Finite Group Databasebeta

← C11×#24284 #14601477

Subgroups — C11×#24284 #14601477

Order 2816.

1432 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×C11×#472C211yesmaximal, characteristic, complemented
3C2×C11×#471C211yesmaximal, characteristic, complemented
4C11×#3005C211yesmaximal, characteristic, complemented
5C11×#3003C211yesmaximal, characteristic, complemented
6C11×#2930C211yesmaximal, characteristic, complemented
7C11×#2046C211yesmaximal, characteristic, complemented
8C11×#2045C211yesmaximal, characteristic, complemented
9C11×#2019C211yesmaximal, characteristic, complemented
10C11×#2018C211yesmaximal, characteristic, complemented
11C11×#1978C211yesmaximal, characteristic, complemented
12C11×#1977C211yesmaximal, characteristic, complemented
13C11×#1811C211yesmaximal, characteristic, complemented
14C11×#1785C211yesmaximal, characteristic, complemented
15C11×#1783C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C2×C11×#137C2211yescharacteristic, complemented
19C2×C11×AGL(1,ℤ/8)—24no—
20C2×C11×AGL(1,ℤ/8)—24no—
21C2×C11×AGL(1,ℤ/8)—22no—
22C2×C11×AGL(1,ℤ/8)—22no—
23C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
24C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
25C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
26C22×C11×SD16C2211yescharacteristic
27C22×C11×SD16C2211yescharacteristic
28C22×C11×D8C2211yescharacteristic
29C22×C11×D8C2211yescharacteristic
30C2×C11×#131C2211yescharacteristic, complemented
31C22×C11×M16C2211yescharacteristic
32C11×#525C2211yescharacteristic
33C11×#472—24no—
34C11×#471—24no—
35C11×#452—22no—
36C11×#450—22no—
37C11×#449—22no—
38C11×#447—22no—
39C11×#436—22no—
40C11×#435—22no—
41C2×C11×#108C2211yescharacteristic, complemented
42C2×C11×#108C2211yescharacteristic, complemented
43C11×#424C2211yescharacteristic, complemented
44C11×#419C2211yescharacteristic, complemented
45C11×#418C2211yescharacteristic
46C11×#418C2211yescharacteristic
47C11×#418C2211yescharacteristic, complemented
48C2×C11×#101C2211yescharacteristic, complemented
49C2×C11×#101C2211yescharacteristic, complemented
50C2×C11×#100C2211yescharacteristic
51C2×C11×#100C2211yescharacteristic
52C2×C11×#100C2211yescharacteristic
53C2×C11×#100C2211yescharacteristic
54C2×C11×#100C2211yescharacteristic, complemented
55C2×C11×#100C2211yescharacteristic, complemented
56C11×#408C2211yescharacteristic, complemented
57C11×#407C2211yescharacteristic
58C11×#407C2211yescharacteristic
59C11×#407C2211yescharacteristic
60C11×#405C2211yescharacteristic, complemented
61C11×#341C2211yescharacteristic, complemented
62C11×#341C2211yescharacteristic, complemented
63C25×C11—21no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C2×C11×#41C2311yescharacteristic
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11—22no—
73C22×D4×C11—22no—
74C22×D4×C11—21no—
75C22×D4×C11—22no—
76C22×D4×C11—22no—
77C22×D4×C11—21no—
78C22×D4×C11—41no—
79C22×D4×C11—41no—
80C22×D4×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11C2311yescharacteristic
85C11×#137—22no—
86C11×#137—41no—
87C11×AGL(1,ℤ/8)—216no—
88C11×AGL(1,ℤ/8)—216no—
89C11×AGL(1,ℤ/8)—22no—
90C11×AGL(1,ℤ/8)—22no—
91C11×AGL(1,ℤ/8)—22no—
92C11×AGL(1,ℤ/8)—41no—
93C11×AGL(1,ℤ/8)—41no—
94C11×AGL(1,ℤ/8)—41no—
95C2×C11×Q16—21no—
96C2×C11×SD16—22no—
97C2×C11×SD16—22no—
98C2×C11×SD16—21no—
99C2×C11×SD16—21no—
100C2×C11×SD16—21no—
101C2×C11×SD16—21no—
102C2×C11×SD16—22no—
103C2×C11×SD16—21no—
104C2×C11×SD16—21no—
105C2×C11×SD16—22no—
