Finite Group Databasebeta

← C2×C11×#2662 #14611780

Subgroups — C2×C11×#2662 #14611780

Order 2816.

3002 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#126C211yesmaximal, characteristic, complemented
2C22×C11×#124C211yesmaximal, characteristic, complemented
3C11×#2662C2116yesmaximal, direct product factor
4C2×C11×#396C212yesmaximal, complemented
5C2×C11×#395C211yesmaximal, characteristic, complemented
6C2×C11×#394C212yesmaximal, complemented
7C2×C11×#394C211yesmaximal, characteristic, complemented
8C2×C11×#393C211yesmaximal, characteristic, complemented
9C2×C11×#392C211yesmaximal, characteristic
10C2×C11×#390C212yesmaximal, complemented
11C2×C11×#388C212yesmaximal, complemented
12C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C23×D4×C11C2212yes—
16C2×C11×#126—28no—
17C2×C11×#126C2218yescomplemented
18C2×C11×#124—28no—
19C2×C11×#124C2218yescomplemented
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2212yes—
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2212yes—
29C22×C11×C22⋊C4C2212yes—
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2212yes—
32C22×C11×C22⋊C4C2212yes—
33C22×C11×C22⋊C4C2212yes—
34C22×C42×C11C2212yes—
35C22×C42×C11C2211yescharacteristic
36C11×#396C22116yescomplemented
37C11×#395C2218yescomplemented
38C11×#394C2218yescomplemented
39C11×#394C22116yescomplemented
40C11×#393C2218yescomplemented
41C11×#392C2218yes—
42C11×#390C22116yescomplemented
43C11×#388C22116yescomplemented
44C4×C11×C4⋊C4C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2212yes—
48C2×C11×#95C2212yes—
49C25×C11C2311yescharacteristic
50C25×C11C2312yes—
51C22×Q8×C11—24no—
52C22×Q8×C11—44no—
53C22×Q8×C11C2314yes—
54C22×D4×C11—24no—
55C22×D4×C11—28no—
56C22×D4×C11—44no—
57C22×D4×C11—44no—
58C22×D4×C11—44no—
59C22×D4×C11C2314yes—
60C22×D4×C11C2318yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2312yes—
70C11×#126—232no—
71C11×#124—232no—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—28no—
76C2×C11×C4⋊C4—44no—
77C2×C11×C4⋊C4C2318yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2318yes—
82C2×C11×C22⋊C4—28no—
83C2×C11×C22⋊C4—28no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4—28no—
88C2×C11×C22⋊C4—44no—
89C2×C11×C22⋊C4—44no—
90C2×C11×C22⋊C4—44no—
91C2×C11×C22⋊C4C2318yes—
92C2×C11×C22⋊C4C2318yes—
93C2×C11×C22⋊C4C2318yes—
94C2×C11×C22⋊C4C2314yes—
95C2×C11×C22⋊C4C2314yes—
96C2×C11×C22⋊C4C2314yes—
97C2×C11×C22⋊C4C2318yes—
98C2×C11×C22⋊C4C2318yes—
99C2×C11×C22⋊C4C2318yes—
100C2×C42×C11—44no—
101C2×C42×C11D418yescomplemented
102C2×C42×C11C2318yes—
103C2×C42×C11C2314yes—
104C11×#95C2314yes—
105C11×#95C2314yes—
106C11×#95C2318yes—
107C11×#95C2318yes—
108C2×#2662C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11—22no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—24no—
121C24×C11C2412yes—
122C24×C11C2414yes—
123C24×C11C2411yescharacteristic
124C2×Q8×C11—28no—
125C2×Q8×C11—48no—
126C2×Q8×C11—416no—
127C2×D4×C11—28no—
128C2×D4×C11—216no—
129C2×D4×C11—48no—
130C2×D4×C11—48no—
131C2×D4×C11—48no—
132C2×D4×C11—416no—
