Finite Group Databasebeta

← C11×#24283 #14601476

Subgroups — C11×#24283 #14601476

Order 2816.

1304 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#137C211yesmaximal, characteristic, complemented
2C2×C11×#473C211yesmaximal, characteristic, complemented
3C2×C11×#471C211yesmaximal, characteristic, complemented
4C11×#3005C211yesmaximal, characteristic
5C11×#3004C211yesmaximal, characteristic, complemented
6C11×#2930C211yesmaximal, characteristic, complemented
7C11×#2047C211yesmaximal, characteristic, complemented
8C11×#2046C211yesmaximal, characteristic, complemented
9C11×#2020C211yesmaximal, characteristic, complemented
10C11×#2019C211yesmaximal, characteristic, complemented
11C11×#1979C211yesmaximal, characteristic, complemented
12C11×#1977C211yesmaximal, characteristic, complemented
13C11×#1811C211yesmaximal, characteristic, complemented
14C11×#1785C211yesmaximal, characteristic, complemented
15C11×#1784C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C2×C11×#137—24no—
19C2×C11×#137—24no—
20C2×C11×#137—22no—
21C2×C11×#137—22no—
22C2×C11×#137C2211yescharacteristic
23C2×C11×#137C2211yescharacteristic
24C2×C11×#137C2211yescharacteristic
25C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
26C22×C11×Q16C2211yescharacteristic
27C22×C11×Q16C2211yescharacteristic
28C22×C11×SD16C2211yescharacteristic
29C22×C11×SD16C2211yescharacteristic
30C2×C11×#131C2211yescharacteristic
31C22×C11×M16C2211yescharacteristic
32C11×#525C2211yescharacteristic
33C11×#473—24no—
34C11×#471—24no—
35C11×#452—22no—
36C11×#451—22no—
37C11×#449—22no—
38C11×#448—22no—
39C11×#436—22no—
40C11×#435—22no—
41C2×C11×#108C2211yescharacteristic
42C2×C11×#108C2211yescharacteristic
43C11×#424C2211yescharacteristic
44C11×#419C2211yescharacteristic
45C11×#419C2211yescharacteristic
46C11×#419C2211yescharacteristic
47C11×#418C2211yescharacteristic
48C2×C11×#101C2211yescharacteristic
49C2×C11×#101C2211yescharacteristic
50C2×C11×#101C2211yescharacteristic
51C2×C11×#101C2211yescharacteristic
52C2×C11×#101C2211yescharacteristic
53C2×C11×#101C2211yescharacteristic
54C2×C11×#100C2211yescharacteristic
55C2×C11×#100C2211yescharacteristic
56C11×#408C2211yescharacteristic
57C11×#407C2211yescharacteristic
58C11×#407C2211yescharacteristic
59C11×#407C2211yescharacteristic
60C11×#405C2211yescharacteristic
61C11×#341C2211yescharacteristic
62C11×#341C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C2×C11×#41C2311yescharacteristic
70C22×Q8×C11—21no—
71C22×Q8×C11—22no—
72C22×Q8×C11—22no—
73C22×Q8×C11—22no—
74C22×Q8×C11—22no—
75C22×Q8×C11—41no—
76C22×Q8×C11—41no—
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C23×C4×C11—21no—
84C23×C4×C11C2311yescharacteristic
85C11×#137—216no—
86C11×#137—216no—
87C11×#137—22no—
88C11×#137—22no—
89C11×#137—22no—
90C11×#137—41no—
91C11×#137—41no—
92C11×#137—41no—
93C11×AGL(1,ℤ/8)—22no—
94C11×AGL(1,ℤ/8)—41no—
95C2×C11×Q16—22no—
96C2×C11×Q16—22no—
97C2×C11×Q16—21no—
98C2×C11×Q16—21no—
99C2×C11×Q16—21no—
100C2×C11×Q16—22no—
101C2×C11×Q16—21no—
102C2×C11×Q16—21no—
103C2×C11×Q16—22no—
104C2×C11×Q16D414yescomplemented
105C2×C11×SD16—22no—
106C2×C11×SD16—22no—
107C2×C11×SD16—21no—
108C2×C11×SD16—21no—
109C2×C11×SD16—21no—
110C2×C11×SD16—21no—