106C2×C11×SD16D414yescomplemented
107C2×C11×D8—22no—
108C2×C11×D8—22no—
109C2×C11×D8—21no—
110C2×C11×D8—21no—
111C2×C11×D8—21no—
112C2×C11×D8—22no—
113C2×C11×D8—21no—
114C2×C11×D8—21no—
115C2×C11×D8—22no—
116C2×C11×D8D414yescomplemented
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×#102—22no—
144C11×#102—22no—
145C11×#102—22no—
146C11×#101—22no—
147C11×#101—41no—
148C11×#100—22no—
149C11×#100—22no—
150C11×#100—22no—
151C11×#100—41no—
152C11×#100—41no—
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#24284C1111yesmaximal, characteristic, direct product factor, Sylow
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—42no—
165C24×C11—42no—
166C24×C11—42no—
167C24×C11—84no—
168C24×C11#4111yescharacteristic
169C11×#41—28no—
170C11×#41—21no—
171C11×#41—21no—
172C11×#41—21no—
173C11×#41—21no—
174C11×#41—44no—
175C11×#41—44no—
176C11×#41—44no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11C2×D412yes—
183C2×Q8×C11C2×D411yescharacteristic
184C2×D4×C11—28no—
185C2×D4×C11—21no—
186C2×D4×C11—22no—
187C2×D4×C11—21no—
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—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—44no—
203C2×D4×C11—44no—
204C2×D4×C11—42no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11—44no—
208C2×D4×C11—42no—
209C2×D4×C11—42no—
210C2×D4×C11—42no—
211C2×D4×C11C2×D412yes—
212C2×D4×C11C2×D412yes—
213C2×D4×C11C2×D412yes—
214C2×D4×C11C2×D411yescharacteristic
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—42no—
222C22×C4×C11—42no—
223C22×C4×C11—42no—
224C22×C4×C11C2×D412yes—
225C22×C4×C11C2×D412yes—
226C22×C4×C11#4111yescharacteristic
227C22×C4×C11C2411yescharacteristic
228C11×Q16—42no—
229C11×SD16—28no—
230C11×SD16—24no—
231C11×SD16—24no—
232C11×SD16—42no—
233C11×SD16—42no—
234C11×SD16—42no—
235C11×SD16—42no—
236C11×D8—28no—
237C11×D8—24no—
238C11×D8—24no—
239C11×D8—42no—
240C11×D8—42no—
241C11×D8—42no—
242C11×M16—24no—
243C11×M16—24no—
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—21no—
256C11×M16—42no—
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—21no—
265C2×C8×C11—42no—
266C2×C8×C11C2×D412yes—
267C2×C8×C11C2×D411yescharacteristic
268C2×C8×C11C2×D411yescharacteristic
269C2×C8×C11C2×D412yes—
270C2×C8×C11C2×D412yes—
271C11×C4⋊C4—22no—
272C11×C4⋊C4C2×D412yes—
273C11×C22⋊C4—22no—
274C11×C22⋊C4—21no—
275C11×C22⋊C4—22no—
276C42×C11—21no—
277C22×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
278C2×#472C2×C1111yescharacteristic, complemented
279C2×#471C2×C1111yescharacteristic, complemented
280#3005C2×C1111yescharacteristic, complemented
281#3003C2×C1111yescharacteristic, complemented
282#2930C2×C1111yescharacteristic, complemented
283#2046C2×C1111yescharacteristic, complemented
284#2045C2×C1111yescharacteristic, complemented
285#2019C2×C1111yescharacteristic, complemented
286#2018C2×C1111yescharacteristic, complemented
287#1978C2×C1111yescharacteristic, complemented
288#1977C2×C1111yescharacteristic, complemented
289#1811C2×C1111yescharacteristic, complemented
290#1785C2×C1111yescharacteristic, complemented
291#1783C2×C1111yescharacteristic, complemented
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—42no—
299C23×C11—48no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—82no—
307C23×C11—82no—
308C23×C11—82no—
309C23×C11—84no—
310C23×C11—84no—
311C23×C11—88no—
312C23×C11—88no—
313C23×C11#12112yes—
314C23×C11C2×#4111yescharacteristic
315Q8×C11—22no—
316Q8×C11—21no—
317Q8×C11—21no—
318Q8×C11—22no—
319Q8×C11—41no—