133C2×D4×C11—432no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—22no—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D414yes—
155C22×C4×C11C2×D414yes—
156C22×C4×C11#4118yes—
157C22×C4×C11C2414yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2414yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2414yes—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—216no—
170C11×C4⋊C4—48no—
171C11×C22⋊C4—216no—
172C11×C22⋊C4—216no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—216no—
177C11×C22⋊C4—48no—
178C11×C22⋊C4—48no—
179C11×C22⋊C4—48no—
180C42×C11—48no—
181C42×C11C2×D4116yescomplemented
182C22×#126C2×C1111yescharacteristic, complemented
183C22×#124C2×C1111yescharacteristic, complemented
184#2662C2×C11116yesdirect product factor
185C2×#396C2×C1112yescomplemented
186C2×#395C2×C1111yescharacteristic, complemented
187C2×#394C2×C1112yescomplemented
188C2×#394C2×C1111yescharacteristic, complemented
189C2×#393C2×C1111yescharacteristic, complemented
190C2×#392C2×C1111yescharacteristic
191C2×#390C2×C1112yescomplemented
192C2×#388C2×C1112yescomplemented
193C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
194C23×C11—22no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—44no—
207C23×C11—48no—
208C23×C11—48no—
209C23×C11—44no—
210C23×C11—44no—
211C23×C11—48no—
212C23×C11—48no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11—48no—
217C23×C11—48no—
218C23×C11C22×D412yes—
219C23×C11C2×#4114yes—
220C23×C11H(5,𝔽2)14yes—
221C23×C11H(5,𝔽2)12yes—
222C23×C112−1+412yes—
223C23×C11C2511yescharacteristic
224Q8×C11—416no—
225D4×C11—416no—
226D4×C11—432no—
227C2×C4×C11—28no—
228C2×C4×C11—28no—
229C2×C4×C11—28no—
230C2×C4×C11—216no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—44no—
251C2×C4×C11—44no—
252C2×C4×C11—48no—
253C2×C4×C11—44no—
254C2×C4×C11—48no—
255C2×C4×C11C22×D414yes—
256C2×C4×C11C22×D414yes—
257C2×C4×C11C22×D414yes—
258C2×C4×C11C2×#4118yes—
259C23×Q8C22×C1111yescharacteristic
260C23×D4C22×C1111yescharacteristic
261C23×D4C22×C1112yes—
262C2×#126—28no—
263C2×#126C22×C1118yescomplemented
264C2×#124—28no—
265C2×#124C22×C1118yescomplemented
266C22×C4⋊C4C22×C1111yescharacteristic
267C22×C4⋊C4C22×C1112yes—
268C22×C4⋊C4C22×C1111yescharacteristic
269C22×C4⋊C4C22×C1111yescharacteristic
270C22×C4⋊C4C22×C1112yes—
271C22×C22⋊C4C22×C1111yescharacteristic
272C22×C22⋊C4C22×C1112yes—
273C22×C22⋊C4C22×C1111yescharacteristic
274C22×C22⋊C4C22×C1112yes—
275C22×C22⋊C4C22×C1112yes—
276C22×C22⋊C4C22×C1111yescharacteristic
277C22×C22⋊C4C22×C1112yes—
278C22×C22⋊C4C22×C1112yes—
279C22×C22⋊C4C22×C1112yes—
280C22×C42C22×C1112yes—
281C22×C42C22×C1111yescharacteristic
282#396C22×C11116yescomplemented
283#395C22×C1118yescomplemented
284#394C22×C1118yescomplemented
285#394C22×C11116yescomplemented
286#393C22×C1118yescomplemented
287#392C22×C1118yes—
288#390C22×C11116yescomplemented
289#388C22×C11116yescomplemented
290C4×C4⋊C4C22×C1118yescomplemented
291C2×#95C22×C1111yescharacteristic
292C2×#95C22×C1111yescharacteristic
293C2×#95C22×C1112yes—
294C2×#95C22×C1112yes—
295C22×C11—42no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—816no—
