Finite Group Databasebeta

← C2×C11×#2454 #14611892

Subgroups — C2×C11×#2454 #14611892

Order 2816.

3094 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×#125C211yesmaximal, characteristic, complemented
2C22×C4×D4×C11C211yesmaximal, characteristic
3C11×#2454C2116yesmaximal, direct product factor
4C2×C11×#399C212yesmaximal, complemented
5C2×C11×#396C212yesmaximal, complemented
6C2×C11×#390C211yesmaximal, characteristic
7C2×C11×#390C211yesmaximal, characteristic
8C2×C11×#389C211yesmaximal, characteristic, complemented
9C2×C11×#389C211yesmaximal, characteristic, complemented
10C2×C11×#385C212yesmaximal, complemented
11C2×C11×#380C212yesmaximal, complemented
12C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2212yes—
15C2×C11×#125—28no—
16C2×C11×#125C2218yescomplemented
17C2×C4×D4×C11—28no—
18C2×C4×D4×C11C2218yes—
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2212yes—
26C22×C11×C4⋊C4C2212yes—
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2212yes—
29C22×C11×C22⋊C4C2212yes—
30C22×C11×C22⋊C4C2212yes—
31C22×C11×C22⋊C4C2212yes—
32C22×C11×C22⋊C4C2212yes—
33C22×C42×C11C2211yescharacteristic
34C22×C42×C11C2211yescharacteristic
35C22×C42×C11C2211yescharacteristic
36C11×#399C22116yescomplemented
37C11×#396C22116yescomplemented
38C11×#390C2218yes—
39C11×#390C2218yes—
40C11×#389C2218yescomplemented
41C11×#389C2218yescomplemented
42C11×#385C22116yescomplemented
43C11×#380C22116yescomplemented
44C4×C11×C4⋊C4C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2212yes—
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2212yes—
49C25×C11C2312yes—
50C22×D4×C11—24no—
51C22×D4×C11—24no—
52C22×D4×C11Q818yes—
53C22×D4×C11C2314yes—
54C23×C4×C11—28no—
55C23×C4×C11—28no—
56C23×C4×C11—44no—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2312yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2318yes—
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C11×#125—232no—
69C4×D4×C11—232no—
70C2×C11×C4⋊C4—28no—
71C2×C11×C4⋊C4—28no—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—44no—
77C2×C11×C4⋊C4—44no—
78C2×C11×C4⋊C4D418yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2318yes—
82C2×C11×C4⋊C4C2318yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C4⋊C4C2318yes—
86C2×C11×C4⋊C4C2318yes—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C22⋊C4—28no—
89C2×C11×C22⋊C4—28no—
90C2×C11×C22⋊C4—44no—
91C2×C11×C22⋊C4—44no—
92C2×C11×C22⋊C4—44no—
93C2×C11×C22⋊C4C2318yes—
94C2×C11×C22⋊C4C2318yes—
95C2×C11×C22⋊C4C2318yes—
96C2×C11×C22⋊C4C2318yes—
97C2×C11×C22⋊C4C2318yes—
98C2×C42×C11—24no—
99C2×C42×C11—24no—
100C2×C42×C11—24no—
101C2×C42×C11C2314yes—
102C2×C42×C11C2314yes—
103C2×C42×C11C2314yes—
104C11×#95C2314yes—
105C11×#95C2314yes—
106C11×#95C2318yes—
107C11×#95C2318yes—
108C2×#2454C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11C2×Q818yes—
116C24×C11C2414yes—
117C24×C11C2411yescharacteristic
118C2×D4×C11—232no—
119C2×D4×C11—28no—
120C2×D4×C11—28no—
121C2×D4×C11C2×Q8116yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—216no—
147C22×C4×C11—216no—
148C22×C4×C11—48no—
149C22×C4×C11—432no—