320Q8×C11—41no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—22no—
324D4×C11—21no—
325D4×C11—21no—
326D4×C11—22no—
327D4×C11—22no—
328D4×C11—22no—
329D4×C11—48no—
330D4×C11—48no—
331D4×C11—41no—
332D4×C11—41no—
333D4×C11—41no—
334D4×C11—41no—
335D4×C11—41no—
336D4×C11—41no—
337D4×C11—41no—
338D4×C11—41no—
339D4×C11—82no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—21no—
348C2×C4×C11—22no—
349C2×C4×C11—48no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11#12112yes—
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C2×C4×C11H(5,𝔽2)11yescharacteristic
361C8×C11—22no—
362C8×C11—41no—
363C8×C11—41no—
364C8×C11—41no—
365C8×C11—41no—
366C8×C11—41no—
367C8×C11—41no—
368C8×C11#12012yes—
369C8×C11#12012yes—
370C22×#41C22×C1111yescharacteristic
371C23×D4C22×C1111yescharacteristic
372C2×#137C22×C1111yescharacteristic, complemented
373C2×AGL(1,ℤ/8)—24no—
374C2×AGL(1,ℤ/8)—24no—
375C2×AGL(1,ℤ/8)—22no—
376C2×AGL(1,ℤ/8)—22no—
377C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
378C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
379C2×AGL(1,ℤ/8)C22×C1111yescharacteristic, complemented
380C22×SD16C22×C1111yescharacteristic
381C22×SD16C22×C1111yescharacteristic
382C22×D8C22×C1111yescharacteristic
383C22×D8C22×C1111yescharacteristic
384C2×#131C22×C1111yescharacteristic, complemented
385C22×M16C22×C1111yescharacteristic
386#525C22×C1111yescharacteristic
387#472—24no—
388#471—24no—
389#452—22no—
390#450—22no—
391#449—22no—
392#447—22no—
393#436—22no—
394#435—22no—
395C2×#108C22×C1111yescharacteristic, complemented
396C2×#108C22×C1111yescharacteristic, complemented
397#424C22×C1111yescharacteristic, complemented
398#419C22×C1111yescharacteristic, complemented
399#418C22×C1111yescharacteristic
400#418C22×C1111yescharacteristic
401#418C22×C1111yescharacteristic, complemented
402C2×#101C22×C1111yescharacteristic, complemented
403C2×#101C22×C1111yescharacteristic, complemented
404C2×#100C22×C1111yescharacteristic
405C2×#100C22×C1111yescharacteristic
406C2×#100C22×C1111yescharacteristic
407C2×#100C22×C1111yescharacteristic
408C2×#100C22×C1111yescharacteristic, complemented
409C2×#100C22×C1111yescharacteristic, complemented
410#408C22×C1111yescharacteristic, complemented
411#407C22×C1111yescharacteristic
412#407C22×C1111yescharacteristic
413#407C22×C1111yescharacteristic
414#405C22×C1111yescharacteristic, complemented
415#341C22×C1111yescharacteristic, complemented
416#341C22×C1111yescharacteristic, complemented
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—41no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—82no—
429C22×C11—82no—
430C22×C11—82no—
431C22×C11—82no—
432C22×C11—82no—
433C22×C11—82no—
434C22×C11—816no—
435C22×C11—82no—
436C22×C11—82no—
437C22×C11—82no—
438C22×C11C2×#12111yescharacteristic
439C22×C11#54611yescharacteristic
440C22×C11#54611yescharacteristic
441C4×C11—22no—
442C4×C11—42no—
443C4×C11—41no—
444C4×C11—42no—
445C4×C11C2×#12011yescharacteristic
446C4×C11#53511yescharacteristic
447C4×C11D4211yescharacteristic
448C4×C11D4211yescharacteristic
449C25—21no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—41no—
455C2×#41—41no—
456C2×#41C23×C1111yescharacteristic
457C22×Q8C23×C1111yescharacteristic
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—21no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—21no—
464C22×D4—41no—
465C22×D4—41no—
466C22×D4C23×C1111yescharacteristic
467C22×D4C23×C1111yescharacteristic
468C22×D4C23×C1111yescharacteristic