308C22×C11—88no—
309C22×C11#53214yes—
310C22×C11#53514yes—
311C22×C11#53714yes—
312C22×C11#53818yes—
313C22×C11#54218yes—
314C22×C11C23×D411yescharacteristic
315C22×C11C22×#4112yes—
316C22×C11C2×H(5,𝔽2)12yes—
317C22×C11C2×H(5,𝔽2)11yescharacteristic
318C22×C11C2×2−1+411yescharacteristic
319C4×C11—24no—
320C4×C11—24no—
321C4×C11—24no—
322C4×C11—28no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11—44no—
326C4×C11—42no—
327C4×C11—44no—
328C25C23×C1111yescharacteristic
329C25C23×C1112yes—
330C22×Q8—24no—
331C22×Q8—44no—
332C22×Q8C23×C1114yes—
333C22×D4—24no—
334C22×D4—28no—
335C22×D4—44no—
336C22×D4—44no—
337C22×D4—44no—
338C22×D4C23×C1114yes—
339C22×D4C23×C1118yes—
340C23×C4C23×C1111yescharacteristic
341C23×C4C23×C1111yescharacteristic
342C23×C4C23×C1111yescharacteristic
343C23×C4C23×C1112yes—
344C23×C4C23×C1112yes—
345C23×C4C23×C1111yescharacteristic
346C23×C4C23×C1111yescharacteristic
347C23×C4C23×C1111yescharacteristic
348C23×C4C23×C1112yes—
349#126—232no—
350#124—232no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4C23×C1114yes—
357C2×C4⋊C4C23×C1114yes—
358C2×C4⋊C4C23×C1114yes—
359C2×C4⋊C4C23×C1118yes—
360C2×C4⋊C4C23×C1118yes—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4C23×C1118yes—
371C2×C22⋊C4C23×C1118yes—
372C2×C22⋊C4C23×C1114yes—
373C2×C22⋊C4C23×C1114yes—
374C2×C22⋊C4C23×C1114yes—
375C2×C22⋊C4C23×C1118yes—
376C2×C22⋊C4C23×C1118yes—
377C2×C22⋊C4C23×C1118yes—
378C2×C22⋊C4C23×C1118yes—
379C2×C42—44no—
380C2×C42D4×C1118yescomplemented
381C2×C42C23×C1118yes—
382C2×C42C23×C1114yes—
383#95C23×C1114yes—
384#95C23×C1114yes—
385#95C23×C1118yes—
386#95C23×C1118yes—
387C2×C11—84no—
388C2×C11—82no—
389C2×C11#266218yesdirect product factor
390C2×C11C2×#53211yescharacteristic
391C2×C11C2×#53511yescharacteristic
392C2×C11C2×#53711yescharacteristic
393C2×C11C2×#53812yes—
394C2×C11C2×#54212yes—
395C24—22no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—22no—
405C24—22no—
406C24—24no—
407C24C24×C1112yes—
408C24C24×C1114yes—
409C24C24×C1111yescharacteristic
410C2×Q8—28no—
411C2×Q8—48no—
412C2×Q8—416no—
413C2×D4—28no—
414C2×D4—216no—
415C2×D4—48no—
416C2×D4—48no—
417C2×D4—48no—
418C2×D4—416no—
419C2×D4—432no—
420C22×C4—24no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4C2×D4×C1114yes—
440C22×C4C2×D4×C1114yes—
441C22×C4C2×D4×C1114yes—
442C22×C4C11×#4118yes—
443C22×C4C24×C1114yes—
444C22×C4C24×C1112yes—
445C22×C4C24×C1112yes—
446C22×C4C24×C1114yes—
447C22×C4C24×C1112yes—
448C22×C4C24×C1112yes—
449C22×C4C24×C1112yes—
450C22×C4C24×C1112yes—
451C22×C4C24×C1114yes—
452C4⋊C4—28no—
453C4⋊C4—28no—
454C4⋊C4—28no—
455C4⋊C4—216no—
456C4⋊C4—48no—
457C22⋊C4—216no—
458C22⋊C4—216no—
459C22⋊C4—28no—
460C22⋊C4—28no—
461C22⋊C4—28no—
462C22⋊C4—216no—
463C22⋊C4—48no—
464C22⋊C4—48no—
465C22⋊C4—48no—
466C42—48no—
467C42C2×D4×C11116yescomplemented
468C11C2×#266211yescharacteristic, direct product factor, Sylow
469C23—22no—
470C23—24no—
471C23—24no—
472C23—24no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—22no—
479C23—22no—
480C23—24no—
481C23—44no—
482C23—48no—
483C23—48no—
