1111yescharacteristic
379C2×#100C22×C1111yescharacteristic
380C2×#100C22×C1111yescharacteristic
381C2×#100C22×C1111yescharacteristic
382#408C22×C1111yescharacteristic
383#408C22×C1111yescharacteristic
384#405C22×C1111yescharacteristic
385#405C22×C1111yescharacteristic
386C4×M16C22×C1111yescharacteristic
387#343C22×C1111yescharacteristic
388#343C22×C1111yescharacteristic
389#341C22×C1111yescharacteristic
390#341C22×C1111yescharacteristic
391C22×C11—21no—
392C22×C11—21no—
393C22×C11—41no—
394C22×C11—42no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—82no—
398C22×C11—82no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—161no—
405C22×C11—161no—
406C22×C11C2×#12111yescharacteristic
407C22×C11#55311yescharacteristic
408C22×C11#55511yescharacteristic
409C4×C11—21no—
410C4×C11—21no—
411C4×C11—21no—
412C4×C11—21no—
413C4×C11—41no—
414C4×C11—41no—
415C4×C11—41no—
416C4×C11—81no—
417C4×C11—81no—
418C4×C11#52511yescharacteristic
419C4×C11#53511yescharacteristic
420C4×C11#54611yescharacteristic
421C4×C11#55011yescharacteristic
422C2×#41C23×C1111yescharacteristic
423C22×Q8C23×C1111yescharacteristic
424C22×D4C23×C1111yescharacteristic
425C22×D4C23×C1111yescharacteristic
426C23×C4—21no—
427#137—41no—
428#137—41no—
429AGL(1,ℤ/8)—22no—
430AGL(1,ℤ/8)—22no—
431AGL(1,ℤ/8)—41no—
432AGL(1,ℤ/8)—41no—
433C2×Q16—21no—
434C2×SD16—21no—
435C2×SD16—21no—
436C2×SD16—21no—
437C2×SD16—22no—
438C2×SD16—21no—
439C2×SD16—21no—
440C2×SD16—41no—
441C2×D8—21no—
442C2×D8—21no—
443C2×D8—22no—
444C2×D8—21no—
445C2×D8—21no—
446C2×D8—41no—
447C2×M16C23×C1111yescharacteristic
448C2×M16C23×C1111yescharacteristic
449C2×M16C23×C1111yescharacteristic
450C2×M16C23×C1111yescharacteristic
451C2×M16C23×C1111yescharacteristic
452C2×M16C23×C1111yescharacteristic
453C22×C8C23×C1111yescharacteristic
454C22×C8C23×C1111yescharacteristic
455#124—21no—
456#124—21no—
457#124—21no—
458#124—21no—
459C4×Q8D4×C1111yescharacteristic
460C4×Q8D4×C1111yescharacteristic
461C4×D4—21no—
462C4×D4—21no—
463C4×D4—21no—
464C4×D4—21no—
465C4×D4—21no—
466C4×D4—21no—
467C4×D4D4×C1111yescharacteristic
468C4×D4D4×C1111yescharacteristic
469#117—21no—
470#117C23×C1111yescharacteristic
471C2×C4⋊C4C23×C1111yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C42—21no—
476C2×C42C23×C1111yescharacteristic
477#108—41no—
478#108—41no—
479#107—21no—
480#106—21no—
481C4⋊C8—21no—
482C4⋊C8—21no—
483C4⋊C8—21no—
484C4⋊C8—21no—
485C4⋊C8D4×C1111yescharacteristic
486C4⋊C8D4×C1111yescharacteristic
487C4⋊C8D4×C1111yescharacteristic
488C4⋊C8D4×C1111yescharacteristic
489#103—21no—
490#103—21no—
491#103—21no—
492#103—21no—
493#103—21no—
494#102—21no—
495#102—21no—
496#102—21no—
497#102—21no—
498#102—21no—
499#102—21no—
500#102—21no—
501#101—22no—
502#101—41no—
503#100—22no—
504#100—41no—
505#100—41no—
506#100—41no—
507C22⋊C8—21no—
508C22⋊C8—21no—
509C22⋊C8—21no—
510C22⋊C8—21no—
511#97—21no—
512#97—21no—
513#97—21no—
514C4×C8—21no—
515C4×C8—21no—
516C4×C8—21no—
517C2×C11—21no—
518C2×C11—21no—
519C2×C11—81no—
520C2×C11—82no—
521C2×C11—161no—
522C2×C11#241411yescharacteristic
523C2×C11#306711yescharacteristic
524C2×C11#306811yescharacteristic
525C24—21no—
526C24—21no—
527#41—21no—
528#41—21no—
529#41—21no—
530#41—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8C2×D4×C1111yescharacteristic
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
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×D4C2×D4×C1111yescharacteristic
551C2×D4C11×#4112yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—82no—
560C22×C4C11×#4111yescharacteristic