469C23×C4—21no—
470C23×C4C23×C1111yescharacteristic
471#137—22no—
472#137—41no—
473AGL(1,ℤ/8)—216no—
474AGL(1,ℤ/8)—216no—
475AGL(1,ℤ/8)—22no—
476AGL(1,ℤ/8)—22no—
477AGL(1,ℤ/8)—22no—
478AGL(1,ℤ/8)—41no—
479AGL(1,ℤ/8)—41no—
480AGL(1,ℤ/8)—41no—
481C2×Q16—21no—
482C2×SD16—22no—
483C2×SD16—22no—
484C2×SD16—21no—
485C2×SD16—21no—
486C2×SD16—21no—
487C2×SD16—21no—
488C2×SD16—22no—
489C2×SD16—21no—
490C2×SD16—21no—
491C2×SD16—22no—
492C2×SD16D4×C1114yescomplemented
493C2×D8—22no—
494C2×D8—22no—
495C2×D8—21no—
496C2×D8—21no—
497C2×D8—21no—
498C2×D8—22no—
499C2×D8—21no—
500C2×D8—21no—
501C2×D8—22no—
502C2×D8D4×C1114yescomplemented
503#131—22no—
504#131—22no—
505C2×M16—22no—
506C2×M16—22no—
507C2×M16—21no—
508C2×M16D4×C1112yes—
509C2×M16D4×C1112yes—
510C2×M16C23×C1111yescharacteristic
511C2×M16C23×C1111yescharacteristic
512C2×M16C23×C1111yescharacteristic
513C2×M16C23×C1111yescharacteristic
514C2×M16C23×C1111yescharacteristic
515C2×M16C23×C1111yescharacteristic
516C22×C8—21no—
517C22×C8C23×C1111yescharacteristic
518C22×C8C23×C1111yescharacteristic
519#123—21no—
520C22⋊Q8D4×C1112yes—
521#121D4×C1112yes—
522#120—21no—
523C4×D4—22no—
524#117C23×C1111yescharacteristic
525#108—22no—
526#108—22no—
527C4⋊C8—22no—
528#103—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#101—22no—
533#101—41no—
534#100—22no—
535#100—22no—
536#100—22no—
537#100—41no—
538#100—41no—
539#100—41no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—22no—
543C22⋊C8—22no—
544#97—21no—
545C4×C8—21no—
546C2×C11—21no—
547C2×C11—21no—
548C2×C11—42no—
549C2×C11—81no—
550C2×C11—82no—
551C2×C11—82no—
552C2×C11—82no—
553C2×C11#240811yescharacteristic
554C2×C11#306812yes—
555C24—21no—
556C24—21no—
557C24—21no—
558C24—42no—
559C24—42no—
560C24—42no—
561C24—84no—
562C24C11×#4111yescharacteristic
563#41—28no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—21no—
568#41—44no—
569#41—44no—
570#41—44no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8C2×D4×C1112yes—
577C2×Q8C2×D4×C1111yescharacteristic
578C2×D4—28no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—44no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4C2×D4×C1112yes—
606C2×D4C2×D4×C1112yes—
607C2×D4C2×D4×C1112yes—
608C2×D4C2×D4×C1111yescharacteristic
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4C2×D4×C1112yes—
619C22×C4C2×D4×C1112yes—
620C22×C4C11×#4111yescharacteristic
621C22×C4C24×C1111yescharacteristic
622Q16—42no—
623SD16—28no—
624SD16—24no—
625SD16—24no—
626SD16—42no—
627SD16—42no—
628SD16—42no—
629SD16—42no—
630D8—28no—
631D8—24no—
632D8—24no—
633D8—42no—
634D8—42no—
635D8—42no—
636M16—24no—
637M16—24no—
638M16—21no—
639M16—21no—
640M16—21no—
641M16—21no—
642M16—21no—
643M16—21no—
644M16—21no—
645M16—21no—
646M16—21no—
647M16—21no—
648M16—21no—
649M16—21no—
650M16—42no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—42no—
660C2×C8C2×D4×C1112yes—
661C2×C8C2×D4×C1111yescharacteristic
662C2×C8C2×D4×C1111yescharacteristic
663C2×C8C2×D4×C1112yes—
664C2×C8C2×D4×C1112yes—
665C4⋊C4—22no—
666C4⋊C4C2×D4×C1112yes—
667C22⋊C4—22no—
668C22⋊C4—21no—
669C22⋊C4—22no—
670C42—21no—
671C11#2428411yescharacteristic, direct product factor, Sylow
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—42no—
679C23—48no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—82no—
687C23—82no—
688C23—82no—
689C23—84no—
690C23—84no—
691C23—88no—
692C23—88no—
693C23C11×#12112yes—
694C23C2×C11×#4111yescharacteristic
695Q8—22no—
696Q8—21no—
697Q8—21no—
698Q8—22no—