150C22×C4×C11C2×D418yes—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×Q814yes—
153C22×C4×C11#4114yes—
154C22×C4×C11#4114yes—
155C22×C4×C11#4114yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2414yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2414yes—
162C22×C4×C11C2414yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2412yes—
166C11×C4⋊C4—216no—
167C11×C4⋊C4—216no—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—28no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—48no—
173C11×C4⋊C4—48no—
174C11×C4⋊C4C2×D4116yes—
175C11×C22⋊C4—216no—
176C11×C22⋊C4—216no—
177C11×C22⋊C4—48no—
178C11×C22⋊C4—48no—
179C11×C22⋊C4—48no—
180C42×C11—28no—
181C42×C11—28no—
182C42×C11—28no—
183C22×#125C2×C1111yescharacteristic, complemented
184C22×C4×D4C2×C1111yescharacteristic
185#2454C2×C11116yesdirect product factor
186C2×#399C2×C1112yescomplemented
187C2×#396C2×C1112yescomplemented
188C2×#390C2×C1111yescharacteristic
189C2×#390C2×C1111yescharacteristic
190C2×#389C2×C1111yescharacteristic, complemented
191C2×#389C2×C1111yescharacteristic, complemented
192C2×#385C2×C1112yescomplemented
193C2×#380C2×C1112yescomplemented
194C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
195C23×C11—216no—
196C23×C11—216no—
197C23×C11—216no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11C22×D412yes—
209C23×C11C22×Q818yes—
210C23×C11C22×Q812yes—
211C23×C11C2×#4112yes—
212C23×C11C2×#4112yes—
213C23×C11C2×#4112yes—
214C23×C11H(5,𝔽2)12yes—
215C23×C11H(5,𝔽2)12yes—
216C23×C11C2511yescharacteristic
217D4×C11—232no—
218C2×C4×C11—28no—
219C2×C4×C11—28no—
220C2×C4×C11—216no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—432no—
246C2×C4×C11—44no—
247C2×C4×C11—48no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11—44no—
251C2×C4×C11—48no—
252C2×C4×C11C22⋊Q8116yes—
253C2×C4×C11C22×D418yes—
254C2×C4×C11C22×D414yes—
255C2×C4×C11C22×Q814yes—
256C2×C4×C11C2×#4114yes—
257C2×C4×C11C2×#4114yes—
258C2×C4×C11C2×#4114yes—
259C23×D4C22×C1111yescharacteristic
260C24×C4C22×C1112yes—
261C2×#125—28no—
262C2×#125C22×C1118yescomplemented
263C2×C4×D4—28no—
264C2×C4×D4C22×C1118yes—
265C22×C4⋊C4C22×C1112yes—
266C22×C4⋊C4C22×C1111yescharacteristic
267C22×C4⋊C4C22×C1112yes—
268C22×C4⋊C4C22×C1111yescharacteristic
269C22×C4⋊C4C22×C1111yescharacteristic
270C22×C4⋊C4C22×C1111yescharacteristic
271C22×C4⋊C4C22×C1112yes—
272C22×C4⋊C4C22×C1112yes—
273C22×C4⋊C4C22×C1111yescharacteristic
274C22×C22⋊C4C22×C1112yes—
275C22×C22⋊C4C22×C1112yes—
276C22×C22⋊C4C22×C1112yes—
277C22×C22⋊C4C22×C1112yes—
278C22×C22⋊C4C22×C1112yes—
279C22×C42C22×C1111yescharacteristic
280C22×C42C22×C1111yescharacteristic
281C22×C42C22×C1111yescharacteristic
282#399C22×C11116yescomplemented
283#396C22×C11116yescomplemented
284#390C22×C1118yes—
285#390C22×C1118yes—
286#389C22×C1118yescomplemented
287#389C22×C1118yescomplemented
288#385C22×C11116yescomplemented
289#380C22×C11116yescomplemented
290C4×C4⋊C4C22×C1118yescomplemented
291C2×#95C22×C1111yescharacteristic
292C2×#95C22×C1112yes—
293C2×#95C22×C1111yescharacteristic
294C2×#95C22×C1112yes—
295C22×C11—28no—
296C22×C11—28no—