111C2×C11×SD16—22no—
112C2×C11×SD16—21no—
113C2×C11×SD16—21no—
114C2×C11×SD16—22no—
115C2×C11×SD16D414yescomplemented
116C2×C11×D8—21no—
117C11×#131—22no—
118C11×#131—22no—
119C2×C11×M16—22no—
120C2×C11×M16—22no—
121C2×C11×M16—21no—
122C2×C11×M16D412yes—
123C2×C11×M16D412yes—
124C2×C11×M16C2311yescharacteristic
125C2×C11×M16C2311yescharacteristic
126C2×C11×M16C2311yescharacteristic
127C2×C11×M16C2311yescharacteristic
128C2×C11×M16C2311yescharacteristic
129C2×C11×M16C2311yescharacteristic
130C22×C8×C11—21no—
131C22×C8×C11C2311yescharacteristic
132C22×C8×C11C2311yescharacteristic
133C11×#123—21no—
134C11×C22⋊Q8D412yes—
135C11×#121D412yes—
136C11×#120—21no—
137C4×D4×C11—22no—
138C11×#117C2311yescharacteristic
139C11×#108—22no—
140C11×#108—22no—
141C11×C4⋊C8—22no—
142C11×#103—22no—
143C11×#103—22no—
144C11×#103—22no—
145C11×#102—22no—
146C11×#101—22no—
147C11×#101—22no—
148C11×#101—22no—
149C11×#101—41no—
150C11×#101—41no—
151C11×#101—41no—
152C11×#100—22no—
153C11×#100—41no—
154C11×C22⋊C8—22no—
155C11×C22⋊C8—22no—
156C11×C22⋊C8—22no—
157C11×C22⋊C8—22no—
158C11×#97—21no—
159C4×C8×C11—21no—
160#24283C1111yesmaximal, characteristic, direct product factor, Sylow
161C24×C11—21no—
162C24×C11#4111yescharacteristic
163C11×#41—28no—
164C11×#41—21no—
165C11×#41—21no—
166C11×#41—21no—
167C11×#41—21no—
168C11×#41—44no—
169C11×#41—44no—
170C11×#41—44no—
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—28no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—42no—
188C2×Q8×C11—42no—
189C2×Q8×C11—44no—
190C2×Q8×C11—44no—
191C2×Q8×C11—44no—
192C2×Q8×C11—42no—
193C2×Q8×C11C2×D412yes—
194C2×Q8×C11C2×D412yes—
195C2×Q8×C11C2×D412yes—
196C2×Q8×C11C2×D411yescharacteristic
197C2×D4×C11—21no—
198C2×D4×C11—22no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—21no—
203C2×D4×C11—21no—
204C2×D4×C11—42no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11C2×D412yes—
208C2×D4×C11C2×D411yescharacteristic
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—42no—
218C22×C4×C11—42no—
219C22×C4×C11—42no—
220C22×C4×C11—42no—
221C22×C4×C11—42no—
222C22×C4×C11—42no—
223C22×C4×C11C2×D412yes—
224C22×C4×C11C2×D412yes—
225C22×C4×C11#4111yescharacteristic
226C22×C4×C11C2411yescharacteristic
227C11×Q16—28no—
228C11×Q16—24no—
229C11×Q16—24no—
230C11×Q16—42no—
231C11×Q16—42no—
232C11×Q16—42no—
233C11×SD16—28no—
234C11×SD16—24no—
235C11×SD16—24no—
236C11×SD16—42no—
237C11×SD16—42no—
238C11×SD16—42no—
239C11×SD16—42no—
240C11×D8—42no—
241C11×M16—24no—
242C11×M16—24no—
243C11×M16—21no—
244C11×M16—21no—
245C11×M16—21no—
246C11×M16—21no—
247C11×M16—21no—
248C11×M16—21no—
249C11×M16—21no—
250C11×M16—21no—
251C11×M16—21no—
252C11×M16—21no—
253C11×M16—21no—
254C11×M16—21no—
255C11×M16—42no—
256C2×C8×C11—21no—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—42no—
265C2×C8×C11C2×D412yes—
266C2×C8×C11C2×D411yescharacteristic
267C2×C8×C11C2×D411yescharacteristic
268C2×C8×C11C2×D412yes—
269C2×C8×C11C2×D412yes—
270C11×C4⋊C4—22no—
271C11×C4⋊C4C2×D412yes—
272C11×C22⋊C4—22no—
273C11×C22⋊C4—21no—
274C11×C22⋊C4—22no—
275C42×C11—21no—
276C22×#137C2×C1111yescharacteristic, complemented
277C2×#473C2×C1111yescharacteristic, complemented
278C2×#471C2×C1111yescharacteristic, complemented