484C23—44no—
485C23—44no—
486C23—48no—
487C23—48no—
488C23—48no—
489C23—48no—
490C23—48no—
491C23—48no—
492C23—48no—
493C23C22×D4×C1112yes—
494C23C2×C11×#4114yes—
495C23C11×H(5,𝔽2)14yes—
496C23C11×H(5,𝔽2)12yes—
497C23C11×2−1+412yes—
498C23C25×C1111yescharacteristic
499Q8—416no—
500D4—416no—
501D4—432no—
502C2×C4—28no—
503C2×C4—28no—
504C2×C4—28no—
505C2×C4—216no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—48no—
528C2×C4—44no—
529C2×C4—48no—
530C2×C4C22×D4×C1114yes—
531C2×C4C22×D4×C1114yes—
532C2×C4C22×D4×C1114yes—
533C2×C4C2×C11×#4118yes—
534C22—42no—
535C22—44no—
536C22—44no—
537C22—42no—
538C22—42no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22—44no—
543C22—44no—
544C22—44no—
545C22—44no—
546C22—816no—
547C22—88no—
548C22C11×#53214yes—
549C22C11×#53514yes—
550C22C11×#53714yes—
551C22C11×#53818yes—
552C22C11×#54218yes—
553C22C23×D4×C1111yescharacteristic
554C22C22×C11×#4112yes—
555C22C2×C11×H(5,𝔽2)12yes—
556C22C2×C11×H(5,𝔽2)11yescharacteristic
557C22C2×C11×2−1+411yescharacteristic
558C4—24no—
559C4—24no—
560C4—24no—
561C4—28no—
562C4—42no—
563C4—44no—
564C4—42no—
565C4—42no—
566C4—44no—
567C2—84no—
568C2—82no—
569C2C11×#266218yesdirect product factor
570C2C2×C11×#53211yescharacteristic
571C2C2×C11×#53511yescharacteristic
572C2C2×C11×#53711yescharacteristic
573C2C2×C11×#53812yes—
574C2C2×C11×#54212yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC2×C11×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#126C2semidirect
2. C22×C11×#124C2semidirect
3. C11×#2662C2direct (N × H)
4. C2×C11×#396C2semidirect
5. C2×C11×#395C2semidirect
6. C2×C11×#394C2semidirect
7. C2×C11×#394C2semidirect
8. C2×C11×#393C2semidirect
10. C2×C11×#390C2semidirect
11. C2×C11×#388C2semidirect
12. C2×C4×C11×C4⋊C4C2semidirect
17. C2×C11×#126C22semidirect
19. C2×C11×#124C22semidirect
36. C11×#396C22semidirect
37. C11×#395C22semidirect
38. C11×#394C22semidirect
39. C11×#394C22semidirect
40. C11×#393C22semidirect
42. C11×#390C22semidirect
43. C11×#388C22semidirect
44. C4×C11×C4⋊C4C22semidirect
101. C2×C42×C11D4semidirect
108. C2×#2662C11direct (N × H)
181. C42×C11C2×D4semidirect
182. C22×#126C2×C11semidirect
183. C22×#124C2×C11semidirect
184. #2662C2×C11direct (N × H)
185. C2×#396C2×C11semidirect
186. C2×#395C2×C11semidirect
187. C2×#394C2×C11semidirect
188. C2×#394C2×C11semidirect
189. C2×#393C2×C11semidirect
191. C2×#390C2×C11semidirect
192. C2×#388C2×C11semidirect
193. C2×C4×C4⋊C4C2×C11semidirect
263. C2×#126C22×C11semidirect
265. C2×#124C22×C11semidirect
282. #396C22×C11semidirect
283. #395C22×C11semidirect
284. #394C22×C11semidirect
285. #394C22×C11semidirect
286. #393C22×C11semidirect
288. #390C22×C11semidirect
289. #388C22×C11semidirect
290. C4×C4⋊C4C22×C11semidirect
380. C2×C42D4×C11semidirect
389. C2×C11#2662direct (N × H)
467. C42C2×D4×C11semidirect
468. C11C2×#2662direct (N × H)
569. C2C11×#2662direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1262
C22×C11×#1242
C11×#26622
C2×C11×#3962
C2×C11×#3952
C2×C11×#3942
C2×C11×#3932
C2×C11×#3922
C2×C11×#3902
C2×C11×#3882
C2×C4×C11×C4⋊C42
C2×#266211