297C22×C11—28no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—432no—
303C22×C11C2×C22⋊Q814yes—
304C22×C11#52914yes—
305C22×C11#54014yes—
306C22×C11#54614yes—
307C22×C11#55014yes—
308C22×C11#55414yes—
309C22×C11#55414yes—
310C22×C11C23×D411yescharacteristic
311C22×C11C23×Q811yescharacteristic
312C22×C11C22×#4111yescharacteristic
313C22×C11C22×#4111yescharacteristic
314C22×C11C22×#4111yescharacteristic
315C22×C11C2×H(5,𝔽2)11yescharacteristic
316C22×C11C2×H(5,𝔽2)11yescharacteristic
317C4×C11—24no—
318C4×C11—24no—
319C4×C11—28no—
320C4×C11—42no—
321C4×C11—44no—
322C4×C11—42no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11—44no—
326C4×C11C2×C22⋊Q818yes—
327C25C23×C1112yes—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4Q8×C1118yes—
331C22×D4C23×C1114yes—
332C23×C4—28no—
333C23×C4—28no—
334C23×C4—44no—
335C23×C4C23×C1112yes—
336C23×C4C23×C1112yes—
337C23×C4C23×C1111yescharacteristic
338C23×C4C23×C1111yescharacteristic
339C23×C4C23×C1111yescharacteristic
340C23×C4C23×C1111yescharacteristic
341C23×C4C23×C1118yes—
342C23×C4C23×C1112yes—
343C23×C4C23×C1111yescharacteristic
344C23×C4C23×C1111yescharacteristic
345C23×C4C23×C1111yescharacteristic
346#125—232no—
347C4×D4—232no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4D4×C1118yes—
357C2×C4⋊C4C23×C1118yes—
358C2×C4⋊C4C23×C1118yes—
359C2×C4⋊C4C23×C1114yes—
360C2×C4⋊C4C23×C1114yes—
361C2×C4⋊C4C23×C1114yes—
362C2×C4⋊C4C23×C1114yes—
363C2×C4⋊C4C23×C1118yes—
364C2×C4⋊C4C23×C1118yes—
365C2×C4⋊C4C23×C1114yes—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4C23×C1118yes—
372C2×C22⋊C4C23×C1118yes—
373C2×C22⋊C4C23×C1118yes—
374C2×C22⋊C4C23×C1118yes—
375C2×C22⋊C4C23×C1118yes—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42C23×C1114yes—
380C2×C42C23×C1114yes—
381C2×C42C23×C1114yes—
382#95C23×C1114yes—
383#95C23×C1114yes—
384#95C23×C1118yes—
385#95C23×C1118yes—
386C2×C11—48no—
387C2×C11#245418yesdirect product factor
388C2×C11C22×C22⋊Q811yescharacteristic
389C2×C11C2×#52911yescharacteristic
390C2×C11C2×#54011yescharacteristic
391C2×C11C2×#54611yescharacteristic
392C2×C11C2×#55011yescharacteristic
393C2×C11C2×#55411yescharacteristic
394C2×C11C2×#55411yescharacteristic
395C24—24no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24C2×Q8×C1118yes—
402C24C24×C1114yes—
403C24C24×C1111yescharacteristic
404C2×D4—232no—
405C2×D4—28no—
406C2×D4—28no—
407C2×D4C2×Q8×C11116yes—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—216no—
433C22×C4—216no—
434C22×C4—48no—
435C22×C4—432no—
436C22×C4C2×D4×C1118yes—
437C22×C4C2×D4×C1114yes—
438C22×C4C2×Q8×C1114yes—
439C22×C4C11×#4114yes—
440C22×C4C11×#4114yes—
441C22×C4C11×#4114yes—
442C22×C4C24×C1112yes—
443C22×C4C24×C1114yes—
444C22×C4C24×C1112yes—
445C22×C4C24×C1112yes—
446C22×C4C24×C1112yes—
447C22×C4C24×C1114yes—
448C22×C4C24×C1114yes—
449C22×C4C24×C1112yes—
450C22×C4C24×C1112yes—
451C22×C4C24×C1112yes—
452C4⋊C4—216no—
453C4⋊C4—216no—
454C4⋊C4—28no—
455C4⋊C4—28no—
456C4⋊C4—28no—
457C4⋊C4—28no—
458C4⋊C4—48no—
459C4⋊C4—48no—
460C4⋊C4C2×D4×C11116yes—
461C22⋊C4—216no—
462C22⋊C4—216no—
463C22⋊C4—48no—
464C22⋊C4—48no—
465C22⋊C4—48no—
466C42—28no—
467C42—28no—