279#3005C2×C1111yescharacteristic
280#3004C2×C1111yescharacteristic, complemented
281#2930C2×C1111yescharacteristic, complemented
282#2047C2×C1111yescharacteristic, complemented
283#2046C2×C1111yescharacteristic, complemented
284#2020C2×C1111yescharacteristic, complemented
285#2019C2×C1111yescharacteristic, complemented
286#1979C2×C1111yescharacteristic, complemented
287#1977C2×C1111yescharacteristic, complemented
288#1811C2×C1111yescharacteristic, complemented
289#1785C2×C1111yescharacteristic, complemented
290#1784C2×C1111yescharacteristic, complemented
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—22no—
295C23×C11—42no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—82no—
299C23×C11#12112yes—
300C23×C11C2×#4111yescharacteristic
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—21no—
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11—21no—
309Q8×C11—48no—
310Q8×C11—41no—
311Q8×C11—41no—
312Q8×C11—41no—
313Q8×C11—41no—
314Q8×C11—41no—
315Q8×C11—41no—
316D4×C11—22no—
317D4×C11—21no—
318D4×C11—22no—
319D4×C11—21no—
320D4×C11—48no—
321D4×C11—41no—
322D4×C11—41no—
323D4×C11—41no—
324D4×C11—41no—
325D4×C11—82no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—21no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—48no—
338C2×C4×C11—48no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11#12112yes—
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11H(5,𝔽2)11yescharacteristic
353C2×C4×C11H(5,𝔽2)11yescharacteristic
354C8×C11—22no—
355C8×C11—41no—
356C8×C11—41no—
357C8×C11—41no—
358C8×C11—41no—
359C8×C11—41no—
360C8×C11—41no—
361C8×C11#12012yes—
362C8×C11#12012yes—
363C22×#41C22×C1111yescharacteristic
364C23×Q8C22×C1111yescharacteristic
365C2×#137—24no—
366C2×#137—24no—
367C2×#137—22no—
368C2×#137—22no—
369C2×#137C22×C1111yescharacteristic
370C2×#137C22×C1111yescharacteristic
371C2×#137C22×C1111yescharacteristic
372C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
373C22×Q16C22×C1111yescharacteristic
374C22×Q16C22×C1111yescharacteristic
375C22×SD16C22×C1111yescharacteristic
376C22×SD16C22×C1111yescharacteristic
377C2×#131C22×C1111yescharacteristic
378C22×M16C22×C1111yescharacteristic
379#525C22×C1111yescharacteristic
380#473—24no—
381#471—24no—
382#452—22no—
383#451—22no—
384#449—22no—
385#448—22no—
386#436—22no—
387#435—22no—
388C2×#108C22×C1111yescharacteristic
389C2×#108C22×C1111yescharacteristic
390#424C22×C1111yescharacteristic
391#419C22×C1111yescharacteristic
392#419C22×C1111yescharacteristic
393#419C22×C1111yescharacteristic
394#418C22×C1111yescharacteristic
395C2×#101C22×C1111yescharacteristic
396C2×#101C22×C1111yescharacteristic
397C2×#101C22×C1111yescharacteristic
398C2×#101C22×C1111yescharacteristic
399C2×#101C22×C1111yescharacteristic
400C2×#101C22×C1111yescharacteristic
401C2×#100C22×C1111yescharacteristic
402C2×#100C22×C1111yescharacteristic
403#408C22×C1111yescharacteristic
404#407C22×C1111yescharacteristic
405#407C22×C1111yescharacteristic
406#407C22×C1111yescharacteristic
407#405C22×C1111yescharacteristic
408#341C22×C1111yescharacteristic
409#341C22×C1111yescharacteristic
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—41no—
418C22×C11—42no—
419C22×C11—82no—