699Q8—41no—
700Q8—41no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—21no—
705D4—21no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—48no—
710D4—48no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—82no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—48no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4C11×#12112yes—
735C2×C4C22×D4×C1111yescharacteristic
736C2×C4C22×D4×C1111yescharacteristic
737C2×C4C22×D4×C1111yescharacteristic
738C2×C4C22×D4×C1111yescharacteristic
739C2×C4C11×H(5,𝔽2)11yescharacteristic
740C2×C4C11×H(5,𝔽2)11yescharacteristic
741C8—22no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—41no—
747C8—41no—
748C8C11×#12012yes—
749C8C11×#12012yes—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—816no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22C2×C11×#12111yescharacteristic
772C22C11×#54611yescharacteristic
773C22C11×#54611yescharacteristic
774C4—22no—
775C4—42no—
776C4—41no—
777C4—42no—
778C4C2×C11×#12011yescharacteristic
779C4C11×#53511yescharacteristic
780C4D42×C1111yescharacteristic
781C4D42×C1111yescharacteristic
782C2—21no—
783C2—21no—
784C2—42no—
785C2—81no—
786C2—82no—
787C2—82no—
788C2—82no—
789C2C11×#240811yescharacteristic
790C2C11×#306812yes—
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
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×AGL(1,ℤ/8)C2semidirect
2. C2×C11×#472C2semidirect
3. C2×C11×#471C2semidirect
4. C11×#3005C2semidirect
5. C11×#3003C2semidirect
6. C11×#2930C2semidirect
7. C11×#2046C2semidirect
8. C11×#2045C2semidirect
9. C11×#2019C2semidirect
10. C11×#2018C2semidirect
11. C11×#1978C2semidirect
12. C11×#1977C2semidirect
13. C11×#1811C2semidirect
14. C11×#1785C2semidirect
15. C11×#1783C2semidirect
18. C2×C11×#137C22semidirect
25. C2×C11×AGL(1,ℤ/8)C22semidirect
30. C2×C11×#131C22semidirect
41. C2×C11×#108C22semidirect
42. C2×C11×#108C22semidirect
43. C11×#424C22semidirect
44. C11×#419C22semidirect
47. C11×#418C22semidirect
48. C2×C11×#101C22semidirect
49. C2×C11×#101C22semidirect
54. C2×C11×#100C22semidirect
55. C2×C11×#100C22semidirect
56. C11×#408C22semidirect
60. C11×#405C22semidirect
61. C11×#341C22semidirect
62. C11×#341C22semidirect
106. C2×C11×SD16D4semidirect
116. C2×C11×D8D4semidirect
160. #24284C11direct (N × H)
277. C22×AGL(1,ℤ/8)C2×C11semidirect
278. C2×#472C2×C11semidirect
279. C2×#471C2×C11semidirect
280. #3005C2×C11semidirect
281. #3003C2×C11semidirect
282. #2930C2×C11semidirect
283. #2046C2×C11semidirect
284. #2045C2×C11semidirect
285. #2019C2×C11semidirect
286. #2018C2×C11semidirect
287. #1978C2×C11semidirect
288. #1977C2×C11semidirect
289. #1811C2×C11semidirect
290. #1785C2×C11semidirect
291. #1783C2×C11semidirect
372. C2×#137C22×C11semidirect
379. C2×AGL(1,ℤ/8)C22×C11semidirect
384. C2×#131C22×C11semidirect
395. C2×#108C22×C11semidirect
396. C2×#108C22×C11semidirect
397. #424C22×C11semidirect
398. #419C22×C11semidirect
401. #418C22×C11semidirect
402. C2×#101C22×C11semidirect
403. C2×#101C22×C11semidirect
408. C2×#100C22×C11semidirect
409. C2×#100C22×C11semidirect
410. #408C22×C11semidirect
414. #405C22×C11semidirect
415. #341C22×C11semidirect
416. #341C22×C11semidirect
492. C2×SD16D4×C11semidirect
502. C2×D8D4×C11semidirect
671. C11#24284direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×AGL(1,ℤ/8)2
C2×C11×#4722
C2×C11×#4712
C11×#30052
C11×#30032
C11×#29302
C11×#20462
C11×#20452
C11×#20192
C11×#20182
C11×#19782
C11×#19772
C11×#18112
C11×#17852
C11×#17832
#2428411