468C42—28no—
469C11C2×#245411yescharacteristic, direct product factor, Sylow
470C23—216no—
471C23—216no—
472C23—216no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—24no—
479C23—48no—
480C23—48no—
481C23—48no—
482C23—48no—
483C23C22×D4×C1112yes—
484C23C22×Q8×C1118yes—
485C23C22×Q8×C1112yes—
486C23C2×C11×#4112yes—
487C23C2×C11×#4112yes—
488C23C2×C11×#4112yes—
489C23C11×H(5,𝔽2)12yes—
490C23C11×H(5,𝔽2)12yes—
491C23C25×C1111yescharacteristic
492D4—232no—
493C2×C4—28no—
494C2×C4—28no—
495C2×C4—216no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—432no—
521C2×C4—44no—
522C2×C4—48no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—48no—
527C2×C4C11×C22⋊Q8116yes—
528C2×C4C22×D4×C1118yes—
529C2×C4C22×D4×C1114yes—
530C2×C4C22×Q8×C1114yes—
531C2×C4C2×C11×#4114yes—
532C2×C4C2×C11×#4114yes—
533C2×C4C2×C11×#4114yes—
534C22—28no—
535C22—28no—
536C22—28no—
537C22—44no—
538C22—44no—
539C22—44no—
540C22—44no—
541C22—432no—
542C22C2×C11×C22⋊Q814yes—
543C22C11×#52914yes—
544C22C11×#54014yes—
545C22C11×#54614yes—
546C22C11×#55014yes—
547C22C11×#55414yes—
548C22C11×#55414yes—
549C22C23×D4×C1111yescharacteristic
550C22C23×Q8×C1111yescharacteristic
551C22C22×C11×#4111yescharacteristic
552C22C22×C11×#4111yescharacteristic
553C22C22×C11×#4111yescharacteristic
554C22C2×C11×H(5,𝔽2)11yescharacteristic
555C22C2×C11×H(5,𝔽2)11yescharacteristic
556C4—24no—
557C4—24no—
558C4—28no—
559C4—42no—
560C4—44no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—44no—
565C4C2×C11×C22⋊Q818yes—
566C2—48no—
567C2C11×#245418yesdirect product factor
568C2C22×C11×C22⋊Q811yescharacteristic
569C2C2×C11×#52911yescharacteristic
570C2C2×C11×#54011yescharacteristic
571C2C2×C11×#54611yescharacteristic
572C2C2×C11×#55011yescharacteristic
573C2C2×C11×#55411yescharacteristic
574C2C2×C11×#55411yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#125C2semidirect
3. C11×#2454C2direct (N × H)
4. C2×C11×#399C2semidirect
5. C2×C11×#396C2semidirect
8. C2×C11×#389C2semidirect
9. C2×C11×#389C2semidirect
10. C2×C11×#385C2semidirect
11. C2×C11×#380C2semidirect
12. C2×C4×C11×C4⋊C4C2semidirect
16. C2×C11×#125C22semidirect
36. C11×#399C22semidirect
37. C11×#396C22semidirect
40. C11×#389C22semidirect
41. C11×#389C22semidirect
42. C11×#385C22semidirect
43. C11×#380C22semidirect
44. C4×C11×C4⋊C4C22semidirect
108. C2×#2454C11direct (N × H)
183. C22×#125C2×C11semidirect
185. #2454C2×C11direct (N × H)
186. C2×#399C2×C11semidirect
187. C2×#396C2×C11semidirect
190. C2×#389C2×C11semidirect
191. C2×#389C2×C11semidirect
192. C2×#385C2×C11semidirect
193. C2×#380C2×C11semidirect
194. C2×C4×C4⋊C4C2×C11semidirect
262. C2×#125C22×C11semidirect
282. #399C22×C11semidirect
283. #396C22×C11semidirect
286. #389C22×C11semidirect
287. #389C22×C11semidirect
288. #385C22×C11semidirect
289. #380C22×C11semidirect
290. C4×C4⋊C4C22×C11semidirect
387. C2×C11#2454direct (N × H)
469. C11C2×#2454direct (N × H)
567. C2C11×#2454direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1252
C22×C4×D4×C112
C11×#24542
C2×C11×#3992
C2×C11×#3962
C2×C11×#3902
C2×C11×#3892
C2×C11×#3852
C2×C11×#3802
C2×C4×C11×C4⋊C42
C2×#245411