420C22×C11—82no—
421C22×C11—82no—
422C22×C11C2×#12111yescharacteristic
423C22×C11#54611yescharacteristic
424C22×C11#54611yescharacteristic
425C4×C11—22no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11—41no—
430C4×C11—42no—
431C4×C11C2×#12011yescharacteristic
432C4×C11#53511yescharacteristic
433C4×C11D4211yescharacteristic
434C4×C11D4211yescharacteristic
435C2×#41—22no—
436C2×#41—22no—
437C2×#41—22no—
438C2×#41—22no—
439C2×#41—41no—
440C2×#41—41no—
441C2×#41C23×C1111yescharacteristic
442C22×Q8—21no—
443C22×Q8—22no—
444C22×Q8—22no—
445C22×Q8—22no—
446C22×Q8—22no—
447C22×Q8—41no—
448C22×Q8—41no—
449C22×Q8C23×C1111yescharacteristic
450C22×Q8C23×C1111yescharacteristic
451C22×Q8C23×C1111yescharacteristic
452C22×D4—21no—
453C22×D4C23×C1111yescharacteristic
454C23×C4—21no—
455C23×C4—21no—
456C23×C4C23×C1111yescharacteristic
457#137—216no—
458#137—216no—
459#137—22no—
460#137—22no—
461#137—22no—
462#137—41no—
463#137—41no—
464#137—41no—
465AGL(1,ℤ/8)—22no—
466AGL(1,ℤ/8)—41no—
467C2×Q16—22no—
468C2×Q16—22no—
469C2×Q16—21no—
470C2×Q16—21no—
471C2×Q16—21no—
472C2×Q16—22no—
473C2×Q16—21no—
474C2×Q16—21no—
475C2×Q16—22no—
476C2×Q16D4×C1114yescomplemented
477C2×SD16—22no—
478C2×SD16—22no—
479C2×SD16—21no—
480C2×SD16—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×SD16—22no—
484C2×SD16—21no—
485C2×SD16—21no—
486C2×SD16—22no—
487C2×SD16D4×C1114yescomplemented
488C2×D8—21no—
489#131—22no—
490#131—22no—
491C2×M16—22no—
492C2×M16—22no—
493C2×M16—21no—
494C2×M16D4×C1112yes—
495C2×M16D4×C1112yes—
496C2×M16C23×C1111yescharacteristic
497C2×M16C23×C1111yescharacteristic
498C2×M16C23×C1111yescharacteristic
499C2×M16C23×C1111yescharacteristic
500C2×M16C23×C1111yescharacteristic
501C2×M16C23×C1111yescharacteristic
502C22×C8—21no—
503C22×C8C23×C1111yescharacteristic
504C22×C8C23×C1111yescharacteristic
505#123—21no—
506C22⋊Q8D4×C1112yes—
507#121D4×C1112yes—
508#120—21no—
509C4×D4—22no—
510#117C23×C1111yescharacteristic
511#108—22no—
512#108—22no—
513C4⋊C8—22no—
514#103—22no—
515#103—22no—
516#103—22no—
517#102—22no—
518#101—22no—
519#101—22no—
520#101—22no—
521#101—41no—
522#101—41no—
523#101—41no—
524#100—22no—
525#100—41no—
526C22⋊C8—22no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—22no—
530#97—21no—
531C4×C8—21no—
532C2×C11—21no—
533C2×C11—21no—
534C2×C11—42no—
535C2×C11—81no—
536C2×C11—82no—
537C2×C11#240811yescharacteristic
538C2×C11#306912yes—
539C24—21no—
540C24C11×#4111yescharacteristic
541#41—28no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—44no—
547#41—44no—
548#41—44no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—28no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—42no—
566C2×Q8—42no—
567C2×Q8—44no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—42no—
571C2×Q8C2×D4×C1112yes—
572C2×Q8C2×D4×C1112yes—
573C2×Q8C2×D4×C1112yes—
574C2×Q8C2×D4×C1111yescharacteristic
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4C2×D4×C1112yes—
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—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4C2×D4×C1112yes—
602C22×C4C2×D4×C1112yes—
603C22×C4C11×#4111yescharacteristic
604C22×C4C24×C1111yescharacteristic
605Q16—28no—
606Q16—24no—
607Q16—24no—
608Q16—42no—