561C22×C4C11×#4111yescharacteristic
562C22×C4C24×C1111yescharacteristic
563Q16—42no—
564SD16—24no—
565SD16—42no—
566SD16—42no—
567SD16—42no—
568SD16—42no—
569D8—24no—
570D8—42no—
571D8—42no—
572D8—42no—
573M16—21no—
574M16—21no—
575M16—21no—
576M16—21no—
577M16—21no—
578M16—21no—
579M16—21no—
580M16—21no—
581M16—21no—
582M16—21no—
583M16—21no—
584M16C11×#4112yes—
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×C8—21no—
594C2×C8—21no—
595C2×C8C2×D4×C1111yescharacteristic
596C2×C8C2×D4×C1111yescharacteristic
597C2×C8C2×D4×C1111yescharacteristic
598C2×C8C2×D4×C1111yescharacteristic
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4C2×D4×C1111yescharacteristic
604C4⋊C4C2×D4×C1111yescharacteristic
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42C2×D4×C1111yescharacteristic
618C42C2×D4×C1111yescharacteristic
619C42C2×D4×C1111yescharacteristic
620C42C2×D4×C1111yescharacteristic
621C11#2467411yescharacteristic, direct product factor, Sylow
622C23—21no—
623C23—22no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23C2×C11×#4111yescharacteristic
634Q8—21no—
635Q8—21no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640D4—21no—
641D4—22no—
642D4—21no—
643D4—22no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—81no—
665C2×C4—82no—
666C2×C4—82no—
667C2×C4—81no—
668C2×C4C11×#12111yescharacteristic
669C2×C4C11×#12111yescharacteristic
670C2×C4C11×#12111yescharacteristic
671C2×C4C11×#12111yescharacteristic
672C2×C4C22×D4×C1111yescharacteristic
673C2×C4C22×D4×C1111yescharacteristic
674C2×C4C2×C11×#4111yescharacteristic
675C2×C4C2×C11×#4111yescharacteristic
676C2×C4C11×H(5,𝔽2)11yescharacteristic
677C2×C4C11×H(5,𝔽2)11yescharacteristic
678C8—22no—
679C8—21no—
680C8—21no—
681C8—21no—
682C8—21no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C22—21no—
689C22—21no—
690C22—41no—
691C22—42no—
692C22—41no—
693C22—41no—
694C22—82no—
695C22—82no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—161no—
702C22—161no—
703C22C2×C11×#12111yescharacteristic
704C22C11×#55311yescharacteristic
705C22C11×#55511yescharacteristic
706C4—21no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—81no—
714C4—81no—
715C4C11×#52511yescharacteristic
716C4C11×#53511yescharacteristic
717C4C11×#54611yescharacteristic
718C4C11×#55011yescharacteristic
719C2—21no—
720C2—21no—
721C2—81no—
722C2—82no—
723C2—161no—
724C2C11×#241411yescharacteristic
725C2C11×#306711yescharacteristic
726C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2018C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3040C2semidirect
2. C2×C11×#463C2semidirect
3. C4×C11×AGL(1,ℤ/8)C2semidirect
4. C11×#2925C2semidirect
5. C11×#2052C2semidirect
6. C11×#2051C2semidirect
7. C11×#2019C2semidirect
9. C11×#1978C2semidirect
10. C11×#1977C2semidirect
11. C11×#1967C2semidirect
12. C11×#1950C2semidirect
13. C11×#1931C2semidirect
14. C11×#1930C2semidirect
15. C11×#1800C2semidirect
162. #24674C11direct (N × H)
259. #3040C2×C11semidirect
260. C2×#463C2×C11semidirect
261. C4×AGL(1,ℤ/8)C2×C11semidirect
262. #2925C2×C11semidirect
263. #2052C2×C11semidirect
264. #2051C2×C11semidirect
265. #2019C2×C11semidirect
267. #1978C2×C11semidirect
268. #1977C2×C11semidirect
269. #1967C2×C11semidirect
270. #1950C2×C11semidirect
271. #1931C2×C11semidirect
272. #1930C2×C11semidirect
273. #1800C2×C11semidirect
621. C11#24674direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30402
C2×C11×#4632
C4×C11×AGL(1,ℤ/8)2
C11×#29252
C11×#20522
C11×#20512
C11×#20192
C11×#20182
C11×#19782
C11×#19772
C11×#19672
C11×#19502
C11×#19312
C11×#19302
C11×#18002
#2467411