609Q16—42no—
610Q16—42no—
611SD16—28no—
612SD16—24no—
613SD16—24no—
614SD16—42no—
615SD16—42no—
616SD16—42no—
617SD16—42no—
618D8—42no—
619M16—24no—
620M16—24no—
621M16—21no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—21no—
633M16—42no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—42no—
643C2×C8C2×D4×C1112yes—
644C2×C8C2×D4×C1111yescharacteristic
645C2×C8C2×D4×C1111yescharacteristic
646C2×C8C2×D4×C1112yes—
647C2×C8C2×D4×C1112yes—
648C4⋊C4—22no—
649C4⋊C4C2×D4×C1112yes—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C42—21no—
654C11#2428311yescharacteristic, direct product factor, Sylow
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—82no—
663C23C11×#12112yes—
664C23C2×C11×#4111yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—21no—
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—21no—
673Q8—48no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680D4—22no—
681D4—21no—
682D4—22no—
683D4—21no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—82no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—48no—
702C2×C4—48no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4C11×#12112yes—
712C2×C4C22×D4×C1111yescharacteristic
713C2×C4C22×D4×C1111yescharacteristic
714C2×C4C22×D4×C1111yescharacteristic
715C2×C4C22×D4×C1111yescharacteristic
716C2×C4C11×H(5,𝔽2)11yescharacteristic
717C2×C4C11×H(5,𝔽2)11yescharacteristic
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C8C11×#12012yes—
726C8C11×#12012yes—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22C2×C11×#12111yescharacteristic
740C22C11×#54611yescharacteristic
741C22C11×#54611yescharacteristic
742C4—22no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—41no—
747C4—42no—
748C4C2×C11×#12011yescharacteristic
749C4C11×#53511yescharacteristic
750C4D42×C1111yescharacteristic
751C4D42×C1111yescharacteristic
752C2—21no—
753C2—21no—
754C2—42no—
755C2—81no—
756C2—82no—
757C2C11×#240811yescharacteristic
758C2C11×#306912yes—
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3005C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#137C2semidirect
2. C2×C11×#473C2semidirect
3. C2×C11×#471C2semidirect
5. C11×#3004C2semidirect
6. C11×#2930C2semidirect
7. C11×#2047C2semidirect
8. C11×#2046C2semidirect
9. C11×#2020C2semidirect
10. C11×#2019C2semidirect
11. C11×#1979C2semidirect
12. C11×#1977C2semidirect
13. C11×#1811C2semidirect
14. C11×#1785C2semidirect
15. C11×#1784C2semidirect
104. C2×C11×Q16D4semidirect
115. C2×C11×SD16D4semidirect
160. #24283C11direct (N × H)
276. C22×#137C2×C11semidirect
277. C2×#473C2×C11semidirect
278. C2×#471C2×C11semidirect
280. #3004C2×C11semidirect
281. #2930C2×C11semidirect
282. #2047C2×C11semidirect
283. #2046C2×C11semidirect
284. #2020C2×C11semidirect
285. #2019C2×C11semidirect
286. #1979C2×C11semidirect
287. #1977C2×C11semidirect
288. #1811C2×C11semidirect
289. #1785C2×C11semidirect
290. #1784C2×C11semidirect
476. C2×Q16D4×C11semidirect
487. C2×SD16D4×C11semidirect
654. C11#24283direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1372
C2×C11×#4732
C2×C11×#4712
C11×#30052
C11×#30042
C11×#29302
C11×#20472
C11×#20462
C11×#20202
C11×#20192
C11×#19792
C11×#19772
C11×#18112
C11×#17852
C11×#17842
